create operation count for gauss jordan in matlab in matlab

main.m
function [x, ops] = gauss_jordan(A, b)
% Inputs:
% A: Coefficient matrix
% b: Right-hand side vector
% Outputs:
% x: Solution vector
% ops: Total number of arithmetic operations performed

[m, n] = size(A);
if m ~= n || size(b, 2) ~= 1 || size(b, 1) ~= m
    error('Invalid input dimensions');
end

% Augment matrix with right-hand side vector
A = [A b];

ops = 0; % Initialize operation count
for k = 1:m % Iterate over rows
    ops = ops + n; % n subtractions and n multiplications
  
    % Partial pivoting
    [~, p] = max(abs(A(k:m, k)));
    p = p + k - 1;
    if p ~= k
        A([k,p], :) = A([p,k], :);
        ops = ops + n; % n swaps
    end
    
    % Normalize pivot row
    A(k, :) = A(k, :) / A(k, k);
    ops = ops + n - 1; % n divisions
    
    % Eliminate entries below pivot
    for i = k+1:m
        A(i, :) = A(i, :) - A(i, k)*A(k, :);
        ops = ops + 2*n - 1; % n multiplications and n subtractions
    end
end

for k = m:-1:2 % Iterate over rows backwards
    % Eliminate entries above pivot
    for i = k-1:-1:1
        A(i, :) = A(i, :) - A(i, k)*A(k, :);
        ops = ops + 2*n - 1; % n multiplications and n subtractions
    end
end

x = A(:, end); % Extract solution vector
ops = ops + m; % m assignments

end
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