def test_integrator_comparison():
f = lambda x: np.sin(x)
F = lambda x: -np.cos(x)
expected_answer = F(np.pi) - F(0)
a, b, N = 0, np.pi, 129000 #Lowest N for normal integrate.
a, b, B = 0, np.pi, 90700 #Lowest N for mid integrate.
assert (Integrator.integrate(f, a, b, N) - expected_answer < 1E-10)
assert (Integrator.midpoint_integrate(f, a, b, B) - expected_answer <
1E-10)
assert (numpy_integrator.integrator(f, a, b, N) - expected_answer < 1E-10)
assert (numpy_integrator.midpoint_integrator(f, a, b, B) - expected_answer
< 1E-10)
assert (abs(numba(f, a, b, N) - expected_answer) < 1E-10)
assert (abs(numba_integrate(f, a, b, B) - expected_answer) < 1E-10)
assert (abs(
cython_integrator.integrate_g(a, b, N) - expected_answer < 1E-10))
assert (abs(
cython_integrator.cython_integrate_mid(a, b, B) -
expected_answer < 1E-10))
with open('report6.txt', 'a') as out:
out.write("Lowest N for normal integrate is: {}.\n".format(N))
out.write("Lowest N for mid integrate is: {}.\n".format(
B)) #Printing result to report3.txt
def __init__(self, x0: np.ndarray, F: Callable, H: np.ndarray,
Q: np.ndarray, R: np.ndarray, dt: float):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.ndim = x0.shape[0]
rep_ndim = self.ndim * (self.ndim + 1) # representational dimension
def f(t, state, z_t, F_t):
x_t, P_t = self.load_vars(state)
z_t = z_t[:, np.newaxis]
K_t = P_t @ self.H @ np.linalg.inv(self.R)
d_x = F_t @ x_t + K_t @ (z_t - self.H @ x_t)
d_P = F_t @ P_t + P_t @ F_t.T + self.Q - K_t @ self.R @ K_t.T
d_state = np.concatenate((d_x, d_P), axis=1)
return d_state.ravel() # Flatten for integrate.ode
def g(t, state):
return np.zeros((rep_ndim, rep_ndim))
x0 = x0[:, np.newaxis]
P0 = np.eye(self.ndim)
self.x_t = x0
self.P_t = P0
iv = np.concatenate((x0, P0),
axis=1).ravel() # Flatten for integrate.ode
self.r = Integrator(f, g, rep_ndim)
self.r.set_initial_value(iv, 0.)
def func2(self, x):
integrator = Integrator(self.hamiltonian)
tstart = 0
tend = self.period
xfinal = integrator.integrate(x, tstart, tend, self.integration_method)
#print("difference = {}".format(x-xfinal))
#print("func output : {}".format(x-xfinal))
return x - xfinal
def main():
print("start!!")
model = Rocket_Model_6DoF()
# state and input list
X = np.empty(shape=[model.n_x, K])
U = np.empty(shape=[model.n_u, K])
# INITIALIZATION
sigma = model.t_f_guess
X, U = model.initialize_trajectory(X, U)
integrator = Integrator(model, K)
problem = SCProblem(model, K)
converged = False
w_delta = W_DELTA
for it in range(iterations):
t0_it = time()
print('-' * 18 + ' Iteration {str(it + 1).zfill(2)} ' + '-' * 18)
A_bar, B_bar, C_bar, S_bar, z_bar = integrator.calculate_discretization(X, U, sigma)
problem.set_parameters(A_bar=A_bar, B_bar=B_bar, C_bar=C_bar, S_bar=S_bar, z_bar=z_bar,
X_last=X, U_last=U, sigma_last=sigma,
weight_sigma=W_SIGMA, weight_nu=W_NU,
weight_delta=w_delta, weight_delta_sigma=W_DELTA_SIGMA)
problem.solve()
X = problem.get_variable('X')
U = problem.get_variable('U')
sigma = problem.get_variable('sigma')
delta_norm = problem.get_variable('delta_norm')
sigma_norm = problem.get_variable('sigma_norm')
nu_norm = np.linalg.norm(problem.get_variable('nu'), np.inf)
print('delta_norm', delta_norm)
print('sigma_norm', sigma_norm)
print('nu_norm', nu_norm)
if delta_norm < 1e-3 and sigma_norm < 1e-3 and nu_norm < 1e-7:
converged = True
w_delta *= 1.5
print('Time for iteration', time() - t0_it, 's')
if converged:
print('Converged after {it + 1} iterations.')
break
plot_animation(X, U)
print("done!!")
class TestIntegrator(unittest.TestCase):
def setUp(self):
self.integrator = Integrator()
def test_integrated(self):
packageA = pk.Package.make(value=numpy.array((1, 2, 3)), timestamp=0)
packageB = pk.Package.make(value=numpy.array((1, 2, 3)), timestamp=2)
self.integrator.handle(packageA)
expected = (3, 6, 9)
actual = tuple(self.integrator.handle(packageB).value)
self.assertEqual(actual, expected)
def test_integral_of_linear_function():
"""Integral of f(x) = 2x from 0 to 1 with 1m steps"""
f = lambda x: 2 * x
F = lambda x: 2 * x**2 / 2
expected_answer = F(1) - F(0)
a, b, N = 0, 1, 1000000
assert abs(Integrator.integrate(f, a, b, N) - expected_answer) < 1E-5
def test_integral_of_constant_function():
""" Integral of f(x) = 2. From 0 to 1 with 100k steps """
f = lambda x: 2
F = lambda x: 2 * x
expected_answer = F(1) - F(0)
a, b, N = 0, 1, 100000
assert abs(Integrator.integrate(f, a, b, N) - expected_answer) < 1E-11
def setup_integrator(self, context):
""" Setup the additional particle arrays for integration.
