How to generate square zero one matrix with specific characteristics

How to generate square zero one matrix to satisfy this condition ( number of ones/ number of rows ^2)=0.7 or 0.6,.... Any number from 0 to 1

Answer 1

[BhaTTa]

To generate a square matrix of zeros and ones such that the proportion of ones to the total number of elements is a specified value (e.g., 0.7 or 0.6), you can follow these steps in MATLAB:

1. Determine the size of the matrix. Let's say you want an n×nn \times nn×n matrix.
2. Calculate the total number of elements in the matrix, which is n2n^2n2.
3. Determine the number of ones required based on the proportion. For a proportion ppp, the number of ones should be round(p×n2)\text{round}(p \times n^2)round(p×n2).
4. Generate a matrix with the required number of ones and zeros.
5. Randomly shuffle the elements to ensure the ones and zeros are randomly distributed.

Here's a MATLAB script that accomplishes these steps:

function matrix = generateBinaryMatrix(n, proportion)
    % Input:
    % n - Size of the square matrix (n x n)
    % proportion - Desired proportion of ones (between 0 and 1)
    
    % Calculate the total number of elements
    totalElements = n^2;
    
    % Calculate the number of ones needed
    numOnes = round(proportion * totalElements);
    
    % Create a vector with the required number of ones and zeros
    matrixVector = [ones(1, numOnes), zeros(1, totalElements - numOnes)];
    
    % Shuffle the vector to randomize the placement of ones and zeros
    shuffledVector = matrixVector(randperm(totalElements));
    
    % Reshape the vector into an n x n matrix
    matrix = reshape(shuffledVector, n, n);
end

% Example usage:
n = 5; % Size of the matrix
proportion = 0.7; % Proportion of ones
binaryMatrix = generateBinaryMatrix(n, proportion);

% Display the matrix
disp(binaryMatrix);