55 lines
1.3 KiB
Matlab
55 lines
1.3 KiB
Matlab
function [a, b, N] = min_fibonacci(fun_expression, alpha, beta, epsilon, lambda)
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%
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% Use Binet's formula instead of matlab's recursive fibonacci
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% implementation
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fib = @(n) ( ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5)) );
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% Error checking
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if lambda <= 0 || epsilon <= 0
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error ('Convergence criteria not met')
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end
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% Init variables
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a = alpha;
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b = beta;
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fun = matlabFunction(fun_expression);
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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) + (fib(N-2) / fib(N)) * (b(1) - a(1));
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x_2 = a(1) + (fib(N-1) / fib(N)) * (b(1) - a(1));
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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 fun(x_1) < fun(x_2)
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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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x_1 = a(k+1) + (fib(N-k-2) / fib(N-k)) * (b(k+1) - a(k+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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x_2 = a(k+1) + (fib(N-k-1) / fib(N-k)) * (b(k+1) - a(k+1));
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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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if fun(x_1) < fun(x_2)
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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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