 ZUNGTR(3) generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD

## SYNOPSIS

SUBROUTINE ZUNGTR(
UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

CHARACTER UPLO

INTEGER INFO, LDA, LWORK, N

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

## PURPOSE

ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

## ARGUMENTS

UPLO (input) CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors from ZHETRD; = 'L': Lower triangle of A contains elementary reflectors from ZHETRD.
N (input) INTEGER
The order of the matrix Q. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors, as returned by ZHETRD. On exit, the N-by-N unitary matrix Q.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= N.
TAU (input) COMPLEX*16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= N-1. For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value