SYNOPSIS

SUBROUTINE SGESV(

N, NRHS, A, LDA, IPIV, B, LDB, INFO )

    

INTEGER INFO, LDA, LDB, N, NRHS

    

INTEGER IPIV( * )

    

REAL A( LDA, * ), B( LDB, * )

PURPOSE

SGESV computes the solution to a real system of linear equations
   A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as

   A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

ARGUMENTS

N (input) INTEGER

The number of linear equations, i.e., the order of the matrix A. N >= 0.

NRHS (input) INTEGER

The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

A (input/output) REAL array, dimension (LDA,N)

On entry, the N-by-N coefficient matrix A. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).

IPIV (output) INTEGER array, dimension (N)

The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).

B (input/output) REAL array, dimension (LDB,NRHS)

On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB (input) INTEGER

The leading dimension of the array B. LDB >= max(1,N).

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.