def run(t,
re_0=8.0,
ri_0=12.0,
J_ee=2.1,
J_ie=1.9,
J_ei=1.5,
J_ii=1.1,
tau_e=10e-3,
tau_i=30e-3,
I_e=12,
I_i=8,
sigma=1,
dt=1e-4):
rs_0 = asarray([re_0, ri_0, re_0, ri_0, re_0, ri_0])
# !
times = create_times((0, t), dt)
# If sigma > 0: we re-define xjw as a stochastic ODE.
g = partial(ornstein_uhlenbeck, sigma=sigma, loc=[0, 1]) # re/i locs
f = partial(xjw,
J_ee=J_ee,
J_ei=J_ei,
J_ie=J_ie,
J_ii=J_ii,
tau_e=tau_e,
tau_i=tau_i,
I_e=I_e,
I_i=I_i)
rs = itoint(f, g, rs_0, times)
return times, rs
def main():
alpha = np.linspace(0.001,0.1,N)
kappa = np.linspace(2,0.02,N)
avgdev = np.linspace(0.1,0.001,N)
rho = np.linspace(-0.95,-0.4,N)
tspan = np.linspace(0,10,1001)
xo = np.array([0,0.05])
foda_men = h5py.File('stochastic_heston.h5','a')
foda_men.require_dataset("Heston",((20*N**4),1001,2),dtype='float32')
i=1
for al in alpha:
for k in kappa:
for m in avgdev:
for r in rho:
def f(x,t):
return np.array([0,-al*(x[1]-m)])
def G(x,t):
return np.array([[x[1],0],[k*r,k*np.sqrt(1-r*r)]])
for j in range(20):
foda_men["Heston"][i,:,:] = sdeint.itoint(f, G, xo, tspan)
i += 1
if (i%100 == 0):
print(i)
print(i)
def burgers(t: Type[np.ndarray], N: int) -> Type[np.ndarray]:
#
# Compute the bla bla bla
#
# Input:
# t
# N
#
# Output:
# output
#
B = np.diag([0])
# diagonal, so independent Brownian motions
T = t[-1]
result = []
def f(x, t):
res = np.sqrt(x**2 - 16 * (T - t))
return -4 / (x + res) if (res.imag > 0) else -4 / (x - res)
for j in range(0, N, 1):
bremen = sdeint.itoint(f, lambda x, t: B, -5 + 10 * j / N + 1j / 1000,
t)
munich = bremen[-1]
result.append(np.complex(munich[0]))
output = np.empty(len(result), np.complex128)
for i in range(len(result)):
output[i] = np.complex(result[i])
return output
def test_mismatched_f():
tspan = np.arange(0.0, 2000.0, 0.002)
y0 = np.zeros(3)
f = lambda y, t: np.array([1.0, 2.0, 3.0, 4.0])
G = lambda y, t: np.ones((3, 3))
with pytest.raises(sdeint.SDEValueError):
y = sdeint.itoint(f, G, y0, tspan)
def test_mismatched_f():
tspan = np.arange(0.0, 2000.0, 0.002)
y0 = np.zeros(3)
f = lambda y, t: np.array([1.0, 2.0, 3.0, 4.0])
G = lambda y, t: np.ones((3, 3))
with pytest.raises(sdeint.SDEValueError):
y = sdeint.itoint(f, G, y0, tspan)
def integrate_sde(init_states, t, f, sigma, num_t=100, **interp_kwargs):
try:
from sdeint import itoint
except:
raise ImportError("Please install sdeint using `pip install sdeint`")
init_states = np.atleast_2d(init_states)
n, d = init_states.shape
if isarray(t):
if len(t) == 1:
t = np.linspace(0, t[0], num_t)
elif len(t) == 2:
t = np.linspace(t[0], t[-1], num_t)
else:
t = np.linspace(0, t, num_t)
if callable(sigma):
D_func = sigma
elif isarray(sigma):
if sigma.ndim == 1:
sigma = np.diag(sigma)
D_func = lambda x, t: sigma
else:
sigma = sigma * np.eye(d)
D_func = lambda x, t: sigma
trajs = []
for y0 in init_states:
y = itoint(lambda x, t: f(x), D_func, y0, t)
trajs.append(y)
if n == 1:
trajs = trajs[0]
return np.array(trajs)
def solve(self, time_vector=np.linspace(0, 10, 10000)):
soln = sdeint.itoint(self.rate_of_experience, self.noise, self.experiences_of_choices, time_vector)
low_values_indices = soln < 0 # Where values are low
soln[low_values_indices] = 0
self.plot(soln,time_vector)
def test_ito_1D_additive():
tspan = np.arange(0.0, 2000.0, 0.002)
y0 = 0.0
f = lambda y, t: -1.0 * y
G = lambda y, t: 0.2
y = sdeint.itoint(f, G, y0, tspan)
assert(np.isclose(np.mean(y), 0.0, rtol=0, atol=1e-02))
assert(np.isclose(np.var(y), 0.2*0.2/2, rtol=1e-01, atol=0))
def test_ito_1D_additive():
tspan = np.arange(0.0, 2000.0, 0.002)
y0 = 0.0
f = lambda y, t: -1.0 * y
G = lambda y, t: 0.2
y = sdeint.itoint(f, G, y0, tspan)
assert (np.isclose(np.mean(y), 0.0, rtol=0, atol=1e-02))
assert (np.isclose(np.var(y), 0.2 * 0.2 / 2, rtol=1e-01, atol=0))
def repetitive_sims(K, N, theta0, omega, Nsims):
solutions = list()
for _ in itertools.repeat(None, Nsims):
f, G = kuramoto(omega, K, N, 1)
tspan = np.linspace(0, t_end, steps)
solution = itoint(f, G, theta0, tspan)
solutions.append(solution)
solution = np.mod(solution, 2 * np.pi)
solution -= np.pi
return solutions
def calc_for_oscillation_with_Ito(m, init_cond, alpha, Tmax, ito, int_finish,
step):
tspan = np.arange(0.0, int_finish + step, step)
forcing = -1.0 * m.Ft(tspan)
parameters = {}
parameters['Tmax'] = Tmax
parameters['alpha'] = alpha
m.update_parameters(parameters)
def G(y, t):
return np.array([[ito, 0.0, 0.0, 0.0], [0.0, ito, 0.0, 0.0],
[0.0, 0.0, ito, 0.0], [0.0, 0.0, 0.0, ito]])
result = sdeint.itoint(m.rhs_ode, G, init_cond, tspan)
return tspan, result, forcing
def solve(self, time_vector=np.linspace(0, 10, 10000)):
t = time_vector
soln = sdeint.itoint(self.rate_of_experience, self.noise, self.experiences_of_choices, time_vector)
low_values_indices = soln < 0 # Where values are low
soln[low_values_indices] = 0
#print(soln)
# for i in range(len(self.orbits_for_exp_at_node_1[0])):
# if self.orbits_for_exp_at_node_1[0][i] < 0:
# self.orbits_for_exp_at_node_1[0][i] = 0
# if self.orbits_for_exp_at_node_1[1][i] < 0:
# self.orbits_for_exp_at_node_1[1][i] = 0
self.plot(soln,t)
def integrate_piece(t, N_end, K, r_res, r_chal, a_RC, a_CR, mode='ode'):
if mode == 'sde':
f = dN_dt_stochatic(K, r_res, r_chal, a_RC, a_CR)
G = brownian(K, r_res, r_chal, a_RC, a_CR)
N = sdeint.itoint(f, G, N_end, t)
elif mode == 'ctmc':
t, N = gillespie(t[0], t[-1], N_end[0], N_end[1], K, r_res, r_chal,
a_RC, a_CR)
else:
N = integrate.odeint(dN_dt,
N_end,
t,
args=(K, r_res, r_chal, a_RC, a_CR),
Dfun=d2N_dt2)
return (t, N)
def simulate(self, initial_state: Union[float, list, np.array],
initial_time: float, final_time: float,
t_delta_integration: float) -> Tuple[np.array, np.array]:
"""
Integrate the system using an sdeint built-in SDE solver.
