fixing code to have diagonal (1's) having the first matrix start with a zero

% Gauss Jordan Elimination for a system of equations
% Matrix form of the problem: [A]{x} = {b}
% [A] matrix of coefficients
% {x} column vector of unknowns
% {b} column vector of forcing parameters or constants
 
%% Clear
clear
clc
 
% Set format to display
format short
 
% Define matrix [A]
% Pivoting.... a bad example
A = [0 2 1; 1 1 2; 2 1 1];
b = [4; 6; 7];
 
% Augment the matrix [A] into [Ag]
Ag = [A b];
 
disp('Initial augmented matrix: ')
disp(Ag);
 
%% Main GJ loop
m = size(Ag,1);  % Number of rows
 
for ii = 1:m
    % Normalize the pivot row | get pivot element and pivot row
    p_row = Ag(ii,:);
    p_el = Ag(ii,ii);
    n_row = p_row/p_el; % Normalization of the pivot row
    Ag(ii,:) = n_row;   % Reassigning normalized row into Ag
    
    % Perform the row operations
    for jj = 1:m
        if ii ~= jj
            Ag(jj,:) = round(n_row*(-1*Ag(jj,ii)) + Ag(jj,:),4);
        end
            
    end
    
    % Display the current matrix Ag
    disp('Current Ag: ');
    disp(Ag)
    pause(3)
end

this is the code i have but how can i fix it to implement the Gauss Jordan elimination process, implement pivoting (i.e. swapping the order of rows in the augmented matrix Ag) in order for the method not to crash due to the potential for division by zero.

Answer 1

[Adrián Szemenyei]

If I understand the question correctly you just have to do this: if the pivot is zero, check the elements under the pivot, change the rows.

Note that you do not actually need to go through all the elements one-by-one (using 2 for loops).

In matlab you can do arithmetics on matrices and on arrays.

Like this:

Ag = [A b];
m=size(Ag,1);
for i=1:m
   if Ag(i,i)==0 %if the pivot is zero
       tmp=find(Ag(:,i)~=0);
       tmp=tmp(tmp>i);
       if isempty(tmp)
           disp('singular');
           break;
       end
       tmp=tmp(1); %I choose the first but you can choose one randomly using the randperm fnc as an index 
       Ag([i,tmp],:)=Ag([tmp,i],:);%swap rows
   end
   Ag(i,:)=Ag(i,:) ./ Ag(i,i);%ones in the diagonal
   Ag(i+1:m,:)=Ag(i+1:m,:) - ( Ag(i+1:m,i) .* Ag(i,:) ) ;
   Ag(1:i-1,:)=Ag(1:i-1,:) - ( Ag(1:i-1,i) .* Ag(i,:) ) ; 
   
end

You might want to save which rows you swapped...