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ThrottleThrottle
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Labs 1-4 source codes were added
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‎.gitignore

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*.pyc
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*.swp
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*.asv
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*~
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*.db
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.idea/
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*.aux
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*.toc
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*.out
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*.log
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*.gz
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*.blg
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*.bbl
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rpz/.deps/
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rpz/tex/rpz.pdf
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rpz/tex/inc/
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‎lab01_04/Lab1_4 (1).pdf

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‎lab01_04/source/launcher.m

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clear;
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clc;
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optimizer = optimizer();
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a = 0.0;
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b = 1.0;
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eps1 = 0.01;
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eps2 = 0.0001;
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eps3 = 0.000001;
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optimizer.draw(a, b, 1000);
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%[result, value] = optimizer.RadixSearch(a, b, eps3, 4);
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%[result, value, res_a, res_b] = optimizer.GoldenSectionSearch(a, b, eps3, 0);
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%[result, value] = optimizer.Newton(a, b, eps3, 1e-5);
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[result, value] = optimizer.Parabola(a, b, eps3, 5);

‎lab01_04/source/optimizer.m

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classdef optimizer < handle
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properties
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count
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end
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methods
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%% âû÷èñëÿåìàÿ ôóíêöèÿ
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function y = f(this,x)
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this.count = this.count + 1;
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%y = exp((x^4 + 2*x^3 - 5*x + 6) / 5) + cosh(1 / (-15*x^3 + 10*x + 5 * sqrt(10))) - 3.0;
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y = sinh((3*x^4 - x + sqrt(17) - 3) / 2) + sin((5^(1/3) * x^3 - 5^(1/3) * x + 1 - 2 * 5^(1/3))/(-x^3 + x + 2));
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end
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%% ñáðîñ ñ÷åñò÷èêà âûçîâà ôóíêöèè
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function reset(this)
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this.count = 0;
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end
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%% ïîñòðîåíèå ãðàôèêà ôóíêöèè
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function draw(this, a, b, n)
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step = (b - a) / n;
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x = a : step : b;
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y = zeros(n + 1, 1);
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for i = 1 : n + 1
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y(i,1) = this.f(x(i));
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end
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plot(x, y(:,1));
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end
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%% ìåòîä ïîðàçðÿäíîãî ïîèñêà
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function [x, y] = RadixSearch(this, a, b, eps, k)
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fprintf('==== Ìåòîä ïîðàçðÿäíîãî ïîèñêà ====\nÎòðåçîê: a=%f, b=%f\nÒî÷íîñòü: eps=%f;\nk=%d\n', [a,b,eps,k]);
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this.reset();
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delta = (b-a) / k;
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x = a;
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f0 = this.f(x);
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fprintf('Íà÷àëî ïîèñêà: delta=%.7f; x=%.7f; f(x)=%.7f\n', [delta,x,f0]);
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while abs(delta) > eps
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while (x >= a) && (x <= b)
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x = x + delta;
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f1 = this.f(x);
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fprintf('f(%.7f)=%.7f\n', [x, f1]);
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if f1 > f0
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break;
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end
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f0 = f1;
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end
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f0 = f1;
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delta = - delta / k;
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fprintf('Ìåíÿåì íàïðàâëåíèå ïîèñêà: delta=%.7f\n', delta);
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end
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disp('Ïîèñê çàêîí÷åí: äîñòèãíóòà òðåáóåìàÿ òî÷íîñòü');
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y = f1;
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fprintf('xmin=%.7f\nf(xmin)=%.7f\n', [x,y])
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fprintf('Êîë-âî âûçîâîâ: %d\n', [this.count])
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end
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%% ìåòîä çîëîòîãî ñå÷åíèÿ
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function [x, y, res_a, res_b] = GoldenSectionSearch(this, a, b, eps, stop)
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if nargin < 5
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stop = -1;
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end
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fprintf('==== Ìåòîä çîëîòîãî ñå÷åíèÿ ====\nÎòðåçîê: a=%f, b=%f\nÒî÷íîñòü: eps=%f;\n\tÊîë-âî èòåðàöèé: stop=%d.\n\n', [a,b,eps,stop]);
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this.reset();
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tau = (sqrt(5) - 1) / 2;
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interval = b - a;
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x1 = a + (1 - tau) * interval;
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x2 = a + tau * interval;
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f1 = this.f(x1);
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f2 = this.f(x2);
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exec_count = 0;
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%fprintf('Íà÷àëî ïîèñêà:\n\tîòðåçîê: a=%.7f; b=%.7f;\n\tòî÷êè ðàçáèåíèÿ: f(%.7f)=%.7f; f(%.7f)=%.7f\n', [a, b, x1, f1, x2, f2]);
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while (abs(interval) > eps) && (exec_count - stop ~= 0)
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fprintf('-> Èòåðàöèÿ %d\nÈñõîäíûé îòðåçîê:\n\ta=%.7f; b=%.7f;\n\tòî÷êè ðàçáèåíèÿ: f(%.7f)=%.7f; f(%.7f)=%.7f\n\n', [exec_count+1, a, b, x1, f1, x2, f2]);
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if f1 < f2
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b = x2;
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interval = b-a;
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x2 = x1;
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x1 = a + (1 - tau) * interval;
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f2 = f1;
