From 634f90b25b251282d008d95e341b9c8c349d9da2 Mon Sep 17 00:00:00 2001 From: Christos Choutouridis Date: Wed, 6 Nov 2024 00:43:45 +0200 Subject: [PATCH] Switch to a polymorphic method invokation --- Work 1/scripts/GivenEnv.m | 33 +++---- Work 1/scripts/Work1.m | 37 ++++++++ Work 1/scripts/bisection/bisection_interval.m | 48 ---------- .../bisection/bisection_over_epsilon.m | 41 --------- .../scripts/bisection/bisection_over_lambda.m | 44 ---------- Work 1/scripts/bisection_over_epsilon.m | 62 +++++++++++++ ...over_iterations_min_bisection_der_fun1.png | Bin 0 -> 113792 bytes ...over_iterations_min_bisection_der_fun2.png | Bin 0 -> 113565 bytes ...over_iterations_min_bisection_der_fun3.png | Bin 0 -> 115081 bytes ...val_over_iterations_min_bisection_fun1.png | Bin 0 -> 114537 bytes ...val_over_iterations_min_bisection_fun2.png | Bin 0 -> 114052 bytes ...val_over_iterations_min_bisection_fun3.png | Bin 0 -> 115632 bytes ...val_over_iterations_min_fibonacci_fun1.png | Bin 0 -> 121827 bytes ...val_over_iterations_min_fibonacci_fun2.png | Bin 0 -> 120963 bytes ...val_over_iterations_min_fibonacci_fun3.png | Bin 0 -> 122946 bytes ...ver_iterations_min_golden_section_fun1.png | Bin 0 -> 120357 bytes ...ver_iterations_min_golden_section_fun2.png | Bin 0 -> 120031 bytes ...ver_iterations_min_golden_section_fun3.png | Bin 0 -> 121602 bytes .../iter_over_epsilon_min_bisection.png | Bin 0 -> 69323 bytes .../iter_over_lambda_min_bisection.png | Bin 0 -> 73489 bytes .../iter_over_lambda_min_bisection_der.png | Bin 0 -> 76630 bytes .../iter_over_lambda_min_fibonacci.png | Bin 0 -> 71754 bytes .../iter_over_lambda_min_golden_section.png | Bin 0 -> 71883 bytes .../golden_section/golden_section_interval.m | 45 ---------- .../golden_section_over_lambda.m | 39 -------- Work 1/scripts/interval_over_iterations.m | 82 +++++++++++++++++ Work 1/scripts/iterations_over_lambda.m | 83 ++++++++++++++++++ .../bisection.m => min_bisection.m} | 67 +++++++------- Work 1/scripts/min_bisection_der.m | 36 ++++++++ Work 1/scripts/min_fibonacci.m | 54 ++++++++++++ .../golden_section.m => min_golden_section.m} | 73 ++++++++------- 31 files changed, 441 insertions(+), 303 deletions(-) create mode 100644 Work 1/scripts/Work1.m delete mode 100644 Work 1/scripts/bisection/bisection_interval.m delete mode 100644 Work 1/scripts/bisection/bisection_over_epsilon.m delete mode 100644 Work 1/scripts/bisection/bisection_over_lambda.m create mode 100644 Work 1/scripts/bisection_over_epsilon.m create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_bisection_der_fun1.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_bisection_der_fun2.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_bisection_der_fun3.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_bisection_fun1.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_bisection_fun2.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_bisection_fun3.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_fibonacci_fun1.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_fibonacci_fun2.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_fibonacci_fun3.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_golden_section_fun1.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_golden_section_fun2.png create mode 100644 Work 1/scripts/figures/interval_over_iterations_min_golden_section_fun3.png create mode 100644 Work 1/scripts/figures/iter_over_epsilon_min_bisection.png create mode 100644 Work 1/scripts/figures/iter_over_lambda_min_bisection.png create mode 100644 Work 1/scripts/figures/iter_over_lambda_min_bisection_der.png create mode 100644 Work 1/scripts/figures/iter_over_lambda_min_fibonacci.png create mode 100644 Work 1/scripts/figures/iter_over_lambda_min_golden_section.png delete mode 100644 Work 1/scripts/golden_section/golden_section_interval.m delete mode 100644 Work 1/scripts/golden_section/golden_section_over_lambda.m create mode 100644 Work 1/scripts/interval_over_iterations.m create mode 100644 Work 1/scripts/iterations_over_lambda.m rename Work 1/scripts/{bisection/bisection.m => min_bisection.m} (74%) create mode 100644 Work 