phase_mag_plot

This repository contains some sage/cython code for producing plots with logarithmic contouring. At some point in the future, I intend to put this (and related) functionality directly into sage, but for now this is where this lives.

This is designed to work with a relatively up-to-date version of sage running python3. I have not tested it with python2.

To use this code right now, use load("phase_mag_plot.spyx") from a running sage session, and then phase_mag_complex_plot to produce a plot. The arguments and description of phase_mag_complex_plot is almost identical to those of complex_plot within sage. The resulting plot can be manipulated in the same matplotlib-inspired ways as other graphics in sage.

Note also that the contours are more sensitive the the argument plot_points than the coloration; to produce high-quality images, it is necessary to use several plotting points.

~$ git clone https://github.com/davidlowryduda/phase_mag_plot
...
~$ cd phase_mag_plot
...
sage: load("phase_mag_plot.spyx")
Compiling ./phase_mag_plot.spyx...
sage: phase_mag_complex_plot(sqrt(x), (-5, 5), (-5, 5), plot_points=400)
# produces a plot of the square root function

# note that standard plotting tooling is still available, eg
g = phase_mag_complex_plot((x-3)*(x+3*i)*x^2, (-5, 5), (-5, 5), plot_points=500)
g.show()

g.axes(show=False)
g.show()

This also includes a tile-type contour (inspired heavily from the domain coloring methods of Elias Wegert) that can be activated by calling tiled=True. For example,

g = phase_mag_complex_plot((x-3)*(x+3*i)*x^2, (-5, 5), (-5, 5), tiled=True, plot_points=500)
g.axes(show=False)
g.show()

If you encounter any bugs or have any questions, let me know.

colormapplot

This repository also contains a version of colormapplot. This is a plotting routine with similar calling semantics as phase_mag_complex_plot and sage's default complex_plot, but which allows one to use matplotlib compatible colormaps to source the colors.

Note that this is not currently indexed in the reference Zenodo implementation.

For example,

# After loading color_complex_plot
g = color_complex_plot((x-3)*(x+3*i)*x^2, (-5, 5), (-5, 5), plot_points=500)
g.axes(show=False)
g.show()

By default, the colormap is chosen to be the cividis colormap. See Optimizing colormaps with consideration for color vision deficiency to enable accurate interpretation of scientific data by Nunez, Anderton, and Renslow for more information about this particular colormap.

This can handle any matplotlib compatible colormap. For example, if you prefer the colormap ocean, then you can use

import matplotlib.cm
g = color_complex_plot((x-3)*(x+3*i)*x^2, (-5, 5), (-5, 5),
                       cmap=matplotlib.cm.ocean,   # <--- new line
                       tiled=True, plot_points=500)
g.axes_color('white')
g.axes_label_color('white')
g.tick_label_color('white')
g.show()

I don't know why you would choose this colormap. And this colormap shows that certain defaults have been chosen that don't quite apply equally.

Not all functions look equally good in all colormaps, but now you can try them out.

License

This is closely modified from sage itself, and thus it is available under GPLv3+. A copy of this license is included in this repository, and a link is available in each source file.