From 18b26d44464fc155b486cd78590cd3bae28e9cae Mon Sep 17 00:00:00 2001 From: Jamie Gardner Date: Thu, 26 Dec 2024 13:26:15 +0000 Subject: [PATCH 01/23] Use gunicorn rather than docker --- .github/workflows/deploy.yml | 7 ++++--- wsgi.py | 3 +++ 2 files changed, 7 insertions(+), 3 deletions(-) create mode 100644 wsgi.py diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml index 869bf40..427e195 100644 --- a/.github/workflows/deploy.yml +++ b/.github/workflows/deploy.yml @@ -39,10 +39,11 @@ jobs: run: | ssh target << 'EOF' cd /srv/trust.tgo.dev/current - docker compose down - git reset --hard HEAD git pull - docker compose up -d --build --remove-orphans --force-recreate + cd .. + source venv/bin/activate + pip install -r current/requirements.txt + deactivate EOF - name: Reload NGINX diff --git a/wsgi.py b/wsgi.py new file mode 100644 index 0000000..4384e54 --- /dev/null +++ b/wsgi.py @@ -0,0 +1,3 @@ +from main import create_app + +app = create_app() \ No newline at end of file From 2d4b0b7b96762b3c89199d28757a6471c137438b Mon Sep 17 00:00:00 2001 From: Jamie Gardner Date: Thu, 26 Dec 2024 13:33:04 +0000 Subject: [PATCH 02/23] Better deploy script --- .github/workflows/deploy.yml | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml index 427e195..a85ac22 100644 --- a/.github/workflows/deploy.yml +++ b/.github/workflows/deploy.yml @@ -38,12 +38,17 @@ jobs: - name: Update app run: | ssh target << 'EOF' + # Update code cd /srv/trust.tgo.dev/current git pull + # Update dependencies cd .. source venv/bin/activate pip install -r current/requirements.txt deactivate + # Update frontend + cd current + flask vite build EOF - name: Reload NGINX From d9f709f1a64db024ab022ea84da08f87e033bdbc Mon Sep 17 00:00:00 2001 From: Jamie Gardner Date: Thu, 26 Dec 2024 13:43:42 +0000 Subject: [PATCH 03/23] Prefix each case file --- .../{safety_U0T.csv => ctLS_dc_motor_safety_U0T.csv} | 0 .../{safety_X0T.csv => ctLS_dc_motor_safety_X0T.csv} | 0 .../{safety_X1T.csv => ctLS_dc_motor_safety_X1T.csv} | 0 .../{stability_U0T.csv => ctLS_dc_motor_stability_U0T.csv} | 0 .../{stability_X0T.csv => ctLS_dc_motor_stability_X0T.csv} | 0 .../{stability_X1T.csv => ctLS_dc_motor_stability_X1T.csv} | 0 .../{safety_U0T.csv => ctLS_high_order_4_safety_U0T.csv} | 0 .../{safety_X0T.csv => ctLS_high_order_4_safety_X0T.csv} | 0 .../{safety_X1T.csv => ctLS_high_order_4_safety_X1T.csv} | 0 .../{stability_U0T.csv => ctLS_high_order_4_stability_U0T.csv} | 0 .../{stability_X0T.csv => ctLS_high_order_4_stability_X0T.csv} | 0 .../{stability_X1T.csv => ctLS_high_order_4_stability_X1T.csv} | 0 .../{safety_U0T.csv => ctLS_high_order_6_safety_U0T.csv} | 0 .../{safety_X0T.csv => ctLS_high_order_6_safety_X0T.csv} | 0 .../{safety_X1T.csv => ctLS_high_order_6_safety_X1T.csv} | 0 .../{stability_U0T.csv => ctLS_high_order_6_stability_U0T.csv} | 0 .../{stability_X0T.csv => ctLS_high_order_6_stability_X0T.csv} | 0 .../{stability_X1T.csv => ctLS_high_order_6_stability_X1T.csv} | 0 .../{safety_U0T.csv => ctLS_high_order_8_safety_U0T.csv} | 0 .../{safety_X0T.csv => ctLS_high_order_8_safety_X0T.csv} | 0 .../{safety_X1T.csv => ctLS_high_order_8_safety_X1T.csv} | 0 .../{stability_U0T.csv => ctLS_high_order_8_stability_U0T.csv} | 0 .../{stability_X0T.csv => ctLS_high_order_8_stability_X0T.csv} | 0 .../{stability_X1T.csv => ctLS_high_order_8_stability_X1T.csv} | 0 ...fety_U0T.csv => ctLS_room_temperature_system_1_safety_U0T.csv} | 0 ...fety_X0T.csv => ctLS_room_temperature_system_1_safety_X0T.csv} | 0 ...fety_X1T.csv => ctLS_room_temperature_system_1_safety_X1T.csv} | 0 ...y_U0T.csv => ctLS_room_temperature_system_1_stability_U0T.csv} | 0 ...y_X0T.csv => ctLS_room_temperature_system_1_stability_X0T.csv} | 0 ...y_X1T.csv => ctLS_room_temperature_system_1_stability_X1T.csv} | 0 .../{safety_U0T.csv => ctLS_two_tank_system_safety_U0T.csv} | 0 .../{safety_X0T.csv => ctLS_two_tank_system_safety_X0T.csv} | 0 .../{safety_X1T.csv => ctLS_two_tank_system_safety_X1T.csv} | 0 .../{stability_U0T.csv => ctLS_two_tank_system_stability_U0T.csv} | 0 .../{stability_X0T.csv => ctLS_two_tank_system_stability_X0T.csv} | 0 .../{stability_X1T.csv => ctLS_two_tank_system_stability_X1T.csv} | 0 ...sv => ctNPS_lotka_volterra_predator_prey_model_safety_U0T.csv} | 0 ...sv => ctNPS_lotka_volterra_predator_prey_model_safety_X0T.csv} | 0 ...sv => ctNPS_lotka_volterra_predator_prey_model_safety_X1T.csv} | 0 ...=> ctNPS_lotka_volterra_predator_prey_model_stability_U0T.csv} | 0 ...=> ctNPS_lotka_volterra_predator_prey_model_stability_X0T.csv} | 0 ...=> ctNPS_lotka_volterra_predator_prey_model_stability_X1T.csv} | 0 ...safety_U0T.csv => ctNPS_van_der_pol_oscillator_safety_U0T.csv} | 0 ...safety_X0T.csv => ctNPS_van_der_pol_oscillator_safety_X0T.csv} | 0 ...safety_X1T.csv => ctNPS_van_der_pol_oscillator_safety_X1T.csv} | 0 ...ity_U0T.csv => ctNPS_van_der_pol_oscillator_stability_U0T.csv} | 0 ...ity_X0T.csv => ctNPS_van_der_pol_oscillator_stability_X0T.csv} | 0 ...ity_X1T.csv => ctNPS_van_der_pol_oscillator_stability_X1T.csv} | 0 .../{safety_U0T.csv => dtLS_dc_motor_safety_U0T.csv} | 0 .../{safety_X0T.csv => dtLS_dc_motor_safety_X0T.csv} | 0 .../{safety_X1T.csv => dtLS_dc_motor_safety_X1T.csv} | 0 .../{stability_U0T.csv => dtLS_dc_motor_stability_U0T.csv} | 0 .../{stability_X0T.csv => dtLS_dc_motor_stability_X0T.csv} | 0 .../{stability_X1T.csv => dtLS_dc_motor_stability_X1T.csv} | 0 .../{safety_U0T.csv => dtLS_high_order_4_safety_U0T.csv} | 0 .../{safety_X0T.csv => dtLS_high_order_4_safety_X0T.csv} | 0 .../{safety_X1T.csv => dtLS_high_order_4_safety_X1T.csv} | 0 .../{stability_U0T.csv => dtLS_high_order_4_stability_U0T.csv} | 0 .../{stability_X0T.csv => dtLS_high_order_4_stability_X0T.csv} | 0 .../{stability_X1T.csv => dtLS_high_order_4_stability_X1T.csv} | 0 .../{safety_U0T.csv => dtLS_high_order_6_safety_U0T.csv} | 0 .../{safety_X0T.csv => dtLS_high_order_6_safety_X0T.csv} | 0 .../{safety_X1T.csv => dtLS_high_order_6_safety_X1T.csv} | 0 .../{stability_U0T.csv => dtLS_high_order_6_stability_U0T.csv} | 0 .../{stability_X0T.csv => dtLS_high_order_6_stability_X0T.csv} | 0 .../{stability_X1T.csv => dtLS_high_order_6_stability_X1T.csv} | 0 .../{safety_U0T.csv => dtLS_high_order_8_safety_U0T.csv} | 0 .../{safety_X0T.csv => dtLS_high_order_8_safety_X0T.csv} | 0 .../{safety_X1T.csv => dtLS_high_order_8_safety_X1T.csv} | 0 .../{stability_U0T.csv => dtLS_high_order_8_stability_U0T.csv} | 0 .../{stability_X0T.csv => dtLS_high_order_8_stability_X0T.csv} | 0 .../{stability_X1T.csv => dtLS_high_order_8_stability_X1T.csv} | 0 ...fety_U0T.csv => dtLS_room_temperature_system_1_safety_U0T.csv} | 0 ...fety_X0T.csv => dtLS_room_temperature_system_1_safety_X0T.csv} | 0 ...fety_X1T.csv => dtLS_room_temperature_system_1_safety_X1T.csv} | 0 ...y_U0T.csv => dtLS_room_temperature_system_1_stability_U0T.csv} | 0 ...y_X0T.csv => dtLS_room_temperature_system_1_stability_X0T.csv} | 0 ...y_X1T.csv => dtLS_room_temperature_system_1_stability_X1T.csv} | 0 ...fety_U0T.csv => dtLS_room_temperature_system_2_safety_U0T.csv} | 0 ...fety_X0T.csv => dtLS_room_temperature_system_2_safety_X0T.csv} | 0 ...fety_X1T.csv => dtLS_room_temperature_system_2_safety_X1T.csv} | 0 ...y_U0T.csv => dtLS_room_temperature_system_2_stability_U0T.csv} | 0 ...y_X0T.csv => dtLS_room_temperature_system_2_stability_X0T.csv} | 0 ...y_X1T.csv => dtLS_room_temperature_system_2_stability_X1T.csv} | 0 .../{safety_U0T.csv => dtLS_two_tank_system_safety_U0T.csv} | 0 .../{safety_X0T.csv => dtLS_two_tank_system_safety_X0T.csv} | 0 .../{safety_X1T.csv => dtLS_two_tank_system_safety_X1T.csv} | 0 .../{stability_U0T.csv => dtLS_two_tank_system_stability_U0T.csv} | 0 .../{stability_X0T.csv => dtLS_two_tank_system_stability_X0T.csv} | 0 .../{stability_X1T.csv => dtLS_two_tank_system_stability_X1T.csv} | 0 .../{safety_U0T.csv => dtNPS_lorenz_attractor_safety_U0T.csv} | 0 .../{safety_X0T.csv => dtNPS_lorenz_attractor_safety_X0T.csv} | 0 .../{safety_X1T.csv => dtNPS_lorenz_attractor_safety_X1T.csv} | 0 ...stability_U0T.csv => dtNPS_lorenz_attractor_stability_U0T.csv} | 0 ...stability_X0T.csv => dtNPS_lorenz_attractor_stability_X0T.csv} | 0 ...stability_X1T.csv => dtNPS_lorenz_attractor_stability_X1T.csv} | 0 ..._U0T.csv => dtNPS_lotka_volterra_predator_prey_safety_U0T.csv} | 0 ..._X0T.csv => dtNPS_lotka_volterra_predator_prey_safety_X0T.csv} | 0 ..._X1T.csv => dtNPS_lotka_volterra_predator_prey_safety_X1T.csv} | 0 ...T.csv => dtNPS_lotka_volterra_predator_prey_stability_U0T.csv} | 0 ...T.csv => dtNPS_lotka_volterra_predator_prey_stability_X0T.csv} | 0 ...T.csv => dtNPS_lotka_volterra_predator_prey_stability_X1T.csv} | 0 102 files changed, 0 insertions(+), 0 deletions(-) rename storage/cases/ctLS_dc_motor/{safety_U0T.csv => ctLS_dc_motor_safety_U0T.csv} (100%) rename storage/cases/ctLS_dc_motor/{safety_X0T.csv => ctLS_dc_motor_safety_X0T.csv} (100%) rename storage/cases/ctLS_dc_motor/{safety_X1T.csv => ctLS_dc_motor_safety_X1T.csv} (100%) rename storage/cases/ctLS_dc_motor/{stability_U0T.csv => ctLS_dc_motor_stability_U0T.csv} (100%) rename storage/cases/ctLS_dc_motor/{stability_X0T.csv => ctLS_dc_motor_stability_X0T.csv} (100%) rename storage/cases/ctLS_dc_motor/{stability_X1T.csv => ctLS_dc_motor_stability_X1T.csv} (100%) rename storage/cases/ctLS_high_order_4/{safety_U0T.csv => ctLS_high_order_4_safety_U0T.csv} (100%) rename storage/cases/ctLS_high_order_4/{safety_X0T.csv => ctLS_high_order_4_safety_X0T.csv} (100%) rename storage/cases/ctLS_high_order_4/{safety_X1T.csv => ctLS_high_order_4_safety_X1T.csv} (100%) rename storage/cases/ctLS_high_order_4/{stability_U0T.csv => ctLS_high_order_4_stability_U0T.csv} (100%) rename storage/cases/ctLS_high_order_4/{stability_X0T.csv => ctLS_high_order_4_stability_X0T.csv} (100%) rename storage/cases/ctLS_high_order_4/{stability_X1T.csv => ctLS_high_order_4_stability_X1T.csv} (100%) rename storage/cases/ctLS_high_order_6/{safety_U0T.csv => ctLS_high_order_6_safety_U0T.csv} (100%) rename storage/cases/ctLS_high_order_6/{safety_X0T.csv => ctLS_high_order_6_safety_X0T.csv} (100%) rename storage/cases/ctLS_high_order_6/{safety_X1T.csv => ctLS_high_order_6_safety_X1T.csv} (100%) rename storage/cases/ctLS_high_order_6/{stability_U0T.csv => ctLS_high_order_6_stability_U0T.csv} (100%) rename storage/cases/ctLS_high_order_6/{stability_X0T.csv => ctLS_high_order_6_stability_X0T.csv} (100%) rename storage/cases/ctLS_high_order_6/{stability_X1T.csv => ctLS_high_order_6_stability_X1T.csv} (100%) rename storage/cases/ctLS_high_order_8/{safety_U0T.csv => ctLS_high_order_8_safety_U0T.csv} (100%) rename storage/cases/ctLS_high_order_8/{safety_X0T.csv => ctLS_high_order_8_safety_X0T.csv} (100%) rename storage/cases/ctLS_high_order_8/{safety_X1T.csv => ctLS_high_order_8_safety_X1T.csv} (100%) rename storage/cases/ctLS_high_order_8/{stability_U0T.csv => ctLS_high_order_8_stability_U0T.csv} (100%) rename storage/cases/ctLS_high_order_8/{stability_X0T.csv => ctLS_high_order_8_stability_X0T.csv} (100%) rename storage/cases/ctLS_high_order_8/{stability_X1T.csv => ctLS_high_order_8_stability_X1T.csv} (100%) rename storage/cases/ctLS_room_temperature_system_1/{safety_U0T.csv => ctLS_room_temperature_system_1_safety_U0T.csv} (100%) rename storage/cases/ctLS_room_temperature_system_1/{safety_X0T.csv => ctLS_room_temperature_system_1_safety_X0T.csv} (100%) rename storage/cases/ctLS_room_temperature_system_1/{safety_X1T.csv => ctLS_room_temperature_system_1_safety_X1T.csv} (100%) rename storage/cases/ctLS_room_temperature_system_1/{stability_U0T.csv => ctLS_room_temperature_system_1_stability_U0T.csv} (100%) rename storage/cases/ctLS_room_temperature_system_1/{stability_X0T.csv => ctLS_room_temperature_system_1_stability_X0T.csv} (100%) rename storage/cases/ctLS_room_temperature_system_1/{stability_X1T.csv => ctLS_room_temperature_system_1_stability_X1T.csv} (100%) rename storage/cases/ctLS_two_tank_system/{safety_U0T.csv => ctLS_two_tank_system_safety_U0T.csv} (100%) rename storage/cases/ctLS_two_tank_system/{safety_X0T.csv => ctLS_two_tank_system_safety_X0T.csv} (100%) rename storage/cases/ctLS_two_tank_system/{safety_X1T.csv => ctLS_two_tank_system_safety_X1T.csv} (100%) rename storage/cases/ctLS_two_tank_system/{stability_U0T.csv => ctLS_two_tank_system_stability_U0T.csv} (100%) rename storage/cases/ctLS_two_tank_system/{stability_X0T.csv => ctLS_two_tank_system_stability_X0T.csv} (100%) rename storage/cases/ctLS_two_tank_system/{stability_X1T.csv => ctLS_two_tank_system_stability_X1T.csv} (100%) rename storage/cases/ctNPS_lotka_volterra_predator_prey_model/{safety_U0T.csv => ctNPS_lotka_volterra_predator_prey_model_safety_U0T.csv} (100%) rename storage/cases/ctNPS_lotka_volterra_predator_prey_model/{safety_X0T.csv => ctNPS_lotka_volterra_predator_prey_model_safety_X0T.csv} (100%) rename storage/cases/ctNPS_lotka_volterra_predator_prey_model/{safety_X1T.csv => ctNPS_lotka_volterra_predator_prey_model_safety_X1T.csv} (100%) rename storage/cases/ctNPS_lotka_volterra_predator_prey_model/{stability_U0T.csv => ctNPS_lotka_volterra_predator_prey_model_stability_U0T.csv} (100%) rename storage/cases/ctNPS_lotka_volterra_predator_prey_model/{stability_X0T.csv => ctNPS_lotka_volterra_predator_prey_model_stability_X0T.csv} (100%) rename storage/cases/ctNPS_lotka_volterra_predator_prey_model/{stability_X1T.csv => ctNPS_lotka_volterra_predator_prey_model_stability_X1T.csv} (100%) rename storage/cases/ctNPS_van_der_pol_oscillator/{safety_U0T.csv => ctNPS_van_der_pol_oscillator_safety_U0T.csv} (100%) rename storage/cases/ctNPS_van_der_pol_oscillator/{safety_X0T.csv => ctNPS_van_der_pol_oscillator_safety_X0T.csv} (100%) rename storage/cases/ctNPS_van_der_pol_oscillator/{safety_X1T.csv => ctNPS_van_der_pol_oscillator_safety_X1T.csv} (100%) rename storage/cases/ctNPS_van_der_pol_oscillator/{stability_U0T.csv => ctNPS_van_der_pol_oscillator_stability_U0T.csv} (100%) rename storage/cases/ctNPS_van_der_pol_oscillator/{stability_X0T.csv => ctNPS_van_der_pol_oscillator_stability_X0T.csv} (100%) rename storage/cases/ctNPS_van_der_pol_oscillator/{stability_X1T.csv => ctNPS_van_der_pol_oscillator_stability_X1T.csv} (100%) rename storage/cases/dtLS_dc_motor/{safety_U0T.csv => dtLS_dc_motor_safety_U0T.csv} (100%) rename storage/cases/dtLS_dc_motor/{safety_X0T.csv => dtLS_dc_motor_safety_X0T.csv} (100%) rename storage/cases/dtLS_dc_motor/{safety_X1T.csv => dtLS_dc_motor_safety_X1T.csv} (100%) rename storage/cases/dtLS_dc_motor/{stability_U0T.csv => dtLS_dc_motor_stability_U0T.csv} (100%) rename storage/cases/dtLS_dc_motor/{stability_X0T.csv => dtLS_dc_motor_stability_X0T.csv} (100%) rename storage/cases/dtLS_dc_motor/{stability_X1T.csv => dtLS_dc_motor_stability_X1T.csv} (100%) rename storage/cases/dtLS_high_order_4/{safety_U0T.csv => dtLS_high_order_4_safety_U0T.csv} (100%) rename storage/cases/dtLS_high_order_4/{safety_X0T.csv => dtLS_high_order_4_safety_X0T.csv} (100%) rename storage/cases/dtLS_high_order_4/{safety_X1T.csv => dtLS_high_order_4_safety_X1T.csv} (100%) rename storage/cases/dtLS_high_order_4/{stability_U0T.csv => dtLS_high_order_4_stability_U0T.csv} (100%) rename storage/cases/dtLS_high_order_4/{stability_X0T.csv => dtLS_high_order_4_stability_X0T.csv} (100%) rename storage/cases/dtLS_high_order_4/{stability_X1T.csv => dtLS_high_order_4_stability_X1T.csv} (100%) rename storage/cases/dtLS_high_order_6/{safety_U0T.csv => dtLS_high_order_6_safety_U0T.csv} (100%) rename storage/cases/dtLS_high_order_6/{safety_X0T.csv => dtLS_high_order_6_safety_X0T.csv} (100%) rename storage/cases/dtLS_high_order_6/{safety_X1T.csv => dtLS_high_order_6_safety_X1T.csv} (100%) rename storage/cases/dtLS_high_order_6/{stability_U0T.csv => dtLS_high_order_6_stability_U0T.csv} (100%) rename storage/cases/dtLS_high_order_6/{stability_X0T.csv => dtLS_high_order_6_stability_X0T.csv} (100%) rename storage/cases/dtLS_high_order_6/{stability_X1T.csv => dtLS_high_order_6_stability_X1T.csv} (100%) rename storage/cases/dtLS_high_order_8/{safety_U0T.csv => dtLS_high_order_8_safety_U0T.csv} (100%) rename storage/cases/dtLS_high_order_8/{safety_X0T.csv => dtLS_high_order_8_safety_X0T.csv} (100%) rename storage/cases/dtLS_high_order_8/{safety_X1T.csv => dtLS_high_order_8_safety_X1T.csv} (100%) rename storage/cases/dtLS_high_order_8/{stability_U0T.csv => dtLS_high_order_8_stability_U0T.csv} (100%) rename storage/cases/dtLS_high_order_8/{stability_X0T.csv => dtLS_high_order_8_stability_X0T.csv} (100%) rename storage/cases/dtLS_high_order_8/{stability_X1T.csv => dtLS_high_order_8_stability_X1T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_1/{safety_U0T.csv => dtLS_room_temperature_system_1_safety_U0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_1/{safety_X0T.csv => dtLS_room_temperature_system_1_safety_X0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_1/{safety_X1T.csv => dtLS_room_temperature_system_1_safety_X1T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_1/{stability_U0T.csv => dtLS_room_temperature_system_1_stability_U0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_1/{stability_X0T.csv => dtLS_room_temperature_system_1_stability_X0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_1/{stability_X1T.csv => dtLS_room_temperature_system_1_stability_X1T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_2/{safety_U0T.csv => dtLS_room_temperature_system_2_safety_U0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_2/{safety_X0T.csv => dtLS_room_temperature_system_2_safety_X0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_2/{safety_X1T.csv => dtLS_room_temperature_system_2_safety_X1T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_2/{stability_U0T.csv => dtLS_room_temperature_system_2_stability_U0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_2/{stability_X0T.csv => dtLS_room_temperature_system_2_stability_X0T.csv} (100%) rename storage/cases/dtLS_room_temperature_system_2/{stability_X1T.csv => dtLS_room_temperature_system_2_stability_X1T.csv} (100%) rename storage/cases/dtLS_two_tank_system/{safety_U0T.csv => dtLS_two_tank_system_safety_U0T.csv} (100%) rename storage/cases/dtLS_two_tank_system/{safety_X0T.csv => dtLS_two_tank_system_safety_X0T.csv} (100%) rename storage/cases/dtLS_two_tank_system/{safety_X1T.csv => dtLS_two_tank_system_safety_X1T.csv} (100%) rename storage/cases/dtLS_two_tank_system/{stability_U0T.csv => dtLS_two_tank_system_stability_U0T.csv} (100%) rename storage/cases/dtLS_two_tank_system/{stability_X0T.csv => dtLS_two_tank_system_stability_X0T.csv} (100%) rename storage/cases/dtLS_two_tank_system/{stability_X1T.csv => dtLS_two_tank_system_stability_X1T.csv} (100%) rename storage/cases/dtNPS_lorenz_attractor/{safety_U0T.csv => dtNPS_lorenz_attractor_safety_U0T.csv} (100%) rename storage/cases/dtNPS_lorenz_attractor/{safety_X0T.csv => dtNPS_lorenz_attractor_safety_X0T.csv} (100%) rename storage/cases/dtNPS_lorenz_attractor/{safety_X1T.csv => dtNPS_lorenz_attractor_safety_X1T.csv} (100%) rename storage/cases/dtNPS_lorenz_attractor/{stability_U0T.csv => dtNPS_lorenz_attractor_stability_U0T.csv} (100%) rename storage/cases/dtNPS_lorenz_attractor/{stability_X0T.csv => dtNPS_lorenz_attractor_stability_X0T.csv} (100%) rename storage/cases/dtNPS_lorenz_attractor/{stability_X1T.csv => dtNPS_lorenz_attractor_stability_X1T.csv} (100%) rename storage/cases/dtNPS_lotka_volterra_predator_prey/{safety_U0T.csv => dtNPS_lotka_volterra_predator_prey_safety_U0T.csv} (100%) rename storage/cases/dtNPS_lotka_volterra_predator_prey/{safety_X0T.csv => dtNPS_lotka_volterra_predator_prey_safety_X0T.csv} (100%) rename storage/cases/dtNPS_lotka_volterra_predator_prey/{safety_X1T.csv => dtNPS_lotka_volterra_predator_prey_safety_X1T.csv} (100%) rename storage/cases/dtNPS_lotka_volterra_predator_prey/{stability_U0T.csv => dtNPS_lotka_volterra_predator_prey_stability_U0T.csv} (100%) rename storage/cases/dtNPS_lotka_volterra_predator_prey/{stability_X0T.csv => dtNPS_lotka_volterra_predator_prey_stability_X0T.csv} (100%) rename storage/cases/dtNPS_lotka_volterra_predator_prey/{stability_X1T.csv => dtNPS_lotka_volterra_predator_prey_stability_X1T.csv} (100%) diff --git a/storage/cases/ctLS_dc_motor/safety_U0T.csv b/storage/cases/ctLS_dc_motor/ctLS_dc_motor_safety_U0T.csv similarity index 100% rename from storage/cases/ctLS_dc_motor/safety_U0T.csv rename to storage/cases/ctLS_dc_motor/ctLS_dc_motor_safety_U0T.csv diff --git a/storage/cases/ctLS_dc_motor/safety_X0T.csv b/storage/cases/ctLS_dc_motor/ctLS_dc_motor_safety_X0T.csv similarity index 100% rename from storage/cases/ctLS_dc_motor/safety_X0T.csv rename to storage/cases/ctLS_dc_motor/ctLS_dc_motor_safety_X0T.csv diff --git a/storage/cases/ctLS_dc_motor/safety_X1T.csv b/storage/cases/ctLS_dc_motor/ctLS_dc_motor_safety_X1T.csv similarity index 100% rename from storage/cases/ctLS_dc_motor/safety_X1T.csv rename to storage/cases/ctLS_dc_motor/ctLS_dc_motor_safety_X1T.csv diff --git a/storage/cases/ctLS_dc_motor/stability_U0T.csv b/storage/cases/ctLS_dc_motor/ctLS_dc_motor_stability_U0T.csv similarity index 100% rename from storage/cases/ctLS_dc_motor/stability_U0T.csv rename to storage/cases/ctLS_dc_motor/ctLS_dc_motor_stability_U0T.csv diff --git a/storage/cases/ctLS_dc_motor/stability_X0T.csv b/storage/cases/ctLS_dc_motor/ctLS_dc_motor_stability_X0T.csv similarity index 100% rename from storage/cases/ctLS_dc_motor/stability_X0T.csv rename to storage/cases/ctLS_dc_motor/ctLS_dc_motor_stability_X0T.csv diff --git a/storage/cases/ctLS_dc_motor/stability_X1T.csv b/storage/cases/ctLS_dc_motor/ctLS_dc_motor_stability_X1T.csv similarity index 100% rename from storage/cases/ctLS_dc_motor/stability_X1T.csv rename to storage/cases/ctLS_dc_motor/ctLS_dc_motor_stability_X1T.csv diff --git a/storage/cases/ctLS_high_order_4/safety_U0T.csv b/storage/cases/ctLS_high_order_4/ctLS_high_order_4_safety_U0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_4/safety_U0T.csv rename to storage/cases/ctLS_high_order_4/ctLS_high_order_4_safety_U0T.csv diff --git a/storage/cases/ctLS_high_order_4/safety_X0T.csv b/storage/cases/ctLS_high_order_4/ctLS_high_order_4_safety_X0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_4/safety_X0T.csv rename to storage/cases/ctLS_high_order_4/ctLS_high_order_4_safety_X0T.csv diff --git a/storage/cases/ctLS_high_order_4/safety_X1T.csv b/storage/cases/ctLS_high_order_4/ctLS_high_order_4_safety_X1T.csv similarity index 100% rename from storage/cases/ctLS_high_order_4/safety_X1T.csv rename to storage/cases/ctLS_high_order_4/ctLS_high_order_4_safety_X1T.csv diff --git a/storage/cases/ctLS_high_order_4/stability_U0T.csv b/storage/cases/ctLS_high_order_4/ctLS_high_order_4_stability_U0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_4/stability_U0T.csv rename to storage/cases/ctLS_high_order_4/ctLS_high_order_4_stability_U0T.csv diff --git a/storage/cases/ctLS_high_order_4/stability_X0T.csv b/storage/cases/ctLS_high_order_4/ctLS_high_order_4_stability_X0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_4/stability_X0T.csv rename to storage/cases/ctLS_high_order_4/ctLS_high_order_4_stability_X0T.csv diff --git a/storage/cases/ctLS_high_order_4/stability_X1T.csv b/storage/cases/ctLS_high_order_4/ctLS_high_order_4_stability_X1T.csv similarity index 100% rename from storage/cases/ctLS_high_order_4/stability_X1T.csv rename to storage/cases/ctLS_high_order_4/ctLS_high_order_4_stability_X1T.csv diff --git a/storage/cases/ctLS_high_order_6/safety_U0T.csv b/storage/cases/ctLS_high_order_6/ctLS_high_order_6_safety_U0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_6/safety_U0T.csv rename to storage/cases/ctLS_high_order_6/ctLS_high_order_6_safety_U0T.csv diff --git a/storage/cases/ctLS_high_order_6/safety_X0T.csv b/storage/cases/ctLS_high_order_6/ctLS_high_order_6_safety_X0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_6/safety_X0T.csv rename to storage/cases/ctLS_high_order_6/ctLS_high_order_6_safety_X0T.csv diff --git a/storage/cases/ctLS_high_order_6/safety_X1T.csv b/storage/cases/ctLS_high_order_6/ctLS_high_order_6_safety_X1T.csv similarity index 100% rename from storage/cases/ctLS_high_order_6/safety_X1T.csv rename to storage/cases/ctLS_high_order_6/ctLS_high_order_6_safety_X1T.csv diff --git a/storage/cases/ctLS_high_order_6/stability_U0T.csv b/storage/cases/ctLS_high_order_6/ctLS_high_order_6_stability_U0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_6/stability_U0T.csv rename to storage/cases/ctLS_high_order_6/ctLS_high_order_6_stability_U0T.csv diff --git a/storage/cases/ctLS_high_order_6/stability_X0T.csv b/storage/cases/ctLS_high_order_6/ctLS_high_order_6_stability_X0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_6/stability_X0T.csv rename to storage/cases/ctLS_high_order_6/ctLS_high_order_6_stability_X0T.csv diff --git a/storage/cases/ctLS_high_order_6/stability_X1T.csv b/storage/cases/ctLS_high_order_6/ctLS_high_order_6_stability_X1T.csv similarity index 100% rename from storage/cases/ctLS_high_order_6/stability_X1T.csv rename to storage/cases/ctLS_high_order_6/ctLS_high_order_6_stability_X1T.csv diff --git a/storage/cases/ctLS_high_order_8/safety_U0T.csv b/storage/cases/ctLS_high_order_8/ctLS_high_order_8_safety_U0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_8/safety_U0T.csv rename to storage/cases/ctLS_high_order_8/ctLS_high_order_8_safety_U0T.csv diff --git a/storage/cases/ctLS_high_order_8/safety_X0T.csv b/storage/cases/ctLS_high_order_8/ctLS_high_order_8_safety_X0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_8/safety_X0T.csv rename to storage/cases/ctLS_high_order_8/ctLS_high_order_8_safety_X0T.csv diff --git a/storage/cases/ctLS_high_order_8/safety_X1T.csv b/storage/cases/ctLS_high_order_8/ctLS_high_order_8_safety_X1T.csv similarity index 100% rename from storage/cases/ctLS_high_order_8/safety_X1T.csv rename to storage/cases/ctLS_high_order_8/ctLS_high_order_8_safety_X1T.csv diff --git a/storage/cases/ctLS_high_order_8/stability_U0T.csv b/storage/cases/ctLS_high_order_8/ctLS_high_order_8_stability_U0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_8/stability_U0T.csv rename to storage/cases/ctLS_high_order_8/ctLS_high_order_8_stability_U0T.csv diff --git a/storage/cases/ctLS_high_order_8/stability_X0T.csv b/storage/cases/ctLS_high_order_8/ctLS_high_order_8_stability_X0T.csv similarity index 100% rename from storage/cases/ctLS_high_order_8/stability_X0T.csv rename to storage/cases/ctLS_high_order_8/ctLS_high_order_8_stability_X0T.csv diff --git a/storage/cases/ctLS_high_order_8/stability_X1T.csv b/storage/cases/ctLS_high_order_8/ctLS_high_order_8_stability_X1T.csv similarity index 100% rename from storage/cases/ctLS_high_order_8/stability_X1T.csv rename to storage/cases/ctLS_high_order_8/ctLS_high_order_8_stability_X1T.csv diff --git a/storage/cases/ctLS_room_temperature_system_1/safety_U0T.csv b/storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_safety_U0T.csv similarity index 100% rename from storage/cases/ctLS_room_temperature_system_1/safety_U0T.csv rename to storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_safety_U0T.csv diff --git a/storage/cases/ctLS_room_temperature_system_1/safety_X0T.csv b/storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_safety_X0T.csv similarity index 100% rename from storage/cases/ctLS_room_temperature_system_1/safety_X0T.csv rename to storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_safety_X0T.csv diff --git a/storage/cases/ctLS_room_temperature_system_1/safety_X1T.csv b/storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_safety_X1T.csv similarity index 100% rename from storage/cases/ctLS_room_temperature_system_1/safety_X1T.csv rename to storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_safety_X1T.csv diff --git a/storage/cases/ctLS_room_temperature_system_1/stability_U0T.csv b/storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_stability_U0T.csv similarity index 100% rename from storage/cases/ctLS_room_temperature_system_1/stability_U0T.csv rename to storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_stability_U0T.csv diff --git a/storage/cases/ctLS_room_temperature_system_1/stability_X0T.csv b/storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_stability_X0T.csv similarity index 100% rename from storage/cases/ctLS_room_temperature_system_1/stability_X0T.csv rename to storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_stability_X0T.csv diff --git a/storage/cases/ctLS_room_temperature_system_1/stability_X1T.csv b/storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_stability_X1T.csv similarity index 100% rename from storage/cases/ctLS_room_temperature_system_1/stability_X1T.csv rename to storage/cases/ctLS_room_temperature_system_1/ctLS_room_temperature_system_1_stability_X1T.csv diff --git a/storage/cases/ctLS_two_tank_system/safety_U0T.csv b/storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_safety_U0T.csv similarity index 100% rename from storage/cases/ctLS_two_tank_system/safety_U0T.csv rename to storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_safety_U0T.csv diff --git a/storage/cases/ctLS_two_tank_system/safety_X0T.csv b/storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_safety_X0T.csv similarity index 100% rename from storage/cases/ctLS_two_tank_system/safety_X0T.csv rename to storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_safety_X0T.csv diff --git a/storage/cases/ctLS_two_tank_system/safety_X1T.csv b/storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_safety_X1T.csv similarity index 100% rename from storage/cases/ctLS_two_tank_system/safety_X1T.csv rename to storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_safety_X1T.csv diff --git a/storage/cases/ctLS_two_tank_system/stability_U0T.csv b/storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_stability_U0T.csv similarity index 100% rename from storage/cases/ctLS_two_tank_system/stability_U0T.csv rename to storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_stability_U0T.csv diff --git a/storage/cases/ctLS_two_tank_system/stability_X0T.csv b/storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_stability_X0T.csv similarity index 100% rename from storage/cases/ctLS_two_tank_system/stability_X0T.csv rename to storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_stability_X0T.csv diff --git a/storage/cases/ctLS_two_tank_system/stability_X1T.csv b/storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_stability_X1T.csv similarity index 100% rename from storage/cases/ctLS_two_tank_system/stability_X1T.csv rename to storage/cases/ctLS_two_tank_system/ctLS_two_tank_system_stability_X1T.csv diff --git a/storage/cases/ctNPS_lotka_volterra_predator_prey_model/safety_U0T.csv b/storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_safety_U0T.csv similarity index 100% rename from storage/cases/ctNPS_lotka_volterra_predator_prey_model/safety_U0T.csv rename to storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_safety_U0T.csv diff --git a/storage/cases/ctNPS_lotka_volterra_predator_prey_model/safety_X0T.csv b/storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_safety_X0T.csv similarity index 100% rename from storage/cases/ctNPS_lotka_volterra_predator_prey_model/safety_X0T.csv rename to storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_safety_X0T.csv diff --git a/storage/cases/ctNPS_lotka_volterra_predator_prey_model/safety_X1T.csv b/storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_safety_X1T.csv similarity index 100% rename from storage/cases/ctNPS_lotka_volterra_predator_prey_model/safety_X1T.csv rename to storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_safety_X1T.csv diff --git a/storage/cases/ctNPS_lotka_volterra_predator_prey_model/stability_U0T.csv b/storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_stability_U0T.csv similarity index 100% rename from storage/cases/ctNPS_lotka_volterra_predator_prey_model/stability_U0T.csv rename to storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_stability_U0T.csv diff --git a/storage/cases/ctNPS_lotka_volterra_predator_prey_model/stability_X0T.csv b/storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_stability_X0T.csv similarity index 100% rename from storage/cases/ctNPS_lotka_volterra_predator_prey_model/stability_X0T.csv rename to storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_stability_X0T.csv diff --git a/storage/cases/ctNPS_lotka_volterra_predator_prey_model/stability_X1T.csv b/storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_stability_X1T.csv similarity index 100% rename from storage/cases/ctNPS_lotka_volterra_predator_prey_model/stability_X1T.csv rename to storage/cases/ctNPS_lotka_volterra_predator_prey_model/ctNPS_lotka_volterra_predator_prey_model_stability_X1T.csv diff --git a/storage/cases/ctNPS_van_der_pol_oscillator/safety_U0T.csv b/storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_safety_U0T.csv similarity index 100% rename from storage/cases/ctNPS_van_der_pol_oscillator/safety_U0T.csv rename to storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_safety_U0T.csv diff --git a/storage/cases/ctNPS_van_der_pol_oscillator/safety_X0T.csv b/storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_safety_X0T.csv similarity index 100% rename from storage/cases/ctNPS_van_der_pol_oscillator/safety_X0T.csv rename to storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_safety_X0T.csv diff --git a/storage/cases/ctNPS_van_der_pol_oscillator/safety_X1T.csv b/storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_safety_X1T.csv similarity index 100% rename from storage/cases/ctNPS_van_der_pol_oscillator/safety_X1T.csv rename to storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_safety_X1T.csv diff --git a/storage/cases/ctNPS_van_der_pol_oscillator/stability_U0T.csv b/storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_stability_U0T.csv similarity index 100% rename from storage/cases/ctNPS_van_der_pol_oscillator/stability_U0T.csv rename to storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_stability_U0T.csv diff --git a/storage/cases/ctNPS_van_der_pol_oscillator/stability_X0T.csv b/storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_stability_X0T.csv similarity index 100% rename from storage/cases/ctNPS_van_der_pol_oscillator/stability_X0T.csv rename to storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_stability_X0T.csv diff --git a/storage/cases/ctNPS_van_der_pol_oscillator/stability_X1T.csv b/storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_stability_X1T.csv similarity index 100% rename from storage/cases/ctNPS_van_der_pol_oscillator/stability_X1T.csv rename to storage/cases/ctNPS_van_der_pol_oscillator/ctNPS_van_der_pol_oscillator_stability_X1T.csv diff --git a/storage/cases/dtLS_dc_motor/safety_U0T.csv b/storage/cases/dtLS_dc_motor/dtLS_dc_motor_safety_U0T.csv similarity index 100% rename from storage/cases/dtLS_dc_motor/safety_U0T.csv rename to storage/cases/dtLS_dc_motor/dtLS_dc_motor_safety_U0T.csv diff --git a/storage/cases/dtLS_dc_motor/safety_X0T.csv b/storage/cases/dtLS_dc_motor/dtLS_dc_motor_safety_X0T.csv similarity index 100% rename from storage/cases/dtLS_dc_motor/safety_X0T.csv rename to 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rename from storage/cases/dtLS_dc_motor/stability_X1T.csv rename to storage/cases/dtLS_dc_motor/dtLS_dc_motor_stability_X1T.csv diff --git a/storage/cases/dtLS_high_order_4/safety_U0T.csv b/storage/cases/dtLS_high_order_4/dtLS_high_order_4_safety_U0T.csv similarity index 100% rename from storage/cases/dtLS_high_order_4/safety_U0T.csv rename to storage/cases/dtLS_high_order_4/dtLS_high_order_4_safety_U0T.csv diff --git a/storage/cases/dtLS_high_order_4/safety_X0T.csv b/storage/cases/dtLS_high_order_4/dtLS_high_order_4_safety_X0T.csv similarity index 100% rename from storage/cases/dtLS_high_order_4/safety_X0T.csv rename to storage/cases/dtLS_high_order_4/dtLS_high_order_4_safety_X0T.csv diff --git a/storage/cases/dtLS_high_order_4/safety_X1T.csv b/storage/cases/dtLS_high_order_4/dtLS_high_order_4_safety_X1T.csv similarity index 100% rename from storage/cases/dtLS_high_order_4/safety_X1T.csv rename to storage/cases/dtLS_high_order_4/dtLS_high_order_4_safety_X1T.csv diff --git 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similarity index 100% rename from storage/cases/dtLS_high_order_6/safety_U0T.csv rename to storage/cases/dtLS_high_order_6/dtLS_high_order_6_safety_U0T.csv diff --git a/storage/cases/dtLS_high_order_6/safety_X0T.csv b/storage/cases/dtLS_high_order_6/dtLS_high_order_6_safety_X0T.csv similarity index 100% rename from storage/cases/dtLS_high_order_6/safety_X0T.csv rename to storage/cases/dtLS_high_order_6/dtLS_high_order_6_safety_X0T.csv diff --git a/storage/cases/dtLS_high_order_6/safety_X1T.csv b/storage/cases/dtLS_high_order_6/dtLS_high_order_6_safety_X1T.csv similarity index 100% rename from storage/cases/dtLS_high_order_6/safety_X1T.csv rename to storage/cases/dtLS_high_order_6/dtLS_high_order_6_safety_X1T.csv diff --git a/storage/cases/dtLS_high_order_6/stability_U0T.csv b/storage/cases/dtLS_high_order_6/dtLS_high_order_6_stability_U0T.csv similarity index 100% rename from storage/cases/dtLS_high_order_6/stability_U0T.csv rename to 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b/storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_safety_U0T.csv similarity index 100% rename from storage/cases/dtLS_two_tank_system/safety_U0T.csv rename to storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_safety_U0T.csv diff --git a/storage/cases/dtLS_two_tank_system/safety_X0T.csv b/storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_safety_X0T.csv similarity index 100% rename from storage/cases/dtLS_two_tank_system/safety_X0T.csv rename to storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_safety_X0T.csv diff --git a/storage/cases/dtLS_two_tank_system/safety_X1T.csv b/storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_safety_X1T.csv similarity index 100% rename from storage/cases/dtLS_two_tank_system/safety_X1T.csv rename to storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_safety_X1T.csv diff --git a/storage/cases/dtLS_two_tank_system/stability_U0T.csv b/storage/cases/dtLS_two_tank_system/dtLS_two_tank_system_stability_U0T.csv similarity index 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storage/cases/dtNPS_lorenz_attractor/safety_U0T.csv rename to storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_safety_U0T.csv diff --git a/storage/cases/dtNPS_lorenz_attractor/safety_X0T.csv b/storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_safety_X0T.csv similarity index 100% rename from storage/cases/dtNPS_lorenz_attractor/safety_X0T.csv rename to storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_safety_X0T.csv diff --git a/storage/cases/dtNPS_lorenz_attractor/safety_X1T.csv b/storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_safety_X1T.csv similarity index 100% rename from storage/cases/dtNPS_lorenz_attractor/safety_X1T.csv rename to storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_safety_X1T.csv diff --git a/storage/cases/dtNPS_lorenz_attractor/stability_U0T.csv b/storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_stability_U0T.csv similarity index 100% rename from storage/cases/dtNPS_lorenz_attractor/stability_U0T.csv rename to storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_stability_U0T.csv diff --git a/storage/cases/dtNPS_lorenz_attractor/stability_X0T.csv b/storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_stability_X0T.csv similarity index 100% rename from storage/cases/dtNPS_lorenz_attractor/stability_X0T.csv rename to storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_stability_X0T.csv diff --git a/storage/cases/dtNPS_lorenz_attractor/stability_X1T.csv b/storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_stability_X1T.csv similarity index 100% rename from storage/cases/dtNPS_lorenz_attractor/stability_X1T.csv rename to storage/cases/dtNPS_lorenz_attractor/dtNPS_lorenz_attractor_stability_X1T.csv diff --git a/storage/cases/dtNPS_lotka_volterra_predator_prey/safety_U0T.csv b/storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_safety_U0T.csv similarity index 100% rename from storage/cases/dtNPS_lotka_volterra_predator_prey/safety_U0T.csv rename to storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_safety_U0T.csv diff --git a/storage/cases/dtNPS_lotka_volterra_predator_prey/safety_X0T.csv b/storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_safety_X0T.csv similarity index 100% rename from storage/cases/dtNPS_lotka_volterra_predator_prey/safety_X0T.csv rename to storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_safety_X0T.csv diff --git a/storage/cases/dtNPS_lotka_volterra_predator_prey/safety_X1T.csv b/storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_safety_X1T.csv similarity index 100% rename from storage/cases/dtNPS_lotka_volterra_predator_prey/safety_X1T.csv rename to storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_safety_X1T.csv diff --git a/storage/cases/dtNPS_lotka_volterra_predator_prey/stability_U0T.csv b/storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_stability_U0T.csv similarity index 100% rename from storage/cases/dtNPS_lotka_volterra_predator_prey/stability_U0T.csv rename to storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_stability_U0T.csv diff --git a/storage/cases/dtNPS_lotka_volterra_predator_prey/stability_X0T.csv b/storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_stability_X0T.csv similarity index 100% rename from storage/cases/dtNPS_lotka_volterra_predator_prey/stability_X0T.csv rename to storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_stability_X0T.csv diff --git a/storage/cases/dtNPS_lotka_volterra_predator_prey/stability_X1T.csv b/storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_stability_X1T.csv similarity index 100% rename from storage/cases/dtNPS_lotka_volterra_predator_prey/stability_X1T.csv rename to storage/cases/dtNPS_lotka_volterra_predator_prey/dtNPS_lotka_volterra_predator_prey_stability_X1T.csv From f93b9a844830fad264f32ed63702193e2000610e Mon Sep 17 00:00:00 2001 From: Jamie Gardner Date: Fri, 24 Jan 2025 15:15:35 +0000 Subject: [PATCH 04/23] Add citation --- README.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/README.md b/README.md index 6e3e59b..948a2dd 100644 --- a/README.md +++ b/README.md @@ -229,11 +229,11 @@ The arXiv version of the paper is located [here](). ``` @misc{trust2024, - title={TRUST: Controller Synthesis for Unknown Models Using a Single Trajectory}, - author={Jamie Gardner and Ben Wooding and Amy Nejati and Abolfazl Lavaei}, - year={2024}, + title={TRUST: StabiliTy and Safety ContRoller Synthesis for Unknown Dynamical Models Using a Single Trajectory}, + author={Jamie Gardne, Ben Wooding, Amy Nejati, and Abolfazl Lavaei}, + year={2025}, eprint={tbc}, - journal={tbc}, + journal={28th ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2025)}, primaryClass={eess.SY} } ``` From 54de593eaae2f599a433436f6f1fa061713669ce Mon Sep 17 00:00:00 2001 From: Abolfazl Lavaei <54770071+ALavaei@users.noreply.github.com> Date: Sat, 25 Jan 2025 07:11:25 +0000 Subject: [PATCH 05/23] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 948a2dd..99c0765 100644 --- a/README.md +++ b/README.md @@ -228,7 +228,7 @@ The arXiv version of the paper is located [here](). ### Citing TRUST ``` -@misc{trust2024, +@misc{trust2025, title={TRUST: StabiliTy and Safety ContRoller Synthesis for Unknown Dynamical Models Using a Single Trajectory}, author={Jamie Gardne, Ben Wooding, Amy Nejati, and Abolfazl Lavaei}, year={2025}, From 5735384c26f87ab4e91435bffaa97bb4e1a6345d Mon Sep 17 00:00:00 2001 From: Abolfazl Lavaei <54770071+ALavaei@users.noreply.github.com> Date: Sat, 25 Jan 2025 07:12:06 +0000 Subject: [PATCH 06/23] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 99c0765..05c8098 100644 --- a/README.md +++ b/README.md @@ -228,7 +228,7 @@ The arXiv version of the paper is located [here](). ### Citing TRUST ``` -@misc{trust2025, +@misc{TRUST2025, title={TRUST: StabiliTy and Safety ContRoller Synthesis for Unknown Dynamical Models Using a Single Trajectory}, author={Jamie Gardne, Ben Wooding, Amy Nejati, and Abolfazl Lavaei}, year={2025}, From c7a94c1220aa04de0005e49033a8e8024892b82d Mon Sep 17 00:00:00 2001 From: Jamie Gardner Date: Mon, 7 Apr 2025 13:19:49 +0100 Subject: [PATCH 07/23] Ensure no local changes in pipeline --- .github/workflows/deploy.yml | 11 +- TRUST-docs/IEEEtran.bst | 2409 +++++++++++++++++++++++++++ TRUST-docs/IEEEtrantools.sty | 2799 ++++++++++++++++++++++++++++++++ TRUST-docs/acmart.cls | 2544 +++++++++++++++++++++++++++++ TRUST-docs/biblio.bib | 466 ++++++ TRUST-docs/main.tex | 1152 +++++++++++++ TRUST-docs/out/main.aux | 198 +++ TRUST-docs/out/main.bbl | 121 ++ TRUST-docs/out/main.blg | 62 + TRUST-docs/out/main.out | 22 + TRUST-docs/out/main.pdf | Bin 0 -> 545608 bytes TRUST-docs/out/main.synctex.gz | Bin 0 -> 167239 bytes app/models/safety_barrier.py | 2 - 13 files changed, 9779 insertions(+), 7 deletions(-) create mode 100755 TRUST-docs/IEEEtran.bst create mode 100755 TRUST-docs/IEEEtrantools.sty create mode 100755 TRUST-docs/acmart.cls create mode 100644 TRUST-docs/biblio.bib create mode 100644 TRUST-docs/main.tex create mode 100644 TRUST-docs/out/main.aux create mode 100644 TRUST-docs/out/main.bbl create mode 100644 TRUST-docs/out/main.blg create mode 100644 TRUST-docs/out/main.out create mode 100644 TRUST-docs/out/main.pdf create mode 100644 TRUST-docs/out/main.synctex.gz diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml index a85ac22..77db701 100644 --- a/.github/workflows/deploy.yml +++ b/.github/workflows/deploy.yml @@ -40,15 +40,16 @@ jobs: ssh target << 'EOF' # Update code cd /srv/trust.tgo.dev/current - git pull + git reset --hard HEAD + git pull # Update dependencies cd .. source venv/bin/activate - pip install -r current/requirements.txt - deactivate + pip install --quiet -r current/requirements.txt # Update frontend - cd current - flask vite build + cd current/vite + nvm use --lts + npm build EOF - name: Reload NGINX diff --git a/TRUST-docs/IEEEtran.bst b/TRUST-docs/IEEEtran.bst new file mode 100755 index 0000000..3e7a50e --- /dev/null +++ b/TRUST-docs/IEEEtran.bst @@ -0,0 +1,2409 @@ +%% +%% IEEEtran.bst +%% BibTeX Bibliography Style file for IEEE Journals and Conferences (unsorted) +%% Version 1.14 (2015/08/26) +%% +%% Copyright (c) 2003-2015 Michael Shell +%% +%% Original starting code base and algorithms obtained from the output of +%% Patrick W. Daly's makebst package as well as from prior versions of +%% IEEE BibTeX styles: +%% +%% 1. Howard Trickey and Oren Patashnik's ieeetr.bst (1985/1988) +%% 2. Silvano Balemi and Richard H. Roy's IEEEbib.bst (1993) +%% +%% Support sites: +%% http://www.michaelshell.org/tex/ieeetran/ +%% http://www.ctan.org/pkg/ieeetran +%% and/or +%% http://www.ieee.org/ +%% +%% For use with BibTeX version 0.99a or later +%% +%% This is a numerical citation style. +%% +%%************************************************************************* +%% Legal Notice: +%% This code is offered as-is without any warranty either expressed or +%% implied; without even the implied warranty of MERCHANTABILITY or +%% FITNESS FOR A PARTICULAR PURPOSE! +%% User assumes all risk. +%% In no event shall the IEEE or any contributor to this code be liable for +%% any damages or losses, including, but not limited to, incidental, +%% consequential, or any other damages, resulting from the use or misuse +%% of any information contained here. +%% +%% All comments are the opinions of their respective authors and are not +%% necessarily endorsed by the IEEE. +%% +%% This work is distributed under the LaTeX Project Public License (LPPL) +%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, +%% distributed and modified. A copy of the LPPL, version 1.3, is included +%% in the base LaTeX documentation of all distributions of LaTeX released +%% 2003/12/01 or later. +%% Retain all contribution notices and credits. +%% ** Modified files should be clearly indicated as such, including ** +%% ** renaming them and changing author support contact information. ** +%%************************************************************************* + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% DEFAULTS FOR THE CONTROLS OF THE BST STYLE %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% These are the defaults for the user adjustable controls. The values used +% here can be overridden by the user via IEEEtranBSTCTL entry type. + +% NOTE: The recommended LaTeX command to invoke a control entry type is: +% +%\makeatletter +%\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}} +%\def\@bstctlcite[#1]#2{\@bsphack +% \@for\@citeb:=#2\do{% +% \edef\@citeb{\expandafter\@firstofone\@citeb}% +% \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}% +% \@esphack} +%\makeatother +% +% It is called at the start of the document, before the first \cite, like: +% \bstctlcite{IEEEexample:BSTcontrol} +% +% IEEEtran.cls V1.6 and later does provide this command. + + + +% #0 turns off the display of the number for articles. +% #1 enables +FUNCTION {default.is.use.number.for.article} { #1 } + + +% #0 turns off the display of the paper and type fields in @inproceedings. +% #1 enables +FUNCTION {default.is.use.paper} { #1 } + + +% #0 turns off the display of urls +% #1 enables +FUNCTION {default.is.use.url} { #1 } + + +% #0 turns off the forced use of "et al." +% #1 enables +FUNCTION {default.is.forced.et.al} { #0 } + + +% The maximum number of names that can be present beyond which an "et al." +% usage is forced. Be sure that num.names.shown.with.forced.et.al (below) +% is not greater than this value! +% Note: There are many instances of references in IEEE journals which have +% a very large number of authors as well as instances in which "et al." is +% used profusely. +FUNCTION {default.max.num.names.before.forced.et.al} { #10 } + + +% The number of names that will be shown with a forced "et al.". +% Must be less than or equal to max.num.names.before.forced.et.al +FUNCTION {default.num.names.shown.with.forced.et.al} { #1 } + + +% #0 turns off the alternate interword spacing for entries with URLs. +% #1 enables +FUNCTION {default.is.use.alt.interword.spacing} { #1 } + + +% If alternate interword spacing for entries with URLs is enabled, this is +% the interword spacing stretch factor that will be used. For example, the +% default "4" here means that the interword spacing in entries with URLs can +% stretch to four times normal. Does not have to be an integer. Note that +% the value specified here can be overridden by the user in their LaTeX +% code via a command such as: +% "\providecommand\BIBentryALTinterwordstretchfactor{1.5}" in addition to +% that via the IEEEtranBSTCTL entry type. +FUNCTION {default.ALTinterwordstretchfactor} { "4" } + + +% #0 turns off the "dashification" of repeated (i.e., identical to those +% of the previous entry) names. The IEEE normally does this. +% #1 enables +FUNCTION {default.is.dash.repeated.names} { #1 } + + +% The default name format control string. +FUNCTION {default.name.format.string}{ "{f.~}{vv~}{ll}{, jj}" } + + +% The default LaTeX font command for the names. +FUNCTION {default.name.latex.cmd}{ "" } + + +% The default URL prefix. +FUNCTION {default.name.url.prefix}{ "[Online]. Available:" } + + +% Other controls that cannot be accessed via IEEEtranBSTCTL entry type. + +% #0 turns off the terminal startup banner/completed message so as to +% operate more quietly. +% #1 enables +FUNCTION {is.print.banners.to.terminal} { #1 } + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FILE VERSION AND BANNER %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION{bst.file.version} { "1.14" } +FUNCTION{bst.file.date} { "2015/08/26" } +FUNCTION{bst.file.website} { "http://www.michaelshell.org/tex/ieeetran/bibtex/" } + +FUNCTION {banner.message} +{ is.print.banners.to.terminal + { "-- IEEEtran.bst version" " " * bst.file.version * + " (" * bst.file.date * ") " * "by Michael Shell." * + top$ + "-- " bst.file.website * + top$ + "-- See the " quote$ * "IEEEtran_bst_HOWTO.pdf" * quote$ * " manual for usage information." * + top$ + } + { skip$ } + if$ +} + +FUNCTION {completed.message} +{ is.print.banners.to.terminal + { "" + top$ + "Done." + top$ + } + { skip$ } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%%% +%% STRING CONSTANTS %% +%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {bbl.and}{ "and" } +FUNCTION {bbl.etal}{ "et~al." } +FUNCTION {bbl.editors}{ "eds." } +FUNCTION {bbl.editor}{ "ed." } +FUNCTION {bbl.edition}{ "ed." } +FUNCTION {bbl.volume}{ "vol." } +FUNCTION {bbl.of}{ "of" } +FUNCTION {bbl.number}{ "no." } +FUNCTION {bbl.in}{ "in" } +FUNCTION {bbl.pages}{ "pp." } +FUNCTION {bbl.page}{ "p." } +FUNCTION {bbl.chapter}{ "ch." } +FUNCTION {bbl.paper}{ "paper" } +FUNCTION {bbl.part}{ "pt." } +FUNCTION {bbl.patent}{ "Patent" } +FUNCTION {bbl.patentUS}{ "U.S." } +FUNCTION {bbl.revision}{ "Rev." } +FUNCTION {bbl.series}{ "ser." } +FUNCTION {bbl.standard}{ "Std." } +FUNCTION {bbl.techrep}{ "Tech. Rep." } +FUNCTION {bbl.mthesis}{ "Master's thesis" } +FUNCTION {bbl.phdthesis}{ "Ph.D. dissertation" } +FUNCTION {bbl.st}{ "st" } +FUNCTION {bbl.nd}{ "nd" } +FUNCTION {bbl.rd}{ "rd" } +FUNCTION {bbl.th}{ "th" } + + +% This is the LaTeX spacer that is used when a larger than normal space +% is called for (such as just before the address:publisher). +FUNCTION {large.space} { "\hskip 1em plus 0.5em minus 0.4em\relax " } + +% The LaTeX code for dashes that are used to represent repeated names. +% Note: Some older IEEE journals used something like +% "\rule{0.275in}{0.5pt}\," which is fairly thick and runs right along +% the baseline. However, the IEEE now uses a thinner, above baseline, +% six dash long sequence. +FUNCTION {repeated.name.dashes} { "------" } + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% PREDEFINED STRING MACROS %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +MACRO {jan} {"Jan."} +MACRO {feb} {"Feb."} +MACRO {mar} {"Mar."} +MACRO {apr} {"Apr."} +MACRO {may} {"May"} +MACRO {jun} {"Jun."} +MACRO {jul} {"Jul."} +MACRO {aug} {"Aug."} +MACRO {sep} {"Sep."} +MACRO {oct} {"Oct."} +MACRO {nov} {"Nov."} +MACRO {dec} {"Dec."} + + + +%%%%%%%%%%%%%%%%%% +%% ENTRY FIELDS %% +%%%%%%%%%%%%%%%%%% + +ENTRY + { address + assignee + author + booktitle + chapter + day + dayfiled + edition + editor + howpublished + institution + intype + journal + key + language + month + monthfiled + nationality + note + number + organization + pages + paper + publisher + school + series + revision + title + type + url + volume + year + yearfiled + CTLuse_article_number + CTLuse_paper + CTLuse_url + CTLuse_forced_etal + CTLmax_names_forced_etal + CTLnames_show_etal + CTLuse_alt_spacing + CTLalt_stretch_factor + CTLdash_repeated_names + CTLname_format_string + CTLname_latex_cmd + CTLname_url_prefix + } + {} + { label } + + + + +%%%%%%%%%%%%%%%%%%%%%%% +%% INTEGER VARIABLES %% +%%%%%%%%%%%%%%%%%%%%%%% + +INTEGERS { prev.status.punct this.status.punct punct.std + punct.no punct.comma punct.period + prev.status.space this.status.space space.std + space.no space.normal space.large + prev.status.quote this.status.quote quote.std + quote.no quote.close + prev.status.nline this.status.nline nline.std + nline.no nline.newblock + status.cap cap.std + cap.no cap.yes} + +INTEGERS { longest.label.width multiresult nameptr namesleft number.label numnames } + +INTEGERS { is.use.number.for.article + is.use.paper + is.use.url + is.forced.et.al + max.num.names.before.forced.et.al + num.names.shown.with.forced.et.al + is.use.alt.interword.spacing + is.dash.repeated.names} + + +%%%%%%%%%%%%%%%%%%%%%% +%% STRING VARIABLES %% +%%%%%%%%%%%%%%%%%%%%%% + +STRINGS { bibinfo + longest.label + oldname + s + t + ALTinterwordstretchfactor + name.format.string + name.latex.cmd + name.url.prefix} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%% +%% LOW LEVEL FUNCTIONS %% +%%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {initialize.controls} +{ default.is.use.number.for.article 'is.use.number.for.article := + default.is.use.paper 'is.use.paper := + default.is.use.url 'is.use.url := + default.is.forced.et.al 'is.forced.et.al := + default.max.num.names.before.forced.et.al 'max.num.names.before.forced.et.al := + default.num.names.shown.with.forced.et.al 'num.names.shown.with.forced.et.al := + default.is.use.alt.interword.spacing 'is.use.alt.interword.spacing := + default.is.dash.repeated.names 'is.dash.repeated.names := + default.ALTinterwordstretchfactor 'ALTinterwordstretchfactor := + default.name.format.string 'name.format.string := + default.name.latex.cmd 'name.latex.cmd := + default.name.url.prefix 'name.url.prefix := +} + + +% This IEEEtran.bst features a very powerful and flexible mechanism for +% controlling the capitalization, punctuation, spacing, quotation, and +% newlines of the formatted entry fields. (Note: IEEEtran.bst does not need +% or use the newline/newblock feature, but it has been implemented for +% possible future use.) The output states of IEEEtran.bst consist of +% multiple independent attributes and, as such, can be thought of as being +% vectors, rather than the simple scalar values ("before.all", +% "mid.sentence", etc.) used in most other .bst files. +% +% The more flexible and complex design used here was motivated in part by +% the IEEE's rather unusual bibliography style. For example, the IEEE ends the +% previous field item with a period and large space prior to the publisher +% address; the @electronic entry types use periods as inter-item punctuation +% rather than the commas used by the other entry types; and URLs are never +% followed by periods even though they are the last item in the entry. +% Although it is possible to accommodate these features with the conventional +% output state system, the seemingly endless exceptions make for convoluted, +% unreliable and difficult to maintain code. +% +% IEEEtran.bst's output state system can be easily understood via a simple +% illustration of two most recently formatted entry fields (on the stack): +% +% CURRENT_ITEM +% "PREVIOUS_ITEM +% +% which, in this example, is to eventually appear in the bibliography as: +% +% "PREVIOUS_ITEM," CURRENT_ITEM +% +% It is the job of the output routine to take the previous item off of the +% stack (while leaving the current item at the top of the stack), apply its +% trailing punctuation (including closing quote marks) and spacing, and then +% to write the result to BibTeX's output buffer: +% +% "PREVIOUS_ITEM," +% +% Punctuation (and spacing) between items is often determined by both of the +% items rather than just the first one. The presence of quotation marks +% further complicates the situation because, in standard English, trailing +% punctuation marks are supposed to be contained within the quotes. +% +% IEEEtran.bst maintains two output state (aka "status") vectors which +% correspond to the previous and current (aka "this") items. Each vector +% consists of several independent attributes which track punctuation, +% spacing, quotation, and newlines. Capitalization status is handled by a +% separate scalar because the format routines, not the output routine, +% handle capitalization and, therefore, there is no need to maintain the +% capitalization attribute for both the "previous" and "this" items. +% +% When a format routine adds a new item, it copies the current output status +% vector to the previous output status vector and (usually) resets the +% current (this) output status vector to a "standard status" vector. Using a +% "standard status" vector in this way allows us to redefine what we mean by +% "standard status" at the start of each entry handler and reuse the same +% format routines under the various inter-item separation schemes. For +% example, the standard status vector for the @book entry type may use +% commas for item separators, while the @electronic type may use periods, +% yet both entry handlers exploit many of the exact same format routines. +% +% Because format routines have write access to the output status vector of +% the previous item, they can override the punctuation choices of the +% previous format routine! Therefore, it becomes trivial to implement rules +% such as "Always use a period and a large space before the publisher." By +% pushing the generation of the closing quote mark to the output routine, we +% avoid all the problems caused by having to close a quote before having all +% the information required to determine what the punctuation should be. +% +% The IEEEtran.bst output state system can easily be expanded if needed. +% For instance, it is easy to add a "space.tie" attribute value if the +% bibliography rules mandate that two items have to be joined with an +% unbreakable space. + +FUNCTION {initialize.status.constants} +{ #0 'punct.no := + #1 'punct.comma := + #2 'punct.period := + #0 'space.no := + #1 'space.normal := + #2 'space.large := + #0 'quote.no := + #1 'quote.close := + #0 'cap.no := + #1 'cap.yes := + #0 'nline.no := + #1 'nline.newblock := +} + +FUNCTION {std.status.using.comma} +{ punct.comma 'punct.std := + space.normal 'space.std := + quote.no 'quote.std := + nline.no 'nline.std := + cap.no 'cap.std := +} + +FUNCTION {std.status.using.period} +{ punct.period 'punct.std := + space.normal 'space.std := + quote.no 'quote.std := + nline.no 'nline.std := + cap.yes 'cap.std := +} + +FUNCTION {initialize.prev.this.status} +{ punct.no 'prev.status.punct := + space.no 'prev.status.space := + quote.no 'prev.status.quote := + nline.no 'prev.status.nline := + punct.no 'this.status.punct := + space.no 'this.status.space := + quote.no 'this.status.quote := + nline.no 'this.status.nline := + cap.yes 'status.cap := +} + +FUNCTION {this.status.std} +{ punct.std 'this.status.punct := + space.std 'this.status.space := + quote.std 'this.status.quote := + nline.std 'this.status.nline := +} + +FUNCTION {cap.status.std}{ cap.std 'status.cap := } + +FUNCTION {this.to.prev.status} +{ this.status.punct 'prev.status.punct := + this.status.space 'prev.status.space := + this.status.quote 'prev.status.quote := + this.status.nline 'prev.status.nline := +} + + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ { skip$ } + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + { skip$ } + if$ +} + + +% convert the strings "yes" or "no" to #1 or #0 respectively +FUNCTION {yes.no.to.int} +{ "l" change.case$ duplicate$ + "yes" = + { pop$ #1 } + { duplicate$ "no" = + { pop$ #0 } + { "unknown boolean " quote$ * swap$ * quote$ * + " in " * cite$ * warning$ + #0 + } + if$ + } + if$ +} + + +% pushes true if the single char string on the stack is in the +% range of "0" to "9" +FUNCTION {is.num} +{ chr.to.int$ + duplicate$ "0" chr.to.int$ < not + swap$ "9" chr.to.int$ > not and +} + +% multiplies the integer on the stack by a factor of 10 +FUNCTION {bump.int.mag} +{ #0 'multiresult := + { duplicate$ #0 > } + { #1 - + multiresult #10 + + 'multiresult := + } + while$ +pop$ +multiresult +} + +% converts a single character string on the stack to an integer +FUNCTION {char.to.integer} +{ duplicate$ + is.num + { chr.to.int$ "0" chr.to.int$ - } + {"noninteger character " quote$ * swap$ * quote$ * + " in integer field of " * cite$ * warning$ + #0 + } + if$ +} + +% converts a string on the stack to an integer +FUNCTION {string.to.integer} +{ duplicate$ text.length$ 'namesleft := + #1 'nameptr := + #0 'numnames := + { nameptr namesleft > not } + { duplicate$ nameptr #1 substring$ + char.to.integer numnames bump.int.mag + + 'numnames := + nameptr #1 + + 'nameptr := + } + while$ +pop$ +numnames +} + + + + +% The output routines write out the *next* to the top (previous) item on the +% stack, adding punctuation and such as needed. Since IEEEtran.bst maintains +% the output status for the top two items on the stack, these output +% routines have to consider the previous output status (which corresponds to +% the item that is being output). Full independent control of punctuation, +% closing quote marks, spacing, and newblock is provided. +% +% "output.nonnull" does not check for the presence of a previous empty +% item. +% +% "output" does check for the presence of a previous empty item and will +% remove an empty item rather than outputing it. +% +% "output.warn" is like "output", but will issue a warning if it detects +% an empty item. + +FUNCTION {output.nonnull} +{ swap$ + prev.status.punct punct.comma = + { "," * } + { skip$ } + if$ + prev.status.punct punct.period = + { add.period$ } + { skip$ } + if$ + prev.status.quote quote.close = + { "''" * } + { skip$ } + if$ + prev.status.space space.normal = + { " " * } + { skip$ } + if$ + prev.status.space space.large = + { large.space * } + { skip$ } + if$ + write$ + prev.status.nline nline.newblock = + { newline$ "\newblock " write$ } + { skip$ } + if$ +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.warn} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +% "fin.entry" is the output routine that handles the last item of the entry +% (which will be on the top of the stack when "fin.entry" is called). + +FUNCTION {fin.entry} +{ this.status.punct punct.no = + { skip$ } + { add.period$ } + if$ + this.status.quote quote.close = + { "''" * } + { skip$ } + if$ +write$ +newline$ +} + + +FUNCTION {is.last.char.not.punct} +{ duplicate$ + "}" * add.period$ + #-1 #1 substring$ "." = +} + +FUNCTION {is.multiple.pages} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {capitalize}{ "u" change.case$ "t" change.case$ } + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\emph{" swap$ * "}" * } + if$ +} + +FUNCTION {do.name.latex.cmd} +{ name.latex.cmd + empty$ + { skip$ } + { name.latex.cmd "{" * swap$ * "}" * } + if$ +} + +% IEEEtran.bst uses its own \BIBforeignlanguage command which directly +% invokes the TeX hyphenation patterns without the need of the Babel +% package. Babel does a lot more than switch hyphenation patterns and +% its loading can cause unintended effects in many class files (such as +% IEEEtran.cls). +FUNCTION {select.language} +{ duplicate$ empty$ 'pop$ + { language empty$ 'skip$ + { "\BIBforeignlanguage{" language * "}{" * swap$ * "}" * } + if$ + } + if$ +} + +FUNCTION {tie.or.space.prefix} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ +} + +FUNCTION {get.bbl.editor} +{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ } + +FUNCTION {space.word}{ " " swap$ * " " * } + + +% Field Conditioners, Converters, Checkers and External Interfaces + +FUNCTION {empty.field.to.null.string} +{ duplicate$ empty$ + { pop$ "" } + { skip$ } + if$ +} + +FUNCTION {either.or.check} +{ empty$ + { pop$ } + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {empty.entry.warn} +{ author empty$ title empty$ howpublished empty$ + month empty$ year empty$ note empty$ url empty$ + and and and and and and + { "all relevant fields are empty in " cite$ * warning$ } + 'skip$ + if$ +} + + +% The bibinfo system provides a way for the electronic parsing/acquisition +% of a bibliography's contents as is done by ReVTeX. For example, a field +% could be entered into the bibliography as: +% \bibinfo{volume}{2} +% Only the "2" would show up in the document, but the LaTeX \bibinfo command +% could do additional things with the information. IEEEtran.bst does provide +% a \bibinfo command via "\providecommand{\bibinfo}[2]{#2}". However, it is +% currently not used as the bogus bibinfo functions defined here output the +% entry values directly without the \bibinfo wrapper. The bibinfo functions +% themselves (and the calls to them) are retained for possible future use. +% +% bibinfo.check avoids acting on missing fields while bibinfo.warn will +% issue a warning message if a missing field is detected. Prior to calling +% the bibinfo functions, the user should push the field value and then its +% name string, in that order. + +FUNCTION {bibinfo.check} +{ swap$ duplicate$ missing$ + { pop$ pop$ "" } + { duplicate$ empty$ + { swap$ pop$ } + { swap$ pop$ } + if$ + } + if$ +} + +FUNCTION {bibinfo.warn} +{ swap$ duplicate$ missing$ + { swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ "" } + { duplicate$ empty$ + { swap$ "empty " swap$ * " in " * cite$ * warning$ } + { swap$ pop$ } + if$ + } + if$ +} + + +% The IEEE separates large numbers with more than 4 digits into groups of +% three. The IEEE uses a small space to separate these number groups. +% Typical applications include patent and page numbers. + +% number of consecutive digits required to trigger the group separation. +FUNCTION {large.number.trigger}{ #5 } + +% For numbers longer than the trigger, this is the blocksize of the groups. +% The blocksize must be less than the trigger threshold, and 2 * blocksize +% must be greater than the trigger threshold (can't do more than one +% separation on the initial trigger). +FUNCTION {large.number.blocksize}{ #3 } + +% What is actually inserted between the number groups. +FUNCTION {large.number.separator}{ "\," } + +% So as to save on integer variables by reusing existing ones, numnames +% holds the current number of consecutive digits read and nameptr holds +% the number that will trigger an inserted space. +FUNCTION {large.number.separate} +{ 't := + "" + #0 'numnames := + large.number.trigger 'nameptr := + { t empty$ not } + { t #-1 #1 substring$ is.num + { numnames #1 + 'numnames := } + { #0 'numnames := + large.number.trigger 'nameptr := + } + if$ + t #-1 #1 substring$ swap$ * + t #-2 global.max$ substring$ 't := + numnames nameptr = + { duplicate$ #1 nameptr large.number.blocksize - substring$ swap$ + nameptr large.number.blocksize - #1 + global.max$ substring$ + large.number.separator swap$ * * + nameptr large.number.blocksize - 'numnames := + large.number.blocksize #1 + 'nameptr := + } + { skip$ } + if$ + } + while$ +} + +% Converts all single dashes "-" to double dashes "--". +FUNCTION {n.dashify} +{ large.number.separate + 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + + +% This function detects entries with names that are identical to that of +% the previous entry and replaces the repeated names with dashes (if the +% "is.dash.repeated.names" user control is nonzero). +FUNCTION {name.or.dash} +{ 's := + oldname empty$ + { s 'oldname := s } + { s oldname = + { is.dash.repeated.names + { repeated.name.dashes } + { s 'oldname := s } + if$ + } + { s 'oldname := s } + if$ + } + if$ +} + +% Converts the number string on the top of the stack to +% "numerical ordinal form" (e.g., "7" to "7th"). There is +% no artificial limit to the upper bound of the numbers as the +% two least significant digits determine the ordinal form. +FUNCTION {num.to.ordinal} +{ duplicate$ #-2 #1 substring$ "1" = + { bbl.th * } + { duplicate$ #-1 #1 substring$ "1" = + { bbl.st * } + { duplicate$ #-1 #1 substring$ "2" = + { bbl.nd * } + { duplicate$ #-1 #1 substring$ "3" = + { bbl.rd * } + { bbl.th * } + if$ + } + if$ + } + if$ + } + if$ +} + +% If the string on the top of the stack begins with a number, +% (e.g., 11th) then replace the string with the leading number +% it contains. Otherwise retain the string as-is. s holds the +% extracted number, t holds the part of the string that remains +% to be scanned. +FUNCTION {extract.num} +{ duplicate$ 't := + "" 's := + { t empty$ not } + { t #1 #1 substring$ + t #2 global.max$ substring$ 't := + duplicate$ is.num + { s swap$ * 's := } + { pop$ "" 't := } + if$ + } + while$ + s empty$ + 'skip$ + { pop$ s } + if$ +} + +% Converts the word number string on the top of the stack to +% Arabic string form. Will be successful up to "tenth". +FUNCTION {word.to.num} +{ duplicate$ "l" change.case$ 's := + s "first" = + { pop$ "1" } + { skip$ } + if$ + s "second" = + { pop$ "2" } + { skip$ } + if$ + s "third" = + { pop$ "3" } + { skip$ } + if$ + s "fourth" = + { pop$ "4" } + { skip$ } + if$ + s "fifth" = + { pop$ "5" } + { skip$ } + if$ + s "sixth" = + { pop$ "6" } + { skip$ } + if$ + s "seventh" = + { pop$ "7" } + { skip$ } + if$ + s "eighth" = + { pop$ "8" } + { skip$ } + if$ + s "ninth" = + { pop$ "9" } + { skip$ } + if$ + s "tenth" = + { pop$ "10" } + { skip$ } + if$ +} + + +% Converts the string on the top of the stack to numerical +% ordinal (e.g., "11th") form. +FUNCTION {convert.edition} +{ duplicate$ empty$ 'skip$ + { duplicate$ #1 #1 substring$ is.num + { extract.num + num.to.ordinal + } + { word.to.num + duplicate$ #1 #1 substring$ is.num + { num.to.ordinal } + { "edition ordinal word " quote$ * edition * quote$ * + " may be too high (or improper) for conversion" * " in " * cite$ * warning$ + } + if$ + } + if$ + } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% LATEX BIBLIOGRAPHY CODE %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {start.entry} +{ newline$ + "\bibitem{" write$ + cite$ write$ + "}" write$ + newline$ + "" + initialize.prev.this.status +} + +% Here we write out all the LaTeX code that we will need. The most involved +% code sequences are those that control the alternate interword spacing and +% foreign language hyphenation patterns. The heavy use of \providecommand +% gives users a way to override the defaults. Special thanks to Javier Bezos, +% Johannes Braams, Robin Fairbairns, Heiko Oberdiek, Donald Arseneau and all +% the other gurus on comp.text.tex for their help and advice on the topic of +% \selectlanguage, Babel and BibTeX. +FUNCTION {begin.bib} +{ "% Generated by IEEEtran.bst, version: " bst.file.version * " (" * bst.file.date * ")" * + write$ newline$ + preamble$ empty$ 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" longest.label * "}" * + write$ newline$ + "\providecommand{\url}[1]{#1}" + write$ newline$ + "\csname url@samestyle\endcsname" + write$ newline$ + "\providecommand{\newblock}{\relax}" + write$ newline$ + "\providecommand{\bibinfo}[2]{#2}" + write$ newline$ + "\providecommand{\BIBentrySTDinterwordspacing}{\spaceskip=0pt\relax}" + write$ newline$ + "\providecommand{\BIBentryALTinterwordstretchfactor}{" + ALTinterwordstretchfactor * "}" * + write$ newline$ + "\providecommand{\BIBentryALTinterwordspacing}{\spaceskip=\fontdimen2\font plus " + write$ newline$ + "\BIBentryALTinterwordstretchfactor\fontdimen3\font minus \fontdimen4\font\relax}" + write$ newline$ + "\providecommand{\BIBforeignlanguage}[2]{{%" + write$ newline$ + "\expandafter\ifx\csname l@#1\endcsname\relax" + write$ newline$ + "\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}%" + write$ newline$ + "\typeout{** loaded for the language `#1'. Using the pattern for}%" + write$ newline$ + "\typeout{** the default language instead.