## MB04OY

### Applying an elementary reflector (using in-line code for a low order) to a matrix C = trans( trans(A) trans(B) ), from the left, where A has one row

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

Purpose

```  To apply a real elementary reflector H to a real (m+1)-by-n
matrix C = [ A ], from the left, where A has one row. H is
[ B ]
represented in the form
( 1 )
H = I - tau * u *u',    u  = (   ),
( v )
where tau is a real scalar and v is a real m-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 MB04OY( M, N, V, TAU, A, LDA, B, LDB, DWORK )
C     .. Scalar Arguments ..
INTEGER           LDA, LDB, M, N
DOUBLE PRECISION  TAU
C     .. Array Arguments ..
DOUBLE PRECISION  A( LDA, * ), B( LDB, * ), DWORK( * ), V( * )

```
Arguments

Input/Output Parameters

```  M       (input) INTEGER
The number of rows of the matrix B.  M >= 0.

N       (input) INTEGER
The number of columns of the matrices A and B.  N >= 0.

V       (input) DOUBLE PRECISION array, dimension (M)
The vector v in the representation of H.

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

A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading 1-by-N part of this array must
contain the matrix A.
On exit, the leading 1-by-N part of this array contains
the updated matrix A (the first row of H * C).

LDA     INTEGER
The leading dimension of array A.  LDA >= 1.

B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)
On entry, the leading M-by-N part of this array must
contain the matrix B.
On exit, the leading M-by-N part of this array contains
the updated matrix B (the last m rows of H * C).

LDB     INTEGER
The leading dimension of array B.  LDB >= MAX(1,M).

```
Workspace
```  DWORK   DOUBLE PRECISION array, dimension (N)
DWORK is not referenced if H has order less than 11.

```
Method
```  The routine applies the elementary reflector H, taking the special
structure of C into account.

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

```
```  None
```
Example

Program Text

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