Generate Random Matrix 0's,1's

Mohammad Al ja'idi (view profile)

on 13 Jun 2019
Latest activity Commented on by Mohammad Al ja'idi

Mohammad Al ja'idi (view profile)

on 14 Jun 2019
Accepted Answer by John D'Errico

John D'Errico (view profile)

clould you please assist me to solve the following question:
I need to get random of (0,1) matrices with size (n*m) with the following constraints:
• Each row has only one (1) and the other values are (0's)
as in the following example:
Example :: for matrix (3*2) as we see we have only one (1) in each row and the other columns are 0's
[1 0 0
1 0 0]
---------
[1 0 0
0 1 0]
---------
[1 0 0
0 0 1]
--------
[0 1 0
1 0 0]
----------
[0 1 0
0 1 0]
---------
[0 1 0
0 0 1]
--------
[0 0 1
1 0 0]
--------
[0 0 1
0 1 0]
--------
[0 0 1
0 0 1]

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Mohammad Al ja'idi (view profile)

on 13 Jun 2019
i did this solution before but the problem is the location of 1 is always locate at the same column
John D'Errico

John D'Errico (view profile)

on 13 Jun 2019
I MIGHT answer, except your question is inconsistent. Are you looking for random matrices, or ALL POSSIBILITIES? You say both, in different places.
Note that there are m^n possible such matrices, given a matrix sixze of n rows, m columns. Do you want to create all of them? or only some, at random?

Mohammad Al ja'idi (view profile)

on 13 Jun 2019
Hello mr. John D'Errico
yes i need only some of them at random distribution for 1's which each row has only one (1) and the rest are 0's, this is my code which I suppose 10 random matrices, but the problem that the 1's are always on the same column, how can i make the 1's distributed randomly.
matno = 10; % the number of random possiblities
rows=10;
columns=3;
matrices = zeros(rows,columns,matno);
for i=1:matno
matrices(:,randi(columns),i)=1;
end

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Answer by John D'Errico

John D'Errico (view profile)

on 13 Jun 2019
Edited by John D'Errico

John D'Errico (view profile)

on 13 Jun 2019

Easy enough.
matno = 10; % the number of random possiblities
rows=10;
columns=3;
Now we want to create a matrix of size (rows,columns,matno), such that each row has exactly one element that is 1, and the placement of that 1 is random. This is most simply done by creating a matrix of size (matno*rows,columns), where each of those rows has exactly one true element.
The location of those 1's will be:
cloc = randi(columns,[matno*rows,1]);
matrices = zeros(matno*rows,columns);
matrices(sub2ind([matno*rows,columns],(1:(matno*rows))',cloc)) = 1;
matrices = permute(reshape(matrices,matno,rows,columns),[2 3 1]);
matrices
matrices(:,:,1) =
0 0 1
0 0 1
1 0 0
0 1 0
0 1 0
1 0 0
1 0 0
0 0 1
0 0 1
1 0 0
matrices(:,:,2) =
0 1 0
1 0 0
1 0 0
0 0 1
1 0 0
0 0 1
1 0 0
0 1 0
1 0 0
0 0 1
matrices(:,:,3) =
1 0 0
1 0 0
1 0 0
0 1 0
0 1 0
1 0 0
1 0 0
0 1 0
0 0 1
1 0 0
matrices(:,:,4) =
0 1 0
0 0 1
0 1 0
0 1 0
0 0 1
0 0 1
0 1 0
0 1 0
0 1 0
1 0 0
matrices(:,:,5) =
1 0 0
1 0 0
0 1 0
0 0 1
1 0 0
1 0 0
0 0 1
0 1 0
0 1 0
0 1 0
matrices(:,:,6) =
0 0 1
0 0 1
1 0 0
1 0 0
0 0 1
0 1 0
0 1 0
1 0 0
0 0 1
0 1 0
matrices(:,:,7) =
1 0 0
0 0 1
1 0 0
0 1 0
0 0 1
1 0 0
0 0 1
0 0 1
0 1 0
1 0 0
matrices(:,:,8) =
0 0 1
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
1 0 0
0 1 0
0 1 0
0 0 1
matrices(:,:,9) =
0 0 1
1 0 0
0 0 1
1 0 0
1 0 0
0 1 0
0 1 0
0 0 1
0 0 1
1 0 0
matrices(:,:,10) =
1 0 0
1 0 0
1 0 0
0 0 1
0 1 0
0 1 0
1 0 0
0 1 0
1 0 0
0 1 0
Easy. Almost trivial. To prove that the result has exactly one 1 in each row, this next result should be a 10x10 array of 1's.
squeeze(sum(matrices,2))
ans =
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
As it is.

Mohammad Al ja'idi (view profile)

on 14 Jun 2019
Great .. thank you so much

on 14 Jun 2019
+1

Guillaume (view profile)

on 13 Jun 2019

Note that a 3x2 is a matrix with 3 rows and 2 columns, not the other way round.
Bearing in mind that there are n^m such matrices of size m x n, which will quickly get out of hand as n and particularly m grows, here is one way:
m = 4; %number of ROWS. demo data
n = 5; %number of COLUMNS. demo data
columns = cell(1, m); %1 x m array to store all possible column combinations
[columns{:}] = ndgrid(1:n); %cartesian product of 1:n across all rows
columns = cat(m+1, columns{:}); %store as one matrix
pages = repmat(1:n^m, 1, m); %matching page for each element of columns
rows = repelem(1:m, n^m); %matching row for each element of columns
result = zeros(m, n, n^m); %destination matrix
result(sub2ind(size(result), rows(:), columns(:), pages(:))) = 1;
result is a m x n x (n^m) matrix where result(:, :, p) is one of your desired matrix.
Note that you could use Matt J's ndSparse function to build a sparse matrix (using the same rows(:), columns(:), pages(:) arguments) instead of a full matrix. It would be a lot more memory efficient.

Mohammad Al ja'idi (view profile)

on 14 Jun 2019
great thank you so much