dgetrs.f

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      SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
      Use numerics
*
*  -- LAPACK routine (version 1.0b) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      Real(l_)   A( LDA, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  DGETRS solves a system of linear equations
*     A * X = B  or  A' * X = B
*  with a general n by n matrix A using the LU factorization computed
*  by DGETRF.
*
*  Arguments
*  =========
*
*  TRANS   (input) CHARACTER*1
*          Specifies the form of the system of equations.
*          = 'N':  A * X = B  (No transpose)
*          = 'T':  A'* X = B  (Transpose)
*          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
*
*  N       (input) INTEGER
*          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) Real(l_) array, dimension (LDA,N)
*          The factors L and U from the factorization A = P*L*U
*          as computed by DGETRF.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  IPIV    (input) INTEGER array, dimension (N)
*          The pivot indices from DGETRF; for 1<=i<=N, row i of the
*          matrix was interchanged with row IPIV(i).
*
*  B       (input/output) Real(l_) array, dimension (LDB,NRHS)
*          On entry, the right hand side vectors B for the system of
*          linear equations.
*          On exit, the solution vectors, X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      Real(l_)   ONE
      PARAMETER( ONE = 1.0_l_ )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOTRAN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLASWP, DTRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      NOTRAN = LSAME( TRANS, 'N' )
      IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
     $    LSAME( TRANS, 'C' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DGETRS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
*
      IF( NOTRAN ) THEN
*
*        Solve A * X = B.
*
*        Apply row interchanges to the right hand sides.
*
         CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 )
*
*        Solve L*X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS,
     $               ONE, A, LDA, B, LDB )
*
*        Solve U*X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
     $               NRHS, ONE, A, LDA, B, LDB )
      ELSE
*
*        Solve A' * X = B.
*
*        Solve U'*X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
     $               ONE, A, LDA, B, LDB )
*
*        Solve L'*X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE,
     $               A, LDA, B, LDB )
*
*        Apply row interchanges to the solution vectors.
*
         CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 )
      END IF
*
      RETURN
*
*     End of DGETRS
*
      END