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man pages->IRIX man pages -> complib/zungrq (3)
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### Contents

ZUNGRQ(3F)							    ZUNGRQ(3F)

### NAME[Toc][Back]

ZUNGRQ - generate an M-by-N complex matrix	Q with orthonormal rows,

### SYNOPSIS[Toc][Back]

SUBROUTINE	ZUNGRQ(	M, N, K, A, LDA, TAU, WORK, LWORK, INFO	)

INTEGER	INFO, K, LDA, LWORK, M,	N

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

### PURPOSE[Toc][Back]

ZUNGRQ generates an M-by-N	complex	matrix Q with orthonormal rows,	which
is	defined	as the last M rows of a	product	of K elementary	reflectors of
order N

Q  =	 H(1)' H(2)' . . . H(k)'

as	returned by ZGERQF.

### ARGUMENTS[Toc][Back]

M	     (input) INTEGER
The number	of rows	of the matrix Q. M >= 0.

N	     (input) INTEGER
The number	of columns of the matrix Q. N >= M.

K	     (input) INTEGER
The number	of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.

A	     (input/output) COMPLEX*16 array, dimension	(LDA,N)
On	entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for	i = 1,2,...,k, as
returned by ZGERQF	in the last k rows of its array	argument A.
On	exit, the M-by-N matrix	Q.

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

TAU     (input) COMPLEX*16	array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector
H(i), as returned by ZGERQF.

WORK    (workspace/output)	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 >= max(1,M).  For optimum
performance LWORK >= M*NB,	where NB is the	optimal	blocksize.

Page 1

ZUNGRQ(3F)							    ZUNGRQ(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument has an illegal value
ZUNGRQ(3F)							    ZUNGRQ(3F)

### NAME[Toc][Back]

ZUNGRQ - generate an M-by-N complex matrix	Q with orthonormal rows,

### SYNOPSIS[Toc][Back]

SUBROUTINE	ZUNGRQ(	M, N, K, A, LDA, TAU, WORK, LWORK, INFO	)

INTEGER	INFO, K, LDA, LWORK, M,	N

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

### PURPOSE[Toc][Back]

ZUNGRQ generates an M-by-N	complex	matrix Q with orthonormal rows,	which
is	defined	as the last M rows of a	product	of K elementary	reflectors of
order N

Q  =	 H(1)' H(2)' . . . H(k)'

as	returned by ZGERQF.

### ARGUMENTS[Toc][Back]

M	     (input) INTEGER
The number	of rows	of the matrix Q. M >= 0.

N	     (input) INTEGER
The number	of columns of the matrix Q. N >= M.

K	     (input) INTEGER
The number	of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.

A	     (input/output) COMPLEX*16 array, dimension	(LDA,N)
On	entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for	i = 1,2,...,k, as
returned by ZGERQF	in the last k rows of its array	argument A.
On	exit, the M-by-N matrix	Q.

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

TAU     (input) COMPLEX*16	array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector
H(i), as returned by ZGERQF.

WORK    (workspace/output)	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 >= max(1,M).  For optimum
performance LWORK >= M*NB,	where NB is the	optimal	blocksize.

Page 1

ZUNGRQ(3F)							    ZUNGRQ(3F)

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

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