## 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.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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