1/scripts/min_bisection_der.m create mode 100644 Work 1/scripts/min_fibonacci.m rename Work 1/scripts/{golden_section/golden_section.m => min_golden_section.m} (80%) diff --git a/Work 1/scripts/GivenEnv.m b/Work 1/scripts/GivenEnv.m index 9fb08f3..ac934ef 100644 --- a/Work 1/scripts/GivenEnv.m +++ b/Work 1/scripts/GivenEnv.m @@ -1,16 +1,17 @@ -% -% Select the given interval: [-1,3] -a_0 = -1; -b_0 = 3; - -% Setup the functions under test -f_1 = @(x) (x-2)^2 + x*log(x+3); -f_2 = @(x) exp(-2*x) + (x-2)^2; -f_3 = @(x) 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]; +% +% Select the given interval: [-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]; \ No newline at end of file diff --git a/Work 1/scripts/Work1.m b/Work 1/scripts/Work1.m new file mode 100644 index 0000000..323d4c5 --- /dev/null +++ b/Work 1/scripts/Work1.m @@ -0,0 +1,37 @@ +% +% +% +% +% +% + + +disp (" "); +disp (" "); +disp ('1. Number of iterations for different epsilon values for min_bisection'); +disp ('----'); +bisection_over_epsilon; + +methods = { + @min_bisection; + @min_golden_section; + @min_fibonacci; + @min_bisection_der +}; + +disp (" "); +disp (" "); +disp ('2. Number of iterations for different lambda values'); +disp ('----'); +for i = 1:length(methods) + iterations_over_lambda(methods{i}); +end + + +disp (" "); +disp (" "); +disp ('3. [a, b] interval convergence'); +disp ('----'); +for i = 1:length(methods) + interval_over_iterations(methods{i}); +end \ No newline at end of file diff --git a/Work 1/scripts/bisection/bisection_interval.m b/Work 1/scripts/bisection/bisection_interval.m deleted file mode 100644 index b52e7ee..0000000 --- a/Work 1/scripts/bisection/bisection_interval.m +++ /dev/null @@ -1,48 +0,0 @@ -% -% Keeping epsilon fixed, plot the [a,b] interval over the iterations for -% different lambda values (min, mid, max)) -% - - -% Clear workspace and load the functions and interval -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: 3 lambda values - -N = 3; -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 -% * Plot the [a,b] interval over iterations for each lambda for each function -% - -for i = 1:length(funs) - figure; - for j = 1:N - [a, b, k(j)] = bisection(funs{i}, a_0, b_0, epsilon, lambda(j)); - subplot(length(funs), 1, j) - plot(1:length(a), a, 'ob') - hold on - plot(1:length(b), b, '*r') - if j == 1 - title(titles(i), 'Interpreter', 'latex') - end - xlabel("Iterations @lambda=" + lambda(j)) - ylabel('[a_k, b_k]') - end -end - - \ No newline at end of file diff --git a/Work 1/scripts/bisection/bisection_over_epsilon.m b/Work 1/scripts/bisection/bisection_over_epsilon.m deleted file mode 100644 index ee20c99..0000000 --- a/Work 1/scripts/bisection/bisection_over_epsilon.m +++ /dev/null @@ -1,41 +0,0 @@ -% -% Keeping lambda (accuracy) fixed, test the iteration needed for different -% epsilon values. -% - - -% Clear workspace and load the functions and interval -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:length(funs) - 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 - - \ No newline at end of file diff --git a/Work 1/scripts/bisection/bisection_over_lambda.m b/Work 1/scripts/bisection/bisection_over_lambda.m deleted file mode 100644 index a415636..0000000 --- a/Work 1/scripts/bisection/bisection_over_lambda.m +++ /dev/null @@ -1,44 +0,0 @@ -% -% Keeping epsilon fixed, test the iteration needed for different lambda -% values. -% - - -% Clear workspace and load the functions and interval -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 - - \ No newline at end of file diff --git a/Work 1/scripts/bisection_over_epsilon.m b/Work 1/scripts/bisection_over_epsilon.m new file mode 100644 index 0000000..1934322 --- /dev/null +++ b/Work 1/scripts/bisection_over_epsilon.m @@ -0,0 +1,62 @@ +% +% Keeping lambda (accuracy) fixed, test the iteration needed for different +% epsilon values. +% + + +% Load the functions and interval +GivenEnv; + +fig_dir = 'figures'; +if ~exist(fig_dir, 'dir') + mkdir(fig_dir); +end + +% Setup +% ======================== + +% 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 (50 epsilon values) + +N = 50; +lambda = 0.01; +de = 0.0001; +epsilon = linspace(de, (lambda/2)-de, N); +k = zeros(1,N); % preallocate k + + +% +% Call the min_bisection method for each epsilon value for each +% function and keep the number of iterations needed. +% Then plot and save the # of iterations k(epsilon) for each function. +% + +figure('Name', 'iterations_over_epsilon_min_bisection', 'NumberTitle', 'off'); +set(gcf, 'Position', [100, 100, 1280, 600]); % Set the figure size to HD + +for i = 1:length(funs) + for j = 1:N + [a, b, k(j)] = min_bisection(funs(i), a_0, b_0, epsilon(j), lambda); + end + fprintf('%20s(%34s ): [a, b]= [%f, %f], iterations(min, max)= (%d, %d)\n', ... + "min_bisection", char(funs(i)), a(end), b(end), k(1), k(N) ); + subplot(1, length(funs), i) + plot(epsilon, k, '-b', 'LineWidth', 1.0) + title(titles(i), 'Interpreter', 'latex') + xlabel('epsilon') + ylabel('Iterations') +end + +% +% Print and save the figures +% +%fig_epsc = fullfile(fig_dir, "iter_over_epsilon_min_bisection" + ".epsc"); +fig_png = fullfile(fig_dir, "iter_over_epsilon_min_bisection" + ".png"); + +%print(gcf, fig_epsc, '-depsc', '-r300'); +print(gcf, fig_png, '-dpng', '-r300'); + + \ No newline at end of file diff --git a/Work 1/scripts/figures/interval_over_iterations_min_bisection_der_fun1.png b/Work 1/scripts/figures/interval_over_iterations_min_bisection_der_fun1.png new file mode 100644 index 0000000000000000000000000000000000000000..a8c6ab09698d63fe8981a4095ab53cf7fb2cb226 GIT binary patch literal 113792 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points (50 lambda values) + +N = 50; +epsilon = 0.001; +lambda_min = 0.0021; +lambda_max = 0.1; +lambda = linspace(lambda_min, lambda_max, N); +k = zeros(1, N); % preallocate k + + +% +% Call the minimum calculation method for each lambda value for each +% function and keep the number of iterations needed. +% Then plot and save the # of iterations k(lambda) for each function. +% +% note: In order to use the same method call for all methods, we force a +% common interface for minimum method functions. Thus some arguments +% will not be needed for some methods (epsilon is not needed for +% bisection _der for example). +% + +figure('Name', "iterations_over_lambda_" + char(method), 'NumberTitle', 'off'); +set(gcf, 'Position', [100, 100, 1280, 600]); % Set the figure size to HD + +disp(" "); +for i = 1:length(funs) + for j = N:-1:1 + [a, b, k(j)] = method(funs(i), a_0, b_0, epsilon, lambda(j)); + end + + fprintf('%20s(%34s ): [a, b]= [%f, %f], iterations(min, max)= (%d, %d)\n', ... + char(method), char(funs(i)), a(end), b(end), k(N), k(1) ); + subplot(1, length(funs), i) + plot(lambda, k, '-b', 'LineWidth', 1.0) + title(titles(i), 'Interpreter', 'latex') + xlabel('lambda') + ylabel('Iterations') +end + + +% +% Print and save the figures +% +%fig_epsc = fullfile(fig_dir, "iter_over_lambda_" + char(method) + ".epsc"); +fig_png = fullfile(fig_dir, "iter_over_lambda_" + char(method) + ".png"); + +%print(gcf, fig_epsc, '-depsc', '-r300'); +print(gcf, fig_png, '-dpng', '-r300'); + + + + \ No newline at end of file diff --git a/Work 1/scripts/bisection/bisection.m b/Work 1/scripts/min_bisection.m similarity index 74% rename from Work 1/scripts/bisection/bisection.m rename to Work 1/scripts/min_bisection.m index 6644f14..f97e667 100644 --- a/Work 1/scripts/bisection/bisection.m +++ b/Work 1/scripts/min_bisection.m @@ -1,33 +1,34 @@ -function [a, b, k] = bisection(fun, alpha, beta, epsilon, lambda) -% -% Detailed explanation goes here -% -% - -% Error checking -if 2*epsilon >= lambda || lambda <= 0 - 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 interval - 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 +function [a, b, k] = min_bisection(fun_expression, alpha, beta, epsilon, lambda) +% +% Detailed explanation goes here +% +% + +% Error checking +if 2*epsilon >= lambda || lambda <= 0 + error ('Convergence criteria not met') +end + +% Init +a = alpha; +b = beta; +fun = matlabFunction(fun_expression); + +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 interval + 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 \ No newline at end of file diff --git a/Work 1/scripts/min_bisection_der.m b/Work 1/scripts/min_bisection_der.m new file mode 100644 index 0000000..aec0366 --- /dev/null +++ b/Work 1/scripts/min_bisection_der.m @@ -0,0 +1,36 @@ +function [a, b, k] = min_bisection_der(fun_expression, alpha, beta, epsilon, lambda) +% +% Detailed explanation goes here +% +% + +% Error checking +if lambda <= 0 + error ('Convergence criteria not met') +end + +% Init output vectors +a = alpha; +b = beta; +dfun = matlabFunction(diff(fun_expression)); + +k=1; +while b(k) - a(k) > lambda + % bisect [a,b] + x_mid = (a(k) + b(k)) / 2; + + % set new search interval + k = k + 1; + df = dfun(x_mid); + if df < 0 + a(k) = x_mid; + b(k) = b(k-1); + elseif df > 0 + a(k) = a(k-1); + b(k) = x_mid; + else % df == 0 + a(k) = x_mid; + b(k) = x_mid; + break; + end +end \ No newline at end of file diff --git a/Work 1/scripts/min_fibonacci.m b/Work 1/scripts/min_fibonacci.m new file mode 100644 index 0000000..0265cdb --- /dev/null +++ b/Work 1/scripts/min_fibonacci.m @@ -0,0 +1,54 @@ +function [a, b, N] = min_fibonacci(fun_expression, alpha, beta, epsilon, lambda) +% + +% Use Binet's formula instead of matlab's recursive fibonacci +% implementation +fib = @(n) ( ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5)) ); + +% Error checking +if lambda <= 0 || epsilon <= 0 + error ('Convergence criteria not met') +end + +% Init variables +a = alpha; +b = beta; +fun = matlabFunction(fun_expression); + +% calculate number of iterations +N=0; +while fibonacci(N) < (b(1) - a(1)) / lambda + N = N + 1; +end + + +% calculate x1, x2 of the first iteration, since the following iteration +% will not require to calculate both +x_1 = a(1) + (fib(N-2) / fib(N)) * (b(1) - a(1)); +x_2 = a(1) + (fib(N-1) / fib(N)) * (b(1) - a(1)); + +% All but the last calculation +for k = 1:N-2 + % set new search interval + if fun(x_1) < fun(x_2) + a(k+1) = a(k); + b(k+1) = x_2; + x_2 = x_1; + x_1 = a(k+1) + (fib(N-k-2) / fib(N-k)) * (b(k+1) - a(k+1)); + else + a(k+1) = x_1; + b(k+1) = b(k); + x_1 = x_2; + x_2 = a(k+1) + (fib(N-k-1) / fib(N-k)) * (b(k+1) - a(k+1)); + end +end + +% Last calculation +x_2 = x_1 + epsilon; +if fun(x_1) < fun(x_2) + a(N) = a(N-1); + b(N) = x_1; +else + a(N) = x_1; + b(N) = b(N-1); +end diff --git a/Work 1/scripts/golden_section/golden_section.m b/Work 1/scripts/min_golden_section.m similarity index 80% rename from Work 1/scripts/golden_section/golden_section.m rename to Work 1/scripts/min_golden_section.m index 681089c..6272df9 100644 --- a/Work 1/scripts/golden_section/golden_section.m +++ b/Work 1/scripts/min_golden_section.m @@ -1,37 +1,36 @@ -function [a, b, k] = golden_section(fun, alpha, beta, lambda) -% - - -% Error checking -if lambda <= 0 - error ('Convergence criteria not met') -end - -% Init variables -gamma = 0.618; -a = alpha; -b = beta; - - -% calculate x1, x2 of the first iteration, since the following iteration -% will not require to calculate both -k=1; -x_1 = a(k) + (1 - gamma)*(b(k) - a(k)); -x_2 = a(k) + gamma*(b(k) - a(k)); - -while b(k) - a(k) > lambda - % set new search interval - k = k + 1; - if fun(x_1) < fun(x_2) - a(k) = a(k-1); - b(k) = x_2; - x_2 = x_1; - x_1 = a(k) + (1 - gamma)*(b(k) - a(k)); - else - a(k) = x_1; - b(k) = b(k-1); - x_1 = x_2; - x_2 = a(k) + gamma*(b(k) - a(k)); - end -end - +function [a, b, k] = min_golden_section(fun_expression, alpha, beta, epsilon, lambda) +% + + +% Error checking +if lambda <= 0 + error ('Convergence criteria not met') +end + +% Init variables +gamma = 0.618; +a = alpha; +b = beta; +fun = matlabFunction(fun_expression); + +% calculate x1, x2 of the first iteration, since the following iteration +% will not require to calculate both +k=1; +x_1 = a(k) + (1 - gamma)*(b(k) - a(k)); +x_2 = a(k) + gamma*(b(k) - a(k)); + +while b(k) - a(k) > lambda + % set new search interval + k = k + 1; + if fun(x_1) < fun(x_2) + a(k) = a(k-1); + b(k) = x_2; + x_2 = x_1; + x_1 = a(k) + (1 - gamma)*(b(k) - a(k)); + else + a(k) = x_1; + b(k) = b(k-1); + x_1 = x_2; + x_2 = a(k) + gamma*(b(k) - a(k)); + end +end

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