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 w v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. APPLICATION : Reflected image of an object householder(); 参照 qr givens 履歴 6.0 Householder reflexion matrix added as second output parameter. Demo householder() added. Help page reviewed.