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f1 = this.f(x1);
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else
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a = x1;
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interval = b - a;
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x1 = x2;
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x2 = a + tau * interval;
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f1 = f2;
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f2 = this.f(x2);
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end
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fprintf('Íîâûé îòðåçîê:\n\ta=%.7f; b=%.7f;\n\tçíà÷åíèÿ ôóíêöèè: f(a)=%.7f; f(b)=%.7f\n\n', [a, b, f1, f2]);
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exec_count = exec_count + 1;
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end
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disp('Ïîèñê çàêîí÷åí: äîñòèãíóòà òðåáóåìàÿ òî÷íîñòü');
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if f1 < f2
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x = x1;
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y = f1;
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else
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x = x2;
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y = f2;
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end
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fprintf('xmin=%.7f\nf(xmin)=%.7f\n', [x,y])
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fprintf('Êîë-âî âûçîâîâ: %d\n', [this.count])
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res_a = a;
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res_b = b;
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fprintf('=============\n\n')
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end
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%% Ìîäèôèöèðîâàííûé ìåòîä Íüþòîíà
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function [x, y] = Newton(this, a, b, eps, h)
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fprintf('==== Ìîäèôèöèðîâàííûé ìåòîä Íüþòîíà ====\nÎòðåçîê: a=%f, b=%f\nÒî÷íîñòü: eps=%f;\n', [a, b, eps]);
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this.reset();
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x = a;
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while 1
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f1 = this.f(x - h);
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f2 = this.f(x + h);
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f = this.f(x);
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x_prev = x;
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p = h * (f2 - f1) / (2 * (f2 - 2*f + f1));
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% ìîäèôèöèðîâàííûé ìåòîä Íüþòîíà
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alpha = 1;
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x_new = x - alpha * p;
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while (x_new < a) || (x_new > b)
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alpha = alpha / 2;
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x_new = x - alpha * p;
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end
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x = x_new;
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if abs(x - x_prev) <= eps
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break
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end
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end
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y = f;
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fprintf('xmin=%.7f\nf(xmin)=%.7f\n', [x,y])
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fprintf('Êîë-âî âûçîâîâ: %d\n', [this.count])
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fprintf('==== êîíåö ====\n')
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end
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%%
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function result = r(this,x1,x2)
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result = x1^2 - x2^2;
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end
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%%
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function result = s(this,x1,x2)
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result = x1 - x2;
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end
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%% Ìåòîä ïàðàáîë
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function [x, y] = Parabola(this, a, b, eps, golden_stop)
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if nargin < 5
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% îòêëþ÷àåì âûïîëíåíèå ìåòîäà çîëîòîãî ñå÷åíèÿ
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golden_stop = 0;
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end
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fprintf('==== Ìåòîä ïàðàáîë ====\nÎòðåçîê: a=%f, b=%f\nÒî÷íîñòü: eps=%f;\n', [a, b, eps]);
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this.reset();
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[xmin, fmin, a, b] = this.GoldenSectionSearch(a, b, eps, golden_stop);
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x = [a, a+b/2, b];
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f = [this.f(x(1)), this.f(x(2)), this.f(x(3))];
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while abs(x(1) - x(3)) > eps
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x_dot = 0.5 * (...
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f(1) * this.r(x(2), x(3)) + ...
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f(2) * this.r(x(3), x(1)) + ...
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f(3) * this.r(x(1), x(2)) ...
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) / (...
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f(1) * this.s(x(2), x(3)) + ...
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f(2) * this.s(x(3), x(1)) + ...
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f(3) * this.s(x(1), x(2))...
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);
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f_dot = this.f(x_dot);
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if (x_dot >= x(2)) && (x_dot <= x(3))
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if f_dot <= f(2)
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x(1) = x(2); f(1) = this.f(x(1));
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x(2) = x_dot; f(2) = this.f(x(2));
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else
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x(3) = x_dot; f(3) = this.f(x(3));
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end
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elseif (x_dot >= x(1)) && (x_dot <= x(2))
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if f_dot <= f(2)
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x(3) = x(2); f(3) = this.f(x(3));
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x(2) = x_dot; f(2) = this.f(x(2));
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else
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x(1) = x_dot; f(1) = this.f(x(1));
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end
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else
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disp('Òî÷êà õ* íàéäåíà âíå îòðåçêà. Ïðèìåíÿåì ìåòîä çîëîòîãî ñå÷åíèÿ.')
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[xmin, fmin, a, b] = this.GoldenSectionSearch(x(1), x(2), eps, golden_stop);
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x = [a, a+b/2, b];
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f = [this.f(x(1)), this.f(x(2)), this.f(x(3))];
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end
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end
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y = f_dot;
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x = x_dot;
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fprintf('xmin=%.7f\nf(xmin)=%.7f\n', [x,y])
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fprintf('Êîë-âî âûçîâîâ: %d\n', [this.count])
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end
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end
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end

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