Parameters:
-----------
context -- the OpenCL context
setup_cl on the calcs must be called when all particle
properties on the particle array are created. This is
important as all device buffers will created.
"""
Integrator.setup_integrator(self)
self.setup_cl(context)
self.cl_precision = self.particles.get_cl_precision()
def setup_integrator(self, context):
""" Setup the additional particle arrays for integration.
Parameters:
-----------
context -- the OpenCL context
setup_cl on the calcs must be called when all particle
properties on the particle array are created. This is
important as all device buffers will created.
"""
Integrator.setup_integrator(self)
self.setup_cl(context)
self.cl_precision = self.particles.get_cl_precision()
def compute_trajectory(self, dev_max, dev_var, dev_thr):
n_chunks, chunk_size_ms, last_chunk_ms = self._get_integration_chunks()
init_cond = self.init_cond
idx = None
for i in range(n_chunks):
if i == n_chunks - 1:
integrator = Integrator(self.m, last_chunk_ms, self.dt)
else:
integrator = Integrator(self.m, chunk_size_ms, self.dt)
integrator.set_initial_conditions(init_cond)
idx = integrator.find_limit_cycle(dev_max, dev_var, dev_thr, methods.EULER)
if idx[1] > idx[0] or i == n_chunks - 1:
return integrator.data[:, idx[0]:idx[1]].copy()
else:
init_cond = integrator.data[:, -1].copy()
def main():
system_state = System_State()
system_state.initialize()
initial_print(system_state.current_state)
integrator = Integrator()
integrator.write_run_informations()
integrator.integrate(system_state)
final_print(system_state.current_state)
def update_system_properties(self, steps=1):
'''
Updated the properties of all the particles in
the system according to the integrator scheme provided
in the integrator class
'''
updated_properties = {}
integrator = Integrator()
for particle in self.particles:
neighbours = self.get_neighbours(particle)
updated_properties = integrator.get_updated_properties\
(particle, neighbours, self.h, \
kernel='cubic-spline')
particle.set_properties(udated_properties)
def integrator(self, name_of_integrator):
if self.__integrators is None:
self.__integrators = Integrator.load_integrators()
print(('Setting the integrator to %s' % name_of_integrator))
# populate the parameters to the integrator
if name_of_integrator in self.__integrators:
self.__integrator = getattr(self.__integrators[name_of_integrator], name_of_integrator)()
self.__integrator.CONST_G = self.CONST_G
self.__integrator.t_end = self.__t_end
self.__integrator.h = self.__h
self.__integrator.t_start = self.__t_start
self.__integrator.output_file = self.output_file
self.__integrator.collision_output_file = self.collision_output_file
self.__integrator.close_encounter_output_file = self.close_encounter_output_file
self.__integrator.store_dt = self.__store_dt
self.__integrator.buffer_len = self.__buffer_len
def initialize(self, config=None):
# Initialize the integrator
self.__integrators = Integrator.load_integrators()
if self.__integrator is None:
print('Use GaussRadau15 as the default integrator...')
self.integrator = 'GaussRadau15'
self.integrator.initialize()
self.integrator.acceleration_method = 'ctypes'
else:
self.__integrator.CONST_G = self.CONST_G
self.__integrator.t_end = self.__t_end
self.__integrator.h = self.__h
self.__integrator.t_start = self.__t_start
self.__integrator.output_file = self.output_file
self.__integrator.store_dt = self.__store_dt
self.__integrator.buffer_len = self.__buffer_len
if config is not None:
# Gravitational parameter
self.integrator.CONST_G = np.array(config['physical_params']['G'])
# Integration parameters
self.integrator = config['integration']['integrator']
self.integrator.initialize()
self.integrator.h = float(config['integration']['h'])
if 'acc_method' in config['integration']:
self.integrator.acceleration_method = config['integration']['acc_method']
else:
self.integrator.acceleration_method = 'ctypes'
# Load sequence of object names
if 'names' in config:
names = config['names']
else:
names = None
# Initial and final times
if self.integrator.t_start == 0:
self.integrator.t_start = float(config['integration']['t0'])
if self.integrator.t_end == 0:
self.integrator.t_end = float(config['integration']['tf'])
self.integrator.active_integrator = config['integration']['integrator']
DataIO.ic_populate(config['initial_conds'], self, names=names)
def test_integral_task_42_43_44_45():
"""approximate the integral of f(x) = x2 from 0 to 1 with 100k steps. This is where I generate all my reportX.txt files as well."""
