dlarz(l) [redhat man page]

DLARZ(l)								 )								  DLARZ(l)

NAME

       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.

       INCV    (input) INTEGER
	       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

LAPACK version 3.0						   15 June 2000 							  DLARZ(l)

DLATZM(l)								 )								 DLATZM(l)

NAME

       DLATZM - routine is deprecated and has been replaced by routine DORMRZ

SYNOPSIS

       SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )

	   CHARACTER	  SIDE

	   INTEGER	  INCV, LDC, M, N

	   DOUBLE	  PRECISION TAU

	   DOUBLE	  PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )

PURPOSE

       This routine is deprecated and has been replaced by routine DORMRZ.  DLATZM applies a Householder matrix generated by DTZRQF to a matrix.

       Let P = I - tau*u*u',   u = ( 1 ),
				   ( v )
       where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if SIDE = 'R'.

       If SIDE equals 'L', let
	      C = [ C1 ] 1
		  [ C2 ] m-1
		    n
       Then C is overwritten by P*C.

       If SIDE equals 'R', let
	      C = [ C1, C2 ] m
		     1	n-1
       Then C is overwritten by C*P.

ARGUMENTS

       SIDE    (input) CHARACTER*1
	       = 'L': form P * C
	       = 'R': form C * P

       M       (input) INTEGER
	       The number of rows of the matrix C.

       N       (input) INTEGER
	       The number of columns of the matrix C.

       V       (input) DOUBLE PRECISION array, dimension
	       (1  +  (M-1)*abs(INCV)) if SIDE = 'L' (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of P. V is not used if
	       TAU = 0.

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

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

       C1      (input/output) DOUBLE PRECISION array, dimension
	       (LDC,N) if SIDE = 'L' (M,1)   if SIDE = 'R' On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 if SIDE = 'R'.

	       On exit, the first row of P*C if SIDE = 'L', or the first column of C*P if SIDE = 'R'.

       C2      (input/output) DOUBLE PRECISION array, dimension
	       (LDC, N)   if SIDE = 'L' (LDC, N-1) if SIDE = 'R' On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the m x (n - 1)	matrix	C2
	       if SIDE = 'R'.

	       On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P if SIDE = 'R'.

       LDC     (input) INTEGER
	       The leading dimension of the arrays C1 and C2. LDC >= (1,M).

       WORK    (workspace) DOUBLE PRECISION array, dimension
	       (N) if SIDE = 'L' (M) if SIDE = 'R'

LAPACK version 3.0						   15 June 2000 							 DLATZM(l)