householderハウスホルダー直交鏡映行列呼び出し手順 householder // demo u = householder(v [,w])[u, H] = householder(v [,w])引数v実数または複素数の列ベクトルwvと同じ大きさの実数または複素数の列ベクトル.
デフォルト値はeye(v)((Ox) axis).
u
unit vector lying in the (v,w) plane and orthogonal
to the bisectrix of (v,w).
Column of size(v) of real or complex numbers.
H
Orthogonal Householder reflexion matrix: H= eye() - 2*u*u'.
H is such that inv(H)==H,
H'==H, and det(H)==-1.
If v and w are real,
H*v is proportional to w.
説明householder(..) computes the unit vector u
lying in the (v,w) plane and orthogonal to the bisectrix of
(v,w).
If v and w are proportional:
If they are opposite, u= v/|v| is returned.
If they are real and have the same direction, u is set
in the (xOy) plane with a priori u(1)>0, and orthogonal to
v (u'*v==0). However,
If they are along (Ox), u = (Oy+) is returned instead.
If v and w are scalars with same
signs, the orthogonal sub-space is restricted to {0}
that can't be normalized:
u and H are then set to
%nan.
If the related reflexion matrix H is computed, for any point A
of column coordinates a, H*a are the coordinates of
the reflected image of A on P.
If v or/and w are in row, they are priorly
transposed into columns.
If v or/and w are [],
[] is returned for u and H.
例APPLICATION : Reflected image of an object
householder();
参照
qr
givens
履歴6.0Householder reflexion matrix added as second output parameter.
Demo householder() added. Help page reviewed.