Comparing decompositions of X and X.T.dot(X)

svd_X_vs_svd_XTX.py

import numpy as np
rng = np.random.RandomState(42)

n_samples, n_features = 100, 50

X = rng.randn(n_samples, n_features)

V1, S1, VT1 = np.linalg.svd(X.T.dot(X), full_matrices=True)
U2, S2, VT2 = np.linalg.svd(X, full_matrices=True)
S3, V3 = np.linalg.eigh(X.T.dot(X))
S3, V3 = S3[::-1], V3[:, ::-1]


import matplotlib.pyplot as plt

plt.figure()
plt.subplot(3, 4, 1)
plt.imshow(VT1 - V1.T, interpolation="nearest")
plt.colorbar()
plt.title("VT1 - V1.T")

plt.subplot(3, 4, 2)
plt.imshow(VT1 - VT2, interpolation="nearest")
plt.colorbar()
plt.title("VT1 - VT2")

plt.subplot(3, 4, 3)
plt.imshow(VT1 - V3.T, interpolation="nearest")
plt.colorbar()
plt.title("VT1 - V3.T")

plt.subplot(3, 4, 4)
plt.imshow(VT2 - V3.T, interpolation="nearest")
plt.colorbar()
plt.title("VT2 - V3.T")

plt.subplot(3, 4, 6)
plt.imshow(VT1 + VT2, interpolation="nearest")
plt.colorbar()
plt.title("VT1 + VT2")

plt.subplot(3, 4, 7)
plt.imshow(VT1 + V3.T, interpolation="nearest")
plt.colorbar()
plt.title("VT1 + V3.T")

plt.subplot(3, 4, 8)
plt.imshow(VT2 + V3.T, interpolation="nearest")
plt.colorbar()
plt.title("VT2 + V3.T")


plt.subplot(3, 4, 10)
plt.plot(S1 - S2 ** 2)
plt.title("S1 - S2 ** 2")

plt.subplot(3, 4, 11)
plt.plot(S1 - S3)
plt.title("S1 - S3")

plt.subplot(3, 4, 12)
plt.plot(S2 ** 2 - S3)
plt.title("S2 ** 2 - S3")

plt.show()