f = lambda x: x**2
F = lambda x: x**3 / 3
expected_answer = F(1) - F(0)
a, b, N = 0, 1, 100000000
###Comparing the selfmade "pure" version with the Numpy one###
t0 = time.clock()
assert abs(Integrator.integrate(f, a, b, N) -
expected_answer) < 1E-5 #Normal integrate function
t1 = time.clock()
t2 = time.clock()
assert abs(numpy_integrator.integrator(f, a, b, N) -
expected_answer) < 1E-5 #Numpy integrate function
t3 = time.clock()
t6 = time.clock()
assert abs(numba(f, a, b, N) -
expected_answer) < 1E-5 #Numba integrate function
t7 = time.clock()
t8 = time.clock()
assert abs(cython_integrator.integrate_f(a, b, N) -
expected_answer) < 1E-5 #Cython integrate function
t9 = time.clock()
with open('report3.txt', 'a') as out:
out.write("N is: {}\nPure function time: {}\n".format(
N, (t1 - t0))) #Printing result to report3.txt
out.write("Numpy function time: {}\n".format(
t3 - t2)) #Printing result to report3.txt
with open('report4.txt', 'a') as out:
out.write("N is: {}\nPure function time: {}\n".format(
N, (t1 - t0))) #Printing result to report3.txt
out.write("Numpy function time: {}\n".format(
t3 - t2)) #Printing result to report3.txt
out.write("Numba function time: {}\n".format(
t7 - t6)) #Printing result to report3.txt
with open('report5.txt', 'a') as out:
out.write("N is: {}\nPure function time: {}\n".format(
N, (t1 - t0))) #Printing result to report3.txt
out.write("Numpy function time: {}\n".format(
t3 - t2)) #Printing result to report3.txt
out.write("Numba function time: {}\n".format(
t7 - t6)) #Printing result to report3.txt
out.write("Cython function time: {}\n".format(t9 - t8))
class KF(LSProcess):
def __init__(self, x0: np.ndarray, F: Callable, H: np.ndarray,
Q: np.ndarray, R: np.ndarray, dt: float):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.ndim = x0.shape[0]
rep_ndim = self.ndim * (self.ndim + 1) # representational dimension
def f(t, state, z_t, F_t):
x_t, P_t = self.load_vars(state)
z_t = z_t[:, np.newaxis]
K_t = P_t @ self.H @ np.linalg.inv(self.R)
d_x = F_t @ x_t + K_t @ (z_t - self.H @ x_t)
d_P = F_t @ P_t + P_t @ F_t.T + self.Q - K_t @ self.R @ K_t.T
d_state = np.concatenate((d_x, d_P), axis=1)
return d_state.ravel() # Flatten for integrate.ode
def g(t, state):
return np.zeros((rep_ndim, rep_ndim))
x0 = x0[:, np.newaxis]
P0 = np.eye(self.ndim)
self.x_t = x0
self.P_t = P0
iv = np.concatenate((x0, P0),
axis=1).ravel() # Flatten for integrate.ode
self.r = Integrator(f, g, rep_ndim)
self.r.set_initial_value(iv, 0.)
def load_vars(self, state: np.ndarray):
state = state.reshape((self.ndim, self.ndim + 1))
x_t, P_t = state[:, :1], state[:, 1:]
return x_t, P_t
def __call__(self, z_t: np.ndarray):
''' Observe through filter '''
self.r.set_f_params(z_t, self.F(self.t))
self.r.integrate(self.t + self.dt)
x_t, P_t = self.load_vars(self.r.y)
self.x_t, self.P_t = x_t, P_t
x_t = np.squeeze(x_t)
err_t = z_t - x_t @ self.H.T
return x_t.copy(), err_t # x_t variable gets reused somewhere...
