MATLAB: Reiteration sequence without Fib function.

recursive relation

I am working on a recursive relation for the Fibonacci sequence without using the fib code in Matlab. My code works, but no matter what I do, I cannot get it to print more than the first three numbers.Any advice is appreciated.

function [x,n] = HW215(~)
x(1)=1;
x(2)=(1+sqrt(5))/2;
for n=3:31   
    x(n)=x(n-1)+x(n-2);  
end

Best Answer

Hi Ann,

Sounds like your function should take the following inputs: the first value of your sequence, the second value of your sequence, and the length of the sequence. The function should also return a vector "x" of iterative pair sums.

Be sure that this code is saved in a file name HW215_Ann.m. Then from the Matlab command window, you can type

 x=HW215_Ann(1,2,30);

to call your function (use any inputs you like, i used 1, 2, and 30). The output "x" should then be in your workspace with the sequence you wanted.

Function below:

function x = HW215_Ann(f1,f2,n)
% f1 and f2 are the first two numbers of the sequence
% n is the length of the sequence
% Checking that function inputs are valid
if ~isnumeric(f1)||~isscalar(f1),
   error('First input "f1" must be numeric scalar.');
end
if ~isnumeric(f2)||~isscalar(f2),
   error('Second input "f3" must be numeric scalar.');
end
if ~isnumeric(n)||~isscalar(n),
   error('Third input "n" must be numeric scalar.');
elseif (n~=round(n))||n<3,
       error('Third input "n" must be an integer 3 or greater.')
end
% pre-allocate memory for x
x=NaN(n,1);
% start off with f1 and f2
x(1)=f1;
x(2)=f2;
% loop to calculate x values
for iter=3:n
    x(iter)=x(iter-1)+x(iter-2);  
end

Functions in Matlab must be saved as .m files with the same name as the as the function's name. Also, you won't need to use return statements in Matlab. The objects you want to return should only be stated in the function declaration. Give this link a read-through.

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MATLAB: Fibonacci series, while loop

Well, what is important to me is you have made a credible effort, and gotten close. In fact, you did compute Fibonacci sequence elements.

First, you should have preallocated the vector a, which would make MATLAB more efficient.

What would i change in the code you show?

N = 16; % how far out
a = zeros(1,N); % preallocation
a(1) = 1;
a(2) = 1;
for n = 3:N % a for loop is simpler to write than a while loop
  a(n) = a(n-1)+a(n-2);
end

But how about that ratio thing? You cannot use the limit function to compute a limit as you did. Sorry. But the limit is just the ratio of two consecutive numbers from that sequence. So now, you want to see how well those ratios approach the expected limit as N grows larger.

ratio = zeros(1,N-1);
for n = 1:N-1
   ratio(n) = a(n)/a(n+1);
end
format long g
ratio'
ans =
                         1
                         2
                       1.5
          1.66666666666667
                       1.6
                     1.625
          1.61538461538462
          1.61904761904762
          1.61764705882353
          1.61818181818182
          1.61797752808989
          1.61805555555556
          1.61802575107296
          1.61803713527851
          1.61803278688525

What is the expected limit supposed to be? It is approaching that theoretical limit?

MATLAB: N th Fibonacci number with function

function [c] = fibo (a, b, n)
n = input('n:');

Every time your user calls your fibo function, you're going to ask them to pass a value into it for n (as the third input) then immediately turn around and prompt them to type in a replacement value for n.

IMO if part of your design requires your user to enter data manually, you should have (at least) two separate functions: the interface function that can call input and then just calls the processing function and the processing function that operates solely on data passed into it (no prompting of the user allowed.)

But that's a bit of an aside. You already have most of what you want. It's not too difficult to translate your first script into a function.

n = input('n:');

Turn this first statement into the function declaration line. "function theOutputs = fibonacci(theInputs)". I'll let you decide what to write in place of theOutputs and theInputs.

fibo = zeros(1,n);
for n = 1:n

Reusing the variable name technically works, but it can be confusing that the role of n kind of changes. I'd use a different variable name for the loop variable.

    if n==1
        fibo(n)=0;
    else
        if n==2
            fibo(n)=1;
        else
    fibo(n)=fibo(n-1)+fibo(n-2);
        end
    end
end
disp(fibo);

Turn this last line into the line that defines whatever variables you need to return. It should assign into whatever variables appear in theOutputs above.

Best Answer

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