zgehd2.f man page

zgehd2.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zgehd2 (integerN, integerILO, integerIHI, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)

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.

Author

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Referenced By

zgehd2(3) is an alias of zgehd2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK