Sparse Matrix with Same number of non-zero values in each column

I want to modify the following function. Right now the function takes n (size of matrix) and outputs a sparse matrix with numbers at random lcations, where each column adds up to 1.

I want the function to: take in n and k, where n is the size of matrix, and k is the number of non-zero elements in each column. Each column still needs to add up to 1. So each non-zero value will be 1/k, and each column will have k non-zero elements. The number of non-zero elements is the same, but the location is randomized. I have attached a photo example of what I want.

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function A = createMatrix(n)
A = sparse(n,n);
maxnel = min(16,n);

for i = 1:n
    nel = floor(rand(1)*maxnel);
    if(nel == 0)
    val = 0;
    else
    val = 1/nel;
    end
    
for j = 1:nel
    col_ind = ceil(rand(1)*n);
    while(A(col_ind,i) ~= 0)
        col_ind = ceil(rand(1)*n);
    end
A(col_ind,i) = val;
end

end

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[Maxine Killingsworth]

Thank you!

Answer 1

[Chunru]

A = createMatrix(8, 4);
full(A)

ans = 8×8

0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0 0.2500 0.2500 0.2500 0 0.2500 0 0 0.2500 0 0 0.2500 0.2500 0 0 0.2500 0 0 0.2500 0 0 0 0 0 0.2500 0 0 0.2500 0 0.2500 0.2500 0 0.2500 0.2500 0 0 0.2500 0.2500 0.2500 0.2500 0 0.2500 0 0 0 0 0 0.2500 0 0 0.2500 0 0.2500 0 0.2500 0

function A = createMatrix(n, k)
A = sparse(n,n);
for i=1:n
    A(randperm(n, k), i) = 1/k;
end
end