NAME

SYNOPSIS

  SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
  CHARACTER * 1 SIDE
  DOUBLE COMPLEX TAU
  DOUBLE COMPLEX V(*), C(LDC,*), WORK(*)
  INTEGER M, N, L, INCV, LDC
 
  SUBROUTINE ZLARZ_64( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
  CHARACTER * 1 SIDE
  DOUBLE COMPLEX TAU
  DOUBLE COMPLEX V(*), C(LDC,*), WORK(*)
  INTEGER*8 M, N, L, INCV, LDC
 

F95 INTERFACE

  SUBROUTINE LARZ( SIDE, [M], [N], L, V, [INCV], TAU, C, [LDC], [WORK])
  CHARACTER(LEN=1) :: SIDE
  COMPLEX(8) :: TAU
  COMPLEX(8), DIMENSION(:) :: V, WORK
  COMPLEX(8), DIMENSION(:,:) :: C
  INTEGER :: M, N, L, INCV, LDC
 
  SUBROUTINE LARZ_64( SIDE, [M], [N], L, V, [INCV], TAU, C, [LDC], 
 *       [WORK])
  CHARACTER(LEN=1) :: SIDE
  COMPLEX(8) :: TAU
  COMPLEX(8), DIMENSION(:) :: V, WORK
  COMPLEX(8), DIMENSION(:,:) :: C
  INTEGER(8) :: M, N, L, INCV, LDC
 

C INTERFACE

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

void zlarz_64(char side, long m, long n, long l, doublecomplex *v, long incv, doublecomplex tau, doublecomplex *c, long ldc);

PURPOSE

      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)

* 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 CTZRZF. 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' .SH FURTHER DETAILS Based on contributions by

  A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA