dgetrs.f

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      SUBROUTINE dgetrs( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     March 31, 1993
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDB,NRHS)
*          On entry, the right hand side matrix B.
*          On exit, the 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
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d+0 )
*     ..
*     .. 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