/**
* Randomly sample a matrix from Wishart Distribution with the given parameters.
*
* @param scale scale parameter for Wishart Distribution.
* @param df degree of freedom for Wishart Distribution.
* @return the sample randomly drawn from the given distribution.
*/
protected DenseMatrix wishart(DenseMatrix scale, double df) {
DenseMatrix A = scale.cholesky();
if (A == null) return null;
int p = scale.numRows();
DenseMatrix z = new DenseMatrix(p, p);
for (int i = 0; i < p; i++) {
for (int j = 0; j < p; j++) {
z.set(i, j, Randoms.gaussian(0, 1));
}
}
SparseVector y = new SparseVector(p);
for (int i = 0; i < p; i++) y.set(i, Randoms.gamma((df - (i + 1)) / 2, 2));
DenseMatrix B = new DenseMatrix(p, p);
B.set(0, 0, y.get(0));
if (p > 1) {
// rest of diagonal:
for (int j = 1; j < p; j++) {
SparseVector zz = new SparseVector(j);
for (int k = 0; k < j; k++) zz.set(k, z.get(k, j));
B.set(j, j, y.get(j) + zz.inner(zz));
}
// first row and column:
for (int j = 1; j < p; j++) {
B.set(0, j, z.get(0, j) * Math.sqrt(y.get(0)));
B.set(j, 0, B.get(0, j)); // mirror
}
}
if (p > 2) {
for (int j = 2; j < p; j++) {
for (int i = 1; i <= j - 1; i++) {
SparseVector zki = new SparseVector(i);
SparseVector zkj = new SparseVector(i);
for (int k = 0; k <= i - 1; k++) {
zki.set(k, z.get(k, i));
zkj.set(k, z.get(k, j));
}
B.set(i, j, z.get(i, j) * Math.sqrt(y.get(i)) + zki.inner(zkj));
B.set(j, i, B.get(i, j)); // mirror
}
}
}
return A.transpose().mult(B).mult(A);
}
