牛顿法线性规划octave实现

#newton_regression.m## Copyright (C) 2013 xiuleili## ## 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 Octave; see the file COPYING.  If not, see## <http://www.gnu.org/licenses/>.## -*- texinfo -*-## @deftypefn {Function File} {} [ theta ] = newton_regression ( x, y)## Return the parameter of linear founction where y = theta[2:n+1]*x + theta(1).##where n is the row of matrix x.## It use newton gradient algorithm obviously.## For example:#### @example## @group## x=[1 4;2 5;5 1; 4 2] y = [ 19 26 19 20]## newton_regression(x, y)##   @result{} [0.0060406   2.9990063   3.9990063]## @end group## @end example## @seealso{stichastic_gradient}## @end deftypefn## Author: xiuleili <xiuleili@XIULEILI>## Created: 2013-05-03function [ theta ] = newton_regression (x,y)[n,m]=size(x);[my,ny]=size(y);if(ny ~= n | my!= 1)error("Error: x should be a matrix with(n,m) and y must be (1,n), where n is the count of training samples.");end;X = [ones(n,1) x]';theta = rand(1, m+1);learning_rate = 0.1;errors = 1;threshold=0.000001;times = 0;% thetaj = thetaj + sum[(y-h(x))*xj]/sum[xj^2]while errors > threshold%sum((y-h(x))*xj)sum_of_error = (y-theta*X)*X';%sum(xj^2)sum_of_xj2 = (diag(X*X'))';theta += learning_rate * sum_of_error./sum_of_xj2;errors = sum((y-theta*X).^2)/2;times ++;printf("[%d] errors = %f", times, errors);disp(theta);if(times > 100000)break;endendendfunction