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Overwrite fibonacci with Binet formula

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This commit is contained in:
Christos Choutouridis 2024-11-06 10:41:23 +02:00
parent 634f90b25b
commit 23b60aac66
1 changed files with 5 additions and 5 deletions
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10
Work 1/scripts/min_fibonacci.m
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@ -3,7 +3,7 @@ function [a, b, N] = min_fibonacci(fun_expression, alpha, beta, epsilon, lambda)
% Use Binet's formula instead of matlab's recursive fibonacci % Use Binet's formula instead of matlab's recursive fibonacci
% implementation % implementation
fib = @(n) ( ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5)) ); fibonacci = @(n) ( ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5)) );
% Error checking % Error checking
if lambda <= 0 || epsilon <= 0 if lambda <= 0 || epsilon <= 0
@ -24,8 +24,8 @@ end
% calculate x1, x2 of the first iteration, since the following iteration % calculate x1, x2 of the first iteration, since the following iteration
% will not require to calculate both % will not require to calculate both
x_1 = a(1) + (fib(N-2) / fib(N)) * (b(1) - a(1)); x_1 = a(1) + (fibonacci(N-2) / fibonacci(N)) * (b(1) - a(1));
x_2 = a(1) + (fib(N-1) / fib(N)) * (b(1) - a(1)); x_2 = a(1) + (fibonacci(N-1) / fibonacci(N)) * (b(1) - a(1));
% All but the last calculation % All but the last calculation
for k = 1:N-2 for k = 1:N-2
@ -34,12 +34,12 @@ for k = 1:N-2
a(k+1) = a(k); a(k+1) = a(k);
b(k+1) = x_2; b(k+1) = x_2;
x_2 = x_1; x_2 = x_1;
x_1 = a(k+1) + (fib(N-k-2) / fib(N-k)) * (b(k+1) - a(k+1)); x_1 = a(k+1) + (fibonacci(N-k-2) / fibonacci(N-k)) * (b(k+1) - a(k+1));
else else
a(k+1) = x_1; a(k+1) = x_1;
b(k+1) = b(k); b(k+1) = b(k);
x_1 = x_2; x_1 = x_2;
x_2 = a(k+1) + (fib(N-k-1) / fib(N-k)) * (b(k+1) - a(k+1)); x_2 = a(k+1) + (fibonacci(N-k-1) / fibonacci(N-k)) * (b(k+1) - a(k+1));
end end
end end