add DPOTSV and DPOTRS LAPACK functions
This commit is contained in:
Axel Kohlmeyer
190
lib/linalg/dposv.f
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190
lib/linalg/dposv.f
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*> \brief <b> DPOSV computes the solution to system of linear equations A * X = B for PO matrices</b>
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DPOSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dposv.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dposv.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dposv.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DPOSV computes the solution to a real system of linear equations
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*> A * X = B,
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*> where A is an N-by-N symmetric positive definite matrix and X and B
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*> are N-by-NRHS matrices.
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*>
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*> The Cholesky decomposition is used to factor A as
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*> A = U**T* U, if UPLO = 'U', or
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*> A = L * L**T, if UPLO = 'L',
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*> where U is an upper triangular matrix and L is a lower triangular
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*> matrix. The factored form of A is then used to solve the system of
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*> equations A * X = B.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': Upper triangle of A is stored;
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*> = 'L': Lower triangle of A is stored.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of linear equations, i.e., the order of the
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*> matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrix B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
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*> N-by-N upper triangular part of A contains the upper
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*> triangular part of the matrix A, and the strictly lower
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*> triangular part of A is not referenced. If UPLO = 'L', the
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*> leading N-by-N lower triangular part of A contains the lower
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, if INFO = 0, the factor U or L from the Cholesky
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*> factorization A = U**T*U or A = L*L**T.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
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*> On entry, the N-by-NRHS right hand side matrix B.
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> > 0: if INFO = i, the leading minor of order i of A is not
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*> positive definite, so the factorization could not be
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*> completed, and the solution has not been computed.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doublePOsolve
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*
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* =====================================================================
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SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
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*
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* -- LAPACK driver routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), B( LDB, * )
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* ..
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*
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* =====================================================================
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*
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL DPOTRF, DPOTRS, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPOSV ', -INFO )
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RETURN
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END IF
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*
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* Compute the Cholesky factorization A = U**T*U or A = L*L**T.
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*
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CALL DPOTRF( UPLO, N, A, LDA, INFO )
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IF( INFO.EQ.0 ) THEN
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*
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* Solve the system A*X = B, overwriting B with X.
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*
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CALL DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
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*
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END IF
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RETURN
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*
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* End of DPOSV
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*
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END
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201
lib/linalg/dpotrs.f
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201
lib/linalg/dpotrs.f
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@ -0,0 +1,201 @@
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*> \brief \b DPOTRS
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DPOTRS + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotrs.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotrs.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotrs.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DPOTRS solves a system of linear equations A*X = B with a symmetric
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*> positive definite matrix A using the Cholesky factorization
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*> A = U**T*U or A = L*L**T computed by DPOTRF.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': Upper triangle of A is stored;
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*> = 'L': Lower triangle of A is stored.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrix B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> The triangular factor U or L from the Cholesky factorization
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*> A = U**T*U or A = L*L**T, as computed by DPOTRF.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
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*> On entry, the right hand side matrix B.
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*> On exit, the solution matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doublePOcomputational
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*
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* =====================================================================
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SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), B( LDB, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL DTRSM, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPOTRS', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 .OR. NRHS.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Solve A*X = B where A = U**T *U.
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*
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* Solve U**T *X = B, overwriting B with X.
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*
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CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
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$ ONE, A, LDA, B, LDB )
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*
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* Solve U*X = B, overwriting B with X.
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*
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CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
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$ NRHS, ONE, A, LDA, B, LDB )
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ELSE
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*
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* Solve A*X = B where A = L*L**T.
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*
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* Solve L*X = B, overwriting B with X.
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*
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CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
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$ NRHS, ONE, A, LDA, B, LDB )
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*
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* Solve L**T *X = B, overwriting B with X.
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*
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CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS,
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$ ONE, A, LDA, B, LDB )
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END IF
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*
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RETURN
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*
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* End of DPOTRS
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*
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END
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