}%" + write$ newline$ + "\else" + write$ newline$ + "\language=\csname l@#1\endcsname" + write$ newline$ + "\fi" + write$ newline$ + "#2}}" + write$ newline$ + "\providecommand{\BIBdecl}{\relax}" + write$ newline$ + "\BIBdecl" + write$ newline$ +} + +FUNCTION {end.bib} +{ newline$ "\end{thebibliography}" write$ newline$ } + +FUNCTION {if.url.alt.interword.spacing} +{ is.use.alt.interword.spacing + { is.use.url + { url empty$ 'skip$ {"\BIBentryALTinterwordspacing" write$ newline$} if$ } + { skip$ } + if$ + } + { skip$ } + if$ +} + +FUNCTION {if.url.std.interword.spacing} +{ is.use.alt.interword.spacing + { is.use.url + { url empty$ 'skip$ {"\BIBentrySTDinterwordspacing" write$ newline$} if$ } + { skip$ } + if$ + } + { skip$ } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%%%%% +%% LONGEST LABEL PASS %% +%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {initialize.longest.label} +{ "" 'longest.label := + #1 'number.label := + #0 'longest.label.width := +} + +FUNCTION {longest.label.pass} +{ type$ "ieeetranbstctl" = + { skip$ } + { number.label int.to.str$ 'label := + number.label #1 + 'number.label := + label width$ longest.label.width > + { label 'longest.label := + label width$ 'longest.label.width := + } + { skip$ } + if$ + } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%% +%% FORMAT HANDLERS %% +%%%%%%%%%%%%%%%%%%%%% + +%% Lower Level Formats (used by higher level formats) + +FUNCTION {format.address.org.or.pub.date} +{ 't := + "" + year empty$ + { "empty year in " cite$ * warning$ } + { skip$ } + if$ + address empty$ t empty$ and + year empty$ and month empty$ and + { skip$ } + { this.to.prev.status + this.status.std + cap.status.std + address "address" bibinfo.check * + t empty$ + { skip$ } + { punct.period 'prev.status.punct := + space.large 'prev.status.space := + address empty$ + { skip$ } + { ": " * } + if$ + t * + } + if$ + year empty$ month empty$ and + { skip$ } + { t empty$ address empty$ and + { skip$ } + { ", " * } + if$ + month empty$ + { year empty$ + { skip$ } + { year "year" bibinfo.check * } + if$ + } + { month "month" bibinfo.check * + year empty$ + { skip$ } + { " " * year "year" bibinfo.check * } + if$ + } + if$ + } + if$ + } + if$ +} + + +FUNCTION {format.names} +{ 'bibinfo := + duplicate$ empty$ 'skip$ { + this.to.prev.status + this.status.std + 's := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + name.format.string + format.name$ + bibinfo bibinfo.check + 't := + nameptr #1 > + { nameptr num.names.shown.with.forced.et.al #1 + = + numnames max.num.names.before.forced.et.al > + is.forced.et.al and and + { "others" 't := + #1 'namesleft := + } + { skip$ } + if$ + namesleft #1 > + { ", " * t do.name.latex.cmd * } + { s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { " " * bbl.etal emphasize * } + { numnames #2 > + { "," * } + { skip$ } + if$ + bbl.and + space.word * t do.name.latex.cmd * + } + if$ + } + if$ + } + { t do.name.latex.cmd } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ + cap.status.std + } if$ +} + + + + +%% Higher Level Formats + +%% addresses/locations + +FUNCTION {format.address} +{ address duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + + + +%% author/editor names + +FUNCTION {format.authors}{ author "author" format.names } + +FUNCTION {format.editors} +{ editor "editor" format.names duplicate$ empty$ 'skip$ + { ", " * + get.bbl.editor + capitalize + * + } + if$ +} + + + +%% date + +FUNCTION {format.date} +{ + month "month" bibinfo.check duplicate$ empty$ + year "year" bibinfo.check duplicate$ empty$ + { swap$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + "there's a month but no year in " cite$ * warning$ } + if$ + * + } + { this.to.prev.status + this.status.std + cap.status.std + swap$ 'skip$ + { + swap$ + " " * swap$ + } + if$ + * + } + if$ +} + +FUNCTION {format.date.electronic} +{ month "month" bibinfo.check duplicate$ empty$ + year "year" bibinfo.check duplicate$ empty$ + { swap$ + { pop$ } + { "there's a month but no year in " cite$ * warning$ + pop$ ")" * "(" swap$ * + this.to.prev.status + punct.no 'this.status.punct := + space.normal 'this.status.space := + quote.no 'this.status.quote := + cap.yes 'status.cap := + } + if$ + } + { swap$ + { swap$ pop$ ")" * "(" swap$ * } + { "(" swap$ * ", " * swap$ * ")" * } + if$ + this.to.prev.status + punct.no 'this.status.punct := + space.normal 'this.status.space := + quote.no 'this.status.quote := + cap.yes 'status.cap := + } + if$ +} + + + +%% edition/title + +% Note: The IEEE considers the edition to be closely associated with +% the title of a book. So, in IEEEtran.bst the edition is normally handled +% within the formatting of the title. The format.edition function is +% retained here for possible future use. +FUNCTION {format.edition} +{ edition duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + convert.edition + status.cap + { "t" } + { "l" } + if$ change.case$ + "edition" bibinfo.check + "~" * bbl.edition * + cap.status.std + } + if$ +} + +% This is used to format the booktitle of a conference proceedings. +% Here we use the "intype" field to provide the user a way to +% override the word "in" (e.g., with things like "presented at") +% Use of intype stops the emphasis of the booktitle to indicate that +% we no longer mean the written conference proceedings, but the +% conference itself. +FUNCTION {format.in.booktitle} +{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + select.language + intype missing$ + { emphasize + bbl.in " " * + } + { intype " " * } + if$ + swap$ * + cap.status.std + } + if$ +} + +% This is used to format the booktitle of collection. +% Here the "intype" field is not supported, but "edition" is. +FUNCTION {format.in.booktitle.edition} +{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + select.language + emphasize + edition empty$ 'skip$ + { ", " * + edition + convert.edition + "l" change.case$ + * "~" * bbl.edition * + } + if$ + bbl.in " " * swap$ * + cap.status.std + } + if$ +} + +FUNCTION {format.article.title} +{ title duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + "t" change.case$ + } + if$ + "title" bibinfo.check + duplicate$ empty$ 'skip$ + { quote.close 'this.status.quote := + is.last.char.not.punct + { punct.std 'this.status.punct := } + { punct.no 'this.status.punct := } + if$ + select.language + "``" swap$ * + cap.status.std + } + if$ +} + +FUNCTION {format.article.title.electronic} +{ title duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + "t" change.case$ + } + if$ + "title" bibinfo.check + duplicate$ empty$ + { skip$ } + { select.language } + if$ +} + +FUNCTION {format.book.title.edition} +{ title "title" bibinfo.check + duplicate$ empty$ + { "empty title in " cite$ * warning$ } + { this.to.prev.status + this.status.std + select.language + emphasize + edition empty$ 'skip$ + { ", " * + edition + convert.edition + status.cap + { "t" } + { "l" } + if$ + change.case$ + * "~" * bbl.edition * + } + if$ + cap.status.std + } + if$ +} + +FUNCTION {format.book.title} +{ title "title" bibinfo.check + duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + select.language + emphasize + } + if$ +} + + + +%% journal + +FUNCTION {format.journal} +{ journal duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + select.language + emphasize + } + if$ +} + + + +%% how published + +FUNCTION {format.howpublished} +{ howpublished duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + + + +%% institutions/organization/publishers/school + +FUNCTION {format.institution} +{ institution duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + +FUNCTION {format.organization} +{ organization duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + +FUNCTION {format.address.publisher.date} +{ publisher "publisher" bibinfo.warn format.address.org.or.pub.date } + +FUNCTION {format.address.publisher.date.nowarn} +{ publisher "publisher" bibinfo.check format.address.org.or.pub.date } + +FUNCTION {format.address.organization.date} +{ organization "organization" bibinfo.check format.address.org.or.pub.date } + +FUNCTION {format.school} +{ school duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + + + +%% volume/number/series/chapter/pages + +FUNCTION {format.volume} +{ volume empty.field.to.null.string + duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + bbl.volume + status.cap + { capitalize } + { skip$ } + if$ + swap$ tie.or.space.prefix + "volume" bibinfo.check + * * + cap.status.std + } + if$ +} + +FUNCTION {format.number} +{ number empty.field.to.null.string + duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + status.cap + { bbl.number capitalize } + { bbl.number } + if$ + swap$ tie.or.space.prefix + "number" bibinfo.check + * * + cap.status.std + } + if$ +} + +FUNCTION {format.number.if.use.for.article} +{ is.use.number.for.article + { format.number } + { "" } + if$ +} + +% The IEEE does not seem to tie the series so closely with the volume +% and number as is done in other bibliography styles. Instead the +% series is treated somewhat like an extension of the title. +FUNCTION {format.series} +{ series empty$ + { "" } + { this.to.prev.status + this.status.std + bbl.series " " * + series "series" bibinfo.check * + cap.status.std + } + if$ +} + + +FUNCTION {format.chapter} +{ chapter empty$ + { "" } + { this.to.prev.status + this.status.std + type empty$ + { bbl.chapter } + { type "l" change.case$ + "type" bibinfo.check + } + if$ + chapter tie.or.space.prefix + "chapter" bibinfo.check + * * + cap.status.std + } + if$ +} + + +% The intended use of format.paper is for paper numbers of inproceedings. +% The paper type can be overridden via the type field. +% We allow the type to be displayed even if the paper number is absent +% for things like "postdeadline paper" +FUNCTION {format.paper} +{ is.use.paper + { paper empty$ + { type empty$ + { "" } + { this.to.prev.status + this.status.std + type "type" bibinfo.check + cap.status.std + } + if$ + } + { this.to.prev.status + this.status.std + type empty$ + { bbl.paper } + { type "type" bibinfo.check } + if$ + " " * paper + "paper" bibinfo.check + * + cap.status.std + } + if$ + } + { "" } + if$ +} + + +FUNCTION {format.pages} +{ pages duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + duplicate$ is.multiple.pages + { + bbl.pages swap$ + n.dashify + } + { + bbl.page swap$ + } + if$ + tie.or.space.prefix + "pages" bibinfo.check + * * + cap.status.std + } + if$ +} + + + +%% technical report number + +FUNCTION {format.tech.report.number} +{ number "number" bibinfo.check + this.to.prev.status + this.status.std + cap.status.std + type duplicate$ empty$ + { pop$ + bbl.techrep + } + { skip$ } + if$ + "type" bibinfo.check + swap$ duplicate$ empty$ + { pop$ } + { tie.or.space.prefix * * } + if$ +} + + + +%% note + +FUNCTION {format.note} +{ note empty$ + { "" } + { this.to.prev.status + this.status.std + punct.period 'this.status.punct := + note #1 #1 substring$ + duplicate$ "{" = + { skip$ } + { status.cap + { "u" } + { "l" } + if$ + change.case$ + } + if$ + note #2 global.max$ substring$ * "note" bibinfo.check + cap.yes 'status.cap := + } + if$ +} + + + +%% patent + +FUNCTION {format.patent.date} +{ this.to.prev.status + this.status.std + year empty$ + { monthfiled duplicate$ empty$ + { "monthfiled" bibinfo.check pop$ "" } + { "monthfiled" bibinfo.check } + if$ + dayfiled duplicate$ empty$ + { "dayfiled" bibinfo.check pop$ "" * } + { "dayfiled" bibinfo.check + monthfiled empty$ + { "dayfiled without a monthfiled in " cite$ * warning$ + * + } + { " " swap$ * * } + if$ + } + if$ + yearfiled empty$ + { "no year or yearfiled in " cite$ * warning$ } + { yearfiled "yearfiled" bibinfo.check + swap$ + duplicate$ empty$ + { pop$ } + { ", " * swap$ * } + if$ + } + if$ + } + { month duplicate$ empty$ + { "month" bibinfo.check pop$ "" } + { "month" bibinfo.check } + if$ + day duplicate$ empty$ + { "day" bibinfo.check pop$ "" * } + { "day" bibinfo.check + month empty$ + { "day without a month in " cite$ * warning$ + * + } + { " " swap$ * * } + if$ + } + if$ + year "year" bibinfo.check + swap$ + duplicate$ empty$ + { pop$ } + { ", " * swap$ * } + if$ + } + if$ + cap.status.std +} + +FUNCTION {format.patent.nationality.type.number} +{ this.to.prev.status + this.status.std + nationality duplicate$ empty$ + { "nationality" bibinfo.warn pop$ "" } + { "nationality" bibinfo.check + duplicate$ "l" change.case$ "united states" = + { pop$ bbl.patentUS } + { skip$ } + if$ + " " * + } + if$ + type empty$ + { bbl.patent "type" bibinfo.check } + { type "type" bibinfo.check } + if$ + * + number duplicate$ empty$ + { "number" bibinfo.warn pop$ } + { "number" bibinfo.check + large.number.separate + swap$ " " * swap$ * + } + if$ + cap.status.std +} + + + +%% standard + +FUNCTION {format.organization.institution.standard.type.number} +{ this.to.prev.status + this.status.std + organization duplicate$ empty$ + { pop$ + institution duplicate$ empty$ + { "institution" bibinfo.warn } + { "institution" bibinfo.warn " " * } + if$ + } + { "organization" bibinfo.warn " " * } + if$ + type empty$ + { bbl.standard "type" bibinfo.check } + { type "type" bibinfo.check } + if$ + * + number duplicate$ empty$ + { "number" bibinfo.check pop$ } + { "number" bibinfo.check + large.number.separate + swap$ " " * swap$ * + } + if$ + cap.status.std +} + +FUNCTION {format.revision} +{ revision empty$ + { "" } + { this.to.prev.status + this.status.std + bbl.revision + revision tie.or.space.prefix + "revision" bibinfo.check + * * + cap.status.std + } + if$ +} + + +%% thesis + +FUNCTION {format.master.thesis.type} +{ this.to.prev.status + this.status.std + type empty$ + { + bbl.mthesis + } + { + type "type" bibinfo.check + } + if$ +cap.status.std +} + +FUNCTION {format.phd.thesis.type} +{ this.to.prev.status + this.status.std + type empty$ + { + bbl.phdthesis + } + { + type "type" bibinfo.check + } + if$ +cap.status.std +} + + + +%% URL + +FUNCTION {format.url} +{ is.use.url + { url empty$ + { "" } + { this.to.prev.status + this.status.std + cap.yes 'status.cap := + name.url.prefix " " * + "\url{" * url * "}" * + punct.no 'this.status.punct := + punct.period 'prev.status.punct := + space.normal 'this.status.space := + space.normal 'prev.status.space := + quote.no 'this.status.quote := + } + if$ + } + { "" } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%% +%% ENTRY HANDLERS %% +%%%%%%%%%%%%%%%%%%%% + + +% Note: In many journals, the IEEE (or the authors) tend not to show the number +% for articles, so the display of the number is controlled here by the +% switch "is.use.number.for.article" +FUNCTION {article} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.journal "journal" bibinfo.check "journal" output.warn + format.volume output + format.number.if.use.for.article output + format.pages output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {book} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + author empty$ + { format.editors "author and editor" output.warn } + { format.authors output.nonnull } + if$ + name.or.dash + format.book.title.edition output + format.series output + author empty$ + { skip$ } + { format.editors output } + if$ + format.address.publisher.date output + format.volume output + format.number output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {booklet} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.article.title "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.date output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {electronic} +{ std.status.using.period + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.date.electronic output + format.article.title.electronic output + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.note output + format.url output + fin.entry + empty.entry.warn + if.url.std.interword.spacing +} + +FUNCTION {inbook} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + author empty$ + { format.editors "author and editor" output.warn } + { format.authors output.nonnull } + if$ + name.or.dash + format.book.title.edition output + format.series output + format.address.publisher.date output + format.volume output + format.number output + format.chapter output + format.pages output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {incollection} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.in.booktitle.edition "booktitle" output.warn + format.series output + format.editors output + format.address.publisher.date.nowarn output + format.volume output + format.number output + format.chapter output + format.pages output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {inproceedings} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.in.booktitle "booktitle" output.warn + format.series output + format.editors output + format.volume output + format.number output + publisher empty$ + { format.address.organization.date output } + { format.organization "organization" bibinfo.check output + format.address.publisher.date output + } + if$ + format.paper output + format.pages output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {manual} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.book.title.edition "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.date output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {mastersthesis} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.master.thesis.type output.nonnull + format.school "school" bibinfo.warn output + format.address "address" bibinfo.check output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {misc} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.article.title output + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.pages output + format.date output + format.note output + format.url output + fin.entry + empty.entry.warn + if.url.std.interword.spacing +} + +FUNCTION {patent} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.article.title output + format.patent.nationality.type.number output + format.patent.date output + format.note output + format.url output + fin.entry + empty.entry.warn + if.url.std.interword.spacing +} + +FUNCTION {periodical} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.editors output + name.or.dash + format.book.title "title" output.warn + format.series output + format.volume output + format.number output + format.organization "organization" bibinfo.check output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {phdthesis} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.phd.thesis.type output.nonnull + format.school "school" bibinfo.warn output + format.address "address" bibinfo.check output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {proceedings} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.editors output + name.or.dash + format.book.title "title" output.warn + format.series output + format.volume output + format.number output + publisher empty$ + { format.address.organization.date output } + { format.organization "organization" bibinfo.check output + format.address.publisher.date output + } + if$ + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {standard} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.book.title "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.organization.institution.standard.type.number output + format.revision output + format.date output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {techreport} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.institution "institution" bibinfo.warn output + format.address "address" bibinfo.check output + format.tech.report.number output.nonnull + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {unpublished} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.date output + format.note "note" output.warn + format.url output + fin.entry + if.url.std.interword.spacing +} + + +% The special entry type which provides the user interface to the +% BST controls +FUNCTION {IEEEtranBSTCTL} +{ is.print.banners.to.terminal + { "** IEEEtran BST control entry " quote$ * cite$ * quote$ * " detected." * + top$ + } + { skip$ } + if$ + CTLuse_article_number + empty$ + { skip$ } + { CTLuse_article_number + yes.no.to.int + 'is.use.number.for.article := + } + if$ + CTLuse_paper + empty$ + { skip$ } + { CTLuse_paper + yes.no.to.int + 'is.use.paper := + } + if$ + CTLuse_url + empty$ + { skip$ } + { CTLuse_url + yes.no.to.int + 'is.use.url := + } + if$ + CTLuse_forced_etal + empty$ + { skip$ } + { CTLuse_forced_etal + yes.no.to.int + 'is.forced.et.al := + } + if$ + CTLmax_names_forced_etal + empty$ + { skip$ } + { CTLmax_names_forced_etal + string.to.integer + 'max.num.names.before.forced.et.al := + } + if$ + CTLnames_show_etal + empty$ + { skip$ } + { CTLnames_show_etal + string.to.integer + 'num.names.shown.with.forced.et.al := + } + if$ + CTLuse_alt_spacing + empty$ + { skip$ } + { CTLuse_alt_spacing + yes.no.to.int + 'is.use.alt.interword.spacing := + } + if$ + CTLalt_stretch_factor + empty$ + { skip$ } + { CTLalt_stretch_factor + 'ALTinterwordstretchfactor := + "\renewcommand{\BIBentryALTinterwordstretchfactor}{" + ALTinterwordstretchfactor * "}" * + write$ newline$ + } + if$ + CTLdash_repeated_names + empty$ + { skip$ } + { CTLdash_repeated_names + yes.no.to.int + 'is.dash.repeated.names := + } + if$ + CTLname_format_string + empty$ + { skip$ } + { CTLname_format_string + 'name.format.string := + } + if$ + CTLname_latex_cmd + empty$ + { skip$ } + { CTLname_latex_cmd + 'name.latex.cmd := + } + if$ + CTLname_url_prefix + missing$ + { skip$ } + { CTLname_url_prefix + 'name.url.prefix := + } + if$ + + + num.names.shown.with.forced.et.al max.num.names.before.forced.et.al > + { "CTLnames_show_etal cannot be greater than CTLmax_names_forced_etal in " cite$ * warning$ + max.num.names.before.forced.et.al 'num.names.shown.with.forced.et.al := + } + { skip$ } + if$ +} + + +%%%%%%%%%%%%%%%%%%% +%% ENTRY ALIASES %% +%%%%%%%%%%%%%%%%%%% +FUNCTION {conference}{inproceedings} +FUNCTION {online}{electronic} +FUNCTION {internet}{electronic} +FUNCTION {webpage}{electronic} +FUNCTION {www}{electronic} +FUNCTION {default.type}{misc} + + + +%%%%%%%%%%%%%%%%%% +%% MAIN PROGRAM %% +%%%%%%%%%%%%%%%%%% + +READ + +EXECUTE {initialize.controls} +EXECUTE {initialize.status.constants} +EXECUTE {banner.message} + +EXECUTE {initialize.longest.label} +ITERATE {longest.label.pass} + +EXECUTE {begin.bib} +ITERATE {call.type$} +EXECUTE {end.bib} + +EXECUTE{completed.message} + + +%% That's all folks, mds. \ No newline at end of file diff --git a/TRUST-docs/IEEEtrantools.sty b/TRUST-docs/IEEEtrantools.sty new file mode 100755 index 0000000..e4a808c --- /dev/null +++ b/TRUST-docs/IEEEtrantools.sty @@ -0,0 +1,2799 @@ +%% +%% IEEEtrantools.sty 2015/08/26 version V1.5 +%% +%% +%% This package provides several popular and unique commands from the +%% IEEEtran.cls class (version 1.8b) file. +%% +%% The provided commands include \IEEEPARstart, \IEEEitemize, \IEEEenumerate, +%% \IEEEdescription as well as the \IEEEeqnarray, \IEEEeqnarraybox family +%% of commands including support commands such as \IEEEstrut, the IEEEproof +%% environment and its support commands and the \IEEEauthorrefmark command. +%% Also provides the \bstctlcite command for the control entry types of +%% IEEEtran.bst V1.00 and later, as well as \IEEEnoauxwrite. +%% +%% IEEEtrantools.sty should not be used with IEEEtran.cls. +%% +%% Support sites: +%% http://www.michaelshell.org/tex/ieeetran/ +%% http://www.ctan.org/pkg/ieeetran +%% +%% +%% Copyright (c) 2002-2015 by Michael Shell +%% See: http://www.michaelshell.org/ +%% for current contact information. +%% +%%************************************************************************* +%% Legal Notice: +%% This code is offered as-is without any warranty either expressed or +%% implied; without even the implied warranty of MERCHANTABILITY or +%% FITNESS FOR A PARTICULAR PURPOSE! +%% User assumes all risk. +%% In no event shall the IEEE or any contributor to this code be liable for +%% any damages or losses, including, but not limited to, incidental, +%% consequential, or any other damages, resulting from the use or misuse +%% of any information contained here. +%% +%% All comments are the opinions of their respective authors and are not +%% necessarily endorsed by the IEEE. +%% +%% This work is distributed under the LaTeX Project Public License (LPPL) +%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, +%% distributed and modified. A copy of the LPPL, version 1.3, is included +%% in the base LaTeX documentation of all distributions of LaTeX released +%% 2003/12/01 or later. +%% Retain all contribution notices and credits. +%% ** Modified files should be clearly indicated as such, including ** +%% ** renaming them and changing author support contact information. ** +%% +%% File list of work: IEEEtrantools.sty, IEEEtrantools_doc.txt +%%************************************************************************* +%% +%% +%% +%% Available package options (e.g., \usepackage[redeflists]{IEEEtrantools} +%% +%% redeflists +%% Causes IEEEtrantools to redefine the standard itemize, enumerate and +%% description (IED) list environments to their IEEE versions. +%% IEEEitemize, IEEEenumerate and IEEEdescription remain available in any +%% case. This option may not be compatible with packages that alter the +%% standard IED list environments. +%% +%% +%%********************************************************************** + + +\ProvidesPackage{IEEEtrantools}[2015/08/26 V1.5 by Michael Shell] +\typeout{-- See the "IEEEtrantools_doc.txt" manual for usage information.} +\typeout{-- http://www.michaelshell.org/tex/ieeetran/tools/} +\NeedsTeXFormat{LaTeX2e} + + +% If \@IEEEeqnarray is detected, error. +{\@ifundefined{@IEEEeqnarray}{\relax}{% +\PackageError{IEEEtrantools}{The IEEEtrantools package is not for use\MessageBreak + with classes that already provide it}% + {Do not load IEEEtrantools - you don't need it.}% +}} + + +% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting +\def\@IEEEclspkgerror{\PackageError{IEEEtrantools}} + + +% define needed flags to indicate document options +\newif\if@IEEETOOLSredeflists +\global\@IEEETOOLSredeflistsfalse + + +% IEEEtran class scratch pad registers +% dimen +\newdimen\@IEEEtrantmpdimenA +\newdimen\@IEEEtrantmpdimenB +\newdimen\@IEEEtrantmpdimenC +% count +\newcount\@IEEEtrantmpcountA +\newcount\@IEEEtrantmpcountB +\newcount\@IEEEtrantmpcountC +% token list +\newtoks\@IEEEtrantmptoksA + + +% declare the options +\DeclareOption{redeflists}{\@IEEETOOLSredefliststrue} +% provide legacy support for retainorgcmds which does nothing now. +\DeclareOption{retainorgcmds}{\@IEEETOOLSredeflistsfalse} + +% get and process any supplied options +\ProcessOptions + + +% store the nominal value of jot +\newdimen\IEEEnormaljot +\IEEEnormaljot\jot\relax +% V1.4 allow for other packages that later change \jot +\AtBeginDocument{\IEEEnormaljot\jot\relax} + + + + +%% -- Command Argument Scanning Support Functions -- + +% Sets the category codes for punctuation to their normal values. +% For local use with argument scanning. +\def\IEEEnormalcatcodespunct{\catcode`\!=12 \catcode`\,=12 \catcode`\:=12 +\catcode`\;=12 \catcode`\`=12 \catcode`\'=12 \catcode`\"=12 \catcode`\.=12 +\catcode`\/=12 \catcode`\?=12 \catcode`\*=12 \catcode`\+=12 \catcode`\-=12 +\catcode`\<=12 \catcode`\>=12 \catcode`\(=12 \catcode`\)=12 \catcode`\[=12 +\catcode`\]=12 \catcode`\==12 \catcode`\|=12} +% Sets the category codes for numbers to their normal values. +% For local use with argument scanning. +\def\IEEEnormalcatcodesnum{\catcode`\0=12 \catcode`\1=12 \catcode`\2=12 +\catcode`\3=12 \catcode`\4=12 \catcode`\5=12 \catcode`\6=12 \catcode`\7=12 +\catcode`\8=12 \catcode`\9=12} +% combined action of \IEEEnormalcatcodespunct and \IEEEnormalcatcodesnum +\def\IEEEnormalcatcodes{\IEEEnormalcatcodespunct\IEEEnormalcatcodesnum} + + +% usage: \@IEEEstripouterbraces*{} +% \@IEEEstripouterbraces fully expands its argument (which it then stores +% in \@IEEEstripouterbracesarg) via \edef, then removes any outer enclosing +% braces, and finally stores the result in the macro +% \@IEEEstrippedouterbraces. +% +% For example: +% \@IEEEstripouterbraces{{{{ab}c}}} +% results in: +% +% \@IEEEstripouterbracesarg ==> a macro containing {{{ab}c}} +% \@IEEEstrippedouterbraces ==> a macro containing {ab}c +% +% the *-star form,\@IEEEstripouterbraces*, does not expand the argument +% contents during processing +\def\@IEEEstripouterbraces{\@ifstar{\let\@IEEEstripouterbracesdef=\def\@@IEEEstripouterbraces}{\let\@IEEEstripouterbracesdef=\edef\@@IEEEstripouterbraces}} + +\def\@@IEEEstripouterbraces#1{\@IEEEstripouterbracesdef\@IEEEstripouterbracesarg{#1}\relax +% If the macro is unchanged after being acquired as a single delimited +% argument, we know we have one sequence of tokens without any enclosing +% braces. Loop until this is true. +\loop + \expandafter\@@@IEEEstripouterbraces\@IEEEstripouterbracesarg\@IEEEgeneralsequenceDELIMITER +\ifx\@IEEEstrippedouterbraces\@IEEEstripouterbracesarg +\else + \let\@IEEEstripouterbracesarg\@IEEEstrippedouterbraces +\repeat} + +\def\@@@IEEEstripouterbraces#1\@IEEEgeneralsequenceDELIMITER{\def\@IEEEstrippedouterbraces{#1}} + + + +% usage: \@IEEEextractgroup*{} +% \@IEEEextractgroup fully expands its argument (which it then stores in +% \@IEEEextractgrouparg) via \edef and then assigns the first "brace group" +% of tokens to the macro \@IEEEextractedgroup. +% The remaining groups, if any, are stored in the macro +% \@IEEEextractedgroupremain. If the argument does not contain the requisite +% groups, the respective macros will be defined to be empty. +% There is an asymmetry in that \@IEEEextractedgroup is stripped of its first +% outer grouping while \@IEEEextractedgroupremain retains even the outer +% grouping (if present) that originally identified it as a group. +% +% For example: +% \@IEEEextractgroup{{{ab}}{c{de}}} +% results in: +% +% \@IEEEextractgrouparg ==> a macro containing {{ab}}{c{de}} +% \@IEEEextractedgroup ==> a macro containing {ab} +% \@IEEEextractedgroupremain ==> a macro containing {c{de}} +% +% The *-star form, \@IEEEextractgroup*, does not expand its argument +% contents during processing. +\def\@IEEEextractgroup{\@ifstar{\let\@IEEEextractgroupdef=\def\@@IEEEextractgroup}{\let\@IEEEextractgroupdef=\edef\@@IEEEextractgroup}} + +\def\@@IEEEextractgroup#1{\@IEEEextractgroupdef\@IEEEextractgrouparg{#1}\relax +% trap the case of an empty extracted group as this would cause problems with +% \@IEEEextractgroupremain's argument acquisition +\ifx\@IEEEextractgrouparg\@empty + \def\@IEEEextractedgroup{}\relax + \def\@IEEEextractedgroupremain{}\relax +\else + % We have to use some dirty tricks here. We want to insert {} around + % whatever remains after the first group so that TeX's argument scanner + % will preserve any originally enclosing braces as well as provide an + % empty argument to acquire even if there isn't a second group. + % In this first of two dirty tricks, we put a } at the end of the structure + % we are going to extract from. The \ifnum0=`{\fi keeps TeX happy to allow + % what would otherwise be an unbalanced macro definition for + % \@@IEEEextractgroup to be acceptable to it. + \ifnum0=`{\fi\expandafter\@IEEEextractgroupremain\@IEEEextractgrouparg}\relax +\fi} + +% In the second part of the dirty tricks, we insert a leading { right after +% the first group is acquired, but before the remainder is. Again, the +% \ifnum0=`}\fi keeps TeX happy during definition time, but will disappear +% during run time. +\def\@IEEEextractgroupremain#1{\def\@IEEEextractedgroup{#1}\expandafter\@@IEEEextractgroupremain\expandafter{\ifnum0=`}\fi} + +\def\@@IEEEextractgroupremain#1{\def\@IEEEextractedgroupremain{#1}} + + + +% usage: \@IEEEextracttoken*{} +% \@IEEEextracttoken fully expands its argument (which it then stores in +% \@IEEEextracttokenarg) via \edef and then the meaning of the first +% nonbrace (but including the empty group) token found is assigned via \let +% to \@IEEEextractedtoken as well as stored in the macro +% \@IEEEextractedtokenmacro. Tokens that would otherwise be discarded during +% the acquisition of the first are stored in \@IEEEextractedtokensdiscarded, +% however their original relative brace nesting depths are not guaranteed to +% be preserved. +% If the argument is empty, or if a first nonbrace token does not exist (or +% is an empty group), \@IEEEextractedtoken will be \relax and +% \@IEEEextractedtokenmacro and \@IEEEextractedtokensdiscarded will be empty. +% +% For example: +% \@IEEEextracttoken{{{ab}{cd}}{{ef}g}} +% results in: +% +% \@IEEEextracttokenarg ==> a macro containing {{ab}{cd}}{{ef}g} +% \@IEEEextractedtoken ==> the letter a +% \@IEEEextractedtokenmacro ==> a macro containing a +% \@IEEEextractedtokensdiscarded ==> a macro containing bcd{ef}g +% +% the *-star form, \@IEEEextracttoken*, does not expand its argument +% contents during processing. +\def\@IEEEextracttoken{\@ifstar{\let\@IEEEextracttokendef=\def\@@IEEEextracttoken}{\let\@IEEEextracttokendef=\edef\@@IEEEextracttoken}} + +\def\@@IEEEextracttoken#1{\@IEEEextracttokendef\@IEEEextracttokenarg{#1}\relax +\def\@IEEEextractedtokensdiscarded{}\relax % initialize to empty +% if the macro is unchanged after being acquired as a single undelimited argument +% with anything after it being stripped off as a delimited argument +% we know we have one token without any enclosing braces. loop until this is true. +\let\@IEEEextracttokencurgroup\@IEEEextracttokenarg +\loop + % trap case of an empty argument as this would cause a problem with + % \@@@IEEEextracttoken's first (nondelimited) argument acquisition + \ifx\@IEEEextracttokencurgroup\@empty + \def\@IEEEextractedtokenmacro{}\relax + \else + \expandafter\@@@IEEEextracttoken\@IEEEextracttokencurgroup\@IEEEgeneralsequenceDELIMITER\relax + \fi + \ifx\@IEEEextractedtokenmacro\@IEEEextracttokencurgroup + \else + \let\@IEEEextracttokencurgroup=\@IEEEextractedtokenmacro +\repeat +% we can safely do a \let= here because there should be at most one token +% the relax is needed to handle the case of no token found +\expandafter\let\expandafter\@IEEEextractedtoken\@IEEEextractedtokenmacro\relax} + +\def\@@@IEEEextracttoken#1#2\@IEEEgeneralsequenceDELIMITER{\def\@IEEEextractedtokenmacro{#1}\relax +\def\@@IEEEextractedtokensdiscarded{#2}\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter +\@IEEEextractedtokensdiscarded\expandafter\expandafter\expandafter +{\expandafter\@@IEEEextractedtokensdiscarded\@IEEEextractedtokensdiscarded}} + + + +% usage: \@IEEEextracttokengroups*{} +% \@IEEEextracttokengroups fully expands its argument (which it then stores +% in \@IEEEextracttokengroupsarg) and then assigns the first "brace group" of +% tokens (with the outermost braces removed) to the macro +% \@IEEEextractedfirstgroup. +% The meaning of the first nonbrace (but including the empty group) token +% within this first group is assigned via \let to \@IEEEextractedfirsttoken +% as well as stored in the macro \@IEEEextractedfirsttokenmacro. If a first +% nonbrace token does not exist (or is an empty group), these will be \relax +% and empty, respectively. Tokens that would otherwise be discarded during +% the acquisition of the first token in the first group are stored in +% \@IEEEextractedfirsttokensdiscarded, however their original relative brace +% nesting depths are not guaranteed to be preserved. +% The first group within this first group is stored in the macro +% \@IEEEextractedfirstfirstgroup. +% Likewise for the next group after the first: \@IEEEextractednextgroup, +% \@IEEEextractednextfirstgroup, \@IEEEextractednextgroupfirsttoken, +% \@IEEEextractednextgroupfirsttokenmacro, and +% \@IEEEextractednextfirsttokensdiscarded. +% All tokens/groups after the first group, including any enclosing braces, +% are stored in the macro \@IEEEextractedafterfirstgroupremain which will +% be empty if none exist. +% +% For example: +% \@IEEEextracttokengroups{{{ab}{cd}}{{ef}g}} +% will result in: +% +% \@IEEEextracttokengroupsarg ==> a macro containing {{ab}{cd}}{{ef}g} +% \@IEEEextractedfirstgroup ==> a macro containing {ab}{cd} +% \@IEEEextractedafterfirstgroupremain ==> a macro containing {{ef}g} +% \@IEEEextractedfirsttoken ==> the letter a +% \@IEEEextractedfirsttokenmacro ==> a macro containing a +% \@IEEEextractedfirsttokensdiscarded ==> a macro containing bcd +% \@IEEEextractedfirstfirstgroup ==> a macro containing ab +% \@IEEEextractednextgroup ==> a macro containing {ef}g +% \@IEEEextractednextfirsttoken ==> the letter e +% \@IEEEextractednextfirsttokenmacro ==> a macro containing e +% \@IEEEextractednextfirsttokensdiscarded ==> a macro containing fg +% \@IEEEextractednextfirstgroup ==> a macro containing ef +% +% If given an empty argument, \@IEEEextractedfirsttoken and +% \@IEEEextractednextfirsttoken will be set to \relax +% and all the macros will be empty. +% the *-star form, \@IEEEextracttokengroups*, does not expand its argument +% contents during processing. +% +% Depends on: \@IEEEextractgroup, \@IEEEextracttoken +\def\@IEEEextracttokengroups{\@ifstar{\let\@IEEEextracttokengroupsdef=\def\@@IEEEextracttokengroups}{\let\@IEEEextracttokengroupsdef=\edef\@@IEEEextracttokengroups}} +\def\@@IEEEextracttokengroups#1{\@IEEEextracttokengroupsdef\@IEEEextracttokengroupsarg{#1}\relax +% begin extraction, these functions are safe with empty arguments +% first group +\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextracttokengroupsarg}\relax +\let\@IEEEextractedfirstgroup\@IEEEextractedgroup +\let\@IEEEextractedafterfirstgroupremain\@IEEEextractedgroupremain +\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax +\let\@IEEEextractedfirsttoken\@IEEEextractedtoken +\let\@IEEEextractedfirsttokenmacro\@IEEEextractedtokenmacro +\let\@IEEEextractedfirsttokensdiscarded\@IEEEextractedtokensdiscarded +% first first group +\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax +\let\@IEEEextractedfirstfirstgroup\@IEEEextractedgroup +% next group +\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedafterfirstgroupremain}\relax +\let\@IEEEextractednextgroup\@IEEEextractedgroup +\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractednextgroup}\relax +\let\@IEEEextractednextfirsttoken\@IEEEextractedtoken +\let\@IEEEextractednextfirsttokenmacro\@IEEEextractedtokenmacro +\let\@IEEEextractednextfirsttokensdiscarded\@IEEEextractedtokensdiscarded +% next first group +\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractednextgroup}\relax +\let\@IEEEextractednextfirstgroup\@IEEEextractedgroup} + + +%% +%% -- End of Command Argument Scanning Support Functions -- + + + + +% -- page setup commands -- + +% The default sample text for calculating margins +\def\IEEEdefaultsampletext{\normalfont\normalsize gT} +\def\IEEEdefaultheadersampletext{\normalfont\normalsize T} +\def\IEEEdefaultfootersampletext{\normalfont\normalsize gT} + + + +% usage: \IEEEsettextwidth{inner margin}{outer margin} +% Sets \textwidth to allow the specified inner and outer margins +% for the current \paperwidth. +\def\IEEEsettextwidth#1#2{\@IEEEtrantmpdimenA\paperwidth +\@IEEEtrantmpdimenB#1\relax +\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB +\@IEEEtrantmpdimenB#2\relax +\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB +\textwidth\@IEEEtrantmpdimenA} + + + +% usage: \IEEEsetsidemargin{mode: i, o, c, a}{margin/offset} +% Sets \oddsidemargin and \evensidemargin to yield the specified margin +% of the given mode. +% The available modes are: +% i = inner margin +% o = outer margin +% c = centered, with the given offset +% a = adjust the margins using the given offset +% For the offsets, positive values increase the inner margin. +% \textwidth should be set properly for the given margins before calling this +% function. +\def\IEEEsetsidemargin#1#2{\@IEEEtrantmpdimenA #2\relax +\@IEEEextracttoken{#1}\relax +% check for mode errors +\ifx\@IEEEextractedtokenmacro\@empty + \@IEEEclspkgerror{Empty mode type in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `i'}{Valid modes for \string\IEEEsetsidemargin\space are: i, o, c and a.}\relax + \let\@IEEEextractedtoken=i\relax + \def\@IEEEextractedtokenmacro{i}\relax +\else + \ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: \string\IEEEsetsidemargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax + \fi +\fi +% handle each mode +\if\@IEEEextractedtoken a\relax + \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax +\else +\if\@IEEEextractedtoken c\relax + \oddsidemargin\paperwidth + \advance\oddsidemargin by -\textwidth + \divide\oddsidemargin by 2\relax + \advance\oddsidemargin by -1in\relax + \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax +\else +\if\@IEEEextractedtoken o\relax + \oddsidemargin\paperwidth + \advance\oddsidemargin by -\textwidth + \advance\oddsidemargin by -\@IEEEtrantmpdimenA + \advance\oddsidemargin by -1in\relax +\else + \if\@IEEEextractedtoken i\relax + \else + \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `i'}% + {Valid modes for \string\IEEEsetsidemargin\space are: i, o, c and a.}% + \fi + \oddsidemargin\@IEEEtrantmpdimenA + \advance\oddsidemargin by -1in\relax +\fi\fi\fi +% odd and even side margins both mean "inner" for single sided pages +\evensidemargin\oddsidemargin +% but are mirrors of each other when twosided is in effect +\if@twoside + \evensidemargin\paperwidth + \advance\evensidemargin by -\textwidth + \advance\evensidemargin by -\oddsidemargin + % have to compensate for both the builtin 1in LaTex offset + % and the fact we already subtracted this offset from \oddsidemargin + \advance\evensidemargin -2in\relax +\fi} + + + +% usage: \IEEEsettextheight[sample text]{top text margin}{bottom text margin} +% Sets \textheight based on the specified top margin and bottom margin. +% Takes into consideration \paperheight, \topskip, and (by default) the +% the actual height and depth of the \IEEEdefaultsampletext text. +\def\IEEEsettextheight{\@ifnextchar [{\@IEEEsettextheight}{\@IEEEsettextheight[\IEEEdefaultsampletext]}} +\def\@IEEEsettextheight[#1]#2#3{\textheight\paperheight\relax + \@IEEEtrantmpdimenA #2\relax + \advance \textheight by -\@IEEEtrantmpdimenA% subtract top margin + \@IEEEtrantmpdimenA #3\relax + \advance \textheight by -\@IEEEtrantmpdimenA% subtract bottom margin + \advance \textheight by \topskip% add \topskip + % subtract off everything above the top, and below the bottom, baselines + \settoheight{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance \textheight by -\@IEEEtrantmpdimenA + \settodepth{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance \textheight by -\@IEEEtrantmpdimenA} + + + +\newdimen\IEEEquantizedlength +\IEEEquantizedlength 0sp\relax +\newdimen\IEEEquantizedlengthdiff +\IEEEquantizedlengthdiff 0sp\relax +\def\IEEEquantizedlengthint{0} + +% usage: \IEEEquantizelength{mode: d, c, i}{base unit}{length} +% Sets the length \IEEEquantizedlength to be an integer multiple of the given +% (nonzero) base unit such that \IEEEquantizedlength approximates the given +% length. +% \IEEEquantizedlengthdiff is a length equal to the difference between the +% \IEEEquantizedlength and the given length. +% \IEEEquantizedlengthint is a macro containing the integer number of base units +% in \IEEEquantizedlength. +% i.e., \IEEEquantizedlength = \IEEEquantizedlengthint * base unit +% The mode determines how \IEEEquantizedlength is quantized: +% d = always decrease (always round down \IEEEquantizeint) +% c = use the closest match +% i = always increase (always round up \IEEEquantizeint) +% In anycase, if the given length is already quantized, +% \IEEEquantizedlengthdiff will be set to zero. +\def\IEEEquantizelength#1#2#3{\begingroup +% work in isolation so as not to externally disturb the \@IEEEtrantmp +% variables +% load the argument values indirectly via \IEEEquantizedlengthdiff +% in case the user refers to our \@IEEEtrantmpdimenX, \IEEEquantizedlength, +% etc. in the arguments. we also will work with these as counters, +% i.e., in sp units +% A has the base unit +\IEEEquantizedlengthdiff #2\relax\relax\relax\relax +\@IEEEtrantmpcountA\IEEEquantizedlengthdiff +% B has the input length +\IEEEquantizedlengthdiff #3\relax\relax\relax\relax +\@IEEEtrantmpcountB\IEEEquantizedlengthdiff +\@IEEEtrantmpdimenA\the\@IEEEtrantmpcountA sp\relax +\@IEEEtrantmpdimenB\the\@IEEEtrantmpcountB sp\relax +% \@IEEEtrantmpcountC will have the quantized int +% \IEEEquantizedlength will have the quantized length +% \@IEEEtrantmpdimenC will have the quantized diff +% initialize them to zero as this is what will be +% exported if an error occurs +\@IEEEtrantmpcountC 0\relax +\IEEEquantizedlength 0sp\relax +\@IEEEtrantmpdimenC 0sp\relax +% extract mode +\@IEEEextracttoken{#1}\relax +% check for mode errors +\ifx\@IEEEextractedtokenmacro\@empty + \@IEEEclspkgerror{Empty mode type in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak + Defaulting to `d'}{Valid modes for \string\IEEEquantizelength\space are: d, c and i.}\relax + \let\@IEEEextractedtoken=d\relax + \def\@IEEEextractedtokenmacro{d}\relax +\else + \ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: \string\IEEEquantizelength\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax + \fi +\fi +% check for base unit is zero error +\ifnum\@IEEEtrantmpcountA=0\relax +\@IEEEclspkgerror{Base unit is zero in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak + \string\IEEEquantizedlength\space and \string\IEEEquantizedlengthdiff\space are set to zero}{Division by zero is not allowed.}\relax +\else% base unit is nonzero + % \@IEEEtrantmpcountC carries the number of integer units + % in the quantized length (integer length \ base) + \@IEEEtrantmpcountC\@IEEEtrantmpcountB\relax + \divide\@IEEEtrantmpcountC by \@IEEEtrantmpcountA\relax + % \IEEEquantizedlength has the (rounded down) quantized length + % = base * int + \IEEEquantizedlength\@IEEEtrantmpdimenA\relax + \multiply\IEEEquantizedlength by \@IEEEtrantmpcountC\relax + % \@IEEEtrantmpdimenC has the difference + % = quantized length - length + \@IEEEtrantmpdimenC\IEEEquantizedlength\relax + \advance\@IEEEtrantmpdimenC by -\@IEEEtrantmpdimenB\relax + % trap special case of length being already quantized + % to avoid a roundup under i option + \ifdim\@IEEEtrantmpdimenC=0sp\relax + \else % length not is already quantized + % set dimenA to carry the upper quantized (absolute value) difference: + % quantizedlength + base - length + \advance\@IEEEtrantmpdimenA by \IEEEquantizedlength\relax + \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB\relax + % set dimenB to carry the lower quantized (absolute value) difference: + % length - quantizedlength + \advance\@IEEEtrantmpdimenB by -\IEEEquantizedlength\relax + % handle each mode + \if\@IEEEextractedtoken c\relax + % compare upper and lower amounts, select upper if lower > upper + \ifdim\@IEEEtrantmpdimenB>\@IEEEtrantmpdimenA\relax + % use upper + \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax + \advance\@IEEEtrantmpcountC by 1\relax + \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA + \else% <=. uselower + % no need to do anything for lower, use output values already setup + \fi + \else% not mode c + \if\@IEEEextractedtoken i\relax + % always round up under i mode + \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax + \advance\@IEEEtrantmpcountC by 1\relax + \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA + \else + \if\@IEEEextractedtoken d\relax + \else + \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak + Defaulting to `d'}% + {Valid modes for \string\IEEEquantizelength\space are: d, c, and i.}\relax + \fi % if d + % no need to do anything for d, use output values already setup + \fi\fi % if i, c + \fi % if length is already quantized +\fi% if base unit is zero +% globally assign the results to macros we use here to escape the enclosing +% group without needing to call \global on any of the \@IEEEtrantmp variables. +% \@IEEEtrantmpcountC has the quantized int +% \IEEEquantizedlength has the quantized length +% \@IEEEtrantmpdimenC has the quantized diff +\xdef\@IEEEquantizedlengthintmacro{\the\@IEEEtrantmpcountC}\relax +\@IEEEtrantmpcountC\IEEEquantizedlength\relax +\xdef\@IEEEquantizedlengthmacro{\the\@IEEEtrantmpcountC}\relax +\@IEEEtrantmpcountC\@IEEEtrantmpdimenC\relax +\xdef\@IEEEquantizedlengthdiffmacro{\the\@IEEEtrantmpcountC}\relax +\endgroup +% locally assign the outputs here from the macros +\expandafter\IEEEquantizedlength\@IEEEquantizedlengthmacro sp\relax +\expandafter\IEEEquantizedlengthdiff\@IEEEquantizedlengthdiffmacro sp\relax +\edef\IEEEquantizedlengthint{\@IEEEquantizedlengthintmacro}\relax} + + + +\newdimen\IEEEquantizedtextheightdiff +\IEEEquantizedtextheightdiff 0sp\relax + +% usage: \IEEEquantizetextheight[base unit]{mode: d, c, i} +% Sets \textheight to be an integer multiple of the current \baselineskip +% (or the optionally specified base unit) plus the first (\topskip) line. +% \IEEEquantizedtextheightdiff is a length equal to the difference between +% the new quantized and original \textheight. +% \IEEEquantizedtextheightlpc is a macro containing the integer number of +% lines per column under the quantized \textheight. i.e., +% \textheight = \IEEEquantizedtextheightlpc * \baselineskip + \topskip +% The mode determines how \textheight is quantized: +% d = always decrease (always round down the number of lines per column) +% c = use the closest match +% i = always increase (always round up the number of lines per column) +% In anycase, if \textheight is already quantized, it will remain unchanged, +% and \IEEEquantizedtextheightdiff will be set to zero. +% Depends on: \IEEEquantizelength +\def\IEEEquantizetextheight{\@ifnextchar [{\@IEEEquantizetextheight}{\@IEEEquantizetextheight[\baselineskip]}} +\def\@IEEEquantizetextheight[#1]#2{\begingroup +% use our \IEEEquantizedtextheightdiff as a scratch pad +% we need to subtract off \topskip before quantization +\IEEEquantizedtextheightdiff\textheight +\advance\IEEEquantizedtextheightdiff by -\topskip\relax +\IEEEquantizelength{#2}{#1}{\IEEEquantizedtextheightdiff} +% add back \topskip line +\advance\IEEEquantizedlength by \topskip +\@IEEEtrantmpcountC\IEEEquantizedlengthint\relax +\advance\@IEEEtrantmpcountC by 1\relax +% globally assign the results to macros we use here to escape the enclosing +% group without needing to call \global on any of the \@IEEEtrantmp variables. +\xdef\@IEEEquantizedtextheightlpcmacro{\the\@IEEEtrantmpcountC}\relax +\@IEEEtrantmpcountC\IEEEquantizedlength\relax +\xdef\@IEEEquantizedtextheightmacro{\the\@IEEEtrantmpcountC}\relax +\@IEEEtrantmpcountC\IEEEquantizedlengthdiff\relax +\xdef\@IEEEquantizedtextheightdiffmacro{\the\@IEEEtrantmpcountC}\relax +\endgroup +% locally assign the outputs here from the macros +\textheight\@IEEEquantizedtextheightmacro sp\relax +\IEEEquantizedtextheightdiff\@IEEEquantizedtextheightdiffmacro sp\relax +\edef\IEEEquantizedtextheightlpc{\@IEEEquantizedtextheightlpcmacro}} + + + +% usage: \IEEEsettopmargin[sample text]{mode: t, b, c, a, q}{margin/offset} +% Sets \topmargin based on the specified vertical margin. +% Takes into consideration the base 1in offset, \headheight, \headsep, +% \topskip, and (by default) the the actual height (or, for the bottom, depth) +% of the \IEEEdefaultsampletext text. +% The available modes are: +% t = top margin +% b = bottom margin +% c = vertically centered, with the given offset +% a = adjust the vertical margins using the given offset +% q = adjust the margins using \IEEEquantizedtextheightdiff and the given offset +% For the offsets, positive values increase the top margin. +% \headheight, \headsep, \topskip and \textheight should be set properly for the +% given margins before calling this function. +\def\IEEEsettopmargin{\@ifnextchar [{\@IEEEsettopmargin}{\@IEEEsettopmargin[\IEEEdefaultsampletext]}} +\def\@IEEEsettopmargin[#1]#2#3{\@IEEEtrantmpdimenA #3\relax +\@IEEEextracttoken{#2}\relax +% check for mode errors +\ifx\@IEEEextractedtokenmacro\@empty + \@IEEEclspkgerror{Empty mode type in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `t'}{Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax + \let\@IEEEextractedtoken=t\relax + \def\@IEEEextractedtokenmacro{t}\relax +\else + \ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: \string\IEEEsettopmargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax + \fi +\fi +% handle each mode +\if\@IEEEextractedtoken a\relax + \advance\topmargin by \@IEEEtrantmpdimenA\relax +\else +\if\@IEEEextractedtoken q\relax + % we need to adjust by half the \IEEEquantizedtextheightdiff value + \@IEEEtrantmpdimenB\IEEEquantizedtextheightdiff\relax + \divide\@IEEEtrantmpdimenB by 2\relax + % a positive \IEEEquantizedtextheightdiff means we need to reduce \topmargin + % because \textheight has been lenghtened + \advance\topmargin by -\@IEEEtrantmpdimenB\relax + \advance\topmargin by \@IEEEtrantmpdimenA\relax +\else +\if\@IEEEextractedtoken c\relax + \topmargin\paperheight + \advance\topmargin by -\textheight + % \textheight includes \topskip, but we should not count topskip whitespace here, backout + \advance \topmargin by \topskip + \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\topmargin by -\@IEEEtrantmpdimenB\relax + \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\topmargin by -\@IEEEtrantmpdimenB\relax + \divide\topmargin by 2\relax + \advance\topmargin by \@IEEEtrantmpdimenA\relax +\else +\if\@IEEEextractedtoken b\relax + \topmargin\paperheight + \advance\topmargin by -\textheight + % \textheight includes \topskip, but we should not count topskip whitespace here, backout + \advance \topmargin by \topskip + \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\topmargin by -\@IEEEtrantmpdimenB\relax + \advance\topmargin by -\@IEEEtrantmpdimenA\relax +\else + \if\@IEEEextractedtoken t\relax + \else + \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `t'}% + {Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax + \fi + \topmargin\@IEEEtrantmpdimenA\relax + \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\topmargin by \@IEEEtrantmpdimenB\relax +\fi\fi % if t, b, c +% convert desired top margin into actual \topmargin +% this is not done for the q or a modes because they are only adjustments +\advance \topmargin by -\topskip +\advance \topmargin by -1in +\advance \topmargin by -\headheight +\advance \topmargin by -\headsep +\fi\fi % if q, a +} + + + +% usage: \IEEEsetheadermargin[header sample][text sample]{mode: t, b, c, a}{margin/offset} +% Differentially adjusts \topmargin and \headsep (such that their sum is unchanged) +% based on the specified header margin. +% Takes into consideration the base 1in offset, \headheight, \topskip, and (by default) +% the actual height (or depth) of the \IEEEdefaultheadersampletext and +% \IEEEdefaultsampletext text. +% The available modes are: +% t = top margin (top of the header text to the top of the page) +% b = bottom margin (bottom of the header text to the top of the main text) +% c = vertically centered between the main text and the top of the page, +% with the given offset +% a = adjust the vertical position using the given offset +% For the offsets, positive values move the header downward. +% \headheight, \headsep, \topskip and \topmargin should be set properly before +% calling this function. +\def\IEEEsetheadermargin{\@ifnextchar [{\@IEEEsetheadermargin}{\@IEEEsetheadermargin[\IEEEdefaultheadersampletext]}} +\def\@IEEEsetheadermargin[#1]{\@ifnextchar [{\@@IEEEsetheadermargin[#1]}{\@@IEEEsetheadermargin[#1][\IEEEdefaultsampletext]}} +\def\@@IEEEsetheadermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax +\@IEEEextracttoken{#3}\relax +% check for mode errors +\ifx\@IEEEextractedtokenmacro\@empty + \@IEEEclspkgerror{Empty mode type in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `t'}{Valid modes for \string\IEEEsetheadermargin\space are: t, b, c, and a.}\relax + \let\@IEEEextractedtoken=t\relax + \def\@IEEEextractedtokenmacro{t}\relax +\else + \ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: \string\IEEEsetheadermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax + \fi +\fi +% handle each mode +\if\@IEEEextractedtoken a\relax + % No need to do anything here and can pass through the adjustment + % value as is. The end adjustment of \topmargin and \headsep will + % do all that is needed +\else +\if\@IEEEextractedtoken c\relax + % get the bottom margin + \@IEEEtrantmpdimenB\headsep\relax + \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + \advance\@IEEEtrantmpdimenB by \topskip + \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the actual header bottom margin + % subtract from it the top header margin + \advance\@IEEEtrantmpdimenB -1in\relax % take into consideration the system 1in offset of the top margin + \advance\@IEEEtrantmpdimenB by -\topmargin + \advance\@IEEEtrantmpdimenB by -\headheight + \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the difference between the bottom and top margins + % we need to adjust by half this amount to center the header + \divide\@IEEEtrantmpdimenB by 2\relax + % and add to offset + \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB +\else +\if\@IEEEextractedtoken b\relax + \@IEEEtrantmpdimenB\headsep\relax + \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + \advance\@IEEEtrantmpdimenB by \topskip + \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the actual header bottom margin + % get the difference between the actual and the desired + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA + \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB +\else + \if\@IEEEextractedtoken t\relax + \else + \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `t'}% + {Valid modes for \string\IEEEsetheadermargin\space are: t, b, c and a.}\relax + \fi + \@IEEEtrantmpdimenB 1in\relax % take into consideration the system 1in offset of the top margin + \advance\@IEEEtrantmpdimenB by \topmargin + \advance\@IEEEtrantmpdimenB by \headheight + \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the actual header top margin + % get the difference between the desired and the actual + \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB +\fi\fi % if t, b, c +\fi % if a +% advance \topmargin by the needed amount and reduce \headsep by the same +% so as not to disturb the location of the main text +\advance\topmargin by \@IEEEtrantmpdimenA\relax +\advance\headsep by -\@IEEEtrantmpdimenA\relax +} + + + +% usage: \IEEEsetfootermargin[footer sample][text sample]{mode: t, b, c, a}{margin/offset} +% Adjusts \footskip based on the specified footer margin. +% Takes into consideration the base 1in offset, \paperheight, \headheight, +% \headsep, \textheight and (by default) the actual height (or depth) of the +% \IEEEdefaultfootersampletext and \IEEEdefaultsampletext text. +% The available modes are: +% t = top margin (top of the footer text to the bottom of the main text) +% b = bottom margin (bottom of the footer text to the bottom of page) +% c = vertically centered between the main text and the bottom of the page, +% with the given offset +% a = adjust the vertical position using the given offset +% For the offsets, positive values move the footer downward. +% \headheight, \headsep, \topskip, \topmargin, and \textheight should be set +% properly before calling this function. +\def\IEEEsetfootermargin{\@ifnextchar [{\@IEEEsetfootermargin}{\@IEEEsetfootermargin[\IEEEdefaultfootersampletext]}} +\def\@IEEEsetfootermargin[#1]{\@ifnextchar [{\@@IEEEsetfootermargin[#1]}{\@@IEEEsetfootermargin[#1][\IEEEdefaultsampletext]}} +\def\@@IEEEsetfootermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax +\@IEEEextracttoken{#3}\relax +% check for mode errors +\ifx\@IEEEextractedtokenmacro\@empty + \@IEEEclspkgerror{Empty mode type in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `t'}{Valid modes for \string\IEEEsetfootermargin\space are: t, b, c, and a.}\relax + \let\@IEEEextractedtoken=t\relax + \def\@IEEEextractedtokenmacro{t}\relax +\else + \ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: \string\IEEEsetfootermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax + \fi +\fi +% handle each mode +\if\@IEEEextractedtoken a\relax + % No need to do anything here and can pass through the adjustment + % value as is. The end adjustment of \footskip will do all that + % is needed +\else +\if\@IEEEextractedtoken c\relax + % calculate the bottom margin + \@IEEEtrantmpdimenB 1in\relax % system 1in offset + \advance\@IEEEtrantmpdimenB\topmargin\relax + \advance\@IEEEtrantmpdimenB\headheight\relax + \advance\@IEEEtrantmpdimenB\headsep\relax + \advance\@IEEEtrantmpdimenB\textheight\relax + \advance\@IEEEtrantmpdimenB\footskip\relax + \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB + \@IEEEtrantmpdimenB\paperheight + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin + % now subtract off the footer top margin + \advance\@IEEEtrantmpdimenB -\footskip\relax + \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC + \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the difference between the bottom + % and top footer margins + % our adjustment must be half this value to center the footer + \divide\@IEEEtrantmpdimenB by 2\relax + % add to the offset + \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB +\else +\if\@IEEEextractedtoken b\relax + % calculate the bottom margin + \@IEEEtrantmpdimenB 1in\relax % system 1in offset + \advance\@IEEEtrantmpdimenB\topmargin\relax + \advance\@IEEEtrantmpdimenB\headheight\relax + \advance\@IEEEtrantmpdimenB\headsep\relax + \advance\@IEEEtrantmpdimenB\textheight\relax + \advance\@IEEEtrantmpdimenB\footskip\relax + \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB + \@IEEEtrantmpdimenB\paperheight + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin + % get the difference between the actual and the desired + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA + \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB +\else + \if\@IEEEextractedtoken t\relax + \else + \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak + Defaulting to `t'}% + {Valid modes for \string\IEEEsetfootermargin\space are: t, b, c and a.}\relax + \fi + \@IEEEtrantmpdimenB\footskip\relax + \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax + \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC + % at this point \@IEEEtrantmpdimenB has the actual footer top margin + % get the difference between the desired and the actual + \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB +\fi\fi % if t, b, c +\fi % if a +% advance \footskip by the needed amount +\advance\footskip by \@IEEEtrantmpdimenA\relax +} + + +% -- End page setup commands -- + + + + +% Itemize, Enumerate and Description (IED) List Controls +% *************************** +% +% +% The IEEE seems to use at least two different values by +% which ITEMIZED list labels are indented to the right +% For The Journal of Lightwave Technology (JLT) and The Journal +% on Selected Areas in Communications (JSAC), they tend to use +% an indention equal to \parindent. For Transactions on Communications +% they tend to indent ITEMIZED lists a little more--- 1.3\parindent. +% We'll provide both values here for you so that you can choose +% which one you like in your document using a command such as: +% setlength{\IEEEilabelindent}{\IEEEilabelindentB} +\newdimen\IEEEilabelindentA +\IEEEilabelindentA \parindent + +\newdimen\IEEEilabelindentB +\IEEEilabelindentB 1.3\parindent +% However, we'll default to using \parindent +% which makes more sense to me +\newdimen\IEEEilabelindent +\IEEEilabelindent \IEEEilabelindentA + + +% This controls the default amount the enumerated list labels +% are indented to the right. +% Normally, this is the same as the paragraph indention +\newdimen\IEEEelabelindent +\IEEEelabelindent \parindent + +% This controls the default amount the description list labels +% are indented to the right. +% Normally, this is the same as the paragraph indention +\newdimen\IEEEdlabelindent +\IEEEdlabelindent \parindent + +% This is the value actually used within the IED lists. +% The IED environments automatically set its value to +% one of the three values above, so global changes do +% not have any effect +\newdimen\IEEElabelindent +\IEEElabelindent \parindent + +% The actual amount labels will be indented is +% \IEEElabelindent multiplied by the factor below +% corresponding to the level of nesting depth +% This provides a means by which the user can +% alter the effective \IEEElabelindent for deeper +% levels +% There may not be such a thing as correct "standard IEEE" +% values. What the IEEE actually does may depend on the specific +% circumstances. +% The first list level almost always has full indention. +% The second levels I've seen have only 75% of the normal indentation +% Three level or greater nestings are very rare. I am guessing +% that they don't use any indentation. +\def\IEEElabelindentfactori{1.0} % almost always one +\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases +\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0? +\def\IEEElabelindentfactoriv{0.0} +\def\IEEElabelindentfactorv{0.0} +\def\IEEElabelindentfactorvi{0.0} + +% value actually used within IED lists, it is auto +% set to one of the 6 values above +% global changes here have no effect +\def\IEEElabelindentfactor{1.0} + +% This controls the default spacing between the end of the IED +% list labels and the list text, when normal text is used for +% the labels. +\newdimen\IEEEiednormlabelsep +\IEEEiednormlabelsep 0.6em + +% This controls the default spacing between the end of the IED +% list labels and the list text, when math symbols are used for +% the labels (nomenclature lists). The IEEE usually increases the +% spacing in these cases +\newdimen\IEEEiedmathlabelsep +\IEEEiedmathlabelsep 1.2em + +% This controls the extra vertical separation put above and +% below each IED list. The IEEE usually puts a little extra spacing +% around each list. However, this spacing is barely noticeable. +\newskip\IEEEiedtopsep +\IEEEiedtopsep 2pt plus 1pt minus 1pt + + +% This command is executed within each IED list environment +% at the beginning of the list. You can use this to set the +% parameters for some/all your IED list(s) without disturbing +% global parameters that affect things other than lists. +% i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}} +% will alter the \labelsep for the next list(s) until +% \IEEEiedlistdecl is redefined. +\def\IEEEiedlistdecl{\relax} + +% This command provides an easy way to set \leftmargin based +% on the \labelwidth, \labelsep and the argument \IEEElabelindent +% Usage: \IEEEcalcleftmargin{width-to-indent-the-label} +% output is in the \leftmargin variable, i.e., effectively: +% \leftmargin = argument + \labelwidth + \labelsep +% Note controlled spacing here, shield end of lines with % +\def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}% +\addtolength{\leftmargin}{\labelwidth}% +\addtolength{\leftmargin}{\labelsep}} + +% This command provides an easy way to set \labelwidth to the +% width of the given text. It is the same as +% \settowidth{\labelwidth}{label-text} +% and useful as a shorter alternative. +% Typically used to set \labelwidth to be the width +% of the longest label in the list +\def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}} + +% When this command is executed, IED lists will use the +% IEEEiedmathlabelsep label separation rather than the normal +% spacing. To have an effect, this command must be executed via +% the \IEEEiedlistdecl or within the option of the IED list +% environments. +\def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}} + +% A flag which controls whether the IED lists automatically +% calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep +% Useful if you want to specify your own \leftmargin +% This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse) +% via the \IEEEiedlistdecl or within the option of the IED list +% environments to have an effect. +\newif\ifIEEEnocalcleftmargin +\IEEEnocalcleftmarginfalse + +% A flag which controls whether \IEEElabelindent is multiplied by +% the \IEEElabelindentfactor for each list level. +% This flag must be set via the \IEEEiedlistdecl or within the option +% of the IED list environments to have an effect. +\newif\ifIEEEnolabelindentfactor +\IEEEnolabelindentfactorfalse + + +% internal variable to indicate type of IED label +% justification +% 0 - left; 1 - center; 2 - right +\def\@IEEEiedjustify{0} + + + +% commands to allow the user to control IED +% label justifications. Use these commands within +% the IED environment option or in the \IEEEiedlistdecl +% Note that changing the normal list justifications +% is nonstandard and the IEEE may not like it if you do so! +% I include these commands as they may be helpful to +% those who are using these enhanced list controls for +% other non-IEEE related LaTeX work. +% itemize and enumerate automatically default to right +% justification, description defaults to left. +\def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left +\def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center +\def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right + + + + +% commands to save to and restore from the list parameter copies +% this allows us to set all the list parameters within +% the list_decl and prevent \list (and its \@list) +% from overriding any of our parameters +% V1.6 use \edefs instead of dimen's to conserve dimen registers +% Note controlled spacing here, shield end of lines with % +\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}% +\edef\@IEEEiedlabelwidth{\the\labelwidth}% +\edef\@IEEEiedlabelsep{\the\labelsep}% +\edef\@IEEEiedleftmargin{\the\leftmargin}% +\edef\@IEEEiedpartopsep{\the\partopsep}% +\edef\@IEEEiedparsep{\the\parsep}% +\edef\@IEEEieditemsep{\the\itemsep}% +\edef\@IEEEiedrightmargin{\the\rightmargin}% +\edef\@IEEEiedlistparindent{\the\listparindent}% +\edef\@IEEEieditemindent{\the\itemindent}} + +% Note controlled spacing here +\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax% +\labelwidth\@IEEEiedlabelwidth\relax% +\labelsep\@IEEEiedlabelsep\relax% +\leftmargin\@IEEEiedleftmargin\relax% +\partopsep\@IEEEiedpartopsep\relax% +\parsep\@IEEEiedparsep\relax% +\itemsep\@IEEEieditemsep\relax% +\rightmargin\@IEEEiedrightmargin\relax% +\listparindent\@IEEEiedlistparindent\relax% +\itemindent\@IEEEieditemindent\relax} + + +% v1.6b provide original LaTeX IED list environments +% note that latex.ltx defines \itemize and \enumerate, but not \description +% which must be created by the base classes +% save original LaTeX itemize and enumerate +\let\LaTeXitemize\itemize +\let\endLaTeXitemize\enditemize +\let\LaTeXenumerate\enumerate +\let\endLaTeXenumerate\endenumerate +% base class should define \description +\let\LaTeXdescription\description +\let\endLaTeXdescription\enddescription + + +% override LaTeX's default IED lists, if the user requested it +\if@IEEETOOLSredeflists +\def\itemize{\@IEEEitemize} +\def\enditemize{\@endIEEEitemize} +\def\enumerate{\@IEEEenumerate} +\def\endenumerate{\@endIEEEenumerate} +\def\description{\@IEEEdescription} +\def\enddescription{\@endIEEEdescription} +\fi + + +% provide the user with the IEEE IED commands +\def\IEEEitemize{\@IEEEitemize} +\def\endIEEEitemize{\@endIEEEitemize} +\def\IEEEenumerate{\@IEEEenumerate} +\def\endIEEEenumerate{\@endIEEEenumerate} +\def\IEEEdescription{\@IEEEdescription} +\def\endIEEEdescription{\@endIEEEdescription} + + +% V1.6 we want to keep the IEEEtran IED list definitions as our own internal +% commands so they are protected against redefinition +\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}} +\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}} +\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}} +\def\@endIEEEitemize{\endlist} +\def\@endIEEEenumerate{\endlist} +\def\@endIEEEdescription{\endlist} + + +% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS +% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS +% IEEEtran itemized list MDS 1/2001 +% Note controlled spacing here, shield end of lines with % +\def\@@IEEEitemize[#1]{% + \ifnum\@itemdepth>3\relax\@toodeep\else% + \ifnum\@listdepth>5\relax\@toodeep\else% + \advance\@itemdepth\@ne% + \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% + % get the IEEElabelindentfactor for this level + \advance\@listdepth\@ne% we need to know what the level WILL be + \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% + \advance\@listdepth-\@ne% undo our increment + \def\@IEEEiedjustify{2}% right justified labels are default + % set other defaults + \IEEEnocalcleftmarginfalse% + \IEEEnolabelindentfactorfalse% + \topsep\IEEEiedtopsep% + \IEEElabelindent\IEEEilabelindent% + \labelsep\IEEEiednormlabelsep% + \partopsep 0ex% + \parsep 0ex% + \itemsep 0ex% + \rightmargin 0em% + \listparindent 0em% + \itemindent 0em% + % calculate the label width + % the user can override this later if + % they specified a \labelwidth + \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}% + \@IEEEsavelistparams% save our list parameters + \list{\csname\@itemitem\endcsname}{% + \@IEEErestorelistparams% override any list{} changes + % to our globals + \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel + \IEEEiedlistdecl% let user alter parameters + #1\relax% + % If the user has requested not to use the + % IEEElabelindent factor, don't revise \IEEElabelindent + \ifIEEEnolabelindentfactor\relax% + \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% + \fi% + % Unless the user has requested otherwise, + % calculate our left margin based + % on \IEEElabelindent, \labelwidth and + % \labelsep + \ifIEEEnocalcleftmargin\relax% + \else\IEEEcalcleftmargin{\IEEElabelindent}% + \fi}\fi\fi}% + + +% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS +% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS +% IEEEtran enumerate list MDS 1/2001 +% Note controlled spacing here, shield end of lines with % +\def\@@IEEEenumerate[#1]{% + \ifnum\@enumdepth>3\relax\@toodeep\else% + \ifnum\@listdepth>5\relax\@toodeep\else% + \advance\@enumdepth\@ne% + \edef\@enumctr{enum\romannumeral\the\@enumdepth}% + % get the IEEElabelindentfactor for this level + \advance\@listdepth\@ne% we need to know what the level WILL be + \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% + \advance\@listdepth-\@ne% undo our increment + \def\@IEEEiedjustify{2}% right justified labels are default + % set other defaults + \IEEEnocalcleftmarginfalse% + \IEEEnolabelindentfactorfalse% + \topsep\IEEEiedtopsep% + \IEEElabelindent\IEEEelabelindent% + \labelsep\IEEEiednormlabelsep% + \partopsep 0ex% + \parsep 0ex% + \itemsep 0ex% + \rightmargin 0em% + \listparindent 0em% + \itemindent 0em% + % calculate the label width + % We'll set it to the width suitable for all labels using + % normalfont 1) to 9) + % The user can override this later + \settowidth{\labelwidth}{9)}% + \@IEEEsavelistparams% save our list parameters + \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}% + \@IEEErestorelistparams% override any list{} changes + % to our globals + \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel + \IEEEiedlistdecl% let user alter parameters + #1\relax% + % If the user has requested not to use the + % IEEElabelindent factor, don't revise \IEEElabelindent + \ifIEEEnolabelindentfactor\relax% + \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% + \fi% + % Unless the user has requested otherwise, + % calculate our left margin based + % on \IEEElabelindent, \labelwidth and + % \labelsep + \ifIEEEnocalcleftmargin\relax% + \else\IEEEcalcleftmargin{\IEEElabelindent}% + \fi}\fi\fi}% + + +% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS +% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS +% IEEEtran description list MDS 1/2001 +% Note controlled spacing here, shield end of lines with % +\def\@@IEEEdescription[#1]{% + \ifnum\@listdepth>5\relax\@toodeep\else% + % get the IEEElabelindentfactor for this level + \advance\@listdepth\@ne% we need to know what the level WILL be + \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% + \advance\@listdepth-\@ne% undo our increment + \def\@IEEEiedjustify{0}% left justified labels are default + % set other defaults + \IEEEnocalcleftmarginfalse% + \IEEEnolabelindentfactorfalse% + \topsep\IEEEiedtopsep% + \IEEElabelindent\IEEEdlabelindent% + % assume normal labelsep + \labelsep\IEEEiednormlabelsep% + \partopsep 0ex% + \parsep 0ex% + \itemsep 0ex% + \rightmargin 0em% + \listparindent 0em% + \itemindent 0em% + % Bogus label width in case the user forgets + % to set it. + % TIP: If you want to see what a variable's width is you + % can use the TeX command \showthe\width-variable to + % display it on the screen during compilation + % (This might be helpful to know when you need to find out + % which label is the widest) + \settowidth{\labelwidth}{Hello}% + \@IEEEsavelistparams% save our list parameters + \list{}{\@IEEErestorelistparams% override any list{} changes + % to our globals + \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel + \IEEEiedlistdecl% let user alter parameters + #1\relax% + % If the user has requested not to use the + % labelindent factor, don't revise \IEEElabelindent + \ifIEEEnolabelindentfactor\relax% + \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% + \fi% + % Unless the user has requested otherwise, + % calculate our left margin based + % on \IEEElabelindent, \labelwidth and + % \labelsep + \ifIEEEnocalcleftmargin\relax% + \else\IEEEcalcleftmargin{\IEEElabelindent}\relax% + \fi}\fi} + +% v1.6b we use one makelabel that does justification as needed. +\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax +\makebox[\labelwidth][l]{\normalfont #1}\else +\if\@IEEEiedjustify 1\relax +\makebox[\labelwidth][c]{\normalfont #1}\else +\makebox[\labelwidth][r]{\normalfont #1}\fi\fi} + + + + + + + + + +% used only by IEEEtran's IEEEeqnarray as other packages may +% have their own, different, implementations +\newcounter{IEEEsubequation}[equation] + +% e.g., "1a" (used only by IEEEtran's IEEEeqnarray) +\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}} +% just like LaTeX2e's \@eqnnum +\def\theequationdis{(\theequation)}% (1) +% IEEEsubequation used only by IEEEtran's IEEEeqnarray +\def\theIEEEsubequationdis{(\theIEEEsubequation)}% (1a) + + + + +%% +%% START OF IEEEeqnarray DEFINITIONS +%% +%% Inspired by the concepts, examples, and previous works of LaTeX +%% coders and developers such as Donald Arseneau, Fred Bartlett, +%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, +%% Roland Winkler and Mark Wooding. +%% I don't make the claim that my work here is even near their calibre. ;) + + +\newif\if@IEEEeqnarrayboxnojot% flag to indicate if the environment was called as the star form +\@IEEEeqnarrayboxnojotfalse + +\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter +% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray +% used by IEEEeqnarraymulticol so that it can work properly in both +\@advanceIEEEeqncolcnttrue + +\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined +\newcount\@IEEEeqncolcnt % tracks how many IEEEeqnarray cols the user actually used + + +% The default math style used by the columns +\def\IEEEeqnarraymathstyle{\displaystyle} +% The default text style used by the columns +% default to using the current font +\def\IEEEeqnarraytextstyle{\relax} + +% like the iedlistdecl but for \IEEEeqnarray +\def\IEEEeqnarraydecl{\relax} +\def\IEEEeqnarrayboxdecl{\relax} + + + +% V1.8 flags to indicate that equation numbering is to persist +\newif\if@IEEEeqnumpersist% +\@IEEEeqnumpersistfalse +\newif\if@IEEEsubeqnumpersist% +\@IEEEsubeqnumpersistfalse +% +% V1.8 flags to indicate if (sub)equation number of last line was preadvanced +\newif\if@IEEEeqnumpreadv% +\@IEEEeqnumpreadvfalse +\newif\if@IEEEsubeqnumpreadv% +\@IEEEsubeqnumpreadvfalse + +\newcount\@IEEEsubeqnnumrollback% saves previous value of IEEEsubequation number in case we need to restore it + +% \yesnumber is the opposite of \nonumber +% a novel concept with the same def as the equationarray package +% However, we give IEEE versions too since some LaTeX packages such as +% the MDWtools mathenv.sty redefine \nonumber to something else. +% This command is intended for use in non-IEEEeqnarray math environments +\providecommand{\yesnumber}{\global\@eqnswtrue} + + +% IEEEyes/nonumber +% V1.8 add persistant * forms +% These commands can alter the type of equation an IEEEeqnarray line is. +\def\IEEEyesnumber{\@ifstar{\global\@IEEEeqnumpersisttrue\global\@IEEEsubeqnumpersistfalse\@IEEEyesnumber}{\@IEEEyesnumber}} + +\def\@IEEEyesnumber{\global\@eqnswtrue +\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray +\ifnum\c@IEEEsubequation>0\relax + \stepcounter{equation}\setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax + \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label +\fi +% even if we reached this eqn num via a preadv, it is legit now +\global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse +\fi} + +\def\IEEEnonumber{\@ifstar{\global\@IEEEeqnumpersistfalse\global\@IEEEsubeqnumpersistfalse\global\@eqnswfalse}{\global\@eqnswfalse}} + + +\def\IEEEyessubnumber{\@ifstar{\global\@IEEEsubeqnumpersisttrue\@IEEEyessubnumber}{\@IEEEyessubnumber}} +% +\def\@IEEEyessubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray + \ifnum\c@IEEEsubequation>0\relax% if it already is a subequation, we are good to go as-is + \else% if we are a regular equation we have to watch out for two cases + \if@IEEEeqnumpreadv% if this equation is the result of a preadvance, backout and bump the sub eqnnum + \global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\addtocounter{IEEEsubequation}{1}\relax + \else% non-preadvanced equations just need initialization of their sub eqnnum + \setcounter{IEEEsubequation}{1}\relax + \fi + \fi% fi already is subequation + \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax + \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label + \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore + \global\@eqnswtrue +\fi} + + +\def\IEEEnosubnumber{\@ifstar{\global\@IEEEsubeqnumpersistfalse\@IEEEnosubnumber}{\@IEEEnosubnumber}} +% +\def\@IEEEnosubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray + \if@eqnsw % we do nothing unless we know we will display because we play with the counters here + % if it currently is a subequation, bump up to the next equation number and turn off the subequation + \ifnum\c@IEEEsubequation>0\relax\addtocounter{equation}{1}\setcounter{IEEEsubequation}{0}\relax + \fi + \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore + \gdef\@currentlabel{\p@equation\theequation}\relax + \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label + \fi +\fi} + + + +% allows users to "push away" equations that get too close to the equation numbers +\def\IEEEeqnarraynumspace{\hphantom{\ifnum\c@IEEEsubequation>0\relax\theIEEEsubequationdis\else\theequationdis\fi}} + +% provides a way to span multiple columns within IEEEeqnarray environments +% will consider \if@advanceIEEEeqncolcnt before globally advancing the +% column counter - so as to work within \IEEEeqnarraybox +% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text} +\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}\relax +% check if column is defined for the precolumn definition +% We have to be careful here because TeX scans for & even within an \iffalse +% where it does not expand macros. So, if we used only one \ifx and a #3 +% appeared in the false branch and the user inserted another alignment +% structure that uses & in the \IEEEeqnarraymulticol{}, TeX will not see that +% there is an inner alignment in the false branch yet still will see any & +% there and will think that they apply to the outer alignment resulting in an +% incomplete \ifx error. +% So, here we use separate checks for the pre and post parts in order to keep +% the #3 outside of all conditionals. +\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax +\csname @IEEEeqnarraycolPRE#2\endcsname +\else% if not, error and use default type +\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak +Using a default centering column instead}% +{You must define IEEEeqnarray column types before use.}% +\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname +\fi +% The ten \relax are to help prevent misleading error messages in case a user +% accidently inserted a macro that tries to acquire additional arguments. +#3\relax\relax\relax\relax\relax\relax\relax\relax\relax\relax +% check if column is defined for the postcolumn definition +\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax +\csname @IEEEeqnarraycolPOST#2\endcsname +\else% if not, use the default type +\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname +\fi +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi} + +% like \omit, but maintains track of the column counter for \IEEEeqnarray +\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi} + + +% provides a way to define a letter referenced column type +% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text} +\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}% +\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}% +\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}} + + +% provides a way to define a numerically referenced inter-column glue types +% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition} +\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}% +\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}} + + +\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types + + +% expands and appends the given argument to the \@IEEEtrantmptoksA token list +% used to build up the \halign preamble +\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}% +\@@IEEEappendtoksA} + +% also appends to \@IEEEtrantmptoksA, but does not expand the argument +% uses \toks8 as a scratchpad register +\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}% +\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}% +\@@IEEEappendNOEXPANDtoksA} + +% define some common column types for the user +% math +\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil} +\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil} +\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$} +\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil} +\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil} +\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$} +% text +\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil} +\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil} +\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{} + +% vertical rules +\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth} +\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth} +\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth} +\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}% +{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth} + +% horizontal rules +\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil} +\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil} + +% plain +\IEEEeqnarraydefcol{x}{}{} +\IEEEeqnarraydefcol{X}{$}{$} + +% the default column type to use in the event a column type is not defined +\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil} + + +% a zero tabskip (used for "-" col types) +\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt} +% a centering tabskip (used for "+" col types) +\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt} + +% top level default tabskip glues for the start, end, and inter-column +% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox +\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue +\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue +\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue + + + +% creates a vertical rule that extends from the bottom to the top a a cell +% Provided in case other packages redefine \vline some other way. +% usage: \IEEEeqnarrayvrule[rule thickness] +% If no argument is provided, \arrayrulewidth will be used for the rule thickness. +\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax} + +% creates a blank separator row +% usage: \IEEEeqnarrayseprow[separation length][font size commands] +% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax] +% blank arguments inherit the default values +% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers +\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}} +\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}} +\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}% +\ifx\@IEEEeqnarrayseprowARGONE\@empty% +% get the skip value, based on the font commands +% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3 +% assign within a bogus box to confine the font changes +{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}% +\else% +{\setbox0=\hbox{#2\relax\global\skip5=#1}}% +\fi% +\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax} + +% creates a blank separator row, but omits all the column templates +% usage: \IEEEeqnarrayseprowcut[separation length][font size commands] +% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax] +% blank arguments inherit the default values +% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers +\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% +\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}} +\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}} +\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}% +\ifx\@IEEEeqnarrayseprowARGONE\@empty% +% get the skip value, based on the font commands +% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3 +% assign within a bogus box to confine the font changes +{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}% +\else% +{\setbox0=\hbox{#2\relax\global\skip5=#1}}% +\fi% +\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax} + + + +% draws a single rule across all the columns optional +% argument determines the rule width, \arrayrulewidth is the default +% updates column counter as needed and turns off struts +% usage: \IEEEeqnarrayrulerow[rule line thickness] +\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% +\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}} +\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule +% turn off any struts +\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax} + + +% draws a double rule by using a single rule row, a separator row, and then +% another single rule row +% first optional argument determines the rule thicknesses, \arrayrulewidth is the default +% second optional argument determines the rule spacing, \doublerulesep is the default +% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing] +\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% +\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}} +\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}% +{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}} +\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}% +% we allow the user to say \IEEEeqnarraydblrulerow[][] +\ifx\@IEEEeqnarraydblrulerowARG\@empty% +\@IEEEeqnarrayrulerow[\arrayrulewidth]% +\else% +\@IEEEeqnarrayrulerow[#1]\relax% +\fi% +\def\@IEEEeqnarraydblrulerowARG{#2}% +\ifx\@IEEEeqnarraydblrulerowARG\@empty% +\\\IEEEeqnarrayseprow[\doublerulesep][\relax]% +\else% +\\\IEEEeqnarrayseprow[#2][\relax]% +\fi% +\\\multispan{\@IEEEeqnnumcols}% +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% +\def\@IEEEeqnarraydblrulerowARG{#1}% +\ifx\@IEEEeqnarraydblrulerowARG\@empty% +\@IEEEeqnarrayrulerow[\arrayrulewidth]% +\else% +\@IEEEeqnarrayrulerow[#1]% +\fi% +} + +% draws a double rule by using a single rule row, a separator (cutting) row, and then +% another single rule row +% first optional argument determines the rule thicknesses, \arrayrulewidth is the default +% second optional argument determines the rule spacing, \doublerulesep is the default +% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing] +\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% +\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}} +\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}% +{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}} +\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}% +% we allow the user to say \IEEEeqnarraydblrulerow[][] +\ifx\@IEEEeqnarraydblrulerowARG\@empty% +\@IEEEeqnarrayrulerow[\arrayrulewidth]% +\else% +\@IEEEeqnarrayrulerow[#1]% +\fi% +\def\@IEEEeqnarraydblrulerowARG{#2}% +\ifx\@IEEEeqnarraydblrulerowARG\@empty% +\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]% +\else% +\\\IEEEeqnarrayseprowcut[#2][\relax]% +\fi% +\\\multispan{\@IEEEeqnnumcols}% +% advance column counter only if the IEEEeqnarray environment wants it +\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% +\def\@IEEEeqnarraydblrulerowARG{#1}% +\ifx\@IEEEeqnarraydblrulerowARG\@empty% +\@IEEEeqnarrayrulerow[\arrayrulewidth]% +\else% +\@IEEEeqnarrayrulerow[#1]% +\fi% +} + + + +% inserts a full row's worth of &'s +% relies on \@IEEEeqnnumcols to provide the correct number of columns +% uses \@IEEEtrantmptoksA, \count0 as scratch registers +\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax% +\loop% add cols if the user did not use them all +\ifnum\count0<\@IEEEeqnnumcols\relax% +\@IEEEappendtoksA{&}% +\advance\count0 by 1\relax% update the col count +\repeat% +\the\@IEEEtrantmptoksA%execute the &'s +} + + + +\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines +\@IEEEeqnarrayISinnerfalse % of an IEEEeqnarray - after the IEEEeqnarraydecl + +\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts +\edef\@IEEEeqnarrayTHEstrutdepth{0pt} + +\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of +\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt} % struts within an IEEEeqnarray + +\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height +\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth + +\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value +\@IEEEeqnarrayusemasterstruttrue % is to be used + + + +% saves the strut height and depth of the master strut +\def\@IEEEeqnarraymasterstrutsave{\relax% +\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% +% remove stretchability +\dimen0\skip0\relax% +\dimen2\skip2\relax% +% save values +\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}% +\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}} + +% restores the strut height and depth of the master strut +\def\@IEEEeqnarraymasterstrutrestore{\relax% +\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax% +% remove stretchability +\dimen0\skip0\relax% +\dimen2\skip2\relax% +% restore values +\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}} + + +% globally restores the strut height and depth to the +% master values and sets the master strut flag to true +\def\@IEEEeqnarraystrutreset{\relax% +\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% +% remove stretchability +\dimen0\skip0\relax% +\dimen2\skip2\relax% +% restore values +\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% +\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% +\global\@IEEEeqnarrayusemasterstruttrue} + + +% if the master strut is not to be used, make the current +% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth +% and the use master strut flag, global +% this allows user strut commands issued in the last column to be carried +% into the isolation/strut column +\def\@IEEEeqnarrayglobalizestrutstatus{\relax% +\if@IEEEeqnarrayusemasterstrut\else% +\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}% +\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}% +\global\@IEEEeqnarrayusemasterstrutfalse% +\fi} + + + +% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands] +% If called outside the lines of an IEEEeqnarray, sets the height +% and depth of both the master and local struts. If called inside +% an IEEEeqnarray line, sets the height and depth of the local strut +% only and sets the flag to indicate the use of the local strut +% values. If the height or depth is left blank, 0.7\normalbaselineskip +% and 0.3\normalbaselineskip will be used, respectively. +% The optional argument can be used to evaluate the lengths under +% a different font size and styles. If none is specified, the current +% font is used. +% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2 +\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}} +\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}% +\ifx\@IEEEeqnarraystrutsizeARG\@empty% +{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}% +\skip0=\skip3\relax% +\else% arg one present +{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}% +\skip0=\skip3\relax% +\fi% if null arg +\def\@IEEEeqnarraystrutsizeARG{#2}% +\ifx\@IEEEeqnarraystrutsizeARG\@empty% +{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}% +\skip2=\skip3\relax% +\else% arg two present +{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}% +\skip2=\skip3\relax% +\fi% if null arg +% remove stretchability, just to be safe +\dimen0\skip0\relax% +\dimen2\skip2\relax% +% dimen0 = height, dimen2 = depth +\if@IEEEeqnarrayISinner% inner does not touch master strut size +\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% +\@IEEEeqnarrayusemasterstrutfalse% do not use master +\else% outer, have to set master strut too +\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}% +\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% +\@IEEEeqnarrayusemasterstruttrue% use master strut +\fi} + + +% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands] +% If called outside the lines of an IEEEeqnarray, adds the given height +% and depth to both the master and local struts. +% If called inside an IEEEeqnarray line, adds the given height and depth +% to the local strut only and sets the flag to indicate the use +% of the local strut values. +% In both cases, if a height or depth is left blank, 0pt is used instead. +% The optional argument can be used to evaluate the lengths under +% a different font size and styles. If none is specified, the current +% font is used. +% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2 +\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}} +\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}% +\ifx\@IEEEeqnarraystrutsizearg\@empty% +\skip0=0pt\relax% +\else% arg one present +{\setbox0=\hbox{#3\relax\global\skip3=#1}}% +\skip0=\skip3\relax% +\fi% if null arg +\def\@IEEEeqnarraystrutsizearg{#2}% +\ifx\@IEEEeqnarraystrutsizearg\@empty% +\skip2=0pt\relax% +\else% arg two present +{\setbox0=\hbox{#3\relax\global\skip3=#2}}% +\skip2=\skip3\relax% +\fi% if null arg +% remove stretchability, just to be safe +\dimen0\skip0\relax% +\dimen2\skip2\relax% +% dimen0 = height, dimen2 = depth +\if@IEEEeqnarrayISinner% inner does not touch master strut size +% get local strut size +\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax% +% add it to the user supplied values +\advance\dimen0 by \skip0\relax% +\advance\dimen2 by \skip2\relax% +% update the local strut size +\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% +\@IEEEeqnarrayusemasterstrutfalse% do not use master +\else% outer, have to set master strut too +% get master strut size +\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% +% add it to the user supplied values +\advance\dimen0 by \skip0\relax% +\advance\dimen2 by \skip2\relax% +% update the local and master strut sizes +\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}% +\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% +\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% +\@IEEEeqnarrayusemasterstruttrue% use master strut +\fi} + + +% allow user a way to see the struts +\newif\ifIEEEvisiblestruts +\IEEEvisiblestrutsfalse + +% inserts an invisible strut using the master or local strut values +% uses scratch registers \skip0, \skip2, \dimen0, \dimen2 +\def\@IEEEeqnarrayinsertstrut{\relax% +\if@IEEEeqnarrayusemasterstrut +% get master strut size +\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% +\else% +% get local strut size +\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax% +\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax% +\fi% +% remove stretchability, probably not needed +\dimen0\skip0\relax% +\dimen2\skip2\relax% +% dimen0 = height, dimen2 = depth +% allow user to see struts if desired +\ifIEEEvisiblestruts% +\vrule width0.2pt height\dimen0 depth\dimen2\relax% +\else% +\vrule width0pt height\dimen0 depth\dimen2\relax\fi} + + +% creates an invisible strut, useable even outside \IEEEeqnarray +% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. +% usage: \IEEEstrut[height][depth][font size commands] +% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax] +% blank arguments inherit the default values +% uses \dimen0, \dimen2, \skip0, \skip2 +\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}} +\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}} +\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}} +\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax% +\def\@IEEEstrutARG{#1}% +\ifx\@IEEEstrutARG\@empty% +\skip0=0.7\normalbaselineskip\relax% +\else% +\skip0=#1\relax% +\fi% +\def\@IEEEstrutARG{#2}% +\ifx\@IEEEstrutARG\@empty% +\skip2=0.3\normalbaselineskip\relax% +\else% +\skip2=#2\relax% +\fi% +% remove stretchability, probably not needed +\dimen0\skip0\relax% +\dimen2\skip2\relax% +\ifIEEEvisiblestruts% +\vrule width0.2pt height\dimen0 depth\dimen2\relax% +\else% +\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}} + + +% enables strut mode by setting a default strut size and then zeroing the +% \baselineskip, \lineskip, \lineskiplimit and \jot +\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]% +\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt} + + +% equation and subequation forms to use to setup hyperref's \@currentHref +\def\@IEEEtheHrefequation{equation.