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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.

**Further Comments**
None

**Example**
**Program Text**

None

**Program Data**
None

**Program Results**
None

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