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

I needed a function like this. Thanks for the post @Daniel!

I worked a little with it because I needed to find several indexes in the same array. I wanted to avoid the overhead of arrayfun (or the like) or calling the function multiple times. So you can pass a bunch of values in range and you will get the indexes in the array.

function idx = findInSorted(x,range)
% Author Dídac Rodríguez Arbonès (May 2018)
% Based on Daniel Roeske's solution:
%   Daniel Roeske 
%   https://github.com/danielroeske/danielsmatlabtools/blob/master/matlab/data/findinsorted.m

    range = sort(range);
    idx = nan(size(range));
    for i=1:numel(range)
        idx(i) = aux(x, range(i));
    end
end

function b = aux(x, lim)
    a=1;
    b=numel(x);
    if lim<=x(1)
       b=a;
    end
    if lim>=x(end)
       a=b;
    end

    while (a+1

I guess you can use a parfor or arrayfun instead. I have not tested myself at what size of range it pays off, though.

Another possible improvement would be to use the previous found indexes (if range is sorted) to decrease the search space. I am skeptical of its potential to save CPU because of the O(log n) runtime.

---

The final function ended up running slightly faster. I used @randomatlabuser 's framework for that:

N = 5e6;    % length of vector
p = 0.99;    % probability
KK = 100;    % number of instances
rntm1 = zeros(KK, 1);    % runtime with ismember
rntm2 = zeros(KK, 1);    % runtime with ismembc
rntm3 = zeros(KK, 1);    % runtime with Daniel's function
for kk = 1:KK
    x = cumsum(rand(N, 1) > p);
    searchfor = x(ceil(4*N/5));

    tic
    range = sort(searchfor);
    idx = nan(size(range));
    for i=1:numel(range)
        idx(i) = aux(x, range(i));
    end

    rntm1(kk) = toc;

    tic
    a=1;
    b=numel(x);
    c=1;
    d=numel(x);
    while (a+1=x(end)
   a=b;
end

while (a+1

It is not a big improvement, but it helps because I need to run several thousand searches.

% Mean of running time
mean([rntm1 rntm2])
% 9.9624e-05  5.6303e-05

% Percentiles of running time
prctile([rntm1 rntm2], [0 25 50 75 100])
% 3.0435e-05  1.0524e-05
% 3.4133e-05  1.2231e-05
% 3.7262e-05  1.3369e-05
% 3.9111e-05  1.4507e-05
%  0.0027426   0.0020301

I hope this can help somebody.

---

EDIT

If there is a significant chance of having exact matches, it pays off to use the very fast built-in ismember before calling the function:

[found, idx] = ismember(range, x);
idx(~found) = arrayfun(@(r) aux(x, r), range(~found));