\theHequation} +\def\@IEEEtheHrefsubequation{equation.\theHequation\alph{IEEEsubequation}} + + +\def\IEEEeqnarray{\@IEEEeqnumpersisttrue\@IEEEsubeqnumpersistfalse\@IEEEeqnarray} +\def\endIEEEeqnarray{\end@IEEEeqnarray} + +\@namedef{IEEEeqnarray*}{\@IEEEeqnumpersistfalse\@IEEEsubeqnumpersistfalse\@IEEEeqnarray} +\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray} + + +% \IEEEeqnarray is an enhanced \eqnarray. +% The star form defaults to not putting equation numbers at the end of each row. +% usage: \IEEEeqnarray[decl]{cols} +\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}} +% We have to be careful here to normalize catcodes just before acquiring the +% cols as that specification may contain punctuation which could be subject +% to document catcode changes. +\def\@@IEEEeqnarray[#1]{\begingroup\IEEEnormalcatcodes\@@@IEEEeqnarray[#1]} +\def\@@@IEEEeqnarray[#1]#2{\endgroup + % default to showing the equation number or not based on whether or not + % the star form was involked + \if@IEEEeqnumpersist\global\@eqnswtrue + \else% not the star form + \global\@eqnswfalse + \fi% if star form + % provide a basic hyperref \theHequation if this has not already been setup (hyperref not loaded, or no section counter) + \@ifundefined{theHequation}{\def\theHequation{\arabic{equation}}}{}\relax + % provide dummy hyperref commands in case hyperref is not loaded + \providecommand{\Hy@raisedlink}[1]{}\relax + \providecommand{\hyper@anchorstart}[1]{}\relax + \providecommand{\hyper@anchorend}{}\relax + \providecommand{\@currentHref}{}\relax + \@IEEEeqnumpreadvfalse% reset eqnpreadv flag + \@IEEEsubeqnumpreadvfalse% reset subeqnpreadv flag + \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign + \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default + \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise + \IEEEvisiblestrutsfalse% diagnostic mode defaults to off + % no extra space unless the user specifically requests it + \lineskip=0pt\relax + \lineskiplimit=0pt\relax + \baselineskip=\normalbaselineskip\relax% + \jot=\IEEEnormaljot\relax% + \mathsurround\z@\relax% no extra spacing around math + \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, + % used in \IEEEeqnarraymulticol and in the preamble build + %V1.8 Here we preadvance to the next equation number. + % If the user later wants a continued subequation, we can roll back. + \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation% + \stepcounter{equation}\@IEEEeqnumpreadvtrue% advance equation counter before first line + \setcounter{IEEEsubequation}{0}% no subequation yet + \let\@IEEEcurrentlabelsave\@currentlabel% save current label as we later change it globally + \let\@IEEEcurrentHrefsave\@currentHref% save current href label as we later change it globally + \def\@currentlabel{\p@equation\theequation}% redefine the ref label + \def\@currentHref{\@IEEEtheHrefequation}% setup hyperref label + \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides + #1\relax% allow user to override defaults + \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers + \global\@IEEEeqncolcnt\z@% col. count = 0 for first line + \@IEEEbuildpreamble{#2}\relax% build the preamble and put it into \@IEEEtrantmptoksA + % put in the column for the equation number + \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first + \toks0={##}% + % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking + \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}% + % add the isolation column + \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% + % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking + \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}% + % add the equation number col to the preamble + \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}% + % note \@IEEEeqnnumcols does not count the equation col or isolation col + % set the starting tabskip glue as determined by the preamble build + \tabskip=\@IEEEBPstartglue\relax + % begin the display alignment + \@IEEEeqnarrayISinnertrue% commands are now within the lines + $$\everycr{}\halign to\displaywidth\bgroup + % "exspand" the preamble + \span\the\@IEEEtrantmptoksA\cr} + +% enter isolation/strut column (or the next column if the user did not use +% every column), record the strut status, complete the columns, do the strut if needed, +% restore counters (to backout any equation setup for a next line that was never used) +% to their correct values and exit +\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup +\if@IEEEsubeqnumpreadv\global\advance\c@IEEEsubequation\m@ne\fi +\if@IEEEeqnumpreadv\global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\fi +\global\let\@currentlabel\@IEEEcurrentlabelsave% restore current label +\global\let\@currentHref\@IEEEcurrentHrefsave% restore current href label +$$\@ignoretrue} + + +% IEEEeqnarray uses a modifed \\ instead of the plain \cr to +% end rows. This allows for things like \\*[vskip amount] +% These "cr" macros are modified versions of those for LaTeX2e's eqnarray +% the {\ifnum0=`} braces must be kept away from the last column to avoid +% altering spacing of its math, so we use & to advance to the next column +% as there is an isolation/strut column after the user's columns +\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column + {\ifnum0=`}\fi + \@ifstar{% + \global\@eqpen\@M\@IEEEeqnarrayYCR + }{% + \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR + }% +} + +\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip} + +\def\@IEEEeqnarrayXCR[#1]{% + \ifnum0=`{\fi}% + \@@IEEEeqnarraycr + \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}% + +\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register + \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column + \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax + \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak + environment}% + {Use fewer \string &'s or put more columns in the IEEEeqnarray column\MessageBreak + specifications.}\relax% + \else + \loop% add cols if the user did not use them all + \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax + \@IEEEappendtoksA{&}% + \advance\@IEEEeqncolcnt by 1\relax% update the col count + \repeat + % this number of &'s will take us the the isolation column + \fi + % execute the &'s + \the\@IEEEtrantmptoksA% + % handle the strut/isolation column + \@IEEEeqnarrayinsertstrut% do the strut if needed + \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray + &% and enter the equation number column + \if@eqnsw% only if we display something + \Hy@raisedlink{\hyper@anchorstart{\@currentHref}}% start a hyperref anchor + \global\@IEEEeqnumpreadvfalse\relax% displaying an equation number means + \global\@IEEEsubeqnumpreadvfalse\relax% the equation counters point to valid equations + % V1.8 Here we setup the counters, currentlabel and status for what would be the *next* + % equation line as would be the case under the current settings. However, there are two problems. + % One problem is that there might not ever be a next line. The second problem is that the user + % may later alter the meaning of a line with commands such as \IEEEyessubnumber. So, to handle + % these cases we have to record the current values of the (sub)equation counters and revert back + % to them if the next line is changed or never comes. The \if@IEEEeqnumpreadv, \if@IEEEsubeqnumpreadv + % and \@IEEEsubeqnnumrollback stuff tracks this. + % The logic to handle all this is surprisingly complex, but a nice feature of the approach here is + % that the equation counters and labels remain valid for what the line would be unless a + % \IEEEyessubnumber et al. later changes it. So, any hyperref links are always correct. + \ifnum\c@IEEEsubequation>0\relax% handle subequation + \theIEEEsubequationdis\relax + \if@IEEEsubeqnumpersist% setup for default type of next line + \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax + \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax + \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label + \else + % if no subeqnum persist, go ahead and setup for a new equation number + \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation + \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax + \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax + \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label + \fi + \else% display a standard equation number + \theequationdis\relax + \setcounter{IEEEsubequation}{0}\relax% not really needed + \if@IEEEsubeqnumpersist% setup for default type of next line + % subequations that follow plain equations carry the same equation number e.g, 5, 5a rather than 5, 6a + \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax + \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax + \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label + \else + % if no subeqnum persist, go ahead and setup for a new equation number + \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation + \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax + \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax + \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label + \fi + \fi% + \Hy@raisedlink{\hyper@anchorend}% end hyperref anchor + \fi% fi only if we display something + % reset the flags to indicate the default preferences of the display of equation numbers + \if@IEEEeqnumpersist\global\@eqnswtrue\else\global\@eqnswfalse\fi + \if@IEEEsubeqnumpersist\global\@eqnswtrue\fi% ditto for the subequation flag + % reset the number of columns the user actually used + \global\@IEEEeqncolcnt\z@\relax + % the real end of the line + \cr} + + + + + +% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything +% inside a vtop, vbox, or vcenter box depending on the letter in the second +% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray, +% equation numbers are not displayed and \IEEEeqnarraybox can be nested. +% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox +% within an hbox. +% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within +% a \hbox{$ $} construct. +% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or +% \IEEEeqnarrayboxt depending on the math mode. +% The third optional argument specifies the width this box is to be set to - +% natural width is the default. +% The * forms do not add \jot line spacing +% usage: \IEEEeqnarraybox[decl][pos][width]{cols} +\def\IEEEeqnarrayboxm{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox} +\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox} +\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox} +\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox} + +\def\IEEEeqnarrayboxt{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox} +\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox} +\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox} +\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox} + +\def\IEEEeqnarraybox{\@IEEEeqnarrayboxnojotfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi% +\@IEEEeqnarraybox} +\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox} + +\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarrayboxnojottrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi% +\@IEEEeqnarraybox} +\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox} + +% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} +% for \vcenter in non-math mode +\newif\if@IEEEeqnarrayboxHBOXSW% +\@IEEEeqnarrayboxHBOXSWfalse + +\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}} +% We have to be careful here to normalize catcodes just before acquiring the +% cols as that specification may contain punctuation which could be subject +% to document catcode changes. +\def\@@IEEEeqnarraybox[#1]{\relax\begingroup\IEEEnormalcatcodes\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}} +\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}} + +% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs +\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\endgroup\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign + \@IEEEeqnarraymasterstrutsave% save current master strut values + \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default + \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise + \IEEEvisiblestrutsfalse% diagnostic mode defaults to off + % no extra space unless the user specifically requests it + \lineskip=0pt\relax% + \lineskiplimit=0pt\relax% + \baselineskip=\normalbaselineskip\relax% + \jot=\IEEEnormaljot\relax% + \mathsurround\z@\relax% no extra spacing around math + % the default end glues are zero for an \IEEEeqnarraybox + \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue + \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue + \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue + \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, + % used in \IEEEeqnarraymulticol and in the preamble build + \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides + #1\relax% allow user to override defaults + \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing + \@IEEEbuildpreamble{#4}\relax% build the preamble and put it into \@IEEEtrantmptoksA + % add an isolation column to the preamble to stop \\'s {} from getting into the last col + \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first + \toks0={##}% + % add the isolation column to the preamble + \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% + % set the starting tabskip glue as determined by the preamble build + \tabskip=\@IEEEBPstartglue\relax + % begin the alignment + \everycr{}% + % use only the very first token to determine the positioning + \@IEEEextracttoken{#2}\relax + \ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: IEEEeqnarraybox position specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax + \fi + % \@IEEEextractedtoken has the first token, the rest are ignored + % if we need to put things into and hbox and go into math mode, do so now + \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi% + % use the appropriate vbox type + \if\@IEEEextractedtoken t\relax\vtop\else\if\@IEEEextractedtoken c\relax% + \vcenter\else\vbox\fi\fi\bgroup% + \@IEEEeqnarrayISinnertrue% commands are now within the lines + \ifx#3\relax\halign\else\halign to #3\relax\fi% + \bgroup + % "exspand" the preamble + \span\the\@IEEEtrantmptoksA\cr} + +% carry strut status and enter the isolation/strut column, +% exit from math mode if needed, and exit +\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status +&% enter isolation/strut column +\@IEEEeqnarrayinsertstrut% do strut if needed +\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values +% reset the strut system for next IEEEeqnarray +% (sets local strut values back to previous master strut values) +\@IEEEeqnarraystrutreset% +% ensure last line, exit from halign, close vbox +\crcr\egroup\egroup% +% exit from math mode and close hbox if needed +\if@IEEEeqnarrayboxHBOXSW $\egroup\fi} + + + +% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to +% end rows. This allows for things like \\[vskip amount] +% This "cr" macros are modified versions those for LaTeX2e's eqnarray +% For IEEEeqnarraybox, \\* is the same as \\ +% the {\ifnum0=`} braces must be kept away from the last column to avoid +% altering spacing of its math, so we use & to advance to the isolation/strut column +% carry strut status into isolation/strut column +\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status +&% enter isolation/strut column +\@IEEEeqnarrayinsertstrut% do strut if needed +% reset the strut system for next line or IEEEeqnarray +\@IEEEeqnarraystrutreset% +{\ifnum0=`}\fi% +\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}} + +% test and setup the optional argument to \\[] +\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip} + +% IEEEeqnarraybox does not automatically increase line spacing by \jot +\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}% +\cr\noalign{\if@IEEEeqnarrayboxnojot\else\vskip\jot\fi\vskip#1\relax}} + + + +% usage: \@IEEEbuildpreamble{column specifiers} +% starts the halign preamble build +% the assembled preamble is put in \@IEEEtrantmptoksA +\def\@IEEEbuildpreamble#1{\@IEEEtrantmptoksA={}% clear token register +\let\@IEEEBPcurtype=u%current column type is not yet known +\let\@IEEEBPprevtype=s%the previous column type was the start +\let\@IEEEBPnexttype=u%next column type is not yet known +% ensure these are valid +\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}% +\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition +% currently acquired numerically referenced glue +% use a name that is easier to remember +\let\@IEEEBPcurnum=\@IEEEtrantmpcountA% +\@IEEEBPcurnum=0% +% tracks number of columns in the preamble +\@IEEEeqnnumcols=0% +% record the default end glues +\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}% +\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}% +\edef\@IEEEedefMACRO{#1}\relax% fully expand the preamble to support macro containers +% now parse the user's column specifications +% \ignorespaces is used as a delimiter, need at least one trailing \relax because +% \@@IEEEbuildpreamble looks into the future +\expandafter\@@IEEEbuildpreamble\@IEEEedefMACRO\ignorespaces\relax\relax} + + +% usage: \@@IEEEbuildpreamble{current column}{next column} +% parses and builds the halign preamble +\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble% +% use only the very first token to check the end +\@IEEEextracttokengroups{#1}\relax +\ifx\@IEEEextractedfirsttoken\ignorespaces\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else% +% identify current and next token type +\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid +\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next +% if curtype is a glue, get the glue def +\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi% +% if curtype is a column, get the column def and set the current column name +\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi% +% if curtype is a numeral, acquire the user defined glue +\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi% +% process the acquired glue +\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi% +% process the acquired col +\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi% +% ready prevtype for next col spec. +\let\@IEEEBPprevtype=\@IEEEBPcurtype% +% be sure and put back the future token(s) as a group +\fi\@@nextIEEEbuildpreamble{#2}} + + +% usage: \@@IEEEfinishpreamble{discarded} +% executed just after preamble build is completed +% warn about zero cols, and if prevtype type = u, put in end tabskip glue +% argument is not used +\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax +\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}% +{At least one column type must be declared for each IEEEeqnarray.}% +\fi%num cols less than 1 +%if last type undefined, set default end tabskip glue +\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi} + + +% usage: \@IEEEgetcoltype{col specifier}{\output}{error more} +% Identify and return the column specifier's type code in the given +% \output macro: +% n = number +% g = glue (any other char in catagory 12) +% c = letter +% e = \ignorespaces (end of sequence) +% u = undefined +% error mode: 0 = no error message, 1 = error on invalid char +\def\@IEEEgetcoltype#1#2#3{% +% use only the very first token to determine the type +\@IEEEextracttoken{#1}\relax +% \@IEEEextractedtoken has the first token, the rest are discarded +\let#2=u\relax% assume invalid until know otherwise +\ifx\@IEEEextractedtoken\ignorespaces\let#2=e\else +\ifcat\@IEEEextractedtoken\relax\else% screen out control sequences +\if0\@IEEEextractedtoken\let#2=n\else +\if1\@IEEEextractedtoken\let#2=n\else +\if2\@IEEEextractedtoken\let#2=n\else +\if3\@IEEEextractedtoken\let#2=n\else +\if4\@IEEEextractedtoken\let#2=n\else +\if5\@IEEEextractedtoken\let#2=n\else +\if6\@IEEEextractedtoken\let#2=n\else +\if7\@IEEEextractedtoken\let#2=n\else +\if8\@IEEEextractedtoken\let#2=n\else +\if9\@IEEEextractedtoken\let#2=n\else +\ifcat,\@IEEEextractedtoken\let#2=g\relax +\else\ifcat a\@IEEEextractedtoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi +\if#2u\relax +\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}% +{Only letters, numerals and certain other symbols are allowed \MessageBreak +as IEEEeqnarray column specifiers.}\fi\fi} + + +% usage: \@IEEEgetcurcol{col specifier} +% verify the letter referenced column exists +% and return its name in \@IEEEBPcurcolname +% if column specifier is invalid, use the default column @IEEEdefault +\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined% +\def\@IEEEBPcurcolname{#1}\else% invalid column name +\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak +Using a default centering column instead}% +{You must define IEEEeqnarray column types before use.}% +\def\@IEEEBPcurcolname{@IEEEdefault}\fi} + + +% usage: \@IEEEgetcurglue{glue specifier}{\output} +% identify the predefined (punctuation) glue value +% and return it in the given output macro +\def\@IEEEgetcurglue#1#2{% +% ! = \! (neg small) -0.16667em (-3/18 em) +% , = \, (small) 0.16667em ( 3/18 em) +% : = \: (med) 0.22222em ( 4/18 em) +% ; = \; (large) 0.27778em ( 5/18 em) +% ' = \quad 1em +% " = \qquad 2em +% . = 0.5\arraycolsep +% / = \arraycolsep +% ? = 2\arraycolsep +% * = 1fil +% + = \@IEEEeqnarraycolSEPcenter +% - = \@IEEEeqnarraycolSEPzero +% Note that all em values are referenced to the math font (textfont2) fontdimen6 +% value for 1em. +% +% use only the very first token to determine the type +\@IEEEextracttoken{#1}\relax +\ifx\@IEEEextractedtokensdiscarded\@empty\else + \typeout{** WARNING: IEEEeqnarray predefined inter-column glue type specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax +\fi +% get the math font 1em value +% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs +% to gain access to the math (\textfont2) font's spacing parameters. +% So we create a bogus box here that uses the math font to ensure +% that \textfont2 is loaded and ready. If this is not done, +% the \textfont2 stuff here may not work. +% Thanks to Bernd Raichle for his 1997 post on this topic. +{\setbox0=\hbox{$\displaystyle\relax$}}% +% fontdimen6 has the width of 1em (a quad). +\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax% +% identify the glue value based on the first token +% we discard anything after the first +\if!\@IEEEextractedtoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else +\if,\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else +\if:\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else +\if;\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else +\if'\@IEEEextractedtoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else +\if"\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else +\if.\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else +\if/\@IEEEextractedtoken\edef#2{\the\arraycolsep}\else +\if?\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else +\if *\@IEEEextractedtoken\edef#2{0pt plus 1fil minus 0pt}\else +\if+\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else +\if-\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPzero}\else +\edef#2{\@IEEEeqnarraycolSEPzero}% +\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak +column specifications. Using a default value of\MessageBreak +0pt instead}% +{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak +IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} + + +% usage: \@IEEEprocessNcol{digit} +% process a numerical digit from the column specification +% and look up the corresponding user defined glue value +% can transform current type from n to g or a as the user defined glue is acquired +\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g% +\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak +specifications. Ignoring consecutive glue specifiers\MessageBreak +after the first}% +{You cannot have two or more glue types next to each other\MessageBreak +in the IEEEeqnarray column specifications.}% +\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded +\@IEEEBPcurnum=0\relax% +\else% if we previously aborted a glue +\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion +\else%acquire this number +% save the previous type before the numerical digits started +\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi% +\multiply\@IEEEBPcurnum by 10\relax% +\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan +\if\@IEEEBPnexttype n\else%close acquisition +\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined% +\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}% +\else%user glue not defined +\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak +column specifications. Using a default value of\MessageBreak +0pt instead}% +{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak +\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}% +\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}% +\fi% glue defined or not +\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue +\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue +\@IEEEBPcurnum=0\relax%ready for next acquisition +\fi%close acquisition, get glue +\fi%discard or acquire number +\fi%prevtype glue or not +} + + +% process an acquired glue +% add any acquired column/glue pair to the preamble +\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions +\else +% if this is the start glue, save it, but do nothing else +% as this is not used in the preamble, but before +\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}% +\else%not the start glue +\if\@IEEEBPprevtype g%ignore if back to back glues +\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak +specifications. Ignoring consecutive glue specifiers\MessageBreak +after the first}% +{You cannot have two or more glue types next to each other\MessageBreak +in the IEEEeqnarray column specifications.}% +\let\@IEEEBPcurtype=a% abort this glue +\else% not a back to back glue +\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble +\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi +\toks0={##}% +% make preamble advance col counter if this environment needs this +\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi +% insert the column defintion into the preamble, being careful not to expand +% the column definition +\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}% +\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}% +\@IEEEappendtoksA{\@IEEEBPcurcolname}% +\@IEEEappendNOEXPANDtoksA{\endcsname}% +\@IEEEappendtoksA{\the\toks0}% +\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax% +\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}% +\@IEEEappendtoksA{\@IEEEBPcurcolname}% +\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax% +\relax\relax\relax\relax\relax\endgroup}% +\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble +\else% error: non-start glue with no pending column +\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak +type in the column specifications. Ignoring this glue\MessageBreak +specifier}% +{Except for the first and last positions, glue can be placed only\MessageBreak +between column types.}% +\let\@IEEEBPcurtype=a% abort this glue +\fi% previous was a column +\fi% back-to-back glues +\fi% is start column glue +\fi% prev type not a +} + + +% process an acquired letter referenced column and, if necessary, add it to the preamble +\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else +\if\@IEEEBPnexttype n\else +% we have a column followed by something other than a glue (or numeral glue) +% so we must add this column to the preamble now +\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first +\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue +\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue +\toks0={##}% +% make preamble advance col counter if this environment needs this +\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi +% insert the column definition into the preamble, being careful not to expand +% the column definition +\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}% +\@IEEEappendtoksA{\@IEEEBPcurcolname}% +\@IEEEappendNOEXPANDtoksA{\endcsname}% +\@IEEEappendtoksA{\the\toks0}% +\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax% +\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}% +\@IEEEappendtoksA{\@IEEEBPcurcolname}% +\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax% +\relax\relax\relax\relax\relax\endgroup}% +\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble +\fi%next type not numeral +\fi%next type not glue +} + + +%% +%% END OF IEEEeqnarray DEFINITIONS +%% + + + + +% \IEEEPARstart +% Definition for the big two line drop cap letter at the beginning of the +% first paragraph of journal papers. The first argument is the first letter +% of the first word, the second argument is the remaining letters of the +% first word which will be rendered in upper case. +% In V1.6 this has been completely rewritten to: +% +% 1. no longer have problems when the user begins an environment +% within the paragraph that uses \IEEEPARstart. +% 2. auto-detect and use the current font family +% 3. revise handling of the space at the end of the first word so that +% interword glue will now work as normal. +% 4. produce correctly aligned edges for the (two) indented lines. +% +% We generalize things via control macros - playing with these is fun too. +% +% V1.7 added more control macros to make it easy for IEEEtrantools.sty users +% to change the font style. +% +% the number of lines that are indented to clear it +% may need to increase if using decenders +\providecommand{\IEEEPARstartDROPLINES}{2} +% minimum number of lines left on a page to allow a \@IEEEPARstart +% Does not take into consideration rubber shrink, so it tends to +% be overly cautious +\providecommand{\IEEEPARstartMINPAGELINES}{2} +% V1.7 the height of the drop cap is adjusted to match the height of this text +% in the current font (when \IEEEPARstart is called). +\providecommand{\IEEEPARstartHEIGHTTEXT}{T} +% the depth the letter is lowered below the baseline +% the height (and size) of the letter is determined by the sum +% of this value and the height of the \IEEEPARstartHEIGHTTEXT in the current +% font. It is a good idea to set this value in terms of the baselineskip +% so that it can respond to changes therein. +\providecommand{\IEEEPARstartDROPDEPTH}{1.1\baselineskip} +% V1.7 the font the drop cap will be rendered in, +% can take zero or one argument. +\providecommand{\IEEEPARstartFONTSTYLE}{\bfseries} +% V1.7 any additional, non-font related commands needed to modify +% the drop cap letter, can take zero or one argument. +\providecommand{\IEEEPARstartCAPSTYLE}{\MakeUppercase} +% V1.7 the font that will be used to render the rest of the word, +% can take zero or one argument. +\providecommand{\IEEEPARstartWORDFONTSTYLE}{\relax} +% V1.7 any additional, non-font related commands needed to modify +% the rest of the word, can take zero or one argument. +\providecommand{\IEEEPARstartWORDCAPSTYLE}{\MakeUppercase} +% This is the horizontal separation distance from the drop letter to the main text. +% Lengths that depend on the font (e.g., ex, em, etc.) will be referenced +% to the font that is active when \IEEEPARstart is called. +\providecommand{\IEEEPARstartSEP}{0.15em} +% V1.7 horizontal offset applied to the left of the drop cap. +\providecommand{\IEEEPARstartHOFFSET}{0em} +% V1.7 Italic correction command applied at the end of the drop cap. +\providecommand{\IEEEPARstartITLCORRECT}{\/} + +% width of the letter output, set globally. Can be used in \IEEEPARstartSEP +% or \IEEEPARstartHOFFSET, but not the height lengths. +\newdimen\IEEEPARstartletwidth +\IEEEPARstartletwidth 0pt\relax + +% definition of \IEEEPARstart +% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES +% +% The token \@IEEEPARstartfont will be globally defined after the first use +% of \IEEEPARstart and will be a font command which creates the big letter +% The first argument is the first letter of the first word and the second +% argument is the rest of the first word(s). +\def\IEEEPARstart#1#2{\par{% +% if this page does not have enough space, break it and lets start +% on a new one +\@IEEEtranneedspace{\IEEEPARstartMINPAGELINES\baselineskip}{\relax}% +% V1.7 move this up here in case user uses \textbf for \IEEEPARstartFONTSTYLE +% which uses command \leavevmode which causes an unwanted \indent to be issued +\noindent +% calculate the desired height of the big letter +% it extends from the top of \IEEEPARstartHEIGHTTEXT in the current font +% down to \IEEEPARstartDROPDEPTH below the current baseline +\settoheight{\@IEEEtrantmpdimenA}{\IEEEPARstartHEIGHTTEXT}% +\addtolength{\@IEEEtrantmpdimenA}{\IEEEPARstartDROPDEPTH}% +% extract the name of the current font in bold +% and place it in \@IEEEPARstartFONTNAME +\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}% +{\IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}% +\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}% +% define a font based on this name with a point size equal to the desired +% height of the drop letter +\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax% +% save this value as a counter (integer) value (sp points) +\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA% +% now get the height of the actual letter produced by this font size +\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\IEEEPARstartCAPSTYLE{#1}}% +% If something bogus happens like the first argument is empty or the +% current font is strange, do not allow a zero height. +\ifdim\@IEEEtrantmpdimenB=0pt\relax% +\typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}% +\typeout{ Forcing the drop letter font size to 10pt.}% +\@IEEEtrantmpdimenB=10pt% +\fi% +% and store it as a counter +\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB% +% Since a font size doesn't exactly correspond to the height of the capital +% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB, +% will be less than that desired, \@IEEEtrantmpcountA +% we need to raise the font size, \@IEEEtrantmpdimenA +% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB +% But, TeX doesn't have floating point division, so we have to use integer +% division. Hence the use of the counters. +% We need to reduce the denominator so that the loss of the remainder will +% have minimal affect on the accuracy of the result +\divide\@IEEEtrantmpcountB by 200% +\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB% +% Then reequalize things when we use TeX's ability to multiply by +% floating point values +\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA% +\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA% +% \@IEEEPARstartfont is globaly set to the calculated font of the big letter +% We need to carry this out of the local calculation area to to create the +% big letter. +\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB% +% Now set \@IEEEtrantmpdimenA to the width of the big letter +% We need to carry this out of the local calculation area to set the +% hanging indent +\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont +\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}}}% +% end of the isolated calculation environment +\global\IEEEPARstartletwidth\@IEEEtrantmpdimenA\relax% +% add in the extra clearance we want +\advance\@IEEEtrantmpdimenA by \IEEEPARstartSEP\relax% +% add in the optional offset +\advance\@IEEEtrantmpdimenA by \IEEEPARstartHOFFSET\relax% +% V1.7 don't allow negative offsets to produce negative hanging indents +\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA +\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi +% \@IEEEtrantmpdimenA has the width of the big letter plus the +% separation space and \@IEEEPARstartfont is the font we need to use +% Now, we make the letter and issue the hanging indent command +% The letter is placed in a box of zero width and height so that other +% text won't be displaced by it. +\hangindent\@IEEEtrantmpdimenB\hangafter=-\IEEEPARstartDROPLINES% +\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}% +\raisebox{-\IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\IEEEPARstartHOFFSET}% +\@IEEEPARstartfont\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}% +\hspace{\IEEEPARstartSEP}}}% +{\IEEEPARstartWORDFONTSTYLE{\IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}} + + + + + + +% determines if the space remaining on a given page is equal to or greater +% than the specified space of argument one +% if not, execute argument two (only if the remaining space is greater than zero) +% and issue a \newpage +% +% example: \@IEEEtranneedspace{2in}{\vfill} +% +% Does not take into consideration rubber shrinkage, so it tends to +% be overly cautious +% Based on an example posted by Donald Arseneau +% Note this macro uses \@IEEEtrantmpdimenB internally for calculations, +% so DO NOT PASS \@IEEEtrantmpdimenB to this routine +% if you need a dimen register, import with \@IEEEtrantmpdimenA instead +\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable +\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left +\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left +\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi% +\newpage% +\fi\endgroup} + + +% \IEEEauthorrefmark +\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or% + \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger% + \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}} + + +% V1.3 IEEEQED and IEEEproof +\def\IEEEproofname{Proof} + +\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box +\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}} +\def\IEEEQED{\IEEEQEDclosed} % default to closed + +%V1.8 flag to indicate if QED symbol is to be shown +\newif\if@IEEEQEDshow \@IEEEQEDshowtrue +\def\IEEEproofindentspace{2\parindent}% V1.8 allow user to change indentation amount if desired +% v1.7 name change to avoid namespace collision with amsthm. Also add support +% for an optional argument. +\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}} +\def\@IEEEproof[#1]{\@IEEEQEDshowtrue\par\noindent\hspace{\IEEEproofindentspace}{\itshape #1: }} +\def\endIEEEproof{\if@IEEEQEDshow\hspace*{\fill}\nobreakspace\IEEEQED\fi\par} +% qedhere for equation environments, similar to AMS \qedhere +\def\IEEEQEDhereeqn{\global\@IEEEQEDshowfalse\eqno\let\eqno\relax\let\leqno\relax + \let\veqno\relax\hbox{\IEEEQED}} +% IEEE style qedhere for IEEEeqnarray and other environments +\def\IEEEQEDhere{\global\@IEEEQEDshowfalse\IEEEQED} +% command to disable QED at end of IEEEproof +\def\IEEEQEDoff{\global\@IEEEQEDshowfalse} + + +% Provide support for the control entries of IEEEtran.bst V1.00 and later. +% V1.7 optional argument allows for a different aux file to be specified in +% order to handle multiple bibliographies. For example, with multibib.sty: +% \newcites{sec}{Secondary Literature} +% \bstctlcite[@auxoutsec]{BSTcontrolhak} +% V1.7 I see no need for \providecommand here. +\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}} +\def\@bstctlcite[#1]#2{\@bsphack + \@for\@citeb:=#2\do{% + \edef\@citeb{\expandafter\@firstofone\@citeb}% + \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}% + \@esphack} + +% \IEEEnoauxwrite{} allows for citations that do not add to or affect +% the order of the existing citation list. Can be useful for \cite +% within \thanks{}. +\DeclareRobustCommand{\IEEEnoauxwrite}[1]{\relax +\if@filesw +\@fileswfalse +#1\relax\relax\relax\relax\relax +\@fileswtrue +\else +#1\relax\relax\relax\relax\relax +\fi} + +% need a backslash character for typeout output +{\catcode`\|=0 \catcode`\\=12 +|xdef|@IEEEbackslash{\}} + + +% hook to allow easy disabling of all legacy warnings +\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno). +Use \@IEEEbackslash #2 instead.}} + + +% V1.4 no longer support these legacy commands +% \def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart} +% \let\labelindent\IEEElabelindent +% \def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin} +% \def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth} +% \def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep} +% \def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc} +% \def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl} +% \def\iedlabeljustifyr{\@IEEElegacywarn{iedlabeljustifyr}{IEEEiedlabeljustifyr}\IEEEiedlabeljustifyr} + + +\endinput +%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtrantools.sty %%%%%%%%%%%%%%%%%%%%%% +% That's all folks! + diff --git a/TRUST-docs/acmart.cls b/TRUST-docs/acmart.cls new file mode 100755 index 0000000..cf83c8a --- /dev/null +++ b/TRUST-docs/acmart.cls @@ -0,0 +1,2544 @@ +%% +%% This is file `acmart.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% acmart.dtx (with options: `class') +%% +%% IMPORTANT NOTICE: +%% +%% For the copyright see the source file. +%% +%% Any modified versions of this file must be renamed +%% with new filenames distinct from acmart.cls. +%% +%% For distribution of the original source see the terms +%% for copying and modification in the file acmart.dtx. +%% +%% This generated file may be distributed as long as the +%% original source files, as listed above, are part of the +%% same distribution. (The sources need not necessarily be +%% in the same archive or directory.) +%% \CharacterTable +%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +%% Digits \0\1\2\3\4\5\6\7\8\9 +%% Exclamation \! Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{acmart} +[2017/08/31 v1.47 Typesetting articles for Association of +Computing Machinery] +\def\@classname{acmart} +\InputIfFileExists{acmart-preload-hook.tex}{% + \ClassWarning{\@classname}{% + I am loading acmart-preload-hook.tex. You are fully responsible + for any problems from now on.}}{} +\RequirePackage{xkeyval} +\RequirePackage{xstring} +\define@choicekey*+{acmart.cls}{format}[\ACM@format\ACM@format@nr]{% + manuscript, acmsmall, acmlarge, acmtog, sigconf, siggraph, + sigplan, sigchi, sigchi-a}[manuscript]{}{% + \ClassError{\@classname}{The option format must be manuscript, + acmsmall, acmlarge, acmtog, sigconf, siggraph, + sigplan, sigchi or sigchi-a}} +\def\@DeclareACMFormat#1{\DeclareOptionX{#1}{\setkeys{acmart.cls}{format=#1}}} +\@DeclareACMFormat{manuscript} +\@DeclareACMFormat{acmsmall} +\@DeclareACMFormat{acmlarge} +\@DeclareACMFormat{acmtog} +\@DeclareACMFormat{sigconf} +\@DeclareACMFormat{siggraph} +\@DeclareACMFormat{sigplan} +\@DeclareACMFormat{sigchi} +\@DeclareACMFormat{sigchi-a} +\ExecuteOptionsX{format} +\define@boolkey+{acmart.cls}[@ACM@]{screen}[true]{% + \if@ACM@screen + \PackageInfo{\@classname}{Using screen mode}% + \else + \PackageInfo{\@classname}{Not using screen mode}% + \fi}{\PackageError{\@classname}{Option screen can be either true or + false}} +\ExecuteOptionsX{screen=false} +\define@boolkey+{acmart.cls}[@ACM@]{acmthm}[true]{% + \if@ACM@acmthm + \PackageInfo{\@classname}{Requiring acmthm}% + \else + \PackageInfo{\@classname}{Suppressing acmthm}% + \fi}{\PackageError{\@classname}{Option acmthm can be either true or + false}} +\ExecuteOptionsX{acmthm=true} +\define@boolkey+{acmart.cls}[@ACM@]{review}[true]{% + \if@ACM@review + \PackageInfo{\@classname}{Using review mode}% + \else + \PackageInfo{\@classname}{Not using review mode}% + \fi}{\PackageError{\@classname}{Option review can be either true or + false}} +\ExecuteOptionsX{review=false} +\define@boolkey+{acmart.cls}[@ACM@]{authorversion}[true]{% + \if@ACM@authorversion + \PackageInfo{\@classname}{Using authorversion mode}% + \else + \PackageInfo{\@classname}{Not using authorversion mode}% + \fi}{\PackageError{\@classname}{Option authorversion can be either true or + false}} +\ExecuteOptionsX{authorversion=false} +\define@boolkey+{acmart.cls}[@ACM@]{natbib}[true]{% + \if@ACM@natbib + \PackageInfo{\@classname}{Explicitly selecting natbib mode}% + \else + \PackageInfo{\@classname}{Explicitly deselecting natbib mode}% + \fi}{\PackageError{\@classname}{Option natbib can be either true or + false}} +\ExecuteOptionsX{natbib=true} +\define@boolkey+{acmart.cls}[@ACM@]{anonymous}[true]{% + \if@ACM@anonymous + \PackageInfo{\@classname}{Using anonymous mode}% + \else + \PackageInfo{\@classname}{Not using anonymous mode}% + \fi}{\PackageError{\@classname}{Option anonymous can be either true or + false}} +\ExecuteOptionsX{anonymous=false} +\define@boolkey+{acmart.cls}[@ACM@]{timestamp}[true]{% + \if@ACM@timestamp + \PackageInfo{\@classname}{Using timestamp mode}% + \else + \PackageInfo{\@classname}{Not using timestamp mode}% + \fi}{\PackageError{\@classname}{Option timestamp can be either true or + false}} +\ExecuteOptionsX{timestamp=false} +\define@boolkey+{acmart.cls}[@ACM@]{authordraft}[true]{% + \if@ACM@authordraft + \PackageInfo{\@classname}{Using authordraft mode}% + \@ACM@timestamptrue + \@ACM@reviewtrue + \else + \PackageInfo{\@classname}{Not using authordraft mode}% + \fi}{\PackageError{\@classname}{Option authordraft can be either true or + false}} +\ExecuteOptionsX{authordraft=false} +\def\ACM@fontsize{} +\DeclareOptionX{9pt}{\edef\ACM@fontsize{\CurrentOption}} +\DeclareOptionX{10pt}{\edef\ACM@fontsize{\CurrentOption}} +\DeclareOptionX{11pt}{\edef\ACM@fontsize{\CurrentOption}} +\DeclareOptionX{12pt}{\edef\ACM@fontsize{\CurrentOption}} +\DeclareOptionX{draft}{\PassOptionsToClass{\CurrentOption}{amsart}} +\DeclareOptionX{*}{\PassOptionsToClass{\CurrentOption}{amsart}} +\ProcessOptionsX +\ClassInfo{\@classname}{Using format \ACM@format, number \ACM@format@nr} +\newif\if@ACM@manuscript +\newif\if@ACM@journal +\newif\if@ACM@sigchiamode +\ifnum\ACM@format@nr=5\relax % siggraph + \ClassWarning{\@classname}{The format `siggraph' is now obsolete. + I am switching to sigconf.} + \setkeys{acmart.cls}{format=sigconf} +\fi +\ifnum\ACM@format@nr=0\relax + \@ACM@manuscripttrue +\else + \@ACM@manuscriptfalse +\fi +\@ACM@sigchiamodefalse +\ifcase\ACM@format@nr +\relax % manuscript + \@ACM@journaltrue +\or % acmsmall + \@ACM@journaltrue +\or % acmlarge + \@ACM@journaltrue +\or % acmtog + \@ACM@journaltrue +\or % sigconf + \@ACM@journalfalse +\or % siggraph + \@ACM@journalfalse + \or % sigplan + \@ACM@journalfalse + \or % sigchi + \@ACM@journalfalse +\or % sigchi-a + \@ACM@journalfalse + \@ACM@sigchiamodetrue +\fi +\ifx\ACM@fontsize\@empty + \ifcase\ACM@format@nr + \relax % manuscript + \def\ACM@fontsize{9pt}% + \or % acmsmall + \def\ACM@fontsize{10pt}% + \or % acmlarge + \def\ACM@fontsize{10pt}% + \or % acmtog + \def\ACM@fontsize{9pt}% + \or % sigconf + \def\ACM@fontsize{9pt}% + \or % siggraph + \def\ACM@fontsize{9pt}% + \or % sigplan + \def\ACM@fontsize{10pt}% + \or % sigchi + \def\ACM@fontsize{10pt}% + \or % sigchi-a + \def\ACM@fontsize{10pt}% + \fi +\fi +\ClassInfo{\@classname}{Using fontsize \ACM@fontsize} +\LoadClass[\ACM@fontsize, reqno]{amsart} +\RequirePackage{microtype} +\RequirePackage{etoolbox} +\RequirePackage{refcount} +\RequirePackage{totpages} +\RequirePackage{environ} +\if@ACM@manuscript +\RequirePackage{setspace} +\onehalfspacing +\fi +\RequirePackage{textcase} +\if@ACM@natbib + \RequirePackage{natbib} + \renewcommand{\bibsection}{% + \section*{\refname}% + \phantomsection\addcontentsline{toc}{section}{\refname}% + } + \renewcommand{\bibfont}{\bibliofont} + \renewcommand\setcitestyle[1]{ + \@for\@tempa:=#1\do + {\def\@tempb{round}\ifx\@tempa\@tempb + \renewcommand\NAT@open{(}\renewcommand\NAT@close{)}\fi + \def\@tempb{square}\ifx\@tempa\@tempb + \renewcommand\NAT@open{[}\renewcommand\NAT@close{]}\fi + \def\@tempb{angle}\ifx\@tempa\@tempb + \renewcommand\NAT@open{$<$}\renewcommand\NAT@close{$>$}\fi + \def\@tempb{curly}\ifx\@tempa\@tempb + \renewcommand\NAT@open{\{}\renewcommand\NAT@close{\}}\fi + \def\@tempb{semicolon}\ifx\@tempa\@tempb + \renewcommand\NAT@sep{;}\fi + \def\@tempb{colon}\ifx\@tempa\@tempb + \renewcommand\NAT@sep{;}\fi + \def\@tempb{comma}\ifx\@tempa\@tempb + \renewcommand\NAT@sep{,}\fi + \def\@tempb{authoryear}\ifx\@tempa\@tempb + \NAT@numbersfalse\fi + \def\@tempb{numbers}\ifx\@tempa\@tempb + \NAT@numberstrue\NAT@superfalse\fi + \def\@tempb{super}\ifx\@tempa\@tempb + \NAT@numberstrue\NAT@supertrue\fi + \def\@tempb{nobibstyle}\ifx\@tempa\@tempb + \let\bibstyle=\@gobble\fi + \def\@tempb{bibstyle}\ifx\@tempa\@tempb + \let\bibstyle=\@citestyle\fi + \def\@tempb{sort}\ifx\@tempa\@tempb + \def\NAT@sort{\@ne}\fi + \def\@tempb{nosort}\ifx\@tempa\@tempb + \def\NAT@sort{\z@}\fi + \def\@tempb{compress}\ifx\@tempa\@tempb + \def\NAT@cmprs{\@ne}\fi + \def\@tempb{nocompress}\ifx\@tempa\@tempb + \def\NAT@cmprs{\@z}\fi + \def\@tempb{sort&compress}\ifx\@tempa\@tempb + \def\NAT@sort{\@ne}\def\NAT@cmprs{\@ne}\fi + \def\@tempb{mcite}\ifx\@tempa\@tempb + \let\NAT@merge\@ne\fi + \def\@tempb{merge}\ifx\@tempa\@tempb + \@ifnum{\NAT@merge<\tw@}{\let\NAT@merge\tw@}{}\fi + \def\@tempb{elide}\ifx\@tempa\@tempb + \@ifnum{\NAT@merge<\thr@@}{\let\NAT@merge\thr@@}{}\fi + \def\@tempb{longnamesfirst}\ifx\@tempa\@tempb + \NAT@longnamestrue\fi + \def\@tempb{nonamebreak}\ifx\@tempa\@tempb + \def\NAT@nmfmt#1{\mbox{\NAT@up#1}}\fi + \expandafter\NAT@find@eq\@tempa=\relax\@nil + \if\@tempc\relax\else + \expandafter\NAT@rem@eq\@tempc + \def\@tempb{open}\ifx\@tempa\@tempb + \xdef\NAT@open{\@tempc}\fi + \def\@tempb{close}\ifx\@tempa\@tempb + \xdef\NAT@close{\@tempc}\fi + \def\@tempb{aysep}\ifx\@tempa\@tempb + \xdef\NAT@aysep{\@tempc}\fi + \def\@tempb{yysep}\ifx\@tempa\@tempb + \xdef\NAT@yrsep{\@tempc}\fi + \def\@tempb{notesep}\ifx\@tempa\@tempb + \xdef\NAT@cmt{\@tempc}\fi + \def\@tempb{citesep}\ifx\@tempa\@tempb + \xdef\NAT@sep{\@tempc}\fi + \fi + }% + \NAT@@setcites + } + \renewcommand\citestyle[1]{% + \ifcsname bibstyle@#1\endcsname% + \csname bibstyle@#1\endcsname\let\bibstyle\@gobble% + \else% + \@latex@error{Undefined `#1' citestyle}% + \fi + }% +\fi +\newcommand{\bibstyle@acmauthoryear}{% + \setcitestyle{% + authoryear,% + open={[},close={]},citesep={;},% + aysep={},yysep={,},% + notesep={, }}} +\newcommand{\bibstyle@acmnumeric}{% + \setcitestyle{% + numbers,sort&compress,% + open={[},close={]},citesep={,},% + notesep={, }}} +\if@ACM@natbib +\citestyle{acmnumeric} +\fi +\def\@startsection#1#2#3#4#5#6{% + \if@noskipsec \leavevmode \fi + \par + \@tempskipa #4\relax + \@afterindenttrue + \ifdim \@tempskipa <\z@ + \@tempskipa -\@tempskipa \@afterindentfalse + \fi + \if@nobreak + \everypar{}% + \else + \addpenalty\@secpenalty\addvspace\@tempskipa + \fi + \@ifstar + {\@ssect{#3}{#4}{#5}{#6}}% + {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}} +\def\@sect#1#2#3#4#5#6[#7]#8{% + \edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}% + \ifnum #2>\c@secnumdepth + \let\@svsec\@empty + \else + \refstepcounter{#1}% + \protected@edef\@svsec{\@seccntformat{#1}\relax}% + \fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup + #6{% + \@hangfrom{\hskip #3\relax\@svsec}% + \interlinepenalty \@M #8\@@par}% + \endgroup + \csname #1mark\endcsname{#7}% + \ifnum #2>\c@secnumdepth \else + \@tochangmeasure{\csname the#1\endcsname}% + \fi + \addcontentsline{toc}{#1}{% + \ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}% + \fi + #7}% + \else + \def\@svsechd{% + #6{\hskip #3\relax + \@svsec #8}% + \csname #1mark\endcsname{#7}% + \ifnum #2>\c@secnumdepth \else + \@tochangmeasure{\csname the#1\endcsname\space}% + \fi + \addcontentsline{toc}{#1}{% + \ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}% + \fi + #7}}% + \fi + \@xsect{#5}} +\def\@xsect#1{% + \@tempskipa #1\relax + \ifdim \@tempskipa>\z@ + \par \nobreak + \vskip \@tempskipa + \@afterheading + \else + \@nobreakfalse + \global\@noskipsectrue + \everypar{% + \if@noskipsec + \global\@noskipsecfalse + {\setbox\z@\lastbox}% + \clubpenalty\@M + \begingroup \@svsechd \endgroup + \unskip + \@tempskipa #1\relax + \hskip -\@tempskipa + \else + \clubpenalty \@clubpenalty + \everypar{}% + \fi}% + \fi + \ignorespaces} +\def\@seccntformat#1{\csname the#1\endcsname\quad} +\def\@ssect#1#2#3#4#5{% + \@tempskipa #3\relax + \ifdim \@tempskipa>\z@ + \begingroup + #4{% + \@hangfrom{\hskip #1}% + \interlinepenalty \@M #5\@@par}% + \endgroup + \else + \def\@svsechd{#4{\hskip #1\relax #5}}% + \fi + \@xsect{#3}} +\def\@starttoc#1#2{\begingroup\makeatletter + \setTrue{#1}% + \par\removelastskip\vskip\z@skip + \@startsection{section}\@M\z@{\linespacing\@plus\linespacing}% + {.5\linespacing}{\centering\contentsnamefont}{#2}% + \@input{\jobname.#1}% + \if@filesw + \@xp\newwrite\csname tf@#1\endcsname + \immediate\@xp\openout\csname tf@#1\endcsname \jobname.#1\relax + \fi + \global\@nobreakfalse \endgroup + \addvspace{32\p@\@plus14\p@}% +} +\def\l@section{\@tocline{1}{0pt}{1pc}{2pc}{}} +\def\l@subsection{\@tocline{2}{0pt}{1pc}{3pc}{}} +\def\l@subsubsection{\@tocline{2}{0pt}{1pc}{5pc}{}} +\let\@footnotemark@nolink\@footnotemark +\let\@footnotetext@nolink\@footnotetext +\RequirePackage[bookmarksnumbered,unicode]{hyperref} +\pdfstringdefDisableCommands{% + \def\unskip{}% + \def\textbullet{- }% + \def\textrightarrow{ -> }% + \def\footnotemark{}% +} +\urlstyle{rm} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge +\or % acmtog +\or % sigconf +\or % siggraph +\or % sigplan + \urlstyle{sf} +\or % sigchi +\or % sigchi-a + \urlstyle{sf} +\fi +\AtEndPreamble{% + \if@ACM@screen + \hypersetup{colorlinks, + linkcolor=ACMRed, + citecolor=ACMPurple, + urlcolor=ACMDarkBlue, + filecolor=ACMDarkBlue} + \else + \hypersetup{hidelinks} + \fi} +\if@ACM@natbib + \let\citeN\cite + \let\cite\citep + \let\citeANP\citeauthor + \let\citeNN\citeyearpar + \let\citeyearNP\citeyear + \let\citeyear\citeyearpar + \let\citeNP\citealt + \DeclareRobustCommand\citeA + {\begingroup\NAT@swafalse + \let\NAT@ctype\@ne\NAT@partrue\NAT@fullfalse\NAT@open\NAT@citetp}% + \providecommand\newblock{}% +\else + \AtBeginDocument{% + \let\shortcite\cite% + \providecommand\citename[1]{#1}} +\fi +\newcommand\shortcite[2][]{% + \ifNAT@numbers\cite[#1]{#2}\else\citeyear[#1]{#2}\fi} +\def\bibliographystyle#1{% + \ifx\@begindocumenthook\@undefined\else + \expandafter\AtBeginDocument + \fi + {\if@filesw + \immediate\write\@auxout{\string\bibstyle{#1}}% + \fi}} +\RequirePackage{graphicx, xcolor} +\definecolor[named]{ACMBlue}{cmyk}{1,0.1,0,0.1} +\definecolor[named]{ACMYellow}{cmyk}{0,0.16,1,0} +\definecolor[named]{ACMOrange}{cmyk}{0,0.42,1,0.01} +\definecolor[named]{ACMRed}{cmyk}{0,0.90,0.86,0} +\definecolor[named]{ACMLightBlue}{cmyk}{0.49,0.01,0,0} +\definecolor[named]{ACMGreen}{cmyk}{0.20,0,1,0.19} +\definecolor[named]{ACMPurple}{cmyk}{0.55,1,0,0.15} +\definecolor[named]{ACMDarkBlue}{cmyk}{1,0.58,0,0.21} +\if@ACM@authordraft + \RequirePackage{draftwatermark} + \SetWatermarkFontSize{0.5in} + \SetWatermarkColor[gray]{.9} + \SetWatermarkText{\parbox{12em}{\centering + Unpublished working draft\\ + Not for distribution}} +\fi +\RequirePackage{geometry} +\ifcase\ACM@format@nr +\relax % manuscript + \geometry{letterpaper,head=13pt, + marginparwidth=6pc,heightrounded}% +\or % acmsmall + \geometry{twoside=true, + includeheadfoot, head=13pt, foot=2pc, + paperwidth=6.75in, paperheight=10in, + top=58pt, bottom=44pt, inner=46pt, outer=46pt, + marginparwidth=2pc,heightrounded + }% +\or % acmlarge + \geometry{twoside=true, head=13pt, foot=2pc, + paperwidth=8.5in, paperheight=11in, + includeheadfoot, + top=78pt, bottom=114pt, inner=81pt, outer=81pt, + marginparwidth=4pc,heightrounded + }% +\or % acmtog + \geometry{twoside=true, head=13pt, foot=2pc, + paperwidth=8.5in, paperheight=11in, + includeheadfoot, columnsep=24pt, + top=52pt, bottom=75pt, inner=52pt, outer=52pt, + marginparwidth=2pc,heightrounded + }% +\or % sigconf + \geometry{twoside=true, head=13pt, + paperwidth=8.5in, paperheight=11in, + includeheadfoot, columnsep=2pc, + top=57pt, bottom=73pt, inner=54pt, outer=54pt, + marginparwidth=2pc,heightrounded + }% +\or % siggraph + \geometry{twoside=true, head=13pt, + paperwidth=8.5in, paperheight=11in, + includeheadfoot, columnsep=2pc, + top=57pt, bottom=73pt, inner=54pt, outer=54pt, + marginparwidth=2pc,heightrounded + }% +\or % sigplan + \geometry{twoside=true, head=13pt, + paperwidth=8.5in, paperheight=11in, + includeheadfoot=false, columnsep=2pc, + top=1in, bottom=1in, inner=0.75in, outer=0.75in, + marginparwidth=2pc,heightrounded + }% +\or % sigchi + \geometry{twoside=true, head=13pt, + paperwidth=8.5in, paperheight=11in, + includeheadfoot, columnsep=2pc, + top=66pt, bottom=73pt, inner=54pt, outer=54pt, + marginparwidth=2pc,heightrounded + }% +\or % sigchi-a + \geometry{twoside=false, head=13pt, + paperwidth=11in, paperheight=8.5in, + includeheadfoot, marginparsep=72pt, + marginparwidth=170pt, columnsep=20pt, + top=72pt, bottom=72pt, left=314pt, right=72pt + }% + \@mparswitchfalse + \reversemarginpar +\fi +\setlength\parindent{10\p@} +\setlength\parskip{\z@} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge +\or % acmtog + \setlength\parindent{9\p@}% +\or % sigconf +\or % siggraph +\or % sigplan +\or % sigchi +\or % sigchi-a +\fi +\setlength\normalparindent{\parindent} +\def\copyrightpermissionfootnoterule{\kern-3\p@ + \hrule \@width \columnwidth \kern 2.6\p@} +\RequirePackage{manyfoot} +\SelectFootnoteRule[2]{copyrightpermission} +\DeclareNewFootnote{authorsaddresses} +\SelectFootnoteRule[2]{copyrightpermission} +\DeclareNewFootnote{copyrightpermission} +\def\footnoterule{\kern-3\p@ + \hrule \@width 4pc \kern 2.6\p@} +\def\endminipage{% + \par + \unskip + \ifvoid\@mpfootins\else + \vskip\skip\@mpfootins + \normalcolor + \unvbox\@mpfootins + \fi + \@minipagefalse %% added 24 May 89 + \color@endgroup + \egroup + \expandafter\@iiiparbox\@mpargs{\unvbox\@tempboxa}} +\def\@makefntext{\noindent\@makefnmark} +\if@ACM@sigchiamode +\long\def\@footnotetext#1{\marginpar{% + \reset@font\small + \interlinepenalty\interfootnotelinepenalty + \protected@edef\@currentlabel{% + \csname p@footnote\endcsname\@thefnmark + }% + \color@begingroup + \@makefntext{% + \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}% + \color@endgroup}}% +\fi +\long\def\@mpfootnotetext#1{% + \global\setbox\@mpfootins\vbox{% + \unvbox\@mpfootins + \reset@font\footnotesize + \hsize\columnwidth + \@parboxrestore + \protected@edef\@currentlabel + {\csname p@mpfootnote\endcsname\@thefnmark}% + \color@begingroup\centering + \@makefntext{% + \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}% + \color@endgroup}} +\def\@makefnmark{\hbox{\@textsuperscript{\normalfont\@thefnmark}}} +\def\@textbottom{\vskip \z@ \@plus 1pt} +\let\@texttop\relax +\RequirePackage{iftex} +\ifPDFTeX +\input{glyphtounicode} +\pdfglyphtounicode{f_f}{FB00} +\pdfglyphtounicode{f_f_i}{FB03} +\pdfglyphtounicode{f_f_l}{FB04} +\pdfglyphtounicode{f_i}{FB01} +\pdfglyphtounicode{t_t}{00740074} +\pdfglyphtounicode{f_t}{00660074} +\pdfglyphtounicode{T_h}{00540068} +\pdfgentounicode=1 +\fi +\RequirePackage{cmap} +\newif\if@ACM@newfonts +\@ACM@newfontstrue +\IfFileExists{libertine.sty}{}{\ClassWarning{\@classname}{You do not + have libertine package installed. Please upgrade your + TeX}\@ACM@newfontsfalse} +\IfFileExists{zi4.sty}{}{\ClassWarning{\@classname}{You do not + have zi4 package installed. Please upgrade your TeX}\@ACM@newfontsfalse} +\IfFileExists{newtxmath.sty}{}{\ClassWarning{\@classname}{You do not + have newtxmath package installed. Please upgrade your + TeX}\@ACM@newfontsfalse} +\if@ACM@newfonts +\RequirePackage[tt=false, type1=true]{libertine} +\RequirePackage[varqu]{zi4} +\RequirePackage[libertine]{newtxmath} +\RequirePackage[T1]{fontenc} +\fi +\let\liningnums\@undefined +\AtEndPreamble{% + \DeclareTextFontCommand{\liningnums}{\libertineLF}} +\if@ACM@sigchiamode + \renewcommand{\familydefault}{\sfdefault} +\fi +\RequirePackage{caption, float} +\captionsetup[table]{position=top} +\if@ACM@journal + \captionsetup{labelfont={sf, small}, + textfont={sf, small}, margin=\z@} + \captionsetup[figure]{name={Fig.}} +\else + \captionsetup{labelfont={bf}, + textfont={bf}, labelsep=colon, margin=\z@} + \ifcase\ACM@format@nr + \relax % manuscript + \or % acmsmall + \or % acmlarge + \or % acmtog + \or % sigconf + \or % siggraph + \captionsetup{textfont={it}} + \or % sigplan + \captionsetup{labelfont={bf}, + textfont={normalfont}, labelsep=period, margin=\z@} + \or % sigchi + \captionsetup[figure]{labelfont={bf, small}, + textfont={bf, small}} + \or % sigchi-a + \captionsetup[figure]{labelfont={bf, small}, + textfont={bf, small}} + \fi +\fi +\newfloat{sidebar}{}{sbar} +\floatname{sidebar}{Sidebar} +\renewenvironment{sidebar}{\Collect@Body\@sidebar}{} +\long\def\@sidebar#1{\bgroup\captionsetup{type=sidebar}% + \marginpar{\small#1}\egroup} +\newenvironment{marginfigure}{\Collect@Body\@marginfigure}{} +\long\def\@marginfigure#1{\bgroup\captionsetup{type=figure}% + \marginpar{\centering\small#1}\egroup} +\newenvironment{margintable}{\Collect@Body\@margintable}{} +\long\def\@margintable#1{\bgroup\captionsetup{type=table}% + \marginpar{\centering\small#1}\egroup} +\newdimen\fulltextwidth +\fulltextwidth=\dimexpr(\textwidth+\marginparwidth+\marginparsep) +\if@ACM@sigchiamode +\def\@dblfloat{\bgroup\columnwidth=\fulltextwidth + \let\@endfloatbox\@endwidefloatbox + \def\@fpsadddefault{\def\@fps{tp}}% + \@float} +\fi +\if@ACM@sigchiamode +\def\end@dblfloat{% + \end@float\egroup} +\fi +\def\@endwidefloatbox{% + \par\vskip\z@skip + \@minipagefalse + \outer@nobreak + \egroup + \color@endbox + \global\setbox\@currbox=\vbox{\moveleft + \dimexpr(\fulltextwidth-\textwidth)\box\@currbox}% + \wd\@currbox=\textwidth +} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge +\or % acmtog +\or % sigconf +\or % siggraph +\or % sigplan +\def\labelenumi{\theenumi.} +\def\labelenumii{\theenumii.} +\def\labelenumiii{\theenumiii.} +\def\labelenumiv{\theenumiv.} +\or % sigchi +\or % sigchi-a +\fi +\newdimen\@ACM@labelwidth +\AtBeginDocument{% + \setlength\labelsep{4pt} + \setlength{\@ACM@labelwidth}{6.5pt} + + %% First-level list: when beginning after the first line of an + %% indented paragraph or ending before an indented paragraph, labels + %% should not hang to the left of the preceding/following text. + \setlength\leftmargini{\z@} + \addtolength\leftmargini{\parindent} + \addtolength\leftmargini{2\labelsep} + \addtolength\leftmargini{\@ACM@labelwidth} + + %% Second-level and higher lists. + \setlength\leftmarginii{\z@} + \addtolength\leftmarginii{0.5\labelsep} + \addtolength\leftmarginii{\@ACM@labelwidth} + \setlength\leftmarginiii{\leftmarginii} + \setlength\leftmarginiv{\leftmarginiii} + \setlength\leftmarginv{\leftmarginiv} + \setlength\leftmarginvi{\leftmarginv} + \@listi} +\newskip\listisep +\listisep\smallskipamount +\def\@listI{\leftmargin\leftmargini + \labelwidth\leftmargini \advance\labelwidth-\labelsep + \listparindent\z@ + \topsep\listisep} +\let\@listi\@listI +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii \advance\labelwidth-\labelsep + \topsep\z@skip} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii \advance\labelwidth-\labelsep} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\leftmarginiv \advance\labelwidth-\labelsep} +\def\@listv{\leftmargin\leftmarginv + \labelwidth\leftmarginv \advance\labelwidth-\labelsep} +\def\@listvi{\leftmargin\leftmarginvi + \labelwidth\leftmarginvi \advance\labelwidth-\labelsep} +\renewcommand{\descriptionlabel}[1]{\upshape\bfseries #1} +\renewenvironment{description}{\list{}{% + \labelwidth\@ACM@labelwidth + \let\makelabel\descriptionlabel}% +}{ + \endlist +} +\let\enddescription=\endlist % for efficiency +\define@choicekey*+{ACM}{acmJournal}[\@journalCode\@journalCode@nr]{% + CIE,% + CSUR,% + IMWUT,% + JACM,% + JDIQ,% + JEA,% + JERIC,% + JETC,% + JOCCH,% + PACMHCI,% + PACMPL,% + POMACS,% + TAAS,% + TACCESS,% + TACO,% + TALG,% + TALLIP,% + TAP,% + TCPS,% + TEAC,% + TECS,% + THRI,% + TIIS,% + TISSEC,% + TIST,% + TKDD,% + TMIS,% + TOCE,% + TOCHI,% + TOCL,% + TOCS,% + TOCT,% + TODAES,% + TODS,% + TOG,% + TOIS,% + TOIT,% + TOMACS,% + TOMM,% + TOMPECS,% + TOMS,% + TOPC,% + TOPS,% + TOPLAS,% + TOS,% + TOSEM,% + TOSN,% + TRETS,% + TSAS,% + TSC,% + TSLP,% + TWEB% +}{% +\ifcase\@journalCode@nr +\relax % CIE + \def\@journalName{ACM Computers in Entertainment}% + \def\@journalNameShort{ACM Comput. Entertain.}% + \def\@permissionCodeOne{1544-3574}% +\or % CSUR + \def\@journalName{ACM Computing Surveys}% + \def\@journalNameShort{ACM Comput. Surv.}% + \def\@permissionCodeOne{0360-0300}% +\or % IMWUT + \def\@journalName{Proceedings of the ACM on Interactive, Mobile, + Wearable and Ubiquitous Technologies}% + \def\@journalNameShort{Proc. ACM Interact. Mob. Wearable Ubiquitous Technol.}% + \def\@permissionCodeOne{2474-9567}% + \@ACM@screentrue + \PackageInfo{\@classname}{Using screen mode due to \@journalCode}% +\or % JACM + \def\@journalName{Journal of the ACM}% + \def\@journalNameShort{J. ACM}% + \def\@permissionCodeOne{0004-5411}% +\or % JDIQ + \def\@journalName{ACM Journal of Data and Information Quality}% + \def\@journalNameShort{ACM J. Data Inform. Quality}% + \def\@permissionCodeOne{1936-1955}% +\or % JEA + \def\@journalName{ACM Journal of Experimental Algorithmics}% + \def\@journalNameShort{ACM J. Exp. Algor.}% + \def\@permissionCodeOne{1084-6654}% +\or % JERIC + \def\@journalName{ACM Journal of Educational Resources in Computing}% + \def\@journalNameShort{ACM J. Edu. Resources in Comput.}% + \def\@permissionCodeOne{1073-0516}% +\or % JETC + \def\@journalName{ACM Journal on Emerging Technologies in Computing Systems}% + \def\@journalNameShort{ACM J. Emerg. Technol. Comput. Syst.}% + \def\@permissionCodeOne{1550-4832}% +\or % JOCCH + \def\@journalName{ACM Journal on Computing and Cultural Heritage}% + \def\@journalName{ACM J. Comput. Cult. Herit.}% +\or % PACMHCI + \def\@journalName{Proceedings of the ACM on Human-Computer Interaction}% + \def\@journalName{Proc. ACM Hum.-Comput. Interact.}% + \def\@permissionCodeOne{2573-0142}% + \@ACM@screentrue + \PackageInfo{\@classname}{Using screen mode due to \@journalCode}% +\or % PACMPL + \def\@journalName{Proceedings of the ACM on Programming Languages}% + \def\@journalName{Proc. ACM Program. Lang.}% + \def\@permissionCodeOne{2475-1421}% + \@ACM@screentrue + \PackageInfo{\@classname}{Using screen mode due to \@journalCode}% +\or % POMACS + \def\@journalName{Proceedings of the ACM on Measurement and Analysis of Computing Systems}% + \def\@journalName{Proc. ACM Meas. Anal. Comput. Syst.}% + \def\@permissionCodeOne{2476-1249}% + \@ACM@screentrue + \PackageInfo{\@classname}{Using screen mode due to \@journalCode}% +\or % TAAS + \def\@journalName{ACM Transactions on Autonomous and Adaptive Systems}% + \def\@journalNameShort{ACM Trans. Autonom. Adapt. Syst.}% + \def\@permissionCodeOne{1556-4665}% +\or % TACCESS + \def\@journalName{ACM Transactions on Accessible Computing}% + \def\@journalNameShort{ACM Trans. Access. Comput.}% + \def\@permissionCodeOne{1936-7228}% +\or % TACO + \def\@journalName{ACM Transactions on Architecture and Code Optimization}% +\or % TALG + \def\@journalName{ACM Transactions on Algorithms}% + \def\@journalNameShort{ACM Trans. Algor.}% + \def\@permissionCodeOne{1549-6325}% +\or % TALLIP + \def\@journalName{ACM Transactions on Asian and Low-Resource Language Information Processing}% + \def\@journalNameShort{ACM Trans. Asian Low-Resour. Lang. Inf. Process.}% + \def\@permissionCodeOne{2375-4699}% +\or % TAP + \def\@journalName{ACM Transactions on Applied Perception}% +\or % TCPS + \def\@journalName{ACM Transactions on Cyber-Physical Systems}% +\or % TEAC + \def\@journalName{ACM Transactions on Economics and Computation}% +\or % TECS + \def\@journalName{ACM Transactions on Embedded Computing Systems}% + \def\@journalNameShort{ACM Trans. Embedd. Comput. Syst.}% + \def\@permissionCodeOne{1539-9087}% +\or % THRI + \def\@journalName{ACM Transactions on Human-Robot Interaction}% + \def\@journalNameShort{ACM Trans. Hum.-Robot Interact.}% + \def\@permissionCodeOne{2573-9522}% +\or % TIIS + \def\@journalName{ACM Transactions on Interactive Intelligent Systems}% + \def\@journalNameShort{ACM Trans. Interact. Intell. Syst.}% + \def\@permissionCodeOne{2160-6455}% +\or % TISSEC + \def\@journalName{ACM Transactions on Information and System Security}% + \def\@journalNameShort{ACM Trans. Info. Syst. Sec.}% + \def\@permissionCodeOne{1094-9224}% +\or % TIST + \def\@journalName{ACM Transactions on Intelligent Systems and Technology}% + \def\@journalNameShort{ACM Trans. Intell. Syst. Technol.}% + \def\@permissionCodeOne{2157-6904}% +\or % TKDD + \def\@journalName{ACM Transactions on Knowledge Discovery from Data}% + \def\@journalNameShort{ACM Trans. Knowl. Discov. Data.}% + \def\@permissionCodeOne{1556-4681}% +\or % TMIS + \def\@journalName{ACM Transactions on Management Information Systems}% + \def\@journalNameShort{ACM Trans. Manag. Inform. Syst.}% + \def\@permissionCodeOne{2158-656X}% +\or % TOCE + \def\@journalName{ACM Transactions on Computing Education}% + \def\@journalNameShort{ACM Trans. Comput. Educ.}% + \def\@permissionCodeOne{1946-6226}% +\or % TOCHI + \def\@journalName{ACM Transactions on Computer-Human Interaction}% + \def\@journalNameShort{ACM Trans. Comput.-Hum. Interact.}% + \def\@permissionCodeOne{1073-0516}% +\or % TOCL + \def\@journalName{ACM Transactions on Computational Logic}% + \def\@journalNameShort{ACM Trans. Comput. Logic}% + \def\@permissionCodeOne{1529-3785}% +\or % TOCS + \def\@journalName{ACM Transactions on Computer Systems}% + \def\@journalNameShort{ACM Trans. Comput. Syst.}% + \def\@permissionCodeOne{0734-2071}% +\or % TOCT + \def\@journalName{ACM Transactions on Computation Theory}% + \def\@journalNameShort{ACM Trans. Comput. Theory}% + \def\@permissionCodeOne{1942-3454}% +\or % TODAES + \def\@journalName{ACM Transactions on Design Automation of Electronic Systems}% + \def\@journalNameShort{ACM Trans. Des. Autom. Electron. Syst.}% + \def\@permissionCodeOne{1084-4309}% +\or % TODS + \def\@journalName{ACM Transactions on Database Systems}% + \def\@journalNameShort{ACM Trans. Datab. Syst.}% + \def\@permissionCodeOne{0362-5915}% +\or % TOG + \def\@journalName{ACM Transactions on Graphics}% + \def\@journalNameShort{ACM Trans. Graph.}% + \def\@permissionCodeOne{0730-0301} +\or % TOIS + \def\@journalName{ACM Transactions on Information Systems}% + \def\@journalName{ACM Transactions on Information Systems}% + \def\@permissionCodeOne{1046-8188}% +\or % TOIT + \def\@journalName{ACM Transactions on Internet Technology}% + \def\@journalNameShort{ACM Trans. Internet Technol.}% + \def\@permissionCodeOne{1533-5399}% +\or % TOMACS + \def\@journalName{ACM Transactions on Modeling and Computer Simulation}% + \def\@journalName{ACM Transactions on Modeling and Computer Simulation}% + \def\@journalNameShort{ACM Trans. Model. Comput. Simul.}% +\or % TOMM + \def\@journalName{ACM Transactions on Multimedia Computing, Communications and Applications}% + \def\@journalNameShort{ACM Trans. Multimedia Comput. Commun. Appl.}% + \def\@permissionCodeOne{1551-6857}% + \def\@permissionCodeTwo{0100}% +\or % TOMPECS + \def\@journalName{ACM Transactions on Modeling and Performance Evaluation of Computing Systems}% + \def\@journalNameShort{ACM Trans. Model. Perform. Eval. Comput. Syst.}% + \def\@permissionCodeOne{2376-3639}% +\or % TOMS + \def\@journalName{ACM Transactions on Mathematical Software}% + \def\@journalNameShort{ACM Trans. Math. Softw.}% + \def\@permissionCodeOne{0098-3500}% +\or % TOPC + \def\@journalName{ACM Transactions on Parallel Computing}% + \def\@journalNameShort{ACM Trans. Parallel Comput.}% + \def\@permissionCodeOne{1539-9087}% +\or % TOPS + \def\@journalName{ACM Transactions on Privacy and Security}% + \def\@journalNameShort{ACM Trans. Priv. Sec.}% + \def\@permissionCodeOne{2471-2566}% +\or % TOPLAS + \def\@journalName{ACM Transactions on Programming Languages and Systems}% + \def\@journalNameShort{ACM Trans. Program. Lang. Syst.}% + \def\@permissionCodeOne{0164-0925}% +\or % TOS + \def\@journalName{ACM Transactions on Storage}% + \def\@journalNameShort{ACM Trans. Storage}% + \def\@permissionCodeOne{1553-3077}% +\or % TOSEM + \def\@journalName{ACM Transactions on Software Engineering and Methodology}% + \def\@journalNameShort{ACM Trans. Softw. Eng. Methodol.}% + \def\@permissionCodeOne{1049-331X}% +\or % TOSN + \def\@journalName{ACM Transactions on Sensor Networks}% + \def\@journalNameShort{ACM Trans. Sensor Netw.}% + \def\@permissionCodeOne{1550-4859}% +\or % TRETS + \def\@journalName{ACM Transactions on Reconfigurable Technology and Systems}% + \def\@journalNameShort{ACM Trans. Reconfig. Technol. Syst.}% + \def\@permissionCodeOne{1936-7406}% +\or % TSAS + \def\@journalName{ACM Transactions on Spatial Algorithms and Systems}% + \def\@journalNameShort{ACM Trans. Spatial Algorithms Syst.}% + \def\@permissionCodeOne{2374-0353}% +\or % TSC + \def\@journalName{ACM Transactions on Social Computing}% + \def\@journalNameShort{ACM Trans. Soc. Comput.}% + \def\@permissionCodeOne{2469-7818}% +\or % TSLP + \def\@journalName{ACM Transactions on Speech and Language Processing}% + \def\@journalNameShort{ACM Trans. Speech Lang. Process.}% + \def\@permissionCodeOne{1550-4875}% +\or % TWEB + \def\@journalName{ACM Transactions on the Web}% + \def\@journalNameShort{ACM Trans. Web}% + \def\@permissionCodeOne{1559-1131}% +\fi +\ClassInfo{\@classname}{Using journal code \@journalCode}% +}{% + \ClassError{\@classname}{Incorrect journal #1}% +}% +\def\acmJournal#1{\setkeys{ACM}{acmJournal=#1}} +\def\@journalCode@nr{0} +\def\@journalName{}% +\def\@journalNameShort{\@journalName}% +\def\@permissionCodeOne{XXXX-XXXX}% +\def\@permissionCodeTwo{}% +\newcommand\acmConference[4][]{% + \gdef\acmConference@shortname{#1}% + \gdef\acmConference@name{#2}% + \gdef\acmConference@date{#3}% + \gdef\acmConference@venue{#4}% + \ifx\acmConference@shortname\@empty + \gdef\acmConference@shortname{#2}% + \fi} +\acmConference[Conference'17]{ACM Conference}{July 2017}{Washington, + DC, USA} +\def\acmBooktitle#1{\gdef\@acmBooktitle{#1}} +\acmBooktitle{Proceedings of \acmConference@name + \ifx\acmConference@name\acmConference@shortname\else + \ (\acmConference@shortname)\fi} +\def\@editorsAbbrev{(Ed.)} +\def\@acmEditors{} +\def\editor#1{\ifx\@acmEditors\@empty + \gdef\@acmEditors{#1}% + \else + \gdef\@editorsAbbrev{(Eds.)}% + \g@addto@macro\@acmEditors{\and#1}% +\fi} +\def\subtitle#1{\def\@subtitle{#1}} +\subtitle{} +\newcount\num@authorgroups +\num@authorgroups=0\relax +\newcount\num@authors +\num@authors=0\relax +\newif\if@insideauthorgroup +\@insideauthorgroupfalse +\renewcommand\author[2][]{% + \global\advance\num@authors by 1\relax + \if@insideauthorgroup\else + \global\advance\num@authorgroups by 1\relax + \global\@insideauthorgrouptrue + \fi + \ifx\addresses\@empty + \if@ACM@anonymous + \gdef\addresses{\@author{Anonymous Author(s)}}% + \gdef\authors{Anonymous Author(s)}% + \else + \gdef\addresses{\@author{#2}}% + \gdef\authors{#2}% + \fi + \else + \if@ACM@anonymous\else + \g@addto@macro\addresses{\and\@author{#2}}% + \g@addto@macro\authors{\and#2}% + \fi + \fi + \if@ACM@anonymous + \ifx\shortauthors\@empty + \gdef\shortauthors{Anon.}% + \fi + \else + \def\@tempa{#1}% + \ifx\@tempa\@empty + \ifx\shortauthors\@empty + \gdef\shortauthors{#2}% + \else + \g@addto@macro\shortauthors{\and#2}% + \fi + \else + \ifx\shortauthors\@empty + \gdef\shortauthors{#1}% + \else + \g@addto@macro\shortauthors{\and#1}% + \fi + \fi + \fi} +\newcommand{\affiliation}[2][]{% + \global\@insideauthorgroupfalse + \if@ACM@anonymous\else + \g@addto@macro\addresses{\affiliation{#1}{#2}}% + \fi} +\define@boolkey+{@ACM@affiliation@}[@ACM@affiliation@]{obeypunctuation}% +[true]{}{\ClassError{\@classname}{obeypunctuation must be true or false}} +\def\additionalaffiliation#1{\authornote{\@additionalaffiliation{#1}}} +\def\@additionalaffiliation#1{\bgroup + \def\position##1{\ignorespaces}% + \def\institution##1{##1\ignorespaces}% + \def\department{\@ifnextchar[{\@department}{\@department[]}}% + \def\@department[##1]##2{\unskip, ##2\ignorespaces}% + \let\streetaddress\position + \let\city\position + \let\state\position + \let\postcode\position + \let\country\position + Also with #1\unskip.