leastsqrrdm.m

基于GM算法和QR分解实现的稳健奇异值分解算法

function [a,b,variance,CombineXY,s] = leastSqrRdm(x,y)
%LEASTSQRRDM Least square computation; x is random;
%   [a, b] = LEASTSQRRDM(X,Y) perform least square computation based on
%   N-by-p data matrix X and N-by-1 vector Y, returns the parameters and variances of
%   the model. Rows of X and Y represent the observations,
%   and columns of X and Y correspond to variables.

%   This arithmatic assumes the both X and X are normally distributed, and
%   the variance of X is equal to Y.(COV(X)=I(p)*a, Var(Y)=a)
%   
%   [a,b,variance] = LEASTSQRRDM(X,Y) return variance of X and Y.
%   
%   $Date: 2008/02/27 23:49:01 $

[n,p] = size(x);
CombineXY = x;
COmbineXY(:,p+1) = y;
%   Center CombineXY by substracting off the column means
CombineXY0 = CombineXY - repmat(mean(CombineXY,1),n,1);
s = CombineXY0'*CombineXY0./(n-1);
[V,D] = eig(s);
b = -V(:,p)./V(p,p);
meanx = mean(x);
a = meanx(:,p+1) - b'*meanx(:,[1:p]);
variance = D(p+1)/n-p-1;