• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

dlarz - applies 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 * 1 SIDE
  INTEGER M, N, L, INCV, LDC
  DOUBLE PRECISION TAU
  DOUBLE PRECISION V(*), C(LDC,*), WORK(*)

  SUBROUTINE DLARZ_64( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
  CHARACTER * 1 SIDE
  INTEGER*8 M, N, L, INCV, LDC
  DOUBLE PRECISION TAU
  DOUBLE PRECISION 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(8) :: TAU
  REAL(8), DIMENSION(:) :: V, WORK
  REAL(8), 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(8) :: TAU
  REAL(8), DIMENSION(:) :: V, WORK
  REAL(8), DIMENSION(:,:) :: C

C INTERFACE

#include <sunperf.h>

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

void dlarz_64(char side, long m, long n, long l, double *v, long incv, double tau, double *c, long ldc);

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 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 meaningful part of the Householder vectors. If SIDE = 'L', M > = L > = 0, if SIDE = 'R', N > = L > = 0.

• V (input)
  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