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

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Anne
Anne 2011-11-2
评论： Image Analyst 2019-1-24
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.
  1 个评论
the cyclist
the cyclist 2011-11-2
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.

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采纳的回答

Image Analyst
Image Analyst 2011-11-2
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
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Raghwan Chitranshu
Raghwan Chitranshu 2019-1-24
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

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更多回答（4 个）

Sven
Sven 2011-11-2
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
  2 个评论
Sven
Sven 2011-11-2
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.

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Naz
Naz 2011-11-2
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
Anne 2011-11-2
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
Walter Roberson 2011-11-2
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
  1 个评论
Anne
Anne 2011-11-3
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...

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