*> \brief \b SPPTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
* 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 realOTHERcomputational
*
* =====================================================================
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