## MB04PY

### Applying an elementary reflector (using in-line code for a low order) to a matrix, from either the left or the right

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To apply a real elementary reflector H to a real m-by-n matrix
C, from either the left or the right. H is represented in the form
( 1 )
H = I - tau * u *u',    u  = (   ),
( v )
where tau is a real scalar and v is a real vector.

If tau = 0, then H is taken to be the unit matrix.

In-line code is used if H has order < 11.

```
Specification
```      SUBROUTINE MB04PY( SIDE, M, N, V, TAU, C, LDC, DWORK )
C     .. Scalar Arguments ..
CHARACTER          SIDE
INTEGER            LDC, M, N
DOUBLE PRECISION   TAU
C     .. Array Arguments ..
DOUBLE PRECISION   C( LDC, * ), DWORK( * ), V( * )

```
Arguments

Mode Parameters

```  SIDE    CHARACTER*1
Indicates whether the elementary reflector should be
applied from the left or from the right, as follows:
= 'L':  Compute H * C;
= 'R':  Compute C * H.

```
Input/Output Parameters
```  M       (input) INTEGER
The number of rows of the matrix C.  M >= 0.

N       (input) INTEGER
The number of columns of the matrix C.  N >= 0.

V       (input) DOUBLE PRECISION array, dimension
(M-1), if SIDE = 'L', or
(N-1), if SIDE = 'R'.
The vector v in the representation of H.

TAU     (input) DOUBLE PRECISION
The scalar factor of the elementary reflector H.

C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the leading M-by-N part of this array must
contain the matrix C.
On exit, the leading M-by-N part of this array contains
the matrix H * C, if SIDE = 'L', or C * H, if SIDE = 'R'.

LDC     INTEGER
The leading dimension of array C.  LDC >= MAX(1,M).

```
Workspace
```  DWORK   DOUBLE PRECISION array, dimension (N), if SIDE = 'L', or
(M), if SIDE = 'R'.
DWORK is not referenced if H has order less than 11.

```
Method
```  The routine applies the elementary reflector H, taking its special
structure into account. The multiplications by the first component
of u (which is 1) are avoided, to increase the efficiency.

```
Numerical Aspects
```  The algorithm is backward stable.

```
```  None
```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```