CODEWITHSUNDEEP
pythonnumpysvdinfinity
user196574
user196574

Reputation: 113

Numpy SVD gives infinite singular values for array with finite elements

I've run into this problem (infinite singular values despite finite entries in an array) several times for relatively small arrays with dimensions around 100 by 100. The arrays are large enough that I've struggled to see a pattern. I give a working example below that I found by rounding the values in one of my matrices, though I wish I could engineer a simpler example.

import numpy as np
kmat = np.zeros((81, 81), dtype='complex')

kmat[([30, 32, 36, 36, 38, 38, 57, 57, 59, 59, 63, 65], [68, 14, 62, 74, 8, 20, 61, 73, 7, 19, 67, 13])] = (0.04+0.03j)
kmat[([31, 31, 37, 58, 64, 64],[35, 47, 41, 40, 34, 46])] = (0.16+0.11j)
kmat[([33, 33, 35, 35, 39, 41, 45, 45, 47, 47, 60, 62, 66, 66, 68, 68, 72, 74], [62, 74,  8, 20, 68, 14, 62, 74,  8, 20, 67, 13, 61, 73,  7, 19, 67, 13])] = (0.03+0.02j)
kmat[([34, 40, 40, 46, 61, 61, 67, 73, 73], [41, 35, 47, 41, 34, 46, 40, 34, 46])] = (0.13+0.09j)

kmat[([30, 30, 32, 32, 36, 38, 57, 59, 63, 63, 65, 65], [62, 74,  8, 20, 68, 14, 67, 13, 61, 73,  7, 19])] = -(0.04+0.03j)
kmat[([31, 37, 37, 58, 58, 64], [41, 35, 47, 34, 46, 40])] = -(0.16+0.11j)
kmat[([33, 35, 39, 39, 41, 41, 45, 47, 60, 60, 62, 62, 66, 68, 72, 72, 74, 74], [68, 14, 62, 74,  8, 20, 68, 14, 61, 73,  7, 19, 67, 13, 61, 73,  7, 19])] = -(0.03+0.02j)
kmat[([34, 34, 40, 46, 46, 61, 67, 67, 73], [35, 47, 41, 35, 47, 40, 34, 46, 40])] = -(0.13+0.09j)

print(np.linalg.svd(kmat, full_matrices = 0, compute_uv = 0))

The output is

[            inf 6.71714225e-001 6.71714225e-001 1.63401346e-001
 1.63401346e-001 1.63401346e-001 5.06904064e-017 4.89771960e-017
 2.03140157e-017 1.72656309e-017 1.40275705e-017 3.53543469e-018
 1.83729709e-018 1.12027584e-018 8.52297427e-020 1.81345172e-033
 1.27726594e-034 8.75935866e-035 2.02878907e-036 9.30164632e-049
 8.54881928e-050 6.95546444e-051 2.49250115e-052 4.92974326e-053
 1.18027016e-064 2.83787877e-066 3.61447306e-067 2.40364993e-069
 2.01469630e-069 6.85315161e-081 1.15983261e-085 9.21712550e-086
 3.87403183e-097 6.63966512e-102 5.67626333e-102 4.16050009e-118
 3.27338859e-134 2.33809507e-150 1.55632960e-166 1.82909508e-182
 1.14892283e-198 1.51906443e-214             nan             nan
             nan             nan             nan             nan
             nan             nan             nan             nan
             nan             nan             nan 0.00000000e+000
 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000
 0.00000000e+000 0.00000000e+000             nan             nan
             nan 0.00000000e+000 0.00000000e+000 0.00000000e+000
 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000
 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000
 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000
 0.00000000e+000]

The largest singular value is returned as infinity, inf. There are also 18 nan returned, as well as well as some nonzero and zero singular values. However, since every element of my array is not infinite, I don't see where this trouble is originating from.

Why is numpy's svd giving an infinite singular value for an array with finite values and what can I do to avoid this?

In searching for the answer, I've tried a variety of 3 by 3 matrices, such as those with a column or row of zeros, but the singular values appear to be fine.

Upvotes: 1

Views: 318

Answers (1)

Сергей Сараев
Сергей Сараев

Reputation: 21

I had the same error on Intel processors. You can fix this by installing the intel-numpy package.

pip install intel-numpy

More information: https://anaconda.org/intel/numpy

Upvotes: 2

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