# zungrq.f man page

zungrq.f —

## Synopsis

### Functions/Subroutines

subroutinezungrq(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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 129 of file zungrq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zungrq(3) is an alias of zungrq.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK