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| author | Nao Pross <np@0hm.ch> | 2022-04-17 23:55:32 +0200 |
|---|---|---|
| committer | Nao Pross <np@0hm.ch> | 2022-04-17 23:55:32 +0200 |
| commit | 85d45cb2a89143fee1f4ac0e188c574b963645c1 (patch) | |
| tree | 4d0857b49e23e664e05a4c2395fa4afc96099cc7 /sph_harm.py | |
| download | FourierOnS2-85d45cb2a89143fee1f4ac0e188c574b963645c1.tar.gz FourierOnS2-85d45cb2a89143fee1f4ac0e188c574b963645c1.zip | |
Add existing code
Diffstat (limited to 'sph_harm.py')
| -rw-r--r-- | sph_harm.py | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/sph_harm.py b/sph_harm.py new file mode 100644 index 0000000..1d6227b --- /dev/null +++ b/sph_harm.py @@ -0,0 +1,71 @@ +# -*- coding: utf-8 -*-
+"""
+date of creation: Fri Mar 25 16:20:46 2022
+-------------------------------------------------
+@author : Manuel Cattaneo
+@contact: cattaneo.manuel@hotmail.com
+-------------------------------------------------
+
+Description:
+ Program used to play around with the spherical harmonics.
+
+Modules:
+"""
+import numpy as np
+# plot stuff
+import matplotlib.pyplot as plt
+import mpl_toolkits.mplot3d.axes3d as axes3d # to plot 3d
+import matplotlib.gridspec as gs # for grid layout
+# spherical harmonics
+from scipy.special import sph_harm
+"""
+------------------------------------------------------------------------------
+"""
+
+if __name__ == '__main__':
+ # grid spec
+ row = 3
+ col = 2*row-1
+ grid_spec = gs.GridSpec(row,col)
+ fig = plt.figure()
+
+ # creating spherical domain
+ N = 50
+ theta, phi = np.meshgrid(np.linspace(0, 2*np.pi, N), # theta in [0, 2pi]
+ np.linspace(0, np.pi, N)) # phi in [0, pi]
+
+ import matplotlib
+ # m < n
+ for y_grid in range(0,row):
+ for i,x_grid in enumerate(range(col//2-y_grid, col-col//2+y_grid)):
+ # real(...) to obtain only the cos(.) part. This is done in order
+ # to have the same functions as the ones at p.518 chapter 12.2.
+ m = y_grid
+ n = m+i+1
+ r = np.real( sph_harm(m, n, theta, phi) ) # Y_n^m
+ # coordinates transformation
+ x = r*np.cos(theta)*np.sin(phi)
+ y = r*np.sin(phi) *np.sin(theta)
+ z = r *np.cos(phi)
+
+ # adding subplot
+ ax = fig.add_subplot(grid_spec[y_grid,x_grid], projection='3d')
+ ax.set_axis_off()
+ ax.set_title(rf'$Y_{n}^{m}(\theta, \phi)$')
+
+ # colors
+ color_dim = r
+ color_min, color_max = color_dim.min(), color_dim.max()
+ norm = matplotlib.colors.Normalize(color_min,color_max)
+ m = plt.cm.ScalarMappable(norm, cmap='jet')
+ m.set_array([])
+ fc = m.to_rgba(color_dim)
+
+ # plot
+ plot = ax.plot_surface(x, y, z, facecolors = fc,
+ rstride=1, cstride=1,
+ # cmap=plt.get_cmap('jet'),
+ linewidth=0, antialiased=False, alpha=0.5)
+
+
+ plt.show()
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