gausselimpivot.m

A very simple Gaussian elimination code in matlab

function [x] = gaussElimPivot(A,b, verbose)
% File gaussElim.m
%   This subroutine will perform Gaussian elmination
%   on the matrix that you pass to it.
%   i.e., given A and b it can be used to find x,
%        Ax = b
%
%   To run this file you will need to specify several
%   things:
%   A - matrix for the left hand side.
%   b - vector for the right hand side
%
%   The routine will return the vector x.
%   ex: [x] = gaussElim(A,b)
%     this will perform Gaussian elminiation to find x.
%
%


 N = max(size(A));


 % Perform Gaussian Elimination
if verbose != 0
 A
 b
end

  for j=2:N,
	 maxVal = A(j-1, j-1);
	 index = j-1;
	 for k=j-1:N,
	   checking = abs(A(k, j-1));
	   if checking > maxVal
	     maxVal = abs(A(k, j-1));     
	     index  = k;
	   end
	 end
	 if index != j-1
	   A([index,j-1],:) = A([j-1,index],:);
	   b([index,j-1],:) = b([j-1,index],:);
	   if verbose != 0
	     printf("***** Swapping %d with %d ******\n", index, j-1);
	     A
	     b
	   end
	 else
	   if verbose != 0
	     printf("***** No Swap ******\n");
	   end
	 end

       for i=j:N,	 
	 m = myRound(myRound(A(i,j-1))/myRound(A(j-1,j-1)));
	 for k=1:N,
	   A(i,k) = myRound(myRound(A(i,k)) - myRound(myRound(A(j-1,k))*myRound(m)));
	 end
	 b(i) = myRound(myRound(b(i)) - myRound(m)*myRound(b(j-1)));
	   if verbose != 0
	     printf("****** Eliminating %d, %d ******\n", i, j-1);
	     A
	     b
	   end
       end
  end

% Perform back substitution

 x = zeros(N,1);
 x(N) = myRound(myRound(b(N))/myRound(A(N,N)));
 
 for j=N-1:-1:1,
   x(j) = myRound(myRound((myRound(b(j))-myRound(A(j,j+1:N)*x(j+1:N))))/myRound(A(j,j)));
 end

 


% A = [.6667 .2857 .2000; .3333 .1429 -.5000; .2000 -.4286 .4000]
% b = [2.867 .8333 -2.400]'

% A = [2 3 1; 4 1 4; 3 4 6]
% b = [-4 9 0]'