\egroup} +\renewcommand{\email}[2][]{% + \if@ACM@anonymous\else + \g@addto@macro\addresses{\email{#1}{#2}}% + \fi} +\def\orcid#1{\unskip\ignorespaces} +\def\authorsaddresses#1{\def\@authorsaddresses{#1}} +\authorsaddresses{\@mkauthorsaddresses} +\def\@titlenotes{} +\def\titlenote#1{% + \g@addto@macro\@title{\footnotemark}% + \if@ACM@anonymous + \g@addto@macro\@titlenotes{% + \stepcounter{footnote}\footnotetext{Title note}}% + \else + \g@addto@macro\@titlenotes{\stepcounter{footnote}\footnotetext{#1}}% + \fi} +\def\@subtitlenotes{} +\def\subtitlenote#1{% + \g@addto@macro\@subtitle{\footnotemark}% + \if@ACM@anonymous + \g@addto@macro\@subtitlenotes{% + \stepcounter{footnote}\footnotetext{Subtitle note}}% + \else + \g@addto@macro\@subtitlenotes{% + \stepcounter{footnote}\footnotetext{#1}}% + \fi} +\def\@authornotes{} +\def\authornote#1{% + \if@ACM@anonymous\else + \g@addto@macro\addresses{\@authornotemark}% + \g@addto@macro\@authornotes{% + \stepcounter{footnote}\footnotetext{#1}}% + \fi} +\newcommand\authornotemark[1][\relax]{% + \ifx#1\relax\relax\relax + \g@addto@macro\addresses{\@authornotemark}% + \else + \g@addto@macro\addresses{\@@authornotemark{#1}}% + \fi} +\def\acmVolume#1{\def\@acmVolume{#1}} +\acmVolume{1} +\def\acmNumber#1{\def\@acmNumber{#1}} +\acmNumber{1} +\def\acmArticle#1{\def\@acmArticle{#1}} +\acmArticle{} +\def\acmArticleSeq#1{\def\@acmArticleSeq{#1}} +\acmArticleSeq{\@acmArticle} +\def\acmYear#1{\def\@acmYear{#1}} +\acmYear{\the\year} +\def\acmMonth#1{\def\@acmMonth{#1}} +\acmMonth{\the\month} +\def\@acmPubDate{\ifcase\@acmMonth\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or + December\fi~\@acmYear} +\def\acmPrice#1{\def\@acmPrice{#1}} +\acmPrice{15.00} +\def\acmSubmissionID#1{\def\@acmSubmissionID{#1}} +\acmSubmissionID{} +\def\acmISBN#1{\def\@acmISBN{#1}} +\acmISBN{978-x-xxxx-xxxx-x/YY/MM} +\def\acmDOI#1{\def\@acmDOI{#1}} +\acmDOI{10.1145/nnnnnnn.nnnnnnn} +\newif\if@ACM@badge +\@ACM@badgefalse +\newlength\@ACM@badge@width +\setlength\@ACM@badge@width{5pc} +\newlength\@ACM@title@width +\newlength\@ACM@badge@skip +\setlength\@ACM@badge@skip{1pc} +\newcommand\acmBadgeR[2][]{\@ACM@badgetrue + \def\@acmBadgeR@url{#1}% + \def\@acmBadgeR@image{#2}} +\def\@acmBadgeR@url{} +\def\@acmBadgeR@image{} +\newcommand\acmBadgeL[2][]{\@ACM@badgetrue + \def\@acmBadgeL@url{#1}% + \def\@acmBadgeL@image{#2}} +\def\@acmBadgeL@url{} +\def\@acmBadgeL@image{} +\def\startPage#1{\def\@startPage{#1}} +\startPage{} +\def\terms#1{\ClassWarning{\@classname}{The command \string\terms{} is + obsolete. I am going to ignore it}} +\def\keywords#1{\def\@keywords{#1}} +\keywords{} +\renewenvironment{abstract}{\Collect@Body\@saveabstract}{} +\long\def\@saveabstract#1{\long\gdef\@abstract{#1}} +\@saveabstract{} +\long\def\@lempty{} +\define@boolkey+{@ACM@topmatter@}[@ACM@]{printccs}[true]{% + \if@ACM@printccs + \ClassInfo{\@classname}{Printing CCS}% + \else + \ClassInfo{\@classname}{Suppressing CCS}% + \fi}{\ClassError{\@classname}{printccs must be true or false}} +\define@boolkey+{@ACM@topmatter@}[@ACM@]{printacmref}[true]{% + \if@ACM@printacmref + \ClassInfo{\@classname}{Printing bibformat}% + \else + \ClassInfo{\@classname}{Suppressing bibformat}% + \fi}{\ClassError{\@classname}{printacmref must be true or false}} +\define@boolkey+{@ACM@topmatter@}[@ACM@]{printfolios}[true]{% + \if@ACM@printfolios + \ClassInfo{\@classname}{Printing folios}% + \else + \ClassInfo{\@classname}{Suppressing folios}% + \fi}{\ClassError{\@classname}{printfolios must be true or false}} +\define@cmdkey{@ACM@topmatter@}[@ACM@]{authorsperrow}[0]{% + \IfInteger{#1}{\ClassInfo{\@classname}{Setting authorsperrow to + #1}}{\ClassWarning{\@classname}{Parameter authorsperrow must be + numerical. Ignoring the input #1}\gdef\@ACM@authorsperrow{0}}} +\def\settopmatter#1{\setkeys{@ACM@topmatter@}{#1}} +\settopmatter{printccs=true, printacmref=true} +\if@ACM@manuscript + \settopmatter{printfolios=true} +\else + \if@ACM@journal + \settopmatter{printfolios=true} + \else + \settopmatter{printfolios=false} + \fi +\fi +\settopmatter{authorsperrow=0} +\def\@received{} +\newcommand\received[2][]{\def\@tempa{#1}% + \ifx\@tempa\@empty + \ifx\@received\@empty + \gdef\@received{Received #2}% + \else + \g@addto@macro{\@received}{; revised #2}% + \fi + \else + \ifx\@received\@empty + \gdef\@received{#1 #2}% + \else + \g@addto@macro{\@received}{; #1 #2}% + \fi + \fi} +\AtEndDocument{% + \ifx\@received\@empty\else + \par\bigskip\noindent\small\normalfont\@received\par + \fi} +\RequirePackage{comment} +\excludecomment{CCSXML} +\let\@concepts\@empty +\newcommand\ccsdesc[2][100]{% + \ccsdesc@parse#1~#2~~\ccsdesc@parse@end} +\RequirePackage{textcomp} +\def\ccsdesc@parse#1~#2~#3~{% + \expandafter\ifx\csname CCS@General@#2\endcsname\relax + \expandafter\gdef\csname CCS@General@#2\endcsname{\textbullet\ + \textbf{#2}}% + \expandafter\gdef\csname CCS@Punctuation@#2\endcsname{; }% + \expandafter\gdef\csname CCS@Specific@#2\endcsname{}% + \g@addto@macro{\@concepts}{\csname CCS@General@#2\endcsname + \csname CCS@Punctuation@#2\endcsname + \csname CCS@Specific@#2\endcsname}% + \fi + \ifx#3\relax\relax\else + \expandafter\gdef\csname CCS@Punctuation@#2\endcsname{ + \textrightarrow\ }% + \expandafter\g@addto@macro\expandafter{\csname CCS@Specific@#2\endcsname}{% + \ifnum#1>499\textbf{#3}; \else + \ifnum#1>299\textit{#3}; \else + #3; \fi\fi}% + \fi +\ccsdesc@parse@finish} +\def\ccsdesc@parse@finish#1\ccsdesc@parse@end{} +\newif\if@printcopyright +\@printcopyrighttrue +\newif\if@printpermission +\@printpermissiontrue +\newif\if@acmowned +\@acmownedtrue +\define@choicekey*{ACM@}{acmcopyrightmode}[% + \acm@copyrightinput\acm@copyrightmode]{none,% + acmcopyright,acmlicensed,rightsretained,% + usgov,usgovmixed,cagov,cagovmixed,% + licensedusgovmixed,% + licensedcagov,licensedcagovmixed,othergov,licensedothergov}{% + \@printpermissiontrue + \@printcopyrighttrue + \@acmownedtrue + \ifnum\acm@copyrightmode=0\relax % none + \@printpermissionfalse + \@printcopyrightfalse + \@acmownedfalse + \fi + \ifnum\acm@copyrightmode=2\relax % acmlicensed + \@acmownedfalse + \fi + \ifnum\acm@copyrightmode=3\relax % rightsretained + \@acmownedfalse + \acmPrice{}% + \fi + \ifnum\acm@copyrightmode=4\relax % usgov + \@printpermissiontrue + \@printcopyrightfalse + \@acmownedfalse + \acmPrice{}% + \fi + \ifnum\acm@copyrightmode=6\relax % cagov + \@acmownedfalse + \fi + \ifnum\acm@copyrightmode=8\relax % licensedusgovmixed + \@acmownedfalse + \fi + \ifnum\acm@copyrightmode=9\relax % licensedcagov + \@acmownedfalse + \fi + \ifnum\acm@copyrightmode=10\relax % licensedcagovmixed + \@acmownedfalse + \fi + \ifnum\acm@copyrightmode=11\relax % othergov + \@acmownedtrue + \fi + \ifnum\acm@copyrightmode=12\relax % licensedothergov + \@acmownedfalse + \fi} +\def\setcopyright#1{\setkeys{ACM@}{acmcopyrightmode=#1}} +\setcopyright{acmcopyright} +\def\@copyrightowner{% + \ifcase\acm@copyrightmode\relax % none + \or % acmcopyright + Association for Computing Machinery. + \or % acmlicensed + Copyright held by the owner/author(s). Publication rights licensed to + Association for Computing Machinery. + \or % rightsretained + Copyright held by the owner/author(s). + \or % usgov + \or % usgovmixed + Association for Computing Machinery. + \or % cagov + Crown in Right of Canada. + \or %cagovmixed + Association for Computing Machinery. + \or %licensedusgovmixed + Copyright held by the owner/author(s). Publication rights licensed to + Association for Computing Machinery. + \or % licensedcagov + Crown in Right of Canada. Publication rights licensed to + Association for Computing Machinery. + \or %licensedcagovmixed + Copyright held by the owner/author(s). Publication rights licensed to + Association for Computing Machinery. + \or % othergov + Association for Computing Machinery. + \or % licensedothergov + Copyright held by the owner/author(s). Publication rights licensed to + Association for Computing Machinery. + \fi} +\def\@formatdoi#1{\url{https://doi.org/#1}} +\def\@copyrightpermission{% + \ifcase\acm@copyrightmode\relax % none + \or % acmcopyright + Permission to make digital or hard copies of all or part of this + work for personal or classroom use is granted without fee provided + that copies are not made or distributed for profit or commercial + advantage and that copies bear this notice and the full citation on + the first page. Copyrights for components of this work owned by + others than ACM must be honored. Abstracting with credit is + permitted. To copy otherwise, or republish, to post on servers or to + redistribute to lists, requires prior specific permission + and\hspace*{.5pt}/or a fee. Request permissions from + permissions@acm.org. + \or % acmlicensed + Permission to make digital or hard copies of all or part of this + work for personal or classroom use is granted without fee provided + that copies are not made or distributed for profit or commercial + advantage and that copies bear this notice and the full citation on + the first page. Copyrights for components of this work owned by + others than the author(s) must be honored. Abstracting with credit + is permitted. To copy otherwise, or republish, to post on servers + or to redistribute to lists, requires prior specific permission + and\hspace*{.5pt}/or a fee. Request permissions from + permissions@acm.org. + \or % rightsretained + Permission to make digital or hard copies of part or all of this work + for personal or classroom use is granted without fee provided that + copies are not made or distributed for profit or commercial advantage + and that copies bear this notice and the full citation on the first + page. Copyrights for third-party components of this work must be + honored. For all other uses, contact the + owner\hspace*{.5pt}/author(s). + \or % usgov + This paper is authored by an employee(s) of the United States + Government and is in the public domain. Non-exclusive copying or + redistribution is allowed, provided that the article citation is + given and the authors and agency are clearly identified as its + source. + \or % usgovmixed + ACM acknowledges that this contribution was authored or co-authored + by an employee, contractor, or affiliate of the United States government. As such, + the United States government retains a nonexclusive, royalty-free right to + publish or reproduce this article, or to allow others to do so, for + government purposes only. + \or % cagov + This article was authored by employees of the Government of Canada. + As such, the Canadian government retains all interest in the + copyright to this work and grants to ACM a nonexclusive, + royalty-free right to publish or reproduce this article, or to allow + others to do so, provided that clear attribution is given both to + the authors and the Canadian government agency employing them. + Permission to make digital or hard copies for personal or classroom + use is granted. Copies must bear this notice and the full citation + on the first page. Copyrights for components of this work owned by + others than the Canadian Government must be honored. To copy + otherwise, distribute, republish, or post, requires prior specific + permission and\hspace*{.5pt}/or a fee. Request permissions from + permissions@acm.org. + \or % cagovmixed + ACM acknowledges that this contribution was co-authored by an + affiliate of the national government of Canada. As such, the Crown + in Right of Canada retains an equal interest in the copyright. + Reprints must include clear attribution to ACM and the author's + government agency affiliation. Permission to make digital or hard + copies for personal or classroom use is granted. Copies must bear + this notice and the full citation on the first page. Copyrights for + components of this work owned by others than ACM must be honored. + To copy otherwise, distribute, republish, or post, requires prior + specific permission and\hspace*{.5pt}/or a fee. Request permissions + from permissions@acm.org. + \or % licensedusgovmixed + Publication rights licensed to ACM\@. ACM acknowledges that this + contribution was authored or co-authored by an employee, contractor + or affiliate of the United States government. As such, the + Government retains a nonexclusive, royalty-free right to publish or + reproduce this article, or to allow others to do so, for Government + purposes only. + \or % licensedcagov + This article was authored by employees of the Government of Canada. + As such, the Canadian government retains all interest in the + copyright to this work and grants to ACM a nonexclusive, + royalty-free right to publish or reproduce this article, or to allow + others to do so, provided that clear attribution is given both to + the authors and the Canadian government agency employing them. + Permission to make digital or hard copies for personal or classroom + use is granted. Copies must bear this notice and the full citation + on the first page. Copyrights for components of this work owned by + others than the Canadian Government must be honored. To copy + otherwise, distribute, republish, or post, requires prior specific + permission and\hspace*{.5pt}/or a fee. Request permissions from + permissions@acm.org. + \or % licensedcagovmixed + Publication rights licensed to ACM\@. ACM acknowledges that this + contribution was authored or co-authored by an employee, contractor + or affiliate of the national government of Canada. As such, the + Government retains a nonexclusive, royalty-free right to publish or + reproduce this article, or to allow others to do so, for Government + purposes only. + \or % othergov + ACM acknowledges that this contribution was authored or co-authored + by an employee, contractor or affiliate of a national government. As + such, the Government retains a nonexclusive, royalty-free right to + publish or reproduce this article, or to allow others to do so, for + Government purposes only. + \or % licensedothergov + Publication rights licensed to ACM\@. ACM acknowledges that this + contribution was authored or co-authored by an employee, contractor + or affiliate of a national government. As such, the Government + retains a nonexclusive, royalty-free right to publish or reproduce + this article, or to allow others to do so, for Government purposes + only. + \fi} +\def\copyrightyear#1{\def\@copyrightyear{#1}} +\copyrightyear{\@acmYear} +\def\@teaserfigures{} +\newenvironment{teaserfigure}{\Collect@Body\@saveteaser}{} +\long\def\@saveteaser#1{\g@addto@macro\@teaserfigures{\@teaser{#1}}} +\renewcommand{\thanks}[1]{% + \@ifnotempty{#1}{% + \if@ACM@anonymous + \g@addto@macro\thankses{\thanks{A note}}% + \else + \g@addto@macro\thankses{\thanks{#1}}% + \fi}} +\newbox\mktitle@bx +\def\maketitle{% + \if@ACM@anonymous + % Anonymize omission of \author-s + \ifnum\num@authorgroups=0\author{}\fi + \fi + \begingroup + \let\@footnotemark\@footnotemark@nolink + \let\@footnotetext\@footnotetext@nolink + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \global\@topnum\z@ % this prevents floats from falling + % at the top of page 1 + \global\@botnum\z@ % we do not want them to be on bottom either + \hsize=\textwidth + \def\@makefnmark{\hbox{\@textsuperscript{\@thefnmark}}}% + \@mktitle\if@ACM@sigchiamode\else\@mkauthors\fi\@mkteasers + \@printtopmatter + \if@ACM@sigchiamode\@mkauthors\fi + \setcounter{footnote}{0}% + \def\@makefnmark{\hbox{\@textsuperscript{\normalfont\@thefnmark}}}% + \@titlenotes + \@subtitlenotes + \@authornotes + \let\@makefnmark\relax \let\@thefnmark\relax + \let\@makefntext\noindent + \ifx\@empty\thankses\else + \footnotetextauthorsaddresses{% + \def\par{\let\par\@par}\parindent\z@\@setthanks}% + \fi + \ifx\@empty\@authorsaddresses\else + \if@ACM@anonymous\else + \if@ACM@journal + \footnotetextauthorsaddresses{% + \def\par{\let\par\@par}\parindent\z@\@setauthorsaddresses}% + \fi + \fi + \fi + \footnotetextcopyrightpermission{% + \if@ACM@authordraft + \raisebox{-2ex}[\z@][\z@]{\makebox[0pt][l]{\large\bfseries + Unpublished + working draft. Not for distribution}}% + \color[gray]{0.9}% + \fi + \parindent\z@\parskip0.1\baselineskip + \if@ACM@authorversion\else + \if@printpermission\@copyrightpermission\par\fi + \fi + \if@ACM@manuscript\else + \if@ACM@journal\else % Print the conference information + {\itshape \acmConference@shortname, \acmConference@date, \acmConference@venue}\par + \fi + \fi + \if@printcopyright + \copyright\ \@copyrightyear\ \@copyrightowner\\ + \else + \@copyrightyear.\ + \fi + \if@ACM@manuscript + Manuscript submitted to ACM\\ + \else + \if@ACM@authorversion + This is the author's version of the work. It is posted here for + your personal use. Not for redistribution. The definitive Version + of Record was published in + \if@ACM@journal + \emph{\@journalName}% + \else + \emph{\@acmBooktitle}% + \fi + \ifx\@acmDOI\@empty + . + \else + , \@formatdoi{\@acmDOI}. + \fi\\ + \else + \if@ACM@journal + \@permissionCodeOne/\@acmYear/\@acmMonth-ART\@acmArticle + \ifx\@acmPrice\@empty\else\ \$\@acmPrice\fi\\ + \@formatdoi{\@acmDOI}% + \else % Conference + \ifx\@acmISBN\@empty\else ACM~ISBN~\@acmISBN + \ifx\@acmPrice\@empty.\else\dots\$\@acmPrice\fi\\\fi + \ifx\@acmDOI\@empty\else\@formatdoi{\@acmDOI}\fi% + \fi + \fi + \fi} + \endgroup + \setcounter{footnote}{0}% + \@mkabstract + \if@ACM@printccs + \ifx\@concepts\@empty\else\bgroup + {\@specialsection{CCS Concepts}% + \@concepts\par}\egroup + \fi + \fi + \ifx\@keywords\@empty\else\bgroup + {\if@ACM@journal + \@specialsection{Additional Key Words and Phrases}% + \else + \@specialsection{Keywords}% + \fi + \@keywords}\par\egroup + \fi + \andify\authors + \andify\shortauthors + \global\let\authors=\authors + \global\let\shortauthors=\shortauthors + \if@ACM@printacmref + \@mkbibcitation + \fi + \hypersetup{pdfauthor={\authors}, + pdftitle={\@title}, + pdfsubject={\@concepts}, + pdfkeywords={\@keywords}}% + \@printendtopmatter + \@afterindentfalse + \@afterheading +} +\def\@specialsection#1{% + \ifcase\ACM@format@nr + \relax % manuscript + \par\medskip\small\noindent#1: % + \or % acmsmall + \par\medskip\small\noindent#1: % + \or % acmlarge + \par\medskip\small\noindent#1: % + \or % acmtog + \par\medskip\small\noindent#1: % + \or % sigconf + \section*{#1}% + \or % siggraph + \section*{#1}% + \or % sigplan + \paragraph*{#1}% + \or % sigchi + \section*{#1}% + \or % sigchi-a + \section*{#1}% + \fi} +\def\@printtopmatter{% + \ifx\@startPage\@empty + \gdef\@startPage{1}% + \else + \setcounter{page}{\@startPage}% + \fi + \thispagestyle{firstpagestyle}% + \noindent + \ifcase\ACM@format@nr + \relax % manuscript + \box\mktitle@bx\par + \or % acmsmall + \box\mktitle@bx\par + \or % acmlarge + \box\mktitle@bx\par + \or % acmtog + \twocolumn[\box\mktitle@bx]% + \or % sigconf + \twocolumn[\box\mktitle@bx]% + \or % siggraph + \twocolumn[\box\mktitle@bx]% + \or % sigplan + \twocolumn[\box\mktitle@bx]% + \or % sigchi + \twocolumn[\box\mktitle@bx]% + \or % sigchi-a + \par\box\mktitle@bx\par\bigskip + \if@ACM@badge + \marginpar{\noindent + \ifx\@acmBadgeL@image\@empty\else + \href{\@acmBadgeL@url}{% + \includegraphics[width=\@ACM@badge@width]{\@acmBadgeL@image}}% + \hskip\@ACM@badge@skip + \fi + \ifx\@acmBadgeR@image\@empty\else + \href{\@acmBadgeR@url}{% + \includegraphics[width=\@ACM@badge@width]{\@acmBadgeR@image}}% + \fi}% + \fi + \fi +} +\def\@mktitle{% + \ifcase\ACM@format@nr + \relax % manuscript + \@mktitle@i + \or % acmsmall + \@mktitle@i + \or % acmlarge + \@mktitle@i + \or % acmtog + \@mktitle@i + \or % sigconf + \@mktitle@iii + \or % siggraph + \@mktitle@iii + \or % sigplan + \@mktitle@iii + \or % sigchi + \@mktitle@iii + \or % sigchi-a + \@mktitle@iv + \fi +} +\def\@titlefont{% + \ifcase\ACM@format@nr + \relax % manuscript + \LARGE\sffamily\bfseries + \or % acmsmall + \LARGE\sffamily\bfseries + \or % acmlarge + \LARGE\sffamily\bfseries + \or % acmtog + \Huge\sffamily + \or % sigconf + \Huge\sffamily\bfseries + \or % siggraph + \Huge\sffamily\bfseries + \or % sigplan + \Huge\bfseries + \or % sigchi + \Huge\sffamily\bfseries + \or % sigchi-a + \Huge\bfseries + \fi} +\def\@subtitlefont{\normalsize + \ifcase\ACM@format@nr + \relax % manuscript + \mdseries + \or % acmsmall + \mdseries + \or % acmlarge + \mdseries + \or % acmtog + \LARGE + \or % sigconf + \LARGE\mdseries + \or % siggraph + \LARGE\mdseries + \or % sigplan + \LARGE\mdseries + \or % sigchi + \LARGE\mdseries + \or % sigchi-a + \mdseries + \fi} +\def\@mktitle@i{\hsize=\textwidth + \@ACM@title@width=\hsize + \ifx\@acmBadgeL@image\@empty\else + \advance\@ACM@title@width by -\@ACM@badge@width + \advance\@ACM@title@width by -\@ACM@badge@skip + \fi + \ifx\@acmBadgeR@image\@empty\else + \advance\@ACM@title@width by -\@ACM@badge@width + \advance\@ACM@title@width by -\@ACM@badge@skip + \fi + \setbox\mktitle@bx=\vbox{\noindent\@titlefont + \ifx\@acmBadgeL@image\@empty\else + \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeL@url}{% + \includegraphics[width=\@ACM@badge@width]{\@acmBadgeL@image}}}% + \hskip\@ACM@badge@skip + \fi + \parbox[t]{\@ACM@title@width}{\raggedright + \@titlefont\noindent + \@title + \ifx\@subtitle\@empty\else + \par\noindent{\@subtitlefont\@subtitle} + \fi}% + \ifx\@acmBadgeR@image\@empty\else + \hskip\@ACM@badge@skip + \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeR@url}{% + \includegraphics[width=\@ACM@badge@width]{\@acmBadgeR@image}}}% + \fi + \par\bigskip}}% +\def\@mktitle@iii{\hsize=\textwidth + \setbox\mktitle@bx=\vbox{\@titlefont\centering + \@ACM@title@width=\hsize + \if@ACM@badge + \advance\@ACM@title@width by -2\@ACM@badge@width + \advance\@ACM@title@width by -2\@ACM@badge@skip + \parbox[b]{\@ACM@badge@width}{\strut + \ifx\@acmBadgeL@image\@empty\else + \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeL@url}{% + \includegraphics[width=\@ACM@badge@width]{\@acmBadgeL@image}}}% + \fi}% + \hskip\@ACM@badge@skip + \fi + \parbox[t]{\@ACM@title@width}{\centering\@titlefont + \@title + \ifx\@subtitle\@empty\else + \par\noindent{\@subtitlefont\@subtitle} + \fi + }% + \if@ACM@badge + \hskip\@ACM@badge@skip + \parbox[b]{\@ACM@badge@width}{\strut + \ifx\@acmBadgeR@image\@empty\else + \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeR@url}{% + \includegraphics[width=\@ACM@badge@width]{\@acmBadgeR@image}}}% + \fi}% + \fi + \par\bigskip}}% +\def\@mktitle@iv{\hsize=\textwidth + \setbox\mktitle@bx=\vbox{\raggedright\leftskip5pc\@titlefont + \noindent\leavevmode\leaders\hrule height 2pt\hfill\kern0pt\par + \noindent\@title + \ifx\@subtitle\@empty\else + \par\noindent\@subtitlefont\@subtitle + \fi + \par\bigskip}}% +\newbox\@ACM@commabox +\def\@ACM@addtoaddress#1{% + \ifvmode\else + \if@ACM@affiliation@obeypunctuation\else + \setbox\@ACM@commabox=\hbox{, }% + \unskip\cleaders\copy\@ACM@commabox\hskip\wd\@ACM@commabox + \fi\fi + #1} +\def\streetaddress#1{\unskip\ignorespaces} +\def\postcode#1{\unskip\ignorespaces} +\if@ACM@journal + \def\position#1{\unskip\ignorespaces} + \def\institution#1{\unskip~#1\ignorespaces} + \def\city#1{\unskip\ignorespaces} + \def\state#1{\unskip\ignorespaces} + \newcommand\department[2][0]{\unskip\ignorespaces} + \def\country#1{\if@ACM@affiliation@obeypunctuation\else, \fi#1\ignorespaces} +\else + \def\position#1{\if@ACM@affiliation@obeypunctuation#1\else#1\par\fi}% + \def\institution#1{\if@ACM@affiliation@obeypunctuation#1\else#1\par\fi}% + \newcommand\department[2][0]{\if@ACM@affiliation@obeypunctuation + #2\else#2\par\fi}% + \let\city\@ACM@addtoaddress + \let\state\@ACM@addtoaddress + \let\country\@ACM@addtoaddress +\fi +\def\@mkauthors{\begingroup + \hsize=\textwidth + \ifcase\ACM@format@nr + \relax % manuscript + \@mkauthors@i + \or % acmsmall + \@mkauthors@i + \or % acmlarge + \@mkauthors@i + \or % acmtog + \@mkauthors@i + \or % sigconf + \@mkauthors@iii + \or % siggraph + \@mkauthors@iii + \or % sigplan + \@mkauthors@iii + \or % sigchi + \@mkauthors@iii + \or % sigchi-a + \@mkauthors@iv + \fi + \endgroup +} +\def\@authorfont{\Large\sffamily} +\def\@affiliationfont{\normalsize\normalfont} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall + \def\@authorfont{\large\sffamily} + \def\@affiliationfont{\small\normalfont} +\or % acmlarge +\or % acmtog + \def\@authorfont{\LARGE\sffamily} + \def\@affiliationfont{\large} +\or % sigconf + \def\@authorfont{\LARGE} + \def\@affiliationfont{\large} +\or % siggraph + \def\@authorfont{\normalsize\normalfont} + \def\@affiliationfont{\normalsize\normalfont} +\or % sigplan + \def\@authorfont{\Large\normalfont} + \def\@affiliationfont{\normalsize\normalfont} +\or % sigchi + \def\@authorfont{\bfseries} + \def\@affiliationfont{\mdseries} +\or % sigchi-a + \def\@authorfont{\bfseries} + \def\@affiliationfont{\mdseries} +\fi +\def\@typeset@author@line{% + \andify\@currentauthors\par\noindent + \@currentauthors\def\@currentauthors{}% + \ifx\@currentaffiliations\@empty\else + \andify\@currentaffiliations + \unskip, {\@currentaffiliations}\par + \fi + \def\@currentaffiliations{}} +\def\@mkauthors@i{% + \def\@currentauthors{}% + \def\@currentaffiliations{}% + \global\let\and\@typeset@author@line + \def\@author##1{% + \ifx\@currentauthors\@empty + \gdef\@currentauthors{\@authorfont\MakeTextUppercase{##1}}% + \else + \g@addto@macro{\@currentauthors}{\and\MakeTextUppercase{##1}}% + \fi + \gdef\and{}}% + \def\email##1##2{}% + \def\affiliation##1##2{% + \def\@tempa{##2}\ifx\@tempa\@empty\else + \ifx\@currentaffiliations\@empty + \gdef\@currentaffiliations{% + \setkeys{@ACM@affiliation@}{obeypunctuation=false}% + \setkeys{@ACM@affiliation@}{##1}% + \@affiliationfont##2}% + \else + \g@addto@macro{\@currentaffiliations}{\and + \setkeys{@ACM@affiliation@}{obeypunctuation=false}% + \setkeys{@ACM@affiliation@}{##1}##2}% + \fi + \fi + \global\let\and\@typeset@author@line}% + \global\setbox\mktitle@bx=\vbox{\noindent\box\mktitle@bx\par\medskip + \noindent\addresses\@typeset@author@line + \par\medskip}% +} +\newbox\author@bx +\newdimen\author@bx@wd +\newskip\author@bx@sep +\author@bx@sep=1pc\relax +\def\@typeset@author@bx{\bgroup\hsize=\author@bx@wd\def\and{\par}% + \global\setbox\author@bx=\vtop{\if@ACM@sigchiamode\else\centering\fi + \@authorfont\@currentauthors\par\@affiliationfont + \@currentaffiliation}\egroup + \box\author@bx\hspace{\author@bx@sep}% + \gdef\@currentauthors{}% + \gdef\@currentaffiliation{}} +\def\@mkauthors@iii{% + \author@bx@wd=\textwidth\relax + \advance\author@bx@wd by -\author@bx@sep\relax + \ifnum\@ACM@authorsperrow>0\relax + \divide\author@bx@wd by \@ACM@authorsperrow\relax + \else + \ifcase\num@authorgroups + \relax % 0? + \or % 1=one author per row + \or % 2=two authors per row + \divide\author@bx@wd by \num@authorgroups\relax + \or % 3=three authors per row + \divide\author@bx@wd by \num@authorgroups\relax + \or % 4=two authors per row (!) + \divide\author@bx@wd by 2\relax + \else % three authors per row + \divide\author@bx@wd by 3\relax + \fi + \fi + \advance\author@bx@wd by -\author@bx@sep\relax + \gdef\@currentauthors{}% + \gdef\@currentaffiliation{}% + \def\@author##1{\ifx\@currentauthors\@empty + \gdef\@currentauthors{\par##1}% + \else + \g@addto@macro\@currentauthors{\par##1}% + \fi + \gdef\and{}}% + \def\email##1##2{\ifx\@currentaffiliation\@empty + \gdef\@currentaffiliation{\nolinkurl{##2}}% + \else + \g@addto@macro\@currentaffiliation{\par\nolinkurl{##2}}% + \fi}% + \def\affiliation##1##2{\ifx\@currentaffiliation\@empty + \gdef\@currentaffiliation{% + \setkeys{@ACM@affiliation@}{obeypunctuation=false}% + \setkeys{@ACM@affiliation@}{##1}##2}% + \else + \g@addto@macro\@currentaffiliation{\par + \setkeys{@ACM@affiliation@}{obeypunctuation=false}% + \setkeys{@ACM@affiliation@}{##1}##2}% + \fi + \global\let\and\@typeset@author@bx +}% + \hsize=\textwidth + \global\setbox\mktitle@bx=\vbox{\noindent + \box\mktitle@bx\par\medskip\leavevmode + \lineskip=1pc\relax\centering\hspace*{-1em}% + \addresses\let\and\@typeset@author@bx\and\par\bigskip}} +\def\@mkauthors@iv{% + \author@bx@wd=\columnwidth\relax + \advance\author@bx@wd by -\author@bx@sep\relax + \ifnum\@ACM@authorsperrow>0\relax + \divide\author@bx@wd by \@ACM@authorsperrow\relax + \else + \ifcase\num@authorgroups + \relax % 0? + \or % 1=one author per row + \else % 2=two authors per row + \divide\author@bx@wd by 2\relax + \fi + \fi + \advance\author@bx@wd by -\author@bx@sep\relax + \gdef\@currentauthors{}% + \gdef\@currentaffiliation{}% + \def\@author##1{\ifx\@currentauthors\@empty + \gdef\@currentauthors{\par##1}% + \else + \g@addto@macro\@currentauthors{\par##1}% + \fi + \gdef\and{}}% + \def\email##1##2{\ifx\@currentaffiliation\@empty + \gdef\@currentaffiliation{\nolinkurl{##2}}% + \else + \g@addto@macro\@currentaffiliation{\par\nolinkurl{##2}}% + \fi}% + \def\affiliation##1##2{\ifx\@currentaffiliation\@empty + \gdef\@currentaffiliation{% + \setkeys{@ACM@affiliation@}{obeypunctuation=false}% + \setkeys{@ACM@affiliation@}{##1}##2}% + \else + \g@addto@macro\@currentaffiliation{\par + \setkeys{@ACM@affiliation@}{obeypunctuation=false}% + \setkeys{@ACM@affiliation@}{##1}##2}% + \fi + \global\let\and\@typeset@author@bx}% + \bgroup\hsize=\columnwidth + \par\raggedright\leftskip=\z@ + \lineskip=1pc\noindent + \addresses\let\and\@typeset@author@bx\and\par\bigskip\egroup} +\def\@mkauthorsaddresses{% + \ifnum\num@authors>1\relax + Authors' \else Author's \fi + \ifnum\num@authorgroups>1\relax + addresses: \else address: \fi + \bgroup + \def\streetaddress##1{\unskip\@addpunct, ##1}% + \def\postcode##1{\unskip\@addpunct, ##1}% + \def\position##1{\unskip\ignorespaces}% + \def\institution##1{\unskip\@addpunct, ##1}% + \def\city##1{\unskip\@addpunct, ##1}% + \def\state##1{\unskip\@addpunct, ##1}% + \renewcommand\department[2][0]{\unskip\@addpunct, ##2}% + \def\country##1{\unskip\@addpunct, ##1}% + \def\and{\unskip\@addpunct; }% + \def\@author##1{##1}% + \def\email##1##2{\unskip\@addpunct, \nolinkurl{##2}}% + \addresses + \egroup} +\def\@setaddresses{} +\def\@authornotemark{\g@addto@macro\@currentauthors{\footnotemark\relax}} +\def\@@authornotemark#1{\g@addto@macro\@currentauthors{\footnotemark[#1]}} +\def\@mkteasers{% + \ifx\@teaserfigures\@empty\else + \def\@teaser##1{\par\bigskip\bgroup + \captionsetup{type=figure}##1\egroup\par} + \global\setbox\mktitle@bx=\vbox{\noindent\box\mktitle@bx\par + \noindent\@teaserfigures\par\medskip}% + \fi} +\def\@mkabstract{\bgroup + \ifx\@abstract\@lempty\else + {\phantomsection\addcontentsline{toc}{section}{Abstract}% + \if@ACM@journal + \small\noindent + \else + \section*{Abstract}% + \fi + \ignorespaces\@abstract\par}% + \fi\egroup} +\def\@mkbibcitation{\bgroup + \def\@pages@word{\ifnum\getrefnumber{TotPages}=1\relax page\else pages\fi}% + \def\footnotemark{}% + \def\\{\unskip{} \ignorespaces}% + \def\footnote{\ClassError{\@classname}{Please do note use footnotes + inside \string\title{} or \string\author{} command! Use + \string\titlenote{} or \string\authornote{} instead!}}% + \def\@article@string{\ifx\@acmArticle\@empty{\ }\else, + Article~\@acmArticle\ \fi}% + \par\medskip\small\noindent{\bfseries ACM Reference Format:}\par\nobreak + \noindent\authors. \@acmYear. \@title + \ifx\@subtitle\@empty. \else: \@subtitle. \fi + \if@ACM@journal + \textit{\@journalNameShort} + \@acmVolume, \@acmNumber \@article@string (\@acmPubDate), + \ref{TotPages}~\@pages@word. + \else + In \textit{\@acmBooktitle}% + \ifx\@acmEditors\@empty\textit{.}\else + \andify\@acmEditors\textit{, }\@acmEditors~\@editorsAbbrev.% + \fi\ + ACM, New York, NY, USA% + \@article@string\unskip, \ref{TotPages}~\@pages@word. + \fi + \@formatdoi{\@acmDOI} +\par\egroup} +\def\@printendtopmatter{\par\bigskip} +\def\@setthanks{\long\def\thanks##1{\par##1\@addpunct.}\thankses} +\def\@setauthorsaddresses{\@authorsaddresses\unskip\@addpunct.} +\RequirePackage{fancyhdr} +\if@ACM@review + \newsavebox{\ACM@linecount@bx} + \newlength\ACM@linecount@bxht + \newcount\ACM@linecount + \ACM@linecount\@ne\relax + \def\ACM@mk@linecount{% + \savebox{\ACM@linecount@bx}[4em][t]{\parbox[t]{4em}{% + \setlength{\ACM@linecount@bxht}{0pt}% + \loop{\color{red}\scriptsize\the\ACM@linecount}\\ + \global\advance\ACM@linecount by \@ne + \addtolength{\ACM@linecount@bxht}{\baselineskip}% + \ifdim\ACM@linecount@bxht<\textheight\repeat + {\color{red}\scriptsize\the\ACM@linecount}\hfill + \global\advance\ACM@linecount by \@ne}}} +\fi +\def\ACM@linecountL{% + \if@ACM@review + \ACM@mk@linecount + \begin{picture}(0,0)% + \put(-26,-22){\usebox{\ACM@linecount@bx}}% + \end{picture}% + \fi} +\def\ACM@linecountR{% + \if@ACM@review + \ACM@mk@linecount + \begin{picture}(0,0)% + \put(20,-22){\usebox{\ACM@linecount@bx}}% + \end{picture}% + \fi} +\if@ACM@timestamp + % Subtracting 30 from \time gives us the effect of rounding-down despite + % \numexpr rounding to nearest + \newcounter{ACM@time@hours} + \setcounter{ACM@time@hours}{\numexpr (\time - 30) / 60 \relax} + \newcounter{ACM@time@minutes} + \setcounter{ACM@time@minutes}{\numexpr \time - \theACM@time@hours * 60 \relax} + \newcommand\ACM@timestamp{% + \footnotesize% + \the\year-\two@digits{\the\month}-\two@digits{\the\day}{ }% + \two@digits{\theACM@time@hours}:\two@digits{\theACM@time@minutes}{ }% + page~\thepage\ (pp. \@startPage-\pageref*{TotPages})% + \ifx\@acmSubmissionID\@empty\relax\else + ~Submission~ID: \@acmSubmissionID + \fi + } +\fi +\def\@shortauthors{\if@ACM@anonymous Anon.\else\shortauthors\fi} +\def\@headfootfont{% + \ifcase\ACM@format@nr + \relax % manuscript + \sffamily + \or % acmsmall + \sffamily + \or % acmlarge + \sffamily + \or % acmtog + \sffamily + \or % sigconf + \sffamily + \or % siggraph + \sffamily + \or % sigplan + \sffamily + \or % sigchi + \sffamily + \or % sigchi-a + \sffamily + \fi} +\fancypagestyle{standardpagestyle}{% + \fancyhf{}% + \renewcommand{\headrulewidth}{\z@}% + \renewcommand{\footrulewidth}{\z@}% + \ifcase\ACM@format@nr + \relax % manuscript + \fancyhead[LE]{\ACM@linecountL\if@ACM@printfolios\thepage\fi}% + \fancyhead[RO]{\if@ACM@printfolios\thepage\fi}% + \fancyhead[RE]{\@shortauthors}% + \fancyhead[LO]{\ACM@linecountL\shorttitle}% + \fancyfoot[RO,LE]{\footnotesize Manuscript submitted to ACM}% + \or % acmsmall + \fancyhead[LE]{\ACM@linecountL\@headfootfont\@acmArticle\if@ACM@printfolios:\thepage\fi}% + \fancyhead[RO]{\@headfootfont\@acmArticle\if@ACM@printfolios:\thepage\fi}% + \fancyhead[RE]{\@headfootfont\@shortauthors}% + \fancyhead[LO]{\ACM@linecountL\@headfootfont\shorttitle}% + \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. + \@acmNumber, Article \@acmArticle. Publication date: \@acmPubDate.}% + \or % acmlarge + \fancyhead[LE]{\ACM@linecountL\@headfootfont + \@acmArticle\if@ACM@printfolios:\thepage\fi\quad\textbullet\quad\@shortauthors}% + \fancyhead[LO]{\ACM@linecountL}% + \fancyhead[RO]{\@headfootfont + \shorttitle\quad\textbullet\quad\@acmArticle\if@ACM@printfolios:\thepage\fi}% + \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. + \@acmNumber, Article \@acmArticle. Publication date: \@acmPubDate.}% + \or % acmtog + \fancyhead[LE]{\ACM@linecountL\@headfootfont + \@acmArticle\if@ACM@printfolios:\thepage\fi\quad\textbullet\quad\@shortauthors}% + \fancyhead[LO]{\ACM@linecountL}% + \fancyhead[RE]{\ACM@linecountR}% + \fancyhead[RO]{\@headfootfont + \shorttitle\quad\textbullet\quad\@acmArticle\if@ACM@printfolios:\thepage\fi\ACM@linecountR}% + \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. + \@acmNumber, Article \@acmArticle. Publication date: \@acmPubDate.}% + \else % Proceedings + \fancyfoot[C]{\if@ACM@printfolios\footnotesize\thepage\fi}% + \fancyhead[LO]{\ACM@linecountL\@headfootfont\shorttitle}% + \fancyhead[RE]{\@headfootfont\@shortauthors\ACM@linecountR}% + \fancyhead[LE]{\ACM@linecountL\@headfootfont\acmConference@shortname, + \acmConference@date, \acmConference@venue}% + \fancyhead[RO]{\@headfootfont\acmConference@shortname, + \acmConference@date, \acmConference@venue\ACM@linecountR}% + \fi + \if@ACM@sigchiamode + \fancyheadoffset[L]{\dimexpr(\marginparsep+\marginparwidth)}% + \fi + \if@ACM@timestamp + \fancyfoot[LO,RE]{\ACM@timestamp} + \fi +} +\pagestyle{standardpagestyle} +\newdimen\@folio@wd +\@folio@wd=\z@ +\newdimen\@folio@ht +\@folio@ht=\z@ +\newdimen\@folio@voffset +\@folio@voffset=\z@ +\def\@folio@max{1} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall + \@folio@wd=45.75pt\relax + \@folio@ht=1.25in\relax + \@folio@voffset=.2in\relax + \def\@folio@max{8} +\or % acmlarge + \@folio@wd=43.25pt\relax + \@folio@ht=79pt\relax + \@folio@voffset=.55in\relax + \def\@folio@max{10} +\fi +\def\@folioblob{\@tempcnta=0\@acmArticleSeq\relax + \ifnum\@tempcnta=0\relax\else + \loop + \ifnum\@tempcnta>\@folio@max\relax + \advance\@tempcnta by - \@folio@max + \repeat + \advance\@tempcnta by -1\relax + \@tempdima=\@folio@ht\relax + \multiply\@tempdima by \the\@tempcnta\relax + \advance\@tempdima by -\@folio@voffset\relax + \begin{picture}(0,0) + \makebox[\z@]{\raisebox{-\@tempdima}{% + \rlap{% + \raisebox{-0.45\@folio@ht}[\z@][\z@]{% + \rule{\@folio@wd}{\@folio@ht}}}% + \parbox{\@folio@wd}{% + \centering + \textcolor{white}{\LARGE\sffamily\bfseries\@acmArticle}}}} + \end{picture}\fi} + +\fancypagestyle{firstpagestyle}{% + \fancyhf{}% + \renewcommand{\headrulewidth}{\z@}% + \renewcommand{\footrulewidth}{\z@}% + \ifcase\ACM@format@nr + \relax % manuscript + \fancyhead[L]{\ACM@linecountL}% + \fancyfoot[RO,LE]{\if@ACM@printfolios\small\thepage\fi}% + \fancyfoot[RE,LO]{\footnotesize Manuscript submitted to ACM}% + \or % acmsmall + \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. + \@acmNumber, Article \@acmArticle. Publication date: + \@acmPubDate.}% + \fancyhead[LE]{\ACM@linecountL\@folioblob}% + \fancyhead[LO]{\ACM@linecountL}% + \fancyhead[RO]{\@folioblob}% + \fancyheadoffset[RO,LE]{0.6\@folio@wd}% + \or % acmlarge + \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. + \@acmNumber, Article \@acmArticle. Publication date: + \@acmPubDate.}% + \fancyhead[RO]{\@folioblob}% + \fancyhead[LE]{\ACM@linecountL\@folioblob}% + \fancyhead[LO]{\ACM@linecountL}% + \fancyheadoffset[RO,LE]{1.4\@folio@wd}% + \or % acmtog + \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. + \@acmNumber, Article \@acmArticle. Publication date: + \@acmPubDate.}% + \fancyhead[L]{\ACM@linecountL}% + \fancyhead[R]{\ACM@linecountR}% + \else % Conference proceedings + \fancyhead[L]{\ACM@linecountL}% + \fancyhead[R]{\ACM@linecountR}% + \fancyfoot[C]{\if@ACM@printfolios\footnotesize\thepage\fi}% + \fi + \if@ACM@timestamp + \ifnum\ACM@format@nr=0\relax % Manuscript + \fancyfoot[LO,RE]{\ACM@timestamp\quad + \footnotesize Manuscript submitted to ACM} + \else + \fancyfoot[LO,RE]{\ACM@timestamp} + \fi + \fi +} +\let\ACM@ps@plain\ps@plain +\let\ACM@ps@myheadings\ps@myheadings +\let\ACM@ps@headings\ps@headings +\def\ACM@restore@pagestyle{% + \let\ps@plain\ACM@ps@plain + \let\ps@myheadings\ACM@ps@myheadings + \let\ps@headings\ACM@ps@headings} +\AtBeginDocument{\ACM@restore@pagestyle} +\renewcommand\section{\@startsection{section}{1}{\z@}% + {-.75\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {.25\baselineskip}% + {\@secfont}} +\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-.75\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {.25\baselineskip}% + {\@subsecfont}} +\renewcommand\subsubsection{\@startsection{subsubsection}{3}{10pt}% + {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {-3.5\p@}% + {\@subsubsecfont\@adddotafter}} +\renewcommand\paragraph{\@startsection{paragraph}{4}{\parindent}% + {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {-3.5\p@}% + {\@parfont\@adddotafter}} +\renewcommand\part{\@startsection{part}{9}{\z@}% + {-10\p@ \@plus -4\p@ \@minus -2\p@}% + {4\p@}% + {\@parfont}} +\def\section@raggedright{\@rightskip\@flushglue + \rightskip\@rightskip + \leftskip\z@skip + \parindent\z@} +\def\@secfont{\sffamily\bfseries\section@raggedright\MakeTextUppercase} +\def\@subsecfont{\sffamily\bfseries\section@raggedright} +\def\@subsubsecfont{\sffamily\itshape} +\def\@parfont{\itshape} +\setcounter{secnumdepth}{3} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge + \def\@secfont{\sffamily\large\section@raggedright\MakeTextUppercase} + \def\@subsecfont{\sffamily\large\section@raggedright} +\or % acmtog + \def\@secfont{\sffamily\large\section@raggedright\MakeTextUppercase} + \def\@subsecfont{\sffamily\large\section@raggedright} +\or % sigconf + \def\@secfont{\bfseries\Large\section@raggedright\MakeTextUppercase} + \def\@subsecfont{\bfseries\Large\section@raggedright} +\or % siggraph + \def\@secfont{\sffamily\bfseries\Large\section@raggedright\MakeTextUppercase} + \def\@subsecfont{\sffamily\bfseries\Large\section@raggedright} +\or % sigplan + \def\@secfont{\bfseries\Large\section@raggedright} + \def\@subsecfont{\bfseries\section@raggedright} + \renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-.75\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {.25\baselineskip}% + {\@subsubsecfont}} + \def\@subsubsecfont{\bfseries\section@raggedright} + \renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}% + {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {-3.5\p@}% + {\@parfont\@addspaceafter}} + \def\@parfont{\bfseries\itshape} + \renewcommand\subparagraph{\@startsection{subparagraph}{5}{\z@}% + {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% + {-3.5\p@}% + {\@subparfont\@addspaceafter}} + \def\@subparfont{\itshape} +\or % sigchi + \setcounter{secnumdepth}{1} + \def\@secfont{\sffamily\bfseries\section@raggedright\MakeTextUppercase} + \def\@subsecfont{\sffamily\bfseries\section@raggedright} +\or % sigchi-a + \setcounter{secnumdepth}{0} + \def\@secfont{\sffamily\bfseries\section@raggedright\MakeTextUppercase} + \def\@subsecfont{\sffamily\bfseries\section@raggedright} +\fi +\def\@adddotafter#1{#1\@addpunct{.}} +\def\@addspaceafter#1{#1\@addpunct{\enspace}} +\providecommand*\@dotsep{4.5} +\def\@acmplainbodyfont{\itshape} +\def\@acmplainindent{\parindent} +\def\@acmplainheadfont{\scshape} +\def\@acmplainnotefont{\@empty} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge +\or % acmtog +\or % sigconf +\or % siggraph +\or % sigplan + \def\@acmplainbodyfont{\itshape} + \def\@acmplainindent{\z@} + \def\@acmplainheadfont{\bfseries} + \def\@acmplainnotefont{\normalfont} +\or % sigchi +\or % sigchi-a +\fi +\newtheoremstyle{acmplain}% + {.5\baselineskip\@plus.2\baselineskip + \@minus.2\baselineskip}% space above + {.5\baselineskip\@plus.2\baselineskip + \@minus.2\baselineskip}% space below + {\@acmplainbodyfont}% body font + {\@acmplainindent}% indent amount + {\@acmplainheadfont}% head font + {.}% punctuation after head + {.5em}% spacing after head + {\thmname{#1}\thmnumber{ #2}\thmnote{ {\@acmplainnotefont(#3)}}}% head spec +\def\@acmdefinitionbodyfont{\normalfont} +\def\@acmdefinitionindent{\parindent} +\def\@acmdefinitionheadfont{\itshape} +\def\@acmdefinitionnotefont{\@empty} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge +\or % acmtog +\or % sigconf +\or % siggraph +\or % sigplan + \def\@acmdefinitionbodyfont{\normalfont} + \def\@acmdefinitionindent{\z@} + \def\@acmdefinitionheadfont{\bfseries} + \def\@acmdefinitionnotefont{\normalfont} +\or % sigchi +\or % sigchi-a +\fi +\newtheoremstyle{acmdefinition}% + {.5\baselineskip\@plus.2\baselineskip + \@minus.2\baselineskip}% space above + {.5\baselineskip\@plus.2\baselineskip + \@minus.2\baselineskip}% space below + {\@acmdefinitionbodyfont}% body font + {\@acmdefinitionindent}% indent amount + {\@acmdefinitionheadfont}% head font + {.}% punctuation after head + {.5em}% spacing after head + {\thmname{#1}\thmnumber{ #2}\thmnote{ {\@acmdefinitionnotefont(#3)}}}% head spec +\theoremstyle{acmplain} +\AtEndPreamble{% + \if@ACM@acmthm + \theoremstyle{acmplain} + \@ifundefined{theorem}{% + \newtheorem{theorem}{Theorem}[section] + }{} + \@ifundefined{conjecture}{% + \newtheorem{conjecture}[theorem]{Conjecture} + }{} + \@ifundefined{proposition}{% + \newtheorem{proposition}[theorem]{Proposition} + }{} + \newtheorem{lemma}[theorem]{Lemma} + \@ifundefined{lemma}{}{} + \@ifundefined{corollary}{% + \newtheorem{corollary}[theorem]{Corollary} + }{} + \theoremstyle{acmdefinition} + \@ifundefined{example}{% + \newtheorem{example}[theorem]{Example} + }{} + \@ifundefined{definition}{% + \newtheorem{definition}[theorem]{Definition} + }{} + \fi + \theoremstyle{acmplain} +} +\def\@proofnamefont{\scshape} +\def\@proofindent{\indent} +\ifcase\ACM@format@nr +\relax % manuscript +\or % acmsmall +\or % acmlarge +\or % acmtog +\or % sigconf +\or % siggraph +\or % sigplan + \def\@proofnamefont{\itshape} + \def\@proofindent{\noindent} +\or % sigchi +\or % sigchi-a +\fi +\renewenvironment{proof}[1][\proofname]{\par + \pushQED{\qed}% + \normalfont \topsep6\p@\@plus6\p@\relax + \trivlist + \item[\@proofindent\hskip\labelsep + {\@proofnamefont #1\@addpunct{.}}]\ignorespaces +}{% + \popQED\endtrivlist\@endpefalse +} +\specialcomment{acks}{% + \begingroup + \section*{Acknowledgments} + \phantomsection\addcontentsline{toc}{section}{Acknowledgments} +}{% + \endgroup +} +\def\grantsponsor#1#2#3{#2} +\newcommand\grantnum[3][]{#3% + \def\@tempa{#1}\ifx\@tempa\@empty\else\space(\url{#1})\fi} +\AtEndPreamble{% +\if@ACM@screen + \includecomment{screenonly} + \excludecomment{printonly} +\else + \excludecomment{screenonly} + \includecomment{printonly} +\fi +\if@ACM@anonymous + \excludecomment{anonsuppress} + \excludecomment{acks} +\else + \includecomment{anonsuppress} +\fi} +\newcommand\showeprint[2][arxiv]{% + \def\@tempa{#1}% + \ifx\@tempa\@empty\def\@tempa{arxiv}\fi + \def\@tempb{arxiv}% + \ifx\@tempa\@tempb + arXiv:\href{http://arxiv.org/abs/#2}{#2}\else arXiv:#2% + \fi} +\normalsize\normalfont\frenchspacing +\endinput +%% +%% End of file `acmart.cls'. diff --git a/TRUST-docs/biblio.bib b/TRUST-docs/biblio.bib new file mode 100644 index 0000000..5f9d0ce --- /dev/null +++ b/TRUST-docs/biblio.bib @@ -0,0 +1,466 @@ +@article{martin2023guarantees, + title = {Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey}, + author = {Martin, Tim and Sch{\"o}n, Thomas B and Allg{\"o}wer, Frank}, + journal = {Annual Reviews in Control}, + pages = {100911}, + year = {2023}, + publisher = {Elsevier} +} + +@article{samari2024single, + title = {From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems}, + author = {Samari, Behrad and Akbarzadeh, Omid and Zaker, Mahdieh and Lavaei, Abolfazl}, + journal = {arXiv preprint arXiv:2409.10026}, + year = {2024} +} + +@inproceedings{breschi2021direct, + title = {Direct data-driven model-reference control with Lyapunov stability guarantees}, + author = {Breschi, Valentina and De Persis, Claudio and Formentin, Simone and Tesi, Pietro}, + booktitle = {2021 60th IEEE conference on decision and control (CDC)}, + pages = {1456--1461}, + year = {2021}, + organization = {IEEE} +} + +@article{bisoffi2022controller, + title = {Controller design for robust invariance from noisy data}, + author = {Bisoffi, Andrea and De Persis, Claudio and Tesi, Pietro}, + journal = {IEEE Transactions on Automatic Control}, + volume = {68}, + number = {1}, + pages = {636--643}, + year = {2022}, + publisher = {IEEE} +} + +@InProceedings{prajna2004safety, + author = "Prajna, Stephen +and Jadbabaie, Ali", + title = "Safety Verification of Hybrid Systems Using Barrier Certificates", + booktitle = "Hybrid Systems: Computation and Control", + year = "2004", + publisher = "Springer Berlin Heidelberg", + pages = "477--492", +} + +@inproceedings{prajna2002introducing, + title = {Introducing SOSTOOLS: A general purpose sum of squares programming solver}, + author = {Prajna, Stephen and Papachristodoulou, Antonis and Parrilo, Pablo A}, + booktitle = {Proceedings of the 41st IEEE Conference on Decision and Control, 2002.}, + volume = {1}, + pages = {741--746}, + year = {2002}, + organization = {IEEE} +} + + +@inproceedings{nejati2022data, + title = {Data-driven controller synthesis of unknown nonlinear polynomial systems via control barrier certificates}, + author = {Nejati, Ameneh and Zhong, Bingzhuo and Caccamo, Marco and Zamani, Majid}, + booktitle = {Learning for Dynamics and Control Conference}, + pages = {763--776}, + year = {2022}, + organization = {PMLR} +} + +@article{prajna2007convex, + title = {Convex programs for temporal verification of nonlinear dynamical systems}, + author = {Prajna, Stephen and Rantzer, Anders}, + journal = {SIAM Journal on Control and Optimization}, + volume = {46}, + number = {3}, + pages = {999--1021}, + year = {2007}, + publisher = {SIAM} +} + +@article{bisoffi2020data, + title = {Data-based guarantees of set invariance properties}, + author = {Bisoffi, Andrea and De Persis, Claudio and Tesi, Pietro}, + journal = {IFAC-PapersOnLine}, + volume = {53}, + number = {2}, + pages = {3953--3958}, + year = {2020}, + publisher = {Elsevier} +} + +@article{willems2005note, + title = {A note on persistency of excitation}, + author = {Willems, Jan C and Rapisarda, Paolo and Markovsky, Ivan and De Moor, Bart LM}, + journal = {Systems \& Control Letters}, + volume = {54}, + number = {4}, + pages = {325--329}, + year = {2005}, + publisher = {Elsevier} +} + +@INPROCEEDINGS{Anand2021kSafety, + author = {Anand, Mahathi and Murali, Vishnu and Trivedi, Ashutosh and Zamani, Majid}, + booktitle = {2021 60th IEEE Conference on Decision and Control (CDC)}, + title = {Safety Verification of Dynamical Systems via k-Inductive Barrier Certificates}, + year = {2021}, + volume = {}, + number = {}, + pages = {1314-1320}, + keywords = {Discrete-time systems;System dynamics;Conferences;Programming;Software;Safety;Trajectory}, + doi = {10.1109/CDC45484.2021.9682889} } + +@inproceedings{anand2022kstochastic, + title = {K-inductive barrier certificates for stochastic systems}, + author = {Anand, Mahathi and Murali, Vishnu and Trivedi, Ashutosh and Zamani, Majid}, + booktitle = {Proceedings of the 25th ACM International Conference on Hybrid Systems: Computation and Control}, + pages = {1--11}, + year = {2022} +} + +@article{wooding2024protect, + title = {PRoTECT: Parallelized Construction of Safety Barrier Certificates for Nonlinear Polynomial Systems}, + author = {Wooding, Ben and Horbanov, Viacheslav and Lavaei, Abolfazl}, + journal = {arXiv preprint arXiv:2404.14804}, + year = {2024} +} + +@inproceedings{abate2021fossil, + title = {{FOSSIL: a software tool for the formal synthesis of lyapunov functions and barrier certificates using neural networks}}, + author = {Abate, Alessandro and Ahmed, Daniele and Edwards, Alec and Giacobbe, Mirco and Peruffo, Andrea}, + booktitle = {Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control}, + pages = {1--11}, + year = {2021} +} + +@article{van2023direct, + title = {Direct data-driven signal temporal logic control of linear systems}, + author = {van Huijgevoort, Birgit C and Verhoek, Chris and T{\'o}th, Roland and Haesaert, Sofie}, + journal = {arXiv preprint arXiv:2304.02297}, + year = {2023} +} + +@article{kazemi2024data, + title = {Data-driven abstraction-based control synthesis}, + author = {Kazemi, Milad and Majumdar, Rupak and Salamati, Mahmoud and Soudjani, Sadegh and Wooding, Ben}, + journal = {Nonlinear Analysis: Hybrid Systems}, + volume = {52}, + pages = {101467}, + year = {2024}, + publisher = {Elsevier} +} + +@inproceedings{prajna2004stochastic, + title = {Stochastic safety verification using barrier certificates}, + author = {Prajna, Stephen and Jadbabaie, Ali and Pappas, George J}, + booktitle = {2004 43rd IEEE conference on decision and control (CDC)}, + volume = {1}, + pages = {929--934}, + year = {2004}, + organization = {IEEE} +} + +@article{prajna2007framework, + title = {A framework for worst-case and stochastic safety verification using barrier certificates}, + author = {Prajna, Stephen and Jadbabaie, Ali and Pappas, George J}, + journal = {IEEE Transactions on Automatic Control}, + volume = {52}, + number = {8}, + pages = {1415--1428}, + year = {2007}, + publisher = {IEEE} +} + +@article{murali2022scenario, + title = {A scenario approach for synthesizing k-inductive barrier certificates}, + author = {Murali, Vishnu and Trivedi, Ashutosh and Zamani, Majid}, + journal = {IEEE Control Systems Letters}, + volume = {6}, + pages = {3247--3252}, + year = {2022}, + publisher = {IEEE} +} + +@article{bak2018t, + title = {{t-Barrier certificates: a continuous analogy to k-induction}}, + author = {Bak, Stanley}, + journal = {IFAC-PapersOnLine}, + volume = {51}, + number = {16}, + pages = {145--150}, + year = {2018}, + publisher = {Elsevier} +} + +@inproceedings{ames2019control, + title = {{Control Barrier Functions: Theory and Applications}}, + author = {Ames, Aaron D and Coogan, Samuel and Egerstedt, Magnus and Notomista, Gennaro and Sreenath, Koushil and Tabuada, Paulo}, + booktitle = {{2019 18th European Control Conference (ECC)}}, + pages = {3420--3431}, + year = {2019}, + organization = {IEEE} +} + +@ARTICLE{Lindemann2019CBF4STL, + author = {Lindemann, Lars and Dimarogonas, Dimos V.}, + journal = {IEEE Control Systems Letters}, + title = {Control Barrier Functions for Signal Temporal Logic Tasks}, + year = {2019}, + volume = {3}, + number = {1}, + pages = {96-101}, + keywords = {Task analysis;Planning;Feedback control;Semantics;Switches;System dynamics;Autonomous systems;constrained control;hybrid systems}, + doi = {10.1109/LCSYS.2018.2853182} } + +@article{mathiesen2022safety, + title = {Safety certification for stochastic systems via neural barrier functions}, + author = {Mathiesen, Frederik Baymler and Calvert, Simeon C and Laurenti, Luca}, + journal = {IEEE Control Systems Letters}, + volume = {7}, + pages = {973--978}, + year = {2022}, + publisher = {IEEE} +} + +@article{salamati2024data, + title = {Data-driven verification and synthesis of stochastic systems via barrier certificates}, + author = {Salamati, Ali and Lavaei, Abolfazl and Soudjani, Sadegh and Zamani, Majid}, + journal = {Automatica}, + volume = {159}, + pages = {111323}, + year = {2024}, + publisher = {Elsevier} +} + +@article{de2019formulas, + title = {Formulas for data-driven control: Stabilization, optimality, and robustness}, + author = {De Persis, Claudio and Tesi, Pietro}, + journal = {IEEE Transactions on Automatic Control}, + volume = {65}, + number = {3}, + pages = {909--924}, + year = {2019}, + publisher = {IEEE} +} + +@article{van2020willems, + title = {Willems’ fundamental lemma for state-space systems and its extension to multiple datasets}, + author = {Van Waarde, Henk J and De Persis, Claudio and Camlibel, M Kanat and Tesi, Pietro}, + journal = {IEEE Control Systems Letters}, + volume = {4}, + number = {3}, + pages = {602--607}, + year = {2020}, + publisher = {IEEE} +} + +@article{dai2023data, + title = {Data-driven optimal output feedback control of linear systems from input-output data}, + author = {Dai, Xiaoyan and De Persis, Claudio and Monshizadeh, Nima}, + journal = {IFAC-PapersOnLine}, + volume = {56}, + number = {2}, + pages = {1376--1381}, + year = {2023}, + publisher = {Elsevier} +} + +@article{guo2021data, + title = {Data-driven stabilization of nonlinear polynomial systems with noisy data}, + author = {Guo, Meichen and De Persis, Claudio and Tesi, Pietro}, + journal = {IEEE Transactions on Automatic Control}, + volume = {67}, + number = {8}, + pages = {4210--4217}, + year = {2021}, + publisher = {IEEE} +} + +@inproceedings{han2015sublinear, + title = {A sublinear algorithm for barrier-certificate-based data-driven model validation of dynamical systems}, + author = {Han, Shuo and Topcu, Ufuk and Pappas, George J}, + booktitle = {2015 54th IEEE conference on decision and control (CDC)}, + pages = {2049--2054}, + year = {2015}, + organization = {IEEE} +} + +@article{nejati2023data, + title = {Data-driven synthesis of safety controllers via multiple control barrier certificates}, + author = {Nejati, Ameneh and Zamani, Majid}, + journal = {IEEE Control Systems Letters}, + year = {2023}, + publisher = {IEEE} +} + +@article{makdesi2023data, + title = {Data-driven models of monotone systems}, + author = {Makdesi, Anas and Girard, Antoine and Fribourg, Laurent}, + journal = {IEEE Transactions on Automatic Control}, + year = {2023}, + publisher = {IEEE} +} + +@inproceedings{fan2017dryvr, + title = {{DryVR}: Data-driven verification and compositional reasoning for automotive systems}, + author = {Fan, Chuchu and Qi, Bolun and Mitra, Sayan and Viswanathan, Mahesh}, + booktitle = {International Conference on Computer Aided Verification}, + pages = {441--461}, + year = {2017}, + organization = {Springer} +} + +@inproceedings{wang2022probabilistic, + title = {Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis}, + author = {Wang, Zheming and Jungers, Rapha{\"e}l M}, + booktitle = {2022 IEEE 61st Conference on Decision and Control (CDC)}, + pages = {5668--5673}, + year = {2022}, + organization = {IEEE} +} + +@inproceedings{ahmad2022adaptive, + title = {Adaptive sampling-based motion planning with control barrier functions}, + author = {Ahmad, Ahmad and Belta, Calin and Tron, Roberto}, + booktitle = {2022 IEEE 61st Conference on Decision and Control (CDC)}, + pages = {4513--4518}, + year = {2022}, + organization = {IEEE} +} + +@article{verdier2022formal, + title = {Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications}, + author = {Verdier, Cees Ferdinand and Kochdumper, Niklas and Althoff, Matthias and Mazo Jr, Manuel}, + journal = {Automatica}, + volume = {139}, + pages = {110184}, + year = {2022}, + publisher = {Elsevier} +} + +@inproceedings{lavaei2021formal, + title = {Formal safety verification of unknown continuous-time systems: a data-driven approach}, + author = {Lavaei, Abolfazl and Nejati, Ameneh and Jagtap, Pushpak and Zamani, Majid}, + booktitle = {Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control}, + pages = {1--2}, + year = {2021} +} + +@inproceedings{badings2022sampling, + title = {Sampling-based robust control of autonomous systems with non-gaussian noise}, + author = {Badings, Thom S and Abate, Alessandro and Jansen, Nils and Parker, David and Poonawala, Hasan A and Stoelinga, Marielle}, + booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, + volume = {36}, + number = {9}, + pages = {9669--9678}, + year = {2022} +} + +@article{badings2023robust, + title = {Robust control for dynamical systems with non-gaussian noise via formal abstractions}, + author = {Badings, Thom and Romao, Licio and Abate, Alessandro and Parker, David and Poonawala, Hasan A and Stoelinga, Marielle and Jansen, Nils}, + journal = {Journal of Artificial Intelligence Research}, + volume = {76}, + pages = {341--391}, + year = {2023} +} + +@book{bochnak2013real, + title = {Real algebraic geometry}, + author = {Bochnak, Jacek and Coste, Michel and Roy, Marie-Fran{\c{c}}oise}, + volume = {36}, + year = {2013}, + publisher = {Springer Science \& Business Media} +} + +@article{ren2024formal, + title = {Formal Synthesis of Safety Controllers via $ k $-Inductive Control Barrier Certificates}, + author = {Ren, Tianxiang and Lin, Wang and Ding, Zuohua}, + journal = {IEEE Transactions on Reliability}, + year = {2024}, + publisher = {IEEE} +} + +@inproceedings{SOSTOOLS, + title = {{Introducing SOSTOOLS: A general purpose sum of squares programming solver}}, + author = {Prajna, Stephen and Papachristodoulou, Antonis and Parrilo, Pablo A}, + booktitle = {Proceedings of the 41st IEEE Conference on Decision and Control, 2002.}, + volume = {1}, + pages = {741--746}, + year = {2002}, + organization = {IEEE} +} + +@inproceedings{verdier2018formal, + title = {Formal synthesis of analytic controllers for sampled-data systems via genetic programming}, + author = {Verdier, Cees F and Mazo, Manuel}, + booktitle = {2018 IEEE Conference on Decision and Control (CDC)}, + pages = {4896--4901}, + year = {2018}, + organization = {IEEE} +} + +@book{campi2018introduction, + title = {Introduction to the scenario approach}, + author = {Campi, Marco C and Garatti, Simone}, + year = {2018}, + publisher = {SIAM} +} + +@book{xiao2023safe, + title = {Safe Autonomy with Control Barrier Functions: Theory and Applications}, + author = {Xiao, Wei and Cassandras, Christos G and Belta, Calin}, + year = {2023}, + publisher = {Springer} +} + +@ARTICLE{nejati2023formal, + author = {Nejati, Ameneh and Lavaei, Abolfazl and Jagtap, Pushpak and Soudjani, Sadegh and Zamani, Majid}, + journal = {IEEE Transactions on Automatic Control}, + title = {Formal Verification of Unknown Discrete- and Continuous-Time Systems: A Data-Driven Approach}, + year = {2023}, + volume = {68}, + number = {5}, + pages = {3011-3024}, } + +@article{parrilo2003semidefinite, + title = {Semidefinite programming relaxations for semialgebraic problems}, + author = {Parrilo, Pablo A}, + journal = {Mathematical programming}, + volume = {96}, + pages = {293--320}, + year = {2003}, + publisher = {Springer} +} + +@article{adewuyi2013dc, + title = {DC motor speed control: A case between PID controller and fuzzy logic controller}, + author = {Adewuyi, Philip A}, + journal = {international journal of multidisciplinary sciences and engineering}, + volume = {4}, + number = {4}, + pages = {36--40}, + year = {2013} +} + +@article{wang2024convex, + title = {Convex co-design of control barrier functions and feedback controllers for linear systems}, + author = {Wang, Han and Margellos, Kostas and Papachristodoulou, Antonis and De Persis, Claudio}, + year = {2024}, + publisher = {IEEE} +} + +@software{Yuan_SumOfSquares_py, + author = {Yuan, Chenyang}, + license = {MIT}, + title = {{SumOfSquares.py}}, + url = {https://github.com/yuanchenyang/SumOfSquares.py} +} + +@misc{samari2024singletrajectory, + title = {From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems}, + author = {Behrad Samari and Omid Akbarzadeh and Mahdieh Zaker and Abolfazl Lavaei}, + year = {2024}, + eprint = {2409.10026}, + archivePrefix = {arXiv}, + primaryClass = {eess.SY}, + url = {https://arxiv.org/abs/2409.10026}, +} \ No newline at end of file diff --git a/TRUST-docs/main.tex b/TRUST-docs/main.tex new file mode 100644 index 0000000..f9be96e --- /dev/null +++ b/TRUST-docs/main.tex @@ -0,0 +1,1152 @@ +\documentclass[sigconf]{acmart} + +\usepackage{booktabs} % For formal tables +\usepackage{IEEEtrantools} +\usepackage{latexsym,amsfonts,amsmath} %amssymb +\usepackage{graphicx} +\usepackage{dsfont} +\usepackage{enumerate} +\usepackage{hyperref} +\newtheorem{claim}{Claim} +\newtheorem{problem}{Problem} +\newtheorem{algorithm}{Algorithm} +\newtheorem{construction}{Construction} +\newtheorem{xca}{Exercise} +\newtheorem{comments}{Comments} +\newtheorem{remark}{Remark} +\newtheorem{assumption}{Assumption} +\newtheorem{fact}{Fact} + +\usepackage{mathrsfs} + +\usepackage{algorithm} +%\usepackage{algorithmic} +\usepackage{algpseudocode} +%================FAUST +\usepackage{xspace} +\newcommand{\software}{\textsf{FAUST}$^{\mathsf 2}$\xspace} +%================= + +\newcommand{\set}[1]{{\{#1 \}}} +\newcommand{\boxspan}{\mathit{span}} +\newcommand{\params}{{\mathsf{q}}} +\renewcommand{\Re}{{\mathbb{R}}} +\newcommand{\R}{{\mathbb{R}}} +\newcommand{\F}{{\mathbb{F}}} +\newcommand{\Q}{{\mathbb{Q}}} +\newcommand{\Ze}{{\mathbb Z}} +\newcommand{\B}{{\mathbb B}} +\newcommand{\Ce}{{\mathbb C}} +\newcommand{\N}{{\mathbb{N}}} +\newcommand{\T}{{\mathbb T}} +\newcommand{\fs}{{\mathbb S}} +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\eg}{\textit{e.g.}} +\newcommand{\ea}{\textit{et al}} +\newcommand{\D}{\displaystyle} +\newcommand{\Pre}{\mathrm{Pre}} +\newcommand{\Post}{\textrm{Post}} +\newcommand{\argmax}{\textrm{arg}\max} +\newcommand{\argmin}{\textrm{arg}\min} +\newcommand{\UP}{\textrm{UP}} +\newcommand{\X}{{\mathbf{X}}} +\newcommand{\Next}{{\mathrm{Next}}} +\newcommand{\Inv}{{\mathrm{Inv}}} +\newcommand{\Reach}{{\mathrm{Reach}}} +\newcommand{\kr}{\textrm{ker}} +\newcommand{\s}{\mathrm{span}} +\renewcommand{\dim}{\mathrm{dim}} +\newcommand{\lie}{\mathrm{Lie}} +\newcommand{\cl}{\mathrm{cl}} +\newcommand{\inte}{\mathrm{int}} +\newcommand{\bd}{\mathrm{bd}} +\newcommand{\E}{\mathrm{End}} +\newcommand{\q}{\mathsf{q}} +\newcommand{\p}{\mathsf{p}} +\newcommand\norm[1]{\left\lVert#1\right\rVert} + +\DeclareMathOperator{\Tr}{Tr} +\newcommand{\note}[1]{\textcolor{red}{(#1)}} +\newcommand{\ra}{\rightarrow} +\newcommand{\insertref}{\textcolor{red}{[ref]}} +\newcommand{\ul}{\underline} +\newcommand{\ol}{\overline} +\newcommand{\Let}{:=} +\newcommand{\EE}{\mathds{E}} +\newcommand{\PP}{\mathds{P}} +\newcommand{\traj}[3]{#1_{#2#3}} +\newcommand{\red}[1]{{\color{red}{#1}}} +\newcommand{\blue}[1]{{\color{blue}{#1}}} +\newcommand{\BW}{\textcolor{red}} +\newcommand{\MZ}[1]{{\textcolor{red}{ \textbf{MZ:} #1}}} + +\newcommand{\intcc}[1]{\ensuremath{{\left[#1\right]}}} +\newcommand{\intoc}[1]{\ensuremath{{\left]#1\right]}}} +\newcommand{\intco}[1]{\ensuremath{{\left[#1\right[}}} +\newcommand{\intoo}[1]{\ensuremath{{\left]#1\right[}}} + +%\linespread{0.9} + +\DeclareMathOperator{\diag}{diag} +\DeclareMathOperator{\im}{im} +\DeclareMathOperator{\ess}{ess} + +\newcommand{\id}{{\mathrm{id}}} +\renewcommand{\emptyset}{{\varnothing}} +\newcommand{\Abolfazl}{\textcolor{blue}} + +\newcommand{\identity}{\mathbb{I}} +% Copyright +%\setcopyright{none} +%\setcopyright{acmcopyright} +%\setcopyright{acmlicensed} +\setcopyright{rightsretained} +%\setcopyright{usgov} +%\setcopyright{usgovmixed} +%\setcopyright{cagov} +%\setcopyright{cagovmixed} + +\newcommand{\initial}{X_I} +\newcommand{\unsafe}{X_U} + +% DOI +%\acmDOI{10.475/123_4} + +% ISBN +%\acmISBN{123-4567-24-567/08/06} + +%Conference +%\acmConference[HSCC'18]{ACM International Conference on Hybrid Systems: Computation and Control }{April 2018}{Porto, Portugal} +%\acmYear{2018} +%\copyrightyear{2018} + +%\acmPrice{15.00} + + +\begin{document} +\copyrightyear{2025} +\acmYear{2025} +\setcopyright{acmlicensed} +\acmConference[HSCC'25]{28th ACM International Conference on Hybrid Systems: Computation and Control, Irvine, California, May 6-9 2025} +\acmBooktitle{May 6-9 2025, Irvine, California, USA} +%\acmPrice{15.00} +%\acmDOI{10.1145/3178126.3178135} +%\acmISBN{978-1-4503-5642-8/18/04} + + +\title[TRUST: Controller Synthesis for Black-Box Systems Using a Single Trajectory]{TRUST: Stabili\underline{\textbf{T}}y and Safety Cont\underline{\textbf{R}}oller Synthesis for Black-Box Systems \underline{\textbf{U}}sing a \underline{\textbf{S}}ingle \underline{\textbf{T}}rajectory} + +\author{Jamie Gardner} +\affiliation{% + \institution{School of Computing} + \institution{Newcastle University} +} +\email{j.gardner3@newcastle.ac.uk} + +\author{Ben Wooding} +\affiliation{% + \institution{School of Computing} + \institution{Newcastle University} +} +\email{ben.wooding@newcastle.ac.uk} + +\author{Amy Nejati} +\affiliation{% + \institution{School of Computing} + \institution{Newcastle University} +} +\email{amy.nejati@newcastle.ac.uk} + +\author{Abolfazl Lavaei} +\affiliation{% + \institution{School of Computing} + \institution{Newcastle University} +} +\email{abolfazl.lavaei@newcastle.ac.uk} + +\begin{abstract} +TRUST is an open-source software tool for the single-trajectory data-driven control synthesis for Stability and safety barrier certificates (BCs). +The tool implements sum-of-squares (SOS) optimizations for the systematic production of both linear and polynomial BCs. By ensuring the persistently-excited state of the input data, which is determined by fulfilling a certain rank condition, the system will compute the stability functions and safety barrier certificates and their respective controllers for an infinite time horizon from the finite-length dataset. + +The stability and safety properties are calculated for four classes of dynamical systems: (i) continuous-time nonlinear polynomial systems, (ii) continuous-time linear systems, (iii) discrete-time nonlinear polynomial systems, and (iv) discrete-time linear systems. +For each of these four scenarios, TRUST can synthesize the stability function and controller or the safety barrier certificate and controller. + +TRUST is a Python-based web application, providing an intuitive and reactive GUI via web technologies, and can be accessed at or installed locally, and supports both manual data entry and data file uploads. +The tool uses the SOS optimization toolbox to solve the stability and safety barrier problems, and the symbolic programming library SymPy to handle the symbolic computations. +Leveraging the power of the Python backend and Javascript frontend, the tool is designed to be user-friendly and accessible on desktop, tablet, and mobile devices. +Physical case studies validate our data-driven approach for each of the four pairs of scenarios. +\end{abstract} + +% The code below should be generated by the tool at +% https://dl.acm.org/ccs.cfm +% Please copy and paste the code instead of the example below. + +\begin{CCSXML} +% +% +% 10003752.10003790.10011119 +% Theory of computation~Abstraction +% 500 +% +% +% 10010520.10010553 +% Computer systems organization~Embedded and cyber-physical systems +% 500 +% +% +% 10003033.10003039.10003041.10003043 +% Networks~Formal specifications +% 300 +% +% + +\end{CCSXML} + +%\ccsdesc[500]{Theory of computation~Abstraction} +%\ccsdesc[500]{Computer systems organization~Embedded and cyber-physical systems} +%\ccsdesc[300]{Networks~Formal specifications} + + +\keywords{Data-Driven Control Synthesis, Safety Verification, Barrier Certificates} + + +\maketitle + + +\section{introduction}\label{sec:introduction} + +\subsection{Motivation for TRUST}\label{subsec:motivation-for-sintra-sb} + +% Opening paragraphs. +% Look at previous works like PRoTECT (and other data-driven approaches from Abolfazl's website). Don't worry about coming up with this, just paraphrase and rewrite from the existing works. +The design of control systems that ensure stability and safety is a fundamental problem in control theory, with applications in safety-critical systems including robotics, aerospace, self-driving cars, and medical devices, to name a few. +Traditional model-based approaches to control synthesis rely on accurate mathematical models of the system dynamics, which are often difficult to obtain, or may not accurately reflect the real-world behavior of the system. +In contrast, data-driven methods have gained popularity due to their ability to handle unknown mathematical models based on the data collected from the system~\cite{nejati2023data}. + +%I. Stability +% A. Introduce the concept of stability in dynamical systems (i.e. what the Lyapunov function is) +% B. Discuss the importance of stability in control synthesis (we deal with asymptotic stability, where we return to a stable equilibrium rather than just stay at it) +A system is considered stable if it either remains at an equilibrium point or returns to it after a disturbance, known as asymptotic stability. +In control synthesis, stability is crucial for ensuring that the system behaves as intended, and does not deviate from its desired behavior. +This assurance comes from the calculation of a Lyapunov function for a system, which serves as a fundamental guarantee across the system's continuous-state space~\cite{breschi2021direct}. + +%II. Safety Barrier +% A. Introduce the concept of safety barrier certificates (we deal with control barrier certificates, where the user can provide the control data, i.e.\ U0) +% B. Explain how safety barrier certs are particularly useful in safety-critical systems, where the system not only needs to be stable but also avoid unsafe regions +% C. Note the use of Sum of Squares (SOS) optimization techniques +In addition to stability, safety barrier certificates formalise the notion of safety in dynamical systems, by ensuring that the system will never enter an unsafe region across an infinite time horizon. +Control barrier certificates (CBCs) are particularly useful for real-world systems, where the data is directly measured through input-output observations, known as a ``single trajectory''~\cite{ren2024formal}. + +%III. Data-driven (single-trajectory) +% A. Highlight the issue with traditional model-based approaches for stability or safety barriers +% 1. The system model is assumed to be known, which isn't realistic. +% B. Introduce data-driven approaches +% 1. More realistic +% 2. Often require large amounts of data, over many trajectories (order of magnitude in the millions) +% 3. Often requires the data to be independent and identically distributed (i.i.d.) +% C. Introduce the concept of single-trajectory data-driven control synthesis +% 1. Use of persistently-excited (full rank) data allows for the system to be analyzed and controlled using a single trajectory +% 1. Reduction in complexity +% 2. Reduction in data requirements + +% We can go into detail about how a single trajectory can be used to synthesize both the Lyapunov function and the barrier certificate. +% - Motivate the tool by highlighting the gap in current tooling. Start by referencing the orginal barrier certificate and stability works. Lead into data-driven tools which are more realistic, but expensive to get the correct data for, so tools should to work accurately with less data, which is where our approach differs. +% DPT19, ACE+19, KMS+24, MTZ22, NZ23, NZCZ22, PR07, SLSZ24, WRMDM05, WMPDP24, XCB23, BDPT20] also cite PRoTECT, FOSSIL, and any other barrier or data tools in the literature, and Ben’s data paper [AAE+21, WHL24, KMS+24]. + +% - Discuss what exactly the Lyapunov function is, as the foundational problem, in terms of what data is needed and how to compute the stability of a system. +% - Follow by specifically exploring Control Barrier Certificates (CBCs) which extend the stability (aka Lyapunov) function for level sets that segment the state space into an initial, safe space and one or more unsafe states. +% - Briefly interlude with the distinction of discrete- vs continuous-time systems (references?) +% - Where does the the differences between linear and nonlinear polynomial systems fit in here? +% The Lyapunov function is particularly useful for analyzing discrete-time systems, where it can be used to determine the behavior of a dynamical system based on its state sequence at each time step. +% However, for continuous-time systems, analysis becomes more complex due to the need for persistence of excitation. + +% - Reference Willems' fundamental lemma for "the concept of persistence of excitation" for continuous-time nonlinear polynomial systems +Willems' Fundamental Lemma provides a necessary condition for the existence of a stability function for continuous-time non-linear polynomial systems~\cite{willems2005note}, thus enabling the design of safety barrier certificates for these systems. +% Include a reference to Sum of Squares optimisation for the computation of the safetyb barrier certificate here? +The computation of these safety barrier certificates can be performed using Sum of Squares (SOS) optimization techniques, using an existing toolbox~\cite{prajna2002introducing}. +It is worth noting that despite many works on the subject of \emph{continuous-time} nonlinear polynomial systems~\cite{bisoffi2020data,bisoffi2022controller,nejati2022data}, few works deal with the more difficult production of results for single-trajectory \emph{discrete-time} non-linear polynomial systems~\cite{martin2023guarantees}. +% - Reference Behrad's paper for the solution to discrete-time nonlinear polynomial system safety +Despite this lack of research, this work implements a cutting-edge theoretical discovery on data-driven methods for the design of stable and safe controllers for this category of system~\cite{samari2024single}. +% - The problem: Finish the paragraph with the challenge of control synthesis for unknown mathematical models +% With this theoretical context in mind, the practical, real-world synthesis of a stable controller, and by extension a safe controller, is quite challenging, especially when the mathematical model of the system is unknown. +However, practical implementation of this research remains scarce, due to the complexity of real-world scenarios where the mathematical model of the system is unknown, or it is expensive in terms of manual effort to first identify and then solve the problem using model-based methods. + +% - The solution: Refer to the intro in Behrad's paper for an intro to the use of data-driven techniques as a reduction in the layers of complexity of the problem, and further how single trajectories and excited states can reduce the amount of data required. +As a solution, data-driven techniques offer a promising reduction in cost and complexity, by leveraging + +% - Break the solution down into its two parts: reduction in complexity, and reduction in data +- Clarify the complexity e.g. the problems like "linear quadratic regulation and robust controller design" (rephrase and reuse the references); "model-reference controller design for linear dynamical systems" (same as previous); "stabilization of polynomial systems" (and again); and how these approaches don't account for state constraints (i.e. the level sets - clarify the relevance?); + +- Then by clarifying the data requirements e.g. other scenario-based programs that require independent and identically distributed (i.i.d.) data which requires the collection of multiple trajectories (in the order of magnitude of millions) + +% - Lead this into the lack of tooling in the area +Recent studies have proposed various data-driven methods for this problem (reference PRoTECT, IMPaCT and FOSSIL), which are much more realistic than traditional model-based approaches. +However, these methods often require a large amount of data to provide accurate guarantees (reference), making them impractical for many real-world applications. + +- Then highlight this gap that SinTra fills, i.e. synthesizing stability functions and safety barrier certificates using persistently-excited, single-trajectory data. + +- Outline the benefits of this tool in terms of the formal guarantees it provides, including the breadth of scenarios for both stability and the extended problem of CBCs. + +\subsection{Related Literature}\label{subsec:related-literature} + +\subsection{Related Software}\label{subsec:related-software} +- Discuss the existing tools in the area, including PRoTECT, IMPaCT, and FOSSIL, and how they differ from SinTra. + +\subsection{Contributions}\label{subsec:contributions} +This tool paper contributes the following novel and noteworthy developments: +%- Review how specifically SinTra fits these needs when able to determine a persistently excited state, and detail what exactly this means, before bringing the user back to the novel contribution. +%- despite finite trajectories considered, the guarantees hold over infinite horizons. Nice interface. Stability and Safety guarantees. etc. +%- Unique contributions are primarily the tool being data-driven, but also by verifying that the samples are persistently excited, we can use single-trajectory data over a fixed time horizon whilst still providing (probabilistic) guarantees for an infinite time horizon, drastically reducing the data required in our tool. Additionally, our tool covers the breadth of scenarios for continuous time and discrete time linear and nonlinear polynomial, all in the one tool. +\begin{enumerate}[i.] +\item TRUST is a first-of-its-kind tool that uses data-driven approaches to synthesize stability functions and safety barrier certificates from a single-trajectory. +\item Implemented as a responsive and reactive Flask web application, TRUST provides an intuitive and user-friendly interface for users to interact with the tool. +\item Real-time client-side updates and error management through asynchronous JavaScript and XML (AJAX) requests provide a seamless user experience across any platform. +\item The server-side Python application leverages the Flask web framework to handle the data processing and computation of the stability functions and safety barrier certificates, following an MVC architecture and test-driven development for high-quality code. +\item TRUST extends the Sum of Squares (SOS) optimization toolbox powered by MOSEK to solve the stability and safety barrier problems for continuous-time and discrete-time linear and nonlinear polynomial systems using the symbolic programming library SymPy. +\item The tool allows for both manual data entry and data file uploads for the X0, U0 and X1 datasets, a simple user experience for defining the state space, initial set, and multiple unsafe sets of the system, and, for nonlinear polynomial systems, the monomial terms. +\item We demonstrate the usefulness of TRUST through eight distinct scenarios, representing the four classes of dynamical system, and their respective stability functions and safety barrier certificates. +\end{enumerate} + +\subsection{Structure of the Paper}\label{subsec:structure-of-the-paper} +This paper is structured as follows: +\begin{enumerate} +\item \hyperref[sec:introduction]{Introduction}: provides the necessary background information on stability functions and safety barrier certificates, and the data-driven approach to control synthesis. +\item \hyperref[sec:overview-of-the-tool]{Overview of the Tool}: gives an overview of the TRUST tool, including the notation used, the inputs required, and the outputs produced. +\item \hyperref[sec:problem-description]{Problem Description}: outlines the problem of stability and safety control synthesis for black-box systems using a single trajectory. +\item \hyperref[sec:scenarios]{Scenarios}: presents the four primary scenarios for continuous-time and discrete-time linear and nonlinear polynomial systems, demonstrating the tool's capabilities. +\item \hyperref[sec:benchmarks-and-case-studies]{Benchmarks and Case Studies}: provides a detailed analysis of the tool's performance through a series of benchmarks and case studies. +\item \hyperref[sec:results]{Results}: presents the results of the benchmarks and case studies, highlighting the tool's effectiveness in solving stability and safety problems. +\end{enumerate} + +% -- Section 2 -- + +\section{Overview of the Tool}\label{sec:overview-of-the-tool} + +\subsection{Notation}\label{subsec:notation} +$\mathbb{R}$, $\mathbb{R}^+_0$, and $\mathbb{R}^+$ denote the set of real numbers, non-negative and positive real numbers, respectively. $\mathbb{N}$ and $\mathbb{N}^+$ denote the set of natural numbers including and excluding zero. $\emptyset$ denotes the empty set. +The notation $\mathbb{R}^{a\times b}$ in general is used to describe a matrix of size $a\times b$ that contains real values, equivalently $\mathbb{N}^{a\times b}$ for natural numbers. +Similarly, a vector of size $n$ is denoted with $\mathbb{R}^n$ or $\mathbb{N}^n$. $A^{-1}$ and $A^\top$ are respectively the inverse and the transpose of matrix $A$. +We use $[a,b]$ for the closed set between $a$ and $b$. + +\subsection{Inputs to the tool}\label{subsec:inputs-to-the-tool} + +\subsubsection{Modes of the Tool} + +\textsf{TRUST} is valuable in solving two main types of problems: +\begin{enumerate} +\item \emph{Stability problems} - synthesizing a control Lyapunov function $\mathcal{V}(x)$ to show stability of the underlying system; +\item \emph{Safety barrier problems} - synthesizing a control barrier certificate $\mathcal{B}(x)$ to guarantee safe behavior of the underlying system. +\end{enumerate} +In addition to these two modes that assume the presence of control inputs, \textsf{TRUST} can satisfy the same problems without control inputs, which are simpler cases for both modes. +Therefore, all parameters relating to the controller or control inputs are optional. + +\subsubsection{Classes of Systems} + +\textsf{TRUST} can handle four main classes of systems; discrete-time linear systems (dt-LS), continuous-time linear systems (ct-LS), discrete-time nonlinear polynomial systems (dt-NPS) and continuous-time nonlinear polynomial systems (ct-NPS). It can handle each of these classes of systems for both the generation of stability functions and safety barrier certificates and their respective controllers. + +\subsubsection{Datasets (\texttt{*.csv}, \texttt{*.txt}, \texttt{*.json})} +\textsf{TRUST} takes in as input the necessary datasets that together contain a \emph{persistently excited} data trajectory, these are expected to be in one of the following common data file extensions; \texttt{*.csv}, \texttt{*.txt}, or \texttt{*.json}. +The data should be sequential over a time horizon of $T\in\mathbb{N}^+$ steps, and may have multiple state dimensions $n\in\mathbb{N}^+$ and input dimensions $m\in\mathbb{N}$. +In the discrete-time cases, the datasets can be represented as: +\begin{align} +\label{eq:data-discrete} +\begin{cases} +&\mathcal{X}_{0} = [x(0),x(1),x(2),\ldots,x(T-1)],\\ +&\mathcal{U}_{0} = [u(0),u(1),u(2),\ldots,u(T-1)],\\ +&\mathcal{X}_{1} = [x(1),x(2),x(3),\ldots,x(T)], +\end{cases} +\end{align} +where $\mathcal{X}_{0}$ is generally the predecessor states, $\mathcal{X}_{1}$ is generally the successor states, and if there are control inputs they are captured by $\mathcal{U}_{0}$. + +\begin{remark} +We remark that the tool can handle $m=0$ when there is no input present, the theoretical results remain largely the same~\BW{[cite my k-inductive paper]} with the key difference being no controller $u$ is designed. +In such a situation $\mathcal{U}_{0}$ is omitted completely. +\end{remark} + +In a small abuse of notation, the continuous-time data is again sequential as: +\begin{align} +\label{eq:data-continuous} +\begin{cases} +&\mathcal{X}_{0} = [x(0),x(\tau),x(2\tau),\ldots,x((T-1)\tau)],\\ +&\mathcal{U}_{0} = [u(0),u(\tau),u(2\tau),\ldots,u((T-1)\tau)],\\ +&\mathcal{X}_{1} = [\dot{x}(0),\dot{x}(\tau),\dot{x}(2\tau),\ldots,\dot{x}((T-1)\tau)], +\end{cases} +\end{align} +where $\tau$ is a fixed sampling time for the system. +Additionally, $\mathcal{X}_{1}$ contains the derivatives of the state at each sampling time. +\begin{remark} +In practice, these derivatives are likely to be approximated, any error handling relating to this approximation is left to the user. +\end{remark} + + +\textsf{TRUST} will check that the data satisfies a rank condition that ensures the data is persistantly excited. +This rank condition is defined as~\cite{de2019formulas} + +\begin{equation} +\label{eq:rank} +\text{rank}\begin{bmatrix} +\mathcal{U}_0 \\ +\hline +\mathcal{X}_0 +\end{bmatrix} = n+m. +\end{equation} + +\subsubsection{Monomials (polynomials in $x$)} +\emph{For nonlinear polynomial systems}, the user should provide a matrix of monomial terms $\mathcal{M}(x)$. +As an example, of this when $x\in\mathbb{R}^2$: $\mathcal{M}(x) = \begin{bmatrix} +x_1^2 & +x_1 x_2 & +x_2 +\end{bmatrix}^\top$ +where here the number of monomial terms is $N=3$ and $N\in\mathbb{N}^+$. + +\subsubsection{Definitions of initial set $X_I$ , unsafe set $X_U$, state space $X$} +For safety barrier problems, the user should define the state space $X$, initial set $X_I$ and unsafe set $X_U$ of the system using hypercubes for the \emph{semi-algebraic sets}~\cite{parrilo2003semidefinite}. +Since they are semi-algebraic, the hypercubes can be described as vectors of polynomials respectively $g_I(x), g_U(x)$ and $g(x)$. \textsf{TRUST} collects the lower bound and the upper bound for each dimension to construct the hypercube. + +\subsection{Outputs from Tool}\label{subsec:outputs-from-tool} + +The outputs of \textsf{TRUST} will depend on the mode chosen. +For stability problems, \textsf{TRUST} will output a Lyapunov function $\mathcal{V}(x)$ based on the data or for safety barrier problems the safety barrier certificate $\mathcal{B}(x)$ and its level sets $\gamma$ and $\lambda$. +If either cannot be synthesized then \textsf{TRUST} will return some sort of error message. + +In both modes the functions, $\mathcal{V}(x)$ or $\mathcal{B}(x)$, are quadratic of the form $x^\top Px$ in the majority of cases and $\mathcal{M}(x)^\top P\mathcal{M}(x)$ in the continuous-time nonlinear polynomial case, where $P\succ 0$ is a symmetric positive definite matrix. +For problems that include data for control inputs $\mathcal{U}_{0}$, we will also return to the user the controller, $u\in\mathbb{R}^m$, synthesized for $\mathcal{V}(x)$ or $\mathcal{B}(x)$. + + +\section{Problem Description}\label{sec:problem-description} + +- A few paragraphs that outline the problem to the reader +- Specifically, detail the notations and definitions used (stability function, barrier function) +- Concisely describe the tool in terms of applications and underlying algorithms (web-based UI, SOS toolbox, symbolic programming) +- Pseudocode of the tool +- Touch on the web stack at a high level as the entry point to the system +- Focus more on the hierarchy of the problems, i.e. the simultaneous equations to solve for P and H, before the SOS conditions. + + +\section{Scenarios}\label{sec:scenarios} + +- Introduce the four systems, each with their safety function and stability barrier function alternatives. +- Include the controller synthesis in each case +- Add a marked-up screenshot of the tool, highlighting each region +- three columns, first for data entry, second for state definitions, third for output +- footer with the title and description, and the primary Calculate action + +%We first define generally the conditions required to find model-based control barrier certificates (CBC) for continuous-time systems, we will then demonstrate how these conditions are used in the data-driven section for the different classes of continuous systems that follow as well as the stability conditions for each of these classes of system. +We remind the reader that the data considered in this section is of the form in equation~\eqref{eq:data-continuous}. + +\subsection{Continuous Time Nonlinear Polynomial Systems}\label{subsec:continuous-time-nonlinear-polynomial-systems} +We consider continuous-time nonlinear polynomial systems (ct-NPS) defined as follows: + +\begin{definition} +\label{def:system-description-ct-NPS} +A ct-NPS is described by the ordinary differential equation +\begin{equation} +\label{eq:ct-NPS} +\Sigma_c: \dot{x} = A\mathcal{M}(x)+Bu +\end{equation} +where $A\in\mathbb{R}^{n\times N}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $\mathcal{M}(x)\in\mathbb{R}^N$ is a vector of monomials in state $x\in X$, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. +\end{definition} + +We now present the following lemma, taken from~\cite{nejati2022data}, to obtain a data-based representation of closed-loop ct-NPS~\eqref{def:system-description-ct-NPS} with controllers $u=K(x)\mathcal{M}(x)$, where $K(x)\in\mathbb{R}^{m\times N}$ is a matrix polynomial, which will be synthesized. + +\begin{lemma}[ct-NPS Q-Lemma~\cite{nejati2022data}] +\label{lem:Q-ctNPS} +Let matrix polynomial $Q(x)$ be a $(T\times N)$ matrix such that +\begin{equation} +\label{eq:Q-matrix-ctNPS} +\mathbb{I}_n = \mathcal{N}_{0}Q(x), +\end{equation} +with +\begin{equation} +\label{eq:data-N0T} +\mathcal{N}_{0} = [\mathcal{M}(x(0)), \mathcal{M}(x(\tau)), \mathcal{M}(x(2\tau)), \ldots, \mathcal{M}(x((T-1)\tau))] +\end{equation}being an $(N\times T)$ full row-rank matrix. +If one sets $u=K(x)\mathcal{M}(x) = \mathcal{U}_{0}Q(x)\mathcal{M}(x)$, then the closed-loop system $\dot{x}=A\mathcal{M}(x)+Bu$ has the following data-based representation: +\begin{equation} +\label{eq:A+BK=X1TQ-ctNPS} +\dot{x} = \mathcal{X}_{1}Q(x)\mathcal{M}(x),\quad\text{equivalently,}\quad A+BK(x) = \mathcal{X}_{1}Q(x). +\end{equation} +\end{lemma} + +Using the above lemma, we now have a data-driven representation of our system using $\mathcal{X}_{1}Q(x)\mathcal{M}(x)$, which we will use to design controllers for CBCs and stability in the following theorems. + +\subsubsection{Control Barrier Certificate} + +\begin{theorem}[Data-Driven ct-NPS CBC~\cite{nejati2022data}] +\label{thm:data-ctNPS-CBC} +Consider the unknown ct-NPS~\eqref{eq:ct-NPS}, \emph{i.e.