Thread Subject:

nchoosek all pairwise combinations

Hello,

There is a vector

A=['a', 'b', 'c', 'd','e']

I would like to make a square matrix of all paiwise interactions of this vector:


a b c d e
a aa ba ca da ea
b ab bb cb db eb
c ac bc cc dc ec
d ad bd cd dd ed
e ae bd ce de ee

However, nchoosek allow me to create only half of this matrix. Is there any function to make all these possible interactions within "A"?

Thanks,
Jerry

On 11/26/2012 10:12 PM, Jerry wrote:
> Hello,
>
> There is a vector
>
> A=['a', 'b', 'c', 'd','e']
>
> I would like to make a square matrix of all paiwise interactions of this vector:
>
>
> a b c d e
> a aa ba ca da ea
> b ab bb cb db eb
> c ac bc cc dc ec
> d ad bd cd dd ed
> e ae bd ce de ee
>
> However, nchoosek allow me to create only half of this matrix.
>Is there any function to make all these possible interactions within "A"?
>

Much easier to do this when your 'a','b', etc... are numerics, not
chars or strings.

What is the reason of using strings for this?
--Nasser

On 11/26/2012 10:12 PM, Jerry wrote:
> Hello,
>
> There is a vector
>
> A=['a', 'b', 'c', 'd','e']
>
> I would like to make a square matrix of all paiwise interactions of this vector:
>
>
> a b c d e
> a aa ba ca da ea
> b ab bb cb db eb
> c ac bc cc dc ec
> d ad bd cd dd ed
> e ae bd ce de ee
>
> However, nchoosek allow me to create only half of this matrix. Is there any function
>to make all these possible interactions within "A"?
>

can't you just make a loop?

---------------------
clear all
A = ['a', 'b', 'c', 'd','e'];
N = size(A,2);
B = cell(N);

for i = 1:N
     for j = 1:N
         B(i,j) = {strcat(A(j),A(i))};
     end
end
--------------------

B =

     'aa' 'ba' 'ca' 'da' 'ea'
     'ab' 'bb' 'cb' 'db' 'eb'
     'ac' 'bc' 'cc' 'dc' 'ec'
     'ad' 'bd' 'cd' 'dd' 'ed'
     'ae' 'be' 'ce' 'de' 'ee'


--Nasser

On 11/27/2012 2:40 AM, Nasser M. Abbasi wrote:

>
> can't you just make a loop?
>
> ---------------------
> clear all
> A = ['a', 'b', 'c', 'd','e'];
> N = size(A,2);
> B = cell(N);
>
> for i = 1:N
> for j = 1:N
> B(i,j) = {strcat(A(j),A(i))};
> end
> end
> --------------------
>
> B =
>
> 'aa' 'ba' 'ca' 'da' 'ea'
> 'ab' 'bb' 'cb' 'db' 'eb'
> 'ac' 'bc' 'cc' 'dc' 'ec'
> 'ad' 'bd' 'cd' 'dd' 'ed'
> 'ae' 'be' 'ce' 'de' 'ee'
>

Another option

--------------------------
clear all
A = ['a', 'b', 'c', 'd','e'];
L = 1:size(A,2);
B = A(allcomb(L,L));
Z = arrayfun(@(i) {strcat(B(i,1),B(i,2))},1:length(B));
reshape(Z,5,5)
--------------------------

which gives the same answer as above

Used allcomb() in
http://www.mathworks.com/matlabcentral/fileexchange/10064

--Nasser

"Jerry " <jerrycholo@gmail.com> wrote in message <k91ej5$bp5$1@newscl01ah.mathworks.com>...
> Hello,
>
> There is a vector
>
> A=['a', 'b', 'c', 'd','e']
>
> I would like to make a square matrix of all paiwise interactions of this vector:
>
>
> a b c d e
> a aa ba ca da ea
> b ab bb cb db eb
> c ac bc cc dc ec
> d ad bd cd dd ed
> e ae bd ce de ee
>
> However, nchoosek allow me to create only half of this matrix. Is there any function to make all these possible interactions within "A"?
>
> Thanks,
> Jerry

There are many ways to achieve such a matrix, but you should think about how you would store your data. Do you really want a character matrix?

A very easy way to obtain the interactions would be using NDGRID

A = 'abcde'
[B1, B2] = ndgrid(A)

which stores the interactions in two separate yet related matrices ...
It all depends on what you want to do with the result!

