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# zungrq(3) [centos man page]

```zungrq.f(3)							      LAPACK							       zungrq.f(3)

NAME
zungrq.f -

SYNOPSIS
Functions/Subroutines
subroutine zungrq (M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGRQ

Function/Subroutine Documentation
subroutine zungrq (integerM, integerN, integerK, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16,
dimension( * )WORK, integerLWORK, integerINFO)
ZUNGRQ

Purpose:

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 H(2)**H . . . H(k)**H

as returned by ZGERQF.

Parameters:
M

M is INTEGER
The number of rows of the matrix Q. M >= 0.

N

N is INTEGER
The number of columns of the matrix Q. N >= M.

K

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

A

A is 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

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

TAU

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

WORK

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

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*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

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

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Definition at line 129 of file zungrq.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zungrq.f(3)```

## Check Out this Related Man Page

```zunglq.f(3)							      LAPACK							       zunglq.f(3)

NAME
zunglq.f -

SYNOPSIS
Functions/Subroutines
subroutine zunglq (M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGLQ

Function/Subroutine Documentation
subroutine zunglq (integerM, integerN, integerK, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16,
dimension( * )WORK, integerLWORK, integerINFO)
ZUNGLQ

Purpose:

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

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

as returned by ZGELQF.

Parameters:
M

M is INTEGER
The number of rows of the matrix Q. M >= 0.

N

N is INTEGER
The number of columns of the matrix Q. N >= M.

K

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

A

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

LDA

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

TAU

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

WORK

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

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*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

INFO is INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument has an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Definition at line 128 of file zunglq.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zunglq.f(3)```