# cungqr.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cungqr.f

## SYNOPSIS

### Functions/Subroutines

subroutine cungqr (M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR

## Function/Subroutine Documentation

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

CUNGQR

Purpose:

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

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

as returned by CGEQRF.
```

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 array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGEQRF in the first 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 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQRF.
```

WORK

```          WORK is COMPLEX 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