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version 1.8, 2011/07/22 07:38:15 version 1.9, 2011/11/21 20:43:12
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   *> \brief \b ZHETRF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHETRF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, LDA, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       COMPLEX*16         A( LDA, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHETRF computes the factorization of a complex Hermitian matrix A
   *> using the Bunch-Kaufman diagonal pivoting method.  The form of the
   *> factorization is
   *>
   *>    A = U*D*U**H  or  A = L*D*L**H
   *>
   *> 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.
   *>
   *> This is the blocked version of the algorithm, calling Level 3 BLAS.
   *> \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 order of the matrix A.  N >= 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, the block diagonal matrix D and the multipliers used
   *>          to obtain the factor U or L (see below for further details).
   *> \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 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] 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.  For best performance
   *>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
   *> \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, and division by zero will occur if it
   *>                is used to solve a system of equations.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16HEcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  If UPLO = 'U', then A = U*D*U**H, where
   *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
   *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
   *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
   *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
   *>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
   *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
   *>
   *>             (   I    v    0   )   k-s
   *>     U(k) =  (   0    I    0   )   s
   *>             (   0    0    I   )   n-k
   *>                k-s   s   n-k
   *>
   *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
   *>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
   *>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
   *>
   *>  If UPLO = 'L', then A = L*D*L**H, where
   *>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
   *>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
   *>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
   *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
   *>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
   *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
   *>
   *>             (   I    0     0   )  k-1
   *>     L(k) =  (   0    I     0   )  s
   *>             (   0    v     I   )  n-k-s+1
   *>                k-1   s  n-k-s+1
   *>
   *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
   *>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
   *>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )        SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, 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, * ), WORK( * )        COMPLEX*16         A( LDA, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHETRF computes the factorization of a complex Hermitian matrix A  
 *  using the Bunch-Kaufman diagonal pivoting method.  The form of the  
 *  factorization is  
 *  
 *     A = U*D*U**H  or  A = L*D*L**H  
 *  
 *  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.  
 *  
 *  This is the blocked version of the algorithm, calling Level 3 BLAS.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 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, the block diagonal matrix D and the multipliers used  
 *          to obtain the factor U or L (see below for further details).  
 *  
 *  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 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.  
 *  
 *  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.  For best performance  
 *          LWORK >= N*NB, where NB is the block size returned by ILAENV.  
 *  
 *  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, and division by zero will occur if it  
 *                is used to solve a system of equations.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  If UPLO = 'U', then A = U*D*U**H, where  
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,  
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to  
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1  
 *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as  
 *  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such  
 *  that if the diagonal block D(k) is of order s (s = 1 or 2), then  
 *  
 *             (   I    v    0   )   k-s  
 *     U(k) =  (   0    I    0   )   s  
 *             (   0    0    I   )   n-k  
 *                k-s   s   n-k  
 *  
 *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).  
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),  
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).  
 *  
 *  If UPLO = 'L', then A = L*D*L**H, where  
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,  
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to  
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1  
 *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as  
 *  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such  
 *  that if the diagonal block D(k) is of order s (s = 1 or 2), then  
 *  
 *             (   I    0     0   )  k-1  
 *     L(k) =  (   0    I     0   )  s  
 *             (   0    v     I   )  n-k-s+1  
 *                k-1   s  n-k-s+1  
 *  
 *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).  
 *  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),  
 *  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
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