# dormr3.f man page

dormr3.f —

## Synopsis

### Functions/Subroutines

subroutinedormr3(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)DORMR3multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine dormr3 (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK, integerINFO)

**DORMR3** multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

**Purpose:**

```
DORMR3 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 = 'C', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q**T if SIDE = 'R' and TRANS = 'C',
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 DTZRZF. 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**T (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.
```

*L*

```
L is INTEGER
The number of columns of the matrix A containing
the meaningful part of the Householder reflectors.
If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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
DTZRZF 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 DTZRZF.
```

*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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Contributors:**

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

**Further Details:**

Definition at line 178 of file dormr3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dormr3(3) is an alias of dormr3.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK