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cplot

Plot complex-valued functions with style.

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

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, 400),
    (-2.0, +2.0, 400),
    # abs_scaling=lambda x: x / (x + 1),  # how to scale the lightness in domain coloring
    # contours_abs=2.0,
    # contours_arg=(-np.pi / 2, 0, np.pi / 2, np.pi),
    # emphasize_abs_contour_1: bool = True,
    # add_colorbars: bool = True,
    # add_axes_labels: bool = True,
    # saturation_adjustment: float = 1.28,
    # min_contour_length = None,
    # linewidth = None,
)
plt.show()

Historically, plotting of complex functions was in one of three ways

Only show the absolute value; sometimes as a 3D plot Only show the phase/the argument in a color wheel (phase portrait) Show contour lines for both arg and abs

Combining all three of them gives you a cplot:

See also Wikipedia: Domain coloring.

Features of this software:

  • cplot uses OKLAB, a perceptually uniform color space for the argument colors. This avoids streaks of colors occurring with other color spaces, e.g., HSL.
  • The contour abs(z) == 1 is emphasized, other abs contours are at 2, 4, 8, etc. and 1/2, 1/4, 1/8, etc., respectively. This makes it easy to tell the absolte value precisely.
  • For arg(z) == 0, the color is green, for arg(z) == pi/2 it's blue, for arg(z) = -pi / 2 it's orange, and for arg(z) = pi it's pink.

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)

Riemann sphere

cplot can also plot functions on the Riemann sphere, a mapping of the complex plane to the unit ball.

import cplot
import numpy as np

cplot.riemann_sphere(np.log)

Gallery

All plots are created with default settings.

z ** 1 z ** 2 z ** 3
Many more plots
1 / z 1 / z ** 2 1 / z ** 3
(z + 1) / (z - 1) Another Möbius transformation A third Möbius transformation
np.real z / abs(z) np.conj
z ** 6 + 1 z ** 6 - 1 z ** (-6) + 1
z ** z (1/z) ** z z ** (1/z)
np.sqrt z**(1/3) z**(1/4)
np.log np.exp np.exp2
np.exp(1 / z) z * np.sin(1 / z) np.cos(1 / z)
exp(- z ** 2) 1 / (1 + z ** 2) Error function
np.sin np.cos np.tan
sec csc cot
np.sinh np.cosh np.tanh
secans hyperbolicus cosecans hyperbolicus cotangent hyperbolicus
np.arcsin np.arccos np.arctan
np.arcsinh np.arccosh np.arctanh
Sinc, sin(z) / z cos(z) / z tan(z) / z
Integral sine Si Integral cosine Ci Lambert W function
Gudermannian function Exponential integral E1 Exponential integral Ei
mpmath.zeta Bernoulli function Dirichlet eta function
Hurwitz zeta function with a = 1/3 Hurwitz zeta function with a = 24/25 Hurwitz zeta function with s = 3 + 4i
scipy.special.gamma reciprocal Gamma scipy.special.loggamma
scipy.special.digamma Polygamma 1 Polygamma 2
Riemann-Siegel theta function Z-function Riemann-Xi
Jacobi elliptic function sn(0.6) cn(0.6) dn(0.6)
Jacobi theta 1 with q=0.1 * exp(0.1j * np.pi)) Jacobi theta 2 with the same q Jacobi theta 3 with the same q
Bessel function, first kind, order 1 Bessel function, first kind, order 2 Bessel function, first kind, order 3
Bessel function, second kind, order 1 Bessel function, second kind, order 2 Bessel function, second kind, order 3
Hankel function of first kind (n=1.0) Hankel function of first kind (n=3.1) Hankel function of second kind (n=1.0)
Fresnel S Fresnel C Faddeeva function
Airy function Ai Bi Exponentially scaled eAi
tanh(pi / 2 * sinh(z)) sinh(pi / 2 * sinh(z)) exp(pi / 2 * sinh(z))
Klein's j-invariant Dedekind eta function
Lambert series with 1s Lambert series with von-Mangoldt-coefficients Lambert series with Liouville-coefficients

Testing

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

tox

Similar projects and further reading

License

This software is published under the GPL-3.0 license. In cases where the constraints of the GPL prevent you from using this software, feel free contact the author.