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version 1.8, 2011/07/22 07:38:18 version 1.9, 2011/11/21 20:43:17
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   *> \brief \b ZLASYF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLASYF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlasyf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlasyf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlasyf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, KB, LDA, LDW, N, NB
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       COMPLEX*16         A( LDA, * ), W( LDW, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZLASYF computes a partial factorization of a complex symmetric matrix
   *> A using the Bunch-Kaufman diagonal pivoting method. The partial
   *> factorization has the form:
   *>
   *> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
   *>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
   *>
   *> A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'
   *>       ( L21  I ) ( 0   A22 ) (  0       I    )
   *>
   *> where the order of D is at most NB. The actual order is returned in
   *> the argument KB, and is either NB or NB-1, or N if N <= NB.
   *> Note that U**T denotes the transpose of U.
   *>
   *> ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
   *> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
   *> A22 (if UPLO = 'L').
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          Specifies whether the upper or lower triangular part of the
   *>          symmetric matrix A is stored:
   *>          = 'U':  Upper triangular
   *>          = 'L':  Lower triangular
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] NB
   *> \verbatim
   *>          NB is INTEGER
   *>          The maximum number of columns of the matrix A that should be
   *>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
   *>          blocks.
   *> \endverbatim
   *>
   *> \param[out] KB
   *> \verbatim
   *>          KB is INTEGER
   *>          The number of columns of A that were actually factored.
   *>          KB is either NB-1 or NB, or N if N <= NB.
   *> \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, A contains details of the partial factorization.
   *> \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.
   *>          If UPLO = 'U', only the last KB elements of IPIV are set;
   *>          if UPLO = 'L', only the first KB elements are set.
   *>
   *>          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[out] W
   *> \verbatim
   *>          W is COMPLEX*16 array, dimension (LDW,NB)
   *> \endverbatim
   *>
   *> \param[in] LDW
   *> \verbatim
   *>          LDW is INTEGER
   *>          The leading dimension of the array W.  LDW >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0: successful exit
   *>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
   *>               has been completed, but the block diagonal matrix D is
   *>               exactly singular.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16SYcomputational
   *
   *  =====================================================================
       SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )        SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational 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
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       COMPLEX*16         A( LDA, * ), W( LDW, * )        COMPLEX*16         A( LDA, * ), W( LDW, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZLASYF computes a partial factorization of a complex symmetric matrix  
 *  A using the Bunch-Kaufman diagonal pivoting method. The partial  
 *  factorization has the form:  
 *  
 *  A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:  
 *        ( 0  U22 ) (  0   D  ) ( U12**T U22**T )  
 *  
 *  A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'  
 *        ( L21  I ) ( 0   A22 ) (  0       I    )  
 *  
 *  where the order of D is at most NB. The actual order is returned in  
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.  
 *  Note that U**T denotes the transpose of U.  
 *  
 *  ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code  
 *  (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or  
 *  A22 (if UPLO = 'L').  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          Specifies whether the upper or lower triangular part of the  
 *          symmetric matrix A is stored:  
 *          = 'U':  Upper triangular  
 *          = 'L':  Lower triangular  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  NB      (input) INTEGER  
 *          The maximum number of columns of the matrix A that should be  
 *          factored.  NB should be at least 2 to allow for 2-by-2 pivot  
 *          blocks.  
 *  
 *  KB      (output) INTEGER  
 *          The number of columns of A that were actually factored.  
 *          KB is either NB-1 or NB, or N if N <= NB.  
 *  
 *  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, A contains details of the partial factorization.  
 *  
 *  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.  
 *          If UPLO = 'U', only the last KB elements of IPIV are set;  
 *          if UPLO = 'L', only the first KB elements are set.  
 *  
 *          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.  
 *  
 *  W       (workspace) COMPLEX*16 array, dimension (LDW,NB)  
 *  
 *  LDW     (input) INTEGER  
 *          The leading dimension of the array W.  LDW >= max(1,N).  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit  
 *          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization  
 *               has been completed, but the block diagonal matrix D is  
 *               exactly singular.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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  Added in v.1.9

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