How to turn a function with a for loop into a recursive function

Hello, I have a task to write a recursive function, that solves a system with an upper-triangular coefficient matrix. I mean, to solve the system: Ax=b, when A is an upper-triangular coefficient matrix

I wrote a function using for loop, howover I don't know how to turn it into a recursive function. Here's my code:

function x=uppermatsolve(M,b);
x=zeros(size(b));
[n,m]=size(M);
x(n,:)=b(n,:)/M(n,n);
for k=n-1:-1:1
    x(k,:)=(b(k,:)-M(k,k+1:n)*x(k+1:n,:))/M(k,k);
end

Any help is greatly appreciated!

Answer 1

[ag]

Hi Lee,

To convert your iterative function into a recursive one, you need to redefine the problem in terms of smaller subproblems. For an upper-triangular matrix, the recursive approach involves solving the last equation first and then recursively solving the reduced system. Here's how you can achieve this:

function x = uppermatsolve_recursive(M, b)
    % Get the size of the matrix
    [n, ~] = size(M);
    
    % Initialize the solution vector
    x = zeros(size(b));
    
    % Call the recursive function
    x = recursiveSolve(M, b, x, n);
end

function x = recursiveSolve(M, b, x, k)
    % Base case: solve the last equation
    if k == 1
        x(k) = b(k) / M(k, k);
    else
        % Recursive case: solve for the current variable
        x(k) = (b(k) - M(k, k+1:end) * x(k+1:end)) / M(k, k);
        % Recursively solve for the next variable
        x = recursiveSolve(M, b, x, k-1);
    end
end

Hope this helps!