} $\dot{x} = A\mathcal{M}(x)+Bu$, with its data-based representation $\dot{x}=\mathcal{X}_{1}Q(x)\mathcal{M}(x)$. +Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q(x)=H(x)P$ such that the following conditions are satisfied +\begin{align} +\label{eq:ctNPS_CBC_data1} +\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) \leq \gamma, &\quad\forall x\in X_I, \\ +\label{eq:ctNPS_CBC_data2} +\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) \geq \lambda, &\quad\forall x\in X_U, +\end{align} +and $\forall x\in X$, +\begin{align} +\label{eq:ctNPS_CBC_data3} +\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top &\leq 0,\\ +\label{eq:ctNPS_CBC_data0} +\mathcal{N}_{0}H(x)&=P^{-1}. +\end{align} +Then $\mathcal{B}(x) = \mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x)$ is a CBC and \newline $u = \mathcal{U}_{0}H(x)[\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x)$ is its corresponding safety controller for the unknown ct-NPS. +\end{theorem} + +\subsubsection{Sum-of-Squares Formulation} +\BW{Add a reference for this formulation.} We present now how to solve equations~\eqref{eq:ctNPS_CBC_data1}-\eqref{eq:ctNPS_CBC_data0} in this first occurrence of the conditions, the CBC conditions for later sections follow similarly but are omitted for brevity. + +We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. +We can solve the following using the SumOfSquares toolbox~\cite{Yuan_SumOfSquares_py} where we also add an additional LMI constraint for the equality~\eqref{eq:ctNPS_CBC_data0}. + +We consider~\eqref{eq:ctNPS_CBC_data0} +and the following are sum-of-squares +\begin{align} +\label{eq:ct-SOS1} +-\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) -& L_I^\top(x)g_I(x) + \gamma, \\ +\label{eq:ct-SOS2} +\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) -& L_U^\top(x)g_U(x) + \lambda, \\ +\label{eq:ct-SOS3} +-[\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top] -& L^\top(x)g(x). +\end{align} + +% We should know $\frac{\partial M}{\partial x}$ since the monomials $M(x)$ are already given to us. + +% To solve first find solutions to +% \begin{equation*} +% P^{-1} = \mathcal{N}_{0}H(x) +% \end{equation*} +% and +% \begin{equation*} +% -[\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top]\geq 0 +% \end{equation*} +% then solve the sum of squares conditions to find $\gamma$ and $\lambda$. Then the barrier certificate is given by $\mathcal{B}(x) = \mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1} \mathcal{M}(x)$ and the controller by $u = \mathcal{U}_{0}H(x)(\mathcal{N}_{0}H(x))^{-1}M(x)$, we also return $\gamma$ and $\lambda$. + +A hierarchical approach to solve Theorem~\ref{thm:data-ctNPS-CBC} is used where first $H(x)$ and $P$ are found in equations~\eqref{eq:ctNPS_CBC_data3}-\eqref{eq:ctNPS_CBC_data0} before equations~\eqref{eq:ctNPS_CBC_data1}-\eqref{eq:ctNPS_CBC_data2} are solved using SOS programming for $\gamma$ and $\lambda$. +This is shown in Algorithm~\ref{alg:ct-nonlinear}. + +\begin{algorithm}[t] +\caption{Hierarchy for ct-NPS CBCs}\label{alg:ct-nonlinear} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U, \mathcal{M}(x)$ +\Ensure \eqref{eq:rank} holds +\Ensure semi-algebraic $X,X_I,X_U$ +\State Solve~\eqref{eq:ctNPS_CBC_data3} and~\eqref{eq:ctNPS_CBC_data0} for $H(x)$ and $P$ via LMIs +%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ +\State Substitute and solve~\eqref{eq:ctNPS_CBC_data1}-\eqref{eq:ctNPS_CBC_data2} via SOS optimization~\eqref{eq:ct-SOS1}-\eqref{eq:ct-SOS3} +\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +\subsubsection{Stability} + +Solving only the last CBC conditions~\eqref{eq:ctNPS_CBC_data3}-\eqref{eq:ctNPS_CBC_data0} with no restriction over a state space $X$ renders the stability problem. + +\begin{theorem}[ct-NPS Stable Controller Design] +\label{thm:ctNPS-stable} +A control Lyapunov function $\mathcal{V}(x)=\mathcal{M}(x)^\top P\mathcal{M}(x)$ guaranteeing stability of the ct-NPS~\eqref{eq:ct-NPS} can be designed by introducing the new variable +\begin{equation*} +\label{eq:Q=HP-ctNPS} +Q(x)=H(x)P, +\end{equation*} +so that any polynomial matrices $H(x)\in\mathbb{R}^{T\times N}$, and $P\in\mathbb{R}^{N\times N}$ satisfying +\begin{align} +\label{eq:stability-ctNPS} +\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top \prec 0, \quad \mathcal{N}_{0}H(x)=P^{-1} +\end{align} +stabilize~\eqref{eq:ct-NPS}. +The controller is given by~\newline$u=\mathcal{U}_{0}Q(x)\mathcal{M}(x) = \mathcal{U}_{0}H(x)[\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x).$ +\end{theorem} + +We remark here that the stability conditions are straightforward to solve using semidefinite programming solvers such as SEDUMI or Mosek \BW{cite whichever we use, and remove the other}. The psuedocode for ct-NPS stability is given in Algorithm~\ref{alg:ct-stab}. + +\begin{algorithm}[t] +\caption{Hierarchy for ct-NPS Stability}\label{alg:ct-stab} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0, \mathcal{M}(x)$ +\Ensure \eqref{eq:rank} holds +\State Solve~\eqref{eq:stability-ctNPS} for $H(x)$ and $P$ via LMIs +\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +\subsection{Continuous Time Linear Systems}\label{subsec:continuous-time-linear-systems} + +We consider continuous-time linear systems (ct-LS) defined as follows: + +\begin{definition} +\label{def:system-description-ct-LS} +A ct-LS is described by the ordinary differential equation +\begin{equation} +\label{eq:ct-LS} +\Sigma_c: \dot{x} = Ax+Bu +\end{equation} +where $A\in\mathbb{R}^{n\times n}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $x\in X$ is a system state, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. +\end{definition} + +\begin{remark} +We remark that in general ct-NPS can be simplified to the linear system by replacing $\mathcal{M}(x)$ with $x$ and $\mathcal{N}_{0}$ with $\mathcal{X}_{0}$. +\end{remark} + +We now present the following lemma, adapted here to ct-LS from the work~\cite{de2019formulas}, to obtain a data-based representation of closed-loop ct-LS~\eqref{def:system-description-ct-LS} with controllers $u=Kx$, where $K\in\mathbb{R}^{m\times n}$ is a matrix, which will be synthesized. + +\begin{lemma}[ct-LS Q-Lemma~\cite{de2019formulas}] +\label{lem:Q-ctLS} +Let matrix $Q$ be a $(T\times n)$ matrix such that +\begin{equation} +\label{eq:Q-matrix-ctLS} +\identity_n = \mathcal{X}_{0}Q, +\end{equation} +where $\mathcal{X}_{0}$ is an $(n\times T)$ full row-rank matrix. +If one sets $u=Kx = \mathcal{U}_{0}Qx$, then the closed-loop system $\dot{x}=Ax+Bu$ has the following data-based representation: +\begin{equation} +\label{eq:A+BK=X1TQ-ctLS} +\dot{x} = \mathcal{X}_{1}Qx,\quad\text{equivalently,}\quad A+BK = \mathcal{X}_{1}Q. +\end{equation} +\end{lemma} + +Using the above lemma, we know have a data-driven representation of our system using $\mathcal{X}_{1}Qx$, which we will use to design controllers for stability and CBCs in the following theorems. + +\subsubsection{Control Barrier Certificates} + +\begin{theorem}[Data-Driven ct-LS CBC~\cite{wang2024convex}] +\label{thm:data-ctLS-CBC} +Consider the unknown ct-LS~\eqref{eq:ct-LS}, \emph{i.e.} $\dot{x} = Ax+Bu$, with its data-based representation $\dot{x}=\mathcal{X}_{1}Qx$. +Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q=HP$ such that the following conditions are satisfied +\begin{align} +\label{eq:ct_CBC_data1} +x^\top [\mathcal{X}_{0}H]^{-1}x \leq \gamma, &\quad\forall x\in X_I, \\ +\label{eq:ct_CBC_data2} +x^\top [\mathcal{X}_{0}H]^{-1}x \geq \lambda, &\quad\forall x\in X_U, +\end{align} +and $\forall x\in X$, +\begin{align} +\label{eq:ct_CBC_data3} +\mathcal{X}_{1}H + H^\top\mathcal{X}_{1}^\top &\leq 0\\ +\label{eq:ct_CBC_data0} +P^{-1} = \mathcal{X}_{0}H. +\end{align} +Then $\mathcal{B}(x) = x^\top [\mathcal{X}_{0}H]^{-1}x$ is a CBC and $u = \mathcal{U}_{0}H[\mathcal{X}_{0}H]^{-1}x$ is its corresponding safety controller for the unknown ct-LS. +\end{theorem} + +% \begin{corollary}[ct-LS controller design] +% \label{cor:ct-LS-controller} +% The controller for~\eqref{eq:ct_CBC_data3} can be designed to avoid the bilinearity between $P$ and $Q$ in a hierarchical manner by introducing $Q=HP$ and solving the following equations +% \begin{equation} +% \label{eq:ctLS-controller} +% H^\top\mathcal{X}_{1}^\top+ \mathcal{X}_{1}H \leq 0, \quad P^{-1} = \mathcal{X}_{0}H. +% \end{equation} +% \end{corollary} + +We can again design a ct-LS CBC using a hierarchical approach as outlined in Algorithm~\ref{alg:ct-linear}. + +\begin{algorithm}[t] +\caption{Hierarchy for ct-LS CBCs}\label{alg:ct-linear} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U$ +\Ensure \eqref{eq:rank} holds +\Ensure semi-algebraic $X,X_I,X_U$ +\State Solve~\eqref{eq:ct_CBC_data3} and~\eqref{eq:ct_CBC_data0} for $H(x)$ and $P$ via LMIs +%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ +\State Substitute and solve~\eqref{eq:ct_CBC_data1}-\eqref{eq:ct_CBC_data2} via SOS optimization +\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +% \subsection{Sum-of-Squares Formulation} + +% We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. We can solve the following using the SumOfSquares~\cite{Yuan_SumOfSquares_py} toolbox where we also add an additional constraint for the equality. We consider matrix $Q\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$ such that +% \begin{equation} +% \mathbb{I} = \mathcal{X}_{0}Q +% \end{equation} +% and the following are sum-of-squares +% \begin{align} +% -x^\top Px -& L_I^\top(x)g_I(x) + \gamma, \\ +% x^\top Px -& L_U^\top(x)g_U(x) + \lambda, \\ +% -[\mathcal{X}_{1}Q + Q^\top\mathcal{X}_{1}^\top] -& L^\top(x)g(x). +% \end{align} + +% Then the barrier certificate is given by $\mathcal{B}(x) = x^\top P x$ and the controller by $u = \mathcal{U}_{0}Qx$, we also return $\gamma$ and $\lambda$. + +\subsubsection{Stability} +We highlight again that solving equations~\eqref{eq:ct_CBC_data3}-\eqref{eq:ct_CBC_data0} without restricting $X$ gives the ct-LS stability conditions as follows. + +\begin{theorem}[ct-LS Stable Controller Design~\cite{de2019formulas}] +\label{thm:ctLS-stable} +A control Lyapunov function $\mathcal{V}(x)=x^\top Px$ guaranteeing stability of the ct-LS~\eqref{eq:ct-LS} can be designed by introducing the new variable +\begin{equation*} +\label{eq:Q=HP-ctLS} +Q=HP, +\end{equation*} +so that any matrices $H\in\mathbb{R}^{T\times n}$, and $P\in\mathbb{R}^{n\times n}$ satisfying +\begin{align} +\label{eq:stability-ctLS} +H^\top\mathcal{X}_{1}^\top + \mathcal{X}_{1}H \prec 0, \quad \mathcal{X}_{0}H=P^{-1} +\end{align} +stabilize~\eqref{eq:ct-LS}. +The controller is given by $u=\mathcal{U}_{0}Qx = \mathcal{U}_{0}H[\mathcal{X}_{0}H]^{-1}x.$ +\end{theorem} + +These conditions for stability are straightforward to solve using standard linear matrix inequality (LMI) solvers. The psuedocode for ct-NPS stability is given in Algorithm~\ref{alg:ctLS-stab}. + +\begin{algorithm}[t] +\caption{Hierarchy for ct-LS Stability}\label{alg:ctLS-stab} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0$ +\Ensure \eqref{eq:rank} holds +\State Solve~\eqref{eq:stability-ctLS} for $H(x)$ and $P$ via LMIs +\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +\subsection{Discrete Time Nonlinear Polynomial Systems}\label{subsec:discrete-time-nonlinear-polynomial-systems} + +We consider discrete-time nonlinear polynomial systems (dt-NPS) defined as follows: + +\begin{definition} +\label{def:system-description-dt-NPS} +A dt-NPS is described by +\begin{equation} +\label{eq:dt-NPS} +\Sigma_d: x^+ = A\mathcal{M}(x)+Bu +\end{equation} +where $A\in\mathbb{R}^{n\times N}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $\mathcal{M}(x)\in\mathbb{R}^N$ is a vector of monomials in state $x\in X$, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. +\end{definition} + +We now present the following lemma, from the work~\cite{samari2024singletrajectory}, to obtain a data-based representation of closed-loop dt-NPS~\eqref{def:system-description-dt-NPS} with controllers $u=K(x)x$, where $K(x)\in\mathbb{R}^{m\times n}$ is a matrix, which will be synthesized. + +\begin{lemma}[dt-NPS Q-Lemma~\cite{samari2024singletrajectory}] +\label{lem:Q-dtNPS} +Let $Q(x)$ be a $(T\times n)$ matrix polynomial such that +\begin{equation} +\label{eq:nonlinear-theta=NQ} +\Theta(x) = \mathcal{N}_{0}Q(x), +\end{equation} +where $\Theta(x)$ is a $(N\times n)$ matrix polynomial +\begin{equation} +\label{eq:nonlinear-M=thetax} +\mathcal{M}(x)=\Theta(x)x, +\end{equation} +and where $\mathcal{N}_{0}$ is an $(N\times T)$ full row-rank matrix: +\begin{equation} +\label{eq:data-N0T-dt} +\mathcal{N}_{0} = [\mathcal{M}(x(0)), \mathcal{M}(x(1)), \mathcal{M}(x(2)), \ldots, \mathcal{M}(x(T-1))]. +\end{equation} If one sets $u=K(x)x = \mathcal{U}_{0}Q(x)x$, then the closed-loop system $x^+=A\mathcal{M}(x)+Bu$ has the following data-based representation: +\begin{equation*} +x^+ = \mathcal{X}_{1}Q(x)x, +\end{equation*} +equivalently +\begin{equation} +\label{eq:nonlinearA+BK=X1TQ} +A\Theta(x)+BK(x) = \mathcal{X}_{1}Q(x). +\end{equation} +\end{lemma} + +Using the above lemma, we now have a data-driven representation of our system using $\mathcal{X}_{1}Q(x)x$, which we will use to design controllers for CBCs and stability in the following theorems. + +\subsubsection{Control Barrier Certificates} + +\begin{theorem}[Data-Driven dt-NPS CBC~\cite{samari2024singletrajectory}] +\label{thm:data-dtNPS-CBC} +Consider the unknown dt-NPS~\eqref{eq:dt-NPS}, \emph{i.e.} $x^+ = A\mathcal{M}(x)+Bu$, with its data-based representation $x^+=\mathcal{X}_{1}Q(x)x$. +Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q(x) = H(x)P$ such that the following conditions are satisfied +\begin{align} +\label{eq:nonlinear-safe_CBC_data1} +x^\top Px \leq \gamma, &\quad\forall x\in X_I, \\ +\label{eq:nonlinear-safe_CBC_data2} +x^\top Px \geq \lambda, &\quad\forall x\in X_U, +\end{align} +and $\forall x\in X$, +\begin{align} +\label{eq:nonlinear-safe_CBC_data3} +\begin{bmatrix} +P^{-1} & H(x)^\top \mathcal{X}_{1}^\top \\ +\mathcal{X}_{1}H(x) & P^{-1} +\end{bmatrix} \geq 0,\\ +\label{eq:nonlinear-safe_CBC_data0} +\Theta(x)P^{-1} = \mathcal{N}_{0}H(x). +\end{align} +Then $\mathcal{B}(x) = x^\top Px$ is a $k$-CBC and $u = \mathcal{U}_{0}H(x)Px$ is its corresponding safety controller for the unknown dt-NPS. +\end{theorem} + +%\BW{Substitute $H=QP^{-1}$.} +% Since~\eqref{eq:nonlinear-safe_CBC_data3} contains unknown matrices $Q(x)$ and $P$ there are bilinearities that should be resolved before solving. One hierarchical method is to find any $Q(x)$ from~\eqref{eq:nonlinear-theta=NQ} and then solve for $P$. We raise the following corollary to show a second method for resolving~\eqref{eq:nonlinear-safe_CBC_data3} simultaneously for $P$ and $Q(x)$, while creating +We use the following hierarchical method for finding the CBC by first solving~\eqref{eq:nonlinear-safe_CBC_data3}-\eqref{eq:nonlinear-safe_CBC_data0} followed by~\eqref{eq:nonlinear-safe_CBC_data1}-\eqref{eq:nonlinear-safe_CBC_data2} afterwards. +A temporary variable $Z=P^{-1}$ can be considered during the solving. +The psuedocode algorithm is described in Algorithm~\ref{alg:dt-nonlinear}. + +\begin{algorithm}[t] +\caption{Hierarchy for dt-NPS CBCs}\label{alg:dt-nonlinear} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U, \mathcal{M}(x)$ +\Ensure \eqref{eq:rank} holds +\Ensure semi-algebraic $X,X_I,X_U$ +\State Solve~\eqref{eq:nonlinear-M=thetax} for $\Theta(x)$ +\State Substitute $\Theta(x)$ in~\eqref{eq:nonlinear-theta=NQ} +\State Solve~\eqref{eq:nonlinear-safe_CBC_data3} and~\eqref{eq:nonlinear-safe_CBC_data0} for $H(x)$ and $P$ via LMIs +%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ +\State Substitute $P$ and solve~\eqref{eq:nonlinear-safe_CBC_data1}-\eqref{eq:nonlinear-safe_CBC_data2} via SOS optimization +\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +% \begin{corollary}[CBC Controller Design] +% \label{cor:dt-NPS-controller} +% We consider matrix $H(x)\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$. We set $Z=P^{-1}$ and $Q(x)Z=H(x)$, such that +% \begin{equation} +% \label{eq:Z=X0H} +% \Theta(x)Z = \mathcal{N}_{0}H(x) +% \end{equation} +% then~\eqref{eq:safe_CBC_data3} can be equivalently represented by +% \begin{equation} +% \label{eq:SchurZ-dtNPS} +% \begin{bmatrix} +% Z & H(x)^\top \mathcal{X}_{1}^\top \\ +% \mathcal{X}_{1}H(x) & Z +% \end{bmatrix} \geq 0,\quad \forall x\in X. +% \end{equation} +% The controller is thus $u=\mathcal{U}_{0}H(x)Z^{-1}x$. +% \end{corollary} + +\subsubsection{Stability} + +\begin{theorem}[dt-NPS Stable Controller Design] +\label{thm:dtNPS-stable} +A control Lyapunov function $\mathcal{V}(x)=x^\top Px$ guaranteeing stability of the dt-NPS~\eqref{eq:dt-NPS} can be designed by introducing the new variable +\begin{equation*} +\label{eq:N0H=ThetaP} +Q(x)Z=H(x), +\end{equation*} +where $Z=P^{-1}$ so that any matrices $H(x)\in\mathbb{R}^{T\times n}$, $\Theta(x)\in\mathbb{R}^{N\times n}$, $P\in\mathbb{R}^{n\times n}$ and $Z\in\mathbb{R}^{n\times n}$ satisfying +\begin{align} +\label{eq:schur-stability-dtNPS} +\begin{bmatrix} +Z & H(x)^\top\mathcal{X}_{1}^\top \\ +\mathcal{X}_{1} H(x) & Z +\end{bmatrix} \succ 0, \quad \mathcal{N}_{0}H(x)=\Theta(x)Z +\end{align} +stabilize~\eqref{eq:dt-NPS}. +The controller is given by $u=\mathcal{U}_{0}H(x)Z^{-1}x.$ +\end{theorem} + +Solving the stability equation~\eqref{eq:schur-stability-dtNPS} is straightforward using standard semidefinite programming solvers such as SEDUMI or Mosek,~\BW{cite whichever we used}. The psuedocode for dt-NPS stability is given in Algorithm~\ref{alg:dt-stab}. + +\begin{algorithm}[t] +\caption{Hierarchy for dt-NPS Stability}\label{alg:dt-stab} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0, \mathcal{M}(x)$ +\Ensure \eqref{eq:rank} holds +\State Solve~\eqref{eq:nonlinear-M=thetax} for $\Theta(x)$ +\State Solve~\eqref{eq:schur-stability-dtNPS} for $H(x)$ and $Z$ via LMIs +\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +% \subsection{Sum-of-Squares Formulation} + +% We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. We can solve the following using the SumOfSquares~\cite{Yuan_SumOfSquares_py} toolbox where we also add an additional constraint for the equality. We consider matrix polynomial $H(x)\in\mathbb{R}^{T\times N}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$ such that +% \begin{equation} +% \Theta(x)P^{-1} = \mathcal{N}_{0}H(x) +% \end{equation} +% and the following are sum-of-squares +% \begin{align} +% -x^\top Px -& L_I^\top(x)g_I(x) + \gamma, \\ +% x^\top Px -& L_U^\top(x)g_U(x) + \lambda, \\ +% \begin{bmatrix} +% P^{-1} & H(x)^\top\mathcal{X}_{1}^\top \\ +% \mathcal{X}_{1}H(x) & P^{-1} +% \end{bmatrix} -& L^\top(x)g(x). +% \end{align} + +% \JG{For solving 4.18, we can assume that $P^{-1} = Z$, so we don't need to repeat that before and after}\newline +% To solve first find solutions to +% \begin{equation*} +% \Theta(x)Z = \mathcal{X}_{0}H(x) +% \end{equation*} +% and +% \begin{equation*} +% \begin{bmatrix} +% Z & H(x)^\top\mathcal{X}_{1}^\top \\ +% \mathcal{X}_{1}H(x) & Z +% \end{bmatrix}\succ 0 +% \end{equation*} +% then solve $P = Z^{-1}$ and solve the sum of squares conditions to find $\gamma$ and $\lambda$. Then the barrier certificate is given by $\mathcal{B}(x) = x^\top P x$ and the controller by $u = \mathcal{U}_{0}H(x)[\mathcal{N}_{0}H(x)]^{-1}x$, we also return $\gamma$ and $\lambda$. + +\subsection{Discrete Time Linear Systems}\label{subsec:discrete-time-linear-systems} + +We consider discrete-time linear systems (dt-LS) defined as follows: + +\begin{definition} +\label{def:system-description-dt-LS} +A dt-LS is described by +\begin{equation} +\label{eq:dt-LS} +\Sigma_d: x^+ = Ax+Bu +\end{equation} +where $A\in\mathbb{R}^{n\times n}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $x\in X$ is a system state, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. +\end{definition} + +\begin{remark} +As it was with ct-NPS to ct-LS, we remark that in general the results for dt-NPS can be simplied to linear systems by replacing $\mathcal{M}(x)$ with $x$, and $\mathcal{N}_{0}$ with $\mathcal{X}_{0}$. +\end{remark} + +We now present the following lemma, adapted here to dt-LS from the work~\cite{de2019formulas}, to obtain a data-based representation of closed-loop dt-LS~\eqref{def:system-description-dt-LS} with controllers $u=Kx$, where $K\in\mathbb{R}^{m\times n}$ is a matrix, which will be synthesized. + +\begin{lemma}[dt-LS Q-Lemma~\cite{de2019formulas}] +\label{lem:Q-dtLS} +Let matrix $Q$ be a $(T\times n)$ matrix such that +\begin{equation} +\label{eq:Q-matrix-dtLS} +\identity_n = \mathcal{X}_{0}Q, +\end{equation} +where $\mathcal{X}_{0}$ is an $(n\times T)$ full row-rank matrix. +If one sets $u=Kx = \mathcal{U}_{0}Qx$, then the closed-loop system $x^+=Ax+Bu$ has the following data-based representation: +\begin{equation} +\label{eq:A+BK=X1TQ-dtLS} +x^+ = \mathcal{X}_{1}Qx,\quad\text{equivalently,}\quad A+BK = \mathcal{X}_{1}Q. +\end{equation} +\end{lemma} + +We use the above lemma, to describe our system in terms of its data-driven representation $\mathcal{X}_{1}Qx$ and use that representation in the following theorems. + +\subsubsection{Control Barrier Certificate} + +\begin{theorem}[Data-Driven dt-LS CBC] +\label{thm:data-dtLS-CBC} +Consider the unknown dt-LS~\eqref{eq:dt-LS}, \emph{i.e.} $x^+ = Ax+Bu$, with its data-based representation $x^+=\mathcal{X}_{1}Qx$. +Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q=HP$ such that the following conditions are satisfied +\begin{align} +\label{eq:safe_CBC_data1} +x^\top Px \leq \gamma, &\quad\forall x\in X_I, \\ +\label{eq:safe_CBC_data2} +x^\top Px \geq \lambda, &\quad\forall x\in X_U, +\end{align} +and $\forall x\in X$, +\begin{align} +\label{eq:safe_CBC_data3} +\begin{bmatrix} +P^{-1} & H^\top\mathcal{X}_{1}^\top \\ +\mathcal{X}_{1}H & P^{-1} +\end{bmatrix} \geq 0, \\ +\label{eq:safe_CBC_data0} +P^{-1} = \mathcal{X}_{0}H. +\end{align} +Then $\mathcal{B}(x) = x^\top Px$ is a CBC and $u = \mathcal{U}_{0}HPx$ is its corresponding safety controller for the unknown dt-LS. +\end{theorem} + +% Since~\eqref{eq:safe_CBC_data3} contains unknown matrices $Q$ and $P$ there are bilinearities that should be resolved before solving. One hierarchical method is to find any $Q$ from~\eqref{eq:Q-matrix-dtLS} and then solve for $P$. We raise the following corollary to show a second method for resolving~\eqref{eq:safe_CBC_data3} simultaneously for $P$ and $Q$, while creating a +By substituting $Z=P^{-1}$, the following hierarchical method is used for finding the CBC by solving~\eqref{eq:safe_CBC_data3}-\eqref{eq:safe_CBC_data0} first to find $H$ and $P^{-1}$ followed by solving~\eqref{eq:safe_CBC_data1}-\eqref{eq:safe_CBC_data2} afterwards. The psuedocode algorithm for this is described in Algorithm~\ref{alg:dt-linear}. + +\begin{algorithm}[t] +\caption{Hierarchy for dt-NPS CBCs}\label{alg:dt-linear} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U$ +\Ensure \eqref{eq:rank} holds +\Ensure semi-algebraic $X,X_I,X_U$ +\State Solve~\eqref{eq:safe_CBC_data3} and~\eqref{eq:safe_CBC_data0} for $H(x)$ and $P$ via LMIs +%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ +\State Substitute and solve~\eqref{eq:safe_CBC_data1}-\eqref{eq:safe_CBC_data2} via SOS optimization +\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + + + +% \begin{corollary}[CBC Controller Design] +% \label{cor:dt-LS-controller} +% We consider matrix $H\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$. We set $Z=P^{-1}$ and $Q=HP$, such that +% \begin{equation} +% \label{eq:Z=X0Hdt} +% Z = \mathcal{X}_{0}H +% \end{equation} +% then~\eqref{eq:safe_CBC_data3} can be equivalently represented by +% \begin{equation} +% \label{eq:SchurZ-dtLS} +% \begin{bmatrix} +% Z & H^\top\mathcal{X}_{1}^\top \\ +% \mathcal{X}_{1}H & Z +% \end{bmatrix} \geq 0,\quad \forall x\in X. +% \end{equation} +% The controller is thus $u=\mathcal{U}_{0}H[\mathcal{X}_{0} H]^{-1}x$. +% \end{corollary} + +% \subsection{Sum-of-Squares Formulation} + +% We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. We can solve the following using the SumOfSquares~\cite{Yuan_SumOfSquares_py} toolbox where we also add an additional constraint for the equality. We consider matrix $H\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$ such that +% \begin{equation} +% P^{-1} = \mathcal{X}_{0}H +% \end{equation} +% and the following are sum-of-squares +% \begin{align} +% -x^\top Px -& L_I^\top(x)g_I(x) + \gamma, \\ +% x^\top Px -& L_U^\top(x)g_U(x) + \lambda, \\ +% \begin{bmatrix} +% P^{-1} & H^\top\mathcal{X}_{1}^\top \\ +% \mathcal{X}_{1}H & P^{-1} +% \end{bmatrix} -& L^\top(x)g(x). +% \end{align} + +% To solve first find solutions to +% \begin{equation*} +% Z = \mathcal{X}_{0}H +% \end{equation*} +% and +% \begin{equation*} +% \begin{bmatrix} +% Z & H^\top\mathcal{X}_{1}^\top \\ +% \mathcal{X}_{1}H & Z +% \end{bmatrix}\succ 0 +% \end{equation*} +% then solve $P = Z^{-1}$ and solve the sum of squares conditions to find $\gamma$ and $\lambda$. Then the barrier certificate is given by $\mathcal{B}(x) = x^\top P x$ and the controller by $u = \mathcal{U}_{0}H[\mathcal{X}_{0}H]^{-1}x$, we also return $\gamma$ and $\lambda$. + +\subsubsection{Stability} + +Removing the restriction over $X$ for conditions~\eqref{eq:safe_CBC_data3}-\eqref{eq:safe_CBC_data0} gives the stability conditions. + +\begin{theorem}[dt-LS Stable Controller Design~\cite{de2019formulas}] +\label{thm:dtLS-stable} +A control Lyapunov function $\mathcal{V}(x)=x^\top Px$ guaranteeing stability of the dt-LS~\eqref{eq:dt-LS} can be designed by introducing the new variable +\begin{equation*} +\label{eq:H=QP} +QZ=H, +\end{equation*} +where $Z=P^{-1}$ and $P\in\mathbb{R}^{n\times n}$ so that any matrices $H\in\mathbb{R}^{T\times n}$, and $Z\in\mathbb{R}^{n\times n}$ satisfying +\begin{align} +\label{eq:schur-stability-dtLS} +\begin{bmatrix} +Z & H^\top\mathcal{X}_{1}^\top \\ +\mathcal{X}_{1} H & Z +\end{bmatrix} \succ 0, \quad \mathcal{X}_{0}H=Z +\end{align} +stabilize~\eqref{eq:dt-LS}. +The controller is given by $u= \mathcal{U}_{0}H[\mathcal{X}_0H]^{-1}x.$ +\end{theorem} + +The above theorem can be solved in a straightforward manner using any LMI solver. The psuedocode for dt-LS stability is given in Algorithm~\ref{alg:dtls-stab}. + +\begin{algorithm}[t] +\caption{Hierarchy for dt-NPS Stability}\label{alg:dtls-stab} +\begin{algorithmic}[1] +\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0$ +\Ensure \eqref{eq:rank} holds +\State Solve~\eqref{eq:schur-stability-dtLS} for $H(x)$ and $Z$ via LMIs +\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ +\end{algorithmic} +\end{algorithm} + +% \section{System Verification \BW{?}} + + +\section{Benchmarks and Case Studies}\label{sec:benchmarks-and-case-studies} + +We consider the following dynamical systems from the literature as case study examples. + +\subsection{Continuous-Time Systems} + +\subsubsection{Nonlinear Systems} +We consider the following ct-NPS systems. + +\noindent\textbf{Jet Engine} +We consider the nonlinear Moore-Greitzer jet engine model~\cite{krstic1995lean}: +\begin{equation*} +\Sigma_c: \begin{cases} +\dot{x}_1(t) = -x_2(t)-1.5x_1^2(t)-0.5x_1^3(t),\\ +\dot{x}_2(t) = x_1(t), +\end{cases} +\end{equation*} +where $x_1=\Phi-1$, $x_2=\Psi - \Lambda -2$, with $\Phi,\Psi,\Lambda$ being, respectively, the mass flow, pressure rise, and a constant. We consider $X = [0.1,1]^2$, $\initial=[0.1,0.5]^2$, and $\unsafe=[0.7,1]^2$. \BW{add details above initial state and trajectory length.} + + +\subsubsection{Linear Systems} +We consider the following ct-LS systems. + +\noindent\textbf{FOSSIL benchmark - High Order 8.} +We consider the following $8$-dimensional benchmark~\cite{abate2021fossil} +\begin{equation*} +\Sigma_c:\begin{cases} +\dot{x}_1(t) = &x_2(t),\\ +\dot{x}_2(t) = &x_3(t),\\ +\dot{x}_3(t) = &x_4(t),\\ +\dot{x}_4(t) = &x_5(t),\\ +\dot{x}_5(t) = &x_6(t),\\ +\dot{x}_6(t) = &x_7(t),\\ +\dot{x}_7(t) = &x_8(t),\\ +\dot{x}_8(t) = &-20x_8(t)-170x_7(t)-800x_6(t) - 2273x_5(t)\\ &-3980x_4(t) - 4180x_3(t) - 2400x_2(t) - 576x_1(t), +\end{cases} +\end{equation*} +with the state space $X=[-2.2,2.2]^8$, initial region $\initial=[0.9,1.1]^8$, and unsafe region $\unsafe=[-2.2,-1.8]^8$. \BW{add details above initial state and trajectory length.} + + +\subsection{Discrete-Time Systems} + +\subsubsection{Nonlinear Systems} +We consider the following dt-NPS systems. + +\noindent\textbf{Lorenz Attractor} +We consider the Lorenz attractor a well studied dynamical system with chaotic behavior. The map has dynamics +\begin{equation*} +\Sigma : \begin{cases} +x_1(k+1) &= x_1(k) + \tau\sigma (x_1(k) + x_2(k)), \\ +x_2(k+1) &= x_2(k) +\\ &\quad\tau (\rho x_1(k) - x_2(k) - x_1(k)x_3(k) + u(k)), \\ +x_3(k+1) &= x_3(k) + \tau (x_1(k)x_2(k)-\beta x_3(k)), +\end{cases} +\end{equation*} +where $\rho=28, \sigma=10,\beta=\frac{8}{3}, tau=10^{-3}$. We consider the state space $X=[-5,5]^3$, initial set $X_I=[-1, 1]^3$ and two unsafe sets $X_U=[-5,-2.5]^3\cup[2.5,5]^3$. We consider monomials from the set $\mathcal{M}(x)=$ \begin{align*} +[x_1(k)~&x_2(k)~x_3(k)~x_1(k)x_2(k)~ x_2x_3(k)~x_1(k)x_3(k)]^\top, +\end{align*} +and collect data $\mathcal{X}_0$ and $\mathcal{X}_1$ with time horizon $T=50$, equivalently $0.05$s, from initial point $(0.5, 0.5,0.5)$ and choose random inputs along the evolution of the trajectory from the set $U=[-100,100]$. + +\noindent\BW{\textbf{Second Nonlinear}} + +\subsubsection{Linear Systems}% +We consider the following dt-LS systems. + +\noindent\textbf{RLC Circuit.} +\begin{align*} +\Sigma : \begin{cases} +i(k+1) = i(k) + \tau(-\frac{R}{L}i(k) - \frac{1}{L}v(k)) + u_1(k), \\ +v(k+1) = v(k) + \tau(\frac{1}{C}i(k)) + u_2(k), +\end{cases} +\end{align*} +We consider the safety of an RLC Circuit, based on~\cite{anand2022kstochastic}, with the dynamics given above, where $i(k)$ denotes the current at time $k$, $v(k)$ is the voltage, $\tau=0.5$s is the sampling time, $R=2\omega$ is the series resistance, $L=9$H is the series inductance, $C=0.5$F is the capacitance of the circuit. We use hypercubes as the state space of the system $X=[-2,2]\times[-4,4]$, initial set $X_I=[0,0.5]\times[0,1]$, and unsafe set $X_U=[1,2]\times[-4,4]$. We construct $\mathcal{X}_{0},\mathcal{U}_{0}$ and $\mathcal{X}_{1}$ by taking a $15$s time horizon trajectory, with initial state $(0,0)$ and random inputs along the evolution of the trajectory from the set $U=[-1,1]\times[-1,1]$. + +\noindent\textbf{DC Motor.} +\begin{align*} +%\label{eq:DC-motor-example} +\Sigma : \begin{cases} +x_1(k+1) = x_1(k) - \tau(\frac{R}{L}x_1(k) + \frac{k_{dc}}{L}x_2(k)) + u_1(k), \\ +x_2(k+1) = x_2(k) + \tau(\frac{k_{dc}}{J}x_1(k) - \frac{b}{J}x_2(k)) + u_2(k), +\end{cases} +\end{align*} +We also consider the safe operation of a DC Motor, based on~\cite{adewuyi2013dc}, with the dynamics given above where $x_1,x_2,R=1,L=0.01,J=0.01$ are the armature current, the rotational speed of the shaft, the electrical resistance, the electrical inductance, and the moment of inertia of the rotor, respectively. In addition, $\tau=0.01$, $b=1$, and $k_{dc}=0.01$, represent, respectively, the sampling time, the motor torque, and the back electromotive force. We use hypercubes as the state space of the system $X=[0.1,0.5]\times[0.1,1]$, initial set $X_I=[0.1,0.4]\times[0.1,0.55]$, and unsafe set $X_U=[0.45,0.5]\times[0.6,1]$. We first construct the matrices $\mathcal{X}_{0},\mathcal{U}_{0}$ and $\mathcal{X}_{1}$ by taking a trajectory with time horizon $15$s. We construct $\mathcal{X}_{0},\mathcal{U}_{0}$ and $\mathcal{X}_{1}$ by taking a $15$s time horizon trajectory, with initial state $(0,0)$ and random inputs along the evolution of the trajectory from the set $U=[-0.1,0.1]\times[-0.1,0.1]$. + +\noindent\textbf{Room Temperature System.} +\begin{equation*} +\Sigma_d:\begin{cases} +x_1(k+1) = (1 - \tau(\alpha + \alpha_{e1}))x_1(k) + \tau\alpha x_2(k) + \tau\alpha_{e1} T_e,\\ +x_2(k+1) = (1 - \tau(\alpha + \alpha_{e2}))x_2(k) + \tau\alpha x_1(k) + \tau\alpha_{e2}T_e, +\end{cases} +\end{equation*} +We consider the two room system from the FOSSIL benchmarks~\cite{abate2021fossil}, with dynamics above, where the discretization parameter $\tau = 5$, heat exchange constants $\alpha = 5\times 10^{-2}, \alpha_{e1} = 5\times 10^{-3}, \alpha_{e2} = 8\times10^{-3}$, and external temperature $T_e = 15$. We consider regions of interest $X=[18,23]^2$, $X_I=[18,19.75]^2$, and $X_U=[22,23]$. \BW{add details above initial state and trajectory length.} This is a verification example as no control inputs are present and no controller is designed. + +\noindent\textbf{Two Tank System.} +\begin{equation*} +\Sigma_d^\varsigma\!:\begin{cases} +h_1(k+1) = (1-\tau\frac{\alpha_1}{A_1})h_1(k) + \tau\frac{q_1(k)}{A_1},\\ +h_2(k+1) = \tau\frac{\alpha_1}{A_2}h_1(k) + (1-\tau\frac{\alpha_2}{A_2})h_2(k) + \tau\frac{q_o(k)}{A_2}, +\end{cases} +\end{equation*} +Consider a two-tank system~\cite{ramos2007mathematical}, characterized by the above difference equations where $h_1$, $h_2$ are heights of the fluid in two tanks. Additionally, $\alpha_i$ and $A_i$ are the valve coefficient and area of tank $i$, and $q_1$ and $q_o$ are the inflow and outflow rate of tank $1$ and $2$, respectively. Furthermore, $\tau=0.1$, $\frac{\alpha_1}{A_1}=1$,$\frac{q_1}{A_1}=4.5$, $\frac{\alpha_1}{A_2}=1$, $\frac{\alpha_2}{A_2}=1$ and $\frac{q_o}{A_2}=-3$. Regions of interest are $X=[1,10]\times[1,10]$, $\initial=[1.75,2.25]\times[1.75,2.25]$, $\unsafe=[9,10]\times[9,10]$. \BW{add details above initial state and trajectory length.} This is a verification example as no control inputs are present and no controller is designed. + +\section{Results}\label{sec:results} +- Create a full page table for the four scenarios, each with the safety function, stability barrier function and controller. +- Compare to other tools both in terms of performance and data requirements +- MATLAB w/ these algorithms? +Presumably can cite Behrad's work for dt-NPS? +- Can we cite PRoTECT but state that we're not comparing since we're not dealing with stochastic systems? +(Yes, but we'll do this in the intro's related materials subsection) + +\bibliographystyle{ieeetran} +\bibliography{biblio} + +\end{document} diff --git a/TRUST-docs/out/main.aux b/TRUST-docs/out/main.aux new file mode 100644 index 0000000..19b4744 --- /dev/null +++ b/TRUST-docs/out/main.aux @@ 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IEEEtran.bst, version: 1.14 (2015/08/26) +\begin{thebibliography}{10} +\providecommand{\url}[1]{#1} +\csname url@samestyle\endcsname +\providecommand{\newblock}{\relax} +\providecommand{\bibinfo}[2]{#2} +\providecommand{\BIBentrySTDinterwordspacing}{\spaceskip=0pt\relax} +\providecommand{\BIBentryALTinterwordstretchfactor}{4} +\providecommand{\BIBentryALTinterwordspacing}{\spaceskip=\fontdimen2\font plus +\BIBentryALTinterwordstretchfactor\fontdimen3\font minus + \fontdimen4\font\relax} +\providecommand{\BIBforeignlanguage}[2]{{% +\expandafter\ifx\csname l@#1\endcsname\relax +\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}% +\typeout{** loaded for the language `#1'. Using the pattern for}% +\typeout{** the default language instead.}% +\else +\language=\csname l@#1\endcsname +\fi +#2}} +\providecommand{\BIBdecl}{\relax} +\BIBdecl + +\bibitem{nejati2023data} +A.~Nejati and M.~Zamani, ``Data-driven synthesis of safety controllers via + multiple control barrier certificates,'' \emph{IEEE Control Systems Letters}, + 2023. + +\bibitem{breschi2021direct} +V.~Breschi, C.~De~Persis, S.~Formentin, and P.~Tesi, ``Direct data-driven + model-reference control with lyapunov stability guarantees,'' in \emph{2021 + 60th IEEE conference on decision and control (CDC)}.\hskip 1em plus 0.5em + minus 0.4em\relax IEEE, 2021, pp. 1456--1461. + +\bibitem{ren2024formal} +T.~Ren, W.~Lin, and Z.~Ding, ``Formal synthesis of safety controllers via $ k + $-inductive control barrier certificates,'' \emph{IEEE Transactions on + Reliability}, 2024. + +\bibitem{willems2005note} +J.~C. Willems, P.~Rapisarda, I.~Markovsky, and B.~L. De~Moor, ``A note on + persistency of excitation,'' \emph{Systems \& Control Letters}, vol.~54, + no.~4, pp. 325--329, 2005. + +\bibitem{prajna2002introducing} +S.~Prajna, A.~Papachristodoulou, and P.~A. Parrilo, ``Introducing sostools: A + general purpose sum of squares programming solver,'' in \emph{Proceedings of + the 41st IEEE Conference on Decision and Control, 2002.}, vol.~1.\hskip 1em + plus 0.5em minus 0.4em\relax IEEE, 2002, pp. 741--746. + +\bibitem{bisoffi2020data} +A.~Bisoffi, C.~De~Persis, and P.~Tesi, ``Data-based guarantees of set + invariance properties,'' \emph{IFAC-PapersOnLine}, vol.~53, no.~2, pp. + 3953--3958, 2020. + +\bibitem{bisoffi2022controller} +------, ``Controller design for robust invariance from noisy data,'' \emph{IEEE + Transactions on Automatic Control}, vol.~68, no.~1, pp. 636--643, 2022. + +\bibitem{nejati2022data} +A.~Nejati, B.~Zhong, M.~Caccamo, and M.~Zamani, ``Data-driven controller + synthesis of unknown nonlinear polynomial systems via control barrier + certificates,'' in \emph{Learning for Dynamics and Control Conference}.\hskip + 1em plus 0.5em minus 0.4em\relax PMLR, 2022, pp. 763--776. + +\bibitem{martin2023guarantees} +T.~Martin, T.~B. Sch{\"o}n, and F.~Allg{\"o}wer, ``Guarantees for data-driven + control of nonlinear systems using semidefinite programming: A survey,'' + \emph{Annual Reviews in Control}, p. 100911, 2023. + +\bibitem{samari2024single} +B.~Samari, O.~Akbarzadeh, M.~Zaker, and A.~Lavaei, ``From a single trajectory + to safety controller synthesis of discrete-time nonlinear polynomial + systems,'' \emph{arXiv preprint arXiv:2409.10026}, 2024. + +\bibitem{de2019formulas} +C.~De~Persis and P.~Tesi, ``Formulas for data-driven control: Stabilization, + optimality, and robustness,'' \emph{IEEE Transactions on Automatic Control}, + vol.~65, no.~3, pp. 909--924, 2019. + +\bibitem{parrilo2003semidefinite} +P.~A. Parrilo, ``Semidefinite programming relaxations for semialgebraic + problems,'' \emph{Mathematical programming}, vol.~96, pp. 293--320, 2003. + +\bibitem{Yuan_SumOfSquares_py} +\BIBentryALTinterwordspacing +C.~Yuan, ``{SumOfSquares.py}.'' [Online]. Available: + \url{https://github.com/yuanchenyang/SumOfSquares.py} +\BIBentrySTDinterwordspacing + +\bibitem{wang2024convex} +H.~Wang, K.~Margellos, A.~Papachristodoulou, and C.~De~Persis, ``Convex + co-design of control barrier functions and feedback controllers for linear + systems,'' 2024. + +\bibitem{samari2024singletrajectory} +\BIBentryALTinterwordspacing +B.~Samari, O.~Akbarzadeh, M.~Zaker, and A.~Lavaei, ``From a single trajectory + to safety controller synthesis of discrete-time nonlinear polynomial + systems,'' 2024. [Online]. Available: \url{https://arxiv.org/abs/2409.10026} +\BIBentrySTDinterwordspacing + +\bibitem{abate2021fossil} +A.~Abate, D.~Ahmed, A.~Edwards, M.~Giacobbe, and A.~Peruffo, ``{FOSSIL: a + software tool for the formal synthesis of lyapunov functions and barrier + certificates using neural networks},'' in \emph{Proceedings of the 24th + International Conference on Hybrid Systems: Computation and Control}, 2021, + pp. 1--11. + +\bibitem{anand2022kstochastic} +M.~Anand, V.~Murali, A.~Trivedi, and M.~Zamani, ``K-inductive barrier + certificates for stochastic systems,'' in \emph{Proceedings of the 25th ACM + International Conference on Hybrid Systems: Computation and Control}, 2022, + pp. 1--11. + +\bibitem{adewuyi2013dc} +P.~A. Adewuyi, ``Dc motor speed control: A case between pid controller and + fuzzy logic controller,'' \emph{international journal of multidisciplinary + sciences and engineering}, vol.~4, no.~4, pp. 36--40, 2013. + +\end{thebibliography} diff --git a/TRUST-docs/out/main.blg b/TRUST-docs/out/main.blg new file mode 100644 index 0000000..5d2fa03 --- /dev/null +++ b/TRUST-docs/out/main.blg @@ -0,0 +1,62 @@ +This is BibTeX, Version 0.99d (TeX Live 2024) +Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 +The top-level auxiliary file: main.aux +The style file: ieeetran.bst +Reallocated singl_function (elt_size=4) to 100 items from 50. +Reallocated singl_function (elt_size=4) to 100 items from 50. +Reallocated singl_function (elt_size=4) to 100 items from 50. +Reallocated wiz_functions (elt_size=4) to 6000 items from 3000. +Reallocated singl_function (elt_size=4) to 100 items from 50. +Database file #1: biblio.bib +Warning--entry type for "Yuan_SumOfSquares_py" isn't style-file 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Date: Mon, 7 Apr 2025 13:55:19 +0100 Subject: [PATCH 08/23] Update README.md --- README.md | 11 +- TRUST-docs/IEEEtran.bst | 2409 --------------------------- TRUST-docs/IEEEtrantools.sty | 2799 -------------------------------- TRUST-docs/acmart.cls | 2544 ----------------------------- TRUST-docs/biblio.bib | 466 ------ TRUST-docs/main.tex | 1152 ------------- TRUST-docs/out/main.aux | 198 --- TRUST-docs/out/main.bbl | 121 -- TRUST-docs/out/main.blg | 62 - TRUST-docs/out/main.out | 22 - TRUST-docs/out/main.pdf | Bin 545608 -> 0 bytes TRUST-docs/out/main.synctex.gz | Bin 167239 -> 0 bytes 12 files changed, 6 insertions(+), 9778 deletions(-) delete mode 100755 TRUST-docs/IEEEtran.bst delete mode 100755 TRUST-docs/IEEEtrantools.sty delete mode 100755 TRUST-docs/acmart.cls delete mode 100644 TRUST-docs/biblio.bib delete mode 100644 TRUST-docs/main.tex delete mode 100644 TRUST-docs/out/main.aux delete mode 100644 TRUST-docs/out/main.bbl delete mode 100644 TRUST-docs/out/main.blg delete mode 100644 TRUST-docs/out/main.out delete mode 100644 TRUST-docs/out/main.pdf delete mode 100644 TRUST-docs/out/main.synctex.gz diff --git a/README.md b/README.md index 05c8098..12fde19 100644 --- a/README.md +++ b/README.md @@ -229,12 +229,13 @@ The arXiv version of the paper is located [here](). ``` @misc{TRUST2025, - title={TRUST: StabiliTy and Safety ContRoller Synthesis for Unknown Dynamical Models Using a Single Trajectory}, - author={Jamie Gardne, Ben Wooding, Amy Nejati, and Abolfazl Lavaei}, + title={TRUST: Stability and Safety Controller Synthesis for Unknown Dynamical Models Using a Single Trajectory}, + author={Jamie Gardner and Ben Wooding and Amy Nejati and Abolfazl Lavaei}, year={2025}, - eprint={tbc}, - journal={28th ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2025)}, - primaryClass={eess.SY} + eprint={2503.08081}, + archivePrefix={arXiv}, + primaryClass={eess.SY}, + url={https://arxiv.org/abs/2503.08081}, } ``` diff --git a/TRUST-docs/IEEEtran.bst b/TRUST-docs/IEEEtran.bst deleted file mode 100755 index 3e7a50e..0000000 --- a/TRUST-docs/IEEEtran.bst +++ /dev/null @@ -1,2409 +0,0 @@ -%% -%% IEEEtran.bst -%% BibTeX Bibliography Style file for IEEE Journals and Conferences (unsorted) -%% Version 1.14 (2015/08/26) -%% -%% Copyright (c) 2003-2015 Michael Shell -%% -%% Original starting code base and algorithms obtained from the output of -%% Patrick W. Daly's makebst package as well as from prior versions of -%% IEEE BibTeX styles: -%% -%% 1. Howard Trickey and Oren Patashnik's ieeetr.bst (1985/1988) -%% 2. Silvano Balemi and Richard H. Roy's IEEEbib.bst (1993) -%% -%% Support sites: -%% http://www.michaelshell.org/tex/ieeetran/ -%% http://www.ctan.org/pkg/ieeetran -%% and/or -%% http://www.ieee.org/ -%% -%% For use with BibTeX version 0.99a or later -%% -%% This is a numerical citation style. -%% -%%************************************************************************* -%% Legal Notice: -%% This code is offered as-is without any warranty either expressed or -%% implied; without even the implied warranty of MERCHANTABILITY or -%% FITNESS FOR A PARTICULAR PURPOSE! -%% User assumes all risk. -%% In no event shall the IEEE or any contributor to this code be liable for -%% any damages or losses, including, but not limited to, incidental, -%% consequential, or any other damages, resulting from the use or misuse -%% of any information contained here. -%% -%% All comments are the opinions of their respective authors and are not -%% necessarily endorsed by the IEEE. -%% -%% This work is distributed under the LaTeX Project Public License (LPPL) -%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, -%% distributed and modified. A copy of the LPPL, version 1.3, is included -%% in the base LaTeX documentation of all distributions of LaTeX released -%% 2003/12/01 or later. -%% Retain all contribution notices and credits. -%% ** Modified files should be clearly indicated as such, including ** -%% ** renaming them and changing author support contact information. ** -%%************************************************************************* - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% DEFAULTS FOR THE CONTROLS OF THE BST STYLE %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% These are the defaults for the user adjustable controls. The values used -% here can be overridden by the user via IEEEtranBSTCTL entry type. - -% NOTE: The recommended LaTeX command to invoke a control entry type is: -% -%\makeatletter -%\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}} -%\def\@bstctlcite[#1]#2{\@bsphack -% \@for\@citeb:=#2\do{% -% \edef\@citeb{\expandafter\@firstofone\@citeb}% -% \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}% -% \@esphack} -%\makeatother -% -% It is called at the start of the document, before the first \cite, like: -% \bstctlcite{IEEEexample:BSTcontrol} -% -% IEEEtran.cls V1.6 and later does provide this command. - - - -% #0 turns off the display of the number for articles. -% #1 enables -FUNCTION {default.is.use.number.for.article} { #1 } - - -% #0 turns off the display of the paper and type fields in @inproceedings. -% #1 enables -FUNCTION {default.is.use.paper} { #1 } - - -% #0 turns off the display of urls -% #1 enables -FUNCTION {default.is.use.url} { #1 } - - -% #0 turns off the forced use of "et al." -% #1 enables -FUNCTION {default.is.forced.et.al} { #0 } - - -% The maximum number of names that can be present beyond which an "et al." -% usage is forced. Be sure that num.names.shown.with.forced.et.al (below) -% is not greater than this value! -% Note: There are many instances of references in IEEE journals which have -% a very large number of authors as well as instances in which "et al." is -% used profusely. -FUNCTION {default.max.num.names.before.forced.et.al} { #10 } - - -% The number of names that will be shown with a forced "et al.". -% Must be less than or equal to max.num.names.before.forced.et.al -FUNCTION {default.num.names.shown.with.forced.et.al} { #1 } - - -% #0 turns off the alternate interword spacing for entries with URLs. -% #1 enables -FUNCTION {default.is.use.alt.interword.spacing} { #1 } - - -% If alternate interword spacing for entries with URLs is enabled, this is -% the interword spacing stretch factor that will be used. For example, the -% default "4" here means that the interword spacing in entries with URLs can -% stretch to four times normal. Does not have to be an integer. Note that -% the value specified here can be overridden by the user in their LaTeX -% code via a command such as: -% "\providecommand\BIBentryALTinterwordstretchfactor{1.5}" in addition to -% that via the IEEEtranBSTCTL entry type. -FUNCTION {default.ALTinterwordstretchfactor} { "4" } - - -% #0 turns off the "dashification" of repeated (i.e., identical to those -% of the previous entry) names. The IEEE normally does this. -% #1 enables -FUNCTION {default.is.dash.repeated.names} { #1 } - - -% The default name format control string. -FUNCTION {default.name.format.string}{ "{f.~}{vv~}{ll}{, jj}" } - - -% The default LaTeX font command for the names. -FUNCTION {default.name.latex.cmd}{ "" } - - -% The default URL prefix. -FUNCTION {default.name.url.prefix}{ "[Online]. Available:" } - - -% Other controls that cannot be accessed via IEEEtranBSTCTL entry type. - -% #0 turns off the terminal startup banner/completed message so as to -% operate more quietly. -% #1 enables -FUNCTION {is.print.banners.to.terminal} { #1 } - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FILE VERSION AND BANNER %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -FUNCTION{bst.file.version} { "1.14" } -FUNCTION{bst.file.date} { "2015/08/26" } -FUNCTION{bst.file.website} { "http://www.michaelshell.org/tex/ieeetran/bibtex/" } - -FUNCTION {banner.message} -{ is.print.banners.to.terminal - { "-- IEEEtran.bst version" " " * bst.file.version * - " (" * bst.file.date * ") " * "by Michael Shell." * - top$ - "-- " bst.file.website * - top$ - "-- See the " quote$ * "IEEEtran_bst_HOWTO.pdf" * quote$ * " manual for usage information." * - top$ - } - { skip$ } - if$ -} - -FUNCTION {completed.message} -{ is.print.banners.to.terminal - { "" - top$ - "Done." - top$ - } - { skip$ } - if$ -} - - - - -%%%%%%%%%%%%%%%%%%%%%% -%% STRING CONSTANTS %% -%%%%%%%%%%%%%%%%%%%%%% - -FUNCTION {bbl.and}{ "and" } -FUNCTION {bbl.etal}{ "et~al." } -FUNCTION {bbl.editors}{ "eds." } -FUNCTION {bbl.editor}{ "ed." } -FUNCTION {bbl.edition}{ "ed." } -FUNCTION {bbl.volume}{ "vol." } -FUNCTION {bbl.of}{ "of" } -FUNCTION {bbl.number}{ "no." } -FUNCTION {bbl.in}{ "in" } -FUNCTION {bbl.pages}{ "pp." } -FUNCTION {bbl.page}{ "p." } -FUNCTION {bbl.chapter}{ "ch." } -FUNCTION {bbl.paper}{ "paper" } -FUNCTION {bbl.part}{ "pt." } -FUNCTION {bbl.patent}{ "Patent" } -FUNCTION {bbl.patentUS}{ "U.S." } -FUNCTION {bbl.revision}{ "Rev." } -FUNCTION {bbl.series}{ "ser." } -FUNCTION {bbl.standard}{ "Std." } -FUNCTION {bbl.techrep}{ "Tech. Rep." } -FUNCTION {bbl.mthesis}{ "Master's thesis" } -FUNCTION {bbl.phdthesis}{ "Ph.D. dissertation" } -FUNCTION {bbl.st}{ "st" } -FUNCTION {bbl.nd}{ "nd" } -FUNCTION {bbl.rd}{ "rd" } -FUNCTION {bbl.th}{ "th" } - - -% This is the LaTeX spacer that is used when a larger than normal space -% is called for (such as just before the address:publisher). -FUNCTION {large.space} { "\hskip 1em plus 0.5em minus 0.4em\relax " } - -% The LaTeX code for dashes that are used to represent repeated names. -% Note: Some older IEEE journals used something like -% "\rule{0.275in}{0.5pt}\," which is fairly thick and runs right along -% the baseline. However, the IEEE now uses a thinner, above baseline, -% six dash long sequence. -FUNCTION {repeated.name.dashes} { "------" } - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% PREDEFINED STRING MACROS %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -MACRO {jan} {"Jan."} -MACRO {feb} {"Feb."} -MACRO {mar} {"Mar."} -MACRO {apr} {"Apr."} -MACRO {may} {"May"} -MACRO {jun} {"Jun."} -MACRO {jul} {"Jul."} -MACRO {aug} {"Aug."} -MACRO {sep} {"Sep."} -MACRO {oct} {"Oct."} -MACRO {nov} {"Nov."} -MACRO {dec} {"Dec."} - - - -%%%%%%%%%%%%%%%%%% -%% ENTRY FIELDS %% -%%%%%%%%%%%%%%%%%% - -ENTRY - { address - assignee - author - booktitle - chapter - day - dayfiled - edition - editor - howpublished - institution - intype - journal - key - language - month - monthfiled - nationality - note - number - organization - pages - paper - publisher - school - series - revision - title - type - url - volume - year - yearfiled - CTLuse_article_number - CTLuse_paper - CTLuse_url - CTLuse_forced_etal - CTLmax_names_forced_etal - CTLnames_show_etal - CTLuse_alt_spacing - CTLalt_stretch_factor - CTLdash_repeated_names - CTLname_format_string - CTLname_latex_cmd - CTLname_url_prefix - } - {} - { label } - - - - -%%%%%%%%%%%%%%%%%%%%%%% -%% INTEGER VARIABLES %% -%%%%%%%%%%%%%%%%%%%%%%% - -INTEGERS { prev.status.punct this.status.punct punct.std - punct.no punct.comma punct.period - prev.status.space this.status.space space.std - space.no space.normal space.large - prev.status.quote this.status.quote quote.std - quote.no quote.close - prev.status.nline this.status.nline nline.std - nline.no nline.newblock - status.cap cap.std - cap.no cap.yes} - -INTEGERS { longest.label.width multiresult nameptr namesleft number.label numnames } - -INTEGERS { is.use.number.for.article - is.use.paper - is.use.url - is.forced.et.al - max.num.names.before.forced.et.al - num.names.shown.with.forced.et.al - is.use.alt.interword.spacing - is.dash.repeated.names} - - -%%%%%%%%%%%%%%%%%%%%%% -%% STRING VARIABLES %% -%%%%%%%%%%%%%%%%%%%%%% - -STRINGS { bibinfo - longest.label - oldname - s - t - ALTinterwordstretchfactor - name.format.string - name.latex.cmd - name.url.prefix} - - - - -%%%%%%%%%%%%%%%%%%%%%%%%% -%% LOW LEVEL FUNCTIONS %% -%%%%%%%%%%%%%%%%%%%%%%%%% - -FUNCTION {initialize.controls} -{ default.is.use.number.for.article 'is.use.number.for.article := - default.is.use.paper 'is.use.paper := - default.is.use.url 'is.use.url := - default.is.forced.et.al 'is.forced.et.al := - default.max.num.names.before.forced.et.al 'max.num.names.before.forced.et.al := - default.num.names.shown.with.forced.et.al 'num.names.shown.with.forced.et.al := - default.is.use.alt.interword.spacing 'is.use.alt.interword.spacing := - default.is.dash.repeated.names 'is.dash.repeated.names := - default.ALTinterwordstretchfactor 'ALTinterwordstretchfactor := - default.name.format.string 'name.format.string := - default.name.latex.cmd 'name.latex.cmd := - default.name.url.prefix 'name.url.prefix := -} - - -% This IEEEtran.bst features a very powerful and flexible mechanism for -% controlling the capitalization, punctuation, spacing, quotation, and -% newlines of the formatted entry fields. (Note: IEEEtran.bst does not need -% or use the newline/newblock feature, but it has been implemented for -% possible future use.) The output states of IEEEtran.bst consist of -% multiple independent attributes and, as such, can be thought of as being -% vectors, rather than the simple scalar values ("before.all", -% "mid.sentence", etc.) used in most other .bst files. -% -% The more flexible and complex design used here was motivated in part by -% the IEEE's rather unusual bibliography style. For example, the IEEE ends the -% previous field item with a period and large space prior to the publisher -% address; the @electronic entry types use periods as inter-item punctuation -% rather than the commas used by the other entry types; and URLs are never -% followed by periods even though they are the last item in the entry. -% Although it is possible to accommodate these features with the conventional -% output state system, the seemingly endless exceptions make for convoluted, -% unreliable and difficult to maintain code. -% -% IEEEtran.bst's output state system can be easily understood via a simple -% illustration of two most recently formatted entry fields (on the stack): -% -% CURRENT_ITEM -% "PREVIOUS_ITEM -% -% which, in this example, is to eventually appear in the bibliography as: -% -% "PREVIOUS_ITEM," CURRENT_ITEM -% -% It is the job of the output routine to take the previous item off of the -% stack (while leaving the current item at the top of the stack), apply its -% trailing punctuation (including closing quote marks) and spacing, and then -% to write the result to BibTeX's output buffer: -% -% "PREVIOUS_ITEM," -% -% Punctuation (and spacing) between items is often determined by both of the -% items rather than just the first one. The presence of quotation marks -% further complicates the situation because, in standard English, trailing -% punctuation marks are supposed to be contained within the quotes. -% -% IEEEtran.bst maintains two output state (aka "status") vectors which -% correspond to the previous and current (aka "this") items. Each vector -% consists of several independent attributes which track punctuation, -% spacing, quotation, and newlines. Capitalization status is handled by a -% separate scalar because the format routines, not the output routine, -% handle capitalization and, therefore, there is no need to maintain the -% capitalization attribute for both the "previous" and "this" items. -% -% When a format routine adds a new item, it copies the current output status -% vector to the previous output status vector and (usually) resets the -% current (this) output status vector to a "standard status" vector. Using a -% "standard status" vector in this way allows us to redefine what we mean by -% "standard status" at the start of each entry handler and reuse the same -% format routines under the various inter-item separation schemes. For -% example, the standard status vector for the @book entry type may use -% commas for item separators, while the @electronic type may use periods, -% yet both entry handlers exploit many of the exact same format routines. -% -% Because format routines have write access to the output status vector of -% the previous item, they can override the punctuation choices of the -% previous format routine! Therefore, it becomes trivial to implement rules -% such as "Always use a period and a large space before the publisher." By -% pushing the generation of the closing quote mark to the output routine, we -% avoid all the problems caused by having to close a quote before having all -% the information required to determine what the punctuation should be. -% -% The IEEEtran.bst output state system can easily be expanded if needed. -% For instance, it is easy to add a "space.tie" attribute value if the -% bibliography rules mandate that two items have to be joined with an -% unbreakable space. - -FUNCTION {initialize.status.constants} -{ #0 'punct.no := - #1 'punct.comma := - #2 'punct.period := - #0 'space.no := - #1 'space.normal := - #2 'space.large := - #0 'quote.no := - #1 'quote.close := - #0 'cap.no := - #1 'cap.yes := - #0 'nline.no := - #1 'nline.newblock := -} - -FUNCTION {std.status.using.comma} -{ punct.comma 'punct.std := - space.normal 'space.std := - quote.no 'quote.std := - nline.no 'nline.std := - cap.no 'cap.std := -} - -FUNCTION {std.status.using.period} -{ punct.period 'punct.std := - space.normal 'space.std := - quote.no 'quote.std := - nline.no 'nline.std := - cap.yes 'cap.std := -} - -FUNCTION {initialize.prev.this.status} -{ punct.no 'prev.status.punct := - space.no 'prev.status.space := - quote.no 'prev.status.quote := - nline.no 'prev.status.nline := - punct.no 'this.status.punct := - space.no 'this.status.space := - quote.no 'this.status.quote := - nline.no 'this.status.nline := - cap.yes 'status.cap := -} - -FUNCTION {this.status.std} -{ punct.std 'this.status.punct := - space.std 'this.status.space := - quote.std 'this.status.quote := - nline.std 'this.status.nline := -} - -FUNCTION {cap.status.std}{ cap.std 'status.cap := } - -FUNCTION {this.to.prev.status} -{ this.status.punct 'prev.status.punct := - this.status.space 'prev.status.space := - this.status.quote 'prev.status.quote := - this.status.nline 'prev.status.nline := -} - - -FUNCTION {not} -{ { #0 } - { #1 } - if$ -} - -FUNCTION {and} -{ { skip$ } - { pop$ #0 } - if$ -} - -FUNCTION {or} -{ { pop$ #1 } - { skip$ } - if$ -} - - -% convert the strings "yes" or "no" to #1 or #0 respectively -FUNCTION {yes.no.to.int} -{ "l" change.case$ duplicate$ - "yes" = - { pop$ #1 } - { duplicate$ "no" = - { pop$ #0 } - { "unknown boolean " quote$ * swap$ * quote$ * - " in " * cite$ * warning$ - #0 - } - if$ - } - if$ -} - - -% pushes true if the single char string on the stack is in the -% range of "0" to "9" -FUNCTION {is.num} -{ chr.to.int$ - duplicate$ "0" chr.to.int$ < not - swap$ "9" chr.to.int$ > not and -} - -% multiplies the integer on the stack by a factor of 10 -FUNCTION {bump.int.mag} -{ #0 'multiresult := - { duplicate$ #0 > } - { #1 - - multiresult #10 + - 'multiresult := - } - while$ -pop$ -multiresult -} - -% converts a single character string on the stack to an integer -FUNCTION {char.to.integer} -{ duplicate$ - is.num - { chr.to.int$ "0" chr.to.int$ - } - {"noninteger character " quote$ * swap$ * quote$ * - " in integer field of " * cite$ * warning$ - #0 - } - if$ -} - -% converts a string on the stack to an integer -FUNCTION {string.to.integer} -{ duplicate$ text.length$ 'namesleft := - #1 'nameptr := - #0 'numnames := - { nameptr namesleft > not } - { duplicate$ nameptr #1 substring$ - char.to.integer numnames bump.int.mag + - 'numnames := - nameptr #1 + - 'nameptr := - } - while$ -pop$ -numnames -} - - - - -% The output routines write out the *next* to the top (previous) item on the -% stack, adding punctuation and such as needed. Since IEEEtran.bst maintains -% the output status for the top two items on the stack, these output -% routines have to consider the previous output status (which corresponds to -% the item that is being output). Full independent control of punctuation, -% closing quote marks, spacing, and newblock is provided. -% -% "output.nonnull" does not check for the presence of a previous empty -% item. -% -% "output" does check for the presence of a previous empty item and will -% remove an empty item rather than outputing it. -% -% "output.warn" is like "output", but will issue a warning if it detects -% an empty item. - -FUNCTION {output.nonnull} -{ swap$ - prev.status.punct punct.comma = - { "," * } - { skip$ } - if$ - prev.status.punct punct.period = - { add.period$ } - { skip$ } - if$ - prev.status.quote quote.close = - { "''" * } - { skip$ } - if$ - prev.status.space space.normal = - { " " * } - { skip$ } - if$ - prev.status.space space.large = - { large.space * } - { skip$ } - if$ - write$ - prev.status.nline nline.newblock = - { newline$ "\newblock " write$ } - { skip$ } - if$ -} - -FUNCTION {output} -{ duplicate$ empty$ - 'pop$ - 'output.nonnull - if$ -} - -FUNCTION {output.warn} -{ 't := - duplicate$ empty$ - { pop$ "empty " t * " in " * cite$ * warning$ } - 'output.nonnull - if$ -} - -% "fin.entry" is the output routine that handles the last item of the entry -% (which will be on the top of the stack when "fin.entry" is called). - -FUNCTION {fin.entry} -{ this.status.punct punct.no = - { skip$ } - { add.period$ } - if$ - this.status.quote quote.close = - { "''" * } - { skip$ } - if$ -write$ -newline$ -} - - -FUNCTION {is.last.char.not.punct} -{ duplicate$ - "}" * add.period$ - #-1 #1 substring$ "." = -} - -FUNCTION {is.multiple.pages} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {capitalize}{ "u" change.case$ "t" change.case$ } - -FUNCTION {emphasize} -{ duplicate$ empty$ - { pop$ "" } - { "\emph{" swap$ * "}" * } - if$ -} - -FUNCTION {do.name.latex.cmd} -{ name.latex.cmd - empty$ - { skip$ } - { name.latex.cmd "{" * swap$ * "}" * } - if$ -} - -% IEEEtran.bst uses its own \BIBforeignlanguage command which directly -% invokes the TeX hyphenation patterns without the need of the Babel -% package. Babel does a lot more than switch hyphenation patterns and -% its loading can cause unintended effects in many class files (such as -% IEEEtran.cls). -FUNCTION {select.language} -{ duplicate$ empty$ 'pop$ - { language empty$ 'skip$ - { "\BIBforeignlanguage{" language * "}{" * swap$ * "}" * } - if$ - } - if$ -} - -FUNCTION {tie.or.space.prefix} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ -} - -FUNCTION {get.bbl.editor} -{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ } - -FUNCTION {space.word}{ " " swap$ * " " * } - - -% Field Conditioners, Converters, Checkers and External Interfaces - -FUNCTION {empty.field.to.null.string} -{ duplicate$ empty$ - { pop$ "" } - { skip$ } - if$ -} - -FUNCTION {either.or.check} -{ empty$ - { pop$ } - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -FUNCTION {empty.entry.warn} -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ url empty$ - and and and and and and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - - -% The bibinfo system provides a way for the electronic parsing/acquisition -% of a bibliography's contents as is done by ReVTeX. For example, a field -% could be entered into the bibliography as: -% \bibinfo{volume}{2} -% Only the "2" would show up in the document, but the LaTeX \bibinfo command -% could do additional things with the information. IEEEtran.bst does provide -% a \bibinfo command via "\providecommand{\bibinfo}[2]{#2}". However, it is -% currently not used as the bogus bibinfo functions defined here output the -% entry values directly without the \bibinfo wrapper. The bibinfo functions -% themselves (and the calls to them) are retained for possible future use. -% -% bibinfo.check avoids acting on missing fields while bibinfo.warn will -% issue a warning message if a missing field is detected. Prior to calling -% the bibinfo functions, the user should push the field value and then its -% name string, in that order. - -FUNCTION {bibinfo.check} -{ swap$ duplicate$ missing$ - { pop$ pop$ "" } - { duplicate$ empty$ - { swap$ pop$ } - { swap$ pop$ } - if$ - } - if$ -} - -FUNCTION {bibinfo.warn} -{ swap$ duplicate$ missing$ - { swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ "" } - { duplicate$ empty$ - { swap$ "empty " swap$ * " in " * cite$ * warning$ } - { swap$ pop$ } - if$ - } - if$ -} - - -% The IEEE separates large numbers with more than 4 digits into groups of -% three. The IEEE uses a small space to separate these number groups. -% Typical applications include patent and page numbers. - -% number of consecutive digits required to trigger the group separation. -FUNCTION {large.number.trigger}{ #5 } - -% For numbers longer than the trigger, this is the blocksize of the groups. -% The blocksize must be less than the trigger threshold, and 2 * blocksize -% must be greater than the trigger threshold (can't do more than one -% separation on the initial trigger). -FUNCTION {large.number.blocksize}{ #3 } - -% What is actually inserted between the number groups. -FUNCTION {large.number.separator}{ "\," } - -% So as to save on integer variables by reusing existing ones, numnames -% holds the current number of consecutive digits read and nameptr holds -% the number that will trigger an inserted space. -FUNCTION {large.number.separate} -{ 't := - "" - #0 'numnames := - large.number.trigger 'nameptr := - { t empty$ not } - { t #-1 #1 substring$ is.num - { numnames #1 + 'numnames := } - { #0 'numnames := - large.number.trigger 'nameptr := - } - if$ - t #-1 #1 substring$ swap$ * - t #-2 global.max$ substring$ 't := - numnames nameptr = - { duplicate$ #1 nameptr large.number.blocksize - substring$ swap$ - nameptr large.number.blocksize - #1 + global.max$ substring$ - large.number.separator swap$ * * - nameptr large.number.blocksize - 'numnames := - large.number.blocksize #1 + 'nameptr := - } - { skip$ } - if$ - } - while$ -} - -% Converts all single dashes "-" to double dashes "--". -FUNCTION {n.dashify} -{ large.number.separate - 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - - -% This function detects entries with names that are identical to that of -% the previous entry and replaces the repeated names with dashes (if the -% "is.dash.repeated.names" user control is nonzero). -FUNCTION {name.or.dash} -{ 's := - oldname empty$ - { s 'oldname := s } - { s oldname = - { is.dash.repeated.names - { repeated.name.dashes } - { s 'oldname := s } - if$ - } - { s 'oldname := s } - if$ - } - if$ -} - -% Converts the number string on the top of the stack to -% "numerical ordinal form" (e.g., "7" to "7th"). There is -% no artificial limit to the upper bound of the numbers as the -% two least significant digits determine the ordinal form. -FUNCTION {num.to.ordinal} -{ duplicate$ #-2 #1 substring$ "1" = - { bbl.th * } - { duplicate$ #-1 #1 substring$ "1" = - { bbl.st * } - { duplicate$ #-1 #1 substring$ "2" = - { bbl.nd * } - { duplicate$ #-1 #1 substring$ "3" = - { bbl.rd * } - { bbl.th * } - if$ - } - if$ - } - if$ - } - if$ -} - -% If the string on the top of the stack begins with a number, -% (e.g., 11th) then replace the string with the leading number -% it contains. Otherwise retain the string as-is. s holds the -% extracted number, t holds the part of the string that remains -% to be scanned. -FUNCTION {extract.num} -{ duplicate$ 't := - "" 's := - { t empty$ not } - { t #1 #1 substring$ - t #2 global.max$ substring$ 't := - duplicate$ is.num - { s swap$ * 's := } - { pop$ "" 't := } - if$ - } - while$ - s empty$ - 'skip$ - { pop$ s } - if$ -} - -% Converts the word number string on the top of the stack to -% Arabic string form. Will be successful up to "tenth". -FUNCTION {word.to.num} -{ duplicate$ "l" change.case$ 's := - s "first" = - { pop$ "1" } - { skip$ } - if$ - s "second" = - { pop$ "2" } - { skip$ } - if$ - s "third" = - { pop$ "3" } - { skip$ } - if$ - s "fourth" = - { pop$ "4" } - { skip$ } - if$ - s "fifth" = - { pop$ "5" } - { skip$ } - if$ - s "sixth" = - { pop$ "6" } - { skip$ } - if$ - s "seventh" = - { pop$ "7" } - { skip$ } - if$ - s "eighth" = - { pop$ "8" } - { skip$ } - if$ - s "ninth" = - { pop$ "9" } - { skip$ } - if$ - s "tenth" = - { pop$ "10" } - { skip$ } - if$ -} - - -% Converts the string on the top of the stack to numerical -% ordinal (e.g., "11th") form. -FUNCTION {convert.edition} -{ duplicate$ empty$ 'skip$ - { duplicate$ #1 #1 substring$ is.num - { extract.num - num.to.ordinal - } - { word.to.num - duplicate$ #1 #1 substring$ is.num - { num.to.ordinal } - { "edition ordinal word " quote$ * edition * quote$ * - " may be too high (or improper) for conversion" * " in " * cite$ * warning$ - } - if$ - } - if$ - } - if$ -} - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% LATEX BIBLIOGRAPHY CODE %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -FUNCTION {start.entry} -{ newline$ - "\bibitem{" write$ - cite$ write$ - "}" write$ - newline$ - "" - initialize.prev.this.status -} - -% Here we write out all the LaTeX code that we will need. The most involved -% code sequences are those that control the alternate interword spacing and -% foreign language hyphenation patterns. The heavy use of \providecommand -% gives users a way to override the defaults. Special thanks to Javier Bezos, -% Johannes Braams, Robin Fairbairns, Heiko Oberdiek, Donald Arseneau and all -% the other gurus on comp.text.tex for their help and advice on the topic of -% \selectlanguage, Babel and BibTeX. -FUNCTION {begin.bib} -{ "% Generated by IEEEtran.bst, version: " bst.file.version * " (" * bst.file.date * ")" * - write$ newline$ - preamble$ empty$ 'skip$ - { preamble$ write$ newline$ } - if$ - "\begin{thebibliography}{" longest.label * "}" * - write$ newline$ - "\providecommand{\url}[1]{#1}" - write$ newline$ - "\csname url@samestyle\endcsname" - write$ newline$ - "\providecommand{\newblock}{\relax}" - write$ newline$ - "\providecommand{\bibinfo}[2]{#2}" - write$ newline$ - "\providecommand{\BIBentrySTDinterwordspacing}{\spaceskip=0pt\relax}" - write$ newline$ - "\providecommand{\BIBentryALTinterwordstretchfactor}{" - ALTinterwordstretchfactor * "}" * - write$ newline$ - "\providecommand{\BIBentryALTinterwordspacing}{\spaceskip=\fontdimen2\font plus " - write$ newline$ - "\BIBentryALTinterwordstretchfactor\fontdimen3\font minus \fontdimen4\font\relax}" - write$ newline$ - "\providecommand{\BIBforeignlanguage}[2]{{%" - write$ newline$ - "\expandafter\ifx\csname l@#1\endcsname\relax" - write$ newline$ - "\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}%" - write$ newline$ - "\typeout{** loaded for the language `#1'. Using the pattern for}%" - write$ newline$ - "\typeout{** the default language instead.}%" - write$ newline$ - "\else" - write$ newline$ - "\language=\csname l@#1\endcsname" - write$ newline$ - "\fi" - write$ newline$ - "#2}}" - write$ newline$ - "\providecommand{\BIBdecl}{\relax}" - write$ newline$ - "\BIBdecl" - write$ newline$ -} - -FUNCTION {end.bib} -{ newline$ "\end{thebibliography}" write$ newline$ } - -FUNCTION {if.url.alt.interword.spacing} -{ is.use.alt.interword.spacing - { is.use.url - { url empty$ 'skip$ {"\BIBentryALTinterwordspacing" write$ newline$} if$ } - { skip$ } - if$ - } - { skip$ } - if$ -} - -FUNCTION {if.url.std.interword.spacing} -{ is.use.alt.interword.spacing - { is.use.url - { url empty$ 'skip$ {"\BIBentrySTDinterwordspacing" write$ newline$} if$ } - { skip$ } - if$ - } - { skip$ } - if$ -} - - - - -%%%%%%%%%%%%%%%%%%%%%%%% -%% LONGEST LABEL PASS %% -%%%%%%%%%%%%%%%%%%%%%%%% - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #1 'number.label := - #0 'longest.label.width := -} - -FUNCTION {longest.label.pass} -{ type$ "ieeetranbstctl" = - { skip$ } - { number.label int.to.str$ 'label := - number.label #1 + 'number.label := - label width$ longest.label.width > - { label 'longest.label := - label width$ 'longest.label.width := - } - { skip$ } - if$ - } - if$ -} - - - - -%%%%%%%%%%%%%%%%%%%%% -%% FORMAT HANDLERS %% -%%%%%%%%%%%%%%%%%%%%% - -%% Lower Level Formats (used by higher level formats) - -FUNCTION {format.address.org.or.pub.date} -{ 't := - "" - year empty$ - { "empty year in " cite$ * warning$ } - { skip$ } - if$ - address empty$ t empty$ and - year empty$ and month empty$ and - { skip$ } - { this.to.prev.status - this.status.std - cap.status.std - address "address" bibinfo.check * - t empty$ - { skip$ } - { punct.period 'prev.status.punct := - space.large 'prev.status.space := - address empty$ - { skip$ } - { ": " * } - if$ - t * - } - if$ - year empty$ month empty$ and - { skip$ } - { t empty$ address empty$ and - { skip$ } - { ", " * } - if$ - month empty$ - { year empty$ - { skip$ } - { year "year" bibinfo.check * } - if$ - } - { month "month" bibinfo.check * - year empty$ - { skip$ } - { " " * year "year" bibinfo.check * } - if$ - } - if$ - } - if$ - } - if$ -} - - -FUNCTION {format.names} -{ 'bibinfo := - duplicate$ empty$ 'skip$ { - this.to.prev.status - this.status.std - 's := - "" 't := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr - name.format.string - format.name$ - bibinfo bibinfo.check - 't := - nameptr #1 > - { nameptr num.names.shown.with.forced.et.al #1 + = - numnames max.num.names.before.forced.et.al > - is.forced.et.al and and - { "others" 't := - #1 'namesleft := - } - { skip$ } - if$ - namesleft #1 > - { ", " * t do.name.latex.cmd * } - { s nameptr "{ll}" format.name$ duplicate$ "others" = - { 't := } - { pop$ } - if$ - t "others" = - { " " * bbl.etal emphasize * } - { numnames #2 > - { "," * } - { skip$ } - if$ - bbl.and - space.word * t do.name.latex.cmd * - } - if$ - } - if$ - } - { t do.name.latex.cmd } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ - cap.status.std - } if$ -} - - - - -%% Higher Level Formats - -%% addresses/locations - -FUNCTION {format.address} -{ address duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - } - if$ -} - - - -%% author/editor names - -FUNCTION {format.authors}{ author "author" format.names } - -FUNCTION {format.editors} -{ editor "editor" format.names duplicate$ empty$ 'skip$ - { ", " * - get.bbl.editor - capitalize - * - } - if$ -} - - - -%% date - -FUNCTION {format.date} -{ - month "month" bibinfo.check duplicate$ empty$ - year "year" bibinfo.check duplicate$ empty$ - { swap$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - "there's a month but no year in " cite$ * warning$ } - if$ - * - } - { this.to.prev.status - this.status.std - cap.status.std - swap$ 'skip$ - { - swap$ - " " * swap$ - } - if$ - * - } - if$ -} - -FUNCTION {format.date.electronic} -{ month "month" bibinfo.check duplicate$ empty$ - year "year" bibinfo.check duplicate$ empty$ - { swap$ - { pop$ } - { "there's a month but no year in " cite$ * warning$ - pop$ ")" * "(" swap$ * - this.to.prev.status - punct.no 'this.status.punct := - space.normal 'this.status.space := - quote.no 'this.status.quote := - cap.yes 'status.cap := - } - if$ - } - { swap$ - { swap$ pop$ ")" * "(" swap$ * } - { "(" swap$ * ", " * swap$ * ")" * } - if$ - this.to.prev.status - punct.no 'this.status.punct := - space.normal 'this.status.space := - quote.no 'this.status.quote := - cap.yes 'status.cap := - } - if$ -} - - - -%% edition/title - -% Note: The IEEE considers the edition to be closely associated with -% the title of a book. So, in IEEEtran.bst the edition is normally handled -% within the formatting of the title. The format.edition function is -% retained here for possible future use. -FUNCTION {format.edition} -{ edition duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - convert.edition - status.cap - { "t" } - { "l" } - if$ change.case$ - "edition" bibinfo.check - "~" * bbl.edition * - cap.status.std - } - if$ -} - -% This is used to format the booktitle of a conference proceedings. -% Here we use the "intype" field to provide the user a way to -% override the word "in" (e.g., with things like "presented at") -% Use of intype stops the emphasis of the booktitle to indicate that -% we no longer mean the written conference proceedings, but the -% conference itself. -FUNCTION {format.in.booktitle} -{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - select.language - intype missing$ - { emphasize - bbl.in " " * - } - { intype " " * } - if$ - swap$ * - cap.status.std - } - if$ -} - -% This is used to format the booktitle of collection. -% Here the "intype" field is not supported, but "edition" is. -FUNCTION {format.in.booktitle.edition} -{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - select.language - emphasize - edition empty$ 'skip$ - { ", " * - edition - convert.edition - "l" change.case$ - * "~" * bbl.edition * - } - if$ - bbl.in " " * swap$ * - cap.status.std - } - if$ -} - -FUNCTION {format.article.title} -{ title duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - "t" change.case$ - } - if$ - "title" bibinfo.check - duplicate$ empty$ 'skip$ - { quote.close 'this.status.quote := - is.last.char.not.punct - { punct.std 'this.status.punct := } - { punct.no 'this.status.punct := } - if$ - select.language - "``" swap$ * - cap.status.std - } - if$ -} - -FUNCTION {format.article.title.electronic} -{ title duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - "t" change.case$ - } - if$ - "title" bibinfo.check - duplicate$ empty$ - { skip$ } - { select.language } - if$ -} - -FUNCTION {format.book.title.edition} -{ title "title" bibinfo.check - duplicate$ empty$ - { "empty title in " cite$ * warning$ } - { this.to.prev.status - this.status.std - select.language - emphasize - edition empty$ 'skip$ - { ", " * - edition - convert.edition - status.cap - { "t" } - { "l" } - if$ - change.case$ - * "~" * bbl.edition * - } - if$ - cap.status.std - } - if$ -} - -FUNCTION {format.book.title} -{ title "title" bibinfo.check - duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - select.language - emphasize - } - if$ -} - - - -%% journal - -FUNCTION {format.journal} -{ journal duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - select.language - emphasize - } - if$ -} - - - -%% how published - -FUNCTION {format.howpublished} -{ howpublished duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - } - if$ -} - - - -%% institutions/organization/publishers/school - -FUNCTION {format.institution} -{ institution duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - } - if$ -} - -FUNCTION {format.organization} -{ organization duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - } - if$ -} - -FUNCTION {format.address.publisher.date} -{ publisher "publisher" bibinfo.warn format.address.org.or.pub.date } - -FUNCTION {format.address.publisher.date.nowarn} -{ publisher "publisher" bibinfo.check format.address.org.or.pub.date } - -FUNCTION {format.address.organization.date} -{ organization "organization" bibinfo.check format.address.org.or.pub.date } - -FUNCTION {format.school} -{ school duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - cap.status.std - } - if$ -} - - - -%% volume/number/series/chapter/pages - -FUNCTION {format.volume} -{ volume empty.field.to.null.string - duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - bbl.volume - status.cap - { capitalize } - { skip$ } - if$ - swap$ tie.or.space.prefix - "volume" bibinfo.check - * * - cap.status.std - } - if$ -} - -FUNCTION {format.number} -{ number empty.field.to.null.string - duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - status.cap - { bbl.number capitalize } - { bbl.number } - if$ - swap$ tie.or.space.prefix - "number" bibinfo.check - * * - cap.status.std - } - if$ -} - -FUNCTION {format.number.if.use.for.article} -{ is.use.number.for.article - { format.number } - { "" } - if$ -} - -% The IEEE does not seem to tie the series so closely with the volume -% and number as is done in other bibliography styles. Instead the -% series is treated somewhat like an extension of the title. -FUNCTION {format.series} -{ series empty$ - { "" } - { this.to.prev.status - this.status.std - bbl.series " " * - series "series" bibinfo.check * - cap.status.std - } - if$ -} - - -FUNCTION {format.chapter} -{ chapter empty$ - { "" } - { this.to.prev.status - this.status.std - type empty$ - { bbl.chapter } - { type "l" change.case$ - "type" bibinfo.check - } - if$ - chapter tie.or.space.prefix - "chapter" bibinfo.check - * * - cap.status.std - } - if$ -} - - -% The intended use of format.paper is for paper numbers of inproceedings. -% The paper type can be overridden via the type field. -% We allow the type to be displayed even if the paper number is absent -% for things like "postdeadline paper" -FUNCTION {format.paper} -{ is.use.paper - { paper empty$ - { type empty$ - { "" } - { this.to.prev.status - this.status.std - type "type" bibinfo.check - cap.status.std - } - if$ - } - { this.to.prev.status - this.status.std - type empty$ - { bbl.paper } - { type "type" bibinfo.check } - if$ - " " * paper - "paper" bibinfo.check - * - cap.status.std - } - if$ - } - { "" } - if$ -} - - -FUNCTION {format.pages} -{ pages duplicate$ empty$ 'skip$ - { this.to.prev.status - this.status.std - duplicate$ is.multiple.pages - { - bbl.pages swap$ - n.dashify - } - { - bbl.page swap$ - } - if$ - tie.or.space.prefix - "pages" bibinfo.check - * * - cap.status.std - } - if$ -} - - - -%% technical report number - -FUNCTION {format.tech.report.number} -{ number "number" bibinfo.check - this.to.prev.status - this.status.std - cap.status.std - type duplicate$ empty$ - { pop$ - bbl.techrep - } - { skip$ } - if$ - "type" bibinfo.check - swap$ duplicate$ empty$ - { pop$ } - { tie.or.space.prefix * * } - if$ -} - - - -%% note - -FUNCTION {format.note} -{ note empty$ - { "" } - { this.to.prev.status - this.status.std - punct.period 'this.status.punct := - note #1 #1 substring$ - duplicate$ "{" = - { skip$ } - { status.cap - { "u" } - { "l" } - if$ - change.case$ - } - if$ - note #2 global.max$ substring$ * "note" bibinfo.check - cap.yes 'status.cap := - } - if$ -} - - - -%% patent - -FUNCTION {format.patent.date} -{ this.to.prev.status - this.status.std - year empty$ - { monthfiled duplicate$ empty$ - { "monthfiled" bibinfo.check pop$ "" } - { "monthfiled" bibinfo.check } - if$ - dayfiled duplicate$ empty$ - { "dayfiled" bibinfo.check pop$ "" * } - { "dayfiled" bibinfo.check - monthfiled empty$ - { "dayfiled without a monthfiled in " cite$ * warning$ - * - } - { " " swap$ * * } - if$ - } - if$ - yearfiled empty$ - { "no year or yearfiled in " cite$ * warning$ } - { yearfiled "yearfiled" bibinfo.check - swap$ - duplicate$ empty$ - { pop$ } - { ", " * swap$ * } - if$ - } - if$ - } - { month duplicate$ empty$ - { "month" bibinfo.check pop$ "" } - { "month" bibinfo.check } - if$ - day duplicate$ empty$ - { "day" bibinfo.check pop$ "" * } - { "day" bibinfo.check - month empty$ - { "day without a month in " cite$ * warning$ - * - } - { " " swap$ * * } - if$ - } - if$ - year "year" bibinfo.check - swap$ - duplicate$ empty$ - { pop$ } - { ", " * swap$ * } - if$ - } - if$ - cap.status.std -} - -FUNCTION {format.patent.nationality.type.number} -{ this.to.prev.status - this.status.std - nationality duplicate$ empty$ - { "nationality" bibinfo.warn pop$ "" } - { "nationality" bibinfo.check - duplicate$ "l" change.case$ "united states" = - { pop$ bbl.patentUS } - { skip$ } - if$ - " " * - } - if$ - type empty$ - { bbl.patent "type" bibinfo.check } - { type "type" bibinfo.check } - if$ - * - number duplicate$ empty$ - { "number" bibinfo.warn pop$ } - { "number" bibinfo.check - large.number.separate - swap$ " " * swap$ * - } - if$ - cap.status.std -} - - - -%% standard - -FUNCTION {format.organization.institution.standard.type.number} -{ this.to.prev.status - this.status.std - organization duplicate$ empty$ - { pop$ - institution duplicate$ empty$ - { "institution" bibinfo.warn } - { "institution" bibinfo.warn " " * } - if$ - } - { "organization" bibinfo.warn " " * } - if$ - type empty$ - { bbl.standard "type" bibinfo.check } - { type "type" bibinfo.check } - if$ - * - number duplicate$ empty$ - { "number" bibinfo.check pop$ } - { "number" bibinfo.check - large.number.separate - swap$ " " * swap$ * - } - if$ - cap.status.std -} - -FUNCTION {format.revision} -{ revision empty$ - { "" } - { this.to.prev.status - this.status.std - bbl.revision - revision tie.or.space.prefix - "revision" bibinfo.check - * * - cap.status.std - } - if$ -} - - -%% thesis - -FUNCTION {format.master.thesis.type} -{ this.to.prev.status - this.status.std - type empty$ - { - bbl.mthesis - } - { - type "type" bibinfo.check - } - if$ -cap.status.std -} - -FUNCTION {format.phd.thesis.type} -{ this.to.prev.status - this.status.std - type empty$ - { - bbl.phdthesis - } - { - type "type" bibinfo.check - } - if$ -cap.status.std -} - - - -%% URL - -FUNCTION {format.url} -{ is.use.url - { url empty$ - { "" } - { this.to.prev.status - this.status.std - cap.yes 'status.cap := - name.url.prefix " " * - "\url{" * url * "}" * - punct.no 'this.status.punct := - punct.period 'prev.status.punct := - space.normal 'this.status.space := - space.normal 'prev.status.space := - quote.no 'this.status.quote := - } - if$ - } - { "" } - if$ -} - - - - -%%%%%%%%%%%%%%%%%%%% -%% ENTRY HANDLERS %% -%%%%%%%%%%%%%%%%%%%% - - -% Note: In many journals, the IEEE (or the authors) tend not to show the number -% for articles, so the display of the number is controlled here by the -% switch "is.use.number.for.article" -FUNCTION {article} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.journal "journal" bibinfo.check "journal" output.warn - format.volume output - format.number.if.use.for.article output - format.pages output - format.date "year" output.warn - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {book} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - author empty$ - { format.editors "author and editor" output.warn } - { format.authors output.nonnull } - if$ - name.or.dash - format.book.title.edition output - format.series output - author empty$ - { skip$ } - { format.editors output } - if$ - format.address.publisher.date output - format.volume output - format.number output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {booklet} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors output - name.or.dash - format.article.title "title" output.warn - format.howpublished "howpublished" bibinfo.check output - format.organization "organization" bibinfo.check output - format.address "address" bibinfo.check output - format.date output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {electronic} -{ std.status.using.period - start.entry - if.url.alt.interword.spacing - format.authors output - name.or.dash - format.date.electronic output - format.article.title.electronic output - format.howpublished "howpublished" bibinfo.check output - format.organization "organization" bibinfo.check output - format.address "address" bibinfo.check output - format.note output - format.url output - fin.entry - empty.entry.warn - if.url.std.interword.spacing -} - -FUNCTION {inbook} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - author empty$ - { format.editors "author and editor" output.warn } - { format.authors output.nonnull } - if$ - name.or.dash - format.book.title.edition output - format.series output - format.address.publisher.date output - format.volume output - format.number output - format.chapter output - format.pages output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {incollection} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.in.booktitle.edition "booktitle" output.warn - format.series output - format.editors output - format.address.publisher.date.nowarn output - format.volume output - format.number output - format.chapter output - format.pages output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {inproceedings} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.in.booktitle "booktitle" output.warn - format.series output - format.editors output - format.volume output - format.number output - publisher empty$ - { format.address.organization.date output } - { format.organization "organization" bibinfo.check output - format.address.publisher.date output - } - if$ - format.paper output - format.pages output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {manual} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors output - name.or.dash - format.book.title.edition "title" output.warn - format.howpublished "howpublished" bibinfo.check output - format.organization "organization" bibinfo.check output - format.address "address" bibinfo.check output - format.date output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {mastersthesis} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.master.thesis.type output.nonnull - format.school "school" bibinfo.warn output - format.address "address" bibinfo.check output - format.date "year" output.warn - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {misc} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors output - name.or.dash - format.article.title output - format.howpublished "howpublished" bibinfo.check output - format.organization "organization" bibinfo.check output - format.address "address" bibinfo.check output - format.pages output - format.date output - format.note output - format.url output - fin.entry - empty.entry.warn - if.url.std.interword.spacing -} - -FUNCTION {patent} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors output - name.or.dash - format.article.title output - format.patent.nationality.type.number output - format.patent.date output - format.note output - format.url output - fin.entry - empty.entry.warn - if.url.std.interword.spacing -} - -FUNCTION {periodical} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.editors output - name.or.dash - format.book.title "title" output.warn - format.series output - format.volume output - format.number output - format.organization "organization" bibinfo.check output - format.date "year" output.warn - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {phdthesis} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.phd.thesis.type output.nonnull - format.school "school" bibinfo.warn output - format.address "address" bibinfo.check output - format.date "year" output.warn - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {proceedings} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.editors output - name.or.dash - format.book.title "title" output.warn - format.series output - format.volume output - format.number output - publisher empty$ - { format.address.organization.date output } - { format.organization "organization" bibinfo.check output - format.address.publisher.date output - } - if$ - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {standard} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors output - name.or.dash - format.book.title "title" output.warn - format.howpublished "howpublished" bibinfo.check output - format.organization.institution.standard.type.number output - format.revision output - format.date output - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {techreport} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.howpublished "howpublished" bibinfo.check output - format.institution "institution" bibinfo.warn output - format.address "address" bibinfo.check output - format.tech.report.number output.nonnull - format.date "year" output.warn - format.note output - format.url output - fin.entry - if.url.std.interword.spacing -} - -FUNCTION {unpublished} -{ std.status.using.comma - start.entry - if.url.alt.interword.spacing - format.authors "author" output.warn - name.or.dash - format.article.title "title" output.warn - format.date output - format.note "note" output.warn - format.url output - fin.entry - if.url.std.interword.spacing -} - - -% The special entry type which provides the user interface to the -% BST controls -FUNCTION {IEEEtranBSTCTL} -{ is.print.banners.to.terminal - { "** IEEEtran BST control entry " quote$ * cite$ * quote$ * " detected." * - top$ - } - { skip$ } - if$ - CTLuse_article_number - empty$ - { skip$ } - { CTLuse_article_number - yes.no.to.int - 'is.use.number.for.article := - } - if$ - CTLuse_paper - empty$ - { skip$ } - { CTLuse_paper - yes.no.to.int - 'is.use.paper := - } - if$ - CTLuse_url - empty$ - { skip$ } - { CTLuse_url - yes.no.to.int - 'is.use.url := - } - if$ - CTLuse_forced_etal - empty$ - { skip$ } - { CTLuse_forced_etal - yes.no.to.int - 'is.forced.et.al := - } - if$ - CTLmax_names_forced_etal - empty$ - { skip$ } - { CTLmax_names_forced_etal - string.to.integer - 'max.num.names.before.forced.et.al := - } - if$ - CTLnames_show_etal - empty$ - { skip$ } - { CTLnames_show_etal - string.to.integer - 'num.names.shown.with.forced.et.al := - } - if$ - CTLuse_alt_spacing - empty$ - { skip$ } - { CTLuse_alt_spacing - yes.no.to.int - 'is.use.alt.interword.spacing := - } - if$ - CTLalt_stretch_factor - empty$ - { skip$ } - { CTLalt_stretch_factor - 'ALTinterwordstretchfactor := - "\renewcommand{\BIBentryALTinterwordstretchfactor}{" - ALTinterwordstretchfactor * "}" * - write$ newline$ - } - if$ - CTLdash_repeated_names - empty$ - { skip$ } - { CTLdash_repeated_names - yes.no.to.int - 'is.dash.repeated.names := - } - if$ - CTLname_format_string - empty$ - { skip$ } - { CTLname_format_string - 'name.format.string := - } - if$ - CTLname_latex_cmd - empty$ - { skip$ } - { CTLname_latex_cmd - 'name.latex.cmd := - } - if$ - CTLname_url_prefix - missing$ - { skip$ } - { CTLname_url_prefix - 'name.url.prefix := - } - if$ - - - num.names.shown.with.forced.et.al max.num.names.before.forced.et.al > - { "CTLnames_show_etal cannot be greater than CTLmax_names_forced_etal in " cite$ * warning$ - max.num.names.before.forced.et.al 'num.names.shown.with.forced.et.al := - } - { skip$ } - if$ -} - - -%%%%%%%%%%%%%%%%%%% -%% ENTRY ALIASES %% -%%%%%%%%%%%%%%%%%%% -FUNCTION {conference}{inproceedings} -FUNCTION {online}{electronic} -FUNCTION {internet}{electronic} -FUNCTION {webpage}{electronic} -FUNCTION {www}{electronic} -FUNCTION {default.type}{misc} - - - -%%%%%%%%%%%%%%%%%% -%% MAIN PROGRAM %% -%%%%%%%%%%%%%%%%%% - -READ - -EXECUTE {initialize.controls} -EXECUTE {initialize.status.constants} -EXECUTE {banner.message} - -EXECUTE {initialize.longest.label} -ITERATE {longest.label.pass} - -EXECUTE {begin.bib} -ITERATE {call.type$} -EXECUTE {end.bib} - -EXECUTE{completed.message} - - -%% That's all folks, mds. \ No newline at end of file diff --git a/TRUST-docs/IEEEtrantools.sty b/TRUST-docs/IEEEtrantools.sty deleted file mode 100755 index e4a808c..0000000 --- a/TRUST-docs/IEEEtrantools.sty +++ /dev/null @@ -1,2799 +0,0 @@ -%% -%% IEEEtrantools.sty 2015/08/26 version V1.5 -%% -%% -%% This package provides several popular and unique commands from the -%% IEEEtran.cls class (version 1.8b) file. -%% -%% The provided commands include \IEEEPARstart, \IEEEitemize, \IEEEenumerate, -%% \IEEEdescription as well as the \IEEEeqnarray, \IEEEeqnarraybox family -%% of commands including support commands such as \IEEEstrut, the IEEEproof -%% environment and its support commands and the \IEEEauthorrefmark command. -%% Also provides the \bstctlcite command for the control entry types of -%% IEEEtran.bst V1.00 and later, as well as \IEEEnoauxwrite. -%% -%% IEEEtrantools.sty should not be used with IEEEtran.cls. -%% -%% Support sites: -%% http://www.michaelshell.org/tex/ieeetran/ -%% http://www.ctan.org/pkg/ieeetran -%% -%% -%% Copyright (c) 2002-2015 by Michael Shell -%% See: http://www.michaelshell.org/ -%% for current contact information. -%% -%%************************************************************************* -%% Legal Notice: -%% This code is offered as-is without any warranty either expressed or -%% implied; without even the implied warranty of MERCHANTABILITY or -%% FITNESS FOR A PARTICULAR PURPOSE! -%% User assumes all risk. -%% In no event shall the IEEE or any contributor to this code be liable for -%% any damages or losses, including, but not limited to, incidental, -%% consequential, or any other damages, resulting from the use or misuse -%% of any information contained here. -%% -%% All comments are the opinions of their respective authors and are not -%% necessarily endorsed by the IEEE. -%% -%% This work is distributed under the LaTeX Project Public License (LPPL) -%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, -%% distributed and modified. A copy of the LPPL, version 1.3, is included -%% in the base LaTeX documentation of all distributions of LaTeX released -%% 2003/12/01 or later. -%% Retain all contribution notices and credits. -%% ** Modified files should be clearly indicated as such, including ** -%% ** renaming them and changing author support contact information. ** -%% -%% File list of work: IEEEtrantools.sty, IEEEtrantools_doc.txt -%%************************************************************************* -%% -%% -%% -%% Available package options (e.g., \usepackage[redeflists]{IEEEtrantools} -%% -%% redeflists -%% Causes IEEEtrantools to redefine the standard itemize, enumerate and -%% description (IED) list environments to their IEEE versions. -%% IEEEitemize, IEEEenumerate and IEEEdescription remain available in any -%% case. This option may not be compatible with packages that alter the -%% standard IED list environments. -%% -%% -%%********************************************************************** - - -\ProvidesPackage{IEEEtrantools}[2015/08/26 V1.5 by Michael Shell] -\typeout{-- See the "IEEEtrantools_doc.txt" manual for usage information.