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

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]

Why do you want to remove the if? What is your end goal? To speed up the code?

Also, please use the layout tools to make your code more readable.

[SA]

Yes, I want to speed up the code

[Ameer Hamza]

Can you write down the equation you are trying to implement with these for loops?

Answer 1

[Vimal Rathod]

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]

Thanks a lot

[SA]

I trying to capture another block of code inside the one above but I am not getting the right results.

I want to include

if i==N-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

in your code and I am using what is below but my answers aren't correct. I don't know what I am doing wrong exactly.

i=1;         
for j=1:M-1
    A(i+(M-1-j)*(N-1),i+(M-1-j)*(N-1))=-2.0/dx^2-2.0/dy^2;  
    B(i+(M-1-j)*(N-1))=B(i+(M-1-j)*(N-1))-cos(y(j))/dx^2;
end

 i=N-1;         
 for j=1:M-1
      A(i+(M-1-j)*(N-1),i+(M-1-j)*(N-1))=-2.0/dx^2-2.0/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-2
  for j=1:M-1
    A(i+(M-1-j)*(N-1),i+(M-1-j)*(N-1))=-2.0/dx^2-2.0/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;
    A(i+(M-1-j)*(N-1),i+1+(M-1-j)*(N-1))=1/dx^2;
  end
end

[Rik]

I would still second the advice from Ameer: post the equations you want to solve. A change of algorithm can increase calculation many times, while optimization can only get you an order of magnitude.

Speaking of optimization: did you pre-allocate A and B?

[SA]

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]

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]

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.