def estimate_constants(update_json=False):
# estimate L_phi_x, L_phi_u using max norm of Jacobians
# max attained at x1 = 1, x2 = -1
L_phi_u = np.sqrt((par.mu + (1 - par.mu))**2 + \
(par.mu -4*(1-par.mu))**2)
n_points = 100
u_grid = np.linspace(-par.umax, +par.umax, n_points)
norm_dphi_dx = np.zeros((n_points, 1))
for i in range(n_points):
u = u_grid[i]
dphi_dx = np.array([[u * (1 - par.mu), 1], [1, -4 * u * (1 - par.mu)]])
norm_dphi_dx[i] = np.linalg.norm(dphi_dx)
L_phi_x = np.max(norm_dphi_dx)
nsim = int(par.Tf / par.Ts)
x0 = par.x0_v[0]
n_scenarios = len(par.x0_v)
n_sqp_it = 3
# estimate a_1, a_2, a_3, sigma, mu_tilde constants based on sampling
VEXACT = np.zeros((nsim, 1, n_scenarios))
SOLEXACTNORM = np.zeros((nsim, 1, n_scenarios))
DELTAVEXACT = np.zeros((nsim - 1, 1, n_scenarios))
XNORMSQ = np.zeros((nsim, 1, n_scenarios))
XNORM = np.zeros((nsim, 1, n_scenarios))
XSIMEXACT = np.zeros((nsim + 1, 2, n_scenarios))
USIMEXACT = np.zeros((nsim, 1, n_scenarios))
exact_ocp_solver = OcpSolver()
for j in range(n_scenarios):
x0 = par.x0_v[j]
# closed loop simulation
XSIMEXACT[0, :, j] = x0
integrator = Integrator(par.ode)
exact_ocp_solver = OcpSolver()
exact_ocp_solver.nlp_eval()
for i in range(nsim):
XNORMSQ[i, 0, j] = np.linalg.norm(XSIMEXACT[i, :, j])**2
XNORM[i, 0, j] = np.linalg.norm(XSIMEXACT[i, :, j])
# update state in OCP solver
exact_ocp_solver.update_x0(XSIMEXACT[i, :, j])
solver_out = exact_ocp_solver.nlp_eval()
status = exact_ocp_solver.get_status()
if status != 'Solve_Succeeded':
raise Exception('Solver returned status {} at iteration {}'\
.format(status, i))
# get primal-dual solution
x = solver_out['x'].full()
lam_g = solver_out['lam_g'].full()
SOLEXACTNORM[i, :, j] = np.linalg.norm(np.vstack([x, lam_g]))
# get first control move
u = solver_out['x'].full()[2]
USIMEXACT[i, 0, j] = u
VEXACT[i, 0, j] = solver_out['f'].full()
XSIMEXACT[i+1,:,j] = integrator.eval(par.Ts, XSIMEXACT[i,:,j], \
u).full().transpose()
for i in range(nsim - 1):
DELTAVEXACT[i, 0, j] = VEXACT[i + 1, 0, j] - VEXACT[i, 0, j]
XSIMEXACT = XSIMEXACT[0:-1, :, :]
VEXACT_OVER_XNORMSQ = []
DELTAVEXACT_OVER_XNORMSQ = []
SOLEXACTNORM_OVER_XNORM = []
VEXACTSQRT_OVER_XNORM = []
for j in range(n_scenarios):
VEXACT_OVER_XNORMSQ.append(np.divide(VEXACT[:, 0, j], XNORMSQ[:, 0,
j]))
DELTAVEXACT_OVER_XNORMSQ.append(np.divide(DELTAVEXACT[:,0,j], \
XNORMSQ[0:-1,0,j]))
SOLEXACTNORM_OVER_XNORM.append(np.divide( \
SOLEXACTNORM[:,0,j], XNORM[:,0,j]))
VEXACTSQRT_OVER_XNORM.append(np.divide(np.sqrt(VEXACT[:,0,j]), \
XNORM[:,0,j]))
# compute constants
a1 = np.min(VEXACT_OVER_XNORMSQ)
a2 = np.max(VEXACT_OVER_XNORMSQ)
a3 = np.min(-1.0 / par.Ts * np.array(DELTAVEXACT_OVER_XNORMSQ))
sigma = np.max(SOLEXACTNORM_OVER_XNORM)
mu_tilde = np.max(VEXACTSQRT_OVER_XNORM)
print('a1 = {}, a2 = {}, a3 = {}, sigma = {}, mu_tilde = {}' \
.format(a1, a2, a3, sigma, mu_tilde))
if a1 < 0 or a2 < 0 or a3 < 0:
raise Exception('One of the a constants is \
negative (a1 = {}, a2 = {}, a3 = {})'.format(a1, a2, a3))
# estimate \hat{\kappa}
ocp_solver = OcpSolver()
lqr_solver = LqrSolver()
ocp_solver.nlp_eval()
XSIM = np.zeros((nsim + 1, 2, n_scenarios))
USIM = np.zeros((nsim, 1, n_scenarios))
VSIMSQRT = np.zeros((nsim, 1, n_scenarios))
ZSIM = np.zeros((nsim, 1, n_scenarios))
DELTAZSIM = np.zeros((nsim, 1, n_scenarios))
VSOSIM = np.zeros((nsim, 1, n_scenarios))
kappa = 0.0
for j in range(len(par.x0_v)):
x0 = par.x0_v[j]
XSIM[0, :, j] = x0
# closed loop simulation
integrator = Integrator(par.ode)
ocp_solver = OcpSolver()
ocp_solver.rti_eval()
ocp_solver.nlp_eval()
ocp_solver.update_x0(XSIM[0, :, j])
for i in range(nsim):
# update state in OCP solver
ocp_solver.update_x0(XSIM[i, :, j])
DELTAZSIM = np.zeros((n_sqp_it, 1))
if LQR_INIT:
lqr_solver.update_x0(XSIM[i, :, j])
lqr_solver.lqr_eval()
lqr_sol = lqr_solver.get_lqr_sol()
ocp_solver.set_sol_lin(lqr_sol)
for k in range(n_sqp_it):
# get primal dual solution (equalities only)
rti_sol = ocp_solver.get_rti_sol()
lam_g = rti_sol['lam_g'].full()
x = rti_sol['x'].full()
z = np.vstack((x, lam_g))
# get primal dual exact sol
exact_sol = ocp_solver.nlp_eval()
nlp_sol = ocp_solver.get_nlp_sol()
exact_lam_g = nlp_sol['lam_g'].full()
exact_x = nlp_sol['x'].full()
exact_z = np.vstack((exact_x, exact_lam_g))
DELTAZSIM[k, 0] = np.linalg.norm(z - exact_z)
# call solver
solver_out = ocp_solver.rti_eval()
status = ocp_solver.get_status()
if status != 'Solve_Succeeded':
raise Exception('Solver returned status {} at iteration {}'\
.format(status, i))
# estimate \hat{kappa}
KAPPAESTIMATE = np.zeros((n_sqp_it, 1))
for k in range(n_sqp_it - 1):
KAPPAESTIMATE[k, 0] = DELTAZSIM[k + 1, 0] / (DELTAZSIM[k, 0])
kappa = np.max([np.max(KAPPAESTIMATE), kappa])
# get first control move
u = solver_out['x'].full()[2]
USIM[i, 0, j] = u
XSIM[i+1,:,j] = integrator.eval(par.Ts, XSIM[i,:,j], \
u).full().transpose()
print('kappa = {}'.format(kappa))
if kappa > 1.0:
raise Exception('kappa bigger than 1.0!')