:param initial_state: initial state of the system;
:param initial_time: initial time of the simulation;
:param final_time: final time of the simulation;
:param t_delta_integration: time between integration intervals.
:return: a numpy array with dimensions [n_times, self.dim].
"""
f = self._build_f()
g = self._build_g()
t_int = np.arange(initial_time, final_time, t_delta_integration)
system_int = sdeint.itoint(f, g, initial_state, t_int)
return system_int.T, t_int.reshape(-1, 1)
def simulate(self, method="BDF", atol=1.e-5, rtol=1.e-6, G=None):
if not self.initial_eq:
print("Equations are not initialised.")
return
if not self.initial_state:
print("Initial conditions are missing.")
return
# set up ode system
def ode_fun(t, y):
r = y[0]
dr = y[1]
Q = y[2:]
M = self.pms_sym.M_mod(r, dr, Q)
F = self.pms_sym.F_mod(r, dr, Q)
v = self.pms_sym.v_mod(r, dr, Q)
return np.concatenate([np.array([dr, F / M]), v])
if G is not None:
if self.t_eval is None:
self.t_eval = np.linspace(0, self.t_end, 1000)
res = si.itoint(lambda y, t: ode_fun(t, y), G, self.y0,
self.t_eval)
self.sol = lambda: 0
self.sol.message = "SDE integrator finished."
self.sol.y = res.T
self.sol.t = self.t_eval
else:
self.sol = solve_ivp(ode_fun, [0, self.t_end],
self.y0,
method=method,
atol=atol,
rtol=rtol,
t_eval=self.t_eval)
self.r = self.sol.y[0, :]
self.dr = self.sol.y[1, :]
self.Q = self.sol.y[2:, :]
def kuramoto(t, N, omega=10, K=3, sigma=0.01, dt=1e-3):
"""Simulate a Kuramoto model."""
times = np.linspace(0, t, int(t / dt))
omegas = np.repeat(omega, N)
theta0 = np.random.uniform(-np.pi * 2, np.pi * 2, size=N)
# Define the model
def _f(theta, t):
# In classic kuramoto...
# each oscillator gets the same wieght K
# normalized by the number of oscillators
c = K / N
# and all oscillators are connected to all
# oscillators
theta = np.atleast_2d(theta) # opt for broadcasting
W = np.sum(np.sin(theta - theta.T), 1)
ep = np.random.normal(0, sigma, N)
return omega + ep + (c * W)
# And the Ito noise term
def _G(_, t):
return np.diag(np.ones(N) * sigma)
# Integrate!
thetas = itoint(_f, _G, theta0, times)
thetas = np.mod(thetas, 2 * np.pi)
thetas -= np.pi
# Move to time domain from the unit circle
waves = []
for n in range(N):
th = thetas[:, n]
f = omegas[n]
wave = np.sin(f * 2 * np.pi * times + th)
waves.append(wave)
waves = np.vstack(waves)
return waves
def simulate(theta0, T, omegas, K, N, sigma, p, dt):
"""Simulate a Kuramoto model."""
times = np.linspace(0, T, int(T / dt))
def G(_, t):
return np.diag(np.ones(N) * sigma)
if np.allclose(p, 1):
def f(theta, t):
return kuramoto(theta, t, omegas, K, N, sigma)
else:
def f(theta, t):
return onoff(theta, t, omegas, K, N, sigma, p)
thetas = itoint(f, G, theta0, times)
thetas = np.mod(thetas, 2 * np.pi)
thetas -= np.pi
return thetas, times
def multiple_driving_functions(x0: RealNumber,
t: RealNumber,
kappa: RealNumber = 1.0) -> List[RealNumber]:
#number of slits: it will be the number of starting points
nslits = len(x0)
#nslits independent Brownian motions with scaling factor kappa
B = np.diag(np.zeros(nslits, dtype=np.complex) + np.sqrt(kappa / nslits))
#defining the equation...
def f(x, t):
res = np.zeros(nslits, dtype=np.complex)
for k in range(0, nslits):
for m in range(0, nslits):
if k != m:
res[k] += 2 / (
x[k] - x[m]
) #res = [ res[k]+2/(x[k]-x[m]) for k in range(0, Nslits) for m in range(0, Nslits, 1) if k!=m
return res
#solving the SDE
result = sdeint.itoint(f, lambda x, t: B, x0, t)
#returning the nslits driving functions
return [list(i) for i in zip(*result)]
def solve(self, **kwargs):
""" Solves initial value problem """
if (len(self.sol) == 0):
# Solve only if not already solved
if(self.method == 'EuMa'):
self.sol_cartesian = sdeint.itoEuler(self.f, self.G, self.y0, self.ts, **kwargs)
elif (self.method == 'Ito'):
self.sol_cartesian = sdeint.itoint(self.f, self.G, self.y0, self.ts, **kwargs)
elif (self.method == 'Strato'):
self.sol_cartesian = sdeint.stratint(self.f, self.G, self.y0, self.ts, **kwargs)
else:
raise ValueError('Only supported methods are EuMa, Ito and Strato')
else:
# Do nothing
pass
if self.topology == 'cartesian':
self.sol = self.sol_cartesian
elif self.topology == 'torus':
self.sol = np.mod(self.sol_cartesian, 2*np.pi)
import numpy as np
import sdeint
A = np.array([[0., -0.], [0., -0.]], dtype=np.complex128)
B = np.hstack([np.diag([1.0, 1.0]), np.diag([1.0j, 1.0j])
]) # diagonal, so independent driving Wiener processes
tspan = np.linspace(0.0, 100.0, 10001)
x0 = np.array([0., 0.], dtype=np.complex128)
def f(x, t):
return A.dot(x)
def G(x, t):
return B
result = sdeint.itoint(f, G, x0, tspan)
print(result)
tspan = N / fs
#t = np.linspace(0.0, 200.0, 10001)
t = np.linspace(0.0, tspan, N + 1)
x0 = 0.1
def f_regular(x, t):
return a * x - b * x**3 + A * np.cos(omega * t + phi)
#return A*np.cos(omega*t+phi)
def f_noise(x, t):
return sigma
result = sdeint.itoint(f_regular, f_noise, x0, t)
x = result[:, 0]
spectrum = np.abs(np.fft.fft(x))**2
#spectrum = np.log(spectrum)
time_step = t[1] - t[0]
freqs = np.fft.fftfreq(x.size, time_step)
#idx = np.argsort(freqs)
idx = np.arange(N / 2)
plt.subplot(3, 1, 1)
plt.plot(t, x)
plt.subplot(3, 1, 2)
plt.plot(freqs[idx], spectrum[idx])
plt.subplot(3, 1, 3)
def load_model_data_io(model_name, N, ds_by = None, dim = None):
if model_name == 'starx':
p_true = (1, 2)
model_type = 'nlar'
burnin = 100
Ntot = burnin + N
c = 0.8
d = 1
a1 = 2
a0 = 1
b1 = 0.5
b0 = -0.5
s = 1
Y = numpy.zeros(Ntot)
X = numpy.zeros(Ntot)
epsX = numpy.random.randn(Ntot)
epsY = numpy.random.randn(Ntot)
for t in range(1, Ntot):
w = norm.cdf(Y[t-1])
Y[t] = c*Y[t-1] + d*epsX[t]
X[t] = w*(b1*X[t-1] + a1*epsY[t]) + (1-w)*(b0*X[t-1] + a0*epsY[t])
Y = Y[burnin:]
X = X[burnin:]
if model_name == 'shenon':
p_true = (2, 2)
model_type = 'nlar'
