def f(x):
kappa1 = x[:, 0]
kappa2 = x[:, 1]
square_diff = x[:, 2]
delta_inf = x[:, 3]
mu = tf.zeros((1, ), dtype=DTYPE)
delta_0 = tf.sqrt(2 * square_diff + tf.square(delta_inf))
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
PrimSq = tfi.PrimSq(mu, delta_0, num_pts=gauss_quad_pts)
IntPrimPrim = tfi.IntPrimPrim(mu,
delta_0,
delta_inf,
num_pts=gauss_quad_pts)
IntPhiPhi = tfi.IntPhiPhi(mu,
delta_0,
delta_inf,
num_pts=gauss_quad_pts)
noise_corr = ((Sw**2 + tf.square(betam)) *
(tf.square(kappa1) + tf.square(kappa2)) + (SI**2) *
(cA**2 + cB**2) + tf.square(rhom * kappa1 + gammaA) +
tf.square(rhom * kappa2 + gammaB))
F = (rhom * rhon * kappa1 + betam * betan *
(kappa1 + kappa2) + cA * SI + rhon * gammaA) * Prime
G = (rhom * rhon * kappa2 + betam * betan *
(kappa1 + kappa2) + cB * SI + rhon * gammaB) * Prime
H = tf.square(g) * (PrimSq - IntPrimPrim) + noise_corr * (delta_0 -
delta_inf)
I = tf.square(g) * IntPhiPhi + noise_corr
return tf.stack([F, G, H, I], axis=1)
def f(x):
mu = x[:, 0]
kappa = x[:, 1]
square_diff = x[:, 2]
delta_inf = x[:, 3]
delta_0 = tf.sqrt(2 * square_diff + tf.square(delta_inf))
Phi = tfi.Phi(mu, delta_0, num_pts=gauss_quad_pts)
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
PrimSq = tfi.PrimSq(mu, delta_0, num_pts=gauss_quad_pts)
IntPrimPrim = tfi.IntPrimPrim(mu,
delta_0,
delta_inf,
num_pts=gauss_quad_pts)
IntPhiPhi = tfi.IntPhiPhi(mu,
delta_0,
delta_inf,
num_pts=gauss_quad_pts)
F = Mm * kappa + MI # mu
G = Mn * Phi + SnI * Prime
H = tf.square(g) * (PrimSq - IntPrimPrim) + (
tf.square(Sm) * tf.square(kappa) + 2 * SmI * kappa +
SI_squared) * (delta_0 - delta_inf)
I = (tf.square(g) * IntPhiPhi + tf.square(Sm) * tf.square(kappa) +
2 * SmI * kappa + SI_squared)
return tf.stack([F, G, H, I], axis=1)
def f(x):
kappa1 = x[:, 0]
kappa2 = x[:, 1]
delta_0 = x[:, 2]
mu = tf.zeros((1, ), dtype=DTYPE)
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
PhiSq = tfi.PhiSq(mu, delta_0, num_pts=gauss_quad_pts)
F = (rhom * rhon * kappa1 + betam * betan * (kappa1 + kappa2) + cA *
(SI**2) + rhon * gammaA) * Prime
G = (rhom * rhon * kappa2 + betam * betan * (kappa1 + kappa2) + cB *
(SI**2) + rhon * gammaB) * Prime
H = (g**2) * PhiSq
H += ((Sy**2) + tf.square(betam)) * (tf.square(kappa1) +
tf.square(kappa2))
H += ((SI**2) * (cA**2 + cB**2) + tf.square(rhom * kappa1 + gammaA) +
tf.square(rhom * kappa2 + gammaB))
return tf.stack([F, G, H], axis=1)
def consistent_solve(y, g, eps, T):
y_1 = y[:, :, :, 0]
y_2 = y[:, :, :, 1]
y_3 = y[:, :, :, 2]
for i in range(T):
Sii = tf.sqrt((Sini / Sin_tf)**2 + Sip**2)
mu = Mm_tf * y_3 + Mi
new1 = g * g * tf_integrals.PhiSq(mu, y_2) + Sim_tf**2 * y_3**2
new1 = new1 + Sii**2
new2 = Mn_tf * tf_integrals.Phi(
mu, y_2) + Sini * tf_integrals.Prime(mu, y_2)
y_new_1 = Mm_tf * new2 + Mi
y_new_2 = (1 - eps) * y_2 + eps * new1
y_new_3 = (1 - eps) * y_3 + eps * new2
y_1 = y_new_1
y_2 = y_new_2
y_3 = y_new_3
y_out = tf.stack([y_1, y_2, y_3], axis=0)
return y_out
def rank2_CDD_chaotic_solve(
kappa1_init,
kappa2_init,
delta_0_init,
delta_inf_init,
cA,
cB,
g,
rhom,
rhon,
betam,
betan,
gammaA,
gammaB,
num_its,
eps,
gauss_quad_pts=50,
db=False,
):
SI = 1.2
Sy = 1.2
SyA = Sy
SyB = Sy
SIA = SI
SIB = SI
SIctxA = 1.0
SIctxB = 1.0
Sw = 1.0
Sm1 = SyA + rhom * SIctxA + betam * Sw
Sm2 = SyB + rhom * SIctxB + betam * Sw
