Making permutations in a matrix

Hi,

I have an nxm matrix. I need to make permutations but the row and coloumn sums must be fixed (only the matrix elements will change).

How can I do that?

Thanks..

Answer 1

[Roger Stafford]

I can only guess at your meaning here of the word 'permutations'. Based on your other similar request at

 http://www.mathworks.com/matlabcentral/answers/75431,

I assume you mean that all matrix entries are to be non-negative integers and that, correspondingly, the permutations are to be considered as among objects for which these are the counts - that is, an arrangement of [5,7,11,4] like objects is considered a "permutation" or rearrangement of [4,7,3,13] objects. (This is not what I would call a true permutation, however.)

With N set to a very large number, the following can approach such a random adjustment in which the row and column sums are preserved with all elements remaining non-negative. Let A be your n x m matrix.

 N = 10000;
 for k = 1:N
   r = randperm(n,2); r1 = r(1); r2 = r(2);
   c = randperm(m,2); c1 = c(1); c2 = c(2);
   d = randi([-min(A(r1,c1),A(r2,c2)),min(A(r1,c2),A(r2,c1))]);
   A([r1,r2],[c1,c2]) = A([r1,r2],[c1,c2]) + [d,-d;-d,d];
 end

At each step this adjusts four elements lying in two columns and two rows so as to preserve row and column sums and such that those elements remain non-negative integers.

(This is a bit crude and cumbersome but it is all I could think of at the moment.)

Answer 2

[Image Analyst]

What is your definition of permute? You mean like shuffle/scramble the columns (each column goes to a different place)? I don't think you can do that, in general, without changing the sums. Look at this matrix

1 2
1 1

There's no way you can permute anything with that without changing either the sum of each column, or the sum of each row. Something is going to change.

Do you have one small example that you can show to demonstrate what you are thinking of?

Answer 3

[Ayse Kazan]

Thank you for the answers. Yes I mean the shuffle. And yes the matrix entries (cells) are non-negative integers. An example;

A = [15 20; 
     10 30; 
     40 30; 
     50 10; 
     15 35]

row sums: 35,40,70,60,50

column sums: 130, 125.

shuffle;

B= [10 25;
    20 20; 
    55 15; 
    40 20; 
    5 45]

row sums: 35,40,70,60,50 (fixed)

column sums: 130, 125 (fixed)

[Image Analyst]

Why do you need this? What is the "use case"? Did you try Roger's code?

[Ayse Kazan]

I need to make shuffles (say N times, like making Bootstrap or Permutation test), then I will make calculations, association analyses like ki-square. This is for my presentation before beginning to write my thesis. This will be like a little example in my presentation.

I met with an error in Roger's code which is;

??? Error using ==> randperm Too many input arguments.

dont know what that is…

[Image Analyst]

Here's Roger's code:

A = [15 20;
  10 30;
  40 30;
  50 10;
  15 35]
sumsAlongRows = sum(A, 2)
sumsAlongColumns = sum(A, 1)
[n, m] = size(A)
N = 10000;
for k = 1:N
  r = randperm(n,2);
  r1 = r(1);
  r2 = r(2);
  c = randperm(m,2);
  c1 = c(1);
  c2 = c(2);
  d = randi([-min(A(r1,c1),A(r2,c2)),min(A(r1,c2),A(r2,c1))]);
  A([r1,r2],[c1,c2]) = A([r1,r2],[c1,c2]) + [d,-d;-d,d];
end
A
sumsAlongRows = sum(A, 2)
sumsAlongColumns = sum(A, 1)

It works fine for me but if you have an old version of MATLAB, you'll have to replace

r = randperm(n,2);

with

r = randperm(n);
r = r(1:2);

and do the same for c.

[Ayse Kazan]

oh super! thank you so much.

yes mine is an old version so I did what so said and it worked!

thanks again. to both Roger and you...

[Payal Verma]

how can i apply it on a image.