Generate Random Matrix 0's,1's

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]

[KALYAN ACHARJYA]

I supposed you asked the same question privious, try it yourself, great way of leraning

*Hint

m=3;
n=2;
mat=zeros(m,n);
mat(:,randi(n))=1

Now make the above code for variable cloumn number, not fixed as shown in the above.

[Mohammad Al ja'idi]

i did this solution before but the problem is the location of 1 is always locate at the same column

[John D'Errico]

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]

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

Answer 1

[John D'Errico]

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]

Great .. thank you so much

[madhan ravi]

+1

Answer 2

[Guillaume]

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]

great answer mr. Guillaume

yes i understand that it needs huge memory in order to excute the code. so how can I select only particular number of matrices (not all possibilities). In my following code i suppose 10 possibilities but I always got the 1's on the same column for each matrix as shown below. How can i make the 1's as random distribution between the columns in each matrix

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

--------------------

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

---------------------------------------

[Guillaume]

My code above generates all 59049 possible matrices of size 10x3 in about a 10th of a second on my computer, so it's unclear how it doesn't answer your question.

Once all have been generated you can easily select a subset if you so wish:

%result: matrix generated by above code
matno = 10;
subset = result(:, :, randperm(size(result, 3), matno)); 

[Mohammad Al ja'idi]

great thank you so much

[madhan ravi]

+1

[Mohammad Al ja'idi]

Hello John D'Errico

what about the duplication in the results