square_diff_init = (tf.square(delta_0_init) -
tf.square(delta_inf_init)) / 2.0
# convergence equations used for langevin-like dynamimcs solver
def f(x):
kappa1 = x[:, 0]
kappa2 = x[:, 1]
square_diff = x[:, 2]
delta_inf = x[:, 3]
mu = tf.zeros((1, ), dtype=DTYPE)
delta_0 = tf.sqrt(2 * square_diff + tf.square(delta_inf))
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
PrimSq = tfi.PrimSq(mu, delta_0, num_pts=gauss_quad_pts)
IntPrimPrim = tfi.IntPrimPrim(mu,
delta_0,
delta_inf,
num_pts=gauss_quad_pts)
IntPhiPhi = tfi.IntPhiPhi(mu,
delta_0,
delta_inf,
num_pts=gauss_quad_pts)
noise_corr = ((Sw**2 + tf.square(betam)) *
(tf.square(kappa1) + tf.square(kappa2)) + (SI**2) *
(cA**2 + cB**2) + tf.square(rhom * kappa1 + gammaA) +
tf.square(rhom * kappa2 + gammaB))
F = (rhom * rhon * kappa1 + betam * betan *
(kappa1 + kappa2) + cA * SI + rhon * gammaA) * Prime
G = (rhom * rhon * kappa2 + betam * betan *
(kappa1 + kappa2) + cB * SI + rhon * gammaB) * Prime
H = tf.square(g) * (PrimSq - IntPrimPrim) + noise_corr * (delta_0 -
delta_inf)
I = tf.square(g) * IntPhiPhi + noise_corr
return tf.stack([F, G, H, I], axis=1)
x_init = tf.stack(
[kappa1_init, kappa2_init, square_diff_init, delta_inf_init], axis=1)
non_neg = [False, False, True, True]
if db:
xs_end, xs = bounded_langevin_dyn(f,
x_init,
eps,
num_its,
non_neg,
db=db)
else:
xs_end = bounded_langevin_dyn(f, x_init, eps, num_its, non_neg, db=db)
kappa1 = xs_end[:, 0]
kappa2 = xs_end[:, 1]
square_diff = xs_end[:, 2]
delta_inf = xs_end[:, 3]
mu = tf.zeros((1, ), dtype=DTYPE)
delta_0 = tf.sqrt(2 * square_diff + tf.square(delta_inf))
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
z = betam * (kappa1 + kappa2) * Prime
if db:
return kappa1, kappa2, delta_0, delta_inf, z, xs
else:
return kappa1, kappa2, delta_0, delta_inf, z
def rank2_CDD_static_solve(
kappa1_init,
kappa2_init,
delta_0_init,
cA,
cB,
g,
rhom,
rhon,
betam,
betan,
gammaA,
gammaB,
num_its,
eps,
gauss_quad_pts=50,
db=False,
):
# Use equations 159 and 160 from M&O 2018
SI = 1.2
Sy = 1.2
# convergence equations used for langevin-like dynamimcs solver
def f(x):
kappa1 = x[:, 0]
kappa2 = x[:, 1]
delta_0 = x[:, 2]
mu = tf.zeros((1, ), dtype=DTYPE)
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
PhiSq = tfi.PhiSq(mu, delta_0, num_pts=gauss_quad_pts)
F = (rhom * rhon * kappa1 + betam * betan * (kappa1 + kappa2) + cA *
(SI**2) + rhon * gammaA) * Prime
G = (rhom * rhon * kappa2 + betam * betan * (kappa1 + kappa2) + cB *
(SI**2) + rhon * gammaB) * Prime
H = (g**2) * PhiSq
H += ((Sy**2) + tf.square(betam)) * (tf.square(kappa1) +
tf.square(kappa2))
H += ((SI**2) * (cA**2 + cB**2) + tf.square(rhom * kappa1 + gammaA) +
tf.square(rhom * kappa2 + gammaB))
return tf.stack([F, G, H], axis=1)
x_init = tf.stack([kappa1_init, kappa2_init, delta_0_init], axis=1)
non_neg = [False, False, True]
if db:
xs_end, xs = bounded_langevin_dyn(f,
x_init,
eps,
num_its,
non_neg,
db=db)
else:
xs_end = bounded_langevin_dyn(f, x_init, eps, num_its, non_neg, db=db)
kappa1 = xs_end[:, 0]
kappa2 = xs_end[:, 1]
delta_0 = xs_end[:, 2]
mu = tf.zeros((1, ), dtype=DTYPE)
Prime = tfi.Prime(mu, delta_0, num_pts=gauss_quad_pts)
z = betam * (kappa1 + kappa2) * Prime
if db:
return kappa1, kappa2, delta_0, z, xs
else:
return kappa1, kappa2, delta_0, z