# dormr2.f - Man Page

SRC/dormr2.f

## Synopsis

### Functions/Subroutines

subroutine dormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine dormr2 (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).

Purpose:

``` DORMR2 overwrites the general real m by n matrix C with

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**T* C  if SIDE = 'L' and TRANS = 'T', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**T if SIDE = 'R' and TRANS = 'T',

where Q is a real orthogonal matrix defined as the product of k
elementary reflectors

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

as returned by DGERQF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.```
Parameters

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left
= 'R': apply Q or Q**T from the Right```

TRANS

```          TRANS is CHARACTER*1
= 'N': apply Q  (No transpose)
= 'T': apply Q' (Transpose)```

M

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

N

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

K

```          K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.```

A

```          A is DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
The 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.
A is modified by the routine but restored on exit.```

LDA

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

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.```

C

```          C is DOUBLE PRECISION array, dimension (LDC,N)
On entry, the m by n matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.```

LDC

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

WORK

```          WORK is DOUBLE PRECISION array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'```

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.

Definition at line 157 of file dormr2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dormr2(3) is an alias of dormr2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK