Question

I have given a list of indices, e.g. i = [3 5] and a vector v = 1:6. I need a function f which returns the logical map for the vector v given the indices i, e.g.:

f(i, length(v)) = [0 0 1 0 1 0]

Since I will call this function several million times, I would like to make it as fast as possible. Is there a builtin function which performs this task?

Answer 1

I know I’m late in the game, but I really wanted to find a faster solution which is just as elegant as ismember. And indeed there is one, that employs the undocumented ismembc function:

ismembc(v, i)

Benchmark

N = 7;
i = [3 5];

%// slayton's solution
tic
for ii = 1:1e5
    clear idx;
    idx(N) = false;
    idx(i) = true;
end
toc

%// H.Muster's solution
tic
for ii = 1:1e5
    v = 1:N;
    idx = ismember(v, i);
end
toc

%// Jonas' solution
tic
for ii = 1:1e5
    idx = sparse(i, 1, true, N, 1);
end
toc

%// ismembc solution
tic
for ii = 1:1e5
    v = 1:N;
    idx = ismembc(v, i);
end
toc

Here’s what I got:

Elapsed time is 1.482971 seconds.
Elapsed time is 6.369626 seconds.
Elapsed time is 2.039481 seconds.
Elapsed time is 0.776234 seconds.

Amazingly, ismembc is indeed the fastest!

Edit:
For very large values of N (i.e. when v is a large array), the faster solution is actually slayton’s (and HebeleHododo’s, for that matter). You have quite a variety of strategies to choose from, pick carefully 🙂

Edit by H.Muster:
Here’s are benchmark results including _ismemberoneoutput:

Slayton's solution:
   Elapsed time is 1.075650 seconds.
ismember:
   Elapsed time is 3.163412 seconds.
ismembc:
   Elapsed time is 0.390953 seconds.
_ismemberoneoutput:
   Elapsed time is 0.477098 seconds.

Interestingly, Jonas’ solution does not run for me, as I get an Index exceeds matrix dimensions. error…

Edit by hoogamaphone:
It’s worth noting that ismembc requires both inputs to be numerical, sorted, non-sparse, non-NaN values, which is a detail that could be easily missed in the source documentation.