SYNOPSIS

SUBROUTINE SLARZ(

SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )

    

CHARACTER SIDE

    

INTEGER INCV, L, LDC, M, N

    

REAL TAU

    

REAL C( LDC, * ), V( * ), WORK( * )

PURPOSE

SLARZ 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'
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.

ARGUMENTS

SIDE (input) CHARACTER*1

= 'L': form H * C
= 'R': form C * H

M (input) INTEGER

The number of rows of the matrix C.

N (input) INTEGER

The number of columns of the matrix C.

L (input) 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 (input) 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 (input) INTEGER

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

TAU (input) REAL

The value tau in the representation of H.

C (input/output) 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 (input) INTEGER

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

WORK (workspace) REAL array, dimension

(N) if SIDE = 'L' or (M) if SIDE = 'R'

FURTHER DETAILS

Based on contributions by

  A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA