From d42725109acb298e8a2b7833921e423a46a04592 Mon Sep 17 00:00:00 2001 From: Christos Choutouridis Date: Fri, 8 Nov 2024 10:03:55 +0200 Subject: [PATCH] Report started - Add output parameter to methods for objective function calls - Adjust the code to reduce objective function calls to some methods --- Work 1/report/f.png | Bin 0 -> 79073 bytes Work 1/report/report.pdf | Bin 52473 -> 610299 bytes Work 1/report/report.tex | 165 +++++++++++++++++- Work 1/scripts/Work1.m | 11 +- Work 1/scripts/bisection_over_epsilon.m | 24 +-- ...over_iterations_min_bisection_der_fun1.png | Bin 113792 -> 117596 bytes ...over_iterations_min_bisection_der_fun2.png | Bin 113565 -> 117297 bytes ...over_iterations_min_bisection_der_fun3.png | Bin 115081 -> 119850 bytes ...val_over_iterations_min_bisection_fun1.png | Bin 114537 -> 118155 bytes ...val_over_iterations_min_bisection_fun2.png | Bin 114052 -> 117786 bytes ...val_over_iterations_min_bisection_fun3.png | Bin 115632 -> 120330 bytes ...val_over_iterations_min_fibonacci_fun1.png | Bin 121827 -> 125536 bytes ...val_over_iterations_min_fibonacci_fun2.png | Bin 120963 -> 124858 bytes ...val_over_iterations_min_fibonacci_fun3.png | Bin 122946 -> 127359 bytes ...ver_iterations_min_golden_section_fun1.png | Bin 120357 -> 124097 bytes ...ver_iterations_min_golden_section_fun2.png | Bin 120031 -> 123847 bytes ...ver_iterations_min_golden_section_fun3.png | Bin 121602 -> 126063 bytes .../iter_over_epsilon_min_bisection.png | Bin 69323 -> 82755 bytes .../iter_over_lambda_min_bisection.png | Bin 73489 -> 88129 bytes .../iter_over_lambda_min_bisection_der.png | Bin 76630 -> 84832 bytes .../iter_over_lambda_min_fibonacci.png | Bin 71754 -> 85901 bytes .../iter_over_lambda_min_golden_section.png | Bin 71883 -> 80450 bytes Work 1/scripts/interval_over_iterations.m | 28 +-- Work 1/scripts/iterations_over_lambda.m | 27 +-- Work 1/scripts/min_bisection.m | 28 ++- Work 1/scripts/min_bisection_der.m | 31 +++- Work 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met') +if alpha > beta || 2*epsilon >= lambda || lambda <= 0 + error ('Input criteria not met') end % Init a = alpha; b = beta; -fun = matlabFunction(fun_expression); +fun = matlabFunction(fun_expr); k=1; @@ -31,4 +44,7 @@ while b(k) - a(k) > lambda a(k) = x_1; b(k) = b(k-1); end -end \ No newline at end of file +end + +% Set objective function calls +n = 2*k; diff --git a/Work 1/scripts/min_bisection_der.m b/Work 1/scripts/min_bisection_der.m index aec0366..d830635 100644 --- a/Work 1/scripts/min_bisection_der.m +++ b/Work 1/scripts/min_bisection_der.m @@ -1,12 +1,29 @@ -function [a, b, k] = min_bisection_der(fun_expression, alpha, beta, epsilon, lambda) +function [a, b, k, n] = min_bisection_der(fun_expression, alpha, beta, epsilon, lambda) +% Bisection using derivatives method for finding the local minimum of a +% function. % -% Detailed explanation goes here +% fun_expr: (symbolic expression over x) The symbolic expression of the +% objective function +% alpha: (number) The starting point of the interval in which we seek +% for minimum +% beta: (number) The ending point of the interval in which we seek +% for minimum +% epsilon: (number) The epsilon value +% **note:** +% epsilon in not used in this method, but it is part of the +% method calling interface. +% lambda: (number) The lambda value (accuracy) % +% return: +% a: (vector) Starting points of the interval for each iteration +% b: (vector) Ending points of the interval for each iteration +% k: (number) The number of iterations +% n: (number) The calls of objective function fun_expr % % Error checking -if lambda <= 0 - error ('Convergence criteria not met') +if alpha > beta || lambda <= 0 + error ('Input criteria not met') end % Init output vectors @@ -33,4 +50,8 @@ while b(k) - a(k) > lambda b(k) = x_mid; break; end -end \ No newline at end of file +end + +% Update the objctive function calls. In this case the derivative of the +% function ;) +n = k; diff --git a/Work 1/scripts/min_fibonacci.m b/Work 1/scripts/min_fibonacci.m index 0ade515..37c9f01 100644 --- a/Work 1/scripts/min_fibonacci.m +++ b/Work 1/scripts/min_fibonacci.m @@ -1,22 +1,38 @@ -function [a, b, N] = min_fibonacci(fun_expression, alpha, beta, epsilon, lambda) +function [a, b, N, nn] = min_fibonacci(fun_expression, alpha, beta, epsilon, lambda) +% Fibonacci method for finding the local minimum of a function. % +% fun_expr: (symbolic expression over x) The symbolic expression of the +% objective function +% alpha: (number) The starting point of the interval in which we seek +% for minimum +% beta: (number) The ending point of the interval in which we seek +% for minimum +% epsilon: (number) The epsilon value (the interval of the last step) +% lambda: (number) The lambda value (accuracy) +% +% return: +% a: (vector) Starting points of the interval for each iteration +% b: (vector) Ending points of the interval for each iteration +% N: (number) The number of iterations needed. +% nn: (number) The calls of objective function fun_expr +% + +% Error checking +if alpha > beta || lambda <= 0 || epsilon <= 0 + error ('Input criteria not met') +end % Use Binet's formula instead of matlab's recursive fibonacci % implementation fibonacci = @(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; +N = 0; while fibonacci(N) < (b(1) - a(1)) / lambda N = N + 1; end @@ -52,3 +68,7 @@ else a(N) = x_1; b(N) = b(N-1); end + +% Set objective function calls +nn = 2*N -2; + diff --git a/Work 1/scripts/min_golden_section.m b/Work 1/scripts/min_golden_section.m index 6272df9..820d3f2 100644 --- a/Work 1/scripts/min_golden_section.m +++ b/Work 1/scripts/min_golden_section.m @@ -1,10 +1,28 @@ -function [a, b, k] = min_golden_section(fun_expression, alpha, beta, epsilon, lambda) +function [a, b, k, n] = min_golden_section(fun_expression, alpha, beta, epsilon, lambda) +% Golden section method for finding the local minimum of a function. +% +% fun_expr: (symbolic expression over x) The symbolic expression of the +% objective function +% alpha: (number) The starting point of the interval in which we seek +% for minimum +% beta: (number) The ending point of the interval in which we seek +% for minimum +% epsilon: (number) The epsilon value +% **note:** +% epsilon in not used in this method, but it is part of the +% method calling interface. +% lambda: (number) The lambda value (accuracy) +% +% return: +% a: (vector) Starting points of the interval for each iteration +% b: (vector) Ending points of the interval for each iteration +% k: (number) The number of iterations +% n: (number) The calls of objective function fun_expr % - % Error checking -if lambda <= 0 - error ('Convergence criteria not met') +if alpha > beta || lambda <= 0 + error ('Input criteria not met') end % Init variables @@ -19,18 +37,28 @@ k=1; x_1 = a(k) + (1 - gamma)*(b(k) - a(k)); x_2 = a(k) + gamma*(b(k) - a(k)); +f1 = fun(x_1); +f2 = fun(x_2); while b(k) - a(k) > lambda % set new search interval k = k + 1; - if fun(x_1) < fun(x_2) + if f1 < f2 a(k) = a(k-1); b(k) = x_2; x_2 = x_1; + f2 = f1; x_1 = a(k) + (1 - gamma)*(b(k) - a(k)); + f1 = fun(x_1); else a(k) = x_1; b(k) = b(k-1); x_1 = x_2; + f1 = f2; x_2 = a(k) + gamma*(b(k) - a(k)); + f2 = fun(x_2); end end + +% Set objective function calls +n = k+1; +

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