} -\typeout{-- http://www.michaelshell.org/tex/ieeetran/tools/} -\NeedsTeXFormat{LaTeX2e} - - -% If \@IEEEeqnarray is detected, error. -{\@ifundefined{@IEEEeqnarray}{\relax}{% -\PackageError{IEEEtrantools}{The IEEEtrantools package is not for use\MessageBreak - with classes that already provide it}% - {Do not load IEEEtrantools - you don't need it.}% -}} - - -% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting -\def\@IEEEclspkgerror{\PackageError{IEEEtrantools}} - - -% define needed flags to indicate document options -\newif\if@IEEETOOLSredeflists -\global\@IEEETOOLSredeflistsfalse - - -% IEEEtran class scratch pad registers -% dimen -\newdimen\@IEEEtrantmpdimenA -\newdimen\@IEEEtrantmpdimenB -\newdimen\@IEEEtrantmpdimenC -% count -\newcount\@IEEEtrantmpcountA -\newcount\@IEEEtrantmpcountB -\newcount\@IEEEtrantmpcountC -% token list -\newtoks\@IEEEtrantmptoksA - - -% declare the options -\DeclareOption{redeflists}{\@IEEETOOLSredefliststrue} -% provide legacy support for retainorgcmds which does nothing now. -\DeclareOption{retainorgcmds}{\@IEEETOOLSredeflistsfalse} - -% get and process any supplied options -\ProcessOptions - - -% store the nominal value of jot -\newdimen\IEEEnormaljot -\IEEEnormaljot\jot\relax -% V1.4 allow for other packages that later change \jot -\AtBeginDocument{\IEEEnormaljot\jot\relax} - - - - -%% -- Command Argument Scanning Support Functions -- - -% Sets the category codes for punctuation to their normal values. -% For local use with argument scanning. -\def\IEEEnormalcatcodespunct{\catcode`\!=12 \catcode`\,=12 \catcode`\:=12 -\catcode`\;=12 \catcode`\`=12 \catcode`\'=12 \catcode`\"=12 \catcode`\.=12 -\catcode`\/=12 \catcode`\?=12 \catcode`\*=12 \catcode`\+=12 \catcode`\-=12 -\catcode`\<=12 \catcode`\>=12 \catcode`\(=12 \catcode`\)=12 \catcode`\[=12 -\catcode`\]=12 \catcode`\==12 \catcode`\|=12} -% Sets the category codes for numbers to their normal values. -% For local use with argument scanning. -\def\IEEEnormalcatcodesnum{\catcode`\0=12 \catcode`\1=12 \catcode`\2=12 -\catcode`\3=12 \catcode`\4=12 \catcode`\5=12 \catcode`\6=12 \catcode`\7=12 -\catcode`\8=12 \catcode`\9=12} -% combined action of \IEEEnormalcatcodespunct and \IEEEnormalcatcodesnum -\def\IEEEnormalcatcodes{\IEEEnormalcatcodespunct\IEEEnormalcatcodesnum} - - -% usage: \@IEEEstripouterbraces*{} -% \@IEEEstripouterbraces fully expands its argument (which it then stores -% in \@IEEEstripouterbracesarg) via \edef, then removes any outer enclosing -% braces, and finally stores the result in the macro -% \@IEEEstrippedouterbraces. -% -% For example: -% \@IEEEstripouterbraces{{{{ab}c}}} -% results in: -% -% \@IEEEstripouterbracesarg ==> a macro containing {{{ab}c}} -% \@IEEEstrippedouterbraces ==> a macro containing {ab}c -% -% the *-star form,\@IEEEstripouterbraces*, does not expand the argument -% contents during processing -\def\@IEEEstripouterbraces{\@ifstar{\let\@IEEEstripouterbracesdef=\def\@@IEEEstripouterbraces}{\let\@IEEEstripouterbracesdef=\edef\@@IEEEstripouterbraces}} - -\def\@@IEEEstripouterbraces#1{\@IEEEstripouterbracesdef\@IEEEstripouterbracesarg{#1}\relax -% If the macro is unchanged after being acquired as a single delimited -% argument, we know we have one sequence of tokens without any enclosing -% braces. Loop until this is true. -\loop - \expandafter\@@@IEEEstripouterbraces\@IEEEstripouterbracesarg\@IEEEgeneralsequenceDELIMITER -\ifx\@IEEEstrippedouterbraces\@IEEEstripouterbracesarg -\else - \let\@IEEEstripouterbracesarg\@IEEEstrippedouterbraces -\repeat} - -\def\@@@IEEEstripouterbraces#1\@IEEEgeneralsequenceDELIMITER{\def\@IEEEstrippedouterbraces{#1}} - - - -% usage: \@IEEEextractgroup*{} -% \@IEEEextractgroup fully expands its argument (which it then stores in -% \@IEEEextractgrouparg) via \edef and then assigns the first "brace group" -% of tokens to the macro \@IEEEextractedgroup. -% The remaining groups, if any, are stored in the macro -% \@IEEEextractedgroupremain. If the argument does not contain the requisite -% groups, the respective macros will be defined to be empty. -% There is an asymmetry in that \@IEEEextractedgroup is stripped of its first -% outer grouping while \@IEEEextractedgroupremain retains even the outer -% grouping (if present) that originally identified it as a group. -% -% For example: -% \@IEEEextractgroup{{{ab}}{c{de}}} -% results in: -% -% \@IEEEextractgrouparg ==> a macro containing {{ab}}{c{de}} -% \@IEEEextractedgroup ==> a macro containing {ab} -% \@IEEEextractedgroupremain ==> a macro containing {c{de}} -% -% The *-star form, \@IEEEextractgroup*, does not expand its argument -% contents during processing. -\def\@IEEEextractgroup{\@ifstar{\let\@IEEEextractgroupdef=\def\@@IEEEextractgroup}{\let\@IEEEextractgroupdef=\edef\@@IEEEextractgroup}} - -\def\@@IEEEextractgroup#1{\@IEEEextractgroupdef\@IEEEextractgrouparg{#1}\relax -% trap the case of an empty extracted group as this would cause problems with -% \@IEEEextractgroupremain's argument acquisition -\ifx\@IEEEextractgrouparg\@empty - \def\@IEEEextractedgroup{}\relax - \def\@IEEEextractedgroupremain{}\relax -\else - % We have to use some dirty tricks here. We want to insert {} around - % whatever remains after the first group so that TeX's argument scanner - % will preserve any originally enclosing braces as well as provide an - % empty argument to acquire even if there isn't a second group. - % In this first of two dirty tricks, we put a } at the end of the structure - % we are going to extract from. The \ifnum0=`{\fi keeps TeX happy to allow - % what would otherwise be an unbalanced macro definition for - % \@@IEEEextractgroup to be acceptable to it. - \ifnum0=`{\fi\expandafter\@IEEEextractgroupremain\@IEEEextractgrouparg}\relax -\fi} - -% In the second part of the dirty tricks, we insert a leading { right after -% the first group is acquired, but before the remainder is. Again, the -% \ifnum0=`}\fi keeps TeX happy during definition time, but will disappear -% during run time. -\def\@IEEEextractgroupremain#1{\def\@IEEEextractedgroup{#1}\expandafter\@@IEEEextractgroupremain\expandafter{\ifnum0=`}\fi} - -\def\@@IEEEextractgroupremain#1{\def\@IEEEextractedgroupremain{#1}} - - - -% usage: \@IEEEextracttoken*{} -% \@IEEEextracttoken fully expands its argument (which it then stores in -% \@IEEEextracttokenarg) via \edef and then the meaning of the first -% nonbrace (but including the empty group) token found is assigned via \let -% to \@IEEEextractedtoken as well as stored in the macro -% \@IEEEextractedtokenmacro. Tokens that would otherwise be discarded during -% the acquisition of the first are stored in \@IEEEextractedtokensdiscarded, -% however their original relative brace nesting depths are not guaranteed to -% be preserved. -% If the argument is empty, or if a first nonbrace token does not exist (or -% is an empty group), \@IEEEextractedtoken will be \relax and -% \@IEEEextractedtokenmacro and \@IEEEextractedtokensdiscarded will be empty. -% -% For example: -% \@IEEEextracttoken{{{ab}{cd}}{{ef}g}} -% results in: -% -% \@IEEEextracttokenarg ==> a macro containing {{ab}{cd}}{{ef}g} -% \@IEEEextractedtoken ==> the letter a -% \@IEEEextractedtokenmacro ==> a macro containing a -% \@IEEEextractedtokensdiscarded ==> a macro containing bcd{ef}g -% -% the *-star form, \@IEEEextracttoken*, does not expand its argument -% contents during processing. -\def\@IEEEextracttoken{\@ifstar{\let\@IEEEextracttokendef=\def\@@IEEEextracttoken}{\let\@IEEEextracttokendef=\edef\@@IEEEextracttoken}} - -\def\@@IEEEextracttoken#1{\@IEEEextracttokendef\@IEEEextracttokenarg{#1}\relax -\def\@IEEEextractedtokensdiscarded{}\relax % initialize to empty -% if the macro is unchanged after being acquired as a single undelimited argument -% with anything after it being stripped off as a delimited argument -% we know we have one token without any enclosing braces. loop until this is true. -\let\@IEEEextracttokencurgroup\@IEEEextracttokenarg -\loop - % trap case of an empty argument as this would cause a problem with - % \@@@IEEEextracttoken's first (nondelimited) argument acquisition - \ifx\@IEEEextracttokencurgroup\@empty - \def\@IEEEextractedtokenmacro{}\relax - \else - \expandafter\@@@IEEEextracttoken\@IEEEextracttokencurgroup\@IEEEgeneralsequenceDELIMITER\relax - \fi - \ifx\@IEEEextractedtokenmacro\@IEEEextracttokencurgroup - \else - \let\@IEEEextracttokencurgroup=\@IEEEextractedtokenmacro -\repeat -% we can safely do a \let= here because there should be at most one token -% the relax is needed to handle the case of no token found -\expandafter\let\expandafter\@IEEEextractedtoken\@IEEEextractedtokenmacro\relax} - -\def\@@@IEEEextracttoken#1#2\@IEEEgeneralsequenceDELIMITER{\def\@IEEEextractedtokenmacro{#1}\relax -\def\@@IEEEextractedtokensdiscarded{#2}\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter -\@IEEEextractedtokensdiscarded\expandafter\expandafter\expandafter -{\expandafter\@@IEEEextractedtokensdiscarded\@IEEEextractedtokensdiscarded}} - - - -% usage: \@IEEEextracttokengroups*{} -% \@IEEEextracttokengroups fully expands its argument (which it then stores -% in \@IEEEextracttokengroupsarg) and then assigns the first "brace group" of -% tokens (with the outermost braces removed) to the macro -% \@IEEEextractedfirstgroup. -% The meaning of the first nonbrace (but including the empty group) token -% within this first group is assigned via \let to \@IEEEextractedfirsttoken -% as well as stored in the macro \@IEEEextractedfirsttokenmacro. If a first -% nonbrace token does not exist (or is an empty group), these will be \relax -% and empty, respectively. Tokens that would otherwise be discarded during -% the acquisition of the first token in the first group are stored in -% \@IEEEextractedfirsttokensdiscarded, however their original relative brace -% nesting depths are not guaranteed to be preserved. -% The first group within this first group is stored in the macro -% \@IEEEextractedfirstfirstgroup. -% Likewise for the next group after the first: \@IEEEextractednextgroup, -% \@IEEEextractednextfirstgroup, \@IEEEextractednextgroupfirsttoken, -% \@IEEEextractednextgroupfirsttokenmacro, and -% \@IEEEextractednextfirsttokensdiscarded. -% All tokens/groups after the first group, including any enclosing braces, -% are stored in the macro \@IEEEextractedafterfirstgroupremain which will -% be empty if none exist. -% -% For example: -% \@IEEEextracttokengroups{{{ab}{cd}}{{ef}g}} -% will result in: -% -% \@IEEEextracttokengroupsarg ==> a macro containing {{ab}{cd}}{{ef}g} -% \@IEEEextractedfirstgroup ==> a macro containing {ab}{cd} -% \@IEEEextractedafterfirstgroupremain ==> a macro containing {{ef}g} -% \@IEEEextractedfirsttoken ==> the letter a -% \@IEEEextractedfirsttokenmacro ==> a macro containing a -% \@IEEEextractedfirsttokensdiscarded ==> a macro containing bcd -% \@IEEEextractedfirstfirstgroup ==> a macro containing ab -% \@IEEEextractednextgroup ==> a macro containing {ef}g -% \@IEEEextractednextfirsttoken ==> the letter e -% \@IEEEextractednextfirsttokenmacro ==> a macro containing e -% \@IEEEextractednextfirsttokensdiscarded ==> a macro containing fg -% \@IEEEextractednextfirstgroup ==> a macro containing ef -% -% If given an empty argument, \@IEEEextractedfirsttoken and -% \@IEEEextractednextfirsttoken will be set to \relax -% and all the macros will be empty. -% the *-star form, \@IEEEextracttokengroups*, does not expand its argument -% contents during processing. -% -% Depends on: \@IEEEextractgroup, \@IEEEextracttoken -\def\@IEEEextracttokengroups{\@ifstar{\let\@IEEEextracttokengroupsdef=\def\@@IEEEextracttokengroups}{\let\@IEEEextracttokengroupsdef=\edef\@@IEEEextracttokengroups}} -\def\@@IEEEextracttokengroups#1{\@IEEEextracttokengroupsdef\@IEEEextracttokengroupsarg{#1}\relax -% begin extraction, these functions are safe with empty arguments -% first group -\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextracttokengroupsarg}\relax -\let\@IEEEextractedfirstgroup\@IEEEextractedgroup -\let\@IEEEextractedafterfirstgroupremain\@IEEEextractedgroupremain -\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax -\let\@IEEEextractedfirsttoken\@IEEEextractedtoken -\let\@IEEEextractedfirsttokenmacro\@IEEEextractedtokenmacro -\let\@IEEEextractedfirsttokensdiscarded\@IEEEextractedtokensdiscarded -% first first group -\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax -\let\@IEEEextractedfirstfirstgroup\@IEEEextractedgroup -% next group -\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedafterfirstgroupremain}\relax -\let\@IEEEextractednextgroup\@IEEEextractedgroup -\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractednextgroup}\relax -\let\@IEEEextractednextfirsttoken\@IEEEextractedtoken -\let\@IEEEextractednextfirsttokenmacro\@IEEEextractedtokenmacro -\let\@IEEEextractednextfirsttokensdiscarded\@IEEEextractedtokensdiscarded -% next first group -\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractednextgroup}\relax -\let\@IEEEextractednextfirstgroup\@IEEEextractedgroup} - - -%% -%% -- End of Command Argument Scanning Support Functions -- - - - - -% -- page setup commands -- - -% The default sample text for calculating margins -\def\IEEEdefaultsampletext{\normalfont\normalsize gT} -\def\IEEEdefaultheadersampletext{\normalfont\normalsize T} -\def\IEEEdefaultfootersampletext{\normalfont\normalsize gT} - - - -% usage: \IEEEsettextwidth{inner margin}{outer margin} -% Sets \textwidth to allow the specified inner and outer margins -% for the current \paperwidth. -\def\IEEEsettextwidth#1#2{\@IEEEtrantmpdimenA\paperwidth -\@IEEEtrantmpdimenB#1\relax -\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB -\@IEEEtrantmpdimenB#2\relax -\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB -\textwidth\@IEEEtrantmpdimenA} - - - -% usage: \IEEEsetsidemargin{mode: i, o, c, a}{margin/offset} -% Sets \oddsidemargin and \evensidemargin to yield the specified margin -% of the given mode. -% The available modes are: -% i = inner margin -% o = outer margin -% c = centered, with the given offset -% a = adjust the margins using the given offset -% For the offsets, positive values increase the inner margin. -% \textwidth should be set properly for the given margins before calling this -% function. -\def\IEEEsetsidemargin#1#2{\@IEEEtrantmpdimenA #2\relax -\@IEEEextracttoken{#1}\relax -% check for mode errors -\ifx\@IEEEextractedtokenmacro\@empty - \@IEEEclspkgerror{Empty mode type in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `i'}{Valid modes for \string\IEEEsetsidemargin\space are: i, o, c and a.}\relax - \let\@IEEEextractedtoken=i\relax - \def\@IEEEextractedtokenmacro{i}\relax -\else - \ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: \string\IEEEsetsidemargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax - \fi -\fi -% handle each mode -\if\@IEEEextractedtoken a\relax - \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax -\else -\if\@IEEEextractedtoken c\relax - \oddsidemargin\paperwidth - \advance\oddsidemargin by -\textwidth - \divide\oddsidemargin by 2\relax - \advance\oddsidemargin by -1in\relax - \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax -\else -\if\@IEEEextractedtoken o\relax - \oddsidemargin\paperwidth - \advance\oddsidemargin by -\textwidth - \advance\oddsidemargin by -\@IEEEtrantmpdimenA - \advance\oddsidemargin by -1in\relax -\else - \if\@IEEEextractedtoken i\relax - \else - \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `i'}% - {Valid modes for \string\IEEEsetsidemargin\space are: i, o, c and a.}% - \fi - \oddsidemargin\@IEEEtrantmpdimenA - \advance\oddsidemargin by -1in\relax -\fi\fi\fi -% odd and even side margins both mean "inner" for single sided pages -\evensidemargin\oddsidemargin -% but are mirrors of each other when twosided is in effect -\if@twoside - \evensidemargin\paperwidth - \advance\evensidemargin by -\textwidth - \advance\evensidemargin by -\oddsidemargin - % have to compensate for both the builtin 1in LaTex offset - % and the fact we already subtracted this offset from \oddsidemargin - \advance\evensidemargin -2in\relax -\fi} - - - -% usage: \IEEEsettextheight[sample text]{top text margin}{bottom text margin} -% Sets \textheight based on the specified top margin and bottom margin. -% Takes into consideration \paperheight, \topskip, and (by default) the -% the actual height and depth of the \IEEEdefaultsampletext text. -\def\IEEEsettextheight{\@ifnextchar [{\@IEEEsettextheight}{\@IEEEsettextheight[\IEEEdefaultsampletext]}} -\def\@IEEEsettextheight[#1]#2#3{\textheight\paperheight\relax - \@IEEEtrantmpdimenA #2\relax - \advance \textheight by -\@IEEEtrantmpdimenA% subtract top margin - \@IEEEtrantmpdimenA #3\relax - \advance \textheight by -\@IEEEtrantmpdimenA% subtract bottom margin - \advance \textheight by \topskip% add \topskip - % subtract off everything above the top, and below the bottom, baselines - \settoheight{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance \textheight by -\@IEEEtrantmpdimenA - \settodepth{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance \textheight by -\@IEEEtrantmpdimenA} - - - -\newdimen\IEEEquantizedlength -\IEEEquantizedlength 0sp\relax -\newdimen\IEEEquantizedlengthdiff -\IEEEquantizedlengthdiff 0sp\relax -\def\IEEEquantizedlengthint{0} - -% usage: \IEEEquantizelength{mode: d, c, i}{base unit}{length} -% Sets the length \IEEEquantizedlength to be an integer multiple of the given -% (nonzero) base unit such that \IEEEquantizedlength approximates the given -% length. -% \IEEEquantizedlengthdiff is a length equal to the difference between the -% \IEEEquantizedlength and the given length. -% \IEEEquantizedlengthint is a macro containing the integer number of base units -% in \IEEEquantizedlength. -% i.e., \IEEEquantizedlength = \IEEEquantizedlengthint * base unit -% The mode determines how \IEEEquantizedlength is quantized: -% d = always decrease (always round down \IEEEquantizeint) -% c = use the closest match -% i = always increase (always round up \IEEEquantizeint) -% In anycase, if the given length is already quantized, -% \IEEEquantizedlengthdiff will be set to zero. -\def\IEEEquantizelength#1#2#3{\begingroup -% work in isolation so as not to externally disturb the \@IEEEtrantmp -% variables -% load the argument values indirectly via \IEEEquantizedlengthdiff -% in case the user refers to our \@IEEEtrantmpdimenX, \IEEEquantizedlength, -% etc. in the arguments. we also will work with these as counters, -% i.e., in sp units -% A has the base unit -\IEEEquantizedlengthdiff #2\relax\relax\relax\relax -\@IEEEtrantmpcountA\IEEEquantizedlengthdiff -% B has the input length -\IEEEquantizedlengthdiff #3\relax\relax\relax\relax -\@IEEEtrantmpcountB\IEEEquantizedlengthdiff -\@IEEEtrantmpdimenA\the\@IEEEtrantmpcountA sp\relax -\@IEEEtrantmpdimenB\the\@IEEEtrantmpcountB sp\relax -% \@IEEEtrantmpcountC will have the quantized int -% \IEEEquantizedlength will have the quantized length -% \@IEEEtrantmpdimenC will have the quantized diff -% initialize them to zero as this is what will be -% exported if an error occurs -\@IEEEtrantmpcountC 0\relax -\IEEEquantizedlength 0sp\relax -\@IEEEtrantmpdimenC 0sp\relax -% extract mode -\@IEEEextracttoken{#1}\relax -% check for mode errors -\ifx\@IEEEextractedtokenmacro\@empty - \@IEEEclspkgerror{Empty mode type in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak - Defaulting to `d'}{Valid modes for \string\IEEEquantizelength\space are: d, c and i.}\relax - \let\@IEEEextractedtoken=d\relax - \def\@IEEEextractedtokenmacro{d}\relax -\else - \ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: \string\IEEEquantizelength\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax - \fi -\fi -% check for base unit is zero error -\ifnum\@IEEEtrantmpcountA=0\relax -\@IEEEclspkgerror{Base unit is zero in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak - \string\IEEEquantizedlength\space and \string\IEEEquantizedlengthdiff\space are set to zero}{Division by zero is not allowed.}\relax -\else% base unit is nonzero - % \@IEEEtrantmpcountC carries the number of integer units - % in the quantized length (integer length \ base) - \@IEEEtrantmpcountC\@IEEEtrantmpcountB\relax - \divide\@IEEEtrantmpcountC by \@IEEEtrantmpcountA\relax - % \IEEEquantizedlength has the (rounded down) quantized length - % = base * int - \IEEEquantizedlength\@IEEEtrantmpdimenA\relax - \multiply\IEEEquantizedlength by \@IEEEtrantmpcountC\relax - % \@IEEEtrantmpdimenC has the difference - % = quantized length - length - \@IEEEtrantmpdimenC\IEEEquantizedlength\relax - \advance\@IEEEtrantmpdimenC by -\@IEEEtrantmpdimenB\relax - % trap special case of length being already quantized - % to avoid a roundup under i option - \ifdim\@IEEEtrantmpdimenC=0sp\relax - \else % length not is already quantized - % set dimenA to carry the upper quantized (absolute value) difference: - % quantizedlength + base - length - \advance\@IEEEtrantmpdimenA by \IEEEquantizedlength\relax - \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB\relax - % set dimenB to carry the lower quantized (absolute value) difference: - % length - quantizedlength - \advance\@IEEEtrantmpdimenB by -\IEEEquantizedlength\relax - % handle each mode - \if\@IEEEextractedtoken c\relax - % compare upper and lower amounts, select upper if lower > upper - \ifdim\@IEEEtrantmpdimenB>\@IEEEtrantmpdimenA\relax - % use upper - \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax - \advance\@IEEEtrantmpcountC by 1\relax - \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA - \else% <=. uselower - % no need to do anything for lower, use output values already setup - \fi - \else% not mode c - \if\@IEEEextractedtoken i\relax - % always round up under i mode - \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax - \advance\@IEEEtrantmpcountC by 1\relax - \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA - \else - \if\@IEEEextractedtoken d\relax - \else - \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak - Defaulting to `d'}% - {Valid modes for \string\IEEEquantizelength\space are: d, c, and i.}\relax - \fi % if d - % no need to do anything for d, use output values already setup - \fi\fi % if i, c - \fi % if length is already quantized -\fi% if base unit is zero -% globally assign the results to macros we use here to escape the enclosing -% group without needing to call \global on any of the \@IEEEtrantmp variables. -% \@IEEEtrantmpcountC has the quantized int -% \IEEEquantizedlength has the quantized length -% \@IEEEtrantmpdimenC has the quantized diff -\xdef\@IEEEquantizedlengthintmacro{\the\@IEEEtrantmpcountC}\relax -\@IEEEtrantmpcountC\IEEEquantizedlength\relax -\xdef\@IEEEquantizedlengthmacro{\the\@IEEEtrantmpcountC}\relax -\@IEEEtrantmpcountC\@IEEEtrantmpdimenC\relax -\xdef\@IEEEquantizedlengthdiffmacro{\the\@IEEEtrantmpcountC}\relax -\endgroup -% locally assign the outputs here from the macros -\expandafter\IEEEquantizedlength\@IEEEquantizedlengthmacro sp\relax -\expandafter\IEEEquantizedlengthdiff\@IEEEquantizedlengthdiffmacro sp\relax -\edef\IEEEquantizedlengthint{\@IEEEquantizedlengthintmacro}\relax} - - - -\newdimen\IEEEquantizedtextheightdiff -\IEEEquantizedtextheightdiff 0sp\relax - -% usage: \IEEEquantizetextheight[base unit]{mode: d, c, i} -% Sets \textheight to be an integer multiple of the current \baselineskip -% (or the optionally specified base unit) plus the first (\topskip) line. -% \IEEEquantizedtextheightdiff is a length equal to the difference between -% the new quantized and original \textheight. -% \IEEEquantizedtextheightlpc is a macro containing the integer number of -% lines per column under the quantized \textheight. i.e., -% \textheight = \IEEEquantizedtextheightlpc * \baselineskip + \topskip -% The mode determines how \textheight is quantized: -% d = always decrease (always round down the number of lines per column) -% c = use the closest match -% i = always increase (always round up the number of lines per column) -% In anycase, if \textheight is already quantized, it will remain unchanged, -% and \IEEEquantizedtextheightdiff will be set to zero. -% Depends on: \IEEEquantizelength -\def\IEEEquantizetextheight{\@ifnextchar [{\@IEEEquantizetextheight}{\@IEEEquantizetextheight[\baselineskip]}} -\def\@IEEEquantizetextheight[#1]#2{\begingroup -% use our \IEEEquantizedtextheightdiff as a scratch pad -% we need to subtract off \topskip before quantization -\IEEEquantizedtextheightdiff\textheight -\advance\IEEEquantizedtextheightdiff by -\topskip\relax -\IEEEquantizelength{#2}{#1}{\IEEEquantizedtextheightdiff} -% add back \topskip line -\advance\IEEEquantizedlength by \topskip -\@IEEEtrantmpcountC\IEEEquantizedlengthint\relax -\advance\@IEEEtrantmpcountC by 1\relax -% globally assign the results to macros we use here to escape the enclosing -% group without needing to call \global on any of the \@IEEEtrantmp variables. -\xdef\@IEEEquantizedtextheightlpcmacro{\the\@IEEEtrantmpcountC}\relax -\@IEEEtrantmpcountC\IEEEquantizedlength\relax -\xdef\@IEEEquantizedtextheightmacro{\the\@IEEEtrantmpcountC}\relax -\@IEEEtrantmpcountC\IEEEquantizedlengthdiff\relax -\xdef\@IEEEquantizedtextheightdiffmacro{\the\@IEEEtrantmpcountC}\relax -\endgroup -% locally assign the outputs here from the macros -\textheight\@IEEEquantizedtextheightmacro sp\relax -\IEEEquantizedtextheightdiff\@IEEEquantizedtextheightdiffmacro sp\relax -\edef\IEEEquantizedtextheightlpc{\@IEEEquantizedtextheightlpcmacro}} - - - -% usage: \IEEEsettopmargin[sample text]{mode: t, b, c, a, q}{margin/offset} -% Sets \topmargin based on the specified vertical margin. -% Takes into consideration the base 1in offset, \headheight, \headsep, -% \topskip, and (by default) the the actual height (or, for the bottom, depth) -% of the \IEEEdefaultsampletext text. -% The available modes are: -% t = top margin -% b = bottom margin -% c = vertically centered, with the given offset -% a = adjust the vertical margins using the given offset -% q = adjust the margins using \IEEEquantizedtextheightdiff and the given offset -% For the offsets, positive values increase the top margin. -% \headheight, \headsep, \topskip and \textheight should be set properly for the -% given margins before calling this function. -\def\IEEEsettopmargin{\@ifnextchar [{\@IEEEsettopmargin}{\@IEEEsettopmargin[\IEEEdefaultsampletext]}} -\def\@IEEEsettopmargin[#1]#2#3{\@IEEEtrantmpdimenA #3\relax -\@IEEEextracttoken{#2}\relax -% check for mode errors -\ifx\@IEEEextractedtokenmacro\@empty - \@IEEEclspkgerror{Empty mode type in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `t'}{Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax - \let\@IEEEextractedtoken=t\relax - \def\@IEEEextractedtokenmacro{t}\relax -\else - \ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: \string\IEEEsettopmargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax - \fi -\fi -% handle each mode -\if\@IEEEextractedtoken a\relax - \advance\topmargin by \@IEEEtrantmpdimenA\relax -\else -\if\@IEEEextractedtoken q\relax - % we need to adjust by half the \IEEEquantizedtextheightdiff value - \@IEEEtrantmpdimenB\IEEEquantizedtextheightdiff\relax - \divide\@IEEEtrantmpdimenB by 2\relax - % a positive \IEEEquantizedtextheightdiff means we need to reduce \topmargin - % because \textheight has been lenghtened - \advance\topmargin by -\@IEEEtrantmpdimenB\relax - \advance\topmargin by \@IEEEtrantmpdimenA\relax -\else -\if\@IEEEextractedtoken c\relax - \topmargin\paperheight - \advance\topmargin by -\textheight - % \textheight includes \topskip, but we should not count topskip whitespace here, backout - \advance \topmargin by \topskip - \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\topmargin by -\@IEEEtrantmpdimenB\relax - \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\topmargin by -\@IEEEtrantmpdimenB\relax - \divide\topmargin by 2\relax - \advance\topmargin by \@IEEEtrantmpdimenA\relax -\else -\if\@IEEEextractedtoken b\relax - \topmargin\paperheight - \advance\topmargin by -\textheight - % \textheight includes \topskip, but we should not count topskip whitespace here, backout - \advance \topmargin by \topskip - \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\topmargin by -\@IEEEtrantmpdimenB\relax - \advance\topmargin by -\@IEEEtrantmpdimenA\relax -\else - \if\@IEEEextractedtoken t\relax - \else - \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `t'}% - {Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax - \fi - \topmargin\@IEEEtrantmpdimenA\relax - \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\topmargin by \@IEEEtrantmpdimenB\relax -\fi\fi % if t, b, c -% convert desired top margin into actual \topmargin -% this is not done for the q or a modes because they are only adjustments -\advance \topmargin by -\topskip -\advance \topmargin by -1in -\advance \topmargin by -\headheight -\advance \topmargin by -\headsep -\fi\fi % if q, a -} - - - -% usage: \IEEEsetheadermargin[header sample][text sample]{mode: t, b, c, a}{margin/offset} -% Differentially adjusts \topmargin and \headsep (such that their sum is unchanged) -% based on the specified header margin. -% Takes into consideration the base 1in offset, \headheight, \topskip, and (by default) -% the actual height (or depth) of the \IEEEdefaultheadersampletext and -% \IEEEdefaultsampletext text. -% The available modes are: -% t = top margin (top of the header text to the top of the page) -% b = bottom margin (bottom of the header text to the top of the main text) -% c = vertically centered between the main text and the top of the page, -% with the given offset -% a = adjust the vertical position using the given offset -% For the offsets, positive values move the header downward. -% \headheight, \headsep, \topskip and \topmargin should be set properly before -% calling this function. -\def\IEEEsetheadermargin{\@ifnextchar [{\@IEEEsetheadermargin}{\@IEEEsetheadermargin[\IEEEdefaultheadersampletext]}} -\def\@IEEEsetheadermargin[#1]{\@ifnextchar [{\@@IEEEsetheadermargin[#1]}{\@@IEEEsetheadermargin[#1][\IEEEdefaultsampletext]}} -\def\@@IEEEsetheadermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax -\@IEEEextracttoken{#3}\relax -% check for mode errors -\ifx\@IEEEextractedtokenmacro\@empty - \@IEEEclspkgerror{Empty mode type in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `t'}{Valid modes for \string\IEEEsetheadermargin\space are: t, b, c, and a.}\relax - \let\@IEEEextractedtoken=t\relax - \def\@IEEEextractedtokenmacro{t}\relax -\else - \ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: \string\IEEEsetheadermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax - \fi -\fi -% handle each mode -\if\@IEEEextractedtoken a\relax - % No need to do anything here and can pass through the adjustment - % value as is. The end adjustment of \topmargin and \headsep will - % do all that is needed -\else -\if\@IEEEextractedtoken c\relax - % get the bottom margin - \@IEEEtrantmpdimenB\headsep\relax - \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - \advance\@IEEEtrantmpdimenB by \topskip - \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the actual header bottom margin - % subtract from it the top header margin - \advance\@IEEEtrantmpdimenB -1in\relax % take into consideration the system 1in offset of the top margin - \advance\@IEEEtrantmpdimenB by -\topmargin - \advance\@IEEEtrantmpdimenB by -\headheight - \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the difference between the bottom and top margins - % we need to adjust by half this amount to center the header - \divide\@IEEEtrantmpdimenB by 2\relax - % and add to offset - \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB -\else -\if\@IEEEextractedtoken b\relax - \@IEEEtrantmpdimenB\headsep\relax - \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - \advance\@IEEEtrantmpdimenB by \topskip - \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the actual header bottom margin - % get the difference between the actual and the desired - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA - \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB -\else - \if\@IEEEextractedtoken t\relax - \else - \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `t'}% - {Valid modes for \string\IEEEsetheadermargin\space are: t, b, c and a.}\relax - \fi - \@IEEEtrantmpdimenB 1in\relax % take into consideration the system 1in offset of the top margin - \advance\@IEEEtrantmpdimenB by \topmargin - \advance\@IEEEtrantmpdimenB by \headheight - \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the actual header top margin - % get the difference between the desired and the actual - \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB -\fi\fi % if t, b, c -\fi % if a -% advance \topmargin by the needed amount and reduce \headsep by the same -% so as not to disturb the location of the main text -\advance\topmargin by \@IEEEtrantmpdimenA\relax -\advance\headsep by -\@IEEEtrantmpdimenA\relax -} - - - -% usage: \IEEEsetfootermargin[footer sample][text sample]{mode: t, b, c, a}{margin/offset} -% Adjusts \footskip based on the specified footer margin. -% Takes into consideration the base 1in offset, \paperheight, \headheight, -% \headsep, \textheight and (by default) the actual height (or depth) of the -% \IEEEdefaultfootersampletext and \IEEEdefaultsampletext text. -% The available modes are: -% t = top margin (top of the footer text to the bottom of the main text) -% b = bottom margin (bottom of the footer text to the bottom of page) -% c = vertically centered between the main text and the bottom of the page, -% with the given offset -% a = adjust the vertical position using the given offset -% For the offsets, positive values move the footer downward. -% \headheight, \headsep, \topskip, \topmargin, and \textheight should be set -% properly before calling this function. -\def\IEEEsetfootermargin{\@ifnextchar [{\@IEEEsetfootermargin}{\@IEEEsetfootermargin[\IEEEdefaultfootersampletext]}} -\def\@IEEEsetfootermargin[#1]{\@ifnextchar [{\@@IEEEsetfootermargin[#1]}{\@@IEEEsetfootermargin[#1][\IEEEdefaultsampletext]}} -\def\@@IEEEsetfootermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax -\@IEEEextracttoken{#3}\relax -% check for mode errors -\ifx\@IEEEextractedtokenmacro\@empty - \@IEEEclspkgerror{Empty mode type in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `t'}{Valid modes for \string\IEEEsetfootermargin\space are: t, b, c, and a.}\relax - \let\@IEEEextractedtoken=t\relax - \def\@IEEEextractedtokenmacro{t}\relax -\else - \ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: \string\IEEEsetfootermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax - \fi -\fi -% handle each mode -\if\@IEEEextractedtoken a\relax - % No need to do anything here and can pass through the adjustment - % value as is. The end adjustment of \footskip will do all that - % is needed -\else -\if\@IEEEextractedtoken c\relax - % calculate the bottom margin - \@IEEEtrantmpdimenB 1in\relax % system 1in offset - \advance\@IEEEtrantmpdimenB\topmargin\relax - \advance\@IEEEtrantmpdimenB\headheight\relax - \advance\@IEEEtrantmpdimenB\headsep\relax - \advance\@IEEEtrantmpdimenB\textheight\relax - \advance\@IEEEtrantmpdimenB\footskip\relax - \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB - \@IEEEtrantmpdimenB\paperheight - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin - % now subtract off the footer top margin - \advance\@IEEEtrantmpdimenB -\footskip\relax - \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC - \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the difference between the bottom - % and top footer margins - % our adjustment must be half this value to center the footer - \divide\@IEEEtrantmpdimenB by 2\relax - % add to the offset - \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB -\else -\if\@IEEEextractedtoken b\relax - % calculate the bottom margin - \@IEEEtrantmpdimenB 1in\relax % system 1in offset - \advance\@IEEEtrantmpdimenB\topmargin\relax - \advance\@IEEEtrantmpdimenB\headheight\relax - \advance\@IEEEtrantmpdimenB\headsep\relax - \advance\@IEEEtrantmpdimenB\textheight\relax - \advance\@IEEEtrantmpdimenB\footskip\relax - \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB - \@IEEEtrantmpdimenB\paperheight - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin - % get the difference between the actual and the desired - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA - \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB -\else - \if\@IEEEextractedtoken t\relax - \else - \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak - Defaulting to `t'}% - {Valid modes for \string\IEEEsetfootermargin\space are: t, b, c and a.}\relax - \fi - \@IEEEtrantmpdimenB\footskip\relax - \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax - \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC - % at this point \@IEEEtrantmpdimenB has the actual footer top margin - % get the difference between the desired and the actual - \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB -\fi\fi % if t, b, c -\fi % if a -% advance \footskip by the needed amount -\advance\footskip by \@IEEEtrantmpdimenA\relax -} - - -% -- End page setup commands -- - - - - -% Itemize, Enumerate and Description (IED) List Controls -% *************************** -% -% -% The IEEE seems to use at least two different values by -% which ITEMIZED list labels are indented to the right -% For The Journal of Lightwave Technology (JLT) and The Journal -% on Selected Areas in Communications (JSAC), they tend to use -% an indention equal to \parindent. For Transactions on Communications -% they tend to indent ITEMIZED lists a little more--- 1.3\parindent. -% We'll provide both values here for you so that you can choose -% which one you like in your document using a command such as: -% setlength{\IEEEilabelindent}{\IEEEilabelindentB} -\newdimen\IEEEilabelindentA -\IEEEilabelindentA \parindent - -\newdimen\IEEEilabelindentB -\IEEEilabelindentB 1.3\parindent -% However, we'll default to using \parindent -% which makes more sense to me -\newdimen\IEEEilabelindent -\IEEEilabelindent \IEEEilabelindentA - - -% This controls the default amount the enumerated list labels -% are indented to the right. -% Normally, this is the same as the paragraph indention -\newdimen\IEEEelabelindent -\IEEEelabelindent \parindent - -% This controls the default amount the description list labels -% are indented to the right. -% Normally, this is the same as the paragraph indention -\newdimen\IEEEdlabelindent -\IEEEdlabelindent \parindent - -% This is the value actually used within the IED lists. -% The IED environments automatically set its value to -% one of the three values above, so global changes do -% not have any effect -\newdimen\IEEElabelindent -\IEEElabelindent \parindent - -% The actual amount labels will be indented is -% \IEEElabelindent multiplied by the factor below -% corresponding to the level of nesting depth -% This provides a means by which the user can -% alter the effective \IEEElabelindent for deeper -% levels -% There may not be such a thing as correct "standard IEEE" -% values. What the IEEE actually does may depend on the specific -% circumstances. -% The first list level almost always has full indention. -% The second levels I've seen have only 75% of the normal indentation -% Three level or greater nestings are very rare. I am guessing -% that they don't use any indentation. -\def\IEEElabelindentfactori{1.0} % almost always one -\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases -\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0? -\def\IEEElabelindentfactoriv{0.0} -\def\IEEElabelindentfactorv{0.0} -\def\IEEElabelindentfactorvi{0.0} - -% value actually used within IED lists, it is auto -% set to one of the 6 values above -% global changes here have no effect -\def\IEEElabelindentfactor{1.0} - -% This controls the default spacing between the end of the IED -% list labels and the list text, when normal text is used for -% the labels. -\newdimen\IEEEiednormlabelsep -\IEEEiednormlabelsep 0.6em - -% This controls the default spacing between the end of the IED -% list labels and the list text, when math symbols are used for -% the labels (nomenclature lists). The IEEE usually increases the -% spacing in these cases -\newdimen\IEEEiedmathlabelsep -\IEEEiedmathlabelsep 1.2em - -% This controls the extra vertical separation put above and -% below each IED list. The IEEE usually puts a little extra spacing -% around each list. However, this spacing is barely noticeable. -\newskip\IEEEiedtopsep -\IEEEiedtopsep 2pt plus 1pt minus 1pt - - -% This command is executed within each IED list environment -% at the beginning of the list. You can use this to set the -% parameters for some/all your IED list(s) without disturbing -% global parameters that affect things other than lists. -% i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}} -% will alter the \labelsep for the next list(s) until -% \IEEEiedlistdecl is redefined. -\def\IEEEiedlistdecl{\relax} - -% This command provides an easy way to set \leftmargin based -% on the \labelwidth, \labelsep and the argument \IEEElabelindent -% Usage: \IEEEcalcleftmargin{width-to-indent-the-label} -% output is in the \leftmargin variable, i.e., effectively: -% \leftmargin = argument + \labelwidth + \labelsep -% Note controlled spacing here, shield end of lines with % -\def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}% -\addtolength{\leftmargin}{\labelwidth}% -\addtolength{\leftmargin}{\labelsep}} - -% This command provides an easy way to set \labelwidth to the -% width of the given text. It is the same as -% \settowidth{\labelwidth}{label-text} -% and useful as a shorter alternative. -% Typically used to set \labelwidth to be the width -% of the longest label in the list -\def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}} - -% When this command is executed, IED lists will use the -% IEEEiedmathlabelsep label separation rather than the normal -% spacing. To have an effect, this command must be executed via -% the \IEEEiedlistdecl or within the option of the IED list -% environments. -\def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}} - -% A flag which controls whether the IED lists automatically -% calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep -% Useful if you want to specify your own \leftmargin -% This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse) -% via the \IEEEiedlistdecl or within the option of the IED list -% environments to have an effect. -\newif\ifIEEEnocalcleftmargin -\IEEEnocalcleftmarginfalse - -% A flag which controls whether \IEEElabelindent is multiplied by -% the \IEEElabelindentfactor for each list level. -% This flag must be set via the \IEEEiedlistdecl or within the option -% of the IED list environments to have an effect. -\newif\ifIEEEnolabelindentfactor -\IEEEnolabelindentfactorfalse - - -% internal variable to indicate type of IED label -% justification -% 0 - left; 1 - center; 2 - right -\def\@IEEEiedjustify{0} - - - -% commands to allow the user to control IED -% label justifications. Use these commands within -% the IED environment option or in the \IEEEiedlistdecl -% Note that changing the normal list justifications -% is nonstandard and the IEEE may not like it if you do so! -% I include these commands as they may be helpful to -% those who are using these enhanced list controls for -% other non-IEEE related LaTeX work. -% itemize and enumerate automatically default to right -% justification, description defaults to left. -\def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left -\def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center -\def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right - - - - -% commands to save to and restore from the list parameter copies -% this allows us to set all the list parameters within -% the list_decl and prevent \list (and its \@list) -% from overriding any of our parameters -% V1.6 use \edefs instead of dimen's to conserve dimen registers -% Note controlled spacing here, shield end of lines with % -\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}% -\edef\@IEEEiedlabelwidth{\the\labelwidth}% -\edef\@IEEEiedlabelsep{\the\labelsep}% -\edef\@IEEEiedleftmargin{\the\leftmargin}% -\edef\@IEEEiedpartopsep{\the\partopsep}% -\edef\@IEEEiedparsep{\the\parsep}% -\edef\@IEEEieditemsep{\the\itemsep}% -\edef\@IEEEiedrightmargin{\the\rightmargin}% -\edef\@IEEEiedlistparindent{\the\listparindent}% -\edef\@IEEEieditemindent{\the\itemindent}} - -% Note controlled spacing here -\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax% -\labelwidth\@IEEEiedlabelwidth\relax% -\labelsep\@IEEEiedlabelsep\relax% -\leftmargin\@IEEEiedleftmargin\relax% -\partopsep\@IEEEiedpartopsep\relax% -\parsep\@IEEEiedparsep\relax% -\itemsep\@IEEEieditemsep\relax% -\rightmargin\@IEEEiedrightmargin\relax% -\listparindent\@IEEEiedlistparindent\relax% -\itemindent\@IEEEieditemindent\relax} - - -% v1.6b provide original LaTeX IED list environments -% note that latex.ltx defines \itemize and \enumerate, but not \description -% which must be created by the base classes -% save original LaTeX itemize and enumerate -\let\LaTeXitemize\itemize -\let\endLaTeXitemize\enditemize -\let\LaTeXenumerate\enumerate -\let\endLaTeXenumerate\endenumerate -% base class should define \description -\let\LaTeXdescription\description -\let\endLaTeXdescription\enddescription - - -% override LaTeX's default IED lists, if the user requested it -\if@IEEETOOLSredeflists -\def\itemize{\@IEEEitemize} -\def\enditemize{\@endIEEEitemize} -\def\enumerate{\@IEEEenumerate} -\def\endenumerate{\@endIEEEenumerate} -\def\description{\@IEEEdescription} -\def\enddescription{\@endIEEEdescription} -\fi - - -% provide the user with the IEEE IED commands -\def\IEEEitemize{\@IEEEitemize} -\def\endIEEEitemize{\@endIEEEitemize} -\def\IEEEenumerate{\@IEEEenumerate} -\def\endIEEEenumerate{\@endIEEEenumerate} -\def\IEEEdescription{\@IEEEdescription} -\def\endIEEEdescription{\@endIEEEdescription} - - -% V1.6 we want to keep the IEEEtran IED list definitions as our own internal -% commands so they are protected against redefinition -\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}} -\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}} -\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}} -\def\@endIEEEitemize{\endlist} -\def\@endIEEEenumerate{\endlist} -\def\@endIEEEdescription{\endlist} - - -% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS -% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS -% IEEEtran itemized list MDS 1/2001 -% Note controlled spacing here, shield end of lines with % -\def\@@IEEEitemize[#1]{% - \ifnum\@itemdepth>3\relax\@toodeep\else% - \ifnum\@listdepth>5\relax\@toodeep\else% - \advance\@itemdepth\@ne% - \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% - % get the IEEElabelindentfactor for this level - \advance\@listdepth\@ne% we need to know what the level WILL be - \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% - \advance\@listdepth-\@ne% undo our increment - \def\@IEEEiedjustify{2}% right justified labels are default - % set other defaults - \IEEEnocalcleftmarginfalse% - \IEEEnolabelindentfactorfalse% - \topsep\IEEEiedtopsep% - \IEEElabelindent\IEEEilabelindent% - \labelsep\IEEEiednormlabelsep% - \partopsep 0ex% - \parsep 0ex% - \itemsep 0ex% - \rightmargin 0em% - \listparindent 0em% - \itemindent 0em% - % calculate the label width - % the user can override this later if - % they specified a \labelwidth - \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}% - \@IEEEsavelistparams% save our list parameters - \list{\csname\@itemitem\endcsname}{% - \@IEEErestorelistparams% override any list{} changes - % to our globals - \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel - \IEEEiedlistdecl% let user alter parameters - #1\relax% - % If the user has requested not to use the - % IEEElabelindent factor, don't revise \IEEElabelindent - \ifIEEEnolabelindentfactor\relax% - \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% - \fi% - % Unless the user has requested otherwise, - % calculate our left margin based - % on \IEEElabelindent, \labelwidth and - % \labelsep - \ifIEEEnocalcleftmargin\relax% - \else\IEEEcalcleftmargin{\IEEElabelindent}% - \fi}\fi\fi}% - - -% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS -% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS -% IEEEtran enumerate list MDS 1/2001 -% Note controlled spacing here, shield end of lines with % -\def\@@IEEEenumerate[#1]{% - \ifnum\@enumdepth>3\relax\@toodeep\else% - \ifnum\@listdepth>5\relax\@toodeep\else% - \advance\@enumdepth\@ne% - \edef\@enumctr{enum\romannumeral\the\@enumdepth}% - % get the IEEElabelindentfactor for this level - \advance\@listdepth\@ne% we need to know what the level WILL be - \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% - \advance\@listdepth-\@ne% undo our increment - \def\@IEEEiedjustify{2}% right justified labels are default - % set other defaults - \IEEEnocalcleftmarginfalse% - \IEEEnolabelindentfactorfalse% - \topsep\IEEEiedtopsep% - \IEEElabelindent\IEEEelabelindent% - \labelsep\IEEEiednormlabelsep% - \partopsep 0ex% - \parsep 0ex% - \itemsep 0ex% - \rightmargin 0em% - \listparindent 0em% - \itemindent 0em% - % calculate the label width - % We'll set it to the width suitable for all labels using - % normalfont 1) to 9) - % The user can override this later - \settowidth{\labelwidth}{9)}% - \@IEEEsavelistparams% save our list parameters - \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}% - \@IEEErestorelistparams% override any list{} changes - % to our globals - \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel - \IEEEiedlistdecl% let user alter parameters - #1\relax% - % If the user has requested not to use the - % IEEElabelindent factor, don't revise \IEEElabelindent - \ifIEEEnolabelindentfactor\relax% - \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% - \fi% - % Unless the user has requested otherwise, - % calculate our left margin based - % on \IEEElabelindent, \labelwidth and - % \labelsep - \ifIEEEnocalcleftmargin\relax% - \else\IEEEcalcleftmargin{\IEEElabelindent}% - \fi}\fi\fi}% - - -% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS -% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS -% IEEEtran description list MDS 1/2001 -% Note controlled spacing here, shield end of lines with % -\def\@@IEEEdescription[#1]{% - \ifnum\@listdepth>5\relax\@toodeep\else% - % get the IEEElabelindentfactor for this level - \advance\@listdepth\@ne% we need to know what the level WILL be - \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% - \advance\@listdepth-\@ne% undo our increment - \def\@IEEEiedjustify{0}% left justified labels are default - % set other defaults - \IEEEnocalcleftmarginfalse% - \IEEEnolabelindentfactorfalse% - \topsep\IEEEiedtopsep% - \IEEElabelindent\IEEEdlabelindent% - % assume normal labelsep - \labelsep\IEEEiednormlabelsep% - \partopsep 0ex% - \parsep 0ex% - \itemsep 0ex% - \rightmargin 0em% - \listparindent 0em% - \itemindent 0em% - % Bogus label width in case the user forgets - % to set it. - % TIP: If you want to see what a variable's width is you - % can use the TeX command \showthe\width-variable to - % display it on the screen during compilation - % (This might be helpful to know when you need to find out - % which label is the widest) - \settowidth{\labelwidth}{Hello}% - \@IEEEsavelistparams% save our list parameters - \list{}{\@IEEErestorelistparams% override any list{} changes - % to our globals - \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel - \IEEEiedlistdecl% let user alter parameters - #1\relax% - % If the user has requested not to use the - % labelindent factor, don't revise \IEEElabelindent - \ifIEEEnolabelindentfactor\relax% - \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% - \fi% - % Unless the user has requested otherwise, - % calculate our left margin based - % on \IEEElabelindent, \labelwidth and - % \labelsep - \ifIEEEnocalcleftmargin\relax% - \else\IEEEcalcleftmargin{\IEEElabelindent}\relax% - \fi}\fi} - -% v1.6b we use one makelabel that does justification as needed. -\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax -\makebox[\labelwidth][l]{\normalfont #1}\else -\if\@IEEEiedjustify 1\relax -\makebox[\labelwidth][c]{\normalfont #1}\else -\makebox[\labelwidth][r]{\normalfont #1}\fi\fi} - - - - - - - - - -% used only by IEEEtran's IEEEeqnarray as other packages may -% have their own, different, implementations -\newcounter{IEEEsubequation}[equation] - -% e.g., "1a" (used only by IEEEtran's IEEEeqnarray) -\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}} -% just like LaTeX2e's \@eqnnum -\def\theequationdis{(\theequation)}% (1) -% IEEEsubequation used only by IEEEtran's IEEEeqnarray -\def\theIEEEsubequationdis{(\theIEEEsubequation)}% (1a) - - - - -%% -%% START OF IEEEeqnarray DEFINITIONS -%% -%% Inspired by the concepts, examples, and previous works of LaTeX -%% coders and developers such as Donald Arseneau, Fred Bartlett, -%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, -%% Roland Winkler and Mark Wooding. -%% I don't make the claim that my work here is even near their calibre. ;) - - -\newif\if@IEEEeqnarrayboxnojot% flag to indicate if the environment was called as the star form -\@IEEEeqnarrayboxnojotfalse - -\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter -% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray -% used by IEEEeqnarraymulticol so that it can work properly in both -\@advanceIEEEeqncolcnttrue - -\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined -\newcount\@IEEEeqncolcnt % tracks how many IEEEeqnarray cols the user actually used - - -% The default math style used by the columns -\def\IEEEeqnarraymathstyle{\displaystyle} -% The default text style used by the columns -% default to using the current font -\def\IEEEeqnarraytextstyle{\relax} - -% like the iedlistdecl but for \IEEEeqnarray -\def\IEEEeqnarraydecl{\relax} -\def\IEEEeqnarrayboxdecl{\relax} - - - -% V1.8 flags to indicate that equation numbering is to persist -\newif\if@IEEEeqnumpersist% -\@IEEEeqnumpersistfalse -\newif\if@IEEEsubeqnumpersist% -\@IEEEsubeqnumpersistfalse -% -% V1.8 flags to indicate if (sub)equation number of last line was preadvanced -\newif\if@IEEEeqnumpreadv% -\@IEEEeqnumpreadvfalse -\newif\if@IEEEsubeqnumpreadv% -\@IEEEsubeqnumpreadvfalse - -\newcount\@IEEEsubeqnnumrollback% saves previous value of IEEEsubequation number in case we need to restore it - -% \yesnumber is the opposite of \nonumber -% a novel concept with the same def as the equationarray package -% However, we give IEEE versions too since some LaTeX packages such as -% the MDWtools mathenv.sty redefine \nonumber to something else. -% This command is intended for use in non-IEEEeqnarray math environments -\providecommand{\yesnumber}{\global\@eqnswtrue} - - -% IEEEyes/nonumber -% V1.8 add persistant * forms -% These commands can alter the type of equation an IEEEeqnarray line is. -\def\IEEEyesnumber{\@ifstar{\global\@IEEEeqnumpersisttrue\global\@IEEEsubeqnumpersistfalse\@IEEEyesnumber}{\@IEEEyesnumber}} - -\def\@IEEEyesnumber{\global\@eqnswtrue -\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray -\ifnum\c@IEEEsubequation>0\relax - \stepcounter{equation}\setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax - \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label -\fi -% even if we reached this eqn num via a preadv, it is legit now -\global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse -\fi} - -\def\IEEEnonumber{\@ifstar{\global\@IEEEeqnumpersistfalse\global\@IEEEsubeqnumpersistfalse\global\@eqnswfalse}{\global\@eqnswfalse}} - - -\def\IEEEyessubnumber{\@ifstar{\global\@IEEEsubeqnumpersisttrue\@IEEEyessubnumber}{\@IEEEyessubnumber}} -% -\def\@IEEEyessubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray - \ifnum\c@IEEEsubequation>0\relax% if it already is a subequation, we are good to go as-is - \else% if we are a regular equation we have to watch out for two cases - \if@IEEEeqnumpreadv% if this equation is the result of a preadvance, backout and bump the sub eqnnum - \global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\addtocounter{IEEEsubequation}{1}\relax - \else% non-preadvanced equations just need initialization of their sub eqnnum - \setcounter{IEEEsubequation}{1}\relax - \fi - \fi% fi already is subequation - \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax - \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label - \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore - \global\@eqnswtrue -\fi} - - -\def\IEEEnosubnumber{\@ifstar{\global\@IEEEsubeqnumpersistfalse\@IEEEnosubnumber}{\@IEEEnosubnumber}} -% -\def\@IEEEnosubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray - \if@eqnsw % we do nothing unless we know we will display because we play with the counters here - % if it currently is a subequation, bump up to the next equation number and turn off the subequation - \ifnum\c@IEEEsubequation>0\relax\addtocounter{equation}{1}\setcounter{IEEEsubequation}{0}\relax - \fi - \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore - \gdef\@currentlabel{\p@equation\theequation}\relax - \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label - \fi -\fi} - - - -% allows users to "push away" equations that get too close to the equation numbers -\def\IEEEeqnarraynumspace{\hphantom{\ifnum\c@IEEEsubequation>0\relax\theIEEEsubequationdis\else\theequationdis\fi}} - -% provides a way to span multiple columns within IEEEeqnarray environments -% will consider \if@advanceIEEEeqncolcnt before globally advancing the -% column counter - so as to work within \IEEEeqnarraybox -% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text} -\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}\relax -% check if column is defined for the precolumn definition -% We have to be careful here because TeX scans for & even within an \iffalse -% where it does not expand macros. So, if we used only one \ifx and a #3 -% appeared in the false branch and the user inserted another alignment -% structure that uses & in the \IEEEeqnarraymulticol{}, TeX will not see that -% there is an inner alignment in the false branch yet still will see any & -% there and will think that they apply to the outer alignment resulting in an -% incomplete \ifx error. -% So, here we use separate checks for the pre and post parts in order to keep -% the #3 outside of all conditionals. -\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax -\csname @IEEEeqnarraycolPRE#2\endcsname -\else% if not, error and use default type -\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak -Using a default centering column instead}% -{You must define IEEEeqnarray column types before use.}% -\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname -\fi -% The ten \relax are to help prevent misleading error messages in case a user -% accidently inserted a macro that tries to acquire additional arguments. -#3\relax\relax\relax\relax\relax\relax\relax\relax\relax\relax -% check if column is defined for the postcolumn definition -\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax -\csname @IEEEeqnarraycolPOST#2\endcsname -\else% if not, use the default type -\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname -\fi -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi} - -% like \omit, but maintains track of the column counter for \IEEEeqnarray -\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi} - - -% provides a way to define a letter referenced column type -% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text} -\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}% -\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}% -\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}} - - -% provides a way to define a numerically referenced inter-column glue types -% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition} -\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}% -\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}} - - -\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types - - -% expands and appends the given argument to the \@IEEEtrantmptoksA token list -% used to build up the \halign preamble -\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}% -\@@IEEEappendtoksA} - -% also appends to \@IEEEtrantmptoksA, but does not expand the argument -% uses \toks8 as a scratchpad register -\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}% -\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}% -\@@IEEEappendNOEXPANDtoksA} - -% define some common column types for the user -% math -\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil} -\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil} -\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$} -\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil} -\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil} -\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$} -% text -\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil} -\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil} -\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{} - -% vertical rules -\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth} -\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth} -\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth} -\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}% -{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth} - -% horizontal rules -\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil} -\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil} - -% plain -\IEEEeqnarraydefcol{x}{}{} -\IEEEeqnarraydefcol{X}{$}{$} - -% the default column type to use in the event a column type is not defined -\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil} - - -% a zero tabskip (used for "-" col types) -\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt} -% a centering tabskip (used for "+" col types) -\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt} - -% top level default tabskip glues for the start, end, and inter-column -% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox -\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue -\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue -\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue - - - -% creates a vertical rule that extends from the bottom to the top a a cell -% Provided in case other packages redefine \vline some other way. -% usage: \IEEEeqnarrayvrule[rule thickness] -% If no argument is provided, \arrayrulewidth will be used for the rule thickness. -\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax} - -% creates a blank separator row -% usage: \IEEEeqnarrayseprow[separation length][font size commands] -% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax] -% blank arguments inherit the default values -% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers -\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}} -\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}} -\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}% -\ifx\@IEEEeqnarrayseprowARGONE\@empty% -% get the skip value, based on the font commands -% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3 -% assign within a bogus box to confine the font changes -{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}% -\else% -{\setbox0=\hbox{#2\relax\global\skip5=#1}}% -\fi% -\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax} - -% creates a blank separator row, but omits all the column templates -% usage: \IEEEeqnarrayseprowcut[separation length][font size commands] -% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax] -% blank arguments inherit the default values -% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers -\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% -\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}} -\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}} -\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}% -\ifx\@IEEEeqnarrayseprowARGONE\@empty% -% get the skip value, based on the font commands -% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3 -% assign within a bogus box to confine the font changes -{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}% -\else% -{\setbox0=\hbox{#2\relax\global\skip5=#1}}% -\fi% -\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax} - - - -% draws a single rule across all the columns optional -% argument determines the rule width, \arrayrulewidth is the default -% updates column counter as needed and turns off struts -% usage: \IEEEeqnarrayrulerow[rule line thickness] -\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% -\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}} -\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule -% turn off any struts -\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax} - - -% draws a double rule by using a single rule row, a separator row, and then -% another single rule row -% first optional argument determines the rule thicknesses, \arrayrulewidth is the default -% second optional argument determines the rule spacing, \doublerulesep is the default -% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing] -\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% -\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}} -\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}% -{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}} -\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}% -% we allow the user to say \IEEEeqnarraydblrulerow[][] -\ifx\@IEEEeqnarraydblrulerowARG\@empty% -\@IEEEeqnarrayrulerow[\arrayrulewidth]% -\else% -\@IEEEeqnarrayrulerow[#1]\relax% -\fi% -\def\@IEEEeqnarraydblrulerowARG{#2}% -\ifx\@IEEEeqnarraydblrulerowARG\@empty% -\\\IEEEeqnarrayseprow[\doublerulesep][\relax]% -\else% -\\\IEEEeqnarrayseprow[#2][\relax]% -\fi% -\\\multispan{\@IEEEeqnnumcols}% -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% -\def\@IEEEeqnarraydblrulerowARG{#1}% -\ifx\@IEEEeqnarraydblrulerowARG\@empty% -\@IEEEeqnarrayrulerow[\arrayrulewidth]% -\else% -\@IEEEeqnarrayrulerow[#1]% -\fi% -} - -% draws a double rule by using a single rule row, a separator (cutting) row, and then -% another single rule row -% first optional argument determines the rule thicknesses, \arrayrulewidth is the default -% second optional argument determines the rule spacing, \doublerulesep is the default -% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing] -\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% -\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}} -\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}% -{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}} -\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}% -% we allow the user to say \IEEEeqnarraydblrulerow[][] -\ifx\@IEEEeqnarraydblrulerowARG\@empty% -\@IEEEeqnarrayrulerow[\arrayrulewidth]% -\else% -\@IEEEeqnarrayrulerow[#1]% -\fi% -\def\@IEEEeqnarraydblrulerowARG{#2}% -\ifx\@IEEEeqnarraydblrulerowARG\@empty% -\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]% -\else% -\\\IEEEeqnarrayseprowcut[#2][\relax]% -\fi% -\\\multispan{\@IEEEeqnnumcols}% -% advance column counter only if the IEEEeqnarray environment wants it -\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% -\def\@IEEEeqnarraydblrulerowARG{#1}% -\ifx\@IEEEeqnarraydblrulerowARG\@empty% -\@IEEEeqnarrayrulerow[\arrayrulewidth]% -\else% -\@IEEEeqnarrayrulerow[#1]% -\fi% -} - - - -% inserts a full row's worth of &'s -% relies on \@IEEEeqnnumcols to provide the correct number of columns -% uses \@IEEEtrantmptoksA, \count0 as scratch registers -\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax% -\loop% add cols if the user did not use them all -\ifnum\count0<\@IEEEeqnnumcols\relax% -\@IEEEappendtoksA{&}% -\advance\count0 by 1\relax% update the col count -\repeat% -\the\@IEEEtrantmptoksA%execute the &'s -} - - - -\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines -\@IEEEeqnarrayISinnerfalse % of an IEEEeqnarray - after the IEEEeqnarraydecl - -\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts -\edef\@IEEEeqnarrayTHEstrutdepth{0pt} - -\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of -\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt} % struts within an IEEEeqnarray - -\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height -\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth - -\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value -\@IEEEeqnarrayusemasterstruttrue % is to be used - - - -% saves the strut height and depth of the master strut -\def\@IEEEeqnarraymasterstrutsave{\relax% -\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% -% remove stretchability -\dimen0\skip0\relax% -\dimen2\skip2\relax% -% save values -\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}% -\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}} - -% restores the strut height and depth of the master strut -\def\@IEEEeqnarraymasterstrutrestore{\relax% -\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax% -% remove stretchability -\dimen0\skip0\relax% -\dimen2\skip2\relax% -% restore values -\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}} - - -% globally restores the strut height and depth to the -% master values and sets the master strut flag to true -\def\@IEEEeqnarraystrutreset{\relax% -\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% -% remove stretchability -\dimen0\skip0\relax% -\dimen2\skip2\relax% -% restore values -\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% -\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% -\global\@IEEEeqnarrayusemasterstruttrue} - - -% if the master strut is not to be used, make the current -% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth -% and the use master strut flag, global -% this allows user strut commands issued in the last column to be carried -% into the isolation/strut column -\def\@IEEEeqnarrayglobalizestrutstatus{\relax% -\if@IEEEeqnarrayusemasterstrut\else% -\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}% -\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}% -\global\@IEEEeqnarrayusemasterstrutfalse% -\fi} - - - -% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands] -% If called outside the lines of an IEEEeqnarray, sets the height -% and depth of both the master and local struts. If called inside -% an IEEEeqnarray line, sets the height and depth of the local strut -% only and sets the flag to indicate the use of the local strut -% values. If the height or depth is left blank, 0.7\normalbaselineskip -% and 0.3\normalbaselineskip will be used, respectively. -% The optional argument can be used to evaluate the lengths under -% a different font size and styles. If none is specified, the current -% font is used. -% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2 -\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}} -\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}% -\ifx\@IEEEeqnarraystrutsizeARG\@empty% -{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}% -\skip0=\skip3\relax% -\else% arg one present -{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}% -\skip0=\skip3\relax% -\fi% if null arg -\def\@IEEEeqnarraystrutsizeARG{#2}% -\ifx\@IEEEeqnarraystrutsizeARG\@empty% -{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}% -\skip2=\skip3\relax% -\else% arg two present -{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}% -\skip2=\skip3\relax% -\fi% if null arg -% remove stretchability, just to be safe -\dimen0\skip0\relax% -\dimen2\skip2\relax% -% dimen0 = height, dimen2 = depth -\if@IEEEeqnarrayISinner% inner does not touch master strut size -\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% -\@IEEEeqnarrayusemasterstrutfalse% do not use master -\else% outer, have to set master strut too -\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}% -\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% -\@IEEEeqnarrayusemasterstruttrue% use master strut -\fi} - - -% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands] -% If called outside the lines of an IEEEeqnarray, adds the given height -% and depth to both the master and local struts. -% If called inside an IEEEeqnarray line, adds the given height and depth -% to the local strut only and sets the flag to indicate the use -% of the local strut values. -% In both cases, if a height or depth is left blank, 0pt is used instead. -% The optional argument can be used to evaluate the lengths under -% a different font size and styles. If none is specified, the current -% font is used. -% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2 -\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}} -\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}% -\ifx\@IEEEeqnarraystrutsizearg\@empty% -\skip0=0pt\relax% -\else% arg one present -{\setbox0=\hbox{#3\relax\global\skip3=#1}}% -\skip0=\skip3\relax% -\fi% if null arg -\def\@IEEEeqnarraystrutsizearg{#2}% -\ifx\@IEEEeqnarraystrutsizearg\@empty% -\skip2=0pt\relax% -\else% arg two present -{\setbox0=\hbox{#3\relax\global\skip3=#2}}% -\skip2=\skip3\relax% -\fi% if null arg -% remove stretchability, just to be safe -\dimen0\skip0\relax% -\dimen2\skip2\relax% -% dimen0 = height, dimen2 = depth -\if@IEEEeqnarrayISinner% inner does not touch master strut size -% get local strut size -\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax% -% add it to the user supplied values -\advance\dimen0 by \skip0\relax% -\advance\dimen2 by \skip2\relax% -% update the local strut size -\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% -\@IEEEeqnarrayusemasterstrutfalse% do not use master -\else% outer, have to set master strut too -% get master strut size -\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% -% add it to the user supplied values -\advance\dimen0 by \skip0\relax% -\advance\dimen2 by \skip2\relax% -% update the local and master strut sizes -\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}% -\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% -\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% -\@IEEEeqnarrayusemasterstruttrue% use master strut -\fi} - - -% allow user a way to see the struts -\newif\ifIEEEvisiblestruts -\IEEEvisiblestrutsfalse - -% inserts an invisible strut using the master or local strut values -% uses scratch registers \skip0, \skip2, \dimen0, \dimen2 -\def\@IEEEeqnarrayinsertstrut{\relax% -\if@IEEEeqnarrayusemasterstrut -% get master strut size -\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% -\else% -% get local strut size -\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax% -\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax% -\fi% -% remove stretchability, probably not needed -\dimen0\skip0\relax% -\dimen2\skip2\relax% -% dimen0 = height, dimen2 = depth -% allow user to see struts if desired -\ifIEEEvisiblestruts% -\vrule width0.2pt height\dimen0 depth\dimen2\relax% -\else% -\vrule width0pt height\dimen0 depth\dimen2\relax\fi} - - -% creates an invisible strut, useable even outside \IEEEeqnarray -% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. -% usage: \IEEEstrut[height][depth][font size commands] -% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax] -% blank arguments inherit the default values -% uses \dimen0, \dimen2, \skip0, \skip2 -\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}} -\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}} -\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}} -\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax% -\def\@IEEEstrutARG{#1}% -\ifx\@IEEEstrutARG\@empty% -\skip0=0.7\normalbaselineskip\relax% -\else% -\skip0=#1\relax% -\fi% -\def\@IEEEstrutARG{#2}% -\ifx\@IEEEstrutARG\@empty% -\skip2=0.3\normalbaselineskip\relax% -\else% -\skip2=#2\relax% -\fi% -% remove stretchability, probably not needed -\dimen0\skip0\relax% -\dimen2\skip2\relax% -\ifIEEEvisiblestruts% -\vrule width0.2pt height\dimen0 depth\dimen2\relax% -\else% -\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}} - - -% enables strut mode by setting a default strut size and then zeroing the -% \baselineskip, \lineskip, \lineskiplimit and \jot -\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]% -\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt} - - -% equation and subequation forms to use to setup hyperref's \@currentHref -\def\@IEEEtheHrefequation{equation.