LARF - 5.2 English - 68552

LARF applies an elementary reflector to a general rectangular matrix.

Purpose:

 LARF applies 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

       H = I - tau * v * v**T

 where tau is a real scalar and v is a real vector.

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

Parameters:

• SIDE – [in]

  SIDE is CHARACTER*1

  = ‘L’: form H * C

  = ‘R’: form C * H

• M – [in]

  M is INTEGER

  The number of rows of the matrix C.

• N – [in]

  N is INTEGER

  The number of columns of the matrix C.

• V – [in]

  V is REAL array, dimension

  (1 + (M-1)*abs(INCV)) if SIDE = ‘L’

  or (1 + (N-1)*abs(INCV)) if SIDE = ‘R’

  The vector v in the representation of H. V is not used if TAU = 0.

• INCV – [in]

  INCV is INTEGER

  The increment between elements of v. INCV <> 0.

• TAU – [in]

  TAU is REAL

  The value tau in the representation of H.

• C – [inout]

  C is REAL array, dimension (LDC,N)

  On entry, the m by n matrix C.

  On exit, C is overwritten by the matrix H * C if SIDE = ‘L’, or C * H if SIDE = ‘R’.

• LDC – [in]

  LDC is INTEGER

  The leading dimension of the array C. LDC >= fla_max(1,M).

• WORK – [out]

  WORK is REAL array, dimension

  (N) if SIDE = ‘L’

  or (M) if SIDE = ‘R’