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

Asked by Jennifer on 30 Mar 2011
Latest activity Commented on by Jennifer on 31 Mar 2011

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.

## Products

Answer by Walter Roberson on 30 Mar 2011
```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)

Walter Roberson on 30 Mar 2011

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

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

Jennifer on 31 Mar 2011

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.

Teja Muppirala on 31 Mar 2011

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 by Todd Flanagan on 31 Mar 2011
```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`