Factor out & improve accuracy of derivatives calculations in axisartist. #24509
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timhoffm
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Nov 21, 2022
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Good catch, I assumed that the rest of the code always ensures xmin<=xmax, ymin<=ymax, but there's actually test_curvelinear3 which tests the case ymin>ymax; I'm not sure how robust the rest of the codebase is to handle that but I added some sorted() calls to handle that here. |
oscargus
approved these changes
Nov 29, 2022
oscargus
reviewed
Nov 29, 2022
lib/mpl_toolkits/axisartist/tests/test_grid_helper_curvelinear.py
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grid_helper_curvelinear and floating_axes, which can both draw axes that are neither horizontal nor vertical, need to compute the derivatives of the data-coords-to-screen-coords transform (actually, of data-coords-to-data-coords-of-intermediate-horizontal/vertical-axes) to get the angles at which to draw the axes labels, ticks and ticklabels. Factor out this calculation into a _value_and_jacobian helper. Instead of selecting the step size as some fraction of lat_factor/lon_factor/delta_extremes, use the square root of machine precision epsilon, which is standard and (approximately) optimal for non-centered numerical differentiation (see e.g. scipy.optimize.approx_fprime, or the Wikipedia article on numerical differentiation) -- and also happens to avoid introducing an extra paremeter into _value_and_jacobian. Also lift some calculations out of get_tick_iterators (it doesn't really matter whether they are done inside or outside of get_tick_iterators, but dedenting the block is always nice). The increases in tolerances arise because the calculations of the derivatives actually become *more* precise; for example, printing the angle returned by get_axislabel_pos_angle and running test_polar_box shows that previously the axes labels were drawn at angles of (45+1e-11) and 45.135 degrees, whereas they are now drawn at exactly 45 degrees. These tolerances (0.27/0.12) are actually still very small; e.g. removing the text.kerning_factor backcompat setting would require bumping the tolerance to more than 5.
timhoffm
approved these changes
Dec 13, 2022
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grid_helper_curvelinear and floating_axes, which can both draw axes that are neither horizontal nor vertical, need to compute the derivatives of the data-coords-to-screen-coords transform (actually, of data-coords-to-data-coords-of-intermediate-horizontal/vertical-axes) to get the angles at which to draw the axes labels, ticks and ticklabels.
Factor out this calculation into a _value_and_jacobian helper. Instead of selecting the step size as some fraction of
lat_factor/lon_factor/delta_extremes, use the square root of machine precision epsilon, which is standard and (approximately) optimal for non-centered numerical differentiation (see e.g.
scipy.optimize.approx_fprime, or the Wikipedia article on numerical differentiation) -- and also happens to avoid introducing an extra paremeter into _value_and_jacobian.
Also lift some calculations out of get_tick_iterators (it doesn't really matter whether they are done inside or outside of get_tick_iterators, but dedenting the block is always nice).
The increases in tolerances arise because the calculations of the derivatives actually become more precise; for example, printing the angle returned by get_axislabel_pos_angle and running test_polar_box shows that previously the axes labels were drawn at angles of (45+1e-11) and 45.135 degrees, whereas they are now drawn at exactly 45 degrees. These tolerances (0.27/0.12) are actually still very small; e.g. removing the text.kerning_factor backcompat setting would require bumping the tolerance to more than 5.
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Documentation and Tests
pytestpasses)Release Notes
.. versionadded::directive in the docstring and documented indoc/users/next_whats_new/.. versionchanged::directive in the docstring and documented indoc/api/next_api_changes/next_whats_new/README.rstornext_api_changes/README.rst