def compute_gamma(self,A,E,zz_tn_prev,zz_tn,gamma_tn):
"""
Replaces the current value of the gamma parameters with
its updated value, and returns the mean square difference between the two.
"""
# This is the main bottleneck of the code.
# Would be faster if:
# - implemented in C
# - roots() was also implemented in C
d_z = len(gamma_tn)
product_matrix_matrix(zz_tn_prev,A.T,self.mat_d_z_d_z)
product_matrix_matrix(A,self.mat_d_z_d_z,self.mat_d_z_d_z2)
getdiag(self.mat_d_z_d_z2,self.AzzA_prev)
G = diag(zz_tn)+2*self.gamma_prior_beta
H = self.AzzA_prev
a1 = 2.0*(self.gamma_prior_alpha+1.0)
a2 = (4.0*self.gamma_prior_alpha+5.0)*E + H - G
a3 = ((2.0*self.gamma_prior_alpha+3)*E-2.0*G)*E
a4 = -G*E**2
Q = ((3.0*a3/a1)-((a2/a1)**2))/9
R = (9*a1*a2*a3-27*a4*(a1**2)-2*(a2**3))/(54*a1**3)
##delta = Q**3+R**2
#rho = sqrt(-Q**3)
#theta = arccos(R/rho)
theta = arccos(sign(R)*minimum(exp(log(abs(R))-3.0/2.0*log(-Q)),1.0))
#print theta1, theta
#JJ = pow(rho,1.0/3)
HH = sqrt(-Q)
am = 2*HH*cos(theta/3)-a2/(3.0*a1)
am = maximum(abs(am),0.00001)
gamma_mean_diff = sum((am-gamma_tn)**2)/d_z
gamma_tn[:] = am
return gamma_mean_diff
def compute_gamma(self, A, E, zz_tn_prev, zz_tn, gamma_tn):
"""
Replaces the current value of the gamma parameters with
its updated value, and returns the mean square difference between the two.
"""
# This is the main bottleneck of the code.
# Would be faster if:
# - implemented in C
# - roots() was also implemented in C
d_z = len(gamma_tn)
product_matrix_matrix(zz_tn_prev, A.T, self.mat_d_z_d_z)
product_matrix_matrix(A, self.mat_d_z_d_z, self.mat_d_z_d_z2)
getdiag(self.mat_d_z_d_z2, self.AzzA_prev)
G = diag(zz_tn) + 2 * self.gamma_prior_beta
H = self.AzzA_prev
a1 = 2.0 * (self.gamma_prior_alpha + 1.0)
a2 = (4.0 * self.gamma_prior_alpha + 5.0) * E + H - G
a3 = ((2.0 * self.gamma_prior_alpha + 3) * E - 2.0 * G) * E
a4 = -G * E**2
Q = ((3.0 * a3 / a1) - ((a2 / a1)**2)) / 9
R = (9 * a1 * a2 * a3 - 27 * a4 * (a1**2) - 2 * (a2**3)) / (54 * a1**3)
##delta = Q**3+R**2
#rho = sqrt(-Q**3)
#theta = arccos(R/rho)
theta = arccos(
sign(R) * minimum(exp(log(abs(R)) - 3.0 / 2.0 * log(-Q)), 1.0))
#print theta1, theta
#JJ = pow(rho,1.0/3)
HH = sqrt(-Q)
am = 2 * HH * cos(theta / 3) - a2 / (3.0 * a1)
am = maximum(abs(am), 0.00001)
gamma_mean_diff = sum((am - gamma_tn)**2) / d_z
gamma_tn[:] = am
return gamma_mean_diff
def log_det_diff2_log_gamma(self,A,E,zz_tn_prev,zz_tn,gamma_tn):
d_z = len(gamma_tn)
product_matrix_matrix(zz_tn_prev,A.T,self.mat_d_z_d_z)
product_matrix_matrix(A,self.mat_d_z_d_z,self.mat_d_z_d_z2)
getdiag(self.mat_d_z_d_z2,self.AzzA_prev)
G = 0.5*diag(zz_tn)+self.gamma_prior_beta
H = 0.5*self.AzzA_prev
gamma_E_1 = (gamma_tn+E)
gamma_E_2 = gamma_E_1*gamma_E_1
gamma_E_3 = gamma_E_2*gamma_E_1
return sum(log(G/gamma_tn+H*gamma_tn*(E-gamma_tn)/gamma_E_3-0.5*E*gamma_tn/gamma_E_2))
def log_det_diff2_log_gamma(self, A, E, zz_tn_prev, zz_tn, gamma_tn):
d_z = len(gamma_tn)