burnin = 100
Ntot = burnin + N
# C = 0.6 # Used in STE paper.
C = 0.2
# C = 0.01
# s = 0.004 # Used in STE paper
# s = 2*0.004
sY = 0.008
sX = 0.008
Y = numpy.zeros((2, Ntot))
X = numpy.zeros((2, Ntot))
noise = numpy.random.randn(Ntot*4).reshape(4, -1)
noise[:2, :] = noise[0:2, :]*sX
noise[2:, :] = noise[0:2, :]*sY
for t in range(1, Ntot):
Y[0, t] = 1.4 - Y[0, t-1]**2 + 0.3*Y[1, t-1] + noise[0, t]
Y[1, t] = Y[0, t-1] + noise[1, t]
X[0, t] = 1.4 - (C*Y[0, t-1] + (1-C)*X[0, t-1])*X[0, t-1] + 0.3*X[1, t-1] + noise[2, t]
X[1, t] = X[0, t-1] + noise[3, t]
Z = numpy.concatenate((Y[:, t], X[:, t]))
Znorm = numpy.linalg.norm(Z)
if Znorm >= 4:
J = int(numpy.random.choice(1000))
Y[:, t] = Y[:, J]
X[:, t] = X[:, J]
Y = Y[0, burnin:]
X = X[0, burnin:]
if 'lorenz96' in model_name:
model_type = 'nlar'
p_true = numpy.inf
# h = 0.01
h = 0.05
if dim == None:
dim = 47
if ds_by == None:
# ds_by = 5
ds_by = 2
ttot = N*h*ds_by
tburn = 100
tf = ttot + tburn
tspan = numpy.linspace(0.0, tf, int(tf/h))
x0 = numpy.random.rand(dim)
def F(X, t):
d = len(X)
dX = numpy.zeros(d)
for k in range(d):
dX[k] = (X[(k + 1) % d] - X[(k - 2) % d])*X[(k - 1) % d] - X[k] + 5
return dX
def G(x, t):
return B
# dyn_noise = 0
dyn_noise = 0.5
B = numpy.diag([dyn_noise]*dim)
N_biggest = 1000
if N > N_biggest:
num_segments = int(N / N_biggest)+1
tp_per_segment = int(N_biggest*ds_by)
for seg_ind in range(num_segments):
# print("On segment {} of {}...".format(seg_ind+1, num_segments))
result_cur = sdeint.itoint(F, G, x0, tspan[seg_ind*tp_per_segment:(seg_ind+1)*tp_per_segment])
if seg_ind == 0:
result = result_cur
else:
result = numpy.concatenate((result, result_cur))
x0 = result[-1, :]
else:
result = sdeint.itoint(F, G, x0, tspan)
tspan = tspan[int(tburn/h)::ds_by]
result = result[int(tburn/h)::ds_by, :]
Y = result[:, 0]
X = result[:, 1]
return Y, X, p_true, model_type
def load_model_data(model_name, N, ds_by = None, dt = None):
"""
Generate time series from various model systems, including:
arch
(s)logistic
(s)henon
(s)lorenz
(s)rossler
(s)tent
setar
where the 's' prefix indicates a stochastic
difference / differential equation version of the standard
deterministic model.
Parameters
----------
model_name : str
The name of the model to use. See function description
for list of available models.
N : int
The number of time points to simulate from the model
system.
ds_by : int
Specify the amount to downsample a continuous-time
time series by. By default, use the hard coded values.
Returns
-------
x : numpy.array
The time series.
p_true : int
The true model order of the system. If not
a Markov model, p_true = numpy.inf
model_type : str
The model type.
"""
if model_name == 'arch':
# Simulate from an ARCH(1) model:
model_type = 'arch'
p_true = 1
x = numpy.zeros(N)
u = numpy.random.randn(N)
x[:1] = u[:1]
for n in range(1, x.shape[0]):
x[n] = numpy.sqrt(0.5 + 0.5*x[n-1]**2)*u[n]
# Simulate from an ARCH(2) model:
# p_true = 2
# x = numpy.zeros(N)
# u = numpy.random.randn(N)
# x[:2] = u[:2]
# for n in range(2, x.shape[0]):
# x[n] = numpy.sqrt(0.5 + 0.5*x[n-1]**2 + 0.5*x[n-2]**2)*u[n]
if model_name == 'slogistic' or model_name == 'logistic':
# NLAR(1) model from:
#
# **Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems**
model_type = 'nlar'
p_true = 1
x = numpy.zeros(N)
if model_name == 'slogistic':
noise = (numpy.random.rand(N, 48) - 0.5)/2./16.
noise = noise.sum(1)
else:
noise = numpy.zeros(N)
x[0] = numpy.random.rand(1)
for t in range(1, x.shape[0]):
x[t] = 3.68*x[t-1]*(1 - x[t-1]) + 0.4*noise[t]
if x[t] <= 0 or x[t] >= 1:
x[t] = numpy.random.rand(1)
if model_name == 'shenon' or model_name == 'henon':
# NLAR(2) model from:
#
# **On prediction and chaos in stochastic systems**
#
# Namely, stochastic Henon.
#
# Also on page 188 (dp 200) of *Chaos: A Statistical Perpsective*.
model_type = 'nlar'
p_true = 2
burnin = 1000
x = numpy.zeros(N + burnin)
if model_name == 'shenon':
# From original paper:
noise = (numpy.random.rand(N + burnin, 48) - 0.5)/2.
noise = noise.sum(1)
else:
noise = numpy.zeros(N + burnin)
x[:2] = 10*numpy.random.rand(1) - 5
for t in range(2, x.shape[0]):
x[t] = 6.8 - 0.19*x[t-1]**2 + 0.28*x[t-2] + 0.2*noise[t]
if x[t] < -10:
x[t] = 10*numpy.random.rand(1) - 5
x_w_burnin = x.copy()
x = x[burnin:]
if model_name == 'stent' or model_name == 'tent':
# Tent map with noise as from the logistic map.
# This is also a SETAR(1; 1, 1) model, in the
# vein of Tong.
model_type = 'nlar'
p_true = 1
x = numpy.zeros(N)
if model_name == 'stent':
noise = (numpy.random.rand(N, 48) - 0.5)/2./16.
