# Lapack/blas routine to solve y = Ax

1. May 16, 2010

### missfangula

Hello everyone,

I am working on a matrix algebra-based project for an unrelated class, but unfortunately, I have no background in matrix algebra. I have managed so far to do most of the work, but I am stuck in my search for the right BLAS or LAPACK subroutine which could solve the following problem:
y = A*x
where y and x are KNOWN vectors, and A is an UNKNOWN matrix. I have found the subroutine dgemv which solves y = A*x, but with A as a KNOWN matrix and y as a KNOWN vector.

As additional information, A is a 4x4 matrix, y, and x are known 4-d vectors. In matrix A, the bottom row is just 0,0,0,1, and the first three elements of column 4 are the same as the elements of vector y.

So it looks like this:

[knownY] [unknown unknown unknown knownY] [0.0]
[knownY] = [unknown unknown unknown knownY]*[0.0]
[knownY] [unknown unknown unknown knownY] [0.0]
[ 1.0 ] [ 0.0 0.0 0.0 1.0 ] [1.0]

My attempt has been to look through lapack and blas for a subroutine, but I cannot find one where the two vectors are known and the matrix is what I am trying to solve for.

Thanks!
-miss fangula

2. May 18, 2010

### hotvette

Something looks goofy. My interpretation of what you posted is that y = [y1 y2 y3 1]T and x = [0 0 0 1]T. If so, then any values can be used for the 9 unknown elements of A since they are all multiplied by zero.

In general, there are infinitely many solutions to the problem y = Ax, where y and x are known n-vectors and A is an unknown n x n matrix. If you write out the equations you have n equations with n2 unknowns in the form Bc = y, where B is a banded matrix of known values having n rows and n2 columns and c is a vector of n2 unknown elements of A. This is an underdetermined system (i.e. more unknowns than equations) that can be solved for the minimum norm solution using LAPACK routine DGELSD.

Last edited: May 18, 2010