/** * 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); }