noise = noise.sum(1)
else:
noise = numpy.zeros(N)
# No noise:
# noise = numpy.zeros(N)
x[0] = numpy.random.rand(1)
for t in range(1, x.shape[0]):
if x[t-1] < 0.5:
x[t] = 3.68/2.*x[t-1] + 0.4*noise[t]
else:
x[t] = 3.68/2. - 3.68/2.*x[t-1] + 0.4*noise[t]
if x[t] <= 0:
x[t] = numpy.random.rand(1)
if model_name == 'setar':
model_type = 'setar'
# Simulate from a SETAR(2; 1, 1) model:
# p_true = 1
# x = numpy.zeros(N)
# u = numpy.random.randn(N)
# x[:1] = u[:1]
# for n in range(1, x.shape[0]):
# # From "Sieve bootstrap for time series" by Buhlmann in Bernoulli
# if x[n-1] <= 0:
# x[n] = 1.5 - 0.9*x[n-1] + u[n]
# else:
# x[n] = -0.4 - 0.6*x[n-1] + u[n]
# if x[n-1] <= 0:
# x[n] = 1.5 - 0.9*x[n-1] + 0.5*u[n]
# else:
# x[n] = -0.4 - 0.6*x[n-1] + u[n]
# if x[n-1] <= 0:
# x[n] = 1.5 - 0.9*x[n-1] + 0.5*u[n]
# else:
# x[n] = -0.4 + 0.1*x[n-1] + u[n]
# Simulate from a SETAR(2; 2, 2) model:
# p_true = 2
# x = numpy.zeros(N)
# u = numpy.random.randn(N)
# x[:2] = u[:2]
# for n in range(2, x.shape[0]):
# if x[n-1] <= 0:
# x[n] = 1.5 - 0.9*x[n-1] + 0.2*x[n-2] + u[n]
# else:
# x[n] = -0.4 - 0.6*x[n-1] + 0.1*x[n-2] + u[n]
# Simulate from a SETAR(2; 2, 2) model used to model
# the Canadian Lynx data from Tong's *Non-linear
# Time Series*, p. 178:
p_true = 2
x = numpy.zeros(N)
u = numpy.random.randn(N)
x[:2] = 2*numpy.random.rand(2) + 2
for n in range(2, x.shape[0]):
if x[n-2] <= 3.25:
x[n] = 0.62 + 1.25*x[n-1] - 0.43*x[n-2] + numpy.sqrt(0.0381)*u[n]
else:
x[n] = 2.25 + 1.52*x[n-1] - 1.24*x[n-2] + numpy.sqrt(0.0626)*u[n]
if 'lorenz' in model_name:
model_type = 'nlar'
p_true = 4
if dt == None:
h = 0.05
else:
h = dt
if ds_by == None:
ds_by = 2
ttot = N*h*ds_by
tburn = 20
tf = ttot + tburn
tspan = numpy.linspace(0.0, tf, int(tf/h))
x0 = numpy.array([1.0, 1.0, 1.0])
params = [10., 28., 8./3.] # The parameters [s, r, b] for the canonical Lorenz equations
def F(X, t):
s = params[0]
r = params[1]
b = params[2]
x = X[0]
y = X[1]
z = X[2]
dX = numpy.array([s*(y - x), x*(r - z) - y, x*y - b*z])
return dX
def G(x, t):
return B
dim = 3
if model_name == 'slorenz':
dyn_noise = 2
else:
dyn_noise = 0
B = numpy.diag([dyn_noise]*dim)
result = sdeint.itoint(F, G, x0, tspan)
tspan = tspan[int(tburn/h)::ds_by]
result = result[int(tburn/h)::ds_by, :]
x = result[:, 0]
if 'rossler' in model_name:
model_type = 'nlar'
p_true = 4
h = 0.05
if ds_by == None:
ds_by = 5
ttot = N*h*ds_by
tburn = 100
tf = ttot + tburn
tspan = numpy.linspace(0.0, tf, int(tf/h))
x0 = numpy.array([1.0, 1.0, 1.0])
params = [0.1, 0.1, 14]
def F(X, t):
a = params[0]
b = params[1]
c = params[2]
x = X[0]
y = X[1]
z = X[2]
dX = numpy.array([-y - z, x + a*y, b + z*(x - c)])
return dX
def G(x, t):
return B
dim = 3
if model_name == 'srossler':
dyn_noise = 0.1
else:
dyn_noise = 0.0
B = numpy.diag([dyn_noise]*dim)
B[2, 2] = 0
result = sdeint.itoint(F, G, x0, tspan)
tspan = tspan[int(tburn/h)::ds_by]
result = result[int(tburn/h)::ds_by, :]
x = result[:, 0]
y = result[:, 1]
z = result[:, 2]
if 'loriei' in model_name:
model_type = 'nlar'
p_true = 4
# dt = 0.005 # Used in spenra paper
dt = 0.05
N_sim = int(N*2/dt)
# To generate
threshold_val = 50
if model_name == 'loriei':
model_name = 'lorenz'
else:
model_name = 'slorenz'
x, p_true, model_type = load_model_data(model_name, N_sim, ds_by = 1, dt = dt)
time = numpy.linspace(0, N_sim*dt, num = N_sim)
s = x + 25
S = numpy.cumsum(s)*dt
crossing_times = []
for iei_ind in range(1, N):
cur_thresh = iei_ind*threshold_val
where_out = numpy.where((S - cur_thresh > 0))
try:
cross_ind = where_out[0][0]
cross_time = time[cross_ind]
# plt.axhline(cur_thresh)
# plt.axvline(cross_time)
y0 = S[cross_ind - 1]; y1 = S[cross_ind]
x0 = time[cross_ind - 1]; x1 = time[cross_ind]
m = (y1 - y0)/float(x1 - x0)
xc = (cur_thresh - y0)/m + x0
# plt.plot(xc, cur_thresh, '.', color = 'green')
crossing_times.append(xc)
except:
break
iei = numpy.diff(crossing_times)
x = iei
if model_name == 'snanopore':
a=1.
b=1.
c=1.
km=5.
kp=1.
gamx=1.
gamy=100.
alpha=0.1
beta=0.1
model_type = 'nlar'
p_true = numpy.inf
if ds_by == None:
ds_by = 2
delta_t=0.25
T_final = ds_by*N*delta_t
M = int(T_final/delta_t + 1)
tspan = numpy.linspace(0.0, T_final, M)
x0 = numpy.array([1.0, -0.5])
def f(z, t):
#z=[x,y]
dx=-(1/gamx)*(a*numpy.power(z[0],3)-b*z[0]+c*z[1])
if z[0]<0:
H=0
else:
H=1
if z[0]>0:
Hm=0
else:
Hm=1
dy=(1/gamy)*(kp*H-km*Hm)
return numpy.array([dx,dy])
def G(z, t):
B=numpy.diag([alpha,beta])
return B
print('Solving SDE...')
result = sdeint.itoint(f, G, x0, tspan)
x = result[::ds_by, 0]
if model_name == 'shadow_crash':
p_true = 4
model_type = 'nlar'
h = 0.05
if ds_by == None:
ds_by = 2
ttot = N*h*ds_by
tburn = 20
tf = ttot + tburn
tspan = numpy.linspace(0.0, tf, int(tf/h))
x0 = numpy.array([1.0, 1.0])
def F(X, t):
b = 0.42
g = -0.04
x = X[0]
z = X[1]
dX = numpy.array([x - x**2*numpy.exp(-b*x*z), z - z**2*numpy.exp(-g*x)])
return dX
def G(X, t):
# B = numpy.diag([0.4, 0.01])
B = numpy.diag([0.2, 0.01])
x = X[0]
z = X[1]
B[0, 0] = x*B[0, 0]
B[1, 1] = z*B[1, 1]
return B
dim = 2
result = sdeint.itoint(F, G, x0, tspan)
tspan = tspan[int(tburn/h)::ds_by]
result = result[int(tburn/h)::ds_by, :]
x = result[:, 0]
return x, p_true, model_type
dS = dW*dt
S[i] = S[i-1] + dS
return S
###############################################################################
plt.figure()
plt.plot(Wiener(0,1,n,T))
def mu(x,t):
return x**2
def SIG(x, t):
return np.sqrt(x)
tspan = np.linspace(0.0, 1, 10001)
res = sdeint.itoint(mu, SIG, 1, tspan)
plt.figure()
plt.plot(tspan,res.ravel())
def mu2(x,t):
return x + 2
def sig2(x,t):
return np.sin(x)
plt.figure()
tspan2 = np.linspace(0.0, 1, 10001)
for i in range(10):
plt.plot(tspan2, sdeint.itoint(mu2, sig2, 0, tspan2))
def ForwardKolmogorovEquation(drift, diffusion):
X[s] * (b[s] - np.sum(np.dot(A, X)[0, s]))
for s in range(0, len(X))
])
return dydt
def u(X, t):
dydt = np.array([
1. / np.sqrt(SS) * np.sqrt(X[s] *
(b[s] + np.sum(np.dot(A, X)[0, s])))
for s in range(0, len(X))
])
return np.diag(dydt)
x0 = np.array(np.repeat(1., d))
for i in range(0, realization):
stochastic_result = sdeint.itoint(f, u, x0, t)
for cl in range(0, d):
clean_ = np.nan_to_num(stochastic_result[:, cl])
if min(clean_) <= 0:
ext[i] = 1
expected_transition.append(np.sum(ext) / len(ext))
FeasibilitySize.append(SizeFeasibilityDomain(A, normalization))
k = k + 0.002
print SizeFeasibilityDomain(A, normalization), np.sum(ext) / len(ext)
nome_file = 'TransitionProbability_in_%i' % d + 'd.txt'
s = open(nome_file, 'w')
[
s.write('%f %f\n' % (FeasibilitySize[i], expected_transition[i]))
def return_average_utility_for_node3(self,time_vector=np.linspace(0, 10, 10000)):
soln = sdeint.itoint(self.rate_of_experience, self.noise, self.experiences_of_choices, time_vector)
return np.average(np.average(self.utility_gained_at_node_three,0))
def _simulate(self):
"""Private, simulate sde
Returns:
dict of pandas data frame with key 'cells', 'drugs', 'fht'.
"""
def f(x, t):
if x[0] < 1e-8: x[0] = 0
if x[1] < 1e-8: x[1] = 0
if x[2] < 1e-8: x[2] = 0
if x[3] < 1e-8: x[3] = 0
if x[4] < 0: x[4] = 0
if self._dose == 0:
cs_dt = lambda x, t: (self._growth(self.grs, x) - self._quiescere_s(self.ksq, x[4]) - self._transit(self.kspr)) * x[0] + self._transit(self.kprs) * x[1] + self._transit(self.kqs) * x[3]
cpr_dt = lambda x, t: (self._growth(self.grpr, x) - self._quiescere_r(self.kprq) - self._transit(self.kprs)) * x[1] + self._transit(self.kspr) * x[0] + self._transit(self.kqpr) * x[3]
car_dt = lambda x, t: 0
cq_dt = lambda x, t: -(self._transit(self.kqs) + self._transit(self.kqpr)) * x[3] + self._quiescere_s(self.ksq, x[4]) * x[0] + self._quiescere_r(self.kprq) * x[1]
d_dt = lambda x, t: 0
else:
cs_dt = lambda x, t: (self._growth(self.grs, x) - self._quiescere_s(self.ksq, x[4]) - self._transit(self.ksar) - self._death(x[4])) * x[0] + self._transit(self.kprs) * x[1] + self._transit(self.kars) * x[2] + self._transit(self.kqs) * x[3]
cpr_dt = lambda x, t: (self._growth(self.grpr, x) - self._quiescere_r(self.kprq) - self._transit(self.kprs)) * x[1]
car_dt = lambda x, t: (self._growth(self.grar, x) - self._quiescere_r(self.karq) - self._transit(self.kars)) * x[2] + self._transit(self.ksar) * x[0] + self._transit(self.kqar) * x[3]
cq_dt = lambda x, t: -(self._transit(self.kqs) + self._transit(self.kqar)) * x[3] + self._quiescere_s(self.ksq, x[4]) * x[0] + self._quiescere_r(self.kprq) * x[1] + self._quiescere_r(self.karq) * x[2]
d_dt = lambda x, t: self._dose - self.ke * x[4]
a = np.array([cs_dt(x,t), cpr_dt(x,t), car_dt(x,t), cq_dt(x,t), d_dt(x,t)])
return a
def g(x, t):
difu = np.diag(np.repeat(self._sig, len(self.init)))
return difu * x
cth = self._get_cth()
dfcell = pd.DataFrame()
dfdrug = pd.DataFrame()
fht = []
for i in range(self.n):
itg = sdeint.itoint(f, g, self.init, self._tspan)
tdf = pd.DataFrame(itg)
tdf = tdf.drop(tdf.index[len(tdf)-1])
tdfdrug = pd.DataFrame(tdf.iloc[:,-1])
tdfdrug[len(tdfdrug.columns)] = i
tdfdrug[len(tdfdrug.columns)] = pd.Series(self._tspan)
dfdrug = dfdrug.append(tdfdrug)
tdfcell = tdf.iloc[:,0:4]
tdfcell[len(tdfcell.columns)] = tdfcell.sum(axis=1)
tdfcell[len(tdfcell.columns)] = i
tdfcell[len(tdfcell.columns)] = pd.Series(self._tspan)
dfcell = dfcell.append(tdfcell)
tdfcellsum = tdfcell.iloc[:,4]
if tdfcellsum.iloc[-1] < cth:
tfht = np.nan
else:
tfht = [n for n, j in enumerate(tdfcell[4]) if j > cth][0]
fht.append(tfht)
dfcell.columns = ['sensitive', 'primary resistant', 'acquired resistant', 'quiescent', 'total', 'n', 'days']
dfdrug.columns = ['drug conc', 'n', 'days']
dfs = {'cells':dfcell, 'drugs':dfdrug, 'fht':fht}
return dfs
#b = 0.8
tspan = np.linspace(0.0, 600 * np.pi, 50001)
#tspan = np.linspace(0.0, 60*np.pi, 5001)
omega = 1.0
X0 = np.array([1.0, 0.])
def f(X, t):
x, v = X
dxdt = v
dvdt = -omega**2 * x
#return np.zeros(2)
return np.array([dxdt, dvdt])
def g(X, t):
#return np.diag([0., A])
return np.diag([A, A])
A = float(input("A: "))
result = sdeint.itoint(f, g, X0, tspan)
#result = odeint(f, X0, tspan)
x = result[:, 0]
v = result[:, 1]
plt.plot(tspan, x)
plt.plot(tspan, v)
plt.show()
omega = np.ones_like(theta0) * 5 # omega = np.linspace(0, np.pi*2, N) K = np.zeros((N, N)) print(K) K[:, :] = 0 K[2, 3] = 0 dt = 0.01 t_end = 1 steps = t_end / dt # K[:,3] = 100 f, G = kuramoto(omega, K, N, 0.01) from sdeint import itoint tspan = np.linspace(0, t_end, steps) solution = itoint(f, G, theta0, tspan) from matplotlib import pyplot as plt plt.figure(1) plt.subplot(211) plt.plot(tspan, solution) solution = np.mod(solution, 2 * np.pi) solution -= np.pi plt.subplot(212) plt.plot(tspan, solution) plt.show() import itertools dt = 0.1 t_end = 10
def eval_bslr_on_locke(sampling_times,
num_cond,
num_rep,
one_shot,
sigma_co,
sigma_bi,
write_file,
rand_seed=0,
sig_level=0.05,
output='',
num_integration_interval=100,
max_in_deg=3,
rep_avg=True,
diffusion_type='linear'):
"""Evaluate BSLR using network in Locke et al. MSB 2005.
One environmental condition is modeled by the same set of
initial conditions (values) of the gene expression levels,
as well as the same condition-dependent nominal production
variations.
Args:
sampling_times: array
Sampling times as evenly spaced nonnegative
numbers in an increasing order.
num_cond: int
Number of conditions.
num_rep: int
Number of replicates per single time.
one_shot: bool
True if one-shot, False if multi-shot.
sigma_co: float
Condition-dependent production variation level.
sigma_bi: float
Biological production variation level.
write_file: bool
Writes xml file if True. Returns the adjacency
matrix if False.
rand_seed: int
Random number generator seed.
sig_level: float
Significance level.
output: str
Output filename.
num_integration_interval: int
Number of integration intervals for the Ito
integral, evenly spaced over
[0, sampling_times[-1]].
max_in_deg: int
Maximum in-degree used in BSLR.
rep_avg: bool
Do replicate averaging if True. Otherwise take
replicates as different conditions.
diffusion_type: str
Diffusion type. Can be 'linear' or
'michaelis-menten'.
