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version 1.9, 2011/07/22 07:38:15 version 1.10, 2011/11/21 20:43:12
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   *> \brief <b> ZHESV computes the solution to system of linear equations A * X = B for HE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHESV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHESV( 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
   *>
   *> ZHESV computes the solution to a complex system of linear equations
   *>    A * X = B,
   *> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
   *> matrices.
   *>
   *> The diagonal pivoting method is used to factor A as
   *>    A = U * D * U**H,  if UPLO = 'U', or
   *>    A = L * D * L**H,  if UPLO = 'L',
   *> where U (or L) is a product of permutation and unit upper (lower)
   *> triangular matrices, and D is Hermitian 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 Hermitian 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**H or A = L*D*L**H as computed by
   *>          ZHETRF.
   *> \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 ZHETRF.  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
   *>          ZHETRF.
   *>          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 November 2011
   *
   *> \ingroup complex16HEsolve
   *
   *  =====================================================================
       SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,        SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
      $                  LWORK, INFO )       $                  LWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.3.1) --  *  -- LAPACK driver routine (version 3.4.0) --
 *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 * @precisions normal z -> c  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
Line 16 Line 185
       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )        COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHESV computes the solution to a complex system of linear equations  
 *     A * X = B,  
 *  where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS  
 *  matrices.  
 *  
 *  The diagonal pivoting method is used to factor A as  
 *     A = U * D * U**H,  if UPLO = 'U', or  
 *     A = L * D * L**H,  if UPLO = 'L',  
 *  where U (or L) is a product of permutation and unit upper (lower)  
 *  triangular matrices, and D is Hermitian 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 Hermitian 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**H or A = L*D*L**H as computed by  
 *          ZHETRF.  
 *  
 *  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 ZHETRF.  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  
 *          ZHETRF.  
 *          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.  
 *  
 *  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 ..
Removed from v.1.9  
changed lines
  Added in v.1.10

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