matlabrecursionoctave

recursive sqrt(2) ratio function in matlab / octave


I'm trying to create a recursive sqrt(2) ratio function in matlab / octave. I can create the recursive pattern in a spreadsheet see numbers and the corresponding formulas that create them below.

Recursive numbers

Recursive formulas

I'm having trouble getting the function to work correctly in matlab / octave. The a and b values should match the spreadsheet images above.

function f = rtsqrt2(a,b,n)          
  for rr=1:n
    rr
    if (rr==1)
      ab_num(rr,:)=[a,b];

    elseif (rr==2)
      a=a+b+b;
      b=1+b;
      ab_num(rr,:)=[a,b];

    elseif 
      a=a+b+b;
      b=a+b;
      ab_num(rr,:)=[a,b];

    end
  end
  ab_num
end

when I do a rtsqrt2(1,1,10) Error

The first two lines are correct but on the third line I get 7,9 instead of what I should get 7,5 and things get worse from there. How can I fix it so that my recursive function follows the pattern in the first image.

Please note I'm using octave 4 which is similar to matlab and that I plan on using more than just 10 recursions (10 recursions were used just to test with)


Solution

  • Here's an implementation that fits your description. Note the computation (as you described) is iterative not recursive.

    I've included some extra bits in the function to make and display the table.

    function x = rtsqrt2(a, b, n)
    %% Compute the square root of 2 iteratively
    %
    % n = number of iterations
    % a, b  are the initial values
    
    %Initialise the vector A and B to hold the computation for each step
    A = zeros(1, n);
    A(1) = a;
    B = zeros(1, n);
    B(1) = b;
    C = zeros(1, n);
    
    % Compute the values of A and B iteratively
    for k = 2 : n
        A(k) = A(k-1) + 2 * B(k-1);
        B(k) = A(k-1) + B(k-1);
    end
    
    % Compute the entire C vector (a/b) in a vectorised manner
    C = A ./ B;
    % Create a table to display the table like you'd see in excel
    TBL = table(A', B', C');
    TBL.Properties.VariableNames = {'A' 'B' 'C'};
    disp(TBL)
    
    % sqrt(2)
    x = C(end);
    

    Here's the function running:

    >>> rtsqrt2(1, 1, 10)
     A       B        C   
    ____    ____    ______
    
       1       1         1
       3       2       1.5
       7       5       1.4
      17      12    1.4167
      41      29    1.4138
      99      70    1.4143
     239     169    1.4142
     577     408    1.4142
    1393     985    1.4142
    3363    2378    1.4142
    
    
    ans =
    
    1.4142