Returns:
Saves graph file or return adjacency matrix.
"""
# Create a shallow copy of the default parameters.
param_test = get_locke_params()
param_test['sigma_co'] = sigma_co * np.ones((3, 4))
param_test['sigma_bi'] = sigma_bi * np.ones((3, 4))
param_test['diffusion_type'] = diffusion_type
np.random.seed(rand_seed)
# Generate data file.
num_time = len(sampling_times)
num_genes = 4
mrna = np.empty((num_genes, num_cond * num_rep * num_time))
tspan = np.linspace(0, sampling_times[-1], num_integration_interval + 1)
if one_shot:
num_rep_per_traj = num_rep * num_time
else:
num_rep_per_traj = num_rep
for idx_cond in range(num_cond):
# Generate the same 12-dimensional initial
# conditions for all replicates.
exp_init_per_rep = np.random.rand(12)
exp_init = np.empty(12 * num_rep_per_traj)
for idx_rep in range(num_rep_per_traj):
exp_init[idx_rep +
np.arange(12) * num_rep_per_traj] = (exp_init_per_rep)
# Entire solution over the fine tspan as a T-by-12R
# matrix, where T = len(tspan) and R = num_rep_per_traj.
exp_sol = sdeint.itoint(close(locke_drift, param_test),
close(diff_coeff, param_test), exp_init, tspan)
# Sampled expression levels at the coarse times,
# approximated by the closest time in tspan.
exp_sampled = exp_sol[[
int(round(x)) for x in np.asarray(sampling_times) /
sampling_times[-1] * num_integration_interval
], :]
# Reshape the array.
for i in range(num_genes):
for j in range(num_time):
start = idx_cond * num_rep * num_time + j * num_rep
if one_shot:
mrna[i, start:start + num_rep] = (
exp_sampled[j, i * num_rep_per_traj +
j * num_rep:i * num_rep_per_traj +
(j + 1) * num_rep])
else:
mrna[i, start:start +
num_rep] = (exp_sampled[j, i * num_rep:(i + 1) *
num_rep])
sample_ids = [
'c{}_t{}_r{}'.format(k, i, j) for k in range(num_cond)
for i in range(num_time) for j in range(num_rep)
]
mrna_df = pd.DataFrame(data=mrna,
columns=sample_ids,
index=['G1', 'G2', 'G3', 'G4'])
mrna_df.to_csv('exp-locke.csv')
# Generate gene list file.
np.savetxt('gene-list-locke.csv',
[['G1', 'LHY'], ['G2', 'TOC1'], ['G3', 'X'], ['G4', 'Y']],
fmt='%s',
delimiter=',')
# Generate condition list file.
num_rep_alg = num_rep
num_cond_alg = num_cond
if rep_avg:
conditions = list(range(num_cond))
else:
num_rep_alg = 1
num_cond_alg = num_cond * num_rep
conditions = list(range(num_cond_alg))
json.dump([conditions, list(range(num_time))],
open('cond-locke.json', 'w'),
indent=4)
# Generate design file.
samples_df = pd.DataFrame(data=sample_ids)
if rep_avg:
samples_df['cond'] = samples_df[0].apply(lambda x: x.split('_')[0][1:])
else:
samples_df['cond'] = samples_df[0].apply(lambda x: int(
x.split('_')[0][1:]) * num_rep + int(x.split('_')[2][1:]))
samples_df['time'] = samples_df[0].apply(lambda x: x.split('_')[1][1:])
samples_df.to_csv('design-locke.csv', header=False, index=False)
if write_file:
if not output:
output = ('test-t{num_times}-c{num_cond}-bslr'
'-s{sig_level}-r{rand_seed}.xml'.format(
num_times=num_time,
sig_level=sig_level,
rand_seed=rand_seed,
num_cond=num_cond_alg))
# Run BSLR.
causnet.main('-c cond-locke.json '
'-i gene-list-locke.csv -g {output} '
'-x exp-locke.csv '
'-P design-locke.csv '
'-f {sig_level} '
'-m {max_in_deg}'.format(output=output,
num_times=num_time,
sig_level=sig_level,
max_in_deg=max_in_deg).split())
return
else:
parser_dict = causnet.load_parser('design-locke.csv')
adj_mat_sign_rec = causnet.bslr(parser_dict, mrna_df, num_cond_alg,
num_time, num_genes, num_rep_alg,
max_in_deg, sig_level)
return adj_mat_sign_rec
r0 = [8, 12.0] # intial rates (re, ri)
tmax = 1000 # run time, ms
dt = .1 # resolution, ms
# Stim params
d = 1 # drive rate (want 0-1)
scale = .01 * d
Istim = create_I(tmax, d, scale, seed=42)
# Simulate
times = linspace(0, tmax, tmax / dt)
rs0 = asarray(r0 * 8 + [0])
f = partial(xjw, Je_e=3.0, Je_i=3.0, Ji_e=0.0, Ji_i=0.0, k1=0.9, k2=1.2)
g = partial(ornstein_uhlenbeck, sigma=0.5, loc=[0, 1, 6, 7]) # re/i locs
rs = itoint(f, g, rs0, times)
# -------------------------------------
# Select some interesting vars and plot
t = times
Is = rs[16]
re1 = rs[:, 0]
ri1 = rs[:, 1]
re2 = rs[:, 6]
ri2 = rs[:, 7]
# 1
plt.figure(figsize=(14, 10))
plt.subplot(411)
plt.plot(t, [Istim(x) for x in t], 'k', label='1: Stim')
plt.legend(loc='best')
def run_mc(params):
ind = params[0]
pressure = params[1]
drive_freq = params[2]
drive_voltage = params[3]
drive_voltage_noise = params[4]
drive_phase_noise = params[5]
init_angle = params[6]
discretized_phase = params[7]
beta_rot = pressure * np.sqrt(m0) / kappa
drive_amp = np.abs(bu.trap_efield([0, 0, 0, drive_voltage, -1.0*drive_voltage, \
0, 0, 0], nsamp=1)[0])
drive_amp_noise = drive_voltage_noise * (drive_amp / drive_voltage)
seed = seed_init * (ind + 1)
xi_0 = np.array([np.pi/2.0, 0.0, 0.0, \
0.0, 2.0*np.pi*drive_freq, 0.0])
time_constant = Ibead / beta_rot
np.random.seed(seed)
### If desired, set a thermalization time equal to 10x the time constant
### for this particular pressure and Ibead combination
if variable_thermalization:
t_therm = np.min([10.0 * time_constant, 300.0])
nthermfiles = int(t_therm / out_file_length) + 1
else:
t_therm = user_t_therm
nthermfiles = user_nthermfiles
values_to_save = {}
values_to_save['mbead'] = mbead
values_to_save['Ibead'] = Ibead
values_to_save['kappa'] = kappa
values_to_save['beta_rot'] = beta_rot
values_to_save['p0'] = p0
values_to_save['fsamp'] = fsamp
values_to_save['fsim'] = fsim
values_to_save['seed'] = seed
values_to_save['xi_0'] = xi_0
values_to_save['init_angle'] = init_angle
values_to_save['pressure'] = pressure
values_to_save['m0'] = m0
values_to_save['drive_freq'] = drive_freq
values_to_save['drive_amp'] = drive_amp
