iteration with for for a simple computation

Question

Paul Rogers 2020-7-8

评论： Paul Rogers 2020-7-8

采纳的回答： dpb

I'd like do write this expression in a more compact and generic way, like with a for:

T = c(1)*cos(0) + c(2).*cos(1.*acos((m))) + c(3).*cos(2.*acos((m))) + c(4).*cos(3.*acos((m))) +  ...
    c(5).*cos(4.*acos((m)));

where the vector m and c are in attached.

Answer 1

dpb 2020-7-8

One way amongst many...

z=acos(m);      % precompute the constant array
T=c(1)+sum(cell2mat(arrayfun(@(c,i) c*cos(i*z),c(2:end),[1:numel(c)-1].','UniformOutput',false)));

The straight for...end loop might be quicker and probably easier to read.

I don't know if the JIT optimizer can find and eliminate the redundant calculation of acos(m) on its own or not; didn't try any timing tests...

Paul Rogers 2020-7-8

brilliant, thank you a lot, it's a solution I would have never tought!