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

8 views (last 30 days)
Anne on 2 Nov 2011
Commented: Image Analyst on 24 Jan 2019
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 on 2 Nov 2011
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.

Image Analyst on 2 Nov 2011
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
Image Analyst on 24 Jan 2019
It seems like that was solved in this question

Sven on 2 Nov 2011
Try:
% Define your matrix size and randomly pick the number of ones
matSz = [20, 40];
numOnes = randi(matSz(1));
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
##### 2 CommentsShow 1 older commentHide 1 older comment
Sven on 2 Nov 2011
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.

Naz on 2 Nov 2011
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

Anne on 2 Nov 2011
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...

Walter Roberson on 2 Nov 2011
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:
Anne on 3 Nov 2011
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...

### Categories

Find more on Creating and Concatenating Matrices in Help Center and File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by