def fu_0_1_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
omega_star = self.omega_star
V_star = self.V_star
fu_0 = 1 / 2 * (gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
gaussian(invA_B, 0, Delta_2 + inv_A) *
(1 - erf(omega / sqrt(2 * V))))
dfu_0 = 1 / 2 * (
gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(inv(V + Delta_2 + inv_A) * (omega - invA_B) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
2 / sqrt(2 * pi * V_star) * exp(-1 / 2 * omega_star**2 / V_star) *
V_star * inv(Delta_2 + inv_A)) - gaussian(
invA_B, 0, Delta_2 + inv_A) * inv(Delta_2 + inv_A) * invA_B *
(1 - erf(omega / sqrt(2 * V))))
res = 1 / fu_0 * (dfu_0)**2
return res
def gout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
inv_V = inv(V)
V_star = self.V_star
omega_star = self.omega_star
self.fout_()
fout = self.fout
dfout = 1 / 2 * (
gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(inv(V + Delta_2 + inv_A) * (invA_B - omega) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
2 / sqrt(2 * pi * V_star) * exp(-1 / 2 * omega_star**2 / V_star) *
V_star * inv_V) + gaussian(invA_B, 0, Delta_2 + inv_A) *
(-2 / sqrt(2 * pi * V) * exp(-1 / 2 * omega**2 / V)))
if fout < self.threshold_zero:
gout = 0
else:
gout = dfout / fout
self.fout = fout
self.dfout = dfout
self.gout = gout
def fu_1_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
omega_star = self.omega_star
V_star = self.V_star
self.fu_0_()
fu_0 = self.fu_0
dfu_0 = 1 / 2 * (
gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(inv(V + Delta_2 + inv_A) * (omega - invA_B) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
2 / sqrt(2 * pi * V_star) * exp(-1 / 2 * omega_star**2 / V_star) *
V_star * inv(Delta_2 + inv_A)) - gaussian(
invA_B, 0, Delta_2 + inv_A) * inv(Delta_2 + inv_A) * invA_B *
(1 - erf(omega / sqrt(2 * V))))
if fu_0 < self.threshold_zero:
fu_1 = 0
else:
fu_1 = inv_A * dfu_0 / fu_0 + invA_B
self.fu_0 = fu_0
self.dfu_0 = dfu_0
self.fu_1 = fu_1
def fu_2_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
inv_Delta2_A = self.inv_Delta2_A
self.fu_1_()
fu_0 = self.fu_0
fu_1 = self.fu_1
term1 = - 1/2 * inv_Delta2_A * \
gaussian(invA_B, 1, Delta_2 + inv_A) * (1 + erf(omega/sqrt(2*V)))
term2 = 1/2 * (inv_Delta2_A * (1 - invA_B))**2 * gaussian(invA_B, 1, Delta_2 + inv_A) * \
(1 + erf(omega/sqrt(2*V)))
term3 = - 1/2 * inv_Delta2_A * \
gaussian(invA_B, -1, Delta_2 + inv_A) * (1 - erf(omega/sqrt(2*V)))
term4 = 1/2 * (inv_Delta2_A * (-1 - invA_B))**2 * gaussian(invA_B, -1, Delta_2 + inv_A) * \
(1 - erf(omega/sqrt(2*V)))
ddfu_0 = term1 + term2 + term3 + term4
if fu_0 < self.threshold_zero:
fu_2 = 0
else:
fu_2 = inv_A**2 * 1/fu_0 * ddfu_0 + inv_A - \
invA_B**2 + 2 * invA_B * fu_1 - fu_1**2
self.fu_2 = fu_2
def fu_1_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
inv_Delta2_A = self.inv_Delta2_A
self.fu_0_()
fu_0 = self.fu_0
term1 = 1/2 * inv_Delta2_A * \
(1 - invA_B) * gaussian(invA_B, 1, Delta_2 + inv_A) * \
(1 + erf(omega/sqrt(2*V)))
