spptrs.f

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*> \brief \b SPPTRS
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       REAL               AP( * ), B( LDB, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SPPTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A in packed storage using the Cholesky
*> factorization A = U**T*U or A = L*L**T computed by SPPTRF.
*> \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] AP
*> \verbatim
*>          AP is REAL array, dimension (N*(N+1)/2)
*>          The triangular factor U or L from the Cholesky factorization
*>          A = U**T*U or A = L*L**T, packed columnwise in a linear
*>          array.  The j-th column of U or L is stored in the array AP
*>          as follows:
*>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
*>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is REAL 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 pptrs
*
*  =====================================================================
      SUBROUTINE spptrs( UPLO, N, NRHS, AP, 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, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      REAL               AP( * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           stpsv, 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( ldb.LT.max( 1, n ) ) THEN
         info = -6
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SPPTRS', -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.
*
         DO 10 i = 1, nrhs
*
*           Solve U**T *X = B, overwriting B with X.
*
            CALL stpsv( 'Upper', 'Transpose', 'Non-unit', n, ap,
     $                  b( 1, i ), 1 )
*
*           Solve U*X = B, overwriting B with X.
*
            CALL stpsv( 'Upper', 'No transpose', 'Non-unit', n, ap,
     $                  b( 1, i ), 1 )
   10    CONTINUE
      ELSE
*
*        Solve A*X = B where A = L * L**T.
*
         DO 20 i = 1, nrhs
*
*           Solve L*Y = B, overwriting B with X.
*
            CALL stpsv( 'Lower', 'No transpose', 'Non-unit', n, ap,
     $                  b( 1, i ), 1 )
*
*           Solve L**T *X = Y, overwriting B with X.
*
            CALL stpsv( 'Lower', 'Transpose', 'Non-unit', n, ap,
     $                  b( 1, i ), 1 )
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of SPPTRS
*
      END