# How do I avoid using if and else statements in this code

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SA on 1 May 2020
Commented: SA on 7 May 2020
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

Rik on 1 May 2020
Why do you want to remove the if? What is your end goal? To speed up the code?
SA on 1 May 2020
Yes, I want to speed up the code
Ameer Hamza on 1 May 2020
Can you write down the equation you are trying to implement with these for loops?

Vimal Rathod on 5 May 2020
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!

SA on 7 May 2020
Hi Rik,
I am actually solving a differential equation using a difference algorithm and the only equations i was given are  I am using the algorithm to create the equations above but I want to solve the problem without if and else statements
Rik on 7 May 2020
I wouldn't personally care how my code would solve the equations. The more time you put in, the more you can optimize your code. At some point you get to a stage where you need to put in an unreasonable amount of time. Then I would stop.
Are you really sure you simply want to avoid an if/else block? That doesn't make sense to me.
What toolboxes relating to diff equations do you have available?
SA on 7 May 2020
Hi Rik,
Yes, I just want to avoid the if/else block. I want to solve the pde another way (without using the if/else block).
I am not using an toolboxes in matlab. I just want to solve the pde using the difference algorithm.