Using Vector instead of LOOP to solve an equation

Hello,

I am solving an equation using LOOP. Is it possible to eliminate LOOP and use vector instead to solve this equation?

I used below code

   clear;
    clc;
    B=0:1:5;
    D=0;
    E=3;
    N1 = 10*rand(1,5);
    N2 = 5*rand(1,5);

    for ii=1:size(B,2)-1
            A=N1(ii);
            C=N2(ii);
            C1=(A./(4*E*(A*B).^(3/2)));
            C2=(-2*(B.^2+A^2+(D-C).^2));
            C20=A*B;
            C3=sqrt((C20)./((B+A).^2+(D-C).^2));
            C4=(D-C);
            C5=ellipticE(((4*A*B)./((B+A).^2+(D-C).^2)));
            C6=((B-A).^2+(D-C)^2);
            C7=(2./((B-A).^2+(D+C)^2));
            C8=(D+C);
            C9=(B.^2+A^2+(D+C)^2);
            C10=sqrt((A*B)./((B+A).^2+(D+C)^2));
            C11=(((4*A*B)./((B+A).^2+(D+C)^2)));
            C12=((B-A).^2+(D+C)^2);
            C13=( sqrt((A*B)./((B+A).^2+(D-C)^2)));
            C14=(D-C);
            C15=(((4*A*B)./((B+A).^2+(D-C)^2)));
            C16=(((4*A*B)./((B+A).^2+(D+C)^2)));
            C17=((C2.*C3.*C4.*C5)./C6);
            C18=C8.*C9.*C10;
            C19=ellipticE(C11);
            BN=C1.*(C17+(C7.*((C18.*C19)+C12.*( C13.*C14.*ellipticK(C15)-C8*C10.* ellipticK(C16)))));
            In2(ii,:)=BN;
    end
      %This is my tries to use vector
    A = N1;
    C = N2;
    C1=(A./(4*E*(A.*B).^(3/2)));
    C2=(-2*(B.^2+A.^2+(D-C).^2));
    C20=A.*B;
    C3=sqrt((C20)./((B+A).^2+(D-C).^2));
    C4=(D-C);
    C5=ellipticE(((4*A.*B)./((B+A).^2+(D-C).^2)));
    C6=((B-A).^2+(D-C).^2);
    C7=(2./((B-A).^2+(D+C).^2));
    C8=(D+C);
    C9=(B.^2+A.^2+(D+C).^2);
    C10=sqrt((A.*B)./((B+A).^2+(D+C).^2));
    C11=(((4*A.*B)./((B+A).^2+(D+C).^2)));
    C12=((B-A).^2+(D+C).^2);
    C13=( sqrt((A.*B)./((B+A).^2+(D-C).^2)));
    C14=(D-C);
    C15=(((4*A.*B)./((B+A).^2+(D-C).^2)));
    C16=(((4*A.*B)./((B+A).^2+(D+C).^2)));
    C17=((C2.*C3.*C4.*C5)./C6);
    C18=C8.*C9.*C10;
    C19=ellipticE(C11);
    BN1=C1.*(C17+(C7.*((C18.*C19)+C12.*( C13.*C14.*ellipticK(C15)-C8.*C10.* ellipticK(C16)))

[Adam]

Have you tried vectorising it in the most obvious way?

i.e. just get rid of the for loop and indexing and replace * with .* and / with ./ where you multiply or divide by arrays.

I'm not saying that will work straight away, but at first glance I don't see any specific reason why you can't just use standard vectorisation.

[Math Tec]

Thank you. I tried. I updated the code with my tries but it gave me different answer.

[Adam]

Well, with something that complicated you are going to have to setup some tests around that code and keep checking against them when you make changes.

Regarding different answers, your code uses random numbers so you will need to fix the random seed (or for tests hard code in non-random data) to compare different approaches anyway.

Since just doing what I said above doesn't get ride of any of those loads of intermediate variables it shouldn't be difficult to work out at what stage things go wrong.