# zungql.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine zungql (M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQL

## Function/Subroutine Documentation

### subroutine zungql (integer M, integer N, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

ZUNGQL

Purpose:

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

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

as returned by ZGEQLF.```
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. M >= N >= 0.```

K

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

A

```          A is COMPLEX*16 array, dimension (LDA,N)
On entry, the (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQLF in the last k columns 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 ZGEQLF.```

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,N).
For optimum performance LWORK >= N*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:

December 2016

Definition at line 130 of file zungql.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zungql(3) is an alias of zungql.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK