WIP: add bisection method

.gitignore

@@ -4,3 +4,6 @@
 *.log
 *.synctex.gz
 
+# Matlab related
+*.m~
+

Work 1/report/report.tex

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+%
+% Optimization Techniques Assignment 1 report
+%
+% authors:
+%   Χρήστος Χουτουρίδης ΑΕΜ 8997
+%   cchoutou@ece.auth.gr
+
+
+\documentclass[a4paper, 11pt]{AUTHReport}
+
+% Document configuration
+\AuthorName{Χρήστος Χουτουρίδης}
+\AuthorMail{cchoutou@ece.auth.gr}
+\AuthorAEM{8997}
+
+% \CoAuthorName{CoAuthor Name}
+% \CoAuthorMail{CoAuthor Mail}
+% \CoAuthorAEM{AEM}
+
+% \WorkGroup{Ομάδα Χ}
+
+\DocTitle{1η Εργαστηριακή Άσκηση}
+\DocSubTitle{Ελαχιστοποίηση κυρτής συνάρτησης μιας μεταβλητής σε δοσμένο διάστημα}
+
+\Department{Τμήμα ΗΜΜΥ. Τομέας Ηλεκτρονικής}
+\ClassName{Τεχνικές Βελτιστοποίησης}
+
+\InstructorName{Γ. Ροβιθάκης}
+\InstructorMail{rovithak@auth.gr}
+\CurrentDate{\today}
+
+
+\begin{document}
+
+\InsertTitle
+
+\section{Εισαγωγή}
+
+
+
+\end{document}

Work 1/scripts/bisection.m

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+function [a, b, k] = bisection(fun, alpha, beta, epsilon, lambda)
+%
+% Detailed explanation goes here
+%
+%
+
+% Error checking
+if 2*epsilon >= lambda
+    error ('Convergence criteria not met')
+end
+
+% Init output vectors
+a = alpha;
+b = beta;
+
+k=1;
+
+while b(k) - a(k) > lambda
+    % bisect [a,b]
+    mid = (a(k) + b(k)) / 2;
+    x_1 = mid - epsilon;
+    x_2 = mid + epsilon;
+    
+    % set new search reange
+    k = k + 1;
+    if subs(fun, x_1) < subs(fun, x_2)
+        a(k) = a(k-1);
+        b(k) = x_2;
+    else
+        a(k) = x_1;
+        b(k) = b(k-1);
+    end
+end
+

Work 1/scripts/bisectionA_lamdaFixed.m

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+%
+% Keeping l (accuracy) fix, test the iteration needed for different e
+% values.
+%
+
+
+% Clear workspace and load the functions and region
+clear
+
+funGivenEnv;
+
+% * lambda = 0.01
+% * epsilon: e < lambda/2 = 0.005
+% * de: A small step away from zero and lambda/2
+%       de = 0.0001
+% * size: 25 points
+
+size = 25;
+lambda = 0.01;
+de = 0.0001;
+epsilon = linspace(de, (lambda/2)-de, size);
+k = zeros(1,size);
+
+
+%
+% * Call the bisection method for each epsilon value for each function and
+%   keep the number of iterations needed.
+% * Plot the (epsilon, iterations) for each function
+%
+i = 0;
+for f = funs
+    i = i + 1;
+    j = 0;
+    for e = epsilon
+        j = j + 1;
+        [a, b, k(j)] = bisection(f, a_0, b_0, e, lambda);
+    end
+    subplot(1, 3, i)
+    plot(epsilon, k, '-b', 'LineWidth', 1.0)
+    title(titles(i), 'Interpreter', 'latex')
+    xlabel('epsilon')
+    ylabel('Iterations')
+end
+
+    

Work 1/scripts/funGivenEnv.m

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+%
+% Select the given region: [-1,3]
+a_0 = -1;
+b_0 = 3;
+
+% Setup the functions under test
+syms x;
+
+f_1 = (x-2)^2 + x*log(x+3);
+f_2 = exp(-2*x) + (x-2)^2;
+f_3 = exp(x)*(x^3 - 1) + (x-1)*sin(x);
+funs = [f_1, f_2, f_3];
+
+% Setup the function titles
+title_f1 = "$f_1(x) = (x - 2)^2 + x \cdot \ln(x + 3)$";
+title_f2 = "$f_2(x) = e^{-2x} + (x - 2)^2$";
+title_f3 = "$f_3(x) = e^x \cdot (x^3 - 1) + (x - 1) \cdot \sin(x)$";
+titles = [title_f1; title_f2; title_f3];