NAME¶

SLARFG - generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I

SYNOPSIS¶

SUBROUTINE SLARFG(

N, ALPHA, X, INCX, TAU )

INTEGER INCX, N REAL ALPHA, TAU REAL X( * )

PURPOSE¶

SLARFG generates a real elementary reflector H of order n, such that
( x ) ( 0 )
where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form
H = I - tau * ( 1 ) * ( 1 v' ) ,
( v )
where tau is a real scalar and v is a real (n-1)-element
vector.
If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix.
Otherwise 1 <= tau <= 2.

ARGUMENTS¶

N (input) INTEGER

The order of the elementary reflector.

ALPHA (input/output) REAL

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

X (input/output) REAL 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) REAL

The value tau.