const = dict()
const['a1'] = a1
const['a2'] = a2
const['a3'] = a3
const['sigma'] = sigma
const['kappa_hat'] = kappa
const['mu_tilde'] = mu_tilde
const['L_phi_x'] = L_phi_x
const['L_phi_u'] = L_phi_u
if update_json:
with open('constants.json', 'w') as outfile:
json.dump(const, outfile)
return const
class LKF(LSProcess):
def __init__(self, x0: np.ndarray, F: Callable, H: np.ndarray, Q: np.ndarray, R: np.ndarray, dt: float, tau: float = float('inf'), eps=1e-4):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.eta_mu = eta_mu
self.eta_var = eta_var
self.ndim = x0.shape[0]
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.kf_err_hist = []
self.kf = KF(x0, F, H, Q, R, dt)
def f(t, state, z_t, err_hist, F_t):
# TODO fix all stateful references in this body
x_t, P_t, eta_t = self.load_vars(state)
z_t = z_t[:, np.newaxis]
K_t = [email protected]@np.linalg.inv(self.R)
d_eta = np.zeros((self.ndim, self.ndim))
if t > self.tau: # TODO warmup case?
H_inv = np.linalg.inv(self.H)
P_kf_t = self.kf.P_t
P_inv = np.linalg.solve(P_kf_t.T@P_kf_t + self.eps*np.eye(self.ndim), P_kf_t.T)
self.p_inv_t = P_inv
tau_n = int(self.tau / self.dt)
err_t, err_tau = err_hist[-1][:,np.newaxis], err_hist[-tau_n][:,np.newaxis]
d_zz = (err_t@err_t.T - err_tau@err_tau.T) / self.tau
self.e_zz_t = d_zz
# E_z = sum(err_hist[-tau_n:])[:,np.newaxis] / tau_n
# d_uu = ((err_t - err_tau)/self.tau)@(E_z.T) + E_z@(((err_t - err_tau)/self.tau).T)
# self.e_zz_t = d_zz - d_uu
# if np.linalg.norm(d_zz) >= 1.0:
# d_zz = np.zeros((self.ndim, self.ndim))
d_eta = (H_inv@d_zz@H_inv.T@P_inv / 2 - eta_t) / self.tau
F_est = F_t - eta_t
d_x = F_est@x_t + K_t@(z_t - self.H@x_t)
d_P = F_est@P_t + P_t@F_est.T + self.Q - [email protected]@K_t.T
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
self.x_t = x0
# covariance
P0 = np.eye(self.ndim)
self.P_t = P0
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
self.eta_t = eta0
iv = np.concatenate((x0, P0, eta0), axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
def load_vars(self, state: np.ndarray):
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:1+self.ndim], state[:, 1+self.ndim:]
return x_t, P_t, eta_t
def __call__(self, z_t: np.ndarray):
''' Observe through filter '''
_, kf_err_t = self.kf(z_t)
self.kf_err_hist.append(kf_err_t)
self.r.set_f_params(z_t, self.kf_err_hist, self.F(self.t))
self.r.integrate(self.t + self.dt)
x_t, P_t, eta_t = self.load_vars(self.r.y)
self.x_t, self.P_t, self.eta_t = x_t, P_t, eta_t
x_t = np.squeeze(x_t)
err_t = z_t - [email protected]
return x_t.copy(), err_t # x_t variable gets reused somewhere...
