MATLAB: Vectorize the loops within the function

interpolationMATLABprodvectorize

Hi, I am trying to create a function for Lagrange's interpolation and I wanted to know if there is a way to vectorize it that makes the code run faster
function y=lagrange(xx,yy,x)
% xx and yy are vectors of data values, x is the vector I want to interpolate
n=size(xx,2);
y=zeros(1,length(x));
for k=1:length(x)
    for i=1:n
        L=1;
        for j =1:n
            if j~=i
                L=L*(x(k)-xx(j))/(xx(i)-xx(j));
            end
        end
        y(k) =y(k)+yy(i)*L;
    end
end
end
I tried to do the following but the code is actually slower 
for k=1:length(x)
    for i=1:n
        j=1:n;j(j==i)=[];
        L=prod((x(k)-xx(j))./(xx(i)-xx(j)));
        y(k) =y(k)+yy(i)*L;
    end
end
Any help is appreciated, thank you!

Best Answer

In line 3 of the vectorized code, replace 'j(j==i)=[];' with 'j(i) = [ ];' as it takes time for finding i, which in this case is not needed and also consider declaring any fixed array before itself and not inside for loops.
n=size(xx,2);
y=zeros(1,length(x));
nvec = 1:n;
for k=1:length(x)
    for i= nvec
        j=nvec;j(i)=[];
        y(k) =y(k)+yy(i)*prod((xx(j)-x(k))./(xx(j)-xx(i)));
    end
end
Vectorized code often runs much faster than the corresponding code containing loops but not always. Please refer to the following for more information Vectorization.
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