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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.

**Further Comments**
None

**Example**
**Program Text**

None

**Program Data**
None

**Program Results**
None

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