X-Git-Url: http://gitweb.scilab.org/?p=scilab.git;a=blobdiff_plain;f=scilab%2Fmodules%2Flinear_algebra%2Fhelp%2Fpt_BR%2Ffactorization%2Fhouseholder.xml;h=318eef7dc7068b3676110973d0d9e8e1eac5bc62;hp=da47d6d839b2b5f01cb7590645db8e874611cc3a;hb=f0ad1547b5fd8108c7ccc0779d19216160dfdacf;hpb=ed00e2c731e6ced1bfb964b4ca30f11020fc3320 diff --git a/scilab/modules/linear_algebra/help/pt_BR/factorization/householder.xml b/scilab/modules/linear_algebra/help/pt_BR/factorization/householder.xml index da47d6d..318eef7 100644 --- a/scilab/modules/linear_algebra/help/pt_BR/factorization/householder.xml +++ b/scilab/modules/linear_algebra/help/pt_BR/factorization/householder.xml @@ -2,7 +2,8 @@ - + householder matriz de reflexão ortogonal de Householder Seqüência de Chamamento - u=householder(v [,w]) + householder // demo + u = householder(v [,w]) + [u, H] = householder(v [,w]) - + Parâmetros @@ -35,38 +37,166 @@ w vetor coluna de reais ou complexos com o mesmo tamanho que - v. Valor padrão é - eye(v) + v. Valor padrão é eye(v) ((Ox) axis) u - vetor coluna de reais ou complexos + + 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. + - + Descrição - Dados dois vetores coluna v, - w - - de mesmo tamanho, householder(v,w) retorna - um vetor coluna unitário u, tal que - (eye()-2*u*u')*v - - éproporcional a w. - (eye()-2*u*u') é a matriz de reflexão ortogonal de - Householder . + householder(..) computes the unit vector u + lying in the (v,w) plane and orthogonal to the bisectrix of + (v,w). - O valor padrão de w é eye(v). - Neste caso, o vetor (eye()-2*u*u')*v é o - vetor eye(v)*norm(v). + 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. + + + + Exemplos + + + APPLICATION : Reflected image of an object + + + householder(); + Ver Também @@ -79,4 +209,17 @@ + + Histórico + + + 6.0 + + Householder reflexion matrix added as second output parameter. + Demo householder() added. Help page reviewed. + + + + +