gaussSiedelPivot

clear all;
clc;

% Tolerance
tolerance = 5;
Es = 0.5*10^(2-tolerance);

breakFlag = 0;

% Aug matrix
A = [ 3 7 13 76
      1 5 3 28
      12 3 -5 1];

needsPivoting = 0;

% Aug Matrix split
[m,n] = size(A);
B = A(:, n).';
A(:, n) = [];

clear m;
clear n;

[rows, columns] = size(A);


% CONVERGENCE
for i=1:rows
    sum = 0;
    for j=1:columns
        if(i~=j)
            sum = sum + abs( A(i, j) );
        end
    end
    if( abs( A(i, i) ) < sum )
        needsPivoting = 1;
        break;
    end
end

% PIVOTING
if( needsPivoting )
    for i=1:(rows-1)
        for z=2:rows
            sum = 0;
            for j=1:columns
                if(i~=j)
                    sum = sum + abs( A(i, j) );
                end
            end
            if( abs( A(i, i) ) < sum )
                tempRowA = A(i, :);
                tempRowB = B(i);
                A(i, :) = A(z, :);
                B(i) = B(z);
                A(z, :) = tempRowA;
                B(z) = tempRowB;
            end
        end
    end
end

% Gauss Siedel

x = zeros(columns, 1);
n = length(x);
iteration = 1;


while(1)
    for i=1:n
        temp = 0;
        if( iteration==1 )
           for j=1:n
              if(i~=j)
                  temp = temp + A(i, j)*x(j, iteration);
              end
           end
           x(i, iteration) = (B(i) - temp)/A(i, i);
        else
           for j=1:n
              if(i~=j)
                  temp = temp + A(i, j)*x(j, iteration-1);
              end
           end
           x(i, iteration) = (B(i) - temp)/A(i, i);

        end

    end


    for i=1:n
        if( iteration>2 )
            errors(i) = (abs(x(i, iteration) - x(i, iteration-1))/x(i, iteration))*100;
            Ea(iteration-2) = max(errors);
            if( Ea(iteration-2) <= Es )
                breakFlag = 1;
                break;
            end
        end
    end
    if(breakFlag == 1)
        break;
    end
    iteration = iteration + 1;
end

[m, n] = size(x);

display(x(:, n));