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I have a matrix A of size Nx2, N is large. I have another vector b of size nx1 and n<<N. I want to filter out those row indices of A, where both columns could contain any 2 elements of b.

For instance, let

A = [1 2;3 4; 5 6]

b = [1,2,5,6]'

Then output of method(A,b) should be

[1,3]'

(i.e. the first and 3rd rows of A contain 2 elements from b, but not the 2nd row.

I am currently using a combination of ismember and find but seems like ismember is not very efficient because my A, as I said, is very large.

Thanks in advance!

EDIT: (some more background on the problem)

The code has about couple dozen functions of which couple of them call ismember within a loop. The overall code takes several hours to execute when N is in O(1e5) and profiling it showed most of the time is consumed by ismember. The whole point of the question is to verify if (i) ismember is specifically inefficient for large scale code and (ii) are there alternatives that could take only a fraction of ismember 's cputime

EDIT 2: Tried alternative suggestion using 'any'. The cpu time was almost identical.

EDIT 3: Solved. Based on my personal experience, it does seem like ismember is inefficient when used repeatedly used within a large loop. So I replaced it with cellfun (since my 'b' is actually a cell array) & bsxfun and saw 25x speedup. Thanks to everyone that chimed in. I learned a lot!

Cedric Wannaz
on 19 Oct 2017

Edited: Cedric Wannaz
on 19 Oct 2017

EDIT: I took 3 more minutes and I profiled a small test case (N=1e7, n=1e2). ISMEMBER is more efficient!

>> all( any( A == permute( b, [3,2,1] ), 3 ), 2 )

ans =

3×1 logical array

1

0

1

Then FIND if you need indices.

And here the version for below 2016b:

all( any( bsxfun( @eq, A, permute( b, [3,2,1] )), 3 ), 2 )

If speed maters much, it may be faster to avoid pages:

>> any( A(:,1) == b.', 2 ) & any( A(:,2) == b.', 2 )

ans =

3×1 logical array

1

0

1

but you'll have to profile all solutions and also ISMEMBER, because our guesses about performance are often wrong.

Cedric Wannaz
on 19 Oct 2017

Moved here:

There may be ways to pre-process a few things, to eliminate the loop, to parallelize, etc. I built a quick test (with n~10) and you can see that working with an expansion/ANY/etc may be as efficient as Andrei's solution for small values of N, but that as soon as N gets larger ISMEMBER becomes more efficient:

Jan
on 19 Oct 2017

Edited: Jan
on 19 Oct 2017

[EDITED Wrong approach:]

You can save some time with calling the internally used C-Mex function:

bs = sort(b); % Omit if b is sorted already!

find(ismembc(A(:,1), bs) & ismembc(A(:,2), bs))

Then b is sorted once only.

Unfortunately ismembc is not documented. It existed at least from Matlab 5.3 to 2016b, but it might be removed from the toolbox in the future.

[EDITED] No, this is slower that ismember. Obviously Matlab uses faster methods now internally.

Jan
on 19 Oct 2017

:-) Thanks, Andrei.

In modern Matlab versions the "ismembc" is replaced by "_ismemberhelper". As other commands starting with an underscore it can be called through builtin also. Then you can omit the error checking and classification of the inputs by:

% b MUST be sorted!

find(builtin('_ismemberhelper', A(:,1), b) & ...

builtin('_ismemberhelper', A(:,2), b));

The speedup with inputs with 1e7 is negligible. This shortcut is only useful, if you process many small problems.

Walter Roberson
on 19 Oct 2017

Andrei Bobrov
on 19 Oct 2017

Edited: Andrei Bobrov
on 19 Oct 2017

all(ismember(A,b),2)

or

diff(A(all(ismember(A,b),2),:),1,2)~=0

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