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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine dlarfg | ( | integer | N, |
double precision | ALPHA, | ||
double precision, dimension( * ) | X, | ||
integer | INCX, | ||
double precision | TAU | ||
) |
DLARFG generates an elementary reflector (Householder matrix).
Download DLARFG + dependencies [TGZ] [ZIP] [TXT]
DLARFG generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H**T * H = I. ( 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**T ) , ( 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.
[in] | N | N is INTEGER The order of the elementary reflector. |
[in,out] | ALPHA | ALPHA is DOUBLE PRECISION On entry, the value alpha. On exit, it is overwritten with the value beta. |
[in,out] | X | X is DOUBLE PRECISION array, dimension (1+(N-2)*abs(INCX)) On entry, the vector x. On exit, it is overwritten with the vector v. |
[in] | INCX | INCX is INTEGER The increment between elements of X. INCX > 0. |
[out] | TAU | TAU is DOUBLE PRECISION The value tau. |
Definition at line 108 of file dlarfg.f.