--- rpl/lapack/lapack/zlahef.f	2010/08/06 15:32:43	1.4
+++ rpl/lapack/lapack/zlahef.f	2012/12/14 12:30:31	1.12
@@ -1,9 +1,166 @@
+*> \brief \b ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download ZLAHEF + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahef.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahef.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahef.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZLAHEF( 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
+*>
+*> ZLAHEF computes a partial factorization of a complex Hermitian
+*> 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**H U22**H )
+*>
+*> A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  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**H denotes the conjugate transpose of U.
+*>
+*> ZLAHEF is an auxiliary routine called by ZHETRF. 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
+*>          Hermitian 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 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, 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 September 2012
+*
+*> \ingroup complex16HEcomputational
+*
+*  =====================================================================
       SUBROUTINE ZLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
 *
-*  -- LAPACK routine (version 3.2) --
+*  -- LAPACK computational routine (version 3.4.2) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
+*     September 2012
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -14,85 +171,6 @@
       COMPLEX*16         A( LDA, * ), W( LDW, * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZLAHEF computes a partial factorization of a complex Hermitian
-*  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' U22' )
-*
-*  A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  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' denotes the conjugate transpose of U.
-*
-*  ZLAHEF is an auxiliary routine called by ZHETRF. 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
-*          Hermitian 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 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, 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 ..
@@ -344,7 +422,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**H = A11 - U12*W**H
 *
 *        computing blocks of NB columns at a time (note that conjg(W) is
 *        actually stored)
@@ -593,7 +671,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**H = A22 - L21*W**H
 *
 *        computing blocks of NB columns at a time (note that conjg(W) is
 *        actually stored)