Small changes

Work 1/scripts/bisection/bisection.m

@@ -0,0 +1,33 @@
+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 fun(x_1) < 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/bisection/bisection_epsilonFixed.m

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+%
+% Keeping epsilon fixed, test the iteration needed for different lambda
+% values.
+%
+
+
+% Clear workspace and load the functions and region
+clear
+addpath('..');
+GivenEnv;
+
+% * epsilon: e = 0.001
+% * lambda:  l > 2e = 0.001
+% * dl: A small step away from 2e
+%       dl = 0.0001
+% * lambda_max: 0.1
+% * N: 50 points
+
+N = 50;
+epsilon = 0.001;
+dl = 0.0001;
+lambda_max= 0.1;
+lambda = linspace(2*epsilon + dl, lambda_max, N);
+k = zeros(1, N); % preallocate k
+
+
+%
+% * Call the bisection method for each lambda value for each function and
+%   keep the number of iterations needed.
+% * Plot the iterations k(lambda) for each function
+%
+
+for i = 1:length(funs)
+    for j = 1:N
+        [a, b, k(j)] = bisection(funs{i}, a_0, b_0, epsilon, lambda(j));
+    end
+    subplot(1, length(funs), i)
+    plot(lambda, k, '-b', 'LineWidth', 1.0)
+    title(titles(i), 'Interpreter', 'latex')
+    xlabel('lambda')
+    ylabel('Iterations')
+end
+
+  

Work 1/scripts/bisection/bisection_lambdaFixed.m

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+%
+% Keeping l (accuracy) fixed, test the iteration needed for different
+% epsilon values.
+%
+
+
+% Clear workspace and load the functions and region
+clear
+addpath('..');
+GivenEnv;
+
+% * lambda = 0.01
+% * epsilon: e < lambda/2 = 0.005
+% * de: A small step away from zero and lambda/2
+%       de = 0.0001
+% * N: 50 points
+
+N = 50;
+lambda = 0.01;
+de = 0.0001;
+epsilon = linspace(de, (lambda/2)-de, N);
+k = zeros(1,N); % preallocate k
+
+
+%
+% * Call the bisection method for each epsilon value for each function and
+%   keep the number of iterations needed.
+% * Plot the iterations k(epsilon) for each function
+%
+for i = 1:size(funs,2)
+    for j = 1:N
+        [a, b, k(j)] = bisection(funs{i}, a_0, b_0, epsilon(j), lambda);
+    end
+    subplot(1, length(funs), i)
+    plot(epsilon, k, '-b', 'LineWidth', 1.0)
+    title(titles(i), 'Interpreter', 'latex')
+    xlabel('epsilon')
+    ylabel('Iterations')
+end
+
+