Calculate condition number

[ah2048]

Hello,

How to calculate condition number of a matrix?
I have so little experience with math, I just want to get an equivalent code to this function https://numpy.org/doc/stable/reference/generated/numpy.linalg.cond.html#numpy-linalg-cond

[markrogoyski]

Hi @ah2048,

Thank you for your interest in MathPHP.

I see you closed this issue before I had a chance to respond. Did you find an answer or did you want to make a feature request? Let me know. Thanks.

Mark

[ah2048]

Thank you for creating math-php, it is really helped us in our project <3

[ah2048]

Hi @markrogoyski

sorry for closing it without details.

When I went through NumPy package, I found that "numpy.linalg.cond" is using svd, however we cannot do that by math-php svd function because it will be very slow for large matrices due to unnecessary calculations ,
you can see that python svd function supports compute_uv=False argument. so they get only necessary info.

I got help from my friend wrote me this

$Mᵀ = $M->transpose();
$MMᵀ = $M->multiply($Mᵀ);

$eigenvalue = Eigenvalue::jacobiMethod($MMᵀ);

$max = max($eigenvalue);
$min = min($eigenvalue);

$conditionNumber = sqrt($max) / sqrt($min);

But we found that Eigenvalue::jacobiMethod is slow (1 second) for large matrices (30x30) also, so we still struggling.

I cannot open a feature request as I really have very little knowledge experience with this stuff. but it would be very nice to see cond function exists and working well at markrogoyski/math-php.

[Beakerboy]

According to stackoverflow (https://stackoverflow.com/questions/29426357/is-numpy-linalg-cond-returning-the-ratio-of-the-biggest-and-smallest-eigenvalue)

the ratio of singular values is not the same as a the ratio of eigenvalues unless you have a normal matrix. Are you sure the function your friend provided is correct?

[ah2048]

Yes it is working and gives the same results as python "numpy.linalg.cond" even for very large matrices 30x30,
I don't know what is the meaning of "normal matrix"
Check this line https://github.com/numpy/numpy/blob/main/numpy/linalg/linalg.py#L1786