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Xfile = $X; # input matrix X of size m x n
Wfile = $W; # original row factor of size m x r
Hfile = $H; # original col factor of size r x n
m = $rows; # no. of rows of X
n = $cols; # no. of cols of X
r = $rank; # rank of factorization
nnz = $nnz; # no. of nonzeros in X
sigma = ifdef ($sigma, 0.01); # variance of Gaussian noise
fmt = ifdef ($fmt, "binary"); # output format

# generate original factors by sampling from a normal(0,1.0) distribution
W = rand(rows = m, cols = r, pdf = "normal", seed = 123);
H = rand(rows = r, cols = n, pdf = "normal", seed = 456);

I = floor(rand(rows = nnz, cols = 1, min = 1, max = m + 0.999999999));
J = floor(rand(rows = nnz, cols = 1, min = 1, max = n + 0.999999999));
X = rand(rows = nnz, cols = 1, pdf = "normal") * sqrt(sigma);
N = table(I, J, X);
T = (N != 0);
X = T * (W %*% H) + T * N;
write(X, Xfile, format = fmt);
write(W, Wfile, format = fmt);
write(H, Hfile, format = fmt);