sgesv(3F)

NAME
     SGESV - compute the solution to a real system of linear equations  A * X
     = B,

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.