How to speed up for loop with a few calculations?

My question is how to speed up for loop with a number of different calculations, such as abs, multiplication, sqrt, ^2, cos(), and array indexing? (there is array(i) )

for i=ind1:ind2
    A = ( array(i)*(i+ind2) + array(i)*(i+ind1) ) / sqrt((ind2-i)^2 + (ind1-i)^2);
    A = cos(pi*A); 
    % and so on
end

Is it possible to use some really complicated bsxfun(), repmat()? I am not looking for exact solution, just would like to know if it is possible, when, and which functions might be helpful

Answer 1

[Guillaume]

Your question is far too generic to be able to give a precise answer.

The first mistake people do is operate on an array one element at a time instead of operating on the whole array at once. Other than the fact that you constantly overwrite A, this appears to be the mistake you've made in your example.

%assuming array is a row vector
v = ind1:ind2; %make a vector of the values i iterates over
A = (array .* (v + ind2) + array .*(v + ind1)) ./  hypot(ind2 - v, ind1 - v);
A = cos(pi*A);

Note the use of .* and ./ for elementwise operation. See array vs matrix operations.

For more complicated stuff, bsxfun, repmat, ndgrid, etc. may be useful indeed.

[Dawid Smolen]

Although the question was general, you have helped me. Now it seems like basics, but because of the complicated math, I was confused and couldn't think of simple solution. Thank you