leastsqr.asv

基于GM算法和QR分解实现的稳健奇异值分解算法

function [parameter, variance, cov, x0, s0] = leastqur(x,y)
%LEASTQUR Least square computation
%   PARAMETER = LESTQUR(X, Y) performs least square computation on N-by-(P+1) 
%   data matrix X and N-by-1 vector Y, returns the final parameter; Rows of
%   X correspond to observations, column to variables. Rows of Y and rows
%   of X is coherently related; our task is to estimated the relationship
%   between them.
%   
%   This arithmatic assumes the relationship between X and Y is linear and 
%   X isnot random, moreover, each observation is irrelevant and 
%   equally-weighted.
%   
%   [PARAMETER, VARIANCE] = LEASTSQR(X, Y) returns the variance of Y.
%   
%   [PARAMETER, VARIANCE, COV] = LEASTSQR(X, Y) returns the covariance
%   matrix of the returned PARAMETER.
%   
%   $Date: 2008/02/25 16:39:01 $

[n,p] = size(x);
[n2,p2] = size(y);
if n < (p-1)
    warning('The observation isnot big enough for sufficient estimation(n<p-1)');
else
    if n ~= n2
        warning('Row size of x and y should be equal');
    else
    
        if p2 >1 
            warning('There should be only one column in y');
        else 
    
            %   Center X by substracting off the column means
            x0 = x - repmat(mean(x,1),n,1);
            x0(:,1) = 1;
            s0 = x0'*x0;
            parameter = inv(s0)*x0'*y;
            rss = y'*y - parameter'*x0'*y;
            variance = rss/(n-p-1);
            cov = variance*inv(s0);
        end
    end
end