SGETRF的Lapack错误

Question

I am using LAPACK library to solve an optimization problem. I am getting different Lapack errors (Lapack error(1,2,3,4) with SGETRF) . Is there any documentation source, which I can read to understand what exactly these errors mean?

Answer 1

Most of Lapack routines return an error code in the argument INFO . The meaning of this output is specified in the documentation of the function sgetrf()

If INFO is null, then everething is OK ! If INFO <0 , an error was detected in the input parameters. For instance, for sgetrf() :

• INFO=-1 : number of rows of the matrix is negative
• INFO=-2 : number of columns of the matrix is negative
• INFO=-4 : LDA is lower than MAX( 1, M )

The routine xerbla() can be applied to print the right error message:

XERBLA( 'SGETRF', -INFO )

If INFO>0, the document clearly describes what is happening :

U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

This problem can occur if the matrix is singular or ill-conditionned. If the matrix A is singular, there might be different solutions, or no solution at all to the problem Ax=b . If INFO=1, it is likely that the matrix is null.

Hence, testing INFO is to be considered as a good practice as functions such as sgetrf() or sgesv() are called...