CODEWITHSUNDEEP
matlabmatrixsparse-matrix
OBtli
OBtli

Reputation: 3

Create a random sparse matrix with non-zero columns and rows

Is there is a simple way to ensure that the randomly created sparse matrix have non-zero elements in all rows and columns?

I have tried sprand to create m*n matrix

Matrix=sprand(m,n,0.3)

But there is sometimes that a non-zero row or column is found.

I have also tried to create a matrix by creating a sparse vector as row and add a row after row to the matrix.

Edit: I am looking for a small size matrix 5*5 matrix for rxample

Upvotes: 0

Views: 504

Answers (1)

Stewie Griffin
Stewie Griffin

Reputation: 14939

Create the indices manually:

m = 10;
n = 8;
p = 0.3;

r = repmat(randperm(m), 1, n);
c = repmat(randperm(n), 1, m);
row_idx = r(1:ceil(p*m*n));
col_idx = c(1:ceil(p*m*n));
ran_num = rand(1, ceil(p*m*n));

s = sparse(row_idx, col_idx, ran_num, m, n);
full(s)

    0.1842         0         0         0    0.0133         0    0.0620         0
         0         0         0         0    0.2999         0    0.1967         0
         0         0         0    0.1341         0         0         0    0.0934
         0         0    0.4561         0         0         0         0    0.8949
    0.1017    0.0715         0         0         0         0         0         0
    0.0538    0.7363         0         0    0.3321         0         0         0
         0         0    0.5619    0.2973         0    0.4417         0         0
         0         0         0    0.8972         0    0.5972         0         0
         0         0    0.2425         0         0    0.9954         0    0.7455
         0    0.3074         0         0         0         0    0.2126         0

Test of sparsity:

nnz(s)/numel(s)    
ans =    
    0.3000

Below is a smaller example. It's impossible to have a density lower than 0.5, and dimensions 5x5, and still have a non-zero element in all rows and columns.

m = 5;
n = 5;
p = 0.5;

r = repmat(randperm(m), 1, n);
c = repmat(randperm(n), 1, m);
row_idx = r(1:ceil(p*m*n));
col_idx = c(1:ceil(p*m*n));
ran_num = rand(1, ceil(p*m*n));

s = sparse(row_idx, col_idx, ran_num, m, n);
full(s)

ans =

    1.8078         0         0         0         0
         0         0         0    0.7891         0
         0    1.5096         0         0         0
         0         0         0         0    1.0909
         0         0    1.1130         0         0

Upvotes: 2

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