CLARZ(3)                   MathKeisan LAPACK routine                  CLARZ(3)



NAME
       CLARZ  - a complex elementary reflector H to a complex M-by-N matrix C,
       from either the left or the right

SYNOPSIS
       SUBROUTINE CLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )

           CHARACTER     SIDE

           INTEGER       INCV, L, LDC, M, N

           COMPLEX       TAU

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

PURPOSE
       CLARZ applies a complex elementary reflector  H  to  a  complex  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 complex scalar and v is a complex vector.

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

       To apply H' (the conjugate transpose of H), supply  conjg(tau)  instead
       tau.

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


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) COMPLEX array, dimension (1+(L-1)*abs(INCV))
               The  vector v in the representation of H as returned by CTZRZF.
               V is not used if TAU = 0.

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

       TAU     (input) COMPLEX
               The value tau in the representation of H.

       C       (input/output) COMPLEX 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) COMPLEX 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




 LAPACK routine (version 3.1)    November 2006                        CLARZ(3)