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# zunghr

```
NAME
ZUNGHR - generate a complex unitary matrix Q which is
defined as the product of IHI-ILO elementary reflectors of
order N, as returned by ZGEHRD

SYNOPSIS
SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK,
INFO )

INTEGER        IHI, ILO, INFO, LDA, LWORK, N

COMPLEX*16     A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE
ZUNGHR generates a complex unitary matrix Q which is defined
as the product of IHI-ILO elementary reflectors of order N,
as returned by ZGEHRD:

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

ARGUMENTS
N       (input) INTEGER
The order of the matrix Q. N >= 0.

ILO     (input) INTEGER
IHI     (input) INTEGER ILO and IHI must have the
same values as in the previous call of ZGEHRD. Q is
equal to the unit matrix except in the submatrix
Q(ilo+1:ihi,ilo+1:ihi).  If N > 0, 1 <= ILO <= IHI
<= N; otherwise ILO = 1 and IHI = N.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the vectors which define the elementary
reflectors, as returned by ZGEHRD.  On exit, the N-
by-N unitary matrix Q.

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

TAU     (input) COMPLEX*16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elemen-
tary reflector H(i), as returned by ZGEHRD.

WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, where

NB is the optimal blocksize.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```