@property
def ode_shape(self):
return (self.ndim, 1 + 2*self.ndim) # representational dimension: x_t, P_t, eta_t
@property
def ode_ndim(self):
return self.ode_shape[0] * self.ode_shape[1] # for raveled representation
def f_eta(self, eta: np.ndarray):
""" density function of variations """
return stats.multivariate_normal.pdf(eta.ravel(), mean=self.eta_mu.ravel(), cov=self.eta_var.ravel())
def __init__(self, x0: np.ndarray, F: Callable, H: np.ndarray, Q: np.ndarray, R: np.ndarray, dt: float, tau: float = float('inf'), eps=1e-4):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.eta_mu = eta_mu
self.eta_var = eta_var
self.ndim = x0.shape[0]
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.kf_err_hist = []
self.kf = KF(x0, F, H, Q, R, dt)
def f(t, state, z_t, err_hist, F_t):
# TODO fix all stateful references in this body
x_t, P_t, eta_t = self.load_vars(state)
z_t = z_t[:, np.newaxis]
K_t = [email protected]@np.linalg.inv(self.R)
d_eta = np.zeros((self.ndim, self.ndim))
if t > self.tau: # TODO warmup case?
H_inv = np.linalg.inv(self.H)
P_kf_t = self.kf.P_t
P_inv = np.linalg.solve(P_kf_t.T@P_kf_t + self.eps*np.eye(self.ndim), P_kf_t.T)
self.p_inv_t = P_inv
tau_n = int(self.tau / self.dt)
err_t, err_tau = err_hist[-1][:,np.newaxis], err_hist[-tau_n][:,np.newaxis]
d_zz = (err_t@err_t.T - err_tau@err_tau.T) / self.tau
self.e_zz_t = d_zz
# E_z = sum(err_hist[-tau_n:])[:,np.newaxis] / tau_n
# d_uu = ((err_t - err_tau)/self.tau)@(E_z.T) + E_z@(((err_t - err_tau)/self.tau).T)
# self.e_zz_t = d_zz - d_uu
# if np.linalg.norm(d_zz) >= 1.0:
# d_zz = np.zeros((self.ndim, self.ndim))
d_eta = (H_inv@d_zz@H_inv.T@P_inv / 2 - eta_t) / self.tau
F_est = F_t - eta_t
d_x = F_est@x_t + K_t@(z_t - self.H@x_t)
d_P = F_est@P_t + P_t@F_est.T + self.Q - [email protected]@K_t.T
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
self.x_t = x0
# covariance
P0 = np.eye(self.ndim)
self.P_t = P0
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
self.eta_t = eta0
iv = np.concatenate((x0, P0, eta0), axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
def __init__(self,
x0: np.ndarray,
F: Callable,
H: np.ndarray,
Q: np.ndarray,
R: np.ndarray,
dt: float,
tau_rng: list = [float('inf')],
eta_mu: float = 0.,
eta_var: float = 1.,
eps=1e-4):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau_rng = tau_rng
self.eps = eps
self.eta_mu = eta_mu
self.eta_var = max(eta_var, 1e-3) # to avoid singular matrix
self.ndim = x0.shape[0]
self.err_hist = []
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
def f(t, state, z_t, err_hist, F_t):
# TODO fix all stateful references in this body
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:1 +
self.ndim], state[:, 1 +
self.ndim:]
z_t = z_t[:, np.newaxis]
K_t = P_t @ self.H @ np.linalg.inv(self.R)
d_eta = np.zeros((self.ndim, self.ndim))
if t > self.tau_rng[-1]: # TODO warmup case?
H_inv = np.linalg.inv(self.H)
P_inv = np.linalg.solve(
P_t.T @ P_t + self.eps * np.eye(self.ndim), P_t.T)
self.p_inv_t = P_inv
eta_new = np.zeros((self.ndim, self.ndim))
for tau in self.tau_rng:
tau_n = int(tau / self.dt)
err_t, err_tau = err_hist[-1][:, np.newaxis], err_hist[
-tau_n][:, np.newaxis]
d_zz = (err_t @ err_t.T - err_tau @ err_tau.T) / tau
self.e_zz_t = d_zz
# if np.linalg.norm(d_zz) >= 1.0:
# d_zz = np.zeros((self.ndim, self.ndim))
# E_z = sum(err_hist[-tau_n:])[:,np.newaxis] / tau_n
# d_uu = ((err_t - err_tau)/self.tau)@(E_z.T) + E_z@(((err_t - err_tau)/self.tau).T)
# self.e_zz_t = d_zz - d_uu
eta_new += H_inv @ d_zz @ H_inv.T @ P_inv / 2
eta_new /= len(self.tau_rng)
d_eta = eta_new - eta_t
# alpha = self.f_eta(d_eta_new) / self.f_eta(np.zeros((2,2)))
# if stats.uniform.rvs() <= alpha:
# d_eta = d_eta_new / self.dt
F_est = F_t - eta_t
