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*> \brief <b> ZSYSV computes the solution to system of linear equations A * X = B for SY matrices</b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZSYSV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsysv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsysv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsysv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, LDB, LWORK, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYSV computes the solution to a complex system of linear equations
*> A * X = B,
*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
*> matrices.
*>
*> The diagonal pivoting method is used to factor A as
*> A = U * D * U**T, if UPLO = 'U', or
*> A = L * D * L**T, if UPLO = 'L',
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. 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] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
*> N-by-N upper triangular part of A contains the upper
*> triangular part of the matrix A, and the strictly lower
*> triangular part of A is not referenced. If UPLO = 'L', the
*> leading N-by-N lower triangular part of A contains the lower
*> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced.
*>
*> On exit, if INFO = 0, the block diagonal matrix D and the
*> multipliers used to obtain the factor U or L from the
*> factorization A = U*D*U**T or A = L*D*L**T as computed by
*> ZSYTRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the block structure of D, as
*> determined by ZSYTRF. If IPIV(k) > 0, then rows and columns
*> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
*> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
*> then rows and columns k-1 and -IPIV(k) were interchanged and
*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
*> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
*> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
*> diagonal block.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX*16 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] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of WORK. LWORK >= 1, and for best performance
*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
*> ZSYTRF.
*> for LWORK < N, TRS will be done with Level BLAS 2
*> for LWORK >= N, TRS will be done with Level BLAS 3
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error
*> message related to LWORK is issued by XERBLA.
*> \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, D(i,i) is exactly zero. The factorization
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16SYsolve
*
* =====================================================================
SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ LWORK, 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, LDA, LDB, LWORK, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER LWKOPT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZSYTRF, ZSYTRS, ZSYTRS2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
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( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
*
IF( INFO.EQ.0 ) THEN
IF( N.EQ.0 ) THEN
LWKOPT = 1
ELSE
CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
LWKOPT = WORK(1)
END IF
WORK( 1 ) = LWKOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSYSV ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Compute the factorization A = U*D*U**T or A = L*D*L**T.
*
CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
IF ( LWORK.LT.N ) THEN
*
* Solve with TRS ( Use Level BLAS 2)
*
CALL ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
ELSE
*
* Solve with TRS2 ( Use Level BLAS 3)
*
CALL ZSYTRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO )
*
END IF
*
END IF
*
WORK( 1 ) = LWKOPT
*
RETURN
*
* End of ZSYSV
*
END
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