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zgehd2 examples
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Man Page Details
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 Online html documentation available at 
            http://www.netlib.org/lapack/explore-html/ 

 Definition:
 ===========

       SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
 
       .. Scalar Arguments ..
       INTEGER            IHI, ILO, INFO, LDA, N
       ..
       .. Array Arguments ..
       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
       ..
  

 Purpose:
 =============

  ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
  by a unitary similarity transformation:  Q**H * A * Q = H .

 Arguments:
 ==========

  [in] N

          N is INTEGER
          The order of the matrix A.  N >= 0.

  [in] ILO

          ILO is INTEGER

  [in] IHI

          IHI is INTEGER

          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 ZGEBAL; otherwise they should be
          set to 1 and N respectively. See Further Details.
          1 <= ILO <= IHI <= max(1,N).

  [in,out] A

          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
          elements below the first subdiagonal, with the array TAU,
          represent the unitary matrix Q as a product of elementary
          reflectors. See Further Details.

  [in] LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

  [out] TAU

          TAU is COMPLEX*16 array, dimension (N-1)
          The scalar factors of the elementary reflectors (see Further
          Details).

  [out] WORK

          WORK is COMPLEX*16 array, dimension (N)

  [out] INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.

 Authors:
 ========

   Univ. of Tennessee 
   Univ. of California Berkeley 
   Univ. of Colorado Denver 
   NAG Ltd. 

 November 2011

 Further Details:
 =====================

  The matrix Q is represented as a product of (ihi-ilo) elementary
  reflectors

     Q = H(ilo) H(ilo+1) . . . H(ihi-1).

  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) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
  exit in A(i+2:ihi,i), and tau in TAU(i).

  The contents of A are illustrated by the following example, with
  n = 7, ilo = 2 and ihi = 6:

  on entry,                        on exit,

  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
  (                         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).

