cplot 0.5.0

Plot complex-valued functions

Plot complex-valued functions with style.

cplot helps plotting complex-valued functions in a visually appealing manner.

There are two basic building blocks:

• Contours along constant absolute value and/or the constant argument (phase, angle)
• domain coloring, i.e., mapping the absolute value to lightness and the complex argument to the chroma of the representing color

Install with

pip install cplot

and use as

import numpy as np

import cplot


def f(z):
    return np.sin(z ** 3) / z


plt = cplot.plot(
    f,
    (-2.0, +2.0),
    (-2.0, +2.0),
    400,
    # colorbars: bool = True,
    # abs_scaling="h-1.0",        # how to scale the lightness in domain coloring
    # colorspace: str = "cam16",  # ditto
    # abs/args contour lines:
    # levels=("auto", (-np.pi / 2, 0, np.pi / 2, np.pi)),
    # linecolors = "#a0a0a050",
    # linestyles = "solid",
    # linestyle_abs1 = "solid"
)
plt.show()

Other useful functions:

# There is a tripcolor function as well for triangulated 2D domains
cplot.tripcolor(triang, z)

# The function get_srgb1 returns the SRGB1 triple for every complex input value.
# (Accepts arrays, too.)
z = 2 + 5j
val = cplot.get_srgb1(z)

• abs_scaling can be used to adjust the use of colors. h with a value less than 1.0 adds more color which can help isolating the roots and poles (which are still black and white, respectively). h-0.0 ignores the magnitude of f(z) completely. arctan is another possible scaling.

• colorspace can be set to hsl to get the common fully saturated, vibrant colors. This is usually a bad idea since it creates artifacts which are not related with the underlying data. From Wikipedia:

  Since the HSL color space is not perceptually uniform, one can see streaks of perceived brightness at yellow, cyan, and magenta (even though their absolute values are the same as red, green, and blue) and a halo around L = 1/2. Use of the Lab color space corrects this, making the images more accurate, but also makes them more drab/pastel.

  Default is "cam16"; very similar is "cielab" (not shown here).

Consider the test function (math rendered with xdoc)

f(z) = \frac{(z^2 - 1) (z - 2 - 1j)^2}{z^2 + 2 + 2j}

h-1.0	h-0.5	h-0.0

The representation is chosen such that

• values around 0 are black,
• values around infinity are white,
• values around +1 are green,
• values around -1 are deep purple,
• values around +i are blue,
• values around -i are orange.

(Compare to the z¹ reference plot below.)

With this, it is easy to see where a function has very small and very large values, and the multiplicty of zeros and poles is instantly identified by counting the color wheel passes around a black or white point.

Gallery

All plots are created with default settings.

z**1	z**2	z**3

1/z	z / abs(z)	(z+1) / (z-1)

z ** z	(1/z) ** z	z ** (1/z)

np.sqrt	z**(1/3)	z**(1/4)

np.log	np.exp	exp(1/z)

np.sin	np.cos	np.tan

np.sinh	np.cosh	np.tanh

np.arcsin	np.arccos	np.arctan

sin(z) / z	cos(z) / z	tan(z) / z

scipy.special.gamma	scipy.special.digamma	mpmath.zeta

mpmath.siegeltheta	mpmath.siegelz	Riemann-Xi

Testing

To run the cplot unit tests, check out this repository and type

pytest

Similar projects and further reading

• https://github.com/endolith/complex_colormap
• John D. Cook
• Elias Wegert, Visual Complex Functions
• Juan Carlos Ponce Campuzano, DC gallery

License

This software is published under the GPLv3 license.