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222 lines
6.7 KiB
222 lines
6.7 KiB
2 years ago
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*> \brief <b> ZSPSV 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 ZSPSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspsv.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/zspsv.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/zspsv.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 ZSPSV( UPLO, N, NRHS, AP, IPIV, 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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* INTEGER IPIV( * )
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* COMPLEX*16 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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*> ZSPSV computes the solution to a complex system of linear equations
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*> A * X = B,
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*> where A is an N-by-N symmetric matrix stored in packed format and X
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*> and B are N-by-NRHS matrices.
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*>
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*> The diagonal pivoting method is used to factor A as
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*> A = U * D * U**T, if UPLO = 'U', or
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*> A = L * D * L**T, if UPLO = 'L',
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*> where U (or L) is a product of permutation and unit upper (lower)
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*> triangular matrices, D is symmetric and block diagonal with 1-by-1
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*> and 2-by-2 diagonal blocks. The factored form of A is then used to
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*> solve the system of 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 COMPLEX*16 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, the block diagonal matrix D and the multipliers used
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*> to obtain the factor U or L from the factorization
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*> A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as
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*> a packed triangular matrix in the same storage format as A.
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*> \endverbatim
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*>
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*> \param[out] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> Details of the interchanges and the block structure of D, as
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*> determined by ZSPTRF. If IPIV(k) > 0, then rows and columns
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*> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
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*> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
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*> then rows and columns k-1 and -IPIV(k) were interchanged and
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*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
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*> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
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*> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
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*> diagonal block.
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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 COMPLEX*16 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, D(i,i) is exactly zero. The factorization
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*> has been completed, but the block diagonal matrix D is
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*> exactly singular, so the solution could not be
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*> 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 complex16OTHERsolve
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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 = 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 ZSPSV( UPLO, N, NRHS, AP, IPIV, 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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INTEGER IPIV( * )
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COMPLEX*16 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 XERBLA, ZSPTRF, ZSPTRS
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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 = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZSPSV ', -INFO )
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RETURN
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END IF
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*
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* Compute the factorization A = U*D*U**T or A = L*D*L**T.
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*
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CALL ZSPTRF( UPLO, N, AP, IPIV, 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 ZSPTRS( UPLO, N, NRHS, AP, IPIV, 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 ZSPSV
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*
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END
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