--- rpl/lapack/lapack/zlahr2.f	2011/07/22 07:38:17	1.8
+++ rpl/lapack/lapack/zlahr2.f	2011/11/21 20:43:15	1.9
@@ -1,9 +1,190 @@
+*> \brief \b ZLAHR2
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download ZLAHR2 + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahr2.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahr2.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahr2.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            K, LDA, LDT, LDY, N, NB
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16        A( LDA, * ), T( LDT, NB ), TAU( NB ),
+*      $                   Y( LDY, NB )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
+*> matrix A so that elements below the k-th subdiagonal are zero. The
+*> reduction is performed by an unitary similarity transformation
+*> Q**H * A * Q. The routine returns the matrices V and T which determine
+*> Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
+*>
+*> This is an auxiliary routine called by ZGEHRD.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*>          K is INTEGER
+*>          The offset for the reduction. Elements below the k-th
+*>          subdiagonal in the first NB columns are reduced to zero.
+*>          K < N.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*>          NB is INTEGER
+*>          The number of columns to be reduced.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX*16 array, dimension (LDA,N-K+1)
+*>          On entry, the n-by-(n-k+1) general matrix A.
+*>          On exit, the elements on and above the k-th subdiagonal in
+*>          the first NB columns are overwritten with the corresponding
+*>          elements of the reduced matrix; the elements below the k-th
+*>          subdiagonal, with the array TAU, represent the matrix Q as a
+*>          product of elementary reflectors. The other columns of A are
+*>          unchanged. See Further Details.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is COMPLEX*16 array, dimension (NB)
+*>          The scalar factors of the elementary reflectors. See Further
+*>          Details.
+*> \endverbatim
+*>
+*> \param[out] T
+*> \verbatim
+*>          T is COMPLEX*16 array, dimension (LDT,NB)
+*>          The upper triangular matrix T.
+*> \endverbatim
+*>
+*> \param[in] LDT
+*> \verbatim
+*>          LDT is INTEGER
+*>          The leading dimension of the array T.  LDT >= NB.
+*> \endverbatim
+*>
+*> \param[out] Y
+*> \verbatim
+*>          Y is COMPLEX*16 array, dimension (LDY,NB)
+*>          The n-by-nb matrix Y.
+*> \endverbatim
+*>
+*> \param[in] LDY
+*> \verbatim
+*>          LDY is INTEGER
+*>          The leading dimension of the array Y. LDY >= N.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The matrix Q is represented as a product of nb elementary reflectors
+*>
+*>     Q = H(1) H(2) . . . H(nb).
+*>
+*>  Each H(i) has the form
+*>
+*>     H(i) = I - tau * v * v**H
+*>
+*>  where tau is a complex scalar, and v is a complex vector with
+*>  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
+*>  A(i+k+1:n,i), and tau in TAU(i).
+*>
+*>  The elements of the vectors v together form the (n-k+1)-by-nb matrix
+*>  V which is needed, with T and Y, to apply the transformation to the
+*>  unreduced part of the matrix, using an update of the form:
+*>  A := (I - V*T*V**H) * (A - Y*V**H).
+*>
+*>  The contents of A on exit are illustrated by the following example
+*>  with n = 7, k = 3 and nb = 2:
+*>
+*>     ( a   a   a   a   a )
+*>     ( a   a   a   a   a )
+*>     ( a   a   a   a   a )
+*>     ( h   h   a   a   a )
+*>     ( v1  h   a   a   a )
+*>     ( v1  v2  a   a   a )
+*>     ( v1  v2  a   a   a )
+*>
+*>  where a denotes an element of the original matrix A, h denotes a
+*>  modified element of the upper Hessenberg matrix H, and vi denotes an
+*>  element of the vector defining H(i).
+*>
+*>  This subroutine is a slight modification of LAPACK-3.0's DLAHRD
+*>  incorporating improvements proposed by Quintana-Orti and Van de
+*>  Gejin. Note that the entries of A(1:K,2:NB) differ from those
+*>  returned by the original LAPACK-3.0's DLAHRD routine. (This
+*>  subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
+*>  performance of reduction to Hessenberg form," ACM Transactions on
+*>  Mathematical Software, 32(2):180-194, June 2006.
