pythonで球面調和関数

• scipyに球面調和関数を扱うモジュールがある(scipy.special.sph_harmとか)
• shtoolsというのは別の球面調和関数用のライブラリで、pythonから使うときは、shtoolsのラッパーのpyshtoolsを使う(こちら)
• scipyのを使ってお絵かき

import matplotlib.pyplot as plt
from matplotlib import cm, colors
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from scipy.special import sph_harm

phi = np.linspace(0, np.pi, 100)
theta = np.linspace(0, 2*np.pi, 100)
phi, theta = np.meshgrid(phi, theta)

# The Cartesian coordinates of the unit sphere
x = np.sin(phi) * np.cos(theta)
y = np.sin(phi) * np.sin(theta)
z = np.cos(phi)

m, l = 2, 3

# Calculate the spherical harmonic Y(l,m) and normalize to [0,1]
fcolors = sph_harm(m, l, theta, phi).real
m2, l2 = 2, 5
fcolors2 = sph_harm(m2, l2, theta, phi).real

fcolors = fcolors + fcolors2
fmax, fmin = fcolors.max(), fcolors.min()
fcolors = (fcolors - fmin)/(fmax - fmin)

# Set the aspect ratio to 1 so our sphere looks spherical
fig = plt.figure(figsize=plt.figaspect(1.))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, y, z,  rstride=1, cstride=1, facecolors=cm.seismic(fcolors))
# Turn off the axis planes
ax.set_axis_off()
plt.show()

• pyshtoolsを使って、係数をいじる→ipynb @ SHTOOLS