Getting the mapping for a permutation in MATLAB

Question

Say I have two arrays where one is a permutation of the other:

A = [2 1 5 3 7]
B = [7 2 1 3 5]

with no repetitions in either array.

How can I obtain the permutation mapping between both?

E.g. A->B should be:

[2, 3, 5, 4, 1]

which means:

A(1) -> B(2)
A(2) -> B(3)
A(3) -> B(5)
A(4) -> B(4)
A(5) -> B(1)

Update:

Is there a fast vectorized solution that does not use ismember ? In my experience, ismember tends to be slow for very large arrays.

Is it guaranteed that the elements of A and B are unique? — reve_etrange
– reve_etrange, Commented Mar 28, 2012 at 1:24

Nate · Accepted Answer · 2012-03-28 02:33:06Z

19

How about this:

[i a] = sort(A);
[i b] = sort(B);
mapping = b(a)

answered Mar 28, 2012 at 2:33

Nate

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4 Comments

reve_etrange Over a year ago

Speed is about 2x better than ismember.

Nate Over a year ago

Somebody else already did all the hard work optimizing sort. :)

reve_etrange Over a year ago

Apparently it is just a quick sort (so we know who "somebody" is). BTW the performance ratio is about the same across >5 orders of magnitude of array sizes.

Chinasaur Over a year ago

You may get speedup if you sort both vectors in the same call. I believe some versions of Matlab do a better job multithreading in this case? Depending on your hardware, you might also get significantly better speed by sorting in-place, which would require a Mex function.

reve_etrange · Accepted Answer · 2012-03-28 01:22:18Z

7

Use ismember.

[~,idx] = ismember(A,B);

The vector idx will contain indices such that B(idx) == A.

Note that ismember finds the highest indices.

answered Mar 28, 2012 at 1:22

reve_etrange

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Comments

remo · Accepted Answer · 2013-06-17 13:24:13Z

1

You can also use knnsearch, but for not repeated members in both a and b

answered Jun 17, 2013 at 13:24

remo

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Comments

nitin · Accepted Answer · 2012-03-28 00:45:42Z

0

Try this:

for i=1:size(B)
C(:,i) = [i find(B==A(i))]
end

answered Mar 28, 2012 at 0:45

nitin

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2 Comments

reve_etrange Over a year ago

This will cause problems if more than one element of B is equal to an element of A.

yohai Over a year ago

and is less efficient than other solutions

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