201 lines
5.2 KiB
Fortran
201 lines
5.2 KiB
Fortran
*> \brief \b DPPTRS
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download DPPTRS + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrs.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrs.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrs.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DPPTRS 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 DPPTRF.
|
|
*> \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 DOUBLE PRECISION 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 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 doubleOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DPPTRS( 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 ..
|
|
DOUBLE PRECISION AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Local Scalars ..
|
|
LOGICAL UPPER
|
|
INTEGER I
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DTPSV, 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( 'DPPTRS', -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 DTPSV( 'Upper', 'Transpose', 'Non-unit', N, AP,
|
|
$ B( 1, I ), 1 )
|
|
*
|
|
* Solve U*X = B, overwriting B with X.
|
|
*
|
|
CALL DTPSV( '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 DTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
|
|
$ B( 1, I ), 1 )
|
|
*
|
|
* Solve L**T *X = Y, overwriting B with X.
|
|
*
|
|
CALL DTPSV( 'Lower', 'Transpose', 'Non-unit', N, AP,
|
|
$ B( 1, I ), 1 )
|
|
20 CONTINUE
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DPPTRS
|
|
*
|
|
END
|