QR Eigenvalues: 

rebecca_qr

    The prototype for the function you are creating is
       int QREvals(Matrix A,  Vector  v, int n, float Tol)
    where Matrix and Vector refer to our typdef structures.           

 The function will compute the eigenvalues of a A, return the ordered (from largest to smallest) eigenvalues in v, with a maximum of n iterations, untill it satisfies some error estimate less than Tol. It will use thesimplest QR algorithm.  It is well documented.  I test my matrix for symmetry, and document this test in check.c. I use the gsl QR decomposition command within the algorithm. 

The return value is the number of iterations.  In the event the output does not meet the tolerance the dimensioning of v should be set to be the negative of the expected size with float zero entries.  

In main: read in a matrix from stdin (as always redirectable from a file) using our matrix file format, compute the eigenvalues using the procedure, compare these eigenvalues to the output from the gsl eigenvalue commands, and output all eigenvalues to stdout in our vector file format. 


./rebecca_qr < Matrix > out