MATLAB: Generate Random Matrix 0’s,1’s

binary matrixmatrix constraint

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]

Best Answer

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.
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