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slarz(3P)		    Sun Performance Library		     slarz(3P)

NAME
       slarz  -	 applies a real elementary reflector H to a real M-by-N matrix
       C, from either the left or the right

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

       CHARACTER * 1 SIDE
       INTEGER M, N, L, INCV, LDC
       REAL TAU
       REAL V(*), C(LDC,*), WORK(*)

       SUBROUTINE SLARZ_64(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)

       CHARACTER * 1 SIDE
       INTEGER*8 M, N, L, INCV, LDC
       REAL TAU
       REAL V(*), C(LDC,*), WORK(*)

   F95 INTERFACE
       SUBROUTINE LARZ(SIDE, [M], [N], L, V, [INCV], TAU, C, [LDC], [WORK])

       CHARACTER(LEN=1) :: SIDE
       INTEGER :: M, N, L, INCV, LDC
       REAL :: TAU
       REAL, DIMENSION(:) :: V, WORK
       REAL, DIMENSION(:,:) :: C

       SUBROUTINE LARZ_64(SIDE, [M], [N], L, V, [INCV], TAU, C, [LDC], [WORK])

       CHARACTER(LEN=1) :: SIDE
       INTEGER(8) :: M, N, L, INCV, LDC
       REAL :: TAU
       REAL, DIMENSION(:) :: V, WORK
       REAL, DIMENSION(:,:) :: C

   C INTERFACE
       #include <sunperf.h>

       void slarz(char side, int m, int n, int l, float *v,  int  incv,	 float
		 tau, float *c, int ldc);

       void  slarz_64(char  side, long m, long n, long l, float *v, long incv,
		 float tau, float *c, long ldc);

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

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

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

       L (input) The number of entries of the vector V containing the meaning‐
		 ful part of the Householder vectors.  If SIDE = 'L', M	 >=  L
		 >= 0, if SIDE = 'R', N >= L >= 0.

       V (input) REAL  array  of 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)
		 The increment between elements of v. INCV <> 0.

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

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

       WORK (workspace)
		 (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

				  6 Mar 2009			     slarz(3P)

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