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version 1.4, 2010/08/06 15:32:50 version 1.19, 2023/08/07 08:39:38
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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.
   *
   *> \ingroup complex16SYsolve
   *
   *  =====================================================================
       SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,        SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
      $                  LWORK, INFO )       $                  LWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- LAPACK driver routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )        COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  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.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The number of linear equations, i.e., the order of the  
 *          matrix A.  N >= 0.  
 *  
 *  NRHS    (input) INTEGER  
 *          The number of right hand sides, i.e., the number of columns  
 *          of the matrix B.  NRHS >= 0.  
 *  
 *  A       (input/output) 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.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  IPIV    (output) 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.  
 *  
 *  B       (input/output) 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.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= max(1,N).  
 *  
 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The length of WORK.  LWORK >= 1, and for best performance  
 *          LWORK >= max(1,N*NB), where NB is the optimal blocksize for  
 *          ZSYTRF.  
 *  
 *          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.  
 *  
 *  INFO    (output) 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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
       LOGICAL            LQUERY        LOGICAL            LQUERY
       INTEGER            LWKOPT, NB        INTEGER            LWKOPT
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
       LOGICAL            LSAME        LOGICAL            LSAME
       INTEGER            ILAENV        EXTERNAL           LSAME
       EXTERNAL           LSAME, ILAENV  
 *     ..  *     ..
 *     .. External Subroutines ..  *     .. External Subroutines ..
       EXTERNAL           XERBLA, ZSYTRF, ZSYTRS        EXTERNAL           XERBLA, ZSYTRF, ZSYTRS, ZSYTRS2
 *     ..  *     ..
 *     .. Intrinsic Functions ..  *     .. Intrinsic Functions ..
       INTRINSIC          MAX        INTRINSIC          MAX
Line 142 Line 222
          IF( N.EQ.0 ) THEN           IF( N.EQ.0 ) THEN
             LWKOPT = 1              LWKOPT = 1
          ELSE           ELSE
             NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 )              CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
             LWKOPT = N*NB              LWKOPT = INT( DBLE( WORK( 1 ) ) )
          END IF           END IF
          WORK( 1 ) = LWKOPT           WORK( 1 ) = LWKOPT
       END IF        END IF
Line 155 Line 235
          RETURN           RETURN
       END IF        END IF
 *  *
 *     Compute the factorization A = U*D*U' or A = L*D*L'.  *     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *  *
       CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )        CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN        IF( INFO.EQ.0 ) THEN
 *  *
 *        Solve the system A*X = B, overwriting B with X.  *        Solve the system A*X = B, overwriting B with X.
 *  *
          CALL ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )           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        END IF
 *  *
Removed from v.1.4  
changed lines
  Added in v.1.19

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