# Inverting matrix after Cholesky decomposition does not finish for "large" dimension

I'm trying to invert the cholesky decomposition of a matrix. While this works for small a, for around a=~30, it no longer finishes.

From the _print_, I know that the problem is in the last line.

This seems a very odd behavior, as like matrix inversion would blow exponentially, which is not true, but even if it was it shouldn't go from taking 10s to finish to not finishing at all. Moreover, since the matrix N is triangular, shouldn't it even be faster to compute the inverse matrix?

a = 30
M = random_matrix(ZZ, a, x = -a, y = a)
M = M.T * M
N = M.inverse().cholesky()
print "choleskied"
Ni = N.inverse()


Thanks for the help!

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So, I found the problem.

In fact,

N.parent() == Full MatrixSpace of 30 by 30 dense matrices over Algebraic Real Field

since this has infinite precision, the computation takes forever.

This is solved, and the computation is almost instant (as expected), by using finite precision, i.e.

Ni = N.n().inverse()

Maybe this'll help someone.

Cheers! : )

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I cannot accept my answer, unfortunately (not enough points)

( 2019-06-20 00:15:36 +0200 )edit