線形探索アルゴリズムの代表ロジックである黄金分割法のMATLABサンプル

GoldenSectionSample.m

% ------------------------------------------------------------------------
%  Sample file of Golden section method for linear search
%
% file         :       GoldenSectionSample.m
%
% Latest Update:       2013/03/20
%
% Author       :       A.Sakai
%
% ----------------------------------------------------------------------------------

function [] = GoldenSectionSample()
close all;
clear all;

disp('Linear search with golden Section');

%探索範囲 a:最小値　b:最大値
a=-50;
b=100;
[minX minY]=GoldenSection(a,b);

x=[a:0.1:b];
y=[];
for i=1:length(x)
    y=[y f(x(i))];
end
plot(x,y,'-r', 'markersize', 15);hold on;
plot(minX,minY,'.b', 'markersize', 15);hold on;
grid on;


function [minX minY]=GoldenSection(a,b)
%黄金率
GOLDEN_RATIO = 1.6180339887498948482045868343656;

%内分点の計算
x1 = (a-b)/(GOLDEN_RATIO + 1.0) + b;
x2 = (a-b)/GOLDEN_RATIO + b;
%評価関数を両方計算するのは最初だけ
f1 = f(x1);
f2 = f(x2);

while 1
    %ループを回して両点を更新
    if f1 < f2
        a = x2;
        x2 = x1;
        f2 = f1;
        x1 = (a - b)/(GOLDEN_RATIO + 1.0) + b;
        f1 = f(x1);
    else
        b = x1;
        x1 = x2;
        f1 = f2;
        x2 = (a - b)/GOLDEN_RATIO + b;
        f2 = f(x2);
    end
    %収束判定
    if abs(a-b)<=10^-3
        minX=(a+b)/2;
        minY=f((a+b)/2);
        break
    end
end


function y = f(x)
y=(x-2)^2+5;