term2 = 1/2 * inv_Delta2_A * \
(-1 - invA_B) * gaussian(invA_B, -1,
Delta_2 + inv_A) * (1 - erf(omega/sqrt(2*V)))
dfu_0 = term1 + term2
if np.abs(fu_0) < self.threshold_zero:
fu_1 = 0
else:
fu_1 = inv_A * dfu_0 / fu_0 + invA_B
self.fu_0 = fu_0
self.dfu_0 = dfu_0
self.fu_1 = fu_1
def integrand_dfout(self, z, s, j):
A, B, C = self.omega[0], self.V_tilde_inv[1], self.V_tilde[1]
i = 1
omega_tilde = self.omega_tilde(z, i, self.omega, self.inv_V)
term1 = 1/2 * (1 + s * erf(omega_tilde / sqrt(2*C))) * 1 / \
self.V_tilde_inv[1] * (z - self.omega[0]) if j == 0 else 0
tmp = self.inv_V[0, 1] / self.inv_V[1, 1] if j == 0 else 1
term2 = s * gaussian(0, omega_tilde, self.V_tilde[1]) * tmp
res = gaussian(z, A, B) * (term1 + term2)
return res
def fu_0_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
fu_0 = 1/2 * gaussian(invA_B, 1, Delta_2 + inv_A) * (1 + erf(omega/sqrt(2*V))) \
+ 1/2 * gaussian(invA_B, -1, Delta_2 + inv_A) * \
(1 - erf(omega/sqrt(2*V)))
if np.abs(fu_0) < self.threshold_zero:
fu_0 = 0
self.fu_0 = fu_0
def fu_0_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
omega_star = self.omega_star
V_star = self.V_star
fu_0 = 1 / 2 * (gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
gaussian(invA_B, 0, Delta_2 + inv_A) *
(1 - erf(omega / sqrt(2 * V))))
self.fu_0 = fu_0
def fout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
fout = 1/2 * gaussian(invA_B, 1, Delta_2 + inv_A) * (1 + erf(omega/sqrt(2*V))) \
+ 1/2 * gaussian(invA_B, -1, Delta_2 + inv_A) * \
(1 - erf(omega/sqrt(2*V)))
if fout < self.threshold_zero:
fout = 0
self.fout = fout
def integrand_fout(self, z, s):
A, B, C = self.omega[0], self.V_tilde_inv[1], self.V_tilde[1]
i = 1
omega_tilde = self.omega_tilde(z, i, self.omega, self.inv_V)
res = 1/2 * gaussian(z, A, B) * (1 + s *
erf(omega_tilde / sqrt(2*C)))
return res
def fout_gout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
fout = 1/2 * gaussian(invA_B, 1, Delta_2 + inv_A) * (1 + erf(omega/sqrt(2*V))) \
+ 1/2 * gaussian(invA_B, -1, Delta_2 + inv_A) * \
(1 - erf(omega/sqrt(2*V)))
dfout = (gaussian(invA_B, 1, Delta_2 + inv_A) - gaussian(invA_B, -1, Delta_2 + inv_A)) * \
gaussian(omega, 0, V)
res = 1/fout * dfout**2
return res
def fout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
V_star = self.V_star
omega_star = self.omega_star
fout = 1 / 2 * (gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
gaussian(invA_B, 0, Delta_2 + inv_A) *
(1 - erf(omega / sqrt(2 * V))))
if fout < self.threshold_zero:
fout = 0
self.fout = fout
def dfu_0_sign_K2(self):
dfu_0 = np.zeros((self.K))
for i in range(self.K**2):
phi_z = self.configuration_binary(i)
norm = gaussian(self.mu, phi_z, self.Sigma)
s = phi_z[1]
borne_inf, borne_sup = self.select_bornes(phi_z[0])
I = norm * quad(self.integrand_fout, borne_inf, borne_sup,
args=(s))[0]
dfu_0 += self.inv_Sigma.dot(phi_z-self.mu) * I
return dfu_0
def dfout_sign_K2(self):
dfout = np.zeros((self.K))
for i in range(self.K**2):
