Python/Numpy SVD

gistfile1.py

import numpy as np

input = np.zeros((2, 2), dtype=complex)
input[0, 0] = 0.5 + 250j
input[0, 1] = -0.5
input[1, 0] = 0.5
input[1, 1] = -0.5 + 250j

result = np.linalg.svd(input, full_matrices=True)

# In the output we get three matrices, using which we can reconstruct original matrix.
# M = U*Sigma*V. M - original matrix.

# U: 2 by 2 matrix.
print result[0]

# Output:
# [
#   [-0.00141421 -7.07105367e-01j  0.00141421 +7.07105367e-01j]
#   [-0.70710678 -1.85770845e-17j -0.70710678 -1.83443295e-17j]
# ]

# Sigma: 2 by 2 diagonal matrix. Only the diagonal elements are displayed. Others are zeros.

print result[1]

# Output:
# [ 250.5005  249.5005]

# V: 2 by 2 matrix.

print result[2]

# Output:
# [
#   [-0.70710678+0.j          0.00141421-0.70710537j]
#   [ 0.70710678+0.j          0.00141421-0.70710537j]
# ]

# Check for correctness

U = result[0]
V = result[2]

# Cast to Complex data type
s = result[1]
S = np.zeros((2, 2), dtype=complex)
S[:2, :2] = np.diag(s)


# Check the original matrix and the reconstruction.
print np.allclose(input, np.dot(U, np.dot(S, V)))

# Output: True