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authorNao Pross <np@0hm.ch>2022-05-28 20:32:55 +0200
committerNao Pross <np@0hm.ch>2022-05-28 20:32:55 +0200
commite40d26d336a353834461cbd8a86da00f1eb980cb (patch)
tree48150542404870b1e1cf0fca797660fdaceeb189 /presentation
parentUpdate slides (diff)
downloadFourierOnS2-e40d26d336a353834461cbd8a86da00f1eb980cb.tar.gz
FourierOnS2-e40d26d336a353834461cbd8a86da00f1eb980cb.zip
Add script to draw polynomialsHEADmaster
Diffstat (limited to 'presentation')
-rw-r--r--presentation/figures/polynomials.py71
1 files changed, 71 insertions, 0 deletions
diff --git a/presentation/figures/polynomials.py b/presentation/figures/polynomials.py
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+++ b/presentation/figures/polynomials.py
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+import numpy as np
+import pandas as pd
+import scipy.special
+
+import seaborn as sns
+import seaborn_image as isns
+import matplotlib.pyplot as plt
+
+import toolz
+
+# Basis functions for 2D Fourier
+
+@np.vectorize
+@toolz.curry
+def b(m, n, mu, nu):
+ return np.exp(2j * np.pi * (m * mu + n * nu))
+
+N = 100
+H = 4
+
+basis = []
+for m in range(H):
+ for n in range(H + 1):
+ mu = np.linspace(0, 1, N)
+ nu = np.linspace(0, 1, N)
+ muv, nuv = np.meshgrid(mu, nu)
+
+ bs = np.real(b(m, n, muv, nuv))
+ basis.append(bs)
+
+g = isns.ImageGrid(basis, col_wrap=(H + 1), cbar=False)
+g.fig.savefig("flat-basis-functions.pdf")
+
+plt.tight_layout()
+plt.show()
+
+# Legendre Polynomials
+
+N = 100
+
+sns.set_theme("talk", "darkgrid", font_scale=.75)
+fig, axes = plt.subplots(3, 4, figsize=(12, 8))
+
+x = np.linspace(-1, 1, N)
+for n in range(np.prod(axes.shape)):
+ p = scipy.special.lpmv(0, n, x)
+ # axes.ravel()[n].plot(x, p)
+ sns.lineplot(ax=axes.ravel()[n], x=x, y=p)
+
+plt.tight_layout()
+fig.savefig("legendre-polynomials.pdf")
+plt.show()
+
+# Associated Legendre Polynomials
+
+N = 100
+
+sns.set_theme("talk", "darkgrid", font_scale=.75)
+fig, axes = plt.subplots(2, 3, figsize=(12, 8))
+
+x = np.linspace(-1, 1, N)
+
+for m in range(3 * 2):
+ for n in range(5):
+ p = scipy.special.lpmv(m, m + n, x)
+ sns.lineplot(ax=axes.ravel()[m], x=x, y=p)
+ # sns.lineplot(x=x, y=p)
+
+plt.tight_layout()
+fig.savefig("associated-legendre-polynomials.pdf")
+plt.show()