lapack/SRC/dpotrs.f

*> \brief \b DPOTRS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPOTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by DPOTRF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          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] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The triangular factor U or L from the Cholesky factorization
*>          A = U**T*U or A = L*L**T, as computed by DPOTRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*>          On entry, the right hand side matrix B.
*>          On exit, the 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
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doublePOcomputational
*
*  =====================================================================
      SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DTRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) 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 = -7
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPOTRS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
*
      IF( UPPER ) THEN
*
*        Solve A*X = B where A = U**T *U.
*
*        Solve U**T *X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-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 where A = L*L**T.
*
*        Solve L*X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
     $               NRHS, ONE, A, LDA, B, LDB )
*
*        Solve L**T *X = B, overwriting B with X.
*
         CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS,
     $               ONE, A, LDA, B, LDB )
      END IF
*
      RETURN
*
*     End of DPOTRS
*
      END