MATLAB: How to avoid using if and else statements in this code

if and else staements

I want to rewrite this code but without if and else statements. I just want to enhance convergence rate
for i=1:N-1
  for j=1:M-1
    A(i+(M-1-j)*(N-1),i+(M-1-j)*(N-1))=-2/dx^2-2/dy^2;
    B(i+(M-1-j)*(N-1))=B(i+(M-1-j)*(N-1))-(cos(x(i)+y(j))+cos(x(i)-y(j)));
    if i==1         
      B(i+(M-1-j)*(N-1))=B(i+(M-1-j)*(N-1))-cos(y(j))/dx^2;
    else
      A(i+(M-1-j)*(N-1),i-1+(M-1-j)*(N-1))=1/dx^2;
    end
  end 
end

Best Answer

Hi,
If your main goal is to remove the if else statements from the code, you can write the following code first and then write the main for loop with i starting from 2 instead on one and remove the if statement and keep the statement in the else condition.
i = 1;
for j=1:M-1
    A(i+(M-1-j)*(N-1),i+(M-1-j)*(N-1))=-2/dx^2-2/dy^2;    
    B(i+(M-1-j)*(N-1))=B(i+(M-1-j)*(N-1))-cos(y(j))/dx^2;
end
for i=2:N-1
  for j=1:M-1
    A(i+(M-1-j)*(N-1),i+(M-1-j)*(N-1))=-2/dx^2-2/dy^2;
    B(i+(M-1-j)*(N-1))=B(i+(M-1-j)*(N-1))-(cos(x(i)+y(j))+cos(x(i)-y(j)));
    A(i+(M-1-j)*(N-1),i-1+(M-1-j)*(N-1))=1/dx^2;
  end 
end
if you want to further optimize you can vectorize the first loop.
Hope this helps!
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