Using 'for loop' on a function call

Hello everyone !

Hope everyone is safe and healthy considering what is happening around the world.

I'm writing a code to find the multiple roots of a function by the Bisection method. How I'm trying to approach it, is to create a for loop on a function call, so that the Bisection method script iterates one set of x-values where there is a root, displays the root and how many iterations it took to calculate it and moves on to the next set. What I can't seem to figure out is how to make the Bisection method function to iterate multiple time for different sets of x-values.

Here is the main body of my code

f = @(x) sin(((2/9)+2)*(x-(2/4)))-3.*(((x-((2+5)/2)).*(x-((2-5)/2)))/((2/2)^2+(10-2/2)^2))
x_min = [0.4000, 2.0000, 3.3000, 4.6000] % Between the consequtive pairs of x_min and x_max there is a root 
x_max = [0.5000, 2.1000, 3.4000, 4.7000]
tol = 1E-6

for i = 1 : length(x_min) && z == 1 : length(x_max)

[root, n_iter] = Bisection(f, x_min, x_max, tol)
end

And here is the script for the bisection method function

function [root, n_iter] = Bisection(f, x_min, x_max, tol)

x1 = x_min; % assign left boundry
x2 = x_max; % assign right boundary
f1 = f(x1);
f2 = f(x2);

n_it = 0;              % Initiate iteration counter
err = abs((x2 - x1)/(x1 + x2)); % Compute initial error estimate
while err > tol         % Termination ciretiron
    xr = (x1 + x2)/2;   % Find mid-point
    fr = f(xr);         % Evaluate function at mid-point
    if f1*fr < 0        % Check which half has the root and assign variables
        x2 = xr;
        f2 = fr;
    else 
        x1 = xr;
        f1 = fr;
    end
    n_it = n_it + 1;    % Increase iteration counter
    err = abs((x2 - x1)/(2*xr));    % Calculate an estimate error
end

root = (x1 + x2)/2; % Calculate approximation to the root 
n_iter = n_it;

disp(['You found a root! It is at x = ', num2str(root), ' , great!'])
disp(['The number of iterations taken to find the root is ', num2str(n_iter), '.'])

Thank you for taking your time reading my problem !

Answer 1

[BobH]

If you want to iterate along x_min and x_max, you can use a single counter in your for loop

for i = 1 : length(x_min)  % both vectors are same length, so pick either
   [root, n_iter] = Bisection(f, x_min(i), x_max(i), tol)
end

If you want to do them all at once, and eliminate the loop

  [root, n_iter] = arrayfun(@(M,X) Bisection(f, M, X, tol), x_min, x_max);

This creates an array of results

root
root =
    0.4022    2.0007    3.3126    4.6263
n_iter
n_iter =
    17    15    14    14

[Stephen23]

It is recommended to preallocate the output arrays before the loops:

https://www.mathworks.com/help/matlab/matlab_prog/preallocating-arrays.html

For example:

num = numel(x_min);
root   = nan(1,num);
n_iter = nan(1,num);
for k = 1:num
    [root(k), n_iter(k)] = Bisection(f, x_min(k), x_max(k), tol);
end

[BobH]

Yes - excellent addition

[Eligijus Rupsys]

Thank you BobH and Stephen, you really helped me out here ! Very much appreciate your time taken to help me out !! Now my code works flawlessly !