subroutine dgetrs	(	character	TRANS,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

DGETRS

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Purpose:

 DGETRS solves a system of linear equations
    A * X = B  or  A**T * X = B
 with a general N-by-N matrix A using the LU factorization computed
 by DGETRF.

Parameters

[in]	TRANS	TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T* X = B (Transpose) = 'C': A**T* X = B (Conjugate transpose = Transpose)
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2011

Definition at line 123 of file dgetrs.f.

*
*  -- LAPACK computational 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 ..
      CHARACTER          trans
      INTEGER            info, lda, ldb, n, nrhs
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      DOUBLE PRECISION   a( lda, * ), b( ldb, * )
*     ..
*
*  =====================================================================
*
*     .. 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**T * X = B.
*
*        Solve U**T *X = B, overwriting B with X.
*
         CALL dtrsm( 'Left', 'Upper', 'Transpose', 'Non-unit', n, nrhs,
     $               one, a, lda, b, ldb )
*
*        Solve L**T *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
*

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