How to distribute 100 ones in 100 by 100 matrix randomly in all posibilities

I want to make binary matrix, and distribute 100 ones in it, randomly in all possibilities.

What command I have to use plz help.

Answer 1

[Wayne King]

indices = randi(1e4,100,1);
x = zeros(100,100);
x(indices) = 1;

[Amit]

Hey Thanks Wanyne

Can you please tell me how I can find out the maximum number of possibilities of distributionb by matlab command.

[Wayne King]

well there are 10,000 ways to place the first number, 9,999 ways to place the second, 9,998 ways to place the third, and so on down to 9901, that's a very big product!!! You can use factorial(), but I think you're going to get such a large number here that it will probably blow up and return Inf

nchoosek(1e4,100) gives you the number of ways of choosing 100 out of 10,000 where order is NOT important (that is not what you're asking here, what you're asking is bigger). But even nchoosek(1e4,100) is going to throw a warning because it's so large.

[Amit]

while using above code, I am facing a problem i.e. the mean of same matrix (different one's position inside) is changing by doing it again and again.

[Amit]

can you please tell me another command

[Wayne King]

Amit, if by mean of the matrix, you intend to say mean(x), which gives the mean of the columns, then of course it has to change because you are randomly placing ones, so the locations of the ones in the columns changes.

[Jan]

Using RANDI does not ensure that the indices are unqiue. Therefore you cannot be sure, that you really get 100 ones.

[Amit]

@wayne sorry, it is mean(x(:))

[Walter Roberson]

There are 65208469245472575695415972927215718683781335425416743372210247172869206520770178988927510291340552990847853030615947098118282371982392705479271195296127415562705948429404753632271959046657595132854990606768967505457396473467998111950929802400 different matrices

which is about 6.5 * 10^241

It *is* possible to list them all, if you do not need to store them, but it would take a *very* long time to do the listing.

[Amit]

What command I have to use that gives me exactly 100 ones randomly in 100 by 100 binary matrix

Answer 2

[Jan]

You can add a test to Wayne's method to check if the indices are unique:

go = true;
while go
  indices = randi(1e4,100,1);
  go = numel(unique(inidices)) == 100;
  % Or:
  % go = all(diff(sort(indices)));
end
x = zeros(100,100);
x(indices) = 1;

Another approach, which works since Matlab 2011b:

indices = randperm(1e4, 100);

If this is time-critical, you can try FEX: Shuffle.

[Amit]

@Jan Simon

It still varying

[Walter Roberson]

What do you mean by "it is still varying" ?

Answer 3

[Walter Roberson]

idx = randperm(100*100);
x = false(100,100);      %you said you wanted a _binary_ matrix
x(idx(1:100)) = true;

If you have a new enough version of MATLAB,

idx = randperm(100*100,100);
x = false(100,100);
x(idx) = true;

[Amit]

Thanks It works.