How can I avoid using for loop in this functions

This is the function whose speed I want to improve. I know I should use more matrix operation and use less for loop. But I have no idea how to use if-else in matrices.

function y=Besselj_approx(n,z)

y=zeros(1,length(n));
for i=n
    if i>0
        y(i)=1./gamma(i+1).*(z/2).^i;
    elseif i<0
        y(i)=(-1).^(-i)./gamma(-i+1).*(z/2).^(-i);
    else
        y(i)=-z.^2/4+1;
    end
end

Any help is appreciated!

[Rik]

Have you tried logical indexing?

[Dyuman Joshi]

Loops are quite efficient if used properly and the usage above looks good. Although you can club the 1st two conditions together -

if i~=0
    k=abs(i);
    y(i)=sign(i).^(k)./gamma(k+1).*(z/2).^k;
else
    y(i)=-z.^2/4+1;
end

If you are dealing with floating point numbers, I would suggest you to use a tolerance to compare rather than equality.

As Rik mentions, logical indexing is another good option. If you can attach your data, we can run and test the code.

[祥宇 崔]

@Dyuman Joshi Thanks! Guess the for loop is alright.

[祥宇 崔]

@Rik Thanks! I will give it a try.

Answer 1

[KSSV]

function y=Besselj_approx(n,z)
i = n ;
y=zeros(1,length(n));
y(1:end)=-z.^2/4+1;
y(i>0) = 1./gamma(i(i>0)+1).*(z/2).^i(i>0);
y(i<0)=(-1).^(-i(i<0))./gamma(-i(i<0)+1).*(z/2).^(-i(i<0));

[祥宇 崔]

Thanks! This is what I want!