# ungtsqr - Man Page

{un,or}gtsqr: generate Q from latsqr

## Synopsis

### Functions

subroutine cungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
CUNGTSQR
subroutine dorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
DORGTSQR
subroutine sorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
SORGTSQR
subroutine zungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
ZUNGTSQR

## Function Documentation

### subroutine cungtsqr (integer m, integer n, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer lwork, integer info)

CUNGTSQR

Purpose:

``` CUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal
columns, which are the first N columns of a product of comlpex unitary
matrices of order M which are returned by CLATSQR

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

See the documentation for CLATSQR.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A. M >= N >= 0.```

MB

```          MB is INTEGER
The row block size used by CLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).```

NB

```          NB is INTEGER
The column block size used by CLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).```

A

```          A is COMPLEX array, dimension (LDA,N)

On entry:

The elements on and above the diagonal are not accessed.
The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by CLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored) (same format as the output A
below the diagonal in CLATSQR).

On exit:

The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

T

```          T is COMPLEX array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)

The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of NIRB block reflector sequences
is stored in a larger NB-by-N column block of T and consists
of NICB smaller NB-by-NB upper-triangular column blocks.
(same format as the output T in CLATSQR).```

LDT

```          LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).```

WORK

```          (workspace) COMPLEX array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.  LWORK >= (M+NB)*N.
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 had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

``` November 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 174 of file cungtsqr.f.

### subroutine dorgtsqr (integer m, integer n, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer lwork, integer info)

DORGTSQR

Purpose:

``` DORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,
which are the first N columns of a product of real orthogonal
matrices of order M which are returned by DLATSQR

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

See the documentation for DLATSQR.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A. M >= N >= 0.```

MB

```          MB is INTEGER
The row block size used by DLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).```

NB

```          NB is INTEGER
The column block size used by DLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).```

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)

On entry:

The elements on and above the diagonal are not accessed.
The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by DLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored) (same format as the output A
below the diagonal in DLATSQR).

On exit:

The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

T

```          T is DOUBLE PRECISION array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)

The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of NIRB block reflector sequences
is stored in a larger NB-by-N column block of T and consists
of NICB smaller NB-by-NB upper-triangular column blocks.
(same format as the output T in DLATSQR).```

LDT

```          LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).```

WORK

```          (workspace) DOUBLE PRECISION array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.  LWORK >= (M+NB)*N.
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 had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

``` November 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 174 of file dorgtsqr.f.

### subroutine sorgtsqr (integer m, integer n, integer mb, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork, integer info)

SORGTSQR

Purpose:

``` SORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,
which are the first N columns of a product of real orthogonal
matrices of order M which are returned by SLATSQR

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

See the documentation for SLATSQR.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A. M >= N >= 0.```

MB

```          MB is INTEGER
The row block size used by SLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).```

NB

```          NB is INTEGER
The column block size used by SLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).```

A

```          A is REAL array, dimension (LDA,N)

On entry:

The elements on and above the diagonal are not accessed.
The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by SLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored) (same format as the output A
below the diagonal in SLATSQR).

On exit:

The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

T

```          T is REAL array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)

The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of NIRB block reflector sequences
is stored in a larger NB-by-N column block of T and consists
of NICB smaller NB-by-NB upper-triangular column blocks.
(same format as the output T in SLATSQR).```

LDT

```          LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).```

WORK

```          (workspace) REAL array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.  LWORK >= (M+NB)*N.
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 had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

``` November 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 174 of file sorgtsqr.f.

### subroutine zungtsqr (integer m, integer n, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGTSQR

Purpose:

``` ZUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal
columns, which are the first N columns of a product of comlpex unitary
matrices of order M which are returned by ZLATSQR

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

See the documentation for ZLATSQR.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A. M >= N >= 0.```

MB

```          MB is INTEGER
The row block size used by ZLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).```

NB

```          NB is INTEGER
The column block size used by ZLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).```

A

```          A is COMPLEX*16 array, dimension (LDA,N)

On entry:

The elements on and above the diagonal are not accessed.
The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by ZLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored) (same format as the output A
below the diagonal in ZLATSQR).

On exit:

The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

T

```          T is COMPLEX*16 array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)

The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of NIRB block reflector sequences
is stored in a larger NB-by-N column block of T and consists
of NICB smaller NB-by-NB upper-triangular column blocks.
(same format as the output T in ZLATSQR).```

LDT

```          LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).```

WORK

```          (workspace) COMPLEX*16 array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.  LWORK >= (M+NB)*N.
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 had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

``` November 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 174 of file zungtsqr.f.

## Author

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## Info

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