# ung2l - Man Page

{un,or}g2l: step in ungql

## Synopsis

### Functions

subroutine cung2l (m, n, k, a, lda, tau, work, info)
CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).
subroutine dorg2l (m, n, k, a, lda, tau, work, info)
DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
subroutine sorg2l (m, n, k, a, lda, tau, work, info)
SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
subroutine zung2l (m, n, k, a, lda, tau, work, info)
ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

## Function Documentation

### subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose:

``` CUNG2L 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 CGEQLF.```
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 (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGEQLF 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 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQLF.```

WORK

`          WORK is COMPLEX array, dimension (N)`

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 113 of file cung2l.f.

### subroutine dorg2l (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:

``` DORG2L generates an m by n real 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 DGEQLF.```
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 DOUBLE PRECISION 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 DGEQLF 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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQLF.```

WORK

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

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 113 of file dorg2l.f.

### subroutine sorg2l (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:

``` SORG2L generates an m by n real 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 SGEQLF.```
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 REAL 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 SGEQLF 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 REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQLF.```

WORK

`          WORK is REAL array, dimension (N)`

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 113 of file sorg2l.f.

### subroutine zung2l (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose:

``` ZUNG2L 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 (N)`

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