dgesv.f

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*> \brief <b> DGESV computes the solution to system of linear equations A * X = B for GE matrices</b>
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* 
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of linear equations, i.e., the order of the
*>          matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand sides, i.e., the number of columns
*>          of the matrix B.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          The pivot indices that define the permutation matrix P;
*>          row i of the matrix was interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is 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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup doubleGEsolve
*
*  =====================================================================
      SUBROUTINE dgesv( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
*  -- LAPACK driver routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( lda, * ), B( ldb, * )
*     ..
*
*  =====================================================================
*
*     .. 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