DLARZ  - applie a real elementary reflector H to a real M-
       by-N matrix C, from either the left or the right


SYNOPSIS

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

           CHARACTER     SIDE

           INTEGER       INCV, L, LDC, M, N

           DOUBLE        PRECISION TAU

           DOUBLE        PRECISION C( LDC, * ), V( * ), WORK( * )


PURPOSE

       DLARZ 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
       DTZRZF.


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

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

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

       C       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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


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