I can not find the error in this Gauss Seidal equation.

     %  
function x1 = GaussSeidal(a,b,x0,tol)
N=100000;
k=1;
x=x0;
while(k<N)
    n = length(b);
  for j = 1 : n
     x(j)=(b(j)-a(j,1:j-1).*x(1:j-1)-a(j,j+1:n)*x0(j+1:n))/a(j,j);
  end
    x1=x';
    error=x1-x0;
    if norm(error)< tol
         disp('succefful');
         break  
    end
     k=k+1;
     x0=x1;
end
disp(' The number of iteration is');disp(k)
tic;
gs_time=toc;
disp(gs_time);
end
end

 %%Example
a=[5 -2 3;-3 9 1;2 -1 -7];b=[-1 2 3]';x0=[0 0 0]';tol=0.0001;

Answer 1

[Walter Roberson]

You have one too many end statements in your function.

In the line

       x(j)=(b(j)-a(j,1:j-1)*x(1:j-1)-a(j,j+1:n)*x0(j+1:n))/a(j,j);

when j = 1, a(j,j+1:n) is a 1 x 2 vector, and x0(j+1:n) is a 1 x 2 vector. You have the * operator between two 1 x 2 vectors. The * operator is algebraic matrix multiplication, which requires that for an M x N array "*" a P x Q array, that N and P are the same -- M x N * N x Q giving an M x Q result. 1 x 2 * 1 * 2 does not follow that rule and so is an error. Possibly you want the .* operator instead of * but possibly not.

You also have the problem in that line a(j,1:j-1) is empty, which would make the result of a(j,1:j-1)*x(1:j-1) empty as well. An empty array minus something is empty, so you are down to (b(j) - empty)/a(j,j) but a scalar minus empty is empty too, so you are now down to empty / a(j,j) which will be empty as well, leaving you with x(1) = empty . Which is a problem: you cannot store a 0 x 0 array into a slot that expects 1 value.

[Dereje]

But I have the second term which is x0 multiplied by a.

[Walter Roberson]

The a*x0 term is the one that is giving you the error you posted about, as you are trying to do 1 x 2 * 1 x 2 which is not valid for the * operator. You can do 2 x 1 * 1 x 2 giving a 2 x 2 output, or you can do 1 x 2 * 2 x 1 giving a 1 x 1 output, or you can do 1 x 2 .* 1 x 2 giving a 1 x 2 output.

But the result of that will not matter, because when j is 1, a(j,1:j-1) is a(1,1:0) which is empty, and any arithmetic operation on an empty array gives you an empty array. Well, except for using / that is:

>> 53 - []
ans =
     []
>> 53 + []
ans =
     []
>> 53 / []
Error using  / 
Matrix dimensions must agree. 
>> 53 ./ []
ans =
     []
>> 53 .* []
ans =
     []
>> 53 ^ []
ans =
     []

so no matter what size the a * x0 portion comes out, the a(j,1:j-1)*x is going to be empty and the empty will keep forcing results to be empty until you get to the point where you have x(1) = empty and that does not fit.

[Dereje]

When j =1, the term

 a(j,j+1:n)*x0(j+1:n)

Becomes a(1,2:3)*x0(2:3) which should give some value I believe. Besides , I used .* operator but still the error exists.

[Walter Roberson]

It does not matter that a*x0 produces a value. The a*x part is producing empty, and empty minus a value is either empty or an error.

Looks like I need to be more explicit for you:

Your problem is that your code needs to calculate based upon the content of the previous columns, which is a problem when you start your calculation from column 1 because there are no previous columns. So do not start from column 1.

[Dereje]

Exactly this is my problem from the beginning. I tried separately calculate x(1), to use for the next iteration. I will try in different ways. Thanks for the detailed explanation and of course for your fast response!