\theHequation} -\def\@IEEEtheHrefsubequation{equation.\theHequation\alph{IEEEsubequation}} - - -\def\IEEEeqnarray{\@IEEEeqnumpersisttrue\@IEEEsubeqnumpersistfalse\@IEEEeqnarray} -\def\endIEEEeqnarray{\end@IEEEeqnarray} - -\@namedef{IEEEeqnarray*}{\@IEEEeqnumpersistfalse\@IEEEsubeqnumpersistfalse\@IEEEeqnarray} -\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray} - - -% \IEEEeqnarray is an enhanced \eqnarray. -% The star form defaults to not putting equation numbers at the end of each row. -% usage: \IEEEeqnarray[decl]{cols} -\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}} -% We have to be careful here to normalize catcodes just before acquiring the -% cols as that specification may contain punctuation which could be subject -% to document catcode changes. -\def\@@IEEEeqnarray[#1]{\begingroup\IEEEnormalcatcodes\@@@IEEEeqnarray[#1]} -\def\@@@IEEEeqnarray[#1]#2{\endgroup - % default to showing the equation number or not based on whether or not - % the star form was involked - \if@IEEEeqnumpersist\global\@eqnswtrue - \else% not the star form - \global\@eqnswfalse - \fi% if star form - % provide a basic hyperref \theHequation if this has not already been setup (hyperref not loaded, or no section counter) - \@ifundefined{theHequation}{\def\theHequation{\arabic{equation}}}{}\relax - % provide dummy hyperref commands in case hyperref is not loaded - \providecommand{\Hy@raisedlink}[1]{}\relax - \providecommand{\hyper@anchorstart}[1]{}\relax - \providecommand{\hyper@anchorend}{}\relax - \providecommand{\@currentHref}{}\relax - \@IEEEeqnumpreadvfalse% reset eqnpreadv flag - \@IEEEsubeqnumpreadvfalse% reset subeqnpreadv flag - \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign - \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default - \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise - \IEEEvisiblestrutsfalse% diagnostic mode defaults to off - % no extra space unless the user specifically requests it - \lineskip=0pt\relax - \lineskiplimit=0pt\relax - \baselineskip=\normalbaselineskip\relax% - \jot=\IEEEnormaljot\relax% - \mathsurround\z@\relax% no extra spacing around math - \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, - % used in \IEEEeqnarraymulticol and in the preamble build - %V1.8 Here we preadvance to the next equation number. - % If the user later wants a continued subequation, we can roll back. - \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation% - \stepcounter{equation}\@IEEEeqnumpreadvtrue% advance equation counter before first line - \setcounter{IEEEsubequation}{0}% no subequation yet - \let\@IEEEcurrentlabelsave\@currentlabel% save current label as we later change it globally - \let\@IEEEcurrentHrefsave\@currentHref% save current href label as we later change it globally - \def\@currentlabel{\p@equation\theequation}% redefine the ref label - \def\@currentHref{\@IEEEtheHrefequation}% setup hyperref label - \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides - #1\relax% allow user to override defaults - \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers - \global\@IEEEeqncolcnt\z@% col. count = 0 for first line - \@IEEEbuildpreamble{#2}\relax% build the preamble and put it into \@IEEEtrantmptoksA - % put in the column for the equation number - \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first - \toks0={##}% - % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking - \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}% - % add the isolation column - \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% - % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking - \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}% - % add the equation number col to the preamble - \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}% - % note \@IEEEeqnnumcols does not count the equation col or isolation col - % set the starting tabskip glue as determined by the preamble build - \tabskip=\@IEEEBPstartglue\relax - % begin the display alignment - \@IEEEeqnarrayISinnertrue% commands are now within the lines - $$\everycr{}\halign to\displaywidth\bgroup - % "exspand" the preamble - \span\the\@IEEEtrantmptoksA\cr} - -% enter isolation/strut column (or the next column if the user did not use -% every column), record the strut status, complete the columns, do the strut if needed, -% restore counters (to backout any equation setup for a next line that was never used) -% to their correct values and exit -\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup -\if@IEEEsubeqnumpreadv\global\advance\c@IEEEsubequation\m@ne\fi -\if@IEEEeqnumpreadv\global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\fi -\global\let\@currentlabel\@IEEEcurrentlabelsave% restore current label -\global\let\@currentHref\@IEEEcurrentHrefsave% restore current href label -$$\@ignoretrue} - - -% IEEEeqnarray uses a modifed \\ instead of the plain \cr to -% end rows. This allows for things like \\*[vskip amount] -% These "cr" macros are modified versions of those for LaTeX2e's eqnarray -% the {\ifnum0=`} braces must be kept away from the last column to avoid -% altering spacing of its math, so we use & to advance to the next column -% as there is an isolation/strut column after the user's columns -\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column - {\ifnum0=`}\fi - \@ifstar{% - \global\@eqpen\@M\@IEEEeqnarrayYCR - }{% - \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR - }% -} - -\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip} - -\def\@IEEEeqnarrayXCR[#1]{% - \ifnum0=`{\fi}% - \@@IEEEeqnarraycr - \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}% - -\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register - \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column - \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax - \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak - environment}% - {Use fewer \string &'s or put more columns in the IEEEeqnarray column\MessageBreak - specifications.}\relax% - \else - \loop% add cols if the user did not use them all - \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax - \@IEEEappendtoksA{&}% - \advance\@IEEEeqncolcnt by 1\relax% update the col count - \repeat - % this number of &'s will take us the the isolation column - \fi - % execute the &'s - \the\@IEEEtrantmptoksA% - % handle the strut/isolation column - \@IEEEeqnarrayinsertstrut% do the strut if needed - \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray - &% and enter the equation number column - \if@eqnsw% only if we display something - \Hy@raisedlink{\hyper@anchorstart{\@currentHref}}% start a hyperref anchor - \global\@IEEEeqnumpreadvfalse\relax% displaying an equation number means - \global\@IEEEsubeqnumpreadvfalse\relax% the equation counters point to valid equations - % V1.8 Here we setup the counters, currentlabel and status for what would be the *next* - % equation line as would be the case under the current settings. However, there are two problems. - % One problem is that there might not ever be a next line. The second problem is that the user - % may later alter the meaning of a line with commands such as \IEEEyessubnumber. So, to handle - % these cases we have to record the current values of the (sub)equation counters and revert back - % to them if the next line is changed or never comes. The \if@IEEEeqnumpreadv, \if@IEEEsubeqnumpreadv - % and \@IEEEsubeqnnumrollback stuff tracks this. - % The logic to handle all this is surprisingly complex, but a nice feature of the approach here is - % that the equation counters and labels remain valid for what the line would be unless a - % \IEEEyessubnumber et al. later changes it. So, any hyperref links are always correct. - \ifnum\c@IEEEsubequation>0\relax% handle subequation - \theIEEEsubequationdis\relax - \if@IEEEsubeqnumpersist% setup for default type of next line - \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax - \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax - \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label - \else - % if no subeqnum persist, go ahead and setup for a new equation number - \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation - \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax - \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax - \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label - \fi - \else% display a standard equation number - \theequationdis\relax - \setcounter{IEEEsubequation}{0}\relax% not really needed - \if@IEEEsubeqnumpersist% setup for default type of next line - % subequations that follow plain equations carry the same equation number e.g, 5, 5a rather than 5, 6a - \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax - \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax - \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label - \else - % if no subeqnum persist, go ahead and setup for a new equation number - \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation - \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax - \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax - \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label - \fi - \fi% - \Hy@raisedlink{\hyper@anchorend}% end hyperref anchor - \fi% fi only if we display something - % reset the flags to indicate the default preferences of the display of equation numbers - \if@IEEEeqnumpersist\global\@eqnswtrue\else\global\@eqnswfalse\fi - \if@IEEEsubeqnumpersist\global\@eqnswtrue\fi% ditto for the subequation flag - % reset the number of columns the user actually used - \global\@IEEEeqncolcnt\z@\relax - % the real end of the line - \cr} - - - - - -% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything -% inside a vtop, vbox, or vcenter box depending on the letter in the second -% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray, -% equation numbers are not displayed and \IEEEeqnarraybox can be nested. -% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox -% within an hbox. -% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within -% a \hbox{$ $} construct. -% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or -% \IEEEeqnarrayboxt depending on the math mode. -% The third optional argument specifies the width this box is to be set to - -% natural width is the default. -% The * forms do not add \jot line spacing -% usage: \IEEEeqnarraybox[decl][pos][width]{cols} -\def\IEEEeqnarrayboxm{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox} -\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox} -\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox} -\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox} - -\def\IEEEeqnarrayboxt{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox} -\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox} -\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox} -\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox} - -\def\IEEEeqnarraybox{\@IEEEeqnarrayboxnojotfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi% -\@IEEEeqnarraybox} -\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox} - -\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarrayboxnojottrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi% -\@IEEEeqnarraybox} -\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox} - -% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} -% for \vcenter in non-math mode -\newif\if@IEEEeqnarrayboxHBOXSW% -\@IEEEeqnarrayboxHBOXSWfalse - -\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}} -% We have to be careful here to normalize catcodes just before acquiring the -% cols as that specification may contain punctuation which could be subject -% to document catcode changes. -\def\@@IEEEeqnarraybox[#1]{\relax\begingroup\IEEEnormalcatcodes\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}} -\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}} - -% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs -\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\endgroup\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign - \@IEEEeqnarraymasterstrutsave% save current master strut values - \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default - \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise - \IEEEvisiblestrutsfalse% diagnostic mode defaults to off - % no extra space unless the user specifically requests it - \lineskip=0pt\relax% - \lineskiplimit=0pt\relax% - \baselineskip=\normalbaselineskip\relax% - \jot=\IEEEnormaljot\relax% - \mathsurround\z@\relax% no extra spacing around math - % the default end glues are zero for an \IEEEeqnarraybox - \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue - \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue - \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue - \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, - % used in \IEEEeqnarraymulticol and in the preamble build - \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides - #1\relax% allow user to override defaults - \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing - \@IEEEbuildpreamble{#4}\relax% build the preamble and put it into \@IEEEtrantmptoksA - % add an isolation column to the preamble to stop \\'s {} from getting into the last col - \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first - \toks0={##}% - % add the isolation column to the preamble - \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% - % set the starting tabskip glue as determined by the preamble build - \tabskip=\@IEEEBPstartglue\relax - % begin the alignment - \everycr{}% - % use only the very first token to determine the positioning - \@IEEEextracttoken{#2}\relax - \ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: IEEEeqnarraybox position specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax - \fi - % \@IEEEextractedtoken has the first token, the rest are ignored - % if we need to put things into and hbox and go into math mode, do so now - \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi% - % use the appropriate vbox type - \if\@IEEEextractedtoken t\relax\vtop\else\if\@IEEEextractedtoken c\relax% - \vcenter\else\vbox\fi\fi\bgroup% - \@IEEEeqnarrayISinnertrue% commands are now within the lines - \ifx#3\relax\halign\else\halign to #3\relax\fi% - \bgroup - % "exspand" the preamble - \span\the\@IEEEtrantmptoksA\cr} - -% carry strut status and enter the isolation/strut column, -% exit from math mode if needed, and exit -\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status -&% enter isolation/strut column -\@IEEEeqnarrayinsertstrut% do strut if needed -\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values -% reset the strut system for next IEEEeqnarray -% (sets local strut values back to previous master strut values) -\@IEEEeqnarraystrutreset% -% ensure last line, exit from halign, close vbox -\crcr\egroup\egroup% -% exit from math mode and close hbox if needed -\if@IEEEeqnarrayboxHBOXSW $\egroup\fi} - - - -% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to -% end rows. This allows for things like \\[vskip amount] -% This "cr" macros are modified versions those for LaTeX2e's eqnarray -% For IEEEeqnarraybox, \\* is the same as \\ -% the {\ifnum0=`} braces must be kept away from the last column to avoid -% altering spacing of its math, so we use & to advance to the isolation/strut column -% carry strut status into isolation/strut column -\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status -&% enter isolation/strut column -\@IEEEeqnarrayinsertstrut% do strut if needed -% reset the strut system for next line or IEEEeqnarray -\@IEEEeqnarraystrutreset% -{\ifnum0=`}\fi% -\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}} - -% test and setup the optional argument to \\[] -\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip} - -% IEEEeqnarraybox does not automatically increase line spacing by \jot -\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}% -\cr\noalign{\if@IEEEeqnarrayboxnojot\else\vskip\jot\fi\vskip#1\relax}} - - - -% usage: \@IEEEbuildpreamble{column specifiers} -% starts the halign preamble build -% the assembled preamble is put in \@IEEEtrantmptoksA -\def\@IEEEbuildpreamble#1{\@IEEEtrantmptoksA={}% clear token register -\let\@IEEEBPcurtype=u%current column type is not yet known -\let\@IEEEBPprevtype=s%the previous column type was the start -\let\@IEEEBPnexttype=u%next column type is not yet known -% ensure these are valid -\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}% -\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition -% currently acquired numerically referenced glue -% use a name that is easier to remember -\let\@IEEEBPcurnum=\@IEEEtrantmpcountA% -\@IEEEBPcurnum=0% -% tracks number of columns in the preamble -\@IEEEeqnnumcols=0% -% record the default end glues -\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}% -\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}% -\edef\@IEEEedefMACRO{#1}\relax% fully expand the preamble to support macro containers -% now parse the user's column specifications -% \ignorespaces is used as a delimiter, need at least one trailing \relax because -% \@@IEEEbuildpreamble looks into the future -\expandafter\@@IEEEbuildpreamble\@IEEEedefMACRO\ignorespaces\relax\relax} - - -% usage: \@@IEEEbuildpreamble{current column}{next column} -% parses and builds the halign preamble -\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble% -% use only the very first token to check the end -\@IEEEextracttokengroups{#1}\relax -\ifx\@IEEEextractedfirsttoken\ignorespaces\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else% -% identify current and next token type -\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid -\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next -% if curtype is a glue, get the glue def -\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi% -% if curtype is a column, get the column def and set the current column name -\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi% -% if curtype is a numeral, acquire the user defined glue -\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi% -% process the acquired glue -\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi% -% process the acquired col -\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi% -% ready prevtype for next col spec. -\let\@IEEEBPprevtype=\@IEEEBPcurtype% -% be sure and put back the future token(s) as a group -\fi\@@nextIEEEbuildpreamble{#2}} - - -% usage: \@@IEEEfinishpreamble{discarded} -% executed just after preamble build is completed -% warn about zero cols, and if prevtype type = u, put in end tabskip glue -% argument is not used -\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax -\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}% -{At least one column type must be declared for each IEEEeqnarray.}% -\fi%num cols less than 1 -%if last type undefined, set default end tabskip glue -\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi} - - -% usage: \@IEEEgetcoltype{col specifier}{\output}{error more} -% Identify and return the column specifier's type code in the given -% \output macro: -% n = number -% g = glue (any other char in catagory 12) -% c = letter -% e = \ignorespaces (end of sequence) -% u = undefined -% error mode: 0 = no error message, 1 = error on invalid char -\def\@IEEEgetcoltype#1#2#3{% -% use only the very first token to determine the type -\@IEEEextracttoken{#1}\relax -% \@IEEEextractedtoken has the first token, the rest are discarded -\let#2=u\relax% assume invalid until know otherwise -\ifx\@IEEEextractedtoken\ignorespaces\let#2=e\else -\ifcat\@IEEEextractedtoken\relax\else% screen out control sequences -\if0\@IEEEextractedtoken\let#2=n\else -\if1\@IEEEextractedtoken\let#2=n\else -\if2\@IEEEextractedtoken\let#2=n\else -\if3\@IEEEextractedtoken\let#2=n\else -\if4\@IEEEextractedtoken\let#2=n\else -\if5\@IEEEextractedtoken\let#2=n\else -\if6\@IEEEextractedtoken\let#2=n\else -\if7\@IEEEextractedtoken\let#2=n\else -\if8\@IEEEextractedtoken\let#2=n\else -\if9\@IEEEextractedtoken\let#2=n\else -\ifcat,\@IEEEextractedtoken\let#2=g\relax -\else\ifcat a\@IEEEextractedtoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi -\if#2u\relax -\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}% -{Only letters, numerals and certain other symbols are allowed \MessageBreak -as IEEEeqnarray column specifiers.}\fi\fi} - - -% usage: \@IEEEgetcurcol{col specifier} -% verify the letter referenced column exists -% and return its name in \@IEEEBPcurcolname -% if column specifier is invalid, use the default column @IEEEdefault -\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined% -\def\@IEEEBPcurcolname{#1}\else% invalid column name -\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak -Using a default centering column instead}% -{You must define IEEEeqnarray column types before use.}% -\def\@IEEEBPcurcolname{@IEEEdefault}\fi} - - -% usage: \@IEEEgetcurglue{glue specifier}{\output} -% identify the predefined (punctuation) glue value -% and return it in the given output macro -\def\@IEEEgetcurglue#1#2{% -% ! = \! (neg small) -0.16667em (-3/18 em) -% , = \, (small) 0.16667em ( 3/18 em) -% : = \: (med) 0.22222em ( 4/18 em) -% ; = \; (large) 0.27778em ( 5/18 em) -% ' = \quad 1em -% " = \qquad 2em -% . = 0.5\arraycolsep -% / = \arraycolsep -% ? = 2\arraycolsep -% * = 1fil -% + = \@IEEEeqnarraycolSEPcenter -% - = \@IEEEeqnarraycolSEPzero -% Note that all em values are referenced to the math font (textfont2) fontdimen6 -% value for 1em. -% -% use only the very first token to determine the type -\@IEEEextracttoken{#1}\relax -\ifx\@IEEEextractedtokensdiscarded\@empty\else - \typeout{** WARNING: IEEEeqnarray predefined inter-column glue type specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax -\fi -% get the math font 1em value -% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs -% to gain access to the math (\textfont2) font's spacing parameters. -% So we create a bogus box here that uses the math font to ensure -% that \textfont2 is loaded and ready. If this is not done, -% the \textfont2 stuff here may not work. -% Thanks to Bernd Raichle for his 1997 post on this topic. -{\setbox0=\hbox{$\displaystyle\relax$}}% -% fontdimen6 has the width of 1em (a quad). -\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax% -% identify the glue value based on the first token -% we discard anything after the first -\if!\@IEEEextractedtoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else -\if,\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else -\if:\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else -\if;\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else -\if'\@IEEEextractedtoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else -\if"\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else -\if.\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else -\if/\@IEEEextractedtoken\edef#2{\the\arraycolsep}\else -\if?\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else -\if *\@IEEEextractedtoken\edef#2{0pt plus 1fil minus 0pt}\else -\if+\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else -\if-\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPzero}\else -\edef#2{\@IEEEeqnarraycolSEPzero}% -\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak -column specifications. Using a default value of\MessageBreak -0pt instead}% -{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak -IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} - - -% usage: \@IEEEprocessNcol{digit} -% process a numerical digit from the column specification -% and look up the corresponding user defined glue value -% can transform current type from n to g or a as the user defined glue is acquired -\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g% -\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak -specifications. Ignoring consecutive glue specifiers\MessageBreak -after the first}% -{You cannot have two or more glue types next to each other\MessageBreak -in the IEEEeqnarray column specifications.}% -\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded -\@IEEEBPcurnum=0\relax% -\else% if we previously aborted a glue -\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion -\else%acquire this number -% save the previous type before the numerical digits started -\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi% -\multiply\@IEEEBPcurnum by 10\relax% -\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan -\if\@IEEEBPnexttype n\else%close acquisition -\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined% -\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}% -\else%user glue not defined -\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak -column specifications. Using a default value of\MessageBreak -0pt instead}% -{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak -\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}% -\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}% -\fi% glue defined or not -\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue -\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue -\@IEEEBPcurnum=0\relax%ready for next acquisition -\fi%close acquisition, get glue -\fi%discard or acquire number -\fi%prevtype glue or not -} - - -% process an acquired glue -% add any acquired column/glue pair to the preamble -\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions -\else -% if this is the start glue, save it, but do nothing else -% as this is not used in the preamble, but before -\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}% -\else%not the start glue -\if\@IEEEBPprevtype g%ignore if back to back glues -\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak -specifications. Ignoring consecutive glue specifiers\MessageBreak -after the first}% -{You cannot have two or more glue types next to each other\MessageBreak -in the IEEEeqnarray column specifications.}% -\let\@IEEEBPcurtype=a% abort this glue -\else% not a back to back glue -\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble -\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi -\toks0={##}% -% make preamble advance col counter if this environment needs this -\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi -% insert the column defintion into the preamble, being careful not to expand -% the column definition -\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}% -\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}% -\@IEEEappendtoksA{\@IEEEBPcurcolname}% -\@IEEEappendNOEXPANDtoksA{\endcsname}% -\@IEEEappendtoksA{\the\toks0}% -\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax% -\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}% -\@IEEEappendtoksA{\@IEEEBPcurcolname}% -\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax% -\relax\relax\relax\relax\relax\endgroup}% -\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble -\else% error: non-start glue with no pending column -\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak -type in the column specifications. Ignoring this glue\MessageBreak -specifier}% -{Except for the first and last positions, glue can be placed only\MessageBreak -between column types.}% -\let\@IEEEBPcurtype=a% abort this glue -\fi% previous was a column -\fi% back-to-back glues -\fi% is start column glue -\fi% prev type not a -} - - -% process an acquired letter referenced column and, if necessary, add it to the preamble -\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else -\if\@IEEEBPnexttype n\else -% we have a column followed by something other than a glue (or numeral glue) -% so we must add this column to the preamble now -\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first -\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue -\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue -\toks0={##}% -% make preamble advance col counter if this environment needs this -\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi -% insert the column definition into the preamble, being careful not to expand -% the column definition -\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}% -\@IEEEappendtoksA{\@IEEEBPcurcolname}% -\@IEEEappendNOEXPANDtoksA{\endcsname}% -\@IEEEappendtoksA{\the\toks0}% -\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax% -\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}% -\@IEEEappendtoksA{\@IEEEBPcurcolname}% -\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax% -\relax\relax\relax\relax\relax\endgroup}% -\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble -\fi%next type not numeral -\fi%next type not glue -} - - -%% -%% END OF IEEEeqnarray DEFINITIONS -%% - - - - -% \IEEEPARstart -% Definition for the big two line drop cap letter at the beginning of the -% first paragraph of journal papers. The first argument is the first letter -% of the first word, the second argument is the remaining letters of the -% first word which will be rendered in upper case. -% In V1.6 this has been completely rewritten to: -% -% 1. no longer have problems when the user begins an environment -% within the paragraph that uses \IEEEPARstart. -% 2. auto-detect and use the current font family -% 3. revise handling of the space at the end of the first word so that -% interword glue will now work as normal. -% 4. produce correctly aligned edges for the (two) indented lines. -% -% We generalize things via control macros - playing with these is fun too. -% -% V1.7 added more control macros to make it easy for IEEEtrantools.sty users -% to change the font style. -% -% the number of lines that are indented to clear it -% may need to increase if using decenders -\providecommand{\IEEEPARstartDROPLINES}{2} -% minimum number of lines left on a page to allow a \@IEEEPARstart -% Does not take into consideration rubber shrink, so it tends to -% be overly cautious -\providecommand{\IEEEPARstartMINPAGELINES}{2} -% V1.7 the height of the drop cap is adjusted to match the height of this text -% in the current font (when \IEEEPARstart is called). -\providecommand{\IEEEPARstartHEIGHTTEXT}{T} -% the depth the letter is lowered below the baseline -% the height (and size) of the letter is determined by the sum -% of this value and the height of the \IEEEPARstartHEIGHTTEXT in the current -% font. It is a good idea to set this value in terms of the baselineskip -% so that it can respond to changes therein. -\providecommand{\IEEEPARstartDROPDEPTH}{1.1\baselineskip} -% V1.7 the font the drop cap will be rendered in, -% can take zero or one argument. -\providecommand{\IEEEPARstartFONTSTYLE}{\bfseries} -% V1.7 any additional, non-font related commands needed to modify -% the drop cap letter, can take zero or one argument. -\providecommand{\IEEEPARstartCAPSTYLE}{\MakeUppercase} -% V1.7 the font that will be used to render the rest of the word, -% can take zero or one argument. -\providecommand{\IEEEPARstartWORDFONTSTYLE}{\relax} -% V1.7 any additional, non-font related commands needed to modify -% the rest of the word, can take zero or one argument. -\providecommand{\IEEEPARstartWORDCAPSTYLE}{\MakeUppercase} -% This is the horizontal separation distance from the drop letter to the main text. -% Lengths that depend on the font (e.g., ex, em, etc.) will be referenced -% to the font that is active when \IEEEPARstart is called. -\providecommand{\IEEEPARstartSEP}{0.15em} -% V1.7 horizontal offset applied to the left of the drop cap. -\providecommand{\IEEEPARstartHOFFSET}{0em} -% V1.7 Italic correction command applied at the end of the drop cap. -\providecommand{\IEEEPARstartITLCORRECT}{\/} - -% width of the letter output, set globally. Can be used in \IEEEPARstartSEP -% or \IEEEPARstartHOFFSET, but not the height lengths. -\newdimen\IEEEPARstartletwidth -\IEEEPARstartletwidth 0pt\relax - -% definition of \IEEEPARstart -% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES -% -% The token \@IEEEPARstartfont will be globally defined after the first use -% of \IEEEPARstart and will be a font command which creates the big letter -% The first argument is the first letter of the first word and the second -% argument is the rest of the first word(s). -\def\IEEEPARstart#1#2{\par{% -% if this page does not have enough space, break it and lets start -% on a new one -\@IEEEtranneedspace{\IEEEPARstartMINPAGELINES\baselineskip}{\relax}% -% V1.7 move this up here in case user uses \textbf for \IEEEPARstartFONTSTYLE -% which uses command \leavevmode which causes an unwanted \indent to be issued -\noindent -% calculate the desired height of the big letter -% it extends from the top of \IEEEPARstartHEIGHTTEXT in the current font -% down to \IEEEPARstartDROPDEPTH below the current baseline -\settoheight{\@IEEEtrantmpdimenA}{\IEEEPARstartHEIGHTTEXT}% -\addtolength{\@IEEEtrantmpdimenA}{\IEEEPARstartDROPDEPTH}% -% extract the name of the current font in bold -% and place it in \@IEEEPARstartFONTNAME -\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}% -{\IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}% -\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}% -% define a font based on this name with a point size equal to the desired -% height of the drop letter -\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax% -% save this value as a counter (integer) value (sp points) -\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA% -% now get the height of the actual letter produced by this font size -\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\IEEEPARstartCAPSTYLE{#1}}% -% If something bogus happens like the first argument is empty or the -% current font is strange, do not allow a zero height. -\ifdim\@IEEEtrantmpdimenB=0pt\relax% -\typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}% -\typeout{ Forcing the drop letter font size to 10pt.}% -\@IEEEtrantmpdimenB=10pt% -\fi% -% and store it as a counter -\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB% -% Since a font size doesn't exactly correspond to the height of the capital -% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB, -% will be less than that desired, \@IEEEtrantmpcountA -% we need to raise the font size, \@IEEEtrantmpdimenA -% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB -% But, TeX doesn't have floating point division, so we have to use integer -% division. Hence the use of the counters. -% We need to reduce the denominator so that the loss of the remainder will -% have minimal affect on the accuracy of the result -\divide\@IEEEtrantmpcountB by 200% -\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB% -% Then reequalize things when we use TeX's ability to multiply by -% floating point values -\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA% -\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA% -% \@IEEEPARstartfont is globaly set to the calculated font of the big letter -% We need to carry this out of the local calculation area to to create the -% big letter. -\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB% -% Now set \@IEEEtrantmpdimenA to the width of the big letter -% We need to carry this out of the local calculation area to set the -% hanging indent -\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont -\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}}}% -% end of the isolated calculation environment -\global\IEEEPARstartletwidth\@IEEEtrantmpdimenA\relax% -% add in the extra clearance we want -\advance\@IEEEtrantmpdimenA by \IEEEPARstartSEP\relax% -% add in the optional offset -\advance\@IEEEtrantmpdimenA by \IEEEPARstartHOFFSET\relax% -% V1.7 don't allow negative offsets to produce negative hanging indents -\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA -\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi -% \@IEEEtrantmpdimenA has the width of the big letter plus the -% separation space and \@IEEEPARstartfont is the font we need to use -% Now, we make the letter and issue the hanging indent command -% The letter is placed in a box of zero width and height so that other -% text won't be displaced by it. -\hangindent\@IEEEtrantmpdimenB\hangafter=-\IEEEPARstartDROPLINES% -\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}% -\raisebox{-\IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\IEEEPARstartHOFFSET}% -\@IEEEPARstartfont\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}% -\hspace{\IEEEPARstartSEP}}}% -{\IEEEPARstartWORDFONTSTYLE{\IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}} - - - - - - -% determines if the space remaining on a given page is equal to or greater -% than the specified space of argument one -% if not, execute argument two (only if the remaining space is greater than zero) -% and issue a \newpage -% -% example: \@IEEEtranneedspace{2in}{\vfill} -% -% Does not take into consideration rubber shrinkage, so it tends to -% be overly cautious -% Based on an example posted by Donald Arseneau -% Note this macro uses \@IEEEtrantmpdimenB internally for calculations, -% so DO NOT PASS \@IEEEtrantmpdimenB to this routine -% if you need a dimen register, import with \@IEEEtrantmpdimenA instead -\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable -\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left -\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left -\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi% -\newpage% -\fi\endgroup} - - -% \IEEEauthorrefmark -\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or% - \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger% - \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}} - - -% V1.3 IEEEQED and IEEEproof -\def\IEEEproofname{Proof} - -\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box -\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}} -\def\IEEEQED{\IEEEQEDclosed} % default to closed - -%V1.8 flag to indicate if QED symbol is to be shown -\newif\if@IEEEQEDshow \@IEEEQEDshowtrue -\def\IEEEproofindentspace{2\parindent}% V1.8 allow user to change indentation amount if desired -% v1.7 name change to avoid namespace collision with amsthm. Also add support -% for an optional argument. -\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}} -\def\@IEEEproof[#1]{\@IEEEQEDshowtrue\par\noindent\hspace{\IEEEproofindentspace}{\itshape #1: }} -\def\endIEEEproof{\if@IEEEQEDshow\hspace*{\fill}\nobreakspace\IEEEQED\fi\par} -% qedhere for equation environments, similar to AMS \qedhere -\def\IEEEQEDhereeqn{\global\@IEEEQEDshowfalse\eqno\let\eqno\relax\let\leqno\relax - \let\veqno\relax\hbox{\IEEEQED}} -% IEEE style qedhere for IEEEeqnarray and other environments -\def\IEEEQEDhere{\global\@IEEEQEDshowfalse\IEEEQED} -% command to disable QED at end of IEEEproof -\def\IEEEQEDoff{\global\@IEEEQEDshowfalse} - - -% Provide support for the control entries of IEEEtran.bst V1.00 and later. -% V1.7 optional argument allows for a different aux file to be specified in -% order to handle multiple bibliographies. For example, with multibib.sty: -% \newcites{sec}{Secondary Literature} -% \bstctlcite[@auxoutsec]{BSTcontrolhak} -% V1.7 I see no need for \providecommand here. -\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}} -\def\@bstctlcite[#1]#2{\@bsphack - \@for\@citeb:=#2\do{% - \edef\@citeb{\expandafter\@firstofone\@citeb}% - \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}% - \@esphack} - -% \IEEEnoauxwrite{} allows for citations that do not add to or affect -% the order of the existing citation list. Can be useful for \cite -% within \thanks{}. -\DeclareRobustCommand{\IEEEnoauxwrite}[1]{\relax -\if@filesw -\@fileswfalse -#1\relax\relax\relax\relax\relax -\@fileswtrue -\else -#1\relax\relax\relax\relax\relax -\fi} - -% need a backslash character for typeout output -{\catcode`\|=0 \catcode`\\=12 -|xdef|@IEEEbackslash{\}} - - -% hook to allow easy disabling of all legacy warnings -\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno). -Use \@IEEEbackslash #2 instead.}} - - -% V1.4 no longer support these legacy commands -% \def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart} -% \let\labelindent\IEEElabelindent -% \def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin} -% \def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth} -% \def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep} -% \def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc} -% \def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl} -% \def\iedlabeljustifyr{\@IEEElegacywarn{iedlabeljustifyr}{IEEEiedlabeljustifyr}\IEEEiedlabeljustifyr} - - -\endinput -%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtrantools.sty %%%%%%%%%%%%%%%%%%%%%% -% That's all folks! - diff --git a/TRUST-docs/acmart.cls b/TRUST-docs/acmart.cls deleted file mode 100755 index cf83c8a..0000000 --- a/TRUST-docs/acmart.cls +++ /dev/null @@ -1,2544 +0,0 @@ -%% -%% This is file `acmart.cls', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% acmart.dtx (with options: `class') -%% -%% IMPORTANT NOTICE: -%% -%% For the copyright see the source file. -%% -%% Any modified versions of this file must be renamed -%% with new filenames distinct from acmart.cls. -%% -%% For distribution of the original source see the terms -%% for copying and modification in the file acmart.dtx. -%% -%% This generated file may be distributed as long as the -%% original source files, as listed above, are part of the -%% same distribution. (The sources need not necessarily be -%% in the same archive or directory.) -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -\NeedsTeXFormat{LaTeX2e} -\ProvidesClass{acmart} -[2017/08/31 v1.47 Typesetting articles for Association of -Computing Machinery] -\def\@classname{acmart} -\InputIfFileExists{acmart-preload-hook.tex}{% - \ClassWarning{\@classname}{% - I am loading acmart-preload-hook.tex. You are fully responsible - for any problems from now on.}}{} -\RequirePackage{xkeyval} -\RequirePackage{xstring} -\define@choicekey*+{acmart.cls}{format}[\ACM@format\ACM@format@nr]{% - manuscript, acmsmall, acmlarge, acmtog, sigconf, siggraph, - sigplan, sigchi, sigchi-a}[manuscript]{}{% - \ClassError{\@classname}{The option format must be manuscript, - acmsmall, acmlarge, acmtog, sigconf, siggraph, - sigplan, sigchi or sigchi-a}} -\def\@DeclareACMFormat#1{\DeclareOptionX{#1}{\setkeys{acmart.cls}{format=#1}}} -\@DeclareACMFormat{manuscript} -\@DeclareACMFormat{acmsmall} -\@DeclareACMFormat{acmlarge} -\@DeclareACMFormat{acmtog} -\@DeclareACMFormat{sigconf} -\@DeclareACMFormat{siggraph} -\@DeclareACMFormat{sigplan} -\@DeclareACMFormat{sigchi} -\@DeclareACMFormat{sigchi-a} -\ExecuteOptionsX{format} -\define@boolkey+{acmart.cls}[@ACM@]{screen}[true]{% - \if@ACM@screen - \PackageInfo{\@classname}{Using screen mode}% - \else - \PackageInfo{\@classname}{Not using screen mode}% - \fi}{\PackageError{\@classname}{Option screen can be either true or - false}} -\ExecuteOptionsX{screen=false} -\define@boolkey+{acmart.cls}[@ACM@]{acmthm}[true]{% - \if@ACM@acmthm - \PackageInfo{\@classname}{Requiring acmthm}% - \else - \PackageInfo{\@classname}{Suppressing acmthm}% - \fi}{\PackageError{\@classname}{Option acmthm can be either true or - false}} -\ExecuteOptionsX{acmthm=true} -\define@boolkey+{acmart.cls}[@ACM@]{review}[true]{% - \if@ACM@review - \PackageInfo{\@classname}{Using review mode}% - \else - \PackageInfo{\@classname}{Not using review mode}% - \fi}{\PackageError{\@classname}{Option review can be either true or - false}} -\ExecuteOptionsX{review=false} -\define@boolkey+{acmart.cls}[@ACM@]{authorversion}[true]{% - \if@ACM@authorversion - \PackageInfo{\@classname}{Using authorversion mode}% - \else - \PackageInfo{\@classname}{Not using authorversion mode}% - \fi}{\PackageError{\@classname}{Option authorversion can be either true or - false}} -\ExecuteOptionsX{authorversion=false} -\define@boolkey+{acmart.cls}[@ACM@]{natbib}[true]{% - \if@ACM@natbib - \PackageInfo{\@classname}{Explicitly selecting natbib mode}% - \else - \PackageInfo{\@classname}{Explicitly deselecting natbib mode}% - \fi}{\PackageError{\@classname}{Option natbib can be either true or - false}} -\ExecuteOptionsX{natbib=true} -\define@boolkey+{acmart.cls}[@ACM@]{anonymous}[true]{% - \if@ACM@anonymous - \PackageInfo{\@classname}{Using anonymous mode}% - \else - \PackageInfo{\@classname}{Not using anonymous mode}% - \fi}{\PackageError{\@classname}{Option anonymous can be either true or - false}} -\ExecuteOptionsX{anonymous=false} -\define@boolkey+{acmart.cls}[@ACM@]{timestamp}[true]{% - \if@ACM@timestamp - \PackageInfo{\@classname}{Using timestamp mode}% - \else - \PackageInfo{\@classname}{Not using timestamp mode}% - \fi}{\PackageError{\@classname}{Option timestamp can be either true or - false}} -\ExecuteOptionsX{timestamp=false} -\define@boolkey+{acmart.cls}[@ACM@]{authordraft}[true]{% - \if@ACM@authordraft - \PackageInfo{\@classname}{Using authordraft mode}% - \@ACM@timestamptrue - \@ACM@reviewtrue - \else - \PackageInfo{\@classname}{Not using authordraft mode}% - \fi}{\PackageError{\@classname}{Option authordraft can be either true or - false}} -\ExecuteOptionsX{authordraft=false} -\def\ACM@fontsize{} -\DeclareOptionX{9pt}{\edef\ACM@fontsize{\CurrentOption}} -\DeclareOptionX{10pt}{\edef\ACM@fontsize{\CurrentOption}} -\DeclareOptionX{11pt}{\edef\ACM@fontsize{\CurrentOption}} -\DeclareOptionX{12pt}{\edef\ACM@fontsize{\CurrentOption}} -\DeclareOptionX{draft}{\PassOptionsToClass{\CurrentOption}{amsart}} -\DeclareOptionX{*}{\PassOptionsToClass{\CurrentOption}{amsart}} -\ProcessOptionsX -\ClassInfo{\@classname}{Using format \ACM@format, number \ACM@format@nr} -\newif\if@ACM@manuscript -\newif\if@ACM@journal -\newif\if@ACM@sigchiamode -\ifnum\ACM@format@nr=5\relax % siggraph - \ClassWarning{\@classname}{The format `siggraph' is now obsolete. - I am switching to sigconf.} - \setkeys{acmart.cls}{format=sigconf} -\fi -\ifnum\ACM@format@nr=0\relax - \@ACM@manuscripttrue -\else - \@ACM@manuscriptfalse -\fi -\@ACM@sigchiamodefalse -\ifcase\ACM@format@nr -\relax % manuscript - \@ACM@journaltrue -\or % acmsmall - \@ACM@journaltrue -\or % acmlarge - \@ACM@journaltrue -\or % acmtog - \@ACM@journaltrue -\or % sigconf - \@ACM@journalfalse -\or % siggraph - \@ACM@journalfalse - \or % sigplan - \@ACM@journalfalse - \or % sigchi - \@ACM@journalfalse -\or % sigchi-a - \@ACM@journalfalse - \@ACM@sigchiamodetrue -\fi -\ifx\ACM@fontsize\@empty - \ifcase\ACM@format@nr - \relax % manuscript - \def\ACM@fontsize{9pt}% - \or % acmsmall - \def\ACM@fontsize{10pt}% - \or % acmlarge - \def\ACM@fontsize{10pt}% - \or % acmtog - \def\ACM@fontsize{9pt}% - \or % sigconf - \def\ACM@fontsize{9pt}% - \or % siggraph - \def\ACM@fontsize{9pt}% - \or % sigplan - \def\ACM@fontsize{10pt}% - \or % sigchi - \def\ACM@fontsize{10pt}% - \or % sigchi-a - \def\ACM@fontsize{10pt}% - \fi -\fi -\ClassInfo{\@classname}{Using fontsize \ACM@fontsize} -\LoadClass[\ACM@fontsize, reqno]{amsart} -\RequirePackage{microtype} -\RequirePackage{etoolbox} -\RequirePackage{refcount} -\RequirePackage{totpages} -\RequirePackage{environ} -\if@ACM@manuscript -\RequirePackage{setspace} -\onehalfspacing -\fi -\RequirePackage{textcase} -\if@ACM@natbib - \RequirePackage{natbib} - \renewcommand{\bibsection}{% - \section*{\refname}% - \phantomsection\addcontentsline{toc}{section}{\refname}% - } - \renewcommand{\bibfont}{\bibliofont} - \renewcommand\setcitestyle[1]{ - \@for\@tempa:=#1\do - {\def\@tempb{round}\ifx\@tempa\@tempb - \renewcommand\NAT@open{(}\renewcommand\NAT@close{)}\fi - \def\@tempb{square}\ifx\@tempa\@tempb - \renewcommand\NAT@open{[}\renewcommand\NAT@close{]}\fi - \def\@tempb{angle}\ifx\@tempa\@tempb - \renewcommand\NAT@open{$<$}\renewcommand\NAT@close{$>$}\fi - \def\@tempb{curly}\ifx\@tempa\@tempb - \renewcommand\NAT@open{\{}\renewcommand\NAT@close{\}}\fi - \def\@tempb{semicolon}\ifx\@tempa\@tempb - \renewcommand\NAT@sep{;}\fi - \def\@tempb{colon}\ifx\@tempa\@tempb - \renewcommand\NAT@sep{;}\fi - \def\@tempb{comma}\ifx\@tempa\@tempb - \renewcommand\NAT@sep{,}\fi - \def\@tempb{authoryear}\ifx\@tempa\@tempb - \NAT@numbersfalse\fi - \def\@tempb{numbers}\ifx\@tempa\@tempb - \NAT@numberstrue\NAT@superfalse\fi - \def\@tempb{super}\ifx\@tempa\@tempb - \NAT@numberstrue\NAT@supertrue\fi - \def\@tempb{nobibstyle}\ifx\@tempa\@tempb - \let\bibstyle=\@gobble\fi - \def\@tempb{bibstyle}\ifx\@tempa\@tempb - \let\bibstyle=\@citestyle\fi - \def\@tempb{sort}\ifx\@tempa\@tempb - \def\NAT@sort{\@ne}\fi - \def\@tempb{nosort}\ifx\@tempa\@tempb - \def\NAT@sort{\z@}\fi - \def\@tempb{compress}\ifx\@tempa\@tempb - \def\NAT@cmprs{\@ne}\fi - \def\@tempb{nocompress}\ifx\@tempa\@tempb - \def\NAT@cmprs{\@z}\fi - \def\@tempb{sort&compress}\ifx\@tempa\@tempb - \def\NAT@sort{\@ne}\def\NAT@cmprs{\@ne}\fi - \def\@tempb{mcite}\ifx\@tempa\@tempb - \let\NAT@merge\@ne\fi - \def\@tempb{merge}\ifx\@tempa\@tempb - \@ifnum{\NAT@merge<\tw@}{\let\NAT@merge\tw@}{}\fi - \def\@tempb{elide}\ifx\@tempa\@tempb - \@ifnum{\NAT@merge<\thr@@}{\let\NAT@merge\thr@@}{}\fi - \def\@tempb{longnamesfirst}\ifx\@tempa\@tempb - \NAT@longnamestrue\fi - \def\@tempb{nonamebreak}\ifx\@tempa\@tempb - \def\NAT@nmfmt#1{\mbox{\NAT@up#1}}\fi - \expandafter\NAT@find@eq\@tempa=\relax\@nil - \if\@tempc\relax\else - \expandafter\NAT@rem@eq\@tempc - \def\@tempb{open}\ifx\@tempa\@tempb - \xdef\NAT@open{\@tempc}\fi - \def\@tempb{close}\ifx\@tempa\@tempb - \xdef\NAT@close{\@tempc}\fi - \def\@tempb{aysep}\ifx\@tempa\@tempb - \xdef\NAT@aysep{\@tempc}\fi - \def\@tempb{yysep}\ifx\@tempa\@tempb - \xdef\NAT@yrsep{\@tempc}\fi - \def\@tempb{notesep}\ifx\@tempa\@tempb - \xdef\NAT@cmt{\@tempc}\fi - \def\@tempb{citesep}\ifx\@tempa\@tempb - \xdef\NAT@sep{\@tempc}\fi - \fi - }% - \NAT@@setcites - } - \renewcommand\citestyle[1]{% - \ifcsname bibstyle@#1\endcsname% - \csname bibstyle@#1\endcsname\let\bibstyle\@gobble% - \else% - \@latex@error{Undefined `#1' citestyle}% - \fi - }% -\fi -\newcommand{\bibstyle@acmauthoryear}{% - \setcitestyle{% - authoryear,% - open={[},close={]},citesep={;},% - aysep={},yysep={,},% - notesep={, }}} -\newcommand{\bibstyle@acmnumeric}{% - \setcitestyle{% - numbers,sort&compress,% - open={[},close={]},citesep={,},% - notesep={, }}} -\if@ACM@natbib -\citestyle{acmnumeric} -\fi -\def\@startsection#1#2#3#4#5#6{% - \if@noskipsec \leavevmode \fi - \par - \@tempskipa #4\relax - \@afterindenttrue - \ifdim \@tempskipa <\z@ - \@tempskipa -\@tempskipa \@afterindentfalse - \fi - \if@nobreak - \everypar{}% - \else - \addpenalty\@secpenalty\addvspace\@tempskipa - \fi - \@ifstar - {\@ssect{#3}{#4}{#5}{#6}}% - {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}} -\def\@sect#1#2#3#4#5#6[#7]#8{% - \edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}% - \ifnum #2>\c@secnumdepth - \let\@svsec\@empty - \else - \refstepcounter{#1}% - \protected@edef\@svsec{\@seccntformat{#1}\relax}% - \fi - \@tempskipa #5\relax - \ifdim \@tempskipa>\z@ - \begingroup - #6{% - \@hangfrom{\hskip #3\relax\@svsec}% - \interlinepenalty \@M #8\@@par}% - \endgroup - \csname #1mark\endcsname{#7}% - \ifnum #2>\c@secnumdepth \else - \@tochangmeasure{\csname the#1\endcsname}% - \fi - \addcontentsline{toc}{#1}{% - \ifnum #2>\c@secnumdepth \else - \protect\numberline{\csname the#1\endcsname}% - \fi - #7}% - \else - \def\@svsechd{% - #6{\hskip #3\relax - \@svsec #8}% - \csname #1mark\endcsname{#7}% - \ifnum #2>\c@secnumdepth \else - \@tochangmeasure{\csname the#1\endcsname\space}% - \fi - \addcontentsline{toc}{#1}{% - \ifnum #2>\c@secnumdepth \else - \protect\numberline{\csname the#1\endcsname}% - \fi - #7}}% - \fi - \@xsect{#5}} -\def\@xsect#1{% - \@tempskipa #1\relax - \ifdim \@tempskipa>\z@ - \par \nobreak - \vskip \@tempskipa - \@afterheading - \else - \@nobreakfalse - \global\@noskipsectrue - \everypar{% - \if@noskipsec - \global\@noskipsecfalse - {\setbox\z@\lastbox}% - \clubpenalty\@M - \begingroup \@svsechd \endgroup - \unskip - \@tempskipa #1\relax - \hskip -\@tempskipa - \else - \clubpenalty \@clubpenalty - \everypar{}% - \fi}% - \fi - \ignorespaces} -\def\@seccntformat#1{\csname the#1\endcsname\quad} -\def\@ssect#1#2#3#4#5{% - \@tempskipa #3\relax - \ifdim \@tempskipa>\z@ - \begingroup - #4{% - \@hangfrom{\hskip #1}% - \interlinepenalty \@M #5\@@par}% - \endgroup - \else - \def\@svsechd{#4{\hskip #1\relax #5}}% - \fi - \@xsect{#3}} -\def\@starttoc#1#2{\begingroup\makeatletter - \setTrue{#1}% - \par\removelastskip\vskip\z@skip - \@startsection{section}\@M\z@{\linespacing\@plus\linespacing}% - {.5\linespacing}{\centering\contentsnamefont}{#2}% - \@input{\jobname.#1}% - \if@filesw - \@xp\newwrite\csname tf@#1\endcsname - \immediate\@xp\openout\csname tf@#1\endcsname \jobname.#1\relax - \fi - \global\@nobreakfalse \endgroup - \addvspace{32\p@\@plus14\p@}% -} -\def\l@section{\@tocline{1}{0pt}{1pc}{2pc}{}} -\def\l@subsection{\@tocline{2}{0pt}{1pc}{3pc}{}} -\def\l@subsubsection{\@tocline{2}{0pt}{1pc}{5pc}{}} -\let\@footnotemark@nolink\@footnotemark -\let\@footnotetext@nolink\@footnotetext -\RequirePackage[bookmarksnumbered,unicode]{hyperref} -\pdfstringdefDisableCommands{% - \def\unskip{}% - \def\textbullet{- }% - \def\textrightarrow{ -> }% - \def\footnotemark{}% -} -\urlstyle{rm} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall -\or % acmlarge -\or % acmtog -\or % sigconf -\or % siggraph -\or % sigplan - \urlstyle{sf} -\or % sigchi -\or % sigchi-a - \urlstyle{sf} -\fi -\AtEndPreamble{% - \if@ACM@screen - \hypersetup{colorlinks, - linkcolor=ACMRed, - citecolor=ACMPurple, - urlcolor=ACMDarkBlue, - filecolor=ACMDarkBlue} - \else - \hypersetup{hidelinks} - \fi} -\if@ACM@natbib - \let\citeN\cite - \let\cite\citep - \let\citeANP\citeauthor - \let\citeNN\citeyearpar - \let\citeyearNP\citeyear - \let\citeyear\citeyearpar - \let\citeNP\citealt - \DeclareRobustCommand\citeA - {\begingroup\NAT@swafalse - \let\NAT@ctype\@ne\NAT@partrue\NAT@fullfalse\NAT@open\NAT@citetp}% - \providecommand\newblock{}% -\else - \AtBeginDocument{% - \let\shortcite\cite% - \providecommand\citename[1]{#1}} -\fi -\newcommand\shortcite[2][]{% - \ifNAT@numbers\cite[#1]{#2}\else\citeyear[#1]{#2}\fi} -\def\bibliographystyle#1{% - \ifx\@begindocumenthook\@undefined\else - \expandafter\AtBeginDocument - \fi - {\if@filesw - \immediate\write\@auxout{\string\bibstyle{#1}}% - \fi}} -\RequirePackage{graphicx, xcolor} -\definecolor[named]{ACMBlue}{cmyk}{1,0.1,0,0.1} -\definecolor[named]{ACMYellow}{cmyk}{0,0.16,1,0} -\definecolor[named]{ACMOrange}{cmyk}{0,0.42,1,0.01} -\definecolor[named]{ACMRed}{cmyk}{0,0.90,0.86,0} -\definecolor[named]{ACMLightBlue}{cmyk}{0.49,0.01,0,0} -\definecolor[named]{ACMGreen}{cmyk}{0.20,0,1,0.19} -\definecolor[named]{ACMPurple}{cmyk}{0.55,1,0,0.15} -\definecolor[named]{ACMDarkBlue}{cmyk}{1,0.58,0,0.21} -\if@ACM@authordraft - \RequirePackage{draftwatermark} - \SetWatermarkFontSize{0.5in} - \SetWatermarkColor[gray]{.9} - \SetWatermarkText{\parbox{12em}{\centering - Unpublished working draft\\ - Not for distribution}} -\fi -\RequirePackage{geometry} -\ifcase\ACM@format@nr -\relax % manuscript - \geometry{letterpaper,head=13pt, - marginparwidth=6pc,heightrounded}% -\or % acmsmall - \geometry{twoside=true, - includeheadfoot, head=13pt, foot=2pc, - paperwidth=6.75in, paperheight=10in, - top=58pt, bottom=44pt, inner=46pt, outer=46pt, - marginparwidth=2pc,heightrounded - }% -\or % acmlarge - \geometry{twoside=true, head=13pt, foot=2pc, - paperwidth=8.5in, paperheight=11in, - includeheadfoot, - top=78pt, bottom=114pt, inner=81pt, outer=81pt, - marginparwidth=4pc,heightrounded - }% -\or % acmtog - \geometry{twoside=true, head=13pt, foot=2pc, - paperwidth=8.5in, paperheight=11in, - includeheadfoot, columnsep=24pt, - top=52pt, bottom=75pt, inner=52pt, outer=52pt, - marginparwidth=2pc,heightrounded - }% -\or % sigconf - \geometry{twoside=true, head=13pt, - paperwidth=8.5in, paperheight=11in, - includeheadfoot, columnsep=2pc, - top=57pt, bottom=73pt, inner=54pt, outer=54pt, - marginparwidth=2pc,heightrounded - }% -\or % siggraph - \geometry{twoside=true, head=13pt, - paperwidth=8.5in, paperheight=11in, - includeheadfoot, columnsep=2pc, - top=57pt, bottom=73pt, inner=54pt, outer=54pt, - marginparwidth=2pc,heightrounded - }% -\or % sigplan - \geometry{twoside=true, head=13pt, - paperwidth=8.5in, paperheight=11in, - includeheadfoot=false, columnsep=2pc, - top=1in, bottom=1in, inner=0.75in, outer=0.75in, - marginparwidth=2pc,heightrounded - }% -\or % sigchi - \geometry{twoside=true, head=13pt, - paperwidth=8.5in, paperheight=11in, - includeheadfoot, columnsep=2pc, - top=66pt, bottom=73pt, inner=54pt, outer=54pt, - marginparwidth=2pc,heightrounded - }% -\or % sigchi-a - \geometry{twoside=false, head=13pt, - paperwidth=11in, paperheight=8.5in, - includeheadfoot, marginparsep=72pt, - marginparwidth=170pt, columnsep=20pt, - top=72pt, bottom=72pt, left=314pt, right=72pt - }% - \@mparswitchfalse - \reversemarginpar -\fi -\setlength\parindent{10\p@} -\setlength\parskip{\z@} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall -\or % acmlarge -\or % acmtog - \setlength\parindent{9\p@}% -\or % sigconf -\or % siggraph -\or % sigplan -\or % sigchi -\or % sigchi-a -\fi -\setlength\normalparindent{\parindent} -\def\copyrightpermissionfootnoterule{\kern-3\p@ - \hrule \@width \columnwidth \kern 2.6\p@} -\RequirePackage{manyfoot} -\SelectFootnoteRule[2]{copyrightpermission} -\DeclareNewFootnote{authorsaddresses} -\SelectFootnoteRule[2]{copyrightpermission} -\DeclareNewFootnote{copyrightpermission} -\def\footnoterule{\kern-3\p@ - \hrule \@width 4pc \kern 2.6\p@} -\def\endminipage{% - \par - \unskip - \ifvoid\@mpfootins\else - \vskip\skip\@mpfootins - \normalcolor - \unvbox\@mpfootins - \fi - \@minipagefalse %% added 24 May 89 - \color@endgroup - \egroup - \expandafter\@iiiparbox\@mpargs{\unvbox\@tempboxa}} -\def\@makefntext{\noindent\@makefnmark} -\if@ACM@sigchiamode -\long\def\@footnotetext#1{\marginpar{% - \reset@font\small - \interlinepenalty\interfootnotelinepenalty - \protected@edef\@currentlabel{% - \csname p@footnote\endcsname\@thefnmark - }% - \color@begingroup - \@makefntext{% - \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}% - \color@endgroup}}% -\fi -\long\def\@mpfootnotetext#1{% - \global\setbox\@mpfootins\vbox{% - \unvbox\@mpfootins - \reset@font\footnotesize - \hsize\columnwidth - \@parboxrestore - \protected@edef\@currentlabel - {\csname p@mpfootnote\endcsname\@thefnmark}% - \color@begingroup\centering - \@makefntext{% - \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}% - \color@endgroup}} -\def\@makefnmark{\hbox{\@textsuperscript{\normalfont\@thefnmark}}} -\def\@textbottom{\vskip \z@ \@plus 1pt} -\let\@texttop\relax -\RequirePackage{iftex} -\ifPDFTeX -\input{glyphtounicode} -\pdfglyphtounicode{f_f}{FB00} -\pdfglyphtounicode{f_f_i}{FB03} -\pdfglyphtounicode{f_f_l}{FB04} -\pdfglyphtounicode{f_i}{FB01} -\pdfglyphtounicode{t_t}{00740074} -\pdfglyphtounicode{f_t}{00660074} -\pdfglyphtounicode{T_h}{00540068} -\pdfgentounicode=1 -\fi -\RequirePackage{cmap} -\newif\if@ACM@newfonts -\@ACM@newfontstrue -\IfFileExists{libertine.sty}{}{\ClassWarning{\@classname}{You do not - 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Publication rights licensed to - Association for Computing Machinery. - \or % rightsretained - Copyright held by the owner/author(s). - \or % usgov - \or % usgovmixed - Association for Computing Machinery. - \or % cagov - Crown in Right of Canada. - \or %cagovmixed - Association for Computing Machinery. - \or %licensedusgovmixed - Copyright held by the owner/author(s). Publication rights licensed to - Association for Computing Machinery. - \or % licensedcagov - Crown in Right of Canada. Publication rights licensed to - Association for Computing Machinery. - \or %licensedcagovmixed - Copyright held by the owner/author(s). Publication rights licensed to - Association for Computing Machinery. - \or % othergov - Association for Computing Machinery. - \or % licensedothergov - Copyright held by the owner/author(s). Publication rights licensed to - Association for Computing Machinery. - \fi} -\def\@formatdoi#1{\url{https://doi.org/#1}} -\def\@copyrightpermission{% - \ifcase\acm@copyrightmode\relax % none - \or % acmcopyright - Permission to make digital or hard copies of all or part of this - work for personal or classroom use is granted without fee provided - that copies are not made or distributed for profit or commercial - advantage and that copies bear this notice and the full citation on - the first page. Copyrights for components of this work owned by - others than ACM must be honored. Abstracting with credit is - permitted. To copy otherwise, or republish, to post on servers or to - redistribute to lists, requires prior specific permission - and\hspace*{.5pt}/or a fee. Request permissions from - permissions@acm.org. - \or % acmlicensed - Permission to make digital or hard copies of all or part of this - work for personal or classroom use is granted without fee provided - that copies are not made or distributed for profit or commercial - advantage and that copies bear this notice and the full citation on - the first page. Copyrights for components of this work owned by - others than the author(s) must be honored. Abstracting with credit - is permitted. To copy otherwise, or republish, to post on servers - or to redistribute to lists, requires prior specific permission - and\hspace*{.5pt}/or a fee. Request permissions from - permissions@acm.org. - \or % rightsretained - Permission to make digital or hard copies of part or all of this work - for personal or classroom use is granted without fee provided that - copies are not made or distributed for profit or commercial advantage - and that copies bear this notice and the full citation on the first - page. Copyrights for third-party components of this work must be - honored. For all other uses, contact the - owner\hspace*{.5pt}/author(s). - \or % usgov - This paper is authored by an employee(s) of the United States - Government and is in the public domain. Non-exclusive copying or - redistribution is allowed, provided that the article citation is - given and the authors and agency are clearly identified as its - source. - \or % usgovmixed - ACM acknowledges that this contribution was authored or co-authored - by an employee, contractor, or affiliate of the United States government. As such, - the United States government retains a nonexclusive, royalty-free right to - publish or reproduce this article, or to allow others to do so, for - government purposes only. - \or % cagov - This article was authored by employees of the Government of Canada. - As such, the Canadian government retains all interest in the - copyright to this work and grants to ACM a nonexclusive, - royalty-free right to publish or reproduce this article, or to allow - others to do so, provided that clear attribution is given both to - the authors and the Canadian government agency employing them. - Permission to make digital or hard copies for personal or classroom - use is granted. Copies must bear this notice and the full citation - on the first page. Copyrights for components of this work owned by - others than the Canadian Government must be honored. To copy - otherwise, distribute, republish, or post, requires prior specific - permission and\hspace*{.5pt}/or a fee. Request permissions from - permissions@acm.org. - \or % cagovmixed - ACM acknowledges that this contribution was co-authored by an - affiliate of the national government of Canada. As such, the Crown - in Right of Canada retains an equal interest in the copyright. - Reprints must include clear attribution to ACM and the author's - government agency affiliation. Permission to make digital or hard - copies for personal or classroom use is granted. Copies must bear - this notice and the full citation on the first page. Copyrights for - components of this work owned by others than ACM must be honored. - To copy otherwise, distribute, republish, or post, requires prior - specific permission and\hspace*{.5pt}/or a fee. Request permissions - from permissions@acm.org. - \or % licensedusgovmixed - Publication rights licensed to ACM\@. ACM acknowledges that this - contribution was authored or co-authored by an employee, contractor - or affiliate of the United States government. As such, the - Government retains a nonexclusive, royalty-free right to publish or - reproduce this article, or to allow others to do so, for Government - purposes only. - \or % licensedcagov - This article was authored by employees of the Government of Canada. - As such, the Canadian government retains all interest in the - copyright to this work and grants to ACM a nonexclusive, - royalty-free right to publish or reproduce this article, or to allow - others to do so, provided that clear attribution is given both to - the authors and the Canadian government agency employing them. - Permission to make digital or hard copies for personal or classroom - use is granted. Copies must bear this notice and the full citation - on the first page. Copyrights for components of this work owned by - others than the Canadian Government must be honored. To copy - otherwise, distribute, republish, or post, requires prior specific - permission and\hspace*{.5pt}/or a fee. Request permissions from - permissions@acm.org. - \or % licensedcagovmixed - Publication rights licensed to ACM\@. ACM acknowledges that this - contribution was authored or co-authored by an employee, contractor - or affiliate of the national government of Canada. As such, the - Government retains a nonexclusive, royalty-free right to publish or - reproduce this article, or to allow others to do so, for Government - purposes only. - \or % othergov - ACM acknowledges that this contribution was authored or co-authored - by an employee, contractor or affiliate of a national government. As - such, the Government retains a nonexclusive, royalty-free right to - publish or reproduce this article, or to allow others to do so, for - Government purposes only. - \or % licensedothergov - Publication rights licensed to ACM\@. ACM acknowledges that this - contribution was authored or co-authored by an employee, contractor - or affiliate of a national government. As such, the Government - retains a nonexclusive, royalty-free right to publish or reproduce - this article, or to allow others to do so, for Government purposes - only. - \fi} -\def\copyrightyear#1{\def\@copyrightyear{#1}} -\copyrightyear{\@acmYear} -\def\@teaserfigures{} -\newenvironment{teaserfigure}{\Collect@Body\@saveteaser}{} -\long\def\@saveteaser#1{\g@addto@macro\@teaserfigures{\@teaser{#1}}} -\renewcommand{\thanks}[1]{% - \@ifnotempty{#1}{% - \if@ACM@anonymous - \g@addto@macro\thankses{\thanks{A note}}% - \else - \g@addto@macro\thankses{\thanks{#1}}% - \fi}} -\newbox\mktitle@bx -\def\maketitle{% - \if@ACM@anonymous - % Anonymize omission of \author-s - \ifnum\num@authorgroups=0\author{}\fi - \fi - \begingroup - \let\@footnotemark\@footnotemark@nolink - \let\@footnotetext\@footnotetext@nolink - \renewcommand\thefootnote{\@fnsymbol\c@footnote}% - \global\@topnum\z@ % this prevents floats from falling - % at the top of page 1 - \global\@botnum\z@ % we do not want them to be on bottom either - \hsize=\textwidth - \def\@makefnmark{\hbox{\@textsuperscript{\@thefnmark}}}% - \@mktitle\if@ACM@sigchiamode\else\@mkauthors\fi\@mkteasers - \@printtopmatter - \if@ACM@sigchiamode\@mkauthors\fi - \setcounter{footnote}{0}% - \def\@makefnmark{\hbox{\@textsuperscript{\normalfont\@thefnmark}}}% - \@titlenotes - \@subtitlenotes - \@authornotes - \let\@makefnmark\relax \let\@thefnmark\relax - \let\@makefntext\noindent - \ifx\@empty\thankses\else - \footnotetextauthorsaddresses{% - \def\par{\let\par\@par}\parindent\z@\@setthanks}% - \fi - \ifx\@empty\@authorsaddresses\else - \if@ACM@anonymous\else - \if@ACM@journal - \footnotetextauthorsaddresses{% - \def\par{\let\par\@par}\parindent\z@\@setauthorsaddresses}% - \fi - \fi - \fi - \footnotetextcopyrightpermission{% - \if@ACM@authordraft - \raisebox{-2ex}[\z@][\z@]{\makebox[0pt][l]{\large\bfseries - Unpublished - working draft. Not for distribution}}% - \color[gray]{0.9}% - \fi - \parindent\z@\parskip0.1\baselineskip - \if@ACM@authorversion\else - \if@printpermission\@copyrightpermission\par\fi - \fi - \if@ACM@manuscript\else - \if@ACM@journal\else % Print the conference information - {\itshape \acmConference@shortname, \acmConference@date, \acmConference@venue}\par - \fi - \fi - \if@printcopyright - \copyright\ \@copyrightyear\ \@copyrightowner\\ - \else - \@copyrightyear.\ - \fi - \if@ACM@manuscript - Manuscript submitted to ACM\\ - \else - \if@ACM@authorversion - This is the author's version of the work. It is posted here for - your personal use. Not for redistribution. The definitive Version - of Record was published in - \if@ACM@journal - \emph{\@journalName}% - \else - \emph{\@acmBooktitle}% - \fi - \ifx\@acmDOI\@empty - . - \else - , \@formatdoi{\@acmDOI}. - \fi\\ - \else - \if@ACM@journal - \@permissionCodeOne/\@acmYear/\@acmMonth-ART\@acmArticle - \ifx\@acmPrice\@empty\else\ \$\@acmPrice\fi\\ - \@formatdoi{\@acmDOI}% - \else % Conference - \ifx\@acmISBN\@empty\else ACM~ISBN~\@acmISBN - \ifx\@acmPrice\@empty.\else\dots\$\@acmPrice\fi\\\fi - \ifx\@acmDOI\@empty\else\@formatdoi{\@acmDOI}\fi% - \fi - \fi - \fi} - \endgroup - \setcounter{footnote}{0}% - \@mkabstract - \if@ACM@printccs - \ifx\@concepts\@empty\else\bgroup - {\@specialsection{CCS Concepts}% - \@concepts\par}\egroup - \fi - \fi - \ifx\@keywords\@empty\else\bgroup - {\if@ACM@journal - \@specialsection{Additional Key Words and Phrases}% - \else - \@specialsection{Keywords}% - \fi - \@keywords}\par\egroup - \fi - \andify\authors - \andify\shortauthors - \global\let\authors=\authors - \global\let\shortauthors=\shortauthors - \if@ACM@printacmref - \@mkbibcitation - \fi - \hypersetup{pdfauthor={\authors}, - pdftitle={\@title}, - pdfsubject={\@concepts}, - pdfkeywords={\@keywords}}% - \@printendtopmatter - \@afterindentfalse - \@afterheading -} -\def\@specialsection#1{% - \ifcase\ACM@format@nr - \relax % manuscript - \par\medskip\small\noindent#1: % - \or % acmsmall - \par\medskip\small\noindent#1: % - \or % acmlarge - \par\medskip\small\noindent#1: % - \or % acmtog - \par\medskip\small\noindent#1: % - \or % sigconf - \section*{#1}% - \or % siggraph - \section*{#1}% - \or % sigplan - \paragraph*{#1}% - \or % sigchi - \section*{#1}% - \or % sigchi-a - \section*{#1}% - \fi} -\def\@printtopmatter{% - \ifx\@startPage\@empty - \gdef\@startPage{1}% - \else - \setcounter{page}{\@startPage}% - \fi - \thispagestyle{firstpagestyle}% - \noindent - \ifcase\ACM@format@nr - \relax % manuscript - \box\mktitle@bx\par - \or % acmsmall - \box\mktitle@bx\par - \or % acmlarge - \box\mktitle@bx\par - \or % acmtog - \twocolumn[\box\mktitle@bx]% - \or % sigconf - \twocolumn[\box\mktitle@bx]% - \or % siggraph - \twocolumn[\box\mktitle@bx]% - \or % sigplan - \twocolumn[\box\mktitle@bx]% - \or % sigchi - \twocolumn[\box\mktitle@bx]% - \or % sigchi-a - \par\box\mktitle@bx\par\bigskip - \if@ACM@badge - \marginpar{\noindent - \ifx\@acmBadgeL@image\@empty\else - \href{\@acmBadgeL@url}{% - \includegraphics[width=\@ACM@badge@width]{\@acmBadgeL@image}}% - \hskip\@ACM@badge@skip - \fi - \ifx\@acmBadgeR@image\@empty\else - \href{\@acmBadgeR@url}{% - \includegraphics[width=\@ACM@badge@width]{\@acmBadgeR@image}}% - \fi}% - \fi - \fi -} -\def\@mktitle{% - \ifcase\ACM@format@nr - \relax % manuscript - \@mktitle@i - \or % acmsmall - \@mktitle@i - \or % acmlarge - \@mktitle@i - \or % acmtog - \@mktitle@i - \or % sigconf - \@mktitle@iii - \or % siggraph - \@mktitle@iii - \or % sigplan - \@mktitle@iii - \or % sigchi - \@mktitle@iii - \or % sigchi-a - \@mktitle@iv - \fi -} -\def\@titlefont{% - \ifcase\ACM@format@nr - \relax % manuscript - \LARGE\sffamily\bfseries - \or % acmsmall - \LARGE\sffamily\bfseries - \or % acmlarge - \LARGE\sffamily\bfseries - \or % acmtog - \Huge\sffamily - \or % sigconf - \Huge\sffamily\bfseries - \or % siggraph - \Huge\sffamily\bfseries - \or % sigplan - \Huge\bfseries - \or % sigchi - \Huge\sffamily\bfseries - \or % sigchi-a - \Huge\bfseries - \fi} -\def\@subtitlefont{\normalsize - \ifcase\ACM@format@nr - \relax % manuscript - \mdseries - \or % acmsmall - \mdseries - \or % acmlarge - \mdseries - \or % acmtog - \LARGE - \or % sigconf - \LARGE\mdseries - \or % siggraph - \LARGE\mdseries - \or % sigplan - \LARGE\mdseries - \or % sigchi - \LARGE\mdseries - \or % sigchi-a - \mdseries - \fi} -\def\@mktitle@i{\hsize=\textwidth - \@ACM@title@width=\hsize - \ifx\@acmBadgeL@image\@empty\else - \advance\@ACM@title@width by -\@ACM@badge@width - \advance\@ACM@title@width by -\@ACM@badge@skip - \fi - \ifx\@acmBadgeR@image\@empty\else - \advance\@ACM@title@width by -\@ACM@badge@width - \advance\@ACM@title@width by -\@ACM@badge@skip - \fi - \setbox\mktitle@bx=\vbox{\noindent\@titlefont - \ifx\@acmBadgeL@image\@empty\else - \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeL@url}{% - \includegraphics[width=\@ACM@badge@width]{\@acmBadgeL@image}}}% - \hskip\@ACM@badge@skip - \fi - \parbox[t]{\@ACM@title@width}{\raggedright - \@titlefont\noindent - \@title - \ifx\@subtitle\@empty\else - \par\noindent{\@subtitlefont\@subtitle} - \fi}% - \ifx\@acmBadgeR@image\@empty\else - \hskip\@ACM@badge@skip - \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeR@url}{% - \includegraphics[width=\@ACM@badge@width]{\@acmBadgeR@image}}}% - \fi - \par\bigskip}}% -\def\@mktitle@iii{\hsize=\textwidth - \setbox\mktitle@bx=\vbox{\@titlefont\centering - \@ACM@title@width=\hsize - \if@ACM@badge - \advance\@ACM@title@width by -2\@ACM@badge@width - \advance\@ACM@title@width by -2\@ACM@badge@skip - \parbox[b]{\@ACM@badge@width}{\strut - \ifx\@acmBadgeL@image\@empty\else - \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeL@url}{% - \includegraphics[width=\@ACM@badge@width]{\@acmBadgeL@image}}}% - \fi}% - \hskip\@ACM@badge@skip - \fi - \parbox[t]{\@ACM@title@width}{\centering\@titlefont - \@title - \ifx\@subtitle\@empty\else - \par\noindent{\@subtitlefont\@subtitle} - \fi - }% - \if@ACM@badge - \hskip\@ACM@badge@skip - \parbox[b]{\@ACM@badge@width}{\strut - \ifx\@acmBadgeR@image\@empty\else - \raisebox{-.5\baselineskip}[\z@][\z@]{\href{\@acmBadgeR@url}{% - \includegraphics[width=\@ACM@badge@width]{\@acmBadgeR@image}}}% - \fi}% - \fi - \par\bigskip}}% -\def\@mktitle@iv{\hsize=\textwidth - \setbox\mktitle@bx=\vbox{\raggedright\leftskip5pc\@titlefont - \noindent\leavevmode\leaders\hrule height 2pt\hfill\kern0pt\par - \noindent\@title - \ifx\@subtitle\@empty\else - \par\noindent\@subtitlefont\@subtitle - \fi - \par\bigskip}}% -\newbox\@ACM@commabox -\def\@ACM@addtoaddress#1{% - \ifvmode\else - \if@ACM@affiliation@obeypunctuation\else - \setbox\@ACM@commabox=\hbox{, }% - \unskip\cleaders\copy\@ACM@commabox\hskip\wd\@ACM@commabox - \fi\fi - #1} -\def\streetaddress#1{\unskip\ignorespaces} -\def\postcode#1{\unskip\ignorespaces} -\if@ACM@journal - \def\position#1{\unskip\ignorespaces} - \def\institution#1{\unskip~#1\ignorespaces} - \def\city#1{\unskip\ignorespaces} - \def\state#1{\unskip\ignorespaces} - \newcommand\department[2][0]{\unskip\ignorespaces} - \def\country#1{\if@ACM@affiliation@obeypunctuation\else, \fi#1\ignorespaces} -\else - \def\position#1{\if@ACM@affiliation@obeypunctuation#1\else#1\par\fi}% - \def\institution#1{\if@ACM@affiliation@obeypunctuation#1\else#1\par\fi}% - \newcommand\department[2][0]{\if@ACM@affiliation@obeypunctuation - #2\else#2\par\fi}% - \let\city\@ACM@addtoaddress - \let\state\@ACM@addtoaddress - \let\country\@ACM@addtoaddress -\fi -\def\@mkauthors{\begingroup - \hsize=\textwidth - \ifcase\ACM@format@nr - \relax % manuscript - \@mkauthors@i - \or % acmsmall - \@mkauthors@i - \or % acmlarge - \@mkauthors@i - \or % acmtog - \@mkauthors@i - \or % sigconf - \@mkauthors@iii - \or % siggraph - \@mkauthors@iii - \or % sigplan - \@mkauthors@iii - \or % sigchi - \@mkauthors@iii - \or % sigchi-a - \@mkauthors@iv - \fi - \endgroup -} -\def\@authorfont{\Large\sffamily} -\def\@affiliationfont{\normalsize\normalfont} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall - \def\@authorfont{\large\sffamily} - \def\@affiliationfont{\small\normalfont} -\or % acmlarge -\or % acmtog - \def\@authorfont{\LARGE\sffamily} - \def\@affiliationfont{\large} -\or % sigconf - \def\@authorfont{\LARGE} - \def\@affiliationfont{\large} -\or % siggraph - \def\@authorfont{\normalsize\normalfont} - \def\@affiliationfont{\normalsize\normalfont} -\or % sigplan - \def\@authorfont{\Large\normalfont} - \def\@affiliationfont{\normalsize\normalfont} -\or % sigchi - \def\@authorfont{\bfseries} - \def\@affiliationfont{\mdseries} -\or % sigchi-a - \def\@authorfont{\bfseries} - \def\@affiliationfont{\mdseries} -\fi -\def\@typeset@author@line{% - \andify\@currentauthors\par\noindent - \@currentauthors\def\@currentauthors{}% - \ifx\@currentaffiliations\@empty\else - \andify\@currentaffiliations - \unskip, {\@currentaffiliations}\par - \fi - \def\@currentaffiliations{}} -\def\@mkauthors@i{% - \def\@currentauthors{}% - \def\@currentaffiliations{}% - \global\let\and\@typeset@author@line - \def\@author##1{% - \ifx\@currentauthors\@empty - \gdef\@currentauthors{\@authorfont\MakeTextUppercase{##1}}% - \else - \g@addto@macro{\@currentauthors}{\and\MakeTextUppercase{##1}}% - \fi - \gdef\and{}}% - \def\email##1##2{}% - \def\affiliation##1##2{% - \def\@tempa{##2}\ifx\@tempa\@empty\else - \ifx\@currentaffiliations\@empty - \gdef\@currentaffiliations{% - \setkeys{@ACM@affiliation@}{obeypunctuation=false}% - \setkeys{@ACM@affiliation@}{##1}% - \@affiliationfont##2}% - \else - \g@addto@macro{\@currentaffiliations}{\and - \setkeys{@ACM@affiliation@}{obeypunctuation=false}% - \setkeys{@ACM@affiliation@}{##1}##2}% - \fi - \fi - \global\let\and\@typeset@author@line}% - \global\setbox\mktitle@bx=\vbox{\noindent\box\mktitle@bx\par\medskip - \noindent\addresses\@typeset@author@line - \par\medskip}% -} -\newbox\author@bx -\newdimen\author@bx@wd -\newskip\author@bx@sep -\author@bx@sep=1pc\relax -\def\@typeset@author@bx{\bgroup\hsize=\author@bx@wd\def\and{\par}% - \global\setbox\author@bx=\vtop{\if@ACM@sigchiamode\else\centering\fi - \@authorfont\@currentauthors\par\@affiliationfont - \@currentaffiliation}\egroup - \box\author@bx\hspace{\author@bx@sep}% - \gdef\@currentauthors{}% - \gdef\@currentaffiliation{}} -\def\@mkauthors@iii{% - \author@bx@wd=\textwidth\relax - \advance\author@bx@wd by -\author@bx@sep\relax - \ifnum\@ACM@authorsperrow>0\relax - \divide\author@bx@wd by \@ACM@authorsperrow\relax - \else - \ifcase\num@authorgroups - \relax % 0? - \or % 1=one author per row - \or % 2=two authors per row - \divide\author@bx@wd by \num@authorgroups\relax - \or % 3=three authors per row - \divide\author@bx@wd by \num@authorgroups\relax - \or % 4=two authors per row (!) - \divide\author@bx@wd by 2\relax - \else % three authors per row - \divide\author@bx@wd by 3\relax - \fi - \fi - \advance\author@bx@wd by -\author@bx@sep\relax - \gdef\@currentauthors{}% - \gdef\@currentaffiliation{}% - \def\@author##1{\ifx\@currentauthors\@empty - \gdef\@currentauthors{\par##1}% - \else - \g@addto@macro\@currentauthors{\par##1}% - \fi - \gdef\and{}}% - \def\email##1##2{\ifx\@currentaffiliation\@empty - \gdef\@currentaffiliation{\nolinkurl{##2}}% - \else - \g@addto@macro\@currentaffiliation{\par\nolinkurl{##2}}% - \fi}% - \def\affiliation##1##2{\ifx\@currentaffiliation\@empty - \gdef\@currentaffiliation{% - \setkeys{@ACM@affiliation@}{obeypunctuation=false}% - \setkeys{@ACM@affiliation@}{##1}##2}% - \else - \g@addto@macro\@currentaffiliation{\par - \setkeys{@ACM@affiliation@}{obeypunctuation=false}% - \setkeys{@ACM@affiliation@}{##1}##2}% - \fi - \global\let\and\@typeset@author@bx -}% - \hsize=\textwidth - \global\setbox\mktitle@bx=\vbox{\noindent - \box\mktitle@bx\par\medskip\leavevmode - \lineskip=1pc\relax\centering\hspace*{-1em}% - \addresses\let\and\@typeset@author@bx\and\par\bigskip}} -\def\@mkauthors@iv{% - \author@bx@wd=\columnwidth\relax - \advance\author@bx@wd by -\author@bx@sep\relax - \ifnum\@ACM@authorsperrow>0\relax - \divide\author@bx@wd by \@ACM@authorsperrow\relax - \else - \ifcase\num@authorgroups - \relax % 0? - \or % 1=one author per row - \else % 2=two authors per row - \divide\author@bx@wd by 2\relax - \fi - \fi - \advance\author@bx@wd by -\author@bx@sep\relax - \gdef\@currentauthors{}% - \gdef\@currentaffiliation{}% - \def\@author##1{\ifx\@currentauthors\@empty - \gdef\@currentauthors{\par##1}% - \else - \g@addto@macro\@currentauthors{\par##1}% - \fi - \gdef\and{}}% - \def\email##1##2{\ifx\@currentaffiliation\@empty - \gdef\@currentaffiliation{\nolinkurl{##2}}% - \else - \g@addto@macro\@currentaffiliation{\par\nolinkurl{##2}}% - \fi}% - \def\affiliation##1##2{\ifx\@currentaffiliation\@empty - \gdef\@currentaffiliation{% - \setkeys{@ACM@affiliation@}{obeypunctuation=false}% - \setkeys{@ACM@affiliation@}{##1}##2}% - \else - \g@addto@macro\@currentaffiliation{\par - \setkeys{@ACM@affiliation@}{obeypunctuation=false}% - \setkeys{@ACM@affiliation@}{##1}##2}% - \fi - \global\let\and\@typeset@author@bx}% - \bgroup\hsize=\columnwidth - \par\raggedright\leftskip=\z@ - \lineskip=1pc\noindent - \addresses\let\and\@typeset@author@bx\and\par\bigskip\egroup} -\def\@mkauthorsaddresses{% - \ifnum\num@authors>1\relax - Authors' \else Author's \fi - \ifnum\num@authorgroups>1\relax - addresses: \else address: \fi - \bgroup - \def\streetaddress##1{\unskip\@addpunct, ##1}% - \def\postcode##1{\unskip\@addpunct, ##1}% - \def\position##1{\unskip\ignorespaces}% - \def\institution##1{\unskip\@addpunct, ##1}% - \def\city##1{\unskip\@addpunct, ##1}% - \def\state##1{\unskip\@addpunct, ##1}% - \renewcommand\department[2][0]{\unskip\@addpunct, ##2}% - \def\country##1{\unskip\@addpunct, ##1}% - \def\and{\unskip\@addpunct; }% - \def\@author##1{##1}% - \def\email##1##2{\unskip\@addpunct, \nolinkurl{##2}}% - \addresses - \egroup} -\def\@setaddresses{} -\def\@authornotemark{\g@addto@macro\@currentauthors{\footnotemark\relax}} -\def\@@authornotemark#1{\g@addto@macro\@currentauthors{\footnotemark[#1]}} -\def\@mkteasers{% - \ifx\@teaserfigures\@empty\else - \def\@teaser##1{\par\bigskip\bgroup - \captionsetup{type=figure}##1\egroup\par} - \global\setbox\mktitle@bx=\vbox{\noindent\box\mktitle@bx\par - \noindent\@teaserfigures\par\medskip}% - \fi} -\def\@mkabstract{\bgroup - \ifx\@abstract\@lempty\else - {\phantomsection\addcontentsline{toc}{section}{Abstract}% - \if@ACM@journal - \small\noindent - \else - \section*{Abstract}% - \fi - \ignorespaces\@abstract\par}% - \fi\egroup} -\def\@mkbibcitation{\bgroup - \def\@pages@word{\ifnum\getrefnumber{TotPages}=1\relax page\else pages\fi}% - \def\footnotemark{}% - \def\\{\unskip{} \ignorespaces}% - \def\footnote{\ClassError{\@classname}{Please do note use footnotes - inside \string\title{} or \string\author{} command! Use - \string\titlenote{} or \string\authornote{} instead!