d_x = F_est @ x_t + K_t @ (z_t - self.H @ x_t)
d_P = F_est @ P_t + P_t @ F_est.T + self.Q - K_t @ self.R @ K_t.T
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
self.x_t = x0
# covariance
P0 = np.eye(self.ndim)
self.P_t = P0
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
self.eta_t = eta0
iv = np.concatenate((x0, P0, eta0),
axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
0.0, # s_ampa
0.0, # x_nmda
0.0])# s_nmda
#traj = np.load('sgy_period_ref.npy')
m = SGY_neuron()
m.set_parameters(**reference_set)
# unstable parameters
m.par.g_ampa = 0
m.par.g_nmda = 0.09
m.par.w = 1.0
msfi = MSF_Integrator(m)
i = Integrator(m, tmax, dt)
i.set_initial_conditions(init)
# compute periodic trajectory
idx1, idx2 = i.find_limit_cycle(1e-5, test_var_thr=-55)
traj = i.data[:, idx1:idx2].copy()
del i
def floq(gamma):
msfi.compute_Floquet(gamma, dt, traj)
evals,_ = np.linalg.eig(msfi.X[-1])
return np.sort(np.abs(evals))[::-1]#import time
#t1 = time.time()
#msfer.compute_Floquet(1, 0.0005, traj)
#t2 = time.time()
tmax = 5e3 # ms
dt = 0.0005 # ms
n = 100
init = np.array([0.0, # x
0.0, # y
0.0])# z
m = HR_neuron()
m.set_parameters(**reference_set)
m.par.I_ext = 2.5
m.par.eps = 0.1
m.par.row_sum = 1
i = Integrator(m, tmax, dt)
i.set_initial_conditions(init)
msfi = MSF_Integrator(m)
#def plot_traces(idx=0, skip = 10):
#t = np.linspace(0, tmax, np.floor(i.data.shape[1] / skip) + 1)
#plt.figure()
#plt.plot(t, i.data[idx, ::skip])
#plt.show()
def timeit(closure, n):
total_t = 0
for j in range(n):
t1 = time.time()
closure()
t2 = time.time()
def __init__(self,
x0: np.ndarray,
F: Callable,
H: np.ndarray,
Q: np.ndarray,
R: np.ndarray,
dt: float,
tau=float('inf'),
eta_bnd=float('inf'),
eps=1e-4,
gamma=1.):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.eta_bnd = eta_bnd
self.gamma = gamma
self.ndim = x0.shape[0]
self.err_hist = []
self.P_hist = []
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
def f(t, state, z_t, err_hist, F_t):
# TODO fix all stateful references in this body
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:1 +
self.ndim], state[:, 1 +
self.ndim:]
z_t = z_t[:, np.newaxis]
K_t = P_t @ self.H @ np.linalg.inv(self.R)
d_eta = np.zeros((self.ndim, self.ndim))
if t > self.tau: # TODO warmup case?
H_inv = np.linalg.inv(self.H)
P_inv = np.linalg.solve(
P_t.T @ P_t + self.eps * np.eye(self.ndim), P_t.T)
self.p_inv_t = P_inv
tau_n = int(self.tau / self.dt)
err_t, err_tau = err_hist[-1][:, np.newaxis], err_hist[
-tau_n][:, np.newaxis]
p_t, p_tau = self.P_hist[-1], self.P_hist[-tau_n]
# d_zz = (err_t@err_t.T - err_tau@err_tau.T)
d_zz = (err_t @ err_t.T -
err_tau @ err_tau.T) / self.tau - self.H @ (
p_t - p_tau) @ self.H.T / self.tau
self.e_zz_t = d_zz
eta_new = self.gamma * H_inv @ d_zz @ H_inv.T @ P_inv / 2
if np.linalg.norm(eta_new) <= eta_bnd:
d_eta = (eta_new - eta_t) / self.dt
F_est = F_t - eta_t
d_x = F_est @ x_t + K_t @ (z_t - self.H @ x_t)
d_P = F_est @ P_t + P_t @ F_est.T + self.Q - K_t @ self.R @ K_t.T
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
self.x_t = x0
# covariance
P0 = np.eye(self.ndim)
self.P_t = P0
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
self.eta_t = eta0
iv = np.concatenate((x0, P0, eta0),
axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
def __init__(self):
Integrator.__init__(self)
def __init__(self):
Td = par.Tp / par.N
# linearize model
X_lin = ca.MX.sym('X_lin', 2, 1)
U_lin = ca.MX.sym('U_lin', 1, 1)
A_c = ca.Function('A_c', \
[X_lin, U_lin], [ca.jacobian(par.ode(X_lin, U_lin), X_lin)])
A_c = A_c([0, 0], 0).full()
B_c = ca.Function('B_c', \
[X_lin, U_lin], [ca.jacobian(par.ode(X_lin, U_lin), U_lin)])
B_c = B_c([0, 0], 0).full()
# solve continuous-time Riccati equation
Qt, e, K = cn.care(A_c, B_c, par.Q, par.R)
