--- rpl/lapack/lapack/zgghrd.f	2010/12/21 13:53:45	1.7
+++ rpl/lapack/lapack/zgghrd.f	2011/11/21 20:43:10	1.8
@@ -1,10 +1,213 @@
+*> \brief \b ZGGHRD
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download ZGGHRD + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgghrd.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgghrd.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgghrd.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
+*                          LDQ, Z, LDZ, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          COMPQ, COMPZ
+*       INTEGER            IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
+*      $                   Z( LDZ, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper
+*> Hessenberg form using unitary transformations, where A is a
+*> general matrix and B is upper triangular.  The form of the
+*> generalized eigenvalue problem is
+*>    A*x = lambda*B*x,
+*> and B is typically made upper triangular by computing its QR
+*> factorization and moving the unitary matrix Q to the left side
+*> of the equation.
+*>
+*> This subroutine simultaneously reduces A to a Hessenberg matrix H:
+*>    Q**H*A*Z = H
+*> and transforms B to another upper triangular matrix T:
+*>    Q**H*B*Z = T
+*> in order to reduce the problem to its standard form
+*>    H*y = lambda*T*y
+*> where y = Z**H*x.
+*>
+*> The unitary matrices Q and Z are determined as products of Givens
+*> rotations.  They may either be formed explicitly, or they may be
+*> postmultiplied into input matrices Q1 and Z1, so that
+*>      Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H
+*>      Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H
+*> If Q1 is the unitary matrix from the QR factorization of B in the
+*> original equation A*x = lambda*B*x, then ZGGHRD reduces the original
+*> problem to generalized Hessenberg form.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] COMPQ
+*> \verbatim
+*>          COMPQ is CHARACTER*1
+*>          = 'N': do not compute Q;
+*>          = 'I': Q is initialized to the unit matrix, and the
+*>                 unitary matrix Q is returned;
+*>          = 'V': Q must contain a unitary matrix Q1 on entry,
+*>                 and the product Q1*Q is returned.
+*> \endverbatim
+*>
+*> \param[in] COMPZ
+*> \verbatim
+*>          COMPZ is CHARACTER*1
+*>          = 'N': do not compute Q;
+*>          = 'I': Q is initialized to the unit matrix, and the
+*>                 unitary matrix Q is returned;
+*>          = 'V': Q must contain a unitary matrix Q1 on entry,
+*>                 and the product Q1*Q is returned.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrices A and B.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] ILO
+*> \verbatim
+*>          ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHI
+*> \verbatim
+*>          IHI is INTEGER
+*>
+*>          ILO and IHI mark the rows and columns of A which are to be
+*>          reduced.  It is assumed that A is already upper triangular
+*>          in rows and columns 1:ILO-1 and IHI+1:N.  ILO and IHI are
+*>          normally set by a previous call to ZGGBAL; otherwise they
+*>          should be set to 1 and N respectively.
+*>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX*16 array, dimension (LDA, N)
+*>          On entry, the N-by-N general matrix to be reduced.
+*>          On exit, the upper triangle and the first subdiagonal of A
+*>          are overwritten with the upper Hessenberg matrix H, and the
+*>          rest is set to zero.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX*16 array, dimension (LDB, N)
+*>          On entry, the N-by-N upper triangular matrix B.
+*>          On exit, the upper triangular matrix T = Q**H B Z.  The
+*>          elements below the diagonal are set to zero.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] Q
+*> \verbatim
+*>          Q is COMPLEX*16 array, dimension (LDQ, N)
+*>          On entry, if COMPQ = 'V', the unitary matrix Q1, typically
+*>          from the QR factorization of B.
+*>          On exit, if COMPQ='I', the unitary matrix Q, and if
+*>          COMPQ = 'V', the product Q1*Q.
+*>          Not referenced if COMPQ='N'.
+*> \endverbatim
+*>
+*> \param[in] LDQ
+*> \verbatim
+*>          LDQ is INTEGER
+*>          The leading dimension of the array Q.
+*>          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*>          Z is COMPLEX*16 array, dimension (LDZ, N)
+*>          On entry, if COMPZ = 'V', the unitary matrix Z1.
+*>          On exit, if COMPZ='I', the unitary matrix Z, and if
+*>          COMPZ = 'V', the product Z1*Z.
+*>          Not referenced if COMPZ='N'.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*>          LDZ is INTEGER
+*>          The leading dimension of the array Z.
+*>          LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  This routine reduces A to Hessenberg and B to triangular form by
+*>  an unblocked reduction, as described in _Matrix_Computations_,
+*>  by Golub and van Loan (Johns Hopkins Press).
