Hi all,
I wanted to plot complex valued functions with real support:
f : R -> C
The plot should show the absulote value abs(f)^2 and the phase angle(f).
The demand for such a plot type originates from quantum mechanics
where I want to plot |phi> and/or <phi|phi> in this way showing
the phase of the wave function.
For this task I wrote a little script and it works quite well.
But I have a question regarding the color coding of the phase.
Is there a better way to provide the rgb_colors to the line collection?
Any hints to make the script more efficient would help.
I need to run it on hundreds of frames to produce animations.
BTW: You can add this to your gallery page if you want.
Maybe it's helpful to other people.
-- Raoul
from numpy import pi, empty, array
from matplotlib.colors import hsv_to_rgb
from matplotlib.collections import LineCollection
from matplotlib.pyplot import gca, plot
def phaseplot(grid, phase, modulus, label="", color="k", alpha=1.0, linestyle="solid", linewidth=1, marker="None"):
"""Plot the modulus complex valued function $f:R -> C$ together with its phase in a color coded fashion.
@param grid: The grid nodes of the real domain R
@param phase: The phase of the complex domain result f(grid)
@param modulus: The modulus of the complex domain result f(grid)
"""
# Color mapping
hsv_colors = empty((1, len(grid), 3))
hsv_colors[:, :, 0] = 0.5*(pi+phase)/pi
hsv_colors[:, :, 1] = 1.0
hsv_colors[:, :, 2] = 1.0
rgb_colors = hsv_to_rgb(hsv_colors)
# Put all the vertical line into a collection
segments = [ array([[node,0], [node,value]]) for node, value in zip(grid, modulus) ]
line_segments = LineCollection(segments)
# Set some properties of the lines
rgb_colors = line_segments.to_rgba(rgb_colors)
line_segments.set_color(rgb_colors[0])
line_segments.set_linestyle(linestyle)
line_segments.set_linewidth(linewidth)
# Plot to the current axis instance
ax = gca()
ax.add_collection(line_segments)
ax.plot(grid, modulus, color=color, linestyle=linestyle, linewidth=linewidth, alpha=alpha)
if __name__=='__main__':
import numpy as np
from pylab import *
x = np.r_[-1.:1.:1j*2**12]
u = np.exp(-x**2)*(np.cos(10*x) + 1j *np.sin(10*x))
rvals = np.real(u)
ivals = np.imag(u)
cvals = np.conjugate(u)*u
angles = np.angle(u)
figure(figsize=(20,20))
subplot(2,2,1)
phaseplot(x, angles, rvals)
xlabel(r"$\Re \psi$")
subplot(2,2,2)
phaseplot(x, angles, ivals)
xlabel(r"$\Im \psi$")
subplot(2,2,3)
phaseplot(x, angles, cvals)
xlabel(r"$|\psi|^2$")
savefig("phaseplot.png")
#savefig("phaseplot.eps")
show()
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