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zgehd2.f(3) LAPACK zgehd2.f(3)

zgehd2.f -


subroutine zgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
 
ZGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

ZGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.
Purpose:
 ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
 by a unitary similarity transformation:  Q**H * A * Q = H .
Parameters:
N
          N is INTEGER
          The order of the matrix A.  N >= 0.
ILO
          ILO is INTEGER
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).
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.
LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
TAU
          TAU is COMPLEX*16 array, dimension (N-1)
          The scalar factors of the elementary reflectors (see Further
          Details).
WORK
          WORK is COMPLEX*16 array, dimension (N)
INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
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).
Definition at line 150 of file zgehd2.f.

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