
ZGEHD2(l) ) ZGEHD2(l)
NAME
ZGEHD2  reduce a complex general matrix A to upper Hessenberg form H by a unitary simi
larity transformation
SYNOPSIS
SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
INTEGER IHI, ILO, INFO, LDA, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H by a unitary similar
ity transformation: Q' * A * Q = H .
ARGUMENTS
N (input) INTEGER
The order of the matrix A. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER It is assumed that A is already upper triangular in rows
and columns 1:ILO1 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.
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 elements below the first subdiagonal, with the array TAU, represent the
unitary matrix Q as a product of elementary reflectors. See Further Details. LDA
(input) INTEGER The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX*16 array, dimension (N1)
The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
The matrix Q is represented as a product of (ihiilo) elementary reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi1).
Each H(i) has the form
H(i) = I  tau * v * v'
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).
LAPACK version 3.0 15 June 2000 ZGEHD2(l) 
