# unglq - Man Page

{un,or}glq: generate explicit Q from gelqf

## Synopsis

### Functions

subroutine cunglq (m, n, k, a, lda, tau, work, lwork, info)
CUNGLQ
subroutine dorglq (m, n, k, a, lda, tau, work, lwork, info)
DORGLQ
subroutine sorglq (m, n, k, a, lda, tau, work, lwork, info)
SORGLQ
subroutine zunglq (m, n, k, a, lda, tau, work, lwork, info)
ZUNGLQ

## Function Documentation

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

CUNGLQ

Purpose:

``` CUNGLQ 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 (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

NAG Ltd.

Definition at line 126 of file cunglq.f.

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

DORGLQ

Purpose:

``` DORGLQ 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 (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

NAG Ltd.

Definition at line 126 of file dorglq.f.

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

SORGLQ

Purpose:

``` SORGLQ 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 (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

NAG Ltd.

Definition at line 126 of file sorglq.f.

### subroutine zunglq (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)

ZUNGLQ

Purpose:

``` ZUNGLQ 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 (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