Lapack/blas routine to solve y = Ax

[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

 

[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.