def _step_M(self,points,log_resp):
"""
In this step the algorithm updates the values of the parameters (means, covariances,
alpha, beta, nu).
Parameters
----------
points : an array (n_points,dim)
log_resp: an array (n_points,n_components)
an array containing the logarithm of the responsibilities.
"""
n_points,dim = points.shape
resp = np.exp(log_resp)
# Convenient statistics
N = np.sum(resp,axis=0) + 10*np.finfo(resp.dtype).eps #Array (n_components,)
X_barre = 1/N[:,np.newaxis] * np.dot(resp.T,points) #Array (n_components,dim)
S = _full_covariance_matrices(points,X_barre,N,resp,self.reg_covar,self.n_jobs)
#Parameters update
self.alpha = np.asarray([1.0 + N,
self.alpha_0 + np.hstack((np.cumsum(N[::-1])[-2::-1], 0))]).T
self.alpha += np.asarray([-self.pypcoeff * np.ones(self.n_components),
self.pypcoeff * np.arange(self.n_components)]).T
self.beta = self.beta_0 + N
self.nu = self.nu_0 + N
# Weights update
for i in range(self.n_components):
if i==0:
self.log_weights[i] = psi(self.alpha[i][0]) - psi(np.sum(self.alpha[i]))
else:
self.log_weights[i] = psi(self.alpha[i][0]) - psi(np.sum(self.alpha[i]))
self.log_weights[i] += self.log_weights[i-1] + psi(self.alpha[i-1][1]) - psi(self.alpha[i-1][0])
# Means update
means = self.beta_0 * self._means_prior + N[:,np.newaxis] * X_barre
self.means = means * np.reciprocal(self.beta)[:,np.newaxis]
self.means_estimated = self.means
# Covariance update
for i in range(self.n_components):
diff = X_barre[i] - self._means_prior
product = self.beta_0 * N[i]/self.beta[i] * np.outer(diff,diff)
self._inv_prec[i] = self._inv_prec_prior + N[i] * S[i] + product
det_inv_prec = np.linalg.det(self._inv_prec[i])
self._log_det_inv_prec[i] = np.log(det_inv_prec)
self.cov[i] = self._inv_prec[i] / self.nu[i]
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