.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_gallery_images_contours_and_fields_contours_in_optimization_demo.py:
==============================================
Contouring the solution space of optimizations
==============================================
Contour plotting is particularly handy when illustrating the solution
space of optimization problems. Not only can `.axes.Axes.contour` be
used to represent the topography of the objective function, it can be
used to generate boundary curves of the constraint functions. The
constraint lines can be drawn with
`~matplotlib.patheffects.TickedStroke` to distinguish the valid and
invalid sides of the constraint boundaries.
`.axes.Axes.contour` generates curves with larger values to the left
of the contour. The angle parameter is measured zero ahead with
increasing values to the left. Consequently, when using
`~matplotlib.patheffects.TickedStroke` to illustrate a constraint in
a typical optimization problem, the angle should be set between
zero and 180 degrees.
.. image:: /gallery/images_contours_and_fields/images/sphx_glr_contours_in_optimization_demo_001.png
:alt: contours in optimization demo
:class: sphx-glr-single-img
.. code-block:: default
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import patheffects
fig, ax = plt.subplots(figsize=(6, 6))
nx = 101
ny = 105
# Set up survey vectors
xvec = np.linspace(0.001, 4.0, nx)
yvec = np.linspace(0.001, 4.0, ny)
# Set up survey matrices. Design disk loading and gear ratio.
x1, x2 = np.meshgrid(xvec, yvec)
# Evaluate some stuff to plot
obj = x1**2 + x2**2 - 2*x1 - 2*x2 + 2
g1 = -(3*x1 + x2 - 5.5)
g2 = -(x1 + 2*x2 - 4.5)
g3 = 0.8 + x1**-3 - x2
cntr = ax.contour(x1, x2, obj, [0.01, 0.1, 0.5, 1, 2, 4, 8, 16],
colors='black')
ax.clabel(cntr, fmt="%2.1f", use_clabeltext=True)
cg1 = ax.contour(x1, x2, g1, [0], colors='sandybrown')
plt.setp(cg1.collections,
path_effects=[patheffects.withTickedStroke(angle=135)])
cg2 = ax.contour(x1, x2, g2, [0], colors='orangered')
plt.setp(cg2.collections,
path_effects=[patheffects.withTickedStroke(angle=60, length=2)])
cg3 = ax.contour(x1, x2, g3, [0], colors='mediumblue')
plt.setp(cg3.collections,
path_effects=[patheffects.withTickedStroke(spacing=7)])
ax.set_xlim(0, 4)
ax.set_ylim(0, 4)
plt.show()
.. _sphx_glr_download_gallery_images_contours_and_fields_contours_in_optimization_demo.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: contours_in_optimization_demo.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: contours_in_optimization_demo.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
Keywords: matplotlib code example, codex, python plot, pyplot
`Gallery generated by Sphinx-Gallery
`_