~ Jos

On 11/27/2012 3:40 AM, Jos (10584) wrote:

> A very easy way to obtain the interactions would be using NDGRID
>
> A = 'abcde'
> [B1, B2] = ndgrid(A)
>
> which stores the interactions in two separate yet related matrices ...
> It all depends on what you want to do with the result!
>
> ~ Jos
>

Yes, good, but the problem is that the result are
all one long string now (in B1 and B2) and there will need to be much more
work done to go from those to the final result the OP wanted,
which is a cell matrix of only 2 chars/per string in each entry.

--Nasser

"Nasser M. Abbasi" <nma@12000.org> wrote in message <k922jf$sn9$1@speranza.aioe.org>...
> On 11/27/2012 3:40 AM, Jos (10584) wrote:
>
> > A very easy way to obtain the interactions would be using NDGRID
> >
> > A = 'abcde'
> > [B1, B2] = ndgrid(A)
> >
> > which stores the interactions in two separate yet related matrices ...
> > It all depends on what you want to do with the result!
> >
> > ~ Jos
> >
>
> Yes, good, but the problem is that the result are
> all one long string now (in B1 and B2) and there will need to be much more
> work done to go from those to the final result the OP wanted,
> which is a cell matrix of only 2 chars/per string in each entry.
>
> --Nasser
>
>

I did not see the word cell matrix in the OP message ...

but "much more work" is rather overstated:

A = 'abcde'
[B1, B2] = ndgrid(A)
M = reshape(cellstr([B1(:) B2(:)]),5,5)

~ Jos

On 11/27/2012 4:29 AM, Jos (10584) wrote:

>
> I did not see the word cell matrix in the OP message ...
>

Well, they are characters and need to be in a 'matrix',
so I assumed it has to be a cell array.


> but "much more work" is rather overstated:
>
> A = 'abcde'
> [B1, B2] = ndgrid(A)
> M = reshape(cellstr([B1(:) B2(:)]),5,5)
>

Nice. I did not know about cellstr. That is definitly
better. 2 lines shorter than mine :)

--Nasser

"Nasser M. Abbasi" <nma@12000.org> wrote in message
> Nice. I did not know about cellstr. That is definitly
> better. 2 lines shorter than mine :)

... but your code uses my function ALLCOMB which gives you lots of credits ;-)

~ Jos

On 11/27/2012 4:37 AM, Jos (10584) wrote:
> "Nasser M. Abbasi" <nma@12000.org> wrote in message
>> Nice. I did not know about cellstr. That is definitly
>> better. 2 lines shorter than mine :)
>
> ... but your code uses my function ALLCOMB which gives you lots of credits ;-)
>

I had harder time since I did not know about cellstr.

Using cellstr, now it is like this (with the use of allcomb (nice function))

------------------------------
A=['a', 'b', 'c', 'd','e']; N=size(A,2);
reshape(cellstr(A(allcomb(1:N,1:N))),N,N)
--------------------------------

     'aa' 'ba' 'ca' 'da' 'ea'
     'ab' 'bb' 'cb' 'db' 'eb'
     'ac' 'bc' 'cc' 'dc' 'ec'
     'ad' 'bd' 'cd' 'dd' 'ed'
     'ae' 'be' 'ce' 'de' 'ee'

I dont know how I overlooked cellstr. Very useful.


--Nasser

"Nasser M. Abbasi" <nma@12000.org> wrote in message <k925db$3ms$1@speranza.aioe.org>...
> On 11/27/2012 4:37 AM, Jos (10584) wrote:
> > "Nasser M. Abbasi" <nma@12000.org> wrote in message
> >> Nice. I did not know about cellstr. That is definitly
> >> better. 2 lines shorter than mine :)
> >
> > ... but your code uses my function ALLCOMB which gives you lots of credits ;-)
> >
>
> I had harder time since I did not know about cellstr.
>
> Using cellstr, now it is like this (with the use of allcomb (nice function))
>
> ------------------------------
> A=['a', 'b', 'c', 'd','e']; N=size(A,2);
> reshape(cellstr(A(allcomb(1:N,1:N))),N,N)
> --------------------------------
>
> 'aa' 'ba' 'ca' 'da' 'ea'
> 'ab' 'bb' 'cb' 'db' 'eb'
> 'ac' 'bc' 'cc' 'dc' 'ec'
> 'ad' 'bd' 'cd' 'dd' 'ed'
> 'ae' 'be' 'ce' 'de' 'ee'
>
> I dont know how I overlooked cellstr. Very useful.
>
>
> --Nasser
>
>

Note that ALLCOMB and its sibling COMBN are "clever" wrappers around NDGRID.

~ Jos