# ungqr - Man Page

{un,or}gqr: generate explicit Q from geqrf

## Synopsis

### Functions

subroutine cungqr (m, n, k, a, lda, tau, work, lwork, info)
CUNGQR
subroutine dorgqr (m, n, k, a, lda, tau, work, lwork, info)
DORGQR
subroutine sorgqr (m, n, k, a, lda, tau, work, lwork, info)
SORGQR
subroutine zungqr (m, n, k, a, lda, tau, work, lwork, info)
ZUNGQR

## Function 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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file cungqr.f.

### subroutine dorgqr (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)

DORGQR

Purpose:

``` DORGQR generates an M-by-N real 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 DGEQRF.```
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGEQRF 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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.```

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,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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file dorgqr.f.

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

SORGQR

Purpose:

``` SORGQR generates an M-by-N real 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 SGEQRF.```
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGEQRF 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 REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQRF.```

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,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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file sorgqr.f.

### subroutine zungqr (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)

ZUNGQR

Purpose:

``` ZUNGQR 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 ZGEQRF.```
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQRF 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*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.```

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,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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file zungqr.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK