88 lines
2.3 KiB
Matlab
88 lines
2.3 KiB
Matlab
function [a, b, N, n] = min_fibonacci(fun_expression, alpha, beta, epsilon, lambda)
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% Fibonacci method for finding the local minimum of a function.
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%
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% fun_expr: (symbolic expression over x) The symbolic expression of the
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% objective function
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% alpha: (number) The starting point of the interval in which we seek
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% for minimum
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% beta: (number) The ending point of the interval in which we seek
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% for minimum
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% epsilon: (number) The epsilon value (the interval of the last step)
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% lambda: (number) The lambda value (accuracy)
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%
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% return:
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% a: (vector) Starting points of the interval for each iteration
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% b: (vector) Ending points of the interval for each iteration
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% N: (number) The number of iterations needed.
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% nn: (number) The calls of objective function fun_expr
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%
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% Error checking
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if alpha > beta || lambda <= 0 || epsilon <= 0
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error ('Input criteria not met')
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end
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% Use Binet's formula instead of matlab's recursive fibonacci
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% implementation
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fibonacci = @(n) ( ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5)) );
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% Init variables
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a = alpha;
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b = beta;
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n = 0;
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fun = matlabFunction(fun_expression);
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% wrapper call count function
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function r = count_fun(x)
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n = n + 1;
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r = fun(x);
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end
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% calculate number of iterations
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N = 0;
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while fibonacci(N) < (b(1) - a(1)) / lambda
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N = N + 1;
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end
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% calculate x1, x2 of the first iteration, since the following iteration
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% will not require to calculate both
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x_1 = a(1) + (fibonacci(N-2) / fibonacci(N)) * (b(1) - a(1));
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x_2 = a(1) + (fibonacci(N-1) / fibonacci(N)) * (b(1) - a(1));
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f1 = count_fun(x_1);
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f2 = count_fun(x_2);
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% All but the last calculation
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for k = 1:N-2
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% set new search interval
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if f1 <= f2
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a(k+1) = a(k);
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b(k+1) = x_2;
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x_2 = x_1;
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f2 = f1;
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x_1 = a(k+1) + (fibonacci(N-k-2) / fibonacci(N-k)) * (b(k+1) - a(k+1));
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f1 = count_fun(x_1);
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else
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a(k+1) = x_1;
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b(k+1) = b(k);
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x_1 = x_2;
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f1 = f2;
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x_2 = a(k+1) + (fibonacci(N-k-1) / fibonacci(N-k)) * (b(k+1) - a(k+1));
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f2 = count_fun(x_2);
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end
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end
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% Last calculation
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x_2 = x_1 + epsilon;
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f2 = count_fun(x_2);
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if f1 <= f2
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a(N) = a(N-1);
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b(N) = x_1;
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else
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a(N) = x_1;
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b(N) = b(N-1);
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end
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end
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