# SORMR3 (3) - Linux Manuals

sormr3.f -

## SYNOPSIS

### Functions/Subroutines

subroutine sormr3 (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine sormr3 (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK, integerINFO)

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:

``` SORMR3 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 STZRZF. 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 REAL 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
STZRZF 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 REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by STZRZF.
```

C

```          C is REAL 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 REAL 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 sormr3.f.

## Author

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