CLARFG (3) - Linux Man Pages
subroutine clarfg (integerN, complexALPHA, complex, dimension( * )X, integerINCX, complexTAU)
CLARFG generates an elementary reflector (Householder matrix).
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 .
N is INTEGER The order of the elementary reflector.
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 is INTEGER The increment between elements of X. INCX > 0.
TAU is COMPLEX The value tau.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- September 2012
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