Index exceeds array bounds help - Fibonacci Series

Hi everyone. I'm doing an assignment (which needs to be handed in by tomorrow, so I hope to receive a quick help haha) and I have to calculate the golden ration from the Fibonacci Series.

The golden ration is defined as the division of the (N)th and the (N-1)th number of the Fibonacci Series. Here's my script:

 clear;
 close all;
 clc;

 % Input the value of N 

 n_2 = input('This script compute the golden ratio of the Nth and (Nth - 1)th Fibonacci numbers. Enter the  value of N.\nN = ');
 n_1 = n_2 - 1;

 % Find the Fibonacci Series values
 fibonacci(1)  = 1;
 fibonacci(2)  = 1;

 for i = 3:n_2

   fibonacci(i) = fibonacci(i-1) + fibonacci(i-2);

     if i >= 4
       fibonacci(i-3) = []
     end

 end

 golden_ratio = fibonacci(n_2)/fibonacci(n_1);

 % Print results

 fprintf('\nThe golden ration between the %.fth and the %.fth number of the Fibonacci series is %f', n_2, n_1, golden_ratio)

Obviously I can't use the fibonacci function. Also, the assignment ask to "save space": each term of the Fibonacci Series is computed using the two previous terms. For this reason, since at the end we only need the (N)th and (N-1)th terms, we can delete all the other ones as the loop goes. I tried to do this here:

 if i >= 4
       fibonacci(i-3) = []
 end

And here's the problem. The script, without these three line, does work and does give the value of the golden ratio. As soon as I try to implement the "saving-space" lines, I get the error:

 Index exceeds array bounds.

 Error in Copy_of_PS_3 (line 18)
    fibonacci(i) = fibonacci(i-1) + fibonacci(i-2);

How can I fix this? Any help is appreciated. Thank you!

Answer 1

[Walter Roberson]

When you delete something out of the fibonacci variable, MATLAB does not just leave a "hole" not occupied by storage: MATLAB causes the elements afterwards to "fall down" to fill the hole.

For example, if you have 1 2 3 4 5 and you delete the third element, then what you get is not 1 2 (hole) 4 5: it would instead be 1 2 4 5

Hint:

old = 149;
for K = 1 : 20
   if ~mod(old, 2)
     current = old/2;
   else
     current = old * 3 + 1;
   end
   disp(current);
   old = current;
 end

[Matteo Tafuro]

Oh, okay. I got what you mean, but I still don't get how to fix my script

[Walter Roberson]

old2 = ...
old1 = ...
for ...
  new = some computation based upon old1 and old2
  ...
  old2 = old1;
  old1 = new;
end

[Matteo Tafuro]

Worked! My script now is:

 n = input(Enter the value of N = ');

 fibonacci_1 = 1;
 fibonacci_2 = 1;

 for i = 3:n

    fibonacci_3 = fibonacci_2 + fibonacci_1

    if i~=n
        fibonacci_2 = fibonacci_1
        fibonacci_1 = fibonacci_3
    end

 end

 golden_ratio = (fibonacci_3/fibonacci_2);

Thanks a lot guys!

Answer 2

[James Tursa]

"... For this reason, since at the end we only need the (N)th and (N-1)th terms, we can delete all the other ones as the loop goes ..."

Don't do that. First, it doesn't save much memory. Second, the overhead of doing this operation costs more than the savings is worth and it just complicates your code. Just keep the entire array in memory until the end, and then pare it down at that time if you want to.

If you really did want to do this (again, not recommended), your loop would always operate on the 1st and 2nd elements. E.g.,

fibonacci(1)  = 1;
fibonacci(2)  = 1;
    for loop goes here
    fibonacci(3) = fibonacci(1) + fibonacci(2);
    fibonacci(1:2) = fibonacci(2:3);
    end

[Matteo Tafuro]

Indeed, this is what I would do. However the assignment clearly asked to do so

[Matteo Tafuro]

So this:

fibonacci(3) = fibonacci(1) + fibonacci(2);
fibonacci(1:2) = fibonacci(2:3);

Becomes this is in my for loop:

 fibonacci(i) = fibonacci(i-1) + fibonacci(i-2);
 fibonacci(i-1:i-2) = fibonacci(i-2:i)

If I run it,I get another error:

 Unable to perform assignment because the left and right sides have a different number of elements.

 Error in PS_3 (line 19)
    fibonacci(i-1:i-2) = fibonacci(i-2:i)

[Walter Roberson]

i-2:i designates 3 elements, but i-1:i-2 designates 0 elements because when you have A:B then if B<A then the result of the colon operator is empty. If you were to switch it to i-2:i-1 then that would designate two elements rather than 3.

[Matteo Tafuro]

Yes, with

 fibonacci(i-2:i-1) = fibonacci(i-1:i)

it works now. However, with this command the whole Series is different from the original, and the values I get do not belong to the Fibonacci Series anymore