numpy linear algebra basic help

Question

This is what I need to do-

I have this equation-

Ax = y

Where A is a rational m*n matrix (m<=n), and x and y are vectors of the right size. I know A and y, I don't know what x is equal to. I also know that there is no x where Ax equals exactly y. I want to find the vector x' such that Ax' is as close as possible to y. Meaning that (Ax' - y) is as close as possible to (0,0,0,...0).

I know that I need to use either the lstsq function: http://www.scipy.org/doc/numpy_api_docs/numpy.linalg.linalg.html#lstsq

or the svd function: http://www.scipy.org/doc/numpy_api_docs/numpy.linalg.linalg.html#svd

I don't understand the documentation at all. Can someone please show me how to use these functions to solve my problem.

Thanks a lot!!!

Answer 1

The updated documentation may be a bit more helpful... looks like you want

numpy.linalg.lstsq(A, y)

Answer 2

SVD is for the case of m < n, because you don't really have enough degrees of freedom.

The docs for lstsq don't look very helpful. I believe that's least square fitting, for the case where m > n.

If m < n, you'll want SVD.