# sorgtsqr_row.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine sorgtsqr_row (M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
SORGTSQR_ROW

## Function/Subroutine Documentation

### subroutine sorgtsqr_row (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_ROW

Purpose:

``` SORGTSQR_ROW generates an M-by-N real matrix Q_out with
orthonormal columns from the output of SLATSQR. These N orthonormal
columns are the first N columns of a product of complex unitary
matrices Q(k)_in of order M, which are returned by SLATSQR in
a special format.

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

The input matrices Q(k)_in are stored in row and column blocks in A.
See the documentation of SLATSQR for more details on the format of
Q(k)_in, where each Q(k)_in is represented by block Householder
transformations. This routine calls an auxiliary routine SLARFB_GETT,
where the computation is performed on each individual block. The
algorithm first sweeps NB-sized column blocks from the right to left
starting in the bottom row block and continues to the top row block
(hence _ROW in the routine name). This sweep is in reverse order of
the order in which SLATSQR generates the output blocks.```
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 used as
input. 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). See SLATSQR for more details.

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 the 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. See SLATSQR for more details on the format
of T.```

LDT

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

WORK

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

LWORK

```          The dimension of the array WORK.
LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
where NBLOCAL=MIN(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 2020, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 186 of file sorgtsqr_row.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sorgtsqr_row(3) is an alias of sorgtsqr_row.f(3).

Thu Apr 1 2021 Version 3.9.1 LAPACK