X-Git-Url: http://gitweb.scilab.org/?p=scilab.git;a=blobdiff_plain;f=scilab%2Fmodules%2Flinear_algebra%2Fhelp%2Fja_JP%2Ffactorization%2Fhouseholder.xml;h=94c17ed1c31dfa3d1148133a87f632aed382edce;hp=6f8a22e7af0613951b6741a5e2a79d4c57070b07;hb=f0ad1547b5fd8108c7ccc0779d19216160dfdacf;hpb=ed00e2c731e6ced1bfb964b4ca30f11020fc3320 diff --git a/scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml b/scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml index 6f8a22e..94c17ed 100644 --- a/scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml +++ b/scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml @@ -1,9 +1,9 @@ - - householder - ãã¦ã¹ãã«ãã¼ç´äº¤é¡æ è¡å - - - å¼ã³åºãæé  - - u=householder(v [,w]) - + householder // demo + u = householder(v [,w]) + [u, H] = householder(v [,w]) - - - + å¼æ° - - - v - - å®æ°ã¾ãã¯è¤ç´ æ°ã®åãã¯ãã« - - - - w - - - vã¨åãå¤§ããã®å®æ°ã¾ãã¯è¤ç´ æ°ã®åãã¯ãã«. - - ããã©ã«ãå¤ã¯eye(v) - + ããã©ã«ãå¤ã¯eye(v)((Ox) axis). - - - - u - - - å®æ°ã¾ãã¯è¤ç´ æ°ã®åãã¯ãã« - + + 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. + - - - - - - + èª¬æ - - - åãå¤§ããã®åãã¯ãã« - - v, w ãæå®ããã¨, - - householder(v,w) ã¯, - - (eye()-2*u*u')*vãwã«æ¯ä¾ãããããª - - ã¦ãã¿ãªåãã¯ãã«uãè¿ãã¾ã. - - (eye()-2*u*u') ã¯ãã¦ã¹ãã«ãã¼ç´äº¤é¡æ è¡åã§ã. - + householder(..) computes the unit vector u + lying in the (v,w) plane and orthogonal to the bisectrix of + (v,w). - - - w ã®ããã©ã«ãå¤ã¯ eye(v)ã§ã. - - ãã®å ´å,ãã¯ãã« (eye()-2*u*u')*v ã¯ãã¯ãã« - - eye(v)*norm(v)ã§ã. - + 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. + + + + ä¾ + + + APPLICATION : Reflected image of an object + + + householder(); + - åç§ - - - qr - - - givens - - + + å±¥æ­´ + + + 6.0 + + Householder reflexion matrix added as second output parameter. + Demo householder() added. Help page reviewed. + + + + + -