I have an ND array and, for each element in the array, I need to find the index of the largest element in a vector that is below it. I'm doing this maaaany times so I really super extra interested in it being as fast as possible.
I have written a function locate
that I call with some representative example data. (I use arrayfun
to increase the number of times timeit
runs the function to minimize random fluctuations.)
Xmin = 5;
Xmax = 300;
Xn = 40;
X = linspace(Xmin, Xmax, Xn)';
% iters = 1000;
% timeit(@() arrayfun(@(iter) locate(randi(Xmax + 10, 5, 6, 6), X), 1:iters, 'UniformOutput', false))
timeit(@() locate(randi(Xmax + 10, 5, 6, 6), X))
My original version of locate
looked like this:
function indices = locate(x, X)
% Preallocate
indices = ones(size(x));
% Find indices
for ix = 1:numel(x)
if x(ix) <= X(1)
indices(ix) = 1;
elseif x(ix) >= X(end)
indices(ix) = length(X) - 1;
else
indices(ix) = find(X <= x(ix), 1, 'last');
end
end
end
And the fastest version that I can muster looks like this:
function indices = locate(x, X)
% Preallocate
indices = ones(size(x));
% Find indices
% indices(X(1) > x) = 1; % No need as indices are initialized to 1
for iX = 1:length(X) - 1
indices(X(iX) <= x & X(iX + 1) > x) = iX;
end
indices(X(iX) <= x) = length(X) - 1;
end
Can you think of any other way that would be faster?
what you need is basically the 2nd output of histc
[pos,bin]=histc(magic(5),X);
bin(bin==0)=1;