How do i reduce running time in this code

function [f , t] = jacobi2(n)

tic;

if n < 4

error ('n not in the range')

end

n=n^2;

b=zeros(n,1);

b(1,1)=1;

b(n,1)=1;

A = zeros(n,n);

for i=4:(n-3)

for j=4:(n-3)

if i==j

A(i,i)=4;

A(i,i+1)=-1;

A(i,i-1)=-1;

A(i,i+3)=-1;

A(i,i-3)=-1;

A(i+1,i)=-1;

A(i-1,i)=-1;

A(i+3,i)=-1;

A(i-3,i)=-1;

end

end

end

A(1,1)=4;

A(1,2)=-1;

A(3,2)=-1;

A(2,3)=-1;

A(2,1)=-1;

A(2,2)=4;

A(3,3)=4;

A(end,end)=4;

A(end-1,end-1)=4;

A(end-2,end-2)=4;

A(end-3,end-3)=4;

A(end-1,end)=-1;

A(end,end-1)=-1;

A(end-1,end-2)=-1;

A(end-2,end-1)=-1;

epsilon = 1e-3;

f = zeros(n,1);

counter = 0;

flag = 0;

L = tril(A,-1);

D = diag(A);

U = triu(A,1);

B = -1./D.*(L+U);

C = (1./D).*b;

while flag == 0

counter = counter+1;

if counter > 10000

error ('Too many iteration')

end

f_n = (B*f) + C;

if max(abs(f_n-f)/(f_n))<epsilon

flag = 1;

else

f = f_n;

end

end

t=toc;

end

Answer 1

[Swetha Polemoni]

Hi Tzach Berlinsky,

In the code you have provided using nested loops is not necessary. Since the body of loops is executed only when i==j, elimination of one loop can be an option. Replace the nested loops with the following.

for i=4:(n-3)
     A(i,i)=4;
     A(i,i+1)=-1;
     A(i,i-1)=-1;
     A(i,i+3)=-1;
     A(i,i-3)=-1;
     A(i+1,i)=-1;
     A(i-1,i)=-1;
     A(i+3,i)=-1;
     A(i-3,i)=-1;
end

Here is the link to best practices that can be followed to improve performance. You may find it helpful.