+*>
+*  =====================================================================
       SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
 *
-*  -- LAPACK auxiliary routine (version 3.3.1)                        --
+*  -- LAPACK auxiliary 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..--
-*  -- April 2009                                                      --
+*     November 2011
 *
 *     .. Scalar Arguments ..
       INTEGER            K, LDA, LDT, LDY, N, NB
@@ -13,107 +194,6 @@
      $                   Y( LDY, NB )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
-*  matrix A so that elements below the k-th subdiagonal are zero. The
-*  reduction is performed by an unitary similarity transformation
-*  Q**H * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
-*
-*  This is an auxiliary routine called by ZGEHRD.
-*
-*  Arguments
-*  =========
-*
-*  N       (input) INTEGER
-*          The order of the matrix A.
-*
-*  K       (input) INTEGER
-*          The offset for the reduction. Elements below the k-th
-*          subdiagonal in the first NB columns are reduced to zero.
-*          K < N.
-*
-*  NB      (input) INTEGER
-*          The number of columns to be reduced.
-*
-*  A       (input/output) COMPLEX*16 array, dimension (LDA,N-K+1)
-*          On entry, the n-by-(n-k+1) general matrix A.
-*          On exit, the elements on and above the k-th subdiagonal in
-*          the first NB columns are overwritten with the corresponding
-*          elements of the reduced matrix; the elements below the k-th
-*          subdiagonal, with the array TAU, represent the matrix Q as a
-*          product of elementary reflectors. The other columns of A are
-*          unchanged. See Further Details.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max(1,N).
-*
-*  TAU     (output) COMPLEX*16 array, dimension (NB)
-*          The scalar factors of the elementary reflectors. See Further
-*          Details.
-*
-*  T       (output) COMPLEX*16 array, dimension (LDT,NB)
-*          The upper triangular matrix T.
-*
-*  LDT     (input) INTEGER
-*          The leading dimension of the array T.  LDT >= NB.
-*
-*  Y       (output) COMPLEX*16 array, dimension (LDY,NB)
-*          The n-by-nb matrix Y.
-*
-*  LDY     (input) INTEGER
-*          The leading dimension of the array Y. LDY >= N.
-*
-*  Further Details
-*  ===============
-*
-*  The matrix Q is represented as a product of nb elementary reflectors
-*
-*     Q = H(1) H(2) . . . H(nb).
-*
-*  Each H(i) has the form
-*
-*     H(i) = I - tau * v * v**H
-*
-*  where tau is a complex scalar, and v is a complex vector with
-*  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
-*  A(i+k+1:n,i), and tau in TAU(i).
-*
-*  The elements of the vectors v together form the (n-k+1)-by-nb matrix
-*  V which is needed, with T and Y, to apply the transformation to the
-*  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V**H) * (A - Y*V**H).
-*
-*  The contents of A on exit are illustrated by the following example
-*  with n = 7, k = 3 and nb = 2:
-*
-*     ( a   a   a   a   a )
-*     ( a   a   a   a   a )
-*     ( a   a   a   a   a )
-*     ( h   h   a   a   a )
-*     ( v1  h   a   a   a )
-*     ( v1  v2  a   a   a )
-*     ( v1  v2  a   a   a )
-*
-*  where a denotes an element of the original matrix A, h denotes a
-*  modified element of the upper Hessenberg matrix H, and vi denotes an
-*  element of the vector defining H(i).
-*
-*  This subroutine is a slight modification of LAPACK-3.0's DLAHRD
-*  incorporating improvements proposed by Quintana-Orti and Van de
-*  Gejin. Note that the entries of A(1:K,2:NB) differ from those
-*  returned by the original LAPACK-3.0's DLAHRD routine. (This
-*  subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
-*
-*  References
-*  ==========
-*
-*  Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
-*  performance of reduction to Hessenberg form," ACM Transactions on
-*  Mathematical Software, 32(2):180-194, June 2006.
-*
 *  =====================================================================
 *
 *     .. Parameters ..