def _rvs_helper(self): num_samples = 10000 xs = gauss(0, 1).rvs((num_samples, 3)) xs = divide(xs, reshape(norm(xs, 1), (num_samples, 1))) pvalues = self.pdf(xs, normalize=False) fmax = self.pdf_max(normalize=False) return xs[uniform(0, fmax).rvs(num_samples) < pvalues]
def _rvs_helper(self):
num_samples = 10000
xs = gauss(0, 1).rvs((num_samples, 3))
xs = divide(xs, reshape(norm(xs, 1), (num_samples, 1)))
pvalues = self.pdf(xs, normalize=False)
fmax = self.pdf_max(normalize=False)
return xs[uniform(0, fmax).rvs(num_samples) < pvalues]
def GMM(data, k, dim): # Initializing pi, mu and Sigma pi = [1.0/k]*k mu = [] sigma = [] N = len(data) for x in xrange(k): mu.append(ease * (np.random.rand(dim) - 0.5)) cov = 4 * (np.random.rand(dim, dim) - 0.5) cov = np.dot(cov.T, cov) sigma.append(cov) while True: # Estimating Expectation gamma = np.empty(shape=[0, N]) for x in xrange(k): # print sigma[x] Normal= gauss(mean=mu[x], cov=sigma[x]) N_n = pi[x] * Normal.pdf(data) gamma = np.append(gamma, N_n.reshape(1, N), axis=0) print "Shape of the gamma:", np.shape(gamma) for x in xrange(np.shape(gamma)[1]): # print gamma[:,x], gamma[:,x] = gamma[:,x] / np.sum(gamma[:,x]) # print gamma[:,x] # Maximizing Expectation mu = np.dot(gamma, data) for x in xrange(k): N_k = np.sum(mu[x]) mu[x] = mu[x] / N_k pi[x] = N_k / N cov = data - [mu[x]]*N for i in xrange(len(cov)): dummy = np.multiply(np.outer(cov[i], cov[i]), gamma[x][i]) if not is_pos_def(dummy): print "BETA: One of the included matrices is not positive definite!!!" # cov = np.array([np.multiply(np.outer(cov[i], cov[i]), gamma[x][i]) for i in xrange(len(cov))]) cov = np.sum([np.multiply(np.outer(cov[i], cov[i]), gamma[x][i]) for i in xrange(len(cov))], axis=0) # print cov, np.shape(cov) if not is_pos_def(cov): print "BETA: This is not positive definite!!!" sigma[x] = cov print "Shape of sigma", np.shape(sigma)
# Create Original Data
time = np.linspace(0, 1, 101)
M = time.size
N = 30
lam = 0.001
center = np.array([.35, .5, .65])
center2 = np.array([4, 3.7, 4])
sd1 = .05
gam_sd = 8
num_comp = 5
f_orig = np.zeros((M, N * center.size))
omega = 2 * np.pi
cnt = 0
for ii in range(0, center.size):
tmp = gauss(loc=center[ii], scale=.075)
for jj in range(0, N):
f_orig[:, cnt] = normal(center2[ii], sd1) * tmp.pdf(time)
cnt += 1
q_orig = fs.f_to_srsf(f_orig, time)
y_orig = np.ones(q_orig.shape[1], dtype=int)
y_orig[N:2*N] = 2
y_orig[2*N:3*N] = 3
f = np.zeros((M, f_orig.shape[1]))
q = np.zeros((M, f_orig.shape[1]))
cnt = 0
gam_orig = fs.rgam(M, gam_sd, 3*N)
for ii in range(0, center.size):
for ii in range(0, N):