Mercurial > forge
view main/optim/inst/LinearRegression.m @ 7870:b11b5363d680 octave-forge
Get rid of some warnings with Octave-3.3.54+
author | i7tiol |
---|---|
date | Sun, 16 Jan 2011 17:42:02 +0000 |
parents | 2de537641f94 |
children | d30cfca46e8a |
line wrap: on
line source
function [p,y_var,r,p_var]=LinearRegression(F,y,weight) % general linear regression % % [p,y_var,r,p_var]=LinearRegression(F,y) % [p,y_var,r,p_var]=LinearRegression(F,y,weight) % % determine the parameters p_j (j=1,2,...,m) such that the function % f(x) = sum_(i=1,...,m) p_j*f_j(x) fits as good as possible to the % given values y_i = f(x_i) % % parameters % F n*m matrix with the values of the basis functions at the support points % in column j give the values of f_j at the points x_i (i=1,2,...,n) % y n column vector of given values % weight n column vector of given weights % % return values % p m vector with the estimated values of the parameters % y_var estimated variance of the error % r weighted norm of residual % p_var estimated variance of the parameters p_j ## Copyright (C) 2007 Andreas Stahel <Andreas.Stahel@bfh.ch> ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see <http://www.gnu.org/licenses/>. if (nargin < 2 || nargin >= 4) usage('wrong number of arguments in [p,y_var,r,p_var]=LinearRegression(F,y)'); end [rF, cF] = size(F); [ry, cy] =size(y); if (rF ~= ry || cy > 1) error ('LinearRegression: incorrect matrix dimensions'); end if (nargin==2) % set uniform weights if not provided weight=ones(size(y)); end %% Fw=diag(weight)*F; wF=F; for j=1:cF wF(:,j)=weight.*F(:,j); end [Q,R]=qr(wF,0); % estimate the values of the parameters p=R\(Q'*(weight.*y)); residual=F*p-y; % compute the residual vector r=norm(weight.*residual); % and its weighted norm % variance of the weighted y-errors y_var= sum((residual.^2).*(weight.^4))/(rF-cF); if nargout>3 % compute variance of parameters only if needed %% M=inv(R)*Q'*diag(weight); M=inv(R)*Q'; for j=1:cF M(j,:)=M(j,:).*(weight'); end M=M.*M; % square each entry in the matrix M p_var=M*(y_var./(weight.^4)); % variance of the parameters end