SUBROUTINE DGESVF( N, NRHS, A, LDA, IPIV, B, LDB, INFO )

*

*  -- LAPACK driver routine (version 3.1) --

*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..

*     November 2006

*

*     .. Scalar Arguments ..

      INTEGER            INFO, LDA, LDB, N, NRHS

*     ..

*     .. Array Arguments ..

      INTEGER            IPIV( * )

      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )

*     ..

*

*  Purpose

*  =======

*

*  DGESV 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.

*

*  =====================================================================

*

*     .. External Subroutines ..

      EXTERNAL           DGETRF, DGETRS, XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      INFO = 0

      IF( N.LT.0 ) THEN

         INFO = -1

      ELSE IF( NRHS.LT.0 ) THEN

         INFO = -2

      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN

         INFO = -4

      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN

         INFO = -7

      END IF

      IF( INFO.NE.0 ) THEN

         CALL XERBLA( 'DGESV ', -INFO )

         RETURN

      END IF

*

*     Compute the LU factorization of A.

*

      CALL DGETRF( N, N, A, LDA, IPIV, INFO )

      IF( INFO.EQ.0 ) THEN

*

*        Solve the system A*X = B, overwriting B with X.

*

         CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB,

     $                INFO )

      END IF

      RETURN

*

*     End of DGESV

*

      END