zlarfg (l) - Linux Manuals

zlarfg: generates a complex elementary reflector H of order n, such that Haq * ( alpha ) = ( beta ), Haq * H = I

NAME

ZLARFG - generates a complex elementary reflector H of order n, such that Haq * ( alpha ) = ( beta ), Haq * 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
     (   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 vaq ) ,

              ( 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.

Pages related to zlarfg

  • zlarfg (3)
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  • zlarft (l) - forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
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  • zlar1v (l) - computes the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
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