phi_z = self.configuration_binary(i)
norm = gaussian(self.mu, phi_z, self.Sigma)
s = phi_z[1]
borne_inf, borne_sup = self.select_bornes(phi_z[0])
for j in range(self.K):
dfout[j] += norm * quad(self.integrand_dfout, borne_inf, borne_sup,
args=(s, j))[0]
return dfout
def integrand_ddfout(self, z, s, j, k):
A, B, C = self.omega[0], self.V_tilde_inv[1], self.V_tilde[1]
i = 1
omega_tilde = self.omega_tilde(z, i, self.omega, self.inv_V)
term0 = 1 / self.V_tilde_inv[1] * (z - self.omega[0]) if k == 0 else 0
term1 = 1/2 * (1 + s * erf(omega_tilde / sqrt(2*C))) * 1 / \
self.V_tilde_inv[1] * (z - self.omega[0]) if j == 0 else 0
tmp = self.inv_V[0, 1] / self.inv_V[1, 1] if j == 0 else 1
term2 = s * gaussian(0, omega_tilde, self.V_tilde[1]) * tmp
term3 = - 1/2 * (1 + s * erf(omega_tilde / sqrt(2*C))) * 1 / \
self.V_tilde_inv[1] if (j == 0 and k == 0) else 0
term4 = 1 / self.V_tilde_inv[1] * (z - self.omega[0]) if j == 0 else 0
tmp2 = self.inv_V[0, 1] / self.inv_V[1, 1] if k == 0 else 1
term5 = s * gaussian(0, omega_tilde, self.V_tilde[1]) * tmp2
term6 = - s * \
gaussian(0, omega_tilde, self.V_tilde[1]) * \
tmp * 1 / self.V_tilde[1] * omega_tilde * tmp2
res = gaussian(z, A, B) * (term0 * (term1 + term2) +
term3 + term4 * term5 + term6)
return res
def gout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
self.fout_()
fout = self.fout
dfout = (gaussian(invA_B, 1, Delta_2 + inv_A) - gaussian(invA_B, -1, Delta_2 + inv_A)) * \
gaussian(omega, 0, V)
if fout < self.threshold_zero:
gout = 0
else:
gout = dfout / fout
self.fout = fout
self.dfout = dfout
self.gout = gout
def dgout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
inv_V = inv(V)
V_star = self.V_star
omega_star = self.omega_star
self.gout_()
fout = self.fout
gout = self.gout
if self.Nishimori_identity:
ddfout = 0
else:
term1 = - inv(V + Delta_2 + inv_A) * \
(1 + erf(omega_star / sqrt(2 * V_star)))
term2 = inv(V + Delta_2 + inv_A) * (invA_B - omega) * 2 / sqrt(
2 * pi * V_star) * exp(
-1 / 2 * omega_star**2 / V_star) * V_star * inv_V
term3 = - omega_star / V_star * 2 / \
sqrt(2 * pi * V_star) * exp(-1/2 * omega_star **
2 / V_star) * (V_star * inv_V)**2
term4 = inv(V + Delta_2 + inv_A) * (invA_B-omega) * \
(1 + erf(omega_star / sqrt(2 * V_star))) + \
2 / sqrt(2 * pi * V_star) * exp(-1/2 *
omega_star**2 / V_star) * V_star * inv_V
term5 = inv(V + Delta_2 + inv_A) * (invA_B - omega)
term6 = - omega / V * gaussian(invA_B, 0, Delta_2 + inv_A) * \
(- 2 / sqrt(2 * pi * V) * exp(-1/2 * omega**2 / V))
ddfout = 1 / 2 * (gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(term1 + term2 + term3 + term4 * term5) + term6)
if fout < self.threshold_zero:
dgout = 0
else:
dgout = 1 / fout * ddfout - gout**2
self.ddfout = ddfout
self.dgout = dgout
def fu_0_1_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
inv_Delta2_A = self.inv_Delta2_A
fu_0 = 1/2 * gaussian(invA_B, 1, Delta_2 + inv_A) * (1 + erf(omega/sqrt(2*V))) \
