206 lines
5.8 KiB
Fortran
206 lines
5.8 KiB
Fortran
*> \brief <b> CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download CPPSV + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cppsv.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cppsv.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cppsv.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CPPSV computes the solution to a complex system of linear equations
|
|
*> A * X = B,
|
|
*> where A is an N-by-N Hermitian positive definite matrix stored in
|
|
*> packed format and X and B are N-by-NRHS matrices.
|
|
*>
|
|
*> The Cholesky decomposition is used to factor A as
|
|
*> A = U**H * U, if UPLO = 'U', or
|
|
*> A = L * L**H, if UPLO = 'L',
|
|
*> where U is an upper triangular matrix and L is a lower triangular
|
|
*> matrix. The factored form of A is then used to solve the system of
|
|
*> equations A * X = B.
|
|
*> \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 number of linear equations, i.e., 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,out] AP
|
|
*> \verbatim
|
|
*> AP is COMPLEX array, dimension (N*(N+1)/2)
|
|
*> On entry, the upper or lower triangle of the Hermitian matrix
|
|
*> A, packed columnwise in a linear array. The j-th column of A
|
|
*> is stored in the array AP as follows:
|
|
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
|
|
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
|
|
*> See below for further details.
|
|
*>
|
|
*> On exit, if INFO = 0, the factor U or L from the Cholesky
|
|
*> factorization A = U**H*U or A = L*L**H, in the same storage
|
|
*> format as A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] B
|
|
*> \verbatim
|
|
*> B is COMPLEX array, dimension (LDB,NRHS)
|
|
*> On entry, the N-by-NRHS right hand side matrix B.
|
|
*> On exit, if INFO = 0, the N-by-NRHS 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
|
|
*> > 0: if INFO = i, the leading minor of order i of A is not
|
|
*> positive definite, so the factorization could not be
|
|
*> completed, and the solution has not been computed.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date December 2016
|
|
*
|
|
*> \ingroup complexOTHERsolve
|
|
*
|
|
*> \par Further Details:
|
|
* =====================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> The packed storage scheme is illustrated by the following example
|
|
*> when N = 4, UPLO = 'U':
|
|
*>
|
|
*> Two-dimensional storage of the Hermitian matrix A:
|
|
*>
|
|
*> a11 a12 a13 a14
|
|
*> a22 a23 a24
|
|
*> a33 a34 (aij = conjg(aji))
|
|
*> a44
|
|
*>
|
|
*> Packed storage of the upper triangle of A:
|
|
*>
|
|
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
|
|
*
|
|
* -- LAPACK driver routine (version 3.7.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* December 2016
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CPPTRF, CPPTRS, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input parameters.
|
|
*
|
|
INFO = 0
|
|
IF( .NOT.LSAME( UPLO, 'U' ) .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( 'CPPSV ', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the Cholesky factorization A = U**H *U or A = L*L**H.
|
|
*
|
|
CALL CPPTRF( UPLO, N, AP, INFO )
|
|
IF( INFO.EQ.0 ) THEN
|
|
*
|
|
* Solve the system A*X = B, overwriting B with X.
|
|
*
|
|
CALL CPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
|
|
*
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of CPPSV
|
|
*
|
|
END
|