}}% - \def\@article@string{\ifx\@acmArticle\@empty{\ }\else, - Article~\@acmArticle\ \fi}% - \par\medskip\small\noindent{\bfseries ACM Reference Format:}\par\nobreak - \noindent\authors. \@acmYear. \@title - \ifx\@subtitle\@empty. \else: \@subtitle. \fi - \if@ACM@journal - \textit{\@journalNameShort} - \@acmVolume, \@acmNumber \@article@string (\@acmPubDate), - \ref{TotPages}~\@pages@word. - \else - In \textit{\@acmBooktitle}% - \ifx\@acmEditors\@empty\textit{.}\else - \andify\@acmEditors\textit{, }\@acmEditors~\@editorsAbbrev.% - \fi\ - ACM, New York, NY, USA% - \@article@string\unskip, \ref{TotPages}~\@pages@word. - \fi - \@formatdoi{\@acmDOI} -\par\egroup} -\def\@printendtopmatter{\par\bigskip} -\def\@setthanks{\long\def\thanks##1{\par##1\@addpunct.}\thankses} -\def\@setauthorsaddresses{\@authorsaddresses\unskip\@addpunct.} -\RequirePackage{fancyhdr} -\if@ACM@review - \newsavebox{\ACM@linecount@bx} - \newlength\ACM@linecount@bxht - \newcount\ACM@linecount - \ACM@linecount\@ne\relax - \def\ACM@mk@linecount{% - \savebox{\ACM@linecount@bx}[4em][t]{\parbox[t]{4em}{% - \setlength{\ACM@linecount@bxht}{0pt}% - \loop{\color{red}\scriptsize\the\ACM@linecount}\\ - \global\advance\ACM@linecount by \@ne - \addtolength{\ACM@linecount@bxht}{\baselineskip}% - \ifdim\ACM@linecount@bxht<\textheight\repeat - {\color{red}\scriptsize\the\ACM@linecount}\hfill - \global\advance\ACM@linecount by \@ne}}} -\fi -\def\ACM@linecountL{% - \if@ACM@review - \ACM@mk@linecount - \begin{picture}(0,0)% - \put(-26,-22){\usebox{\ACM@linecount@bx}}% - \end{picture}% - \fi} -\def\ACM@linecountR{% - \if@ACM@review - \ACM@mk@linecount - \begin{picture}(0,0)% - \put(20,-22){\usebox{\ACM@linecount@bx}}% - \end{picture}% - \fi} -\if@ACM@timestamp - % Subtracting 30 from \time gives us the effect of rounding-down despite - % \numexpr rounding to nearest - \newcounter{ACM@time@hours} - \setcounter{ACM@time@hours}{\numexpr (\time - 30) / 60 \relax} - \newcounter{ACM@time@minutes} - \setcounter{ACM@time@minutes}{\numexpr \time - \theACM@time@hours * 60 \relax} - \newcommand\ACM@timestamp{% - \footnotesize% - \the\year-\two@digits{\the\month}-\two@digits{\the\day}{ }% - \two@digits{\theACM@time@hours}:\two@digits{\theACM@time@minutes}{ }% - page~\thepage\ (pp. \@startPage-\pageref*{TotPages})% - \ifx\@acmSubmissionID\@empty\relax\else - ~Submission~ID: \@acmSubmissionID - \fi - } -\fi -\def\@shortauthors{\if@ACM@anonymous Anon.\else\shortauthors\fi} -\def\@headfootfont{% - \ifcase\ACM@format@nr - \relax % manuscript - \sffamily - \or % acmsmall - \sffamily - \or % acmlarge - \sffamily - \or % acmtog - \sffamily - \or % sigconf - \sffamily - \or % siggraph - \sffamily - \or % sigplan - \sffamily - \or % sigchi - \sffamily - \or % sigchi-a - \sffamily - \fi} -\fancypagestyle{standardpagestyle}{% - \fancyhf{}% - \renewcommand{\headrulewidth}{\z@}% - \renewcommand{\footrulewidth}{\z@}% - \ifcase\ACM@format@nr - \relax % manuscript - \fancyhead[LE]{\ACM@linecountL\if@ACM@printfolios\thepage\fi}% - \fancyhead[RO]{\if@ACM@printfolios\thepage\fi}% - \fancyhead[RE]{\@shortauthors}% - \fancyhead[LO]{\ACM@linecountL\shorttitle}% - \fancyfoot[RO,LE]{\footnotesize Manuscript submitted to ACM}% - \or % acmsmall - \fancyhead[LE]{\ACM@linecountL\@headfootfont\@acmArticle\if@ACM@printfolios:\thepage\fi}% - \fancyhead[RO]{\@headfootfont\@acmArticle\if@ACM@printfolios:\thepage\fi}% - \fancyhead[RE]{\@headfootfont\@shortauthors}% - \fancyhead[LO]{\ACM@linecountL\@headfootfont\shorttitle}% - \fancyfoot[RO,LE]{\footnotesize \@journalName, Vol. \@acmVolume, No. - \@acmNumber, Article \@acmArticle. 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Publication date: - \@acmPubDate.}% - \fancyhead[L]{\ACM@linecountL}% - \fancyhead[R]{\ACM@linecountR}% - \else % Conference proceedings - \fancyhead[L]{\ACM@linecountL}% - \fancyhead[R]{\ACM@linecountR}% - \fancyfoot[C]{\if@ACM@printfolios\footnotesize\thepage\fi}% - \fi - \if@ACM@timestamp - \ifnum\ACM@format@nr=0\relax % Manuscript - \fancyfoot[LO,RE]{\ACM@timestamp\quad - \footnotesize Manuscript submitted to ACM} - \else - \fancyfoot[LO,RE]{\ACM@timestamp} - \fi - \fi -} -\let\ACM@ps@plain\ps@plain -\let\ACM@ps@myheadings\ps@myheadings -\let\ACM@ps@headings\ps@headings -\def\ACM@restore@pagestyle{% - \let\ps@plain\ACM@ps@plain - \let\ps@myheadings\ACM@ps@myheadings - \let\ps@headings\ACM@ps@headings} -\AtBeginDocument{\ACM@restore@pagestyle} -\renewcommand\section{\@startsection{section}{1}{\z@}% - {-.75\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {.25\baselineskip}% - {\@secfont}} -\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% - {-.75\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {.25\baselineskip}% - {\@subsecfont}} -\renewcommand\subsubsection{\@startsection{subsubsection}{3}{10pt}% - {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {-3.5\p@}% - {\@subsubsecfont\@adddotafter}} -\renewcommand\paragraph{\@startsection{paragraph}{4}{\parindent}% - {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {-3.5\p@}% - {\@parfont\@adddotafter}} -\renewcommand\part{\@startsection{part}{9}{\z@}% - {-10\p@ \@plus -4\p@ \@minus -2\p@}% - {4\p@}% - {\@parfont}} -\def\section@raggedright{\@rightskip\@flushglue - \rightskip\@rightskip - \leftskip\z@skip - \parindent\z@} -\def\@secfont{\sffamily\bfseries\section@raggedright\MakeTextUppercase} -\def\@subsecfont{\sffamily\bfseries\section@raggedright} -\def\@subsubsecfont{\sffamily\itshape} -\def\@parfont{\itshape} -\setcounter{secnumdepth}{3} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall -\or % acmlarge - \def\@secfont{\sffamily\large\section@raggedright\MakeTextUppercase} - \def\@subsecfont{\sffamily\large\section@raggedright} -\or % acmtog - \def\@secfont{\sffamily\large\section@raggedright\MakeTextUppercase} - \def\@subsecfont{\sffamily\large\section@raggedright} -\or % sigconf - \def\@secfont{\bfseries\Large\section@raggedright\MakeTextUppercase} - \def\@subsecfont{\bfseries\Large\section@raggedright} -\or % siggraph - \def\@secfont{\sffamily\bfseries\Large\section@raggedright\MakeTextUppercase} - \def\@subsecfont{\sffamily\bfseries\Large\section@raggedright} -\or % sigplan - \def\@secfont{\bfseries\Large\section@raggedright} - \def\@subsecfont{\bfseries\section@raggedright} - \renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% - {-.75\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {.25\baselineskip}% - {\@subsubsecfont}} - \def\@subsubsecfont{\bfseries\section@raggedright} - \renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}% - {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {-3.5\p@}% - {\@parfont\@addspaceafter}} - \def\@parfont{\bfseries\itshape} - \renewcommand\subparagraph{\@startsection{subparagraph}{5}{\z@}% - {-.5\baselineskip \@plus -2\p@ \@minus -.2\p@}% - {-3.5\p@}% - {\@subparfont\@addspaceafter}} - \def\@subparfont{\itshape} -\or % sigchi - \setcounter{secnumdepth}{1} - \def\@secfont{\sffamily\bfseries\section@raggedright\MakeTextUppercase} - \def\@subsecfont{\sffamily\bfseries\section@raggedright} -\or % sigchi-a - \setcounter{secnumdepth}{0} - \def\@secfont{\sffamily\bfseries\section@raggedright\MakeTextUppercase} - \def\@subsecfont{\sffamily\bfseries\section@raggedright} -\fi -\def\@adddotafter#1{#1\@addpunct{.}} -\def\@addspaceafter#1{#1\@addpunct{\enspace}} -\providecommand*\@dotsep{4.5} -\def\@acmplainbodyfont{\itshape} -\def\@acmplainindent{\parindent} -\def\@acmplainheadfont{\scshape} -\def\@acmplainnotefont{\@empty} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall -\or % acmlarge -\or % acmtog -\or % sigconf -\or % siggraph -\or % sigplan - \def\@acmplainbodyfont{\itshape} - \def\@acmplainindent{\z@} - \def\@acmplainheadfont{\bfseries} - \def\@acmplainnotefont{\normalfont} -\or % sigchi -\or % sigchi-a -\fi -\newtheoremstyle{acmplain}% - {.5\baselineskip\@plus.2\baselineskip - \@minus.2\baselineskip}% space above - {.5\baselineskip\@plus.2\baselineskip - \@minus.2\baselineskip}% space below - {\@acmplainbodyfont}% body font - {\@acmplainindent}% indent amount - {\@acmplainheadfont}% head font - {.}% punctuation after head - {.5em}% spacing after head - {\thmname{#1}\thmnumber{ #2}\thmnote{ {\@acmplainnotefont(#3)}}}% head spec -\def\@acmdefinitionbodyfont{\normalfont} -\def\@acmdefinitionindent{\parindent} -\def\@acmdefinitionheadfont{\itshape} -\def\@acmdefinitionnotefont{\@empty} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall -\or % acmlarge -\or % acmtog -\or % sigconf -\or % siggraph -\or % sigplan - \def\@acmdefinitionbodyfont{\normalfont} - \def\@acmdefinitionindent{\z@} - \def\@acmdefinitionheadfont{\bfseries} - \def\@acmdefinitionnotefont{\normalfont} -\or % sigchi -\or % sigchi-a -\fi -\newtheoremstyle{acmdefinition}% - {.5\baselineskip\@plus.2\baselineskip - \@minus.2\baselineskip}% space above - {.5\baselineskip\@plus.2\baselineskip - \@minus.2\baselineskip}% space below - {\@acmdefinitionbodyfont}% body font - {\@acmdefinitionindent}% indent amount - {\@acmdefinitionheadfont}% head font - {.}% punctuation after head - {.5em}% spacing after head - {\thmname{#1}\thmnumber{ #2}\thmnote{ {\@acmdefinitionnotefont(#3)}}}% head spec -\theoremstyle{acmplain} -\AtEndPreamble{% - \if@ACM@acmthm - \theoremstyle{acmplain} - \@ifundefined{theorem}{% - \newtheorem{theorem}{Theorem}[section] - }{} - \@ifundefined{conjecture}{% - \newtheorem{conjecture}[theorem]{Conjecture} - }{} - \@ifundefined{proposition}{% - \newtheorem{proposition}[theorem]{Proposition} - }{} - \newtheorem{lemma}[theorem]{Lemma} - \@ifundefined{lemma}{}{} - \@ifundefined{corollary}{% - \newtheorem{corollary}[theorem]{Corollary} - }{} - \theoremstyle{acmdefinition} - \@ifundefined{example}{% - \newtheorem{example}[theorem]{Example} - }{} - \@ifundefined{definition}{% - \newtheorem{definition}[theorem]{Definition} - }{} - \fi - \theoremstyle{acmplain} -} -\def\@proofnamefont{\scshape} -\def\@proofindent{\indent} -\ifcase\ACM@format@nr -\relax % manuscript -\or % acmsmall -\or % acmlarge -\or % acmtog -\or % sigconf -\or % siggraph -\or % sigplan - \def\@proofnamefont{\itshape} - \def\@proofindent{\noindent} -\or % sigchi -\or % sigchi-a -\fi -\renewenvironment{proof}[1][\proofname]{\par - \pushQED{\qed}% - \normalfont \topsep6\p@\@plus6\p@\relax - \trivlist - \item[\@proofindent\hskip\labelsep - {\@proofnamefont #1\@addpunct{.}}]\ignorespaces -}{% - \popQED\endtrivlist\@endpefalse -} -\specialcomment{acks}{% - \begingroup - \section*{Acknowledgments} - \phantomsection\addcontentsline{toc}{section}{Acknowledgments} -}{% - \endgroup -} -\def\grantsponsor#1#2#3{#2} -\newcommand\grantnum[3][]{#3% - \def\@tempa{#1}\ifx\@tempa\@empty\else\space(\url{#1})\fi} -\AtEndPreamble{% -\if@ACM@screen - \includecomment{screenonly} - \excludecomment{printonly} -\else - \excludecomment{screenonly} - \includecomment{printonly} -\fi -\if@ACM@anonymous - \excludecomment{anonsuppress} - \excludecomment{acks} -\else - \includecomment{anonsuppress} -\fi} -\newcommand\showeprint[2][arxiv]{% - \def\@tempa{#1}% - \ifx\@tempa\@empty\def\@tempa{arxiv}\fi - \def\@tempb{arxiv}% - \ifx\@tempa\@tempb - arXiv:\href{http://arxiv.org/abs/#2}{#2}\else arXiv:#2% - \fi} -\normalsize\normalfont\frenchspacing -\endinput -%% -%% End of file `acmart.cls'. diff --git a/TRUST-docs/biblio.bib b/TRUST-docs/biblio.bib deleted file mode 100644 index 5f9d0ce..0000000 --- a/TRUST-docs/biblio.bib +++ /dev/null @@ -1,466 +0,0 @@ -@article{martin2023guarantees, - title = {Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey}, - author = {Martin, Tim and Sch{\"o}n, Thomas B and Allg{\"o}wer, Frank}, - journal = {Annual Reviews in Control}, - pages = {100911}, - year = {2023}, - publisher = {Elsevier} -} - -@article{samari2024single, - title = {From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems}, - 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number = {5}, - pages = {3011-3024}, } - -@article{parrilo2003semidefinite, - title = {Semidefinite programming relaxations for semialgebraic problems}, - author = {Parrilo, Pablo A}, - journal = {Mathematical programming}, - volume = {96}, - pages = {293--320}, - year = {2003}, - publisher = {Springer} -} - -@article{adewuyi2013dc, - title = {DC motor speed control: A case between PID controller and fuzzy logic controller}, - author = {Adewuyi, Philip A}, - journal = {international journal of multidisciplinary sciences and engineering}, - volume = {4}, - number = {4}, - pages = {36--40}, - year = {2013} -} - -@article{wang2024convex, - title = {Convex co-design of control barrier functions and feedback controllers for linear systems}, - author = {Wang, Han and Margellos, Kostas and Papachristodoulou, Antonis and De Persis, Claudio}, - year = {2024}, - publisher = {IEEE} -} - -@software{Yuan_SumOfSquares_py, - author = {Yuan, Chenyang}, - license = {MIT}, - title = {{SumOfSquares.py}}, - url = {https://github.com/yuanchenyang/SumOfSquares.py} -} - -@misc{samari2024singletrajectory, - title = {From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems}, - author = {Behrad Samari and Omid Akbarzadeh and Mahdieh Zaker and Abolfazl Lavaei}, - year = {2024}, - eprint = {2409.10026}, - archivePrefix = {arXiv}, - primaryClass = {eess.SY}, - url = {https://arxiv.org/abs/2409.10026}, -} \ No newline at end of file diff --git a/TRUST-docs/main.tex b/TRUST-docs/main.tex deleted file mode 100644 index f9be96e..0000000 --- a/TRUST-docs/main.tex +++ /dev/null @@ -1,1152 +0,0 @@ -\documentclass[sigconf]{acmart} - -\usepackage{booktabs} % For formal tables -\usepackage{IEEEtrantools} -\usepackage{latexsym,amsfonts,amsmath} %amssymb -\usepackage{graphicx} -\usepackage{dsfont} -\usepackage{enumerate} -\usepackage{hyperref} -\newtheorem{claim}{Claim} -\newtheorem{problem}{Problem} -\newtheorem{algorithm}{Algorithm} -\newtheorem{construction}{Construction} -\newtheorem{xca}{Exercise} -\newtheorem{comments}{Comments} -\newtheorem{remark}{Remark} -\newtheorem{assumption}{Assumption} -\newtheorem{fact}{Fact} - -\usepackage{mathrsfs} - -\usepackage{algorithm} -%\usepackage{algorithmic} -\usepackage{algpseudocode} -%================FAUST -\usepackage{xspace} -\newcommand{\software}{\textsf{FAUST}$^{\mathsf 2}$\xspace} -%================= - -\newcommand{\set}[1]{{\{#1 \}}} -\newcommand{\boxspan}{\mathit{span}} -\newcommand{\params}{{\mathsf{q}}} -\renewcommand{\Re}{{\mathbb{R}}} -\newcommand{\R}{{\mathbb{R}}} -\newcommand{\F}{{\mathbb{F}}} -\newcommand{\Q}{{\mathbb{Q}}} -\newcommand{\Ze}{{\mathbb Z}} -\newcommand{\B}{{\mathbb B}} -\newcommand{\Ce}{{\mathbb C}} -\newcommand{\N}{{\mathbb{N}}} -\newcommand{\T}{{\mathbb T}} -\newcommand{\fs}{{\mathbb S}} -\newcommand{\ie}{\textit{i.e.}} -\newcommand{\eg}{\textit{e.g.}} -\newcommand{\ea}{\textit{et al}} -\newcommand{\D}{\displaystyle} -\newcommand{\Pre}{\mathrm{Pre}} -\newcommand{\Post}{\textrm{Post}} -\newcommand{\argmax}{\textrm{arg}\max} -\newcommand{\argmin}{\textrm{arg}\min} -\newcommand{\UP}{\textrm{UP}} -\newcommand{\X}{{\mathbf{X}}} -\newcommand{\Next}{{\mathrm{Next}}} -\newcommand{\Inv}{{\mathrm{Inv}}} -\newcommand{\Reach}{{\mathrm{Reach}}} -\newcommand{\kr}{\textrm{ker}} -\newcommand{\s}{\mathrm{span}} -\renewcommand{\dim}{\mathrm{dim}} -\newcommand{\lie}{\mathrm{Lie}} -\newcommand{\cl}{\mathrm{cl}} -\newcommand{\inte}{\mathrm{int}} -\newcommand{\bd}{\mathrm{bd}} -\newcommand{\E}{\mathrm{End}} -\newcommand{\q}{\mathsf{q}} -\newcommand{\p}{\mathsf{p}} -\newcommand\norm[1]{\left\lVert#1\right\rVert} - -\DeclareMathOperator{\Tr}{Tr} -\newcommand{\note}[1]{\textcolor{red}{(#1)}} -\newcommand{\ra}{\rightarrow} -\newcommand{\insertref}{\textcolor{red}{[ref]}} -\newcommand{\ul}{\underline} -\newcommand{\ol}{\overline} -\newcommand{\Let}{:=} -\newcommand{\EE}{\mathds{E}} -\newcommand{\PP}{\mathds{P}} -\newcommand{\traj}[3]{#1_{#2#3}} -\newcommand{\red}[1]{{\color{red}{#1}}} -\newcommand{\blue}[1]{{\color{blue}{#1}}} -\newcommand{\BW}{\textcolor{red}} -\newcommand{\MZ}[1]{{\textcolor{red}{ \textbf{MZ:} #1}}} - -\newcommand{\intcc}[1]{\ensuremath{{\left[#1\right]}}} -\newcommand{\intoc}[1]{\ensuremath{{\left]#1\right]}}} -\newcommand{\intco}[1]{\ensuremath{{\left[#1\right[}}} -\newcommand{\intoo}[1]{\ensuremath{{\left]#1\right[}}} - -%\linespread{0.9} - -\DeclareMathOperator{\diag}{diag} -\DeclareMathOperator{\im}{im} -\DeclareMathOperator{\ess}{ess} - -\newcommand{\id}{{\mathrm{id}}} -\renewcommand{\emptyset}{{\varnothing}} -\newcommand{\Abolfazl}{\textcolor{blue}} - -\newcommand{\identity}{\mathbb{I}} -% Copyright -%\setcopyright{none} -%\setcopyright{acmcopyright} -%\setcopyright{acmlicensed} -\setcopyright{rightsretained} -%\setcopyright{usgov} -%\setcopyright{usgovmixed} -%\setcopyright{cagov} -%\setcopyright{cagovmixed} - -\newcommand{\initial}{X_I} -\newcommand{\unsafe}{X_U} - -% DOI -%\acmDOI{10.475/123_4} - -% ISBN -%\acmISBN{123-4567-24-567/08/06} - -%Conference -%\acmConference[HSCC'18]{ACM International Conference on Hybrid Systems: Computation and Control }{April 2018}{Porto, Portugal} -%\acmYear{2018} -%\copyrightyear{2018} - -%\acmPrice{15.00} - - -\begin{document} -\copyrightyear{2025} -\acmYear{2025} -\setcopyright{acmlicensed} -\acmConference[HSCC'25]{28th ACM International Conference on Hybrid Systems: Computation and Control, Irvine, California, May 6-9 2025} -\acmBooktitle{May 6-9 2025, Irvine, California, USA} -%\acmPrice{15.00} -%\acmDOI{10.1145/3178126.3178135} -%\acmISBN{978-1-4503-5642-8/18/04} - - -\title[TRUST: Controller Synthesis for Black-Box Systems Using a Single Trajectory]{TRUST: Stabili\underline{\textbf{T}}y and Safety Cont\underline{\textbf{R}}oller Synthesis for Black-Box Systems \underline{\textbf{U}}sing a \underline{\textbf{S}}ingle \underline{\textbf{T}}rajectory} - -\author{Jamie Gardner} -\affiliation{% - \institution{School of Computing} - \institution{Newcastle University} -} -\email{j.gardner3@newcastle.ac.uk} - -\author{Ben Wooding} -\affiliation{% - \institution{School of Computing} - \institution{Newcastle University} -} -\email{ben.wooding@newcastle.ac.uk} - -\author{Amy Nejati} -\affiliation{% - \institution{School of Computing} - \institution{Newcastle University} -} -\email{amy.nejati@newcastle.ac.uk} - -\author{Abolfazl Lavaei} -\affiliation{% - \institution{School of Computing} - \institution{Newcastle University} -} -\email{abolfazl.lavaei@newcastle.ac.uk} - -\begin{abstract} -TRUST is an open-source software tool for the single-trajectory data-driven control synthesis for Stability and safety barrier certificates (BCs). -The tool implements sum-of-squares (SOS) optimizations for the systematic production of both linear and polynomial BCs. By ensuring the persistently-excited state of the input data, which is determined by fulfilling a certain rank condition, the system will compute the stability functions and safety barrier certificates and their respective controllers for an infinite time horizon from the finite-length dataset. - -The stability and safety properties are calculated for four classes of dynamical systems: (i) continuous-time nonlinear polynomial systems, (ii) continuous-time linear systems, (iii) discrete-time nonlinear polynomial systems, and (iv) discrete-time linear systems. -For each of these four scenarios, TRUST can synthesize the stability function and controller or the safety barrier certificate and controller. - -TRUST is a Python-based web application, providing an intuitive and reactive GUI via web technologies, and can be accessed at or installed locally, and supports both manual data entry and data file uploads. -The tool uses the SOS optimization toolbox to solve the stability and safety barrier problems, and the symbolic programming library SymPy to handle the symbolic computations. -Leveraging the power of the Python backend and Javascript frontend, the tool is designed to be user-friendly and accessible on desktop, tablet, and mobile devices. -Physical case studies validate our data-driven approach for each of the four pairs of scenarios. -\end{abstract} - -% The code below should be generated by the tool at -% https://dl.acm.org/ccs.cfm -% Please copy and paste the code instead of the example below. - -\begin{CCSXML} -% -% -% 10003752.10003790.10011119 -% Theory of computation~Abstraction -% 500 -% -% -% 10010520.10010553 -% Computer systems organization~Embedded and cyber-physical systems -% 500 -% -% -% 10003033.10003039.10003041.10003043 -% Networks~Formal specifications -% 300 -% -% - -\end{CCSXML} - -%\ccsdesc[500]{Theory of computation~Abstraction} -%\ccsdesc[500]{Computer systems organization~Embedded and cyber-physical systems} -%\ccsdesc[300]{Networks~Formal specifications} - - -\keywords{Data-Driven Control Synthesis, Safety Verification, Barrier Certificates} - - -\maketitle - - -\section{introduction}\label{sec:introduction} - -\subsection{Motivation for TRUST}\label{subsec:motivation-for-sintra-sb} - -% Opening paragraphs. -% Look at previous works like PRoTECT (and other data-driven approaches from Abolfazl's website). Don't worry about coming up with this, just paraphrase and rewrite from the existing works. -The design of control systems that ensure stability and safety is a fundamental problem in control theory, with applications in safety-critical systems including robotics, aerospace, self-driving cars, and medical devices, to name a few. -Traditional model-based approaches to control synthesis rely on accurate mathematical models of the system dynamics, which are often difficult to obtain, or may not accurately reflect the real-world behavior of the system. -In contrast, data-driven methods have gained popularity due to their ability to handle unknown mathematical models based on the data collected from the system~\cite{nejati2023data}. - -%I. Stability -% A. Introduce the concept of stability in dynamical systems (i.e. what the Lyapunov function is) -% B. Discuss the importance of stability in control synthesis (we deal with asymptotic stability, where we return to a stable equilibrium rather than just stay at it) -A system is considered stable if it either remains at an equilibrium point or returns to it after a disturbance, known as asymptotic stability. -In control synthesis, stability is crucial for ensuring that the system behaves as intended, and does not deviate from its desired behavior. -This assurance comes from the calculation of a Lyapunov function for a system, which serves as a fundamental guarantee across the system's continuous-state space~\cite{breschi2021direct}. - -%II. Safety Barrier -% A. Introduce the concept of safety barrier certificates (we deal with control barrier certificates, where the user can provide the control data, i.e.\ U0) -% B. Explain how safety barrier certs are particularly useful in safety-critical systems, where the system not only needs to be stable but also avoid unsafe regions -% C. Note the use of Sum of Squares (SOS) optimization techniques -In addition to stability, safety barrier certificates formalise the notion of safety in dynamical systems, by ensuring that the system will never enter an unsafe region across an infinite time horizon. -Control barrier certificates (CBCs) are particularly useful for real-world systems, where the data is directly measured through input-output observations, known as a ``single trajectory''~\cite{ren2024formal}. - -%III. Data-driven (single-trajectory) -% A. Highlight the issue with traditional model-based approaches for stability or safety barriers -% 1. The system model is assumed to be known, which isn't realistic. -% B. Introduce data-driven approaches -% 1. More realistic -% 2. Often require large amounts of data, over many trajectories (order of magnitude in the millions) -% 3. Often requires the data to be independent and identically distributed (i.i.d.) -% C. Introduce the concept of single-trajectory data-driven control synthesis -% 1. Use of persistently-excited (full rank) data allows for the system to be analyzed and controlled using a single trajectory -% 1. Reduction in complexity -% 2. Reduction in data requirements - -% We can go into detail about how a single trajectory can be used to synthesize both the Lyapunov function and the barrier certificate. -% - Motivate the tool by highlighting the gap in current tooling. Start by referencing the orginal barrier certificate and stability works. Lead into data-driven tools which are more realistic, but expensive to get the correct data for, so tools should to work accurately with less data, which is where our approach differs. -% DPT19, ACE+19, KMS+24, MTZ22, NZ23, NZCZ22, PR07, SLSZ24, WRMDM05, WMPDP24, XCB23, BDPT20] also cite PRoTECT, FOSSIL, and any other barrier or data tools in the literature, and Ben’s data paper [AAE+21, WHL24, KMS+24]. - -% - Discuss what exactly the Lyapunov function is, as the foundational problem, in terms of what data is needed and how to compute the stability of a system. -% - Follow by specifically exploring Control Barrier Certificates (CBCs) which extend the stability (aka Lyapunov) function for level sets that segment the state space into an initial, safe space and one or more unsafe states. -% - Briefly interlude with the distinction of discrete- vs continuous-time systems (references?) -% - Where does the the differences between linear and nonlinear polynomial systems fit in here? -% The Lyapunov function is particularly useful for analyzing discrete-time systems, where it can be used to determine the behavior of a dynamical system based on its state sequence at each time step. -% However, for continuous-time systems, analysis becomes more complex due to the need for persistence of excitation. - -% - Reference Willems' fundamental lemma for "the concept of persistence of excitation" for continuous-time nonlinear polynomial systems -Willems' Fundamental Lemma provides a necessary condition for the existence of a stability function for continuous-time non-linear polynomial systems~\cite{willems2005note}, thus enabling the design of safety barrier certificates for these systems. -% Include a reference to Sum of Squares optimisation for the computation of the safetyb barrier certificate here? -The computation of these safety barrier certificates can be performed using Sum of Squares (SOS) optimization techniques, using an existing toolbox~\cite{prajna2002introducing}. -It is worth noting that despite many works on the subject of \emph{continuous-time} nonlinear polynomial systems~\cite{bisoffi2020data,bisoffi2022controller,nejati2022data}, few works deal with the more difficult production of results for single-trajectory \emph{discrete-time} non-linear polynomial systems~\cite{martin2023guarantees}. -% - Reference Behrad's paper for the solution to discrete-time nonlinear polynomial system safety -Despite this lack of research, this work implements a cutting-edge theoretical discovery on data-driven methods for the design of stable and safe controllers for this category of system~\cite{samari2024single}. -% - The problem: Finish the paragraph with the challenge of control synthesis for unknown mathematical models -% With this theoretical context in mind, the practical, real-world synthesis of a stable controller, and by extension a safe controller, is quite challenging, especially when the mathematical model of the system is unknown. -However, practical implementation of this research remains scarce, due to the complexity of real-world scenarios where the mathematical model of the system is unknown, or it is expensive in terms of manual effort to first identify and then solve the problem using model-based methods. - -% - The solution: Refer to the intro in Behrad's paper for an intro to the use of data-driven techniques as a reduction in the layers of complexity of the problem, and further how single trajectories and excited states can reduce the amount of data required. -As a solution, data-driven techniques offer a promising reduction in cost and complexity, by leveraging - -% - Break the solution down into its two parts: reduction in complexity, and reduction in data -- Clarify the complexity e.g. the problems like "linear quadratic regulation and robust controller design" (rephrase and reuse the references); "model-reference controller design for linear dynamical systems" (same as previous); "stabilization of polynomial systems" (and again); and how these approaches don't account for state constraints (i.e. the level sets - clarify the relevance?); - -- Then by clarifying the data requirements e.g. other scenario-based programs that require independent and identically distributed (i.i.d.) data which requires the collection of multiple trajectories (in the order of magnitude of millions) - -% - Lead this into the lack of tooling in the area -Recent studies have proposed various data-driven methods for this problem (reference PRoTECT, IMPaCT and FOSSIL), which are much more realistic than traditional model-based approaches. -However, these methods often require a large amount of data to provide accurate guarantees (reference), making them impractical for many real-world applications. - -- Then highlight this gap that SinTra fills, i.e. synthesizing stability functions and safety barrier certificates using persistently-excited, single-trajectory data. - -- Outline the benefits of this tool in terms of the formal guarantees it provides, including the breadth of scenarios for both stability and the extended problem of CBCs. - -\subsection{Related Literature}\label{subsec:related-literature} - -\subsection{Related Software}\label{subsec:related-software} -- Discuss the existing tools in the area, including PRoTECT, IMPaCT, and FOSSIL, and how they differ from SinTra. - -\subsection{Contributions}\label{subsec:contributions} -This tool paper contributes the following novel and noteworthy developments: -%- Review how specifically SinTra fits these needs when able to determine a persistently excited state, and detail what exactly this means, before bringing the user back to the novel contribution. -%- despite finite trajectories considered, the guarantees hold over infinite horizons. Nice interface. Stability and Safety guarantees. etc. -%- Unique contributions are primarily the tool being data-driven, but also by verifying that the samples are persistently excited, we can use single-trajectory data over a fixed time horizon whilst still providing (probabilistic) guarantees for an infinite time horizon, drastically reducing the data required in our tool. Additionally, our tool covers the breadth of scenarios for continuous time and discrete time linear and nonlinear polynomial, all in the one tool. -\begin{enumerate}[i.] -\item TRUST is a first-of-its-kind tool that uses data-driven approaches to synthesize stability functions and safety barrier certificates from a single-trajectory. -\item Implemented as a responsive and reactive Flask web application, TRUST provides an intuitive and user-friendly interface for users to interact with the tool. -\item Real-time client-side updates and error management through asynchronous JavaScript and XML (AJAX) requests provide a seamless user experience across any platform. -\item The server-side Python application leverages the Flask web framework to handle the data processing and computation of the stability functions and safety barrier certificates, following an MVC architecture and test-driven development for high-quality code. -\item TRUST extends the Sum of Squares (SOS) optimization toolbox powered by MOSEK to solve the stability and safety barrier problems for continuous-time and discrete-time linear and nonlinear polynomial systems using the symbolic programming library SymPy. -\item The tool allows for both manual data entry and data file uploads for the X0, U0 and X1 datasets, a simple user experience for defining the state space, initial set, and multiple unsafe sets of the system, and, for nonlinear polynomial systems, the monomial terms. -\item We demonstrate the usefulness of TRUST through eight distinct scenarios, representing the four classes of dynamical system, and their respective stability functions and safety barrier certificates. -\end{enumerate} - -\subsection{Structure of the Paper}\label{subsec:structure-of-the-paper} -This paper is structured as follows: -\begin{enumerate} -\item \hyperref[sec:introduction]{Introduction}: provides the necessary background information on stability functions and safety barrier certificates, and the data-driven approach to control synthesis. -\item \hyperref[sec:overview-of-the-tool]{Overview of the Tool}: gives an overview of the TRUST tool, including the notation used, the inputs required, and the outputs produced. -\item \hyperref[sec:problem-description]{Problem Description}: outlines the problem of stability and safety control synthesis for black-box systems using a single trajectory. -\item \hyperref[sec:scenarios]{Scenarios}: presents the four primary scenarios for continuous-time and discrete-time linear and nonlinear polynomial systems, demonstrating the tool's capabilities. -\item \hyperref[sec:benchmarks-and-case-studies]{Benchmarks and Case Studies}: provides a detailed analysis of the tool's performance through a series of benchmarks and case studies. -\item \hyperref[sec:results]{Results}: presents the results of the benchmarks and case studies, highlighting the tool's effectiveness in solving stability and safety problems. -\end{enumerate} - -% -- Section 2 -- - -\section{Overview of the Tool}\label{sec:overview-of-the-tool} - -\subsection{Notation}\label{subsec:notation} -$\mathbb{R}$, $\mathbb{R}^+_0$, and $\mathbb{R}^+$ denote the set of real numbers, non-negative and positive real numbers, respectively. $\mathbb{N}$ and $\mathbb{N}^+$ denote the set of natural numbers including and excluding zero. $\emptyset$ denotes the empty set. -The notation $\mathbb{R}^{a\times b}$ in general is used to describe a matrix of size $a\times b$ that contains real values, equivalently $\mathbb{N}^{a\times b}$ for natural numbers. -Similarly, a vector of size $n$ is denoted with $\mathbb{R}^n$ or $\mathbb{N}^n$. $A^{-1}$ and $A^\top$ are respectively the inverse and the transpose of matrix $A$. -We use $[a,b]$ for the closed set between $a$ and $b$. - -\subsection{Inputs to the tool}\label{subsec:inputs-to-the-tool} - -\subsubsection{Modes of the Tool} - -\textsf{TRUST} is valuable in solving two main types of problems: -\begin{enumerate} -\item \emph{Stability problems} - synthesizing a control Lyapunov function $\mathcal{V}(x)$ to show stability of the underlying system; -\item \emph{Safety barrier problems} - synthesizing a control barrier certificate $\mathcal{B}(x)$ to guarantee safe behavior of the underlying system. -\end{enumerate} -In addition to these two modes that assume the presence of control inputs, \textsf{TRUST} can satisfy the same problems without control inputs, which are simpler cases for both modes. -Therefore, all parameters relating to the controller or control inputs are optional. - -\subsubsection{Classes of Systems} - -\textsf{TRUST} can handle four main classes of systems; discrete-time linear systems (dt-LS), continuous-time linear systems (ct-LS), discrete-time nonlinear polynomial systems (dt-NPS) and continuous-time nonlinear polynomial systems (ct-NPS). It can handle each of these classes of systems for both the generation of stability functions and safety barrier certificates and their respective controllers. - -\subsubsection{Datasets (\texttt{*.csv}, \texttt{*.txt}, \texttt{*.json})} -\textsf{TRUST} takes in as input the necessary datasets that together contain a \emph{persistently excited} data trajectory, these are expected to be in one of the following common data file extensions; \texttt{*.csv}, \texttt{*.txt}, or \texttt{*.json}. -The data should be sequential over a time horizon of $T\in\mathbb{N}^+$ steps, and may have multiple state dimensions $n\in\mathbb{N}^+$ and input dimensions $m\in\mathbb{N}$. -In the discrete-time cases, the datasets can be represented as: -\begin{align} -\label{eq:data-discrete} -\begin{cases} -&\mathcal{X}_{0} = [x(0),x(1),x(2),\ldots,x(T-1)],\\ -&\mathcal{U}_{0} = [u(0),u(1),u(2),\ldots,u(T-1)],\\ -&\mathcal{X}_{1} = [x(1),x(2),x(3),\ldots,x(T)], -\end{cases} -\end{align} -where $\mathcal{X}_{0}$ is generally the predecessor states, $\mathcal{X}_{1}$ is generally the successor states, and if there are control inputs they are captured by $\mathcal{U}_{0}$. - -\begin{remark} -We remark that the tool can handle $m=0$ when there is no input present, the theoretical results remain largely the same~\BW{[cite my k-inductive paper]} with the key difference being no controller $u$ is designed. -In such a situation $\mathcal{U}_{0}$ is omitted completely. -\end{remark} - -In a small abuse of notation, the continuous-time data is again sequential as: -\begin{align} -\label{eq:data-continuous} -\begin{cases} -&\mathcal{X}_{0} = [x(0),x(\tau),x(2\tau),\ldots,x((T-1)\tau)],\\ -&\mathcal{U}_{0} = [u(0),u(\tau),u(2\tau),\ldots,u((T-1)\tau)],\\ -&\mathcal{X}_{1} = [\dot{x}(0),\dot{x}(\tau),\dot{x}(2\tau),\ldots,\dot{x}((T-1)\tau)], -\end{cases} -\end{align} -where $\tau$ is a fixed sampling time for the system. -Additionally, $\mathcal{X}_{1}$ contains the derivatives of the state at each sampling time. -\begin{remark} -In practice, these derivatives are likely to be approximated, any error handling relating to this approximation is left to the user. -\end{remark} - - -\textsf{TRUST} will check that the data satisfies a rank condition that ensures the data is persistantly excited. -This rank condition is defined as~\cite{de2019formulas} - -\begin{equation} -\label{eq:rank} -\text{rank}\begin{bmatrix} -\mathcal{U}_0 \\ -\hline -\mathcal{X}_0 -\end{bmatrix} = n+m. -\end{equation} - -\subsubsection{Monomials (polynomials in $x$)} -\emph{For nonlinear polynomial systems}, the user should provide a matrix of monomial terms $\mathcal{M}(x)$. -As an example, of this when $x\in\mathbb{R}^2$: $\mathcal{M}(x) = \begin{bmatrix} -x_1^2 & -x_1 x_2 & -x_2 -\end{bmatrix}^\top$ -where here the number of monomial terms is $N=3$ and $N\in\mathbb{N}^+$. - -\subsubsection{Definitions of initial set $X_I$ , unsafe set $X_U$, state space $X$} -For safety barrier problems, the user should define the state space $X$, initial set $X_I$ and unsafe set $X_U$ of the system using hypercubes for the \emph{semi-algebraic sets}~\cite{parrilo2003semidefinite}. -Since they are semi-algebraic, the hypercubes can be described as vectors of polynomials respectively $g_I(x), g_U(x)$ and $g(x)$. \textsf{TRUST} collects the lower bound and the upper bound for each dimension to construct the hypercube. - -\subsection{Outputs from Tool}\label{subsec:outputs-from-tool} - -The outputs of \textsf{TRUST} will depend on the mode chosen. -For stability problems, \textsf{TRUST} will output a Lyapunov function $\mathcal{V}(x)$ based on the data or for safety barrier problems the safety barrier certificate $\mathcal{B}(x)$ and its level sets $\gamma$ and $\lambda$. -If either cannot be synthesized then \textsf{TRUST} will return some sort of error message. - -In both modes the functions, $\mathcal{V}(x)$ or $\mathcal{B}(x)$, are quadratic of the form $x^\top Px$ in the majority of cases and $\mathcal{M}(x)^\top P\mathcal{M}(x)$ in the continuous-time nonlinear polynomial case, where $P\succ 0$ is a symmetric positive definite matrix. -For problems that include data for control inputs $\mathcal{U}_{0}$, we will also return to the user the controller, $u\in\mathbb{R}^m$, synthesized for $\mathcal{V}(x)$ or $\mathcal{B}(x)$. - - -\section{Problem Description}\label{sec:problem-description} - -- A few paragraphs that outline the problem to the reader -- Specifically, detail the notations and definitions used (stability function, barrier function) -- Concisely describe the tool in terms of applications and underlying algorithms (web-based UI, SOS toolbox, symbolic programming) -- Pseudocode of the tool -- Touch on the web stack at a high level as the entry point to the system -- Focus more on the hierarchy of the problems, i.e. the simultaneous equations to solve for P and H, before the SOS conditions. - - -\section{Scenarios}\label{sec:scenarios} - -- Introduce the four systems, each with their safety function and stability barrier function alternatives. -- Include the controller synthesis in each case -- Add a marked-up screenshot of the tool, highlighting each region -- three columns, first for data entry, second for state definitions, third for output -- footer with the title and description, and the primary Calculate action - -%We first define generally the conditions required to find model-based control barrier certificates (CBC) for continuous-time systems, we will then demonstrate how these conditions are used in the data-driven section for the different classes of continuous systems that follow as well as the stability conditions for each of these classes of system. -We remind the reader that the data considered in this section is of the form in equation~\eqref{eq:data-continuous}. - -\subsection{Continuous Time Nonlinear Polynomial Systems}\label{subsec:continuous-time-nonlinear-polynomial-systems} -We consider continuous-time nonlinear polynomial systems (ct-NPS) defined as follows: - -\begin{definition} -\label{def:system-description-ct-NPS} -A ct-NPS is described by the ordinary differential equation -\begin{equation} -\label{eq:ct-NPS} -\Sigma_c: \dot{x} = A\mathcal{M}(x)+Bu -\end{equation} -where $A\in\mathbb{R}^{n\times N}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $\mathcal{M}(x)\in\mathbb{R}^N$ is a vector of monomials in state $x\in X$, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. -\end{definition} - -We now present the following lemma, taken from~\cite{nejati2022data}, to obtain a data-based representation of closed-loop ct-NPS~\eqref{def:system-description-ct-NPS} with controllers $u=K(x)\mathcal{M}(x)$, where $K(x)\in\mathbb{R}^{m\times N}$ is a matrix polynomial, which will be synthesized. - -\begin{lemma}[ct-NPS Q-Lemma~\cite{nejati2022data}] -\label{lem:Q-ctNPS} -Let matrix polynomial $Q(x)$ be a $(T\times N)$ matrix such that -\begin{equation} -\label{eq:Q-matrix-ctNPS} -\mathbb{I}_n = \mathcal{N}_{0}Q(x), -\end{equation} -with -\begin{equation} -\label{eq:data-N0T} -\mathcal{N}_{0} = [\mathcal{M}(x(0)), \mathcal{M}(x(\tau)), \mathcal{M}(x(2\tau)), \ldots, \mathcal{M}(x((T-1)\tau))] -\end{equation}being an $(N\times T)$ full row-rank matrix. -If one sets $u=K(x)\mathcal{M}(x) = \mathcal{U}_{0}Q(x)\mathcal{M}(x)$, then the closed-loop system $\dot{x}=A\mathcal{M}(x)+Bu$ has the following data-based representation: -\begin{equation} -\label{eq:A+BK=X1TQ-ctNPS} -\dot{x} = \mathcal{X}_{1}Q(x)\mathcal{M}(x),\quad\text{equivalently,}\quad A+BK(x) = \mathcal{X}_{1}Q(x). -\end{equation} -\end{lemma} - -Using the above lemma, we now have a data-driven representation of our system using $\mathcal{X}_{1}Q(x)\mathcal{M}(x)$, which we will use to design controllers for CBCs and stability in the following theorems. - -\subsubsection{Control Barrier Certificate} - -\begin{theorem}[Data-Driven ct-NPS CBC~\cite{nejati2022data}] -\label{thm:data-ctNPS-CBC} -Consider the unknown ct-NPS~\eqref{eq:ct-NPS}, \emph{i.e.} $\dot{x} = A\mathcal{M}(x)+Bu$, with its data-based representation $\dot{x}=\mathcal{X}_{1}Q(x)\mathcal{M}(x)$. -Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q(x)=H(x)P$ such that the following conditions are satisfied -\begin{align} -\label{eq:ctNPS_CBC_data1} -\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) \leq \gamma, &\quad\forall x\in X_I, \\ -\label{eq:ctNPS_CBC_data2} -\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) \geq \lambda, &\quad\forall x\in X_U, -\end{align} -and $\forall x\in X$, -\begin{align} -\label{eq:ctNPS_CBC_data3} -\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top &\leq 0,\\ -\label{eq:ctNPS_CBC_data0} -\mathcal{N}_{0}H(x)&=P^{-1}. -\end{align} -Then $\mathcal{B}(x) = \mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x)$ is a CBC and \newline $u = \mathcal{U}_{0}H(x)[\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x)$ is its corresponding safety controller for the unknown ct-NPS. -\end{theorem} - -\subsubsection{Sum-of-Squares Formulation} -\BW{Add a reference for this formulation.} We present now how to solve equations~\eqref{eq:ctNPS_CBC_data1}-\eqref{eq:ctNPS_CBC_data0} in this first occurrence of the conditions, the CBC conditions for later sections follow similarly but are omitted for brevity. - -We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. -We can solve the following using the SumOfSquares toolbox~\cite{Yuan_SumOfSquares_py} where we also add an additional LMI constraint for the equality~\eqref{eq:ctNPS_CBC_data0}. - -We consider~\eqref{eq:ctNPS_CBC_data0} -and the following are sum-of-squares -\begin{align} -\label{eq:ct-SOS1} --\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) -& L_I^\top(x)g_I(x) + \gamma, \\ -\label{eq:ct-SOS2} -\mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x) -& L_U^\top(x)g_U(x) + \lambda, \\ -\label{eq:ct-SOS3} --[\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top] -& L^\top(x)g(x). -\end{align} - -% We should know $\frac{\partial M}{\partial x}$ since the monomials $M(x)$ are already given to us. - -% To solve first find solutions to -% \begin{equation*} -% P^{-1} = \mathcal{N}_{0}H(x) -% \end{equation*} -% and -% \begin{equation*} -% -[\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top]\geq 0 -% \end{equation*} -% then solve the sum of squares conditions to find $\gamma$ and $\lambda$. Then the barrier certificate is given by $\mathcal{B}(x) = \mathcal{M}(x)^\top [\mathcal{N}_{0}H(x)]^{-1} \mathcal{M}(x)$ and the controller by $u = \mathcal{U}_{0}H(x)(\mathcal{N}_{0}H(x))^{-1}M(x)$, we also return $\gamma$ and $\lambda$. - -A hierarchical approach to solve Theorem~\ref{thm:data-ctNPS-CBC} is used where first $H(x)$ and $P$ are found in equations~\eqref{eq:ctNPS_CBC_data3}-\eqref{eq:ctNPS_CBC_data0} before equations~\eqref{eq:ctNPS_CBC_data1}-\eqref{eq:ctNPS_CBC_data2} are solved using SOS programming for $\gamma$ and $\lambda$. -This is shown in Algorithm~\ref{alg:ct-nonlinear}. - -\begin{algorithm}[t] -\caption{Hierarchy for ct-NPS CBCs}\label{alg:ct-nonlinear} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U, \mathcal{M}(x)$ -\Ensure \eqref{eq:rank} holds -\Ensure semi-algebraic $X,X_I,X_U$ -\State Solve~\eqref{eq:ctNPS_CBC_data3} and~\eqref{eq:ctNPS_CBC_data0} for $H(x)$ and $P$ via LMIs -%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ -\State Substitute and solve~\eqref{eq:ctNPS_CBC_data1}-\eqref{eq:ctNPS_CBC_data2} via SOS optimization~\eqref{eq:ct-SOS1}-\eqref{eq:ct-SOS3} -\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -\subsubsection{Stability} - -Solving only the last CBC conditions~\eqref{eq:ctNPS_CBC_data3}-\eqref{eq:ctNPS_CBC_data0} with no restriction over a state space $X$ renders the stability problem. - -\begin{theorem}[ct-NPS Stable Controller Design] -\label{thm:ctNPS-stable} -A control Lyapunov function $\mathcal{V}(x)=\mathcal{M}(x)^\top P\mathcal{M}(x)$ guaranteeing stability of the ct-NPS~\eqref{eq:ct-NPS} can be designed by introducing the new variable -\begin{equation*} -\label{eq:Q=HP-ctNPS} -Q(x)=H(x)P, -\end{equation*} -so that any polynomial matrices $H(x)\in\mathbb{R}^{T\times N}$, and $P\in\mathbb{R}^{N\times N}$ satisfying -\begin{align} -\label{eq:stability-ctNPS} -\frac{\partial M}{\partial x}\mathcal{X}_{1}H(x) + H(x)^\top\mathcal{X}_{1}^\top(\frac{\partial M}{\partial x})^\top \prec 0, \quad \mathcal{N}_{0}H(x)=P^{-1} -\end{align} -stabilize~\eqref{eq:ct-NPS}. -The controller is given by~\newline$u=\mathcal{U}_{0}Q(x)\mathcal{M}(x) = \mathcal{U}_{0}H(x)[\mathcal{N}_{0}H(x)]^{-1}\mathcal{M}(x).$ -\end{theorem} - -We remark here that the stability conditions are straightforward to solve using semidefinite programming solvers such as SEDUMI or Mosek \BW{cite whichever we use, and remove the other}. The psuedocode for ct-NPS stability is given in Algorithm~\ref{alg:ct-stab}. - -\begin{algorithm}[t] -\caption{Hierarchy for ct-NPS Stability}\label{alg:ct-stab} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0, \mathcal{M}(x)$ -\Ensure \eqref{eq:rank} holds -\State Solve~\eqref{eq:stability-ctNPS} for $H(x)$ and $P$ via LMIs -\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -\subsection{Continuous Time Linear Systems}\label{subsec:continuous-time-linear-systems} - -We consider continuous-time linear systems (ct-LS) defined as follows: - -\begin{definition} -\label{def:system-description-ct-LS} -A ct-LS is described by the ordinary differential equation -\begin{equation} -\label{eq:ct-LS} -\Sigma_c: \dot{x} = Ax+Bu -\end{equation} -where $A\in\mathbb{R}^{n\times n}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $x\in X$ is a system state, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. -\end{definition} - -\begin{remark} -We remark that in general ct-NPS can be simplified to the linear system by replacing $\mathcal{M}(x)$ with $x$ and $\mathcal{N}_{0}$ with $\mathcal{X}_{0}$. -\end{remark} - -We now present the following lemma, adapted here to ct-LS from the work~\cite{de2019formulas}, to obtain a data-based representation of closed-loop ct-LS~\eqref{def:system-description-ct-LS} with controllers $u=Kx$, where $K\in\mathbb{R}^{m\times n}$ is a matrix, which will be synthesized. - -\begin{lemma}[ct-LS Q-Lemma~\cite{de2019formulas}] -\label{lem:Q-ctLS} -Let matrix $Q$ be a $(T\times n)$ matrix such that -\begin{equation} -\label{eq:Q-matrix-ctLS} -\identity_n = \mathcal{X}_{0}Q, -\end{equation} -where $\mathcal{X}_{0}$ is an $(n\times T)$ full row-rank matrix. -If one sets $u=Kx = \mathcal{U}_{0}Qx$, then the closed-loop system $\dot{x}=Ax+Bu$ has the following data-based representation: -\begin{equation} -\label{eq:A+BK=X1TQ-ctLS} -\dot{x} = \mathcal{X}_{1}Qx,\quad\text{equivalently,}\quad A+BK = \mathcal{X}_{1}Q. -\end{equation} -\end{lemma} - -Using the above lemma, we know have a data-driven representation of our system using $\mathcal{X}_{1}Qx$, which we will use to design controllers for stability and CBCs in the following theorems. - -\subsubsection{Control Barrier Certificates} - -\begin{theorem}[Data-Driven ct-LS CBC~\cite{wang2024convex}] -\label{thm:data-ctLS-CBC} -Consider the unknown ct-LS~\eqref{eq:ct-LS}, \emph{i.e.} $\dot{x} = Ax+Bu$, with its data-based representation $\dot{x}=\mathcal{X}_{1}Qx$. -Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q=HP$ such that the following conditions are satisfied -\begin{align} -\label{eq:ct_CBC_data1} -x^\top [\mathcal{X}_{0}H]^{-1}x \leq \gamma, &\quad\forall x\in X_I, \\ -\label{eq:ct_CBC_data2} -x^\top [\mathcal{X}_{0}H]^{-1}x \geq \lambda, &\quad\forall x\in X_U, -\end{align} -and $\forall x\in X$, -\begin{align} -\label{eq:ct_CBC_data3} -\mathcal{X}_{1}H + H^\top\mathcal{X}_{1}^\top &\leq 0\\ -\label{eq:ct_CBC_data0} -P^{-1} = \mathcal{X}_{0}H. -\end{align} -Then $\mathcal{B}(x) = x^\top [\mathcal{X}_{0}H]^{-1}x$ is a CBC and $u = \mathcal{U}_{0}H[\mathcal{X}_{0}H]^{-1}x$ is its corresponding safety controller for the unknown ct-LS. -\end{theorem} - -% \begin{corollary}[ct-LS controller design] -% \label{cor:ct-LS-controller} -% The controller for~\eqref{eq:ct_CBC_data3} can be designed to avoid the bilinearity between $P$ and $Q$ in a hierarchical manner by introducing $Q=HP$ and solving the following equations -% \begin{equation} -% \label{eq:ctLS-controller} -% H^\top\mathcal{X}_{1}^\top+ \mathcal{X}_{1}H \leq 0, \quad P^{-1} = \mathcal{X}_{0}H. -% \end{equation} -% \end{corollary} - -We can again design a ct-LS CBC using a hierarchical approach as outlined in Algorithm~\ref{alg:ct-linear}. - -\begin{algorithm}[t] -\caption{Hierarchy for ct-LS CBCs}\label{alg:ct-linear} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U$ -\Ensure \eqref{eq:rank} holds -\Ensure semi-algebraic $X,X_I,X_U$ -\State Solve~\eqref{eq:ct_CBC_data3} and~\eqref{eq:ct_CBC_data0} for $H(x)$ and $P$ via LMIs -%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ -\State Substitute and solve~\eqref{eq:ct_CBC_data1}-\eqref{eq:ct_CBC_data2} via SOS optimization -\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -% \subsection{Sum-of-Squares Formulation} - -% We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. We can solve the following using the SumOfSquares~\cite{Yuan_SumOfSquares_py} toolbox where we also add an additional constraint for the equality. We consider matrix $Q\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$ such that -% \begin{equation} -% \mathbb{I} = \mathcal{X}_{0}Q -% \end{equation} -% and the following are sum-of-squares -% \begin{align} -% -x^\top Px -& L_I^\top(x)g_I(x) + \gamma, \\ -% x^\top Px -& L_U^\top(x)g_U(x) + \lambda, \\ -% -[\mathcal{X}_{1}Q + Q^\top\mathcal{X}_{1}^\top] -& L^\top(x)g(x). -% \end{align} - -% Then the barrier certificate is given by $\mathcal{B}(x) = x^\top P x$ and the controller by $u = \mathcal{U}_{0}Qx$, we also return $\gamma$ and $\lambda$. - -\subsubsection{Stability} -We highlight again that solving equations~\eqref{eq:ct_CBC_data3}-\eqref{eq:ct_CBC_data0} without restricting $X$ gives the ct-LS stability conditions as follows. - -\begin{theorem}[ct-LS Stable Controller Design~\cite{de2019formulas}] -\label{thm:ctLS-stable} -A control Lyapunov function $\mathcal{V}(x)=x^\top Px$ guaranteeing stability of the ct-LS~\eqref{eq:ct-LS} can be designed by introducing the new variable -\begin{equation*} -\label{eq:Q=HP-ctLS} -Q=HP, -\end{equation*} -so that any matrices $H\in\mathbb{R}^{T\times n}$, and $P\in\mathbb{R}^{n\times n}$ satisfying -\begin{align} -\label{eq:stability-ctLS} -H^\top\mathcal{X}_{1}^\top + \mathcal{X}_{1}H \prec 0, \quad \mathcal{X}_{0}H=P^{-1} -\end{align} -stabilize~\eqref{eq:ct-LS}. -The controller is given by $u=\mathcal{U}_{0}Qx = \mathcal{U}_{0}H[\mathcal{X}_{0}H]^{-1}x.$ -\end{theorem} - -These conditions for stability are straightforward to solve using standard linear matrix inequality (LMI) solvers. The psuedocode for ct-NPS stability is given in Algorithm~\ref{alg:ctLS-stab}. - -\begin{algorithm}[t] -\caption{Hierarchy for ct-LS Stability}\label{alg:ctLS-stab} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0$ -\Ensure \eqref{eq:rank} holds -\State Solve~\eqref{eq:stability-ctLS} for $H(x)$ and $P$ via LMIs -\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -\subsection{Discrete Time Nonlinear Polynomial Systems}\label{subsec:discrete-time-nonlinear-polynomial-systems} - -We consider discrete-time nonlinear polynomial systems (dt-NPS) defined as follows: - -\begin{definition} -\label{def:system-description-dt-NPS} -A dt-NPS is described by -\begin{equation} -\label{eq:dt-NPS} -\Sigma_d: x^+ = A\mathcal{M}(x)+Bu -\end{equation} -where $A\in\mathbb{R}^{n\times N}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $\mathcal{M}(x)\in\mathbb{R}^N$ is a vector of monomials in state $x\in X$, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. -\end{definition} - -We now present the following lemma, from the work~\cite{samari2024singletrajectory}, to obtain a data-based representation of closed-loop dt-NPS~\eqref{def:system-description-dt-NPS} with controllers $u=K(x)x$, where $K(x)\in\mathbb{R}^{m\times n}$ is a matrix, which will be synthesized. - -\begin{lemma}[dt-NPS Q-Lemma~\cite{samari2024singletrajectory}] -\label{lem:Q-dtNPS} -Let $Q(x)$ be a $(T\times n)$ matrix polynomial such that -\begin{equation} -\label{eq:nonlinear-theta=NQ} -\Theta(x) = \mathcal{N}_{0}Q(x), -\end{equation} -where $\Theta(x)$ is a $(N\times n)$ matrix polynomial -\begin{equation} -\label{eq:nonlinear-M=thetax} -\mathcal{M}(x)=\Theta(x)x, -\end{equation} -and where $\mathcal{N}_{0}$ is an $(N\times T)$ full row-rank matrix: -\begin{equation} -\label{eq:data-N0T-dt} -\mathcal{N}_{0} = [\mathcal{M}(x(0)), \mathcal{M}(x(1)), \mathcal{M}(x(2)), \ldots, \mathcal{M}(x(T-1))]. -\end{equation} If one sets $u=K(x)x = \mathcal{U}_{0}Q(x)x$, then the closed-loop system $x^+=A\mathcal{M}(x)+Bu$ has the following data-based representation: -\begin{equation*} -x^+ = \mathcal{X}_{1}Q(x)x, -\end{equation*} -equivalently -\begin{equation} -\label{eq:nonlinearA+BK=X1TQ} -A\Theta(x)+BK(x) = \mathcal{X}_{1}Q(x). -\end{equation} -\end{lemma} - -Using the above lemma, we now have a data-driven representation of our system using $\mathcal{X}_{1}Q(x)x$, which we will use to design controllers for CBCs and stability in the following theorems. - -\subsubsection{Control Barrier Certificates} - -\begin{theorem}[Data-Driven dt-NPS CBC~\cite{samari2024singletrajectory}] -\label{thm:data-dtNPS-CBC} -Consider the unknown dt-NPS~\eqref{eq:dt-NPS}, \emph{i.e.} $x^+ = A\mathcal{M}(x)+Bu$, with its data-based representation $x^+=\mathcal{X}_{1}Q(x)x$. -Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q(x) = H(x)P$ such that the following conditions are satisfied -\begin{align} -\label{eq:nonlinear-safe_CBC_data1} -x^\top Px \leq \gamma, &\quad\forall x\in X_I, \\ -\label{eq:nonlinear-safe_CBC_data2} -x^\top Px \geq \lambda, &\quad\forall x\in X_U, -\end{align} -and $\forall x\in X$, -\begin{align} -\label{eq:nonlinear-safe_CBC_data3} -\begin{bmatrix} -P^{-1} & H(x)^\top \mathcal{X}_{1}^\top \\ -\mathcal{X}_{1}H(x) & P^{-1} -\end{bmatrix} \geq 0,\\ -\label{eq:nonlinear-safe_CBC_data0} -\Theta(x)P^{-1} = \mathcal{N}_{0}H(x). -\end{align} -Then $\mathcal{B}(x) = x^\top Px$ is a $k$-CBC and $u = \mathcal{U}_{0}H(x)Px$ is its corresponding safety controller for the unknown dt-NPS. -\end{theorem} - -%\BW{Substitute $H=QP^{-1}$.} -% Since~\eqref{eq:nonlinear-safe_CBC_data3} contains unknown matrices $Q(x)$ and $P$ there are bilinearities that should be resolved before solving. One hierarchical method is to find any $Q(x)$ from~\eqref{eq:nonlinear-theta=NQ} and then solve for $P$. We raise the following corollary to show a second method for resolving~\eqref{eq:nonlinear-safe_CBC_data3} simultaneously for $P$ and $Q(x)$, while creating -We use the following hierarchical method for finding the CBC by first solving~\eqref{eq:nonlinear-safe_CBC_data3}-\eqref{eq:nonlinear-safe_CBC_data0} followed by~\eqref{eq:nonlinear-safe_CBC_data1}-\eqref{eq:nonlinear-safe_CBC_data2} afterwards. -A temporary variable $Z=P^{-1}$ can be considered during the solving. -The psuedocode algorithm is described in Algorithm~\ref{alg:dt-nonlinear}. - -\begin{algorithm}[t] -\caption{Hierarchy for dt-NPS CBCs}\label{alg:dt-nonlinear} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U, \mathcal{M}(x)$ -\Ensure \eqref{eq:rank} holds -\Ensure semi-algebraic $X,X_I,X_U$ -\State Solve~\eqref{eq:nonlinear-M=thetax} for $\Theta(x)$ -\State Substitute $\Theta(x)$ in~\eqref{eq:nonlinear-theta=NQ} -\State Solve~\eqref{eq:nonlinear-safe_CBC_data3} and~\eqref{eq:nonlinear-safe_CBC_data0} for $H(x)$ and $P$ via LMIs -%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ -\State Substitute $P$ and solve~\eqref{eq:nonlinear-safe_CBC_data1}-\eqref{eq:nonlinear-safe_CBC_data2} via SOS optimization -\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -% \begin{corollary}[CBC Controller Design] -% \label{cor:dt-NPS-controller} -% We consider matrix $H(x)\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$. We set $Z=P^{-1}$ and $Q(x)Z=H(x)$, such that -% \begin{equation} -% \label{eq:Z=X0H} -% \Theta(x)Z = \mathcal{N}_{0}H(x) -% \end{equation} -% then~\eqref{eq:safe_CBC_data3} can be equivalently represented by -% \begin{equation} -% \label{eq:SchurZ-dtNPS} -% \begin{bmatrix} -% Z & H(x)^\top \mathcal{X}_{1}^\top \\ -% \mathcal{X}_{1}H(x) & Z -% \end{bmatrix} \geq 0,\quad \forall x\in X. -% \end{equation} -% The controller is thus $u=\mathcal{U}_{0}H(x)Z^{-1}x$. -% \end{corollary} - -\subsubsection{Stability} - -\begin{theorem}[dt-NPS Stable Controller Design] -\label{thm:dtNPS-stable} -A control Lyapunov function $\mathcal{V}(x)=x^\top Px$ guaranteeing stability of the dt-NPS~\eqref{eq:dt-NPS} can be designed by introducing the new variable -\begin{equation*} -\label{eq:N0H=ThetaP} -Q(x)Z=H(x), -\end{equation*} -where $Z=P^{-1}$ so that any matrices $H(x)\in\mathbb{R}^{T\times n}$, $\Theta(x)\in\mathbb{R}^{N\times n}$, $P\in\mathbb{R}^{n\times n}$ and $Z\in\mathbb{R}^{n\times n}$ satisfying -\begin{align} -\label{eq:schur-stability-dtNPS} -\begin{bmatrix} -Z & H(x)^\top\mathcal{X}_{1}^\top \\ -\mathcal{X}_{1} H(x) & Z -\end{bmatrix} \succ 0, \quad \mathcal{N}_{0}H(x)=\Theta(x)Z -\end{align} -stabilize~\eqref{eq:dt-NPS}. -The controller is given by $u=\mathcal{U}_{0}H(x)Z^{-1}x.$ -\end{theorem} - -Solving the stability equation~\eqref{eq:schur-stability-dtNPS} is straightforward using standard semidefinite programming solvers such as SEDUMI or Mosek,~\BW{cite whichever we used}. The psuedocode for dt-NPS stability is given in Algorithm~\ref{alg:dt-stab}. - -\begin{algorithm}[t] -\caption{Hierarchy for dt-NPS Stability}\label{alg:dt-stab} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0, \mathcal{M}(x)$ -\Ensure \eqref{eq:rank} holds -\State Solve~\eqref{eq:nonlinear-M=thetax} for $\Theta(x)$ -\State Solve~\eqref{eq:schur-stability-dtNPS} for $H(x)$ and $Z$ via LMIs -\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -% \subsection{Sum-of-Squares Formulation} - -% We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. We can solve the following using the SumOfSquares~\cite{Yuan_SumOfSquares_py} toolbox where we also add an additional constraint for the equality. We consider matrix polynomial $H(x)\in\mathbb{R}^{T\times N}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$ such that -% \begin{equation} -% \Theta(x)P^{-1} = \mathcal{N}_{0}H(x) -% \end{equation} -% and the following are sum-of-squares -% \begin{align} -% -x^\top Px -& L_I^\top(x)g_I(x) + \gamma, \\ -% x^\top Px -& L_U^\top(x)g_U(x) + \lambda, \\ -% \begin{bmatrix} -% P^{-1} & H(x)^\top\mathcal{X}_{1}^\top \\ -% \mathcal{X}_{1}H(x) & P^{-1} -% \end{bmatrix} -& L^\top(x)g(x). -% \end{align} - -% \JG{For solving 4.18, we can assume that $P^{-1} = Z$, so we don't need to repeat that before and after}\newline -% To solve first find solutions to -% \begin{equation*} -% \Theta(x)Z = \mathcal{X}_{0}H(x) -% \end{equation*} -% and -% \begin{equation*} -% \begin{bmatrix} -% Z & H(x)^\top\mathcal{X}_{1}^\top \\ -% \mathcal{X}_{1}H(x) & Z -% \end{bmatrix}\succ 0 -% \end{equation*} -% then solve $P = Z^{-1}$ and solve the sum of squares conditions to find $\gamma$ and $\lambda$. Then the barrier certificate is given by $\mathcal{B}(x) = x^\top P x$ and the controller by $u = \mathcal{U}_{0}H(x)[\mathcal{N}_{0}H(x)]^{-1}x$, we also return $\gamma$ and $\lambda$. - -\subsection{Discrete Time Linear Systems}\label{subsec:discrete-time-linear-systems} - -We consider discrete-time linear systems (dt-LS) defined as follows: - -\begin{definition} -\label{def:system-description-dt-LS} -A dt-LS is described by -\begin{equation} -\label{eq:dt-LS} -\Sigma_d: x^+ = Ax+Bu -\end{equation} -where $A\in\mathbb{R}^{n\times n}$ and $B\in\mathbb{R}^{n\times m}$ are unknown, $x\in X$ is a system state, and $u\in U$ is a control input, with $X\subset\mathbb{R}^n$, and $U\subset\mathbb{R}^m$ being the state and input sets, respectively. -\end{definition} - -\begin{remark} -As it was with ct-NPS to ct-LS, we remark that in general the results for dt-NPS can be simplied to linear systems by replacing $\mathcal{M}(x)$ with $x$, and $\mathcal{N}_{0}$ with $\mathcal{X}_{0}$. -\end{remark} - -We now present the following lemma, adapted here to dt-LS from the work~\cite{de2019formulas}, to obtain a data-based representation of closed-loop dt-LS~\eqref{def:system-description-dt-LS} with controllers $u=Kx$, where $K\in\mathbb{R}^{m\times n}$ is a matrix, which will be synthesized. - -\begin{lemma}[dt-LS Q-Lemma~\cite{de2019formulas}] -\label{lem:Q-dtLS} -Let matrix $Q$ be a $(T\times n)$ matrix such that -\begin{equation} -\label{eq:Q-matrix-dtLS} -\identity_n = \mathcal{X}_{0}Q, -\end{equation} -where $\mathcal{X}_{0}$ is an $(n\times T)$ full row-rank matrix. -If one sets $u=Kx = \mathcal{U}_{0}Qx$, then the closed-loop system $x^+=Ax+Bu$ has the following data-based representation: -\begin{equation} -\label{eq:A+BK=X1TQ-dtLS} -x^+ = \mathcal{X}_{1}Qx,\quad\text{equivalently,}\quad A+BK = \mathcal{X}_{1}Q. -\end{equation} -\end{lemma} - -We use the above lemma, to describe our system in terms of its data-driven representation $\mathcal{X}_{1}Qx$ and use that representation in the following theorems. - -\subsubsection{Control Barrier Certificate} - -\begin{theorem}[Data-Driven dt-LS CBC] -\label{thm:data-dtLS-CBC} -Consider the unknown dt-LS~\eqref{eq:dt-LS}, \emph{i.e.} $x^+ = Ax+Bu$, with its data-based representation $x^+=\mathcal{X}_{1}Qx$. -Suppose there exists a positive definite symmetric matrix $P\in\mathbb{R}^{n\times n}$ and relationship $Q=HP$ such that the following conditions are satisfied -\begin{align} -\label{eq:safe_CBC_data1} -x^\top Px \leq \gamma, &\quad\forall x\in X_I, \\ -\label{eq:safe_CBC_data2} -x^\top Px \geq \lambda, &\quad\forall x\in X_U, -\end{align} -and $\forall x\in X$, -\begin{align} -\label{eq:safe_CBC_data3} -\begin{bmatrix} -P^{-1} & H^\top\mathcal{X}_{1}^\top \\ -\mathcal{X}_{1}H & P^{-1} -\end{bmatrix} \geq 0, \\ -\label{eq:safe_CBC_data0} -P^{-1} = \mathcal{X}_{0}H. -\end{align} -Then $\mathcal{B}(x) = x^\top Px$ is a CBC and $u = \mathcal{U}_{0}HPx$ is its corresponding safety controller for the unknown dt-LS. -\end{theorem} - -% Since~\eqref{eq:safe_CBC_data3} contains unknown matrices $Q$ and $P$ there are bilinearities that should be resolved before solving. One hierarchical method is to find any $Q$ from~\eqref{eq:Q-matrix-dtLS} and then solve for $P$. We raise the following corollary to show a second method for resolving~\eqref{eq:safe_CBC_data3} simultaneously for $P$ and $Q$, while creating a -By substituting $Z=P^{-1}$, the following hierarchical method is used for finding the CBC by solving~\eqref{eq:safe_CBC_data3}-\eqref{eq:safe_CBC_data0} first to find $H$ and $P^{-1}$ followed by solving~\eqref{eq:safe_CBC_data1}-\eqref{eq:safe_CBC_data2} afterwards. The psuedocode algorithm for this is described in Algorithm~\ref{alg:dt-linear}. - -\begin{algorithm}[t] -\caption{Hierarchy for dt-NPS CBCs}\label{alg:dt-linear} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0,X,X_I,X_U$ -\Ensure \eqref{eq:rank} holds -\Ensure semi-algebraic $X,X_I,X_U$ -\State Solve~\eqref{eq:safe_CBC_data3} and~\eqref{eq:safe_CBC_data0} for $H(x)$ and $P$ via LMIs -%\State Solve~\eqref{eq:Q-matrix-X0} for $Q$ -\State Substitute and solve~\eqref{eq:safe_CBC_data1}-\eqref{eq:safe_CBC_data2} via SOS optimization -\noindent\Statex\textbf{Return:} CBC $\mathcal{B}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - - - -% \begin{corollary}[CBC Controller Design] -% \label{cor:dt-LS-controller} -% We consider matrix $H\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$. We set $Z=P^{-1}$ and $Q=HP$, such that -% \begin{equation} -% \label{eq:Z=X0Hdt} -% Z = \mathcal{X}_{0}H -% \end{equation} -% then~\eqref{eq:safe_CBC_data3} can be equivalently represented by -% \begin{equation} -% \label{eq:SchurZ-dtLS} -% \begin{bmatrix} -% Z & H^\top\mathcal{X}_{1}^\top \\ -% \mathcal{X}_{1}H & Z -% \end{bmatrix} \geq 0,\quad \forall x\in X. -% \end{equation} -% The controller is thus $u=\mathcal{U}_{0}H[\mathcal{X}_{0} H]^{-1}x$. -% \end{corollary} - -% \subsection{Sum-of-Squares Formulation} - -% We now introduce $L_I(x),L_U(x),L(x)$ as vectors of SOS polynomials. We can solve the following using the SumOfSquares~\cite{Yuan_SumOfSquares_py} toolbox where we also add an additional constraint for the equality. We consider matrix $H\in\mathbb{R}^{T\times n}$ and symmetric positive definite matrix $P\in\mathbb{R}^{n\times n}$ such that -% \begin{equation} -% P^{-1} = \mathcal{X}_{0}H -% \end{equation} -% and the following are sum-of-squares -% \begin{align} -% -x^\top Px -& L_I^\top(x)g_I(x) + \gamma, \\ -% x^\top Px -& L_U^\top(x)g_U(x) + \lambda, \\ -% \begin{bmatrix} -% P^{-1} & H^\top\mathcal{X}_{1}^\top \\ -% \mathcal{X}_{1}H & P^{-1} -% \end{bmatrix} -& L^\top(x)g(x). -% \end{align} - -% To solve first find solutions to -% \begin{equation*} -% Z = \mathcal{X}_{0}H -% \end{equation*} -% and -% \begin{equation*} -% \begin{bmatrix} -% Z & H^\top\mathcal{X}_{1}^\top \\ -% \mathcal{X}_{1}H & Z -% \end{bmatrix}\succ 0 -% \end{equation*} -% then solve $P = Z^{-1}$ and solve the sum of squares conditions to find $\gamma$ and $\lambda$. Then the barrier certificate is given by $\mathcal{B}(x) = x^\top P x$ and the controller by $u = \mathcal{U}_{0}H[\mathcal{X}_{0}H]^{-1}x$, we also return $\gamma$ and $\lambda$. - -\subsubsection{Stability} - -Removing the restriction over $X$ for conditions~\eqref{eq:safe_CBC_data3}-\eqref{eq:safe_CBC_data0} gives the stability conditions. - -\begin{theorem}[dt-LS Stable Controller Design~\cite{de2019formulas}] -\label{thm:dtLS-stable} -A control Lyapunov function $\mathcal{V}(x)=x^\top Px$ guaranteeing stability of the dt-LS~\eqref{eq:dt-LS} can be designed by introducing the new variable -\begin{equation*} -\label{eq:H=QP} -QZ=H, -\end{equation*} -where $Z=P^{-1}$ and $P\in\mathbb{R}^{n\times n}$ so that any matrices $H\in\mathbb{R}^{T\times n}$, and $Z\in\mathbb{R}^{n\times n}$ satisfying -\begin{align} -\label{eq:schur-stability-dtLS} -\begin{bmatrix} -Z & H^\top\mathcal{X}_{1}^\top \\ -\mathcal{X}_{1} H & Z -\end{bmatrix} \succ 0, \quad \mathcal{X}_{0}H=Z -\end{align} -stabilize~\eqref{eq:dt-LS}. -The controller is given by $u= \mathcal{U}_{0}H[\mathcal{X}_0H]^{-1}x.$ -\end{theorem} - -The above theorem can be solved in a straightforward manner using any LMI solver. The psuedocode for dt-LS stability is given in Algorithm~\ref{alg:dtls-stab}. - -\begin{algorithm}[t] -\caption{Hierarchy for dt-NPS Stability}\label{alg:dtls-stab} -\begin{algorithmic}[1] -\Require $\mathcal{X}_0,\mathcal{X}_1,\mathcal{U}_0$ -\Ensure \eqref{eq:rank} holds -\State Solve~\eqref{eq:schur-stability-dtLS} for $H(x)$ and $Z$ via LMIs -\noindent\Statex\textbf{Return:} CBC $\mathcal{V}(x)$, Controller $u$ -\end{algorithmic} -\end{algorithm} - -% \section{System Verification \BW{?}} - - -\section{Benchmarks and Case Studies}\label{sec:benchmarks-and-case-studies} - -We consider the following dynamical systems from the literature as case study examples. - -\subsection{Continuous-Time Systems} - -\subsubsection{Nonlinear Systems} -We consider the following ct-NPS systems. - -\noindent\textbf{Jet Engine} -We consider the nonlinear Moore-Greitzer jet engine model~\cite{krstic1995lean}: -\begin{equation*} -\Sigma_c: \begin{cases} -\dot{x}_1(t) = -x_2(t)-1.5x_1^2(t)-0.5x_1^3(t),\\ -\dot{x}_2(t) = x_1(t), -\end{cases} -\end{equation*} -where $x_1=\Phi-1$, $x_2=\Psi - \Lambda -2$, with $\Phi,\Psi,\Lambda$ being, respectively, the mass flow, pressure rise, and a constant. We consider $X = [0.1,1]^2$, $\initial=[0.1,0.5]^2$, and $\unsafe=[0.7,1]^2$. \BW{add details above initial state and trajectory length.} - - -\subsubsection{Linear Systems} -We consider the following ct-LS systems. - -\noindent\textbf{FOSSIL benchmark - High Order 8.} -We consider the following $8$-dimensional benchmark~\cite{abate2021fossil} -\begin{equation*} -\Sigma_c:\begin{cases} -\dot{x}_1(t) = &x_2(t),\\ -\dot{x}_2(t) = &x_3(t),\\ -\dot{x}_3(t) = &x_4(t),\\ -\dot{x}_4(t) = &x_5(t),\\ -\dot{x}_5(t) = &x_6(t),\\ -\dot{x}_6(t) = &x_7(t),\\ -\dot{x}_7(t) = &x_8(t),\\ -\dot{x}_8(t) = &-20x_8(t)-170x_7(t)-800x_6(t) - 2273x_5(t)\\ &-3980x_4(t) - 4180x_3(t) - 2400x_2(t) - 576x_1(t), -\end{cases} -\end{equation*} -with the state space $X=[-2.2,2.2]^8$, initial region $\initial=[0.9,1.1]^8$, and unsafe region $\unsafe=[-2.2,-1.8]^8$. \BW{add details above initial state and trajectory length.} - - -\subsection{Discrete-Time Systems} - -\subsubsection{Nonlinear Systems} -We consider the following dt-NPS systems. - -\noindent\textbf{Lorenz Attractor} -We consider the Lorenz attractor a well studied dynamical system with chaotic behavior. The map has dynamics -\begin{equation*} -\Sigma : \begin{cases} -x_1(k+1) &= x_1(k) + \tau\sigma (x_1(k) + x_2(k)), \\ -x_2(k+1) &= x_2(k) +\\ &\quad\tau (\rho x_1(k) - x_2(k) - x_1(k)x_3(k) + u(k)), \\ -x_3(k+1) &= x_3(k) + \tau (x_1(k)x_2(k)-\beta x_3(k)), -\end{cases} -\end{equation*} -where $\rho=28, \sigma=10,\beta=\frac{8}{3}, tau=10^{-3}$. We consider the state space $X=[-5,5]^3$, initial set $X_I=[-1, 1]^3$ and two unsafe sets $X_U=[-5,-2.5]^3\cup[2.5,5]^3$. We consider monomials from the set $\mathcal{M}(x)=$ \begin{align*} -[x_1(k)~&x_2(k)~x_3(k)~x_1(k)x_2(k)~ x_2x_3(k)~x_1(k)x_3(k)]^\top, -\end{align*} -and collect data $\mathcal{X}_0$ and $\mathcal{X}_1$ with time horizon $T=50$, equivalently $0.05$s, from initial point $(0.5, 0.5,0.5)$ and choose random inputs along the evolution of the trajectory from the set $U=[-100,100]$. - -\noindent\BW{\textbf{Second Nonlinear}} - -\subsubsection{Linear Systems}% -We consider the following dt-LS systems. - -\noindent\textbf{RLC Circuit.} -\begin{align*} -\Sigma : \begin{cases} -i(k+1) = i(k) + \tau(-\frac{R}{L}i(k) - \frac{1}{L}v(k)) + u_1(k), \\ -v(k+1) = v(k) + \tau(\frac{1}{C}i(k)) + u_2(k), -\end{cases} -\end{align*} -We consider the safety of an RLC Circuit, based on~\cite{anand2022kstochastic}, with the dynamics given above, where $i(k)$ denotes the current at time $k$, $v(k)$ is the voltage, $\tau=0.5$s is the sampling time, $R=2\omega$ is the series resistance, $L=9$H is the series inductance, $C=0.5$F is the capacitance of the circuit. We use hypercubes as the state space of the system $X=[-2,2]\times[-4,4]$, initial set $X_I=[0,0.5]\times[0,1]$, and unsafe set $X_U=[1,2]\times[-4,4]$. We construct $\mathcal{X}_{0},\mathcal{U}_{0}$ and $\mathcal{X}_{1}$ by taking a $15$s time horizon trajectory, with initial state $(0,0)$ and random inputs along the evolution of the trajectory from the set $U=[-1,1]\times[-1,1]$. - -\noindent\textbf{DC Motor.} -\begin{align*} -%\label{eq:DC-motor-example} -\Sigma : \begin{cases} -x_1(k+1) = x_1(k) - \tau(\frac{R}{L}x_1(k) + \frac{k_{dc}}{L}x_2(k)) + u_1(k), \\ -x_2(k+1) = x_2(k) + \tau(\frac{k_{dc}}{J}x_1(k) - \frac{b}{J}x_2(k)) + u_2(k), -\end{cases} -\end{align*} -We also consider the safe operation of a DC Motor, based on~\cite{adewuyi2013dc}, with the dynamics given above where $x_1,x_2,R=1,L=0.01,J=0.01$ are the armature current, the rotational speed of the shaft, the electrical resistance, the electrical inductance, and the moment of inertia of the rotor, respectively. In addition, $\tau=0.01$, $b=1$, and $k_{dc}=0.01$, represent, respectively, the sampling time, the motor torque, and the back electromotive force. We use hypercubes as the state space of the system $X=[0.1,0.5]\times[0.1,1]$, initial set $X_I=[0.1,0.4]\times[0.1,0.55]$, and unsafe set $X_U=[0.45,0.5]\times[0.6,1]$. We first construct the matrices $\mathcal{X}_{0},\mathcal{U}_{0}$ and $\mathcal{X}_{1}$ by taking a trajectory with time horizon $15$s. We construct $\mathcal{X}_{0},\mathcal{U}_{0}$ and $\mathcal{X}_{1}$ by taking a $15$s time horizon trajectory, with initial state $(0,0)$ and random inputs along the evolution of the trajectory from the set $U=[-0.1,0.1]\times[-0.1,0.1]$. - -\noindent\textbf{Room Temperature System.} -\begin{equation*} -\Sigma_d:\begin{cases} -x_1(k+1) = (1 - \tau(\alpha + \alpha_{e1}))x_1(k) + \tau\alpha x_2(k) + \tau\alpha_{e1} T_e,\\ -x_2(k+1) = (1 - \tau(\alpha + \alpha_{e2}))x_2(k) + \tau\alpha x_1(k) + \tau\alpha_{e2}T_e, -\end{cases} -\end{equation*} -We consider the two room system from the FOSSIL benchmarks~\cite{abate2021fossil}, with dynamics above, where the discretization parameter $\tau = 5$, heat exchange constants $\alpha = 5\times 10^{-2}, \alpha_{e1} = 5\times 10^{-3}, \alpha_{e2} = 8\times10^{-3}$, and external temperature $T_e = 15$. We consider regions of interest $X=[18,23]^2$, $X_I=[18,19.75]^2$, and $X_U=[22,23]$. \BW{add details above initial state and trajectory length.} This is a verification example as no control inputs are present and no controller is designed. - -\noindent\textbf{Two Tank System.} -\begin{equation*} -\Sigma_d^\varsigma\!:\begin{cases} -h_1(k+1) = (1-\tau\frac{\alpha_1}{A_1})h_1(k) + \tau\frac{q_1(k)}{A_1},\\ -h_2(k+1) = \tau\frac{\alpha_1}{A_2}h_1(k) + (1-\tau\frac{\alpha_2}{A_2})h_2(k) + \tau\frac{q_o(k)}{A_2}, -\end{cases} -\end{equation*} -Consider a two-tank system~\cite{ramos2007mathematical}, characterized by the above difference equations where $h_1$, $h_2$ are heights of the fluid in two tanks. Additionally, $\alpha_i$ and $A_i$ are the valve coefficient and area of tank $i$, and $q_1$ and $q_o$ are the inflow and outflow rate of tank $1$ and $2$, respectively. Furthermore, $\tau=0.1$, $\frac{\alpha_1}{A_1}=1$,$\frac{q_1}{A_1}=4.5$, $\frac{\alpha_1}{A_2}=1$, $\frac{\alpha_2}{A_2}=1$ and $\frac{q_o}{A_2}=-3$. Regions of interest are $X=[1,10]\times[1,10]$, $\initial=[1.75,2.25]\times[1.75,2.25]$, $\unsafe=[9,10]\times[9,10]$. \BW{add details above initial state and trajectory length.} This is a verification example as no control inputs are present and no controller is designed. - -\section{Results}\label{sec:results} -- Create a full page table for the four scenarios, each with the safety function, stability barrier function and controller. -- Compare to other tools both in terms of performance and data requirements -- MATLAB w/ these algorithms? -Presumably can cite Behrad's work for dt-NPS? -- Can we cite PRoTECT but state that we're not comparing since we're not dealing with stochastic systems? -(Yes, but we'll do this in the intro's related materials subsection) - -\bibliographystyle{ieeetran} -\bibliography{biblio} - -\end{document} diff --git a/TRUST-docs/out/main.aux b/TRUST-docs/out/main.aux deleted file mode 100644 index 19b4744..0000000 --- a/TRUST-docs/out/main.aux +++ /dev/null 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IEEEtran.bst, version: 1.14 (2015/08/26) -\begin{thebibliography}{10} -\providecommand{\url}[1]{#1} -\csname url@samestyle\endcsname -\providecommand{\newblock}{\relax} -\providecommand{\bibinfo}[2]{#2} -\providecommand{\BIBentrySTDinterwordspacing}{\spaceskip=0pt\relax} -\providecommand{\BIBentryALTinterwordstretchfactor}{4} -\providecommand{\BIBentryALTinterwordspacing}{\spaceskip=\fontdimen2\font plus -\BIBentryALTinterwordstretchfactor\fontdimen3\font minus - \fontdimen4\font\relax} -\providecommand{\BIBforeignlanguage}[2]{{% -\expandafter\ifx\csname l@#1\endcsname\relax -\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}% -\typeout{** loaded for the language `#1'. Using the pattern for}% -\typeout{** the default language instead.}% -\else -\language=\csname l@#1\endcsname -\fi -#2}} -\providecommand{\BIBdecl}{\relax} -\BIBdecl - -\bibitem{nejati2023data} -A.~Nejati and M.~Zamani, ``Data-driven synthesis of safety controllers via - multiple control barrier certificates,'' \emph{IEEE Control Systems Letters}, - 2023. - -\bibitem{breschi2021direct} -V.~Breschi, C.~De~Persis, S.~Formentin, and P.~Tesi, ``Direct data-driven - model-reference control with lyapunov stability guarantees,'' in \emph{2021 - 60th IEEE conference on decision and control (CDC)}.\hskip 1em plus 0.5em - minus 0.4em\relax IEEE, 2021, pp. 1456--1461. - -\bibitem{ren2024formal} -T.~Ren, W.~Lin, and Z.~Ding, ``Formal synthesis of safety controllers via $ k - $-inductive control barrier certificates,'' \emph{IEEE Transactions on - Reliability}, 2024. - -\bibitem{willems2005note} -J.~C. Willems, P.~Rapisarda, I.~Markovsky, and B.~L. De~Moor, ``A note on - persistency of excitation,'' \emph{Systems \& Control Letters}, vol.~54, - no.~4, pp. 325--329, 2005. - -\bibitem{prajna2002introducing} -S.~Prajna, A.~Papachristodoulou, and P.~A. Parrilo, ``Introducing sostools: A - general purpose sum of squares programming solver,'' in \emph{Proceedings of - the 41st IEEE Conference on Decision and Control, 2002.}, vol.~1.\hskip 1em - plus 0.5em minus 0.4em\relax IEEE, 2002, pp. 741--746. - -\bibitem{bisoffi2020data} -A.~Bisoffi, C.~De~Persis, and P.~Tesi, ``Data-based guarantees of set - invariance properties,'' \emph{IFAC-PapersOnLine}, vol.~53, no.~2, pp. - 3953--3958, 2020. - -\bibitem{bisoffi2022controller} -------, ``Controller design for robust invariance from noisy data,'' \emph{IEEE - Transactions on Automatic Control}, vol.~68, no.~1, pp. 636--643, 2022. - -\bibitem{nejati2022data} -A.~Nejati, B.~Zhong, M.~Caccamo, and M.~Zamani, ``Data-driven controller - synthesis of unknown nonlinear polynomial systems via control barrier - certificates,'' in \emph{Learning for Dynamics and Control Conference}.\hskip - 1em plus 0.5em minus 0.4em\relax PMLR, 2022, pp. 763--776. - -\bibitem{martin2023guarantees} -T.~Martin, T.~B. Sch{\"o}n, and F.~Allg{\"o}wer, ``Guarantees for data-driven - control of nonlinear systems using semidefinite programming: A survey,'' - \emph{Annual Reviews in Control}, p. 100911, 2023. - -\bibitem{samari2024single} -B.~Samari, O.~Akbarzadeh, M.~Zaker, and A.~Lavaei, ``From a single trajectory - to safety controller synthesis of discrete-time nonlinear polynomial - systems,'' \emph{arXiv preprint arXiv:2409.10026}, 2024. - -\bibitem{de2019formulas} -C.~De~Persis and P.~Tesi, ``Formulas for data-driven control: Stabilization, - optimality, and robustness,'' \emph{IEEE Transactions on Automatic Control}, - vol.~65, no.~3, pp. 909--924, 2019. - -\bibitem{parrilo2003semidefinite} -P.~A. Parrilo, ``Semidefinite programming relaxations for semialgebraic - problems,'' \emph{Mathematical programming}, vol.~96, pp. 293--320, 2003. - -\bibitem{Yuan_SumOfSquares_py} -\BIBentryALTinterwordspacing -C.~Yuan, ``{SumOfSquares.py}.'' [Online]. Available: - \url{https://github.com/yuanchenyang/SumOfSquares.py} -\BIBentrySTDinterwordspacing - -\bibitem{wang2024convex} -H.~Wang, K.~Margellos, A.~Papachristodoulou, and C.~De~Persis, ``Convex - co-design of control barrier functions and feedback controllers for linear - systems,'' 2024. - -\bibitem{samari2024singletrajectory} -\BIBentryALTinterwordspacing -B.~Samari, O.~Akbarzadeh, M.~Zaker, and A.~Lavaei, ``From a single trajectory - to safety controller synthesis of discrete-time nonlinear polynomial - systems,'' 2024. [Online]. Available: \url{https://arxiv.org/abs/2409.10026} -\BIBentrySTDinterwordspacing - -\bibitem{abate2021fossil} -A.~Abate, D.~Ahmed, A.~Edwards, M.~Giacobbe, and A.~Peruffo, ``{FOSSIL: a - software tool for the formal synthesis of lyapunov functions and barrier - certificates using neural networks},'' in \emph{Proceedings of the 24th - International Conference on Hybrid Systems: Computation and Control}, 2021, - pp. 1--11. - -\bibitem{anand2022kstochastic} -M.~Anand, V.~Murali, A.~Trivedi, and M.~Zamani, ``K-inductive barrier - certificates for stochastic systems,'' in \emph{Proceedings of the 25th ACM - International Conference on Hybrid Systems: Computation and Control}, 2022, - pp. 1--11. - -\bibitem{adewuyi2013dc} -P.~A. Adewuyi, ``Dc motor speed control: A case between pid controller and - fuzzy logic controller,'' \emph{international journal of multidisciplinary - sciences and engineering}, vol.~4, no.~4, pp. 36--40, 2013. - -\end{thebibliography} diff --git a/TRUST-docs/out/main.blg b/TRUST-docs/out/main.blg deleted file mode 100644 index 5d2fa03..0000000 --- a/TRUST-docs/out/main.blg +++ /dev/null @@ -1,62 +0,0 @@ -This is BibTeX, Version 0.99d (TeX Live 2024) -Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 -The top-level auxiliary file: main.aux -The style file: ieeetran.bst -Reallocated singl_function (elt_size=4) to 100 items from 50. -Reallocated singl_function (elt_size=4) to 100 items from 50. -Reallocated singl_function (elt_size=4) to 100 items from 50. -Reallocated wiz_functions (elt_size=4) to 6000 items from 3000. -Reallocated singl_function (elt_size=4) to 100 items from 50. -Database file #1: biblio.bib -Warning--entry type for "Yuan_SumOfSquares_py" isn't style-file 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za>Xv&tm<=6?HJU$A7L|S;bs)eqE$A!daO4rp$%Io9ggA1@9L|b;NYU`ESf@WK5mK**3Q@59sX))#3fjVqux_=-gn*M0K@QlO;>xFj@_$ z60_DUhIA0yvBi@8mZxhLiw}mpF11)VrN`nopcaWnZVKdkE9Qn~$#Ri!7HdHz5IEL? z@ZmVL7o8W|t}IIys}f`yOJs-M?Y(>sn|)l!@TzQbZf9U03lj`UDtn`zh z9rr}x2;%|zwO21m(&*fGtBk(i%QGy2MGt+s%3s-ni}YVn&!3k`9!>S(2DitdO8K>I zsV9;e$x6U;f8O-Me{*!L>vLrH^A}3IuIn11jb0sp^Dn=@lg%o`7yoWA{`%WLKY!xg z&17ay!fB@A3y!@>;M1br#CPD^8WL0pGFYI@Z!5r2lR)JKYsY-pPxSe`sT%d00yhr I9$NYe0G?1FO#lD@ From 5fa57371176f17c1b406ad86f6a8f6f83993841e Mon Sep 17 00:00:00 2001 From: Ben Wooding <38587669+Kiguli@users.noreply.github.com> Date: Mon, 7 Apr 2025 14:07:23 +0100 Subject: [PATCH 09/23] TRUST Paper (accepted to HSCC) --- .github/workflows/deploy.yml | 18 +++++++++--------- TRUST_arXiv.pdf | Bin 0 -> 3398563 bytes package-lock.json | 2 +- 3 files changed, 10 insertions(+), 10 deletions(-) create mode 100644 TRUST_arXiv.pdf diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml index 77db701..3e8acd0 100644 --- a/.github/workflows/deploy.yml +++ b/.github/workflows/deploy.yml @@ -11,7 +11,7 @@ concurrency: jobs: deploy: - runs-on: ubuntu-latest + runs-on: ubuntu-22.04 steps: - name: Configure SSH @@ -26,8 +26,8 @@ jobs: echo "$SSH_PRIVATE_KEY" > ~/.ssh/github chmod 600 ~/.ssh/github cat >> ~/.ssh/config <?>%QGlP_~}Gs*o^-Rb_jDwV8S52=EP z7%d|mD->xw6e|G(fxVFx6b}ypy_ltqi>cFpP8&lPQxQ{RdlORvdKptYa~BH&Rt`1- zK0YXC7bjCgTPTlBTb1d!Lk5JNGwL32lGA~Ga1w^71OoWTVYp(z+E=JZLt;TB(u0A$ z`s(a~87p{^)sv>~>Kn8BBV%r@)78PanQD~$w%R&bGx5cF-y2vk$5dVVw(H&6S=-(E zHv7Zk%BI?z5eBXCtEO|k91mTyGiy8V)jv^cZ>p(s5YG_@bN_fYZq_7)>!{mnwY(As z2@VpAk96D3BC5R*uT&*2BFd+Vu7asG>^)Ft6N0h=IG|= z*)8p@jp;5PH9d@|hjMM3?o+YV9*-m0`>y< z0coN%W^s$7hF3ue*w8#q8#NgLL#6O?8IJ4FWegFakYT-ZVnKm$sqkKg0Imp!CY3O# z8|kcxzLD$sK1WbXI=IXd!yceK2DyN8oqCX0%;d}fhnhh1nXdtzn!BTL4zDrikq72D z1akf7Ub3G#!Sar5Ff>$F)ocKbX0#W|M*?+ZgU15mr37%?;qpT_`b8O3hJKK|2fd{Q z(a8*!?M)Cp6i;R4clB#(QeN*UiR1<_U&ZU-N2}5HsL$5Zt-+s*07f5dK4-|-17=v3 zFz=QkaEE@)XOk?apMO`TFk)`DSnSL!p)9Bw 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