Add script to draw polynomialsHEADmaster

1 files changed, 71 insertions, 0 deletions

diff --git a/presentation/figures/polynomials.py b/presentation/figures/polynomials.py
new file mode 100644
index 0000000..f622afe
--- /dev/null
+++ b/presentation/figures/polynomials.py
@@ -0,0 +1,71 @@
+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()