LARZ - 5.2 English - 68552

LARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:

 LARZ 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.


 H is a product of k elementary reflectors as   returned by STZRZF.

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.

• L – [in]

  L is INTEGER

  The number of entries of the vector V containing the meaningful part of the Householder vectors.

  If SIDE = ‘L’, M >= L >= 0, if SIDE = ‘R’, N >= L >= 0.

• V – [in]

  V is REAL array, dimension (1+(L-1)*abs(INCV))

  The vector v in the representation of H as returned by STZRZF. 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’