values_to_save['drive_amp_noise'] = drive_amp_noise
values_to_save['drive_phase_noise'] = drive_phase_noise
values_to_save['discretized_phase'] = discretized_phase
values_to_save['t_therm'] = t_therm
if not TEST:
base_filename = os.path.join(base, 'mc_{:d}/'.format(ind))
bu.make_all_pardirs(os.path.join(base_filename, 'derp.txt'))
param_path = os.path.join(base_filename, 'params.p')
pickle.dump(values_to_save, open(param_path, 'wb'))
def E_phi_func(t, t_therm=0.0, init_angle=0.0):
raw_val = 2.0 * np.pi * drive_freq * (t + t_therm) + init_angle
if discretized_phase:
n_disc = int(raw_val / discretized_phase)
return n_disc * discretized_phase
else:
return raw_val
### Matrix for the stochastic driving processes
torque_noise = np.sqrt(4.0 * kb * T * beta_rot)
# B = np.array([[0, 0, 0, 0],
# [0, 0, 0, 0],
# [0, 0, 1.0, 0],
# [0, 0, 0, 1.0]])
B = np.array([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 1.0, 0, 0],
[0, 0, 0, 0, 1.0, 0],
[0, 0, 0, 0, 0, 1.0]])
B *= torque_noise / Ibead
### Define the system such that d(xi) = f(xi, t) * dt
# @jit()
def f(x, t):
torque_theta = drive_amp * p0 * np.sin(0.5 * np.pi - x[0]) \
- 1.0 * beta_rot * x[3]
c_amp = drive_amp
E_phi = E_phi_func(t)
if fterm_noise:
c_amp += drive_amp_noise * np.random.randn()
E_phi += drive_phase_noise * np.random.randn()
torque_phi = c_amp * p0 * np.sin(E_phi - x[1]) * np.sin(x[0]) \
- 1.0 * beta_rot * x[4]
torque_psi = -1.0 * beta_rot * x[5]
return np.array([x[3], x[4], x[5], \
torque_theta / Ibead, \
torque_phi / Ibead, \
torque_psi / Ibead])
### Define the stochastic portion of the system
# @jit()
def G(x, t):
newB = np.zeros((6,6))
if gterm_noise:
E_phi = E_phi_func(t)
amp_noise_term = drive_amp_noise * p0 * np.sin(E_phi - x[1]) * np.sin(x[0])
E_phi_rand = drive_phase_noise * np.random.randn()
phase_noise_term = drive_amp * p0 * np.sin(E_phi_rand) * np.sin(x[0])
newB[4,4] += amp_noise_term + phase_noise_term
return B + newB
### Thermalize
xi_init = np.copy(xi_0)
for i in range(nthermfiles):
t0 = i*out_file_length
tf = (i+1)*out_file_length
nsim = int(out_file_length * fsim)
tvec = np.linspace(t0, tf, nsim+1)
result = sdeint.itoint(f, G, xi_init, tvec).T
xi_init = np.copy(result[:,-1])
### Redefine the system taking into account the thermalization time
### and the desired phase offset
# @jit()
def f(x, t):
torque_theta = drive_amp * p0 * np.sin(0.5 * np.pi - x[0]) \
- 1.0 * beta_rot * x[3]
c_amp = drive_amp
E_phi = E_phi_func(t, t_therm=t_therm, init_angle=init_angle)
if fterm_noise:
c_amp += drive_amp_noise * np.random.randn()
E_phi += drive_phase_noise * np.random.randn()
torque_phi = c_amp * p0 * np.sin(E_phi - x[1]) * np.sin(x[0]) \
- 1.0 * beta_rot * x[4]
torque_psi = -1.0 * beta_rot * x[5]
return np.array([x[3], x[4], x[5], \
torque_theta / Ibead, \
torque_phi / Ibead, \
torque_psi / Ibead])
# @jit()
# def f(x, t):
# torque_theta = - 1.0 * beta_rot * x[2]
# torque_phi = - 1.0 * beta_rot * x[3]
# return np.array([x[2], x[3], torque_theta / Ibead, torque_phi / Ibead])
### Define the stochastic portion of the system
def G(x, t):
newB = np.zeros((6,6))
if gterm_noise:
E_phi = E_phi_func(t, t_therm=t_therm, init_angle=init_angle)
amp_noise_term = drive_amp_noise * p0 * np.sin(E_phi - x[1]) * np.sin(x[0])
E_phi_rand = drive_phase_noise * np.random.randn()
phase_noise_term = drive_amp * p0 * np.sin(E_phi_rand) * np.sin(x[0])
newB[4,4] += amp_noise_term + phase_noise_term
return B + newB
### Run the simulation with the thermalized solution
for i in range(nfiles):
# start = time.time()
t0 = i*out_file_length
tf = (i+1)*out_file_length
nsim = int(out_file_length * fsim)
tvec = np.linspace(t0, tf, nsim+1)
### Solve!
# print('RUNNING SIM')
result = sdeint.itoint(f, G, xi_init, tvec).T
xi_init = np.copy(result[:,-1])
tvec = tvec[:-1]
soln = result[:,:-1]
# print('DOWNSAMPLING')
nsamp = int(out_file_length * fsamp)
# soln_ds, tvec_ds = signal.resample(soln, t=tvec, \
# num=nsamp, axis=-1)
# soln_ds = signal.decimate(soln, int(upsamp))
tvec_ds = tvec[::int(upsamp)]
soln_ds = soln[:,::int(upsamp)]
# plt.plot(tvec, soln[1])
# plt.plot(tvec_ds, soln_ds[1])
# plt.plot(tvec_ds, soln_ds_2[1])
# plt.show()
if not TEST:
out_arr = np.concatenate( (tvec_ds.reshape((1, len(tvec_ds))), soln_ds) )
filename = os.path.join(base_filename, 'outdat_{:d}.h5'.format(i))
fobj = h5py.File(filename, 'w')
fobj.create_dataset('sim_data', data=out_arr, compression='gzip', \
compression_opts=9)
fobj.close()
# stop = time.time()
# print('Time for one file: {:0.1f}'.format(stop-start))
return seed
def return_average_utility(self,time_vector=np.linspace(0, 10, 10000)):
soln = sdeint.itoint(self.rate_of_experience, self.noise, self.experiences_of_choices, time_vector)
return np.average(np.average(self.orbits_utility,0))
def simulate(self, t, inputs=None):
"""
The simulate function takes no, one or multiple inputs and simulates the
system from the current state for all time marks in t. At these time the
control is also updated!
"""
outputDimension = self.system.outputOrder
if outputDimension:
output = np.zeros((t.size, outputDimension))
t0 = t[0]
index = 0
tnew = t
current_sample = 0
num_samples = len(t)
if 'jitter' in self.options:
jitter_range = self.options['jitter']['range']
if jitter_range > (t[1] - t[0]) / 2.:
raise "Too large jitter range. Time steps could change order"
tnew = t + (np.random.rand(t.size) - 0.5) * jitter_range
print("With Jitter!")
# print(t)
# print(tnew)
for timeInstance in tnew[1:]:
# Store observations
if outputDimension:
output[index, :] = self.system.output(self.state)
index += 1
def f(x, t):
"""
Compute the system derivative considering state control and input.
