314 lines
10 KiB
Fortran
314 lines
10 KiB
Fortran
*> \brief <b> CSYSV_RK computes the solution to system of linear equations A * X = B for SY 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 CSYSV_RK + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csysv_rk.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/csysv_rk.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/csysv_rk.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 CSYSV_RK( UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB,
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* WORK, 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 A( LDA, * ), B( LDB, * ), E( * ), 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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*> CSYSV_RK computes the solution to a complex system of linear
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*> equations A * X = B, where A is an N-by-N symmetric matrix
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*> and X and B are N-by-NRHS 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 = P*U*D*(U**T)*(P**T), if UPLO = 'U', or
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*> A = P*L*D*(L**T)*(P**T), if UPLO = 'L',
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*> where U (or L) is unit upper (or lower) triangular matrix,
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*> U**T (or L**T) is the transpose of U (or L), P is a permutation
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*> matrix, P**T is the transpose of P, and D is symmetric and block
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*> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
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*>
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*> CSYTRF_RK is called to compute the factorization of a complex
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*> symmetric matrix. The factored form of A is then used to solve
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*> the system of equations A * X = B by calling BLAS3 routine CSYTRS_3.
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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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*> Specifies whether the upper or lower triangular part of the
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*> symmetric matrix A is stored:
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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 array, dimension (LDA,N)
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*> On entry, the symmetric matrix A.
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*> If UPLO = 'U': the leading N-by-N upper triangular part
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*> of A contains the upper triangular part of the matrix A,
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*> and the strictly lower triangular part of A is not
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*> referenced.
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*>
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*> If UPLO = 'L': the leading N-by-N lower triangular part
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*> of A contains the lower triangular part of the matrix A,
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*> and the strictly upper triangular part of A is not
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*> referenced.
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*>
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*> On exit, if INFO = 0, diagonal of the block diagonal
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*> matrix D and factors U or L as computed by CSYTRF_RK:
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*> a) ONLY diagonal elements of the symmetric block diagonal
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*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
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*> (superdiagonal (or subdiagonal) elements of D
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*> are stored on exit in array E), and
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*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
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*> If UPLO = 'L': factor L in the subdiagonal part of A.
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*>
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*> For more info see the description of CSYTRF_RK routine.
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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] E
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*> \verbatim
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*> E is COMPLEX array, dimension (N)
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*> On exit, contains the output computed by the factorization
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*> routine CSYTRF_RK, i.e. the superdiagonal (or subdiagonal)
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*> elements of the symmetric block diagonal matrix D
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*> with 1-by-1 or 2-by-2 diagonal blocks, where
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*> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
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*> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
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*>
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*> NOTE: For 1-by-1 diagonal block D(k), where
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*> 1 <= k <= N, the element E(k) is set to 0 in both
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*> UPLO = 'U' or UPLO = 'L' cases.
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*>
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*> For more info see the description of CSYTRF_RK routine.
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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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*> as determined by CSYTRF_RK.
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*>
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*> For more info see the description of CSYTRF_RK routine.
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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 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 array, dimension ( MAX(1,LWORK) ).
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*> Work array used in the factorization stage.
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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. For best performance
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*> of factorization stage LWORK >= max(1,N*NB), where NB is
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*> the optimal blocksize for CSYTRF_RK.
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*>
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*> If LWORK = -1, then a workspace query is assumed;
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*> the routine only calculates the optimal size of the WORK
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*> array for factorization stage, returns this value as
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*> the first entry of the WORK array, and no error message
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*> 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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*>
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*> < 0: If INFO = -k, the k-th argument had an illegal value
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*>
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*> > 0: If INFO = k, the matrix A is singular, because:
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*> If UPLO = 'U': column k in the upper
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*> triangular part of A contains all zeros.
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*> If UPLO = 'L': column k in the lower
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*> triangular part of A contains all zeros.
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*>
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*> Therefore D(k,k) is exactly zero, and superdiagonal
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*> elements of column k of U (or subdiagonal elements of
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*> column k of L ) are all zeros. The factorization has
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*> been completed, but the block diagonal matrix D is
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*> exactly singular, and division by zero will occur if
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*> it is used to solve a system of equations.
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*>
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*> NOTE: INFO only stores the first occurrence of
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*> a singularity, any subsequent occurrence of singularity
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*> is not stored in INFO even though the factorization
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*> always completes.
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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 complexSYsolve
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*
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*> \par Contributors:
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* ==================
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*>
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*> \verbatim
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*>
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*> December 2016, 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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SUBROUTINE CSYSV_RK( UPLO, N, NRHS, A, LDA, E, 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 A( LDA, * ), B( LDB, * ), E( * ), 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
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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, CSYTRF_RK, CSYTRS_3
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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 = -9
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ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
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INFO = -11
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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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CALL CSYTRF_RK( UPLO, N, A, LDA, E, IPIV, WORK, -1, INFO )
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LWKOPT = INT( WORK( 1 ) )
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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( 'CSYSV_RK ', -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**T or A = L*D*L**T.
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*
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CALL CSYTRF_RK( UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO )
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*
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IF( INFO.EQ.0 ) THEN
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*
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* Solve the system A*X = B with BLAS3 solver, overwriting B with X.
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*
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CALL CSYTRS_3( UPLO, N, NRHS, A, LDA, E, 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 CSYSV_RK
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*
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END
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