+ 1/2 * gaussian(invA_B, -1, Delta_2 + inv_A) * \
(1 - erf(omega/sqrt(2*V)))
term1 = 1/2 * inv_Delta2_A * \
(1 - invA_B) * gaussian(invA_B, 1, Delta_2 + inv_A) * \
(1 + erf(omega/sqrt(2*V)))
term2 = 1/2 * inv_Delta2_A * \
(-1 - invA_B) * gaussian(invA_B, -1,
Delta_2 + inv_A) * (1 - erf(omega/sqrt(2*V)))
dfu_0 = term1 + term2
res = 1 / fu_0 * (dfu_0)**2
return res
def fu_2_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
omega_star = self.omega_star
V_star = self.V_star
self.fu_1_()
fu_0 = self.fu_0
fu_1 = self.fu_1
term1 = -inv(V + Delta_2 + inv_A) * \
(1 + erf(omega_star / sqrt(2 * V_star)))
term2 = (inv(V + Delta_2 + inv_A) * (omega - invA_B) * 2 /
sqrt(2 * pi * V_star) * exp(-1 / 2 * omega_star**2 / V_star) *
V_star * inv(Delta_2 + inv_A))
term3 = - omega_star / V_star * 2 / sqrt(2 * pi * V_star) * \
exp(-1/2 * omega_star**2 / V_star) * \
(V_star * inv(Delta_2 + inv_A))**2
term4 = (inv(V + Delta_2 + inv_A) * (omega - invA_B) *
(1 + erf(omega_star / sqrt(2 * V_star))) + 2 /
sqrt(2 * pi * V_star) * exp(-1 / 2 * omega_star**2 / V_star) *
V_star * inv(Delta_2 + inv_A)) * (inv(V + Delta_2 + inv_A) *
(omega - invA_B))
term5 = (inv(Delta_2 + inv_A) - (inv(Delta_2 + inv_A) * invA_B) ** 2) * \
(1 - erf(omega / sqrt(2 * V)))
ddfu_0 = 1 / 2 * (gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(term1 + term2 + term3 + term4) -
gaussian(invA_B, 0, Delta_2 + inv_A) * term5)
if fu_0 < self.threshold_zero:
fu_2 = 0
else:
fu_2 = inv_A**2 * 1/fu_0 * ddfu_0 + inv_A - \
invA_B**2 + 2 * invA_B * fu_1 - fu_1**2
self.fu_2 = fu_2
def fu_0_sign_K2(self):
fu_0 = 0
for i in range(self.K**2):
phi_z = self.configuration_binary(i)
norm = gaussian(self.mu, phi_z, self.Sigma)
s = phi_z[1]
borne_inf, borne_sup = self.select_bornes(phi_z[0])
I = quad(self.integrand_fout, borne_inf, borne_sup,
args=(s))[0]
I *= norm
fu_0 += I
self.fu_0 = fu_0
return self.fu_0
def fout_gout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
V_star = self.V_star
omega_star = self.omega_star
fout = 1 / 2 * (gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
gaussian(invA_B, 0, Delta_2 + inv_A) *
(1 - erf(omega / sqrt(2 * V))))
dfout = 1 / 2 * (
gaussian(omega, invA_B, V + Delta_2 + inv_A) *
(inv(V + Delta_2 + inv_A) * (invA_B - omega) *
(1 + erf(omega_star / sqrt(2 * V_star))) +
2 / sqrt(2 * pi * V_star) * exp(-1 / 2 * omega_star**2 / V_star) *
V_star * inv_V) + gaussian(invA_B, 0, Delta_2 + inv_A) *
(-2 / sqrt(2 * pi * V) * exp(-1 / 2 * omega**2 / V)))
res = 1 / fout * dfout**2
return res
def dgout_(self):
omega = self.omega
V = self.V
Delta_2 = self.Delta_2
inv_A = self.inv_A
invA_B = self.invA_B
inv_V = inv(V)
self.gout_()
fout = self.fout
gout = self.gout
if self.Nishimori_identity:
ddfout = 0
else:
ddfout = (gaussian(invA_B, 1, Delta_2 + inv_A) - gaussian(invA_B, -1, Delta_2 + inv_A)) * \
gaussian(omega, 0, V) * (-omega/V)
if fout < self.threshold_zero:
dgout = 0
else:
dgout = 1/fout * ddfout - gout**2
self.ddfout = ddfout
self.dgout = dgout
