cpotrs.f

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*> \brief \b CPOTRS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * ), B( LDB, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CPOTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A using the Cholesky factorization
*> A = U**H*U or A = L*L**H computed by CPOTRF.
*> \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 COMPLEX array, dimension (LDA,N)
*>          The triangular factor U or L from the Cholesky factorization
*>          A = U**H*U or A = L*L**H, as computed by CPOTRF.
*> \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 COMPLEX 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 complexPOcomputational
*
*  =====================================================================
      SUBROUTINE cpotrs( 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 ..
      COMPLEX            A( LDA, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ONE
      parameter( one = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           ctrsm, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'u' )
.NOT..AND..NOT.      IF( UPPER  LSAME( UPLO, 'l' ) ) THEN
         INFO = -1
.LT.      ELSE IF( N0 ) THEN
         INFO = -2
.LT.      ELSE IF( NRHS0 ) THEN
         INFO = -3
.LT.      ELSE IF( LDAMAX( 1, N ) ) THEN
         INFO = -5
.LT.      ELSE IF( LDBMAX( 1, N ) ) THEN
         INFO = -7
      END IF
.NE.      IF( INFO0 ) THEN
         CALL XERBLA( 'cpotrs', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ.      IF( N0  NRHS0 )
     $   RETURN
*
      IF( UPPER ) THEN
*
*        Solve A*X = B where A = U**H *U.
*
*        Solve U**H *X = B, overwriting B with X.
*
         CALL CTRSM( 'left', 'upper', 'conjugate transpose', 'non-unit',
     $               N, NRHS, ONE, A, LDA, B, LDB )
*
*        Solve U*X = B, overwriting B with X.
*
         CALL CTRSM( 'left', 'upper', 'no transpose', 'non-unit', N,
     $               NRHS, ONE, A, LDA, B, LDB )
      ELSE
*
*        Solve A*X = B where A = L*L**H.
*
*        Solve L*X = B, overwriting B with X.
*
         CALL CTRSM( 'left', 'lower', 'no transpose', 'non-unit', N,
     $               NRHS, ONE, A, LDA, B, LDB )
*
*        Solve L**H *X = B, overwriting B with X.
*
         CALL CTRSM( 'left', 'lower', 'conjugate transpose', 'non-unit',
     $               N, NRHS, ONE, A, LDA, B, LDB )
      END IF
*
      RETURN
*
*     End of CPOTRS
*
      END