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE ZGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
      $                   LDQ, Z, LDZ, INFO )
 *
-*  -- LAPACK routine (version 3.2) --
+*  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
+*     November 2011
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ
@@ -15,113 +218,6 @@
      $                   Z( LDZ, * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper
-*  Hessenberg form using unitary transformations, where A is a
-*  general matrix and B is upper triangular.  The form of the
-*  generalized eigenvalue problem is
-*     A*x = lambda*B*x,
-*  and B is typically made upper triangular by computing its QR
-*  factorization and moving the unitary matrix Q to the left side
-*  of the equation.
-*
-*  This subroutine simultaneously reduces A to a Hessenberg matrix H:
-*     Q**H*A*Z = H
-*  and transforms B to another upper triangular matrix T:
-*     Q**H*B*Z = T
-*  in order to reduce the problem to its standard form
-*     H*y = lambda*T*y
-*  where y = Z**H*x.
-*
-*  The unitary matrices Q and Z are determined as products of Givens
-*  rotations.  They may either be formed explicitly, or they may be
-*  postmultiplied into input matrices Q1 and Z1, so that
-*       Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H
-*       Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H
-*  If Q1 is the unitary matrix from the QR factorization of B in the
-*  original equation A*x = lambda*B*x, then ZGGHRD reduces the original
-*  problem to generalized Hessenberg form.
-*
-*  Arguments
-*  =========
-*
-*  COMPQ   (input) CHARACTER*1
-*          = 'N': do not compute Q;
-*          = 'I': Q is initialized to the unit matrix, and the
-*                 unitary matrix Q is returned;
-*          = 'V': Q must contain a unitary matrix Q1 on entry,
-*                 and the product Q1*Q is returned.
-*
-*  COMPZ   (input) CHARACTER*1
-*          = 'N': do not compute Q;
-*          = 'I': Q is initialized to the unit matrix, and the
-*                 unitary matrix Q is returned;
-*          = 'V': Q must contain a unitary matrix Q1 on entry,
-*                 and the product Q1*Q is returned.
-*
-*  N       (input) INTEGER
-*          The order of the matrices A and B.  N >= 0.
-*
-*  ILO     (input) INTEGER
-*  IHI     (input) INTEGER
-*          ILO and IHI mark the rows and columns of A which are to be
-*          reduced.  It is assumed that A is already upper triangular
-*          in rows and columns 1:ILO-1 and IHI+1:N.  ILO and IHI are
-*          normally set by a previous call to ZGGBAL; otherwise they
-*          should be set to 1 and N respectively.
-*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
-*
-*  A       (input/output) COMPLEX*16 array, dimension (LDA, N)
-*          On entry, the N-by-N general matrix to be reduced.
-*          On exit, the upper triangle and the first subdiagonal of A
-*          are overwritten with the upper Hessenberg matrix H, and the
-*          rest is set to zero.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max(1,N).
-*
-*  B       (input/output) COMPLEX*16 array, dimension (LDB, N)
-*          On entry, the N-by-N upper triangular matrix B.
-*          On exit, the upper triangular matrix T = Q**H B Z.  The
-*          elements below the diagonal are set to zero.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max(1,N).
-*
-*  Q       (input/output) COMPLEX*16 array, dimension (LDQ, N)
-*          On entry, if COMPQ = 'V', the unitary matrix Q1, typically
-*          from the QR factorization of B.
-*          On exit, if COMPQ='I', the unitary matrix Q, and if
-*          COMPQ = 'V', the product Q1*Q.
-*          Not referenced if COMPQ='N'.
-*
-*  LDQ     (input) INTEGER
-*          The leading dimension of the array Q.
-*          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
-*
-*  Z       (input/output) COMPLEX*16 array, dimension (LDZ, N)
-*          On entry, if COMPZ = 'V', the unitary matrix Z1.
-*          On exit, if COMPZ='I', the unitary matrix Z, and if
-*          COMPZ = 'V', the product Z1*Z.
-*          Not referenced if COMPZ='N'.
-*
-*  LDZ     (input) INTEGER
-*          The leading dimension of the array Z.
-*          LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise.
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit.
-*          < 0:  if INFO = -i, the i-th argument had an illegal value.
-*
-*  Further Details
-*  ===============
-*
-*  This routine reduces A to Hessenberg and B to triangular form by
-*  an unblocked reduction, as described in _Matrix_Computations_,
-*  by Golub and van Loan (Johns Hopkins Press).
-*
 *  =====================================================================
 *
 *     .. Parameters ..