203 lines
5.7 KiB
Fortran
203 lines
5.7 KiB
Fortran
*> \brief <b> DPPSV computes the solution to system of linear equations A * X = B for OTHER 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 DPPSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppsv.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/dppsv.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/dppsv.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 DPPSV( UPLO, N, NRHS, AP, 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, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AP( * ), 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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*> DPPSV 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 stored in
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*> packed format and X and B 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] AP
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*> \verbatim
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*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
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*> On entry, the upper or lower triangle of the symmetric matrix
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*> A, packed columnwise in a linear array. The j-th column of A
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*> is stored in the array AP as follows:
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
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*> See below for further details.
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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, in the same storage
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*> format as A.
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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 doubleOTHERsolve
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The packed storage scheme is illustrated by the following example
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*> when N = 4, UPLO = 'U':
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*>
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*> Two-dimensional storage of the symmetric matrix A:
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*>
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*> a11 a12 a13 a14
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*> a22 a23 a24
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*> a33 a34 (aij = conjg(aji))
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*> a44
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*>
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*> Packed storage of the upper triangle of A:
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*>
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*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DPPSV( UPLO, N, NRHS, AP, 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, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AP( * ), 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 DPPTRF, DPPTRS, 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( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPPSV ', -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 DPPTRF( UPLO, N, AP, 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 DPPTRS( UPLO, N, NRHS, AP, 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 DPPSV
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*
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END
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