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293 lines
9.1 KiB
293 lines
9.1 KiB
2 years ago
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*> \brief \b ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
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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 ZHESV_ROOK + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv_rook.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/zhesv_rook.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/zhesv_rook.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 ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
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* LWORK, 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, LWORK, N, NRHS
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
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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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*> ZHESV_ROOK 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 Hermitian matrix and X and B are N-by-NRHS
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*> matrices.
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*>
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*> The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used
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*> 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, and D is Hermitian and block diagonal with
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*> 1-by-1 and 2-by-2 diagonal blocks.
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*>
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*> ZHETRF_ROOK is called to compute the factorization of a complex
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*> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
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*> pivoting method.
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*>
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*> The factored form of A is then used to solve the system
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*> of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2).
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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 COMPLEX*16 array, dimension (LDA,N)
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*> On entry, the Hermitian 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 block diagonal matrix D and the
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*> multipliers used to obtain the factor U or L from the
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*> factorization A = U*D*U**H or A = L*D*L**H as computed by
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*> ZHETRF_ROOK.
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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[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.
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*>
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*> If UPLO = 'U':
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*> Only the last KB elements of IPIV are set.
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*>
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*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
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*> interchanged and D(k,k) is a 1-by-1 diagonal block.
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*>
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*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
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*> columns k and -IPIV(k) were interchanged and rows and
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*> columns k-1 and -IPIV(k-1) were inerchaged,
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*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
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*>
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*> If UPLO = 'L':
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*> Only the first KB elements of IPIV are set.
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*>
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*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
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*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
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*>
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*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
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*> columns k and -IPIV(k) were interchanged and rows and
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*> columns k+1 and -IPIV(k+1) were inerchaged,
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*> D(k:k+1,k:k+1) is a 2-by-2 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] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of WORK. LWORK >= 1, and for best performance
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*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
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*> ZHETRF_ROOK.
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*> for LWORK < N, TRS will be done with Level BLAS 2
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*> for LWORK >= N, TRS will be done with Level BLAS 3
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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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 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 complex16HEsolve
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*>
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*> \verbatim
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*>
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*> November 2013, Igor Kozachenko,
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*> Computer Science Division,
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*> University of California, Berkeley
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*>
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*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
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*> School of Mathematics,
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*> University of Manchester
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*>
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*> \endverbatim
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*
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*
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* =====================================================================
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SUBROUTINE ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
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$ LWORK, 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, LWORK, N, NRHS
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER LWKOPT, NB
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZHETRF_ROOK, ZHETRS_ROOK
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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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LQUERY = ( LWORK.EQ.-1 )
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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 = -8
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ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
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INFO = -10
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( N.EQ.0 ) THEN
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LWKOPT = 1
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ELSE
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NB = ILAENV( 1, 'ZHETRF_ROOK', UPLO, N, -1, -1, -1 )
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LWKOPT = N*NB
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END IF
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WORK( 1 ) = LWKOPT
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZHESV_ROOK ', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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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**H or A = L*D*L**H.
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*
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CALL ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, 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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* Solve with TRS ( Use Level BLAS 2)
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*
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CALL ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
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*
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END IF
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*
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WORK( 1 ) = LWKOPT
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*
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RETURN
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*
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* End of ZHESV_ROOK
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*
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END
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