How do I count the number of matching pairs in 2 vectors and use that as colors in a contour plot?

I have 2 vectors A and B. Both are column vectors and both contain 1000 values.

For example:

A=[1,2,5,1,6,2,8,2,9];
B=[3,4,2,3,7,4,5,4,8];

I wish to find out how many times that (A,B) match so that I can create a contour plot of (A,B) which is colour coded in accordance to the number of matching occurrences:

e.g. (1,3) = 2 occurrences (2,4) = 3 occurrences (5,2) = 1 Occurrence ....etc

I know that I need to create a for loop and I was hoping the unique command would work but as yet I have been unable to generate a working code.

Answer 1

[Walter Roberson]

accumarray([A(:), B(:)])

Provided that the values are positive integers. Otherwise,

[bA, mA, nA] = unique(A);
[bB, mB, nB] = unique(B);
accumarray([nA(:), nB(:)])

Then entry (I,J) counts the match bA(I) to bB(J)

[Jennifer]

Thank you for answering. Unfortunately having tried both your methods I get the following error:

??? Error using ==> accumarray

Not enough input arguments.

[Walter Roberson]

Sorry, insert 1 as the second argument, e.g.,

accumarray([A(:), B(:)],1)

[Jennifer]

Brilliant - thank you.

This works with the example I gave above, however with my actual vectors (more than 1500 values) I get the following error message:

??? Error using ==> accumarray

First input SUBS must contain positive integer subscripts.

I have tried rounding the values and also a few other tricks and can't seem to get it to work. It is rather frustrating.

Do you know what might be causing the problem? I can send you the vectors if needed.

Any advice welcome and thanks in advance

[Teja Muppirala]

What Walter wrote should work. You have to feed in nA and nB into accumarray. Are you sure you wrote it correctly?

[bA, mA, nA] = unique(A);

[bB, mB, nB] = unique(B);

accumarray([nA(:), nB(:)],1)

Answer 2

[Todd Flanagan]

A = [1,2,5,1,6,2,8,2,9];
B = [3,4,2,3,7,4,5,4,8];

c = accumarray([A(:), B(:)])

c =

     0     0     2     0     0     0     0     0
     0     0     0     3     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     1     0     0     0     0     0     0
     0     0     0     0     0     0     1     0
     0     0     0     0     0     0     0     0
     0     0     0     0     1     0     0     0
     0     0     0     0     0     0     0     1

looking at unique rows

pairs = unique([A(:), B(:)], 'rows')

pairs =

     1     3
     2     4
     5     2
     6     7
     8     5
     9     8

To find the count for row 1

>> c(1,3)

ans =

     2

If your rows don't contain positive integers, you can still do the problem by converting it to indeces using unique.

Unique can create a vector of the unique elements and also a vector of indeces to reconstruct the original vector based on these values. For example:

>> [bA, mA, nA] = unique(A)

bA =
   1     2     5     6     8     9
mA =
   4     8     3     5     7     9
nA =
   1     2     3     1     4     2     5     2     6

bA(nA) gives you back the original vector but lets you operate in terms of something (indeces) that ensure you are using positive integers.

>> bA(nA)

ans =
    1     2     5     1     6     2     8     2     9

Now to use accumarray:

[bA, mA, nA] = unique(A);
[bB, mB, nB] = unique(B);
accumarray([nA(:), nB(:)],1)

ans =

     0     2     0     0     0     0
     0     0     3     0     0     0
     1     0     0     0     0     0
     0     0     0     0     1     0
     0     0     0     1     0     0
     0     0     0     0     0     1

To find the rows again,

your pairs are now in terms of indeces:

>> pairs = unique([nA(:) nB(:)], 'rows')

pairs =

     1     2
     2     3
     3     1
     4     5
     5     4
     6     6

So, c(1,2) = 2

and the original pair is

>> [bA(1) bB(2)]

ans =

     1     3

[Walter Roberson]

Isn't that what I said? ;-)

[Jennifer]

Thanks guys this is great :)

Now all I got to do is plot A and B in some sort of plot (contour?) coloured in accordance with the number of occurrences that each vector pairing occurs. hrmm.....

[Carlos Goncalves Moreira]

Hi Jennifer,

Did you find a working code to plot these results?

Thanks a lot

[Hassan]

hi, you can use digraph

G=digraph(accumarray([nA(:), nB(:)],1));

Best, HM

Answer 3

[Hassan]

Hi all, The suggested method accumarray([nA(:), nB(:)],1) is good to have counts of pairs in 2D representation. What if I interested in a square matrix, I mean full representation of length n by n?

let's say I have two vectors x=1:10, and y=1:8. accumarray([nA(:), nB(:)],1) will result in 10 by 8 matrix. How can I make the result 10 by 10 with two lines of zeros?

Thanks a lot, HM

[Hassan]

I found the answer... just add a dimension argument next to the 1

 accumarray([nA(:), nB(:)],1,[10 10])