https://discourse.acados.org/t/bug-with-visual-studio-compiler-in-matlab-with-working-fix/1449

Support slack penalties for initial stage in MEX interface.

Follow-up on
https://discourse.acados.org/t/issue-in-setting-slack-variable-on-control-input/1456

The convention is as follows now:
- bounds on u and general linear constraints are also enforced on the
initial node
- bounds on x and nonlinear constraints are fully split and have to be
explicitly stated with `_0` correspondence to be enforced on the stage.

)

Condensing modules now provide
- `condense` - all condensing operations
- `condense_rhs` - condensing the right hand side
- `condense_lhs` - condensing the left hand side

Similarly, regularization modules now provide
- `regularize` - all operations
- `regularize_rhs` - operations on the right hand side
- `regularize_lhs` - operations on the left hand side

Only if RTI is split into preparation and feedback, the `_rhs` / `_lhs`
routines are called.
Otherwise, operations are done all together.
Addresses #1031

NOTE: using convexify with split RTI phase has now relatively overhead,
see #1035
Splitting the computations for `convexify` more efficiently should be
done in another PR.

- **Cast highest level workspace (SQP/SQP-RTI) only in precompute for
more speed**:
This still allows to reuse workspace across modules. This can only break
if one tries to reuse the acados workspace memory from outside.
- **Add CasADi sparsity detection** that is called when creating an
external function.
The CasADi sparsity struct in the generated functions contains an `int`
which always say inputs are sparse, often this is not the case. Thus, we
check now for speed!
- Added `sim_in_assign_and_advance`, this can be called to avoid calling
`calculate_size` twice. Doing this everywhere is rather tedious and does
not save very much.
- **Breaking**: precompute is now required!

On a small benchmark of an RTI with ERK and the cartpole this gives me
>20% speedup, from 78μs to 62μs.

- fix timings for RTI: subtimers `time_qp*`, `time_reg` now start at 0
when starting preparation and count operations in both phases
- cleanup comments
- make enum for RTI phase
- precompute integrator workspace_size

…1040)

In some places `tmp_ux` and `ux` where used in a mixed way, i.e.
`compute_fun` of constraint modules and what was fixed in #1039
- fixes bug when using globalization and cost computation
- fixes bug in globalization with slacks. Constraint was evaluated with
slack values from SQP iterate instead of values from the line search
candidate

Implementation:
- Removed all `tmp_*` pointers in SQP submodules
- Always evaluate at `ux`
- When one wants to evaluate at another iterate, these pointers have to
be temporarily set to another iterate and afterwards reset to the
nominal SQP iterate, as done in `ocp_nlp_evaluate_merit_fun` now.

…examples, Python docs) (#1044)

- formatting: tabs to spaces
- move cost integration memory preparation to precompute

This pull request implements the advanced-step real-time iteration
(AS-RTI)

It is implemented as a feature within the `RTI` module.
In order to use it, set the new options:
- `as_rti_level`
- `as_rti_iter`

The feedback phase of RTI and AS-RTI is the same.
The AS-RTI preparation phase is used instead of the "standard" RTI
preparation phase, when the options above are set.

Additionally, this adds the flag:
- `rti_log_residuals`: which allows to log the residuals within
(AS-)RTI. This was needed for the experiment in the paper, which reports
the residuals of the inner iterations. Limited to convex-over-nonlinear
and external cost modules for now.

The work in this PR is presented in the publication
"Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds
and Fast Implementation in acados" by Jonathan Frey, Armin Nurkanovic,
Moritz Diehl
https://arxiv.org/abs/2403.07101

Limitations:
- AS-RTI-B not implemented for ns > 0.
- AS-RTI-C only implemented for linear inequality constraints.

…inear and nonlinear least-squares costs (#1024)

* add flags indicating whether outer hessian is diagonal
* if outer hessian is diagonal and `ny > 4`, its diagonal Cholesky
factorization `W_chol` is computed manually and stored as `blasfeo_dvec`
* adjust matrix-matrix/matrix-vector multiplications involving `W_chol`
accordingly

---------

Co-authored-by: Jonathan Frey <[email protected]>

In this PR the following changes are suggested:
- all MATLAB examples are updated as suggested in #1009 
- some examples were modified to remove errors caused by calling
outdated structures (e.g., `sim.C_ocp`)
- additional comments were added in some `getting_started` examples
- some models were updated for improved naming consistency (e.g., using
`constr_expr_h` instead of `expr_h`)
- examples and tests were updated to work with the changes in variable
naming
- a test script that runs all the examples is added (also contains test
results on my laptop)
- a few lines were terminated to suppress unnecessary printing

Closes #1049

Co-authored-by: Hannes Homburger <[email protected]>

* cleanup python examples
* add Furuta pendulum

---------

Co-authored-by: Jonathan Frey <[email protected]>