zlarfg(l) [redhat man page]

ZLARFG(l)								 )								 ZLARFG(l)

NAME

       ZLARFG - generate a complex elementary reflector H of order n, such that  H' * ( alpha ) = ( beta ), H' * H = I

SYNOPSIS

       SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )

	   INTEGER	  INCX, N

	   COMPLEX*16	  ALPHA, TAU

	   COMPLEX*16	  X( * )

PURPOSE

       ZLARFG generates a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I.		 (   x	 )   (	 0
       )

       where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form

	     H = I - tau * ( 1 ) * ( 1 v' ) ,
			   ( v )

       where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian.

       If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

       Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .

ARGUMENTS

       N       (input) INTEGER
	       The order of the elementary reflector.

       ALPHA   (input/output) COMPLEX*16
	       On entry, the value alpha.  On exit, it is overwritten with the value beta.

       X       (input/output) COMPLEX*16 array, dimension
	       (1+(N-2)*abs(INCX)) On entry, the vector x.  On exit, it is overwritten with the vector v.

       INCX    (input) INTEGER
	       The increment between elements of X. INCX > 0.

       TAU     (output) COMPLEX*16
	       The value tau.

LAPACK version 3.0						   15 June 2000 							 ZLARFG(l)

clarfg.f(3)							      LAPACK							       clarfg.f(3)

NAME

       clarfg.f -

SYNOPSIS

   Functions/Subroutines
       subroutine clarfg (N, ALPHA, X, INCX, TAU)
	   CLARFG

Function/Subroutine Documentation
   subroutine clarfg (integerN, complexALPHA, complex, dimension( * )X, integerINCX, complexTAU)
       CLARFG

       Purpose:

	    CLARFG generates a complex elementary reflector H of order n, such
	    that

		  H**H * ( alpha ) = ( beta ),	 H**H * H = I.
			 (   x	 )   (	 0  )

	    where alpha and beta are scalars, with beta real, and x is an
	    (n-1)-element complex vector. H is represented in the form

		  H = I - tau * ( 1 ) * ( 1 v**H ) ,
				( v )

	    where tau is a complex scalar and v is a complex (n-1)-element
	    vector. Note that H is not hermitian.

	    If the elements of x are all zero and alpha is real, then tau = 0
	    and H is taken to be the unit matrix.

	    Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .

       Parameters:
	   N

		     N is INTEGER
		     The order of the elementary reflector.

	   ALPHA

		     ALPHA is COMPLEX
		     On entry, the value alpha.
		     On exit, it is overwritten with the value beta.

	   X

		     X is COMPLEX array, dimension
				    (1+(N-2)*abs(INCX))
		     On entry, the vector x.
		     On exit, it is overwritten with the vector v.

	   INCX

		     INCX is INTEGER
		     The increment between elements of X. INCX > 0.

	   TAU

		     TAU is COMPLEX
		     The value tau.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 107 of file clarfg.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       clarfg.f(3)