how do I generate a binary matrix with specified number of 'ones' in each row & column?

Is there any algorithm to do that?

[James Tursa]

Please give a small example.

[nafila aytija]

H=[1 1 1 0 0 1 1 0 0 0 1 0; 1 1 1 1 1 0 0 0 0 0 0 1;0 0 0 0 0 1 1 1 0 1 1 1; 1 0 0 1 0 0 0 1 1 1 0 1; 0 1 0 1 1 0 1 1 1 0 0 0; 0 0 1 0 1 1 0 0 1 1 1 0]; Each column has 3 ones and each row has 6 ones....

Answer 1

[Walter Roberson]

Because the number might be 1, this process is at least as difficult as the n- Rooks puzzle, the task of placing n chess rooks on a n x n board so that they cannot attack each other. You can find more information about the better studied n-Queens problem (diagonals have to be paid attention to) here

[nafila aytija]

But isn't it suppose to be for a square matrix? what if I want to generate a 4*6 matrix with 2 ones in each column and 4 ones in each row?

[Roger Stafford]

That would be impossible Nafila! Two ones in each column with six columns add up to a total of twelve ones, whereas four ones in each row with four rows add up to a total of sixteen ones. That can't be done.

[Walter Roberson]

One thing you have not made clear is whether the task is to generate one such matrix at random, or if the task is to generate all such matrices given the parameters of size and number for row and column?

Answer 2

[KSSV]

If you want a matrix where positions of 0, 1 are random. You may try round(rand(m,n)).

[Walter Roberson]

That will often not have the specified number of 1's in each row and column.

[nafila aytija]

yes....random will generate the random number of bits.not the specified ones......

Answer 3

[Image Analyst]

I think you might mean this:

% Specify 3 1's in each row.
numOnes = 3
% Create a 10 by 10 matrix of false/0's.
rows = 10;
columns = 15;
binaryMatrix = false(rows, columns);
% Go down row by row finding positions for numOnes 1's and assign them
for row = 1 : rows
  % Get locations in this row.
  oneLocations = randperm(columns, numOnes)
  % Assign true/1 to those columns.
  binaryMatrix(row, oneLocations) = true;
end
% Print final result to command window
binaryMatrix

[nafila aytija]

Thank you,I was actually trying to do the same thing. But, here, I am getting only rows with 3 ones,but columns are not giving the desired number of ones I want... Any idea would be appreciated. Thank you !

[Image Analyst]

Well, how many ones do you want in a row? I just picked 3 but it could be any number up to and including the total number of columns in a row. You could even have numOnes be an array where you change the number of 1's in a row on a row-by-row basis.

[Image Analyst]

Oh wait, reading your comment to Walter it looks like you need the number in each column also to be a specified number. In that case, this code will not guarantee that since they're scrambled on a row-by-row basis and does not take other rows into account so you could have any number from 0 to rows in any given column, not necessarily the specified number you want.

[Image Analyst]

By the way, for the special case of a square matrix where you want the same number in the rows and columns, you can do that. The concept is called "Latin Square" - you might want to research it.