clarfg-f(3)

clarfg.f –

Synopsis

Functions/Subroutines

subroutine clarfg (N, ALPHA, X, INCX, TAU)
CLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation

subroutine clarfg (integerN, complexALPHA, complex, dimension( * )X, integerINCX, complexTAU)

CLARFG generates an elementary reflector (Householder matrix).

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 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 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:

September 2012

Definition at line 107 of file clarfg.f.

Author

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