Faster version of find for sorted vectors (MATLAB)

Question

I have code of the following kind in MATLAB:

indices = find([1 2 2 3 3 3 4 5 6 7 7] == 3)

This returns 4,5,6 - the indices of elements in t

Answer 1

ismember will give you all the indexes if you look at the first output:

>> x = [1 2 2 3 3 3 4 5 6 7 7];
>> [tf,loc]=ismember(x,3);
>> inds = find(tf)

inds =

 4     5     6

You just need to use the right order of inputs.

Note that there is a helper function used by ismember that you can call directly:

% ISMEMBC  - S must be sorted - Returns logical vector indicating which 
% elements of A occur in S

tf = ismembc(x,3);
inds = find(tf);

Using ismembc will save computation time since ismember calls issorted first, but this will omit the check.

Note that newer versions of matlab have a builtin called by builtin('_ismemberoneoutput',a,b) with the same functionality.

---

Since the above applications of ismember, etc. are somewhat backwards (searching for each element of x in the second argument rather than the other way around), the code is much slower than necessary. As the OP points out, it is unfortunate that [~,loc]=ismember(3,x) only provides the location of the first occurrence of 3 in x, rather than all. However, if you have a recent version of MATLAB (R2012b+, I think), you can use yet more undocumented builtin functions to get the first an last indexes! These are ismembc2 and builtin('_ismemberfirst',searchfor,x):

firstInd = builtin('_ismemberfirst',searchfor,x);  % find first occurrence
lastInd = ismembc2(searchfor,x);                   % find last occurrence
% lastInd = ismembc2(searchfor,x(firstInd:end))+firstInd-1; % slower
inds = firstInd:lastInd;

Still slower than Daniel R.'s great MATLAB code, but there it is (rntmX added to randomatlabuser's benchmark) just for fun:

mean([rntm1 rntm2 rntm3 rntmX])    
ans =
   0.559204323050486   0.263756852283128   0.000017989974213   0.000153682125682

Here are the bits of documentation for these functions inside ismember.m:

% ISMEMBC2 - S must be sorted - Returns a vector of the locations of
% the elements of A occurring in S.  If multiple instances occur,
% the last occurrence is returned

% ISMEMBERFIRST(A,B) - B must be sorted - Returns a vector of the
% locations of the elements of A occurring in B.  If multiple
% instances occur, the first occurence is returned.

There is actually reference to an ISMEMBERLAST builtin, but it doesn't seem to exist (yet?).