CHOLESKY

This program will compute the Cholesky factorization for a matrix. 
User Inputs:

1) The matrix A (the program is formatted to consider matrix A).

Outputs:
1) It will return a message instructing the user to examine matrix [B]. The lower triangular portion of the factorization is stored. 

Errors Accounted for in the program:

1) If the matrix is not square it will return an error message. 
2) If the factorization produces a zero along the main diagonal it will report the factorization failed (this often happens with non-symmetric matrices). 

Additional Notes: A quick fix to the problem of non-symmetric matrices would be to consider A + transpose(A). This matrix is always symmetric and if this is positive definite, then the matrix A is as well. The decomposition is not the same in general, but you can at least use Cholesky in this context to test for positive definiteness, which is the primary use of Cholesky factorizations.