# ungl2 - Man Page

{un,or}gl2: generate explicit Q, level 2, step in unglq

## Synopsis

### Functions

subroutine cungl2 (m, n, k, a, lda, tau, work, info)
CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
subroutine dorgl2 (m, n, k, a, lda, tau, work, info)
DORGL2
subroutine sorgl2 (m, n, k, a, lda, tau, work, info)
SORGL2
subroutine zungl2 (m, n, k, a, lda, tau, work, info)
ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

## Function Documentation

### subroutine cungl2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:

``` CUNGL2 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 CGELQF.```
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 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 CGELQF 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 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGELQF.```

WORK

`          WORK is COMPLEX array, dimension (M)`

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.

Definition at line 112 of file cungl2.f.

### subroutine dorgl2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORGL2

Purpose:

``` DORGL2 generates an m by n real 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(2) H(1)

as returned by DGELQF.```
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 DOUBLE PRECISION 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 DGELQF 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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGELQF.```

WORK

`          WORK is DOUBLE PRECISION array, dimension (M)`

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.

Definition at line 112 of file dorgl2.f.

### subroutine sorgl2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORGL2

Purpose:

``` SORGL2 generates an m by n real 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(2) H(1)

as returned by SGELQF.```
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 REAL 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 SGELQF 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 REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGELQF.```

WORK

`          WORK is REAL array, dimension (M)`

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.

Definition at line 112 of file sorgl2.f.

### subroutine zungl2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:

``` ZUNGL2 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 (M)`

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