# ungrq - Man Page

{un,or}grq: generate explicit Q from gerqf

## Synopsis

### Functions

subroutine cungrq (m, n, k, a, lda, tau, work, lwork, info)
CUNGRQ
subroutine dorgrq (m, n, k, a, lda, tau, work, lwork, info)
DORGRQ
subroutine sorgrq (m, n, k, a, lda, tau, work, lwork, info)
SORGRQ
subroutine zungrq (m, n, k, a, lda, tau, work, lwork, info)
ZUNGRQ

## Function Documentation

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

CUNGRQ

Purpose:

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

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

as returned by CGERQF.```
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 (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGERQF in the last 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 CGERQF.```

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 127 of file cungrq.f.

### subroutine dorgrq (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)

DORGRQ

Purpose:

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

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

as returned by DGERQF.```
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 (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGERQF in the last 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 DGERQF.```

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 127 of file dorgrq.f.

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

SORGRQ

Purpose:

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

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

as returned by SGERQF.```
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 (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGERQF in the last 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 SGERQF.```

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 127 of file sorgrq.f.

### subroutine zungrq (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)

ZUNGRQ

Purpose:

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

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

as returned by ZGERQF.```
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 (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGERQF in the last 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 ZGERQF.```

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