MB04NY

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

Purpose

  To apply a real elementary reflector H to a real m-by-(n+1)
  matrix C = [ A  B ], from the right, where A has one column. 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 n-vector.

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

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

      SUBROUTINE MB04NY( M, N, V, INCV, TAU, A, LDA, B, LDB, DWORK )
C     .. Scalar Arguments ..
      INTEGER           INCV, LDA, LDB, M, N
      DOUBLE PRECISION  TAU
C     .. Array Arguments ..
      DOUBLE PRECISION  A( LDA, * ), B( LDB, * ), DWORK( * ), V( * )

Input/Output Parameters

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

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

  V       (input) DOUBLE PRECISION array, dimension
          (1+(N-1)*ABS( INCV ))
          The vector v in the representation of H.

  INCV    (input) INTEGER
          The increment between the elements of v.  INCV <> 0.

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

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

  LDA     INTEGER
          The leading dimension of array A.  LDA >= MAX(1,M).

  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 n columns of C * H).

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

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

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

  The algorithm is backward stable.

  None

Program Text

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