Vectorize the loops within the function

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AM
AM el 12 de Feb. de 2020
Comentada: AM el 19 de Feb. de 2020
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!
  2 comentarios
darova
darova el 12 de Feb. de 2020
Vectorized code is not always faster
Sometimes code is more readable with for loops
AM
AM el 19 de Feb. de 2020
I see, thank you!

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Srivardhan Gadila
Srivardhan Gadila el 18 de Feb. de 2020
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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