How to create a random binary matrix with equal number of ones in each column?

Hi All,

I want to create a random binary matrix with equal number of ones in each column.

Appreciate if anyone have an idea to implement this in Matlab.

Thanks.

[the cyclist]

To avoid folks providing answers, and then you saying, "No, that's not what I meant", can you please provide more detail? For example, should each column have equal numbers of zeros and ones? What if there are an odd number of rows? Etc.

Answer 1

[Image Analyst]

This is how I did it:

% Set up parameters.
rows = 10;
columns = 15;
onesPerColumn = 4;
% Initialize matrix.
m = zeros(rows, columns, 'int32')

for col = 1 : columns
  % Get random order of rows.
  randRows = randperm(rows);
  % Pick out "onesPerColumn" rows that will be set to 1.
  rowsWithOne = randRows(1:onesPerColumn);
  % Set those rows only to 1 for this column.
  m(rowsWithOne, col) = 1;
end
% Display m
m

[Anne]

This works fine for me. Thanks a lot....really appreciate it.

[Raghwan Chitranshu]

hello,

How if I also want to keep number of ones in rows to be equal.

what changes shall I perform .

can you help in this

[Image Analyst]

It seems like that was solved in this question

Answer 2

[Sven]

Try:

% Define your matrix size and randomly pick the number of ones
matSz = [20, 40];
numOnes = randi(matSz(1));
% Make your matrix
myMat = false(matSz);
for i = 1:matSz(2)
    myMat(randperm(matSz(1),numOnes), i) = true;
end
% Check that all went as planned
sum(myMat,1)==numOnes

[Anne]

I tried this method, but could not get what I was expecting...

[Sven]

Really? The variable "myMat" is your answer. The last line that prints out a series of ones was just confirmation that all of your columns had "numOnes" true elements in them.

Setting

matSz = [10, 15];

and

numOnes = 4;

gives the exact same output as what you agreed with below.

Answer 3

[Naz]

Since it's a RANDOM matrix, you are not guaranteed to have the same amount of one's and zero's (at least it seems logical to me). In order to get about 1/2 probability you need large matrix. You can try this:

a=rand(1000,1000);
a=round(a);

Check out help file for rand vs. randn

Answer 4

[Anne]

I also need to make sure that this matrix is invertible.

What I currently do is check det(A)=0 & rank(A)<3 using a while loop. But sometimes the while loop runs infinitely and the script does not respond.

Is there any other way to check for non-singular matrices?

Thanks again...

Answer 5

[Walter Roberson]

Anne, you need to define what it means to take an inverse for you binary matrix. You can treat the binary matrix as being composed of the real numbers 0 and 1 and then do an arithmetic inverse on the array, ending up with a non-binary array. Or you can treat the binary matrix as being composed of boolean values over a field with the '*' being equivalent to 'or' and '+' being equivalent to xor, and the task is then to find a second binary matrix such that matrix multiplication using those operations produces the identity matrix.

If you want the inverse to be a binary matrix instead of a real-valued matrix, please see this earlier Question:

http://www.mathworks.com/matlabcentral/answers/16990-galois-field-to-find-the-inverse-of-a-binary-matrix

[Anne]

I was able to figure this out. Now I'm using GF to find the inverse and to check for invertibility I'm using rank(gf(A))=n

this seems to work...

thanks for your answer...