Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / optim-1.2.0 / LinearRegression.m

diff --git a/octave_packages/optim-1.2.0/LinearRegression.m b/octave_packages/optim-1.2.0/LinearRegression.m
new file mode 100644 (file)
index 0000000..8a435db
--- /dev/null
+++ b/octave_packages/optim-1.2.0/LinearRegression.m
@@ -0,0 +1,76 @@
+## 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 3 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/>.
+
+## 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
+
+function [p,y_var,r,p_var]=LinearRegression(F,y,weight)
+
+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
+