phase_mag_plot

UPDATE - now included in sage

An improved version of this code is now in sage as of sage9.6. See the release tour for several examples of how they can be used with sage syntax.

I rewrote the complex_plot function to include what I have previously called ccomplex_plot, phase_mag_plot, and colormap_plot. It includes everything in this repository and slightly more.

Further, it's much faster (thanks to some assistance from other sage developers on using more numpy and less direct cython) and has a few additional features, such as setting how strongly each contour should appear and optionally including both phase and argument contours instead of just phase contours.

In short, Check it out. I keep this repository and the code as demonstrations and relatively readable, clean implementations. But for any use, I suggest using the version in sage.

Finally, I note that in principle it would be possible to extract the speed improvements and provide a standalone visualizer that doesn't require sage --- but I don't do that.

END UPDATE

This repository contains some sage/cython code for producing plots with logarithmic contouring. At some point in the futurein the past, 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.