product_matrix_matrix(zz_tn_prev, A.T, self.mat_d_z_d_z)
product_matrix_matrix(A, self.mat_d_z_d_z, self.mat_d_z_d_z2)
getdiag(self.mat_d_z_d_z2, self.AzzA_prev)
G = 0.5 * diag(zz_tn) + self.gamma_prior_beta
H = 0.5 * self.AzzA_prev
gamma_E_1 = (gamma_tn + E)
gamma_E_2 = gamma_E_1 * gamma_E_1
gamma_E_3 = gamma_E_2 * gamma_E_1
return sum(
log(G / gamma_tn + H * gamma_tn * (E - gamma_tn) / gamma_E_3 -
0.5 * E * gamma_tn / gamma_E_2))
def multivariate_norm_log_pdf(self,x,mu,cov):
# -0.5 * (dot(x-mu,dot(inv(cov),x-mu)) + len(x)*log(2*pi) + log(det(cov)))
self.vec_d_y[:] = x
self.vec_d_y[:] -= mu
solve(cov,reshape(self.vec_d_y,(-1,1)),reshape(self.vec_d_y2,(-1,1)),
self.covf,self.colvecf,self.pivotscov)
ret = dot(self.vec_d_y,self.vec_d_y2)
ret += len(x)*log(2*pi)
lu(cov,self.pcov,self.Lcov,self.Ucov,self.covf,self.pivotscov)
getdiag(self.Ucov,self.vec_d_y)
absolute(self.vec_d_y,self.vec_d_y2)
log(self.vec_d_y2,self.vec_d_y)
ret += sum(self.vec_d_y)
ret *= -0.5
return ret
def multivariate_norm_log_pdf(self, x, mu, cov):
# -0.5 * (dot(x-mu,dot(inv(cov),x-mu)) + len(x)*log(2*pi) + log(det(cov)))
self.vec_d_y[:] = x
self.vec_d_y[:] -= mu
solve(cov, reshape(self.vec_d_y, (-1, 1)),
reshape(self.vec_d_y2, (-1, 1)), self.covf, self.colvecf,
self.pivotscov)
ret = dot(self.vec_d_y, self.vec_d_y2)
ret += len(x) * log(2 * pi)
lu(cov, self.pcov, self.Lcov, self.Ucov, self.covf, self.pivotscov)
getdiag(self.Ucov, self.vec_d_y)
absolute(self.vec_d_y, self.vec_d_y2)
log(self.vec_d_y2, self.vec_d_y)
ret += sum(self.vec_d_y)
ret *= -0.5
return ret
def multivariate_norm_log_pdf(self,x,mu,cov):
#return -0.5 * (dot(x-mu,dot(inv(cov),x-mu)) + len(x)*log(2*pi) + sum(log(eigvals(cov))))
#return_old = -0.5 * (dot(x-mu,solve(cov,x-mu)) + len(x)*log(2*pi) + sum(log(abs(diag(scipy.linalg.lu(cov)[2])))))
self.vec_d_y[:] = x
self.vec_d_y[:] -= mu
solve(cov,reshape(self.vec_d_y,(-1,1)),reshape(self.vec_d_y2,(-1,1)),
self.covf,self.colvecf,self.pivotscov)
ret = dot(self.vec_d_y,self.vec_d_y2)
ret += len(x)*log(2*pi)
lu(cov,self.pcov,self.Lcov,self.Ucov,self.covf,self.pivotscov)
getdiag(self.Ucov,self.vec_d_y)
absolute(self.vec_d_y,self.vec_d_y2)
log(self.vec_d_y2,self.vec_d_y)
ret += sum(self.vec_d_y)
ret *= -0.5
return ret
def multivariate_norm_log_pdf(self, x, mu, cov):
#return -0.5 * (dot(x-mu,dot(inv(cov),x-mu)) + len(x)*log(2*pi) + sum(log(eigvals(cov))))
#return_old = -0.5 * (dot(x-mu,solve(cov,x-mu)) + len(x)*log(2*pi) + sum(log(abs(diag(scipy.linalg.lu(cov)[2])))))
self.vec_d_y[:] = x
self.vec_d_y[:] -= mu
solve(cov, reshape(self.vec_d_y, (-1, 1)),
reshape(self.vec_d_y2, (-1, 1)), self.covf, self.colvecf,
self.pivotscov)
ret = dot(self.vec_d_y, self.vec_d_y2)
ret += len(x) * log(2 * pi)
lu(cov, self.pcov, self.Lcov, self.Ucov, self.covf, self.pivotscov)
getdiag(self.Ucov, self.vec_d_y)
absolute(self.vec_d_y, self.vec_d_y2)
log(self.vec_d_y2, self.vec_d_y)
ret += sum(self.vec_d_y)
ret *= -0.5
return ret