Determinant of a (large) 1554 x 1554 matrix in Python

Question

I need to calculate the determinant of a large 1554,1554 matrix of values with single precision in python. In doing so I encounter a runtime warning:

import numpy as np

from numpy import linalg as LA

a = np.random.random((1554, 1554))

b = np.random.random((1554, 1554))

c = np.dot(a,b)

det = LA.det(c)

RuntimeWarning: overflow encountered in det r = _umath_linalg.det(a, signature=signature)

Any ideas on how I can work around this problem? Many thanks!

Edit: this question is unique in that it specifically refers to computing the determinant of large matrix in double precision, though a possible answer is included here: Can I get the matrix determinant using Numpy?

@JamieMac check [this answer](http://stackoverflow.com/a/19317237/832621) — Saullo G. P. Castro, Sep 24 '16 at 13:22
I am solving the Schlitter equation, for which I need to find the determinant — user 123342, Sep 24 '16 at 13:52
@nluigi I found that any matrices of 313x313 or larger return Inf. — user 123342, Sep 24 '16 at 13:54
Edit: I have found a previous answer to this question here (http://stackoverflow.com/questions/462500/can-i-get-the-matrix-determinant-using-numpy). Thanks for your input and sorry for duplication! — user 123342, Sep 24 '16 at 14:00
To be fair your question is not a duplicate of the linked question even though one of the answers solves your specific problem ... — jadsq, Sep 24 '16 at 14:05

dnalow · Accepted Answer · 2016-09-24T13:31:19.457

2

You can use this relation: https://wikimedia.org/api/rest_v1/media/math/render/svg/f6404a766d86e9d78a5c4f82e05de37469a5f8e9

from https://en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant

So divide your matrix by the mean and then compute the determinant to avoid overflow. Later you can multiply with the mean to the power of n (length of one axis)

edit: I'm not sure if the mean is the ideal choice though. This is more a math question

edited Sep 24 '16 at 13:31

answered Sep 24 '16 at 13:19

dnalow

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OP used np.random.random() to generate his matrices, meaning the mean will be about 0.5. Won't this make the computation *more* complicated? – Max May 24 '19 at 02:50

Determinant of a (large) 1554 x 1554 matrix in Python

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