"""
hom = np.dot(self.system.A, x.reshape(
(self.system.order, 1))).flatten()
control = self.control.fun(t)
input = np.zeros_like(hom)
if inputs:
for signal in inputs:
input += signal.fun(timeInstance)
return hom + control + input
if "noise" in self.options:
# Shock Noise
noise_state = np.zeros(
(self.system.order, len(self.options["noise"])))
for i, noiseSource in enumerate(self.options['noise']):
# print(noiseSource['std'])
if noiseSource['std'] > 0:
# std = np.sqrt(noiseSource["std"] ** 2 * (timeInstance - t0)) * noiseSource["steeringVector"]
std = noiseSource["std"] * noiseSource["steeringVector"]
noise_state[:, i] = std
# noise_state += (np.random.rand() - 0.5 ) * 2 * std
def g(x, t):
return noise_state
else:
def g(x, t):
return np.zeros((self.system.order, 1))
# Solve ordinary differential equation
# self.state = odeint(derivate, self.state, np.array([t0, timeInstance]), mxstep=100, rtol=1e-13, hmin=1e-12)[-1, :]
tspace = np.linspace(t0, timeInstance, 10)
self.state = sdeint.itoint(f, g, self.state, tspace)[-1, :]
# If thermal noise should be simulated
# if "noise" in self.options:
# # Shock Noise
# noise_state = np.zeros(self.system.order)
# for noiseSource in self.options['noise']:
# # print(noiseSource['std'])
# if noiseSource['std'] > 0:
# # std = np.sqrt(noiseSource["std"] ** 2 * (timeInstance - t0)) * noiseSource["steeringVector"]
# std = noiseSource["std"] * noiseSource["steeringVector"]
# noise_state += np.random.randn() * std
# # noise_state += (np.random.rand() - 0.5 ) * 2 * std
# self.state += noise_state
# # Thermal Noise Simulation
# for noiseSource in self.options['noise']:
# if noiseSource['std'] > 0:
# def noiseDerivative(x, t):
# hom = np.dot(self.system.A, x.reshape((self.system.order,1))).flatten()
# noise = np.random.randn() * noiseSource["std"] * noiseSource["steeringVector"]
# return hom + noise
# noise_state = odeint(noiseDerivative, np.zeros_like(self.state), np.array([t0, timeInstance]))[-1, :]
# # print("Noise state %s" %noise_state)
# # print("state before ", self.state)
# self.state += noise_state
# # print("noise ", noise_state)
# # print("state after ", self.state)
# Increase time
t0 = timeInstance
# Update control descisions
# print(self.state)
# Clip if state is out of bound
if True:
bound = 1.
above = self.state > bound
below = self.state < -bound
oob_states = np.arange(self.system.order)[np.logical_or(
above, below)]
if any(oob_states):
# self.log("STATE BOUND EXCEEDED! Sample #: {}".format(current_sample))
# self.log("X_{} = {}".format(oob_states, self.state[oob_states]))
self.num_oob += 1
#self.state[above] = bound
#self.state[below] = -bound
# print(self.state)
current_sample += 1
self.control.update(self.state)
# Print progress every 1e4 samples
try:
if current_sample % (num_samples // 1e4) == 0:
print("Simulation Progress: %.2f%% \r" %
(100 * (current_sample / num_samples)),
end='',
flush=True)
except ZeroDivisionError:
pass
# Return simulation object
return {
't': t,
'control': self.control,
'output': output,
'system': self.system,
'state': self.state,
'options': self.options,
'log': self.logstr,
'num_oob': self.num_oob
}
import numpy as np
import matplotlib.pyplot as plt
import sdeint
a = 1.0
b = 0.8
tspan = np.linspace(0.0, 500.0, 3 * 5001)
x0 = 0.1
def f(x, t):
#return -(a + x*b**2)*(1 - x**2)
return 0.0
def g(x, t):
#return b*(1 - x**2)
return 1.0
count = 100
result = []
for i in range(count):
if i % 5 == 0:
print("{}/{}".format(i, count))
x = sdeint.itoint(f, g, x0, tspan)[:, 0]
plt.plot(tspan, x)
result.append(x)
plt.show()
samples = base_density_1d(300).numpy()
# Define an Ito SDE
def f(x, t):
return -x
D = 1
def g(x, t):
return np.diag(np.sqrt(2 * D) * np.ones(len(x)))
T = 2
tspan = np.linspace(0.0, T, 200)
# Solve the SDE defined above
result = sdeint.itoint(f, g, samples, tspan)
plt.plot(tspan, result)
plt.title('Particle paths')
plt.show()
plt.hist(samples, density=True)
plt.title('True Bimodal Base Density')
plt.xlabel('x')
plt.ylabel('Density')
plt.show()
plt.hist(result[-1], density=True)
plt.title('Prior density ')
plt.show()
def return_area(self, time_vector=np.linspace(0, 10, 10000)):
soln = sdeint.itoint(self.rate_of_experience, self.noise, self.experiences_of_choices, time_vector)
return trapz(self.orbits_for_sum_pi_ei, range(0, len(self.orbits_for_sum_pi_ei)))
return B
result = np.zeros((num_sims, N, 6))
result_ese = np.zeros((num_sims, N, 6))
for i in range(0, num_sims - 1):
x0 = [
np.random.randn(),
np.random.randn(),
np.random.randn(),
np.random.randn(),
np.random.randn(),
np.random.randn()
]
result[i] = sdeint.itoint(f, G, x0, tspan)
result_ese[i] = sdeint.itoint(f_ese, G, x0, tspan)
print(i)
print('Done with integrtion')
num_bins = 20
a = np.ceil(abs(max(np.ndarray.flatten(result[:][:][0]), key=abs))) / 3
step_size = 2 * a / num_bins
def counts(iterable, low, high, bins):
step = (high - low + 0.0) / bins
dist = collections.Counter((float(x) - low) // step for x in iterable)
return [dist[b] for b in range(bins)]
def simulate_meso(self, method="BDF", atol=1.e-5, rtol=1.e-6, G=None):
qgrid = self.qgrid
dqgrid = self.dqgrid
weights = self.weights
inner = slice(1, -1)
left = slice(0, -2)
right = slice(2, None)
# works inplace w.r.t. v!
def upwind(v, rho, dqgrid):
v_pos = 0.5 * (v[inner] + np.abs(v[inner]))
v_neg = 0.5 * (v[inner] - np.abs(v[inner]))
drho = np.zeros_like(rho)
drho[inner] -= v_pos / dqgrid[0:-1] * (rho[inner] - rho[left]
) # * (rho[inner] > 0.5)
drho[inner] -= v_neg / dqgrid[1:] * (rho[right] - rho[inner]
) # * (rho[inner] > 0.5)
return drho
def ode_fun_meso(t, y):
r = y[0]
dr = y[1]
rho = y[2:]
M = self.pms_sym.M_mod_meso(r, dr, rho, qgrid, weights)
F = self.pms_sym.F_mod_meso(r, dr, rho, qgrid, weights)
v = self.pms_sym.v_mod_meso(r, dr, qgrid)
return np.concatenate(
[np.array([dr, F / M]),
upwind(v, rho, dqgrid)])
if G is not None:
def G_func(y, t):
r = y[0]
dr = y[1]
rho = y[2:]
M = self.pms_sym.M_mod_meso(r, dr, rho, qgrid, weights)
return np.concatenate(
[np.array([0, G(y, t) / M]),
upwind(v, rho, dqgrid)])
if self.t_eval is None:
self.t_eval = np.linspace(0, self.t_end, 1000)
res = si.itoint(lambda y, t: ode_fun_meso(t, y), G_func, self.y0,
self.t_eval)
self.sol = lambda: 0
self.sol.message = "SDE integrator finished."
self.sol.y = res.T
self.sol.t = self.t_eval
else:
self.sol = solve_ivp(ode_fun_meso, [0, self.t_end],
self.y0_meso,
method=method,
atol=atol,
rtol=rtol,
t_eval=self.t_eval)
self.r = self.sol.y[0, :]
self.dr = self.sol.y[1, :]
self.rho = self.sol.y[2:, :]