How to generate a binary matrix with a fixed sum in rows and a changeable sum in columns?

Hello everyone !

i have a binary matrix (M,N) .I want to get sum equal to 1 in each row and in columns sum varies between [1 and 6], the sum of all matrix equal to M.

i will be grateful if you could help me

[Torsten]

You know that M is equal to the sum of the column sums. So one possible structure of the matrix should be easy to imagine.

E.g. if the matrix has 2 columns with: column 1 has sum 2 and column 2 has sum 4, can you think of a 6x2 matrix with these properties ?

[Ideth Kara]

how can i put "1" with different index in columns in order to get sum = 3 in each columns and "1" in each row

[Torsten]

What about

   [1 0
    1 0
    0 1
    0 1
    0 1
    0 1]

?

Do you see how to construct one such matrix ?

Of course, you can permute the rows arbitrarily - the resulting matrix will still fulfill the requirements.

Answer 1

[Bruno Luong]

A=kron(eye(5),ones(3,1));
A=A(randperm(end),randperm(end))

A = 15×5

0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0

sum(A,1)

ans = 1×5

3 3 3 3 3

sum(A,2)

ans = 15×1

1 1 1 1 1 1 1 1 1 1

[Ideth Kara]

it's okay but i want to fix the index of "1" in columns not randomly , can i select the position of "1" in each columns ?

for example

A = 15×5

1 0 0 0 0

1 0 0 0 0

1 0 0 0 0

0 0 1 0 0

0 1 0 0 0

0 0 0 0 0

0 1 0 0 0

0 0 0 0 1

0 0 1 0 0

0 1 0 0 0

:

:

[Bruno Luong]

Of course, but then you know where they (the 1s) are. So just put 1 at the place that YOU fix.

[Ideth Kara]

can you explain it more in the example that you mentioned above?

[Bruno Luong]

The first line create the specific matrix that meet the row/column sum requirements.

The second line permutes rows and columns randomly, create a new random matrix, the sums are invariants under these operations, so the new matrix still meets the sum requirements.