# this is the value used in Chen1998!!
# they do not use LQR, but a modified linear controller
# Qt = np.array([[16.5926, 11.5926], [11.5926, 16.5926]])
self.integrator = Integrator(par.ode)
self.x = self.integrator.x
self.u = self.integrator.u
self.Td = Td
# start with an empty NLP
w = []
w0 = []
lbw = []
ubw = []
g = []
lbg = []
ubg = []
Xk = ca.MX.sym('X0', 2, 1)
w += [Xk]
lbw += [0, 0]
ubw += [0, 0]
w0 += [0, 0]
f = 0
# formulate the NLP
for k in range(par.N):
# new NLP variable for the control
Uk = ca.MX.sym('U_' + str(k), 1, 1)
f = f + Td*ca.mtimes(ca.mtimes(Xk.T, par.Q), Xk) \
+ Td*ca.mtimes(ca.mtimes(Uk.T, par.R), Uk)
w += [Uk]
lbw += [-par.umax]
ubw += [par.umax]
w0 += [0.0]
# integrate till the end of the interval
Xk_end = self.integrator.eval(Td, Xk, Uk)
# new NLP variable for state at end of interval
Xk = ca.MX.sym('X_' + str(k + 1), 2, 1)
w += [Xk]
lbw += [-np.inf, -np.inf]
ubw += [np.inf, np.inf]
w0 += [0, 0]
# add equality constraint
g += [Xk_end - Xk]
lbg += [0, 0]
ubg += [0, 0]
f = f + ca.mtimes(ca.mtimes(Xk_end.T, Qt), Xk_end)
g = ca.vertcat(*g)
w = ca.vertcat(*w)
# create an NLP solver
prob = {'f': f, 'x': w, 'g': g}
self.__nlp_solver = ca.nlpsol('solver', 'ipopt', prob)
self.__lbw = lbw
self.__ubw = ubw
self.__lbg = lbg
self.__ubg = ubg
self.__w0 = np.array(w0)
self.__sol_lin = np.array(w0).transpose()
self.__rti_sol = []
self.__nlp_sol = []
# create QP solver
nw = len(w0)
# define linearization point
w_lin = ca.MX.sym('w_lin', nw, 1)
w_qp = ca.MX.sym('w_qp', nw, 1)
# linearized objective = original LLS objective
f_lin = ca.substitute(
f, w, w_qp) + par.alpha * ca.dot(w_qp - w_lin, w_qp - w_lin)
nabla_g = ca.jacobian(g, w).T
g_lin = ca.substitute(g, w, w_lin) + \
ca.mtimes(ca.substitute(nabla_g, w, w_lin).T, w_qp - w_lin)
# create a QP solver
prob = {'f': f_lin, 'x': w_qp, 'g': g_lin, 'p': w_lin}
self.__rti_solver = ca.nlpsol('solver', 'ipopt', prob)
class LKF(LSProcess):
def __init__(self,
x0: np.ndarray,
F: Callable,
H: np.ndarray,
Q: np.ndarray,
R: np.ndarray,
dt: float,
tau=float('inf'),
eps=1e-3):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.ndim = x0.shape[0]
self.err_hist = []
self.eta_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.n_est = 20
def f(t, state, z_t, err_hist, F_t):
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:3], state[:, 3:]
self.p_t = P_t
z_t = z_t[:, np.newaxis]
eta_t = np.zeros((self.ndim, self.ndim))
if self.history_loaded(): # TODO: warmup case?
H_inv = np.linalg.inv(self.H)
P_inv = np.linalg.solve(P_t.T @ P_t + eps * np.eye(2), P_t.T)
self.p_inv_t = P_inv
tau_n = int(self.tau / self.dt)
d_zz = np.zeros((self.ndim, self.ndim))
for i in range(self.n_est):
err_t, err_tau = err_hist[-1 - i][:, np.newaxis], err_hist[
-tau_n - i][:, np.newaxis]
d_zz += (err_t @ err_t.T - err_tau @ err_tau.T) / self.tau
d_zz /= self.n_est
self.e_zz_t = d_zz
eta_t = H_inv @ d_zz @ H_inv.T @ P_inv / 2
# eta_t = np.clip(eta_t, -10, 10)
self.eta_t = eta_t # TODO fix hack
F_est = F_t - eta_t
K_t = P_t @ self.H @ np.linalg.inv(self.R)
d_x = F_est @ x_t + K_t @ (z_t - self.H @ x_t)
d_P = F_est @ P_t + P_t @ F_est.T + self.Q - K_t @ self.R @ K_t.T
d_eta = np.zeros(
(self.ndim, self.ndim)
) # H_inv@(err_t@err_t.T - err_tau@err_tau.T)@H_inv.T@P_inv / (2*tau)
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
# covariance
P0 = np.eye(self.ndim)
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
iv = np.concatenate((x0, P0, eta0),
axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
def __call__(self, z_t: np.ndarray):
''' Observe through filter '''
self.r.set_f_params(z_t, self.err_hist, self.F(self.t))
self.r.integrate(self.t + self.dt)
x_t = np.squeeze(self.r.y.reshape(self.ode_shape)[:, :1])
err_t = z_t - x_t @ self.H.T
self.err_hist.append(err_t)
if self.history_loaded():
self.err_hist = self.err_hist[1:]
return x_t.copy(), err_t # x_t variable gets reused somewhere...
def history_loaded(self):
return self.t > self.tau + self.n_est * self.dt
@property
def ode_shape(self):
return (self.ndim, 1 + 2 * self.ndim
) # representational dimension: x_t, P_t, eta_t
@property
def ode_ndim(self):
return self.ode_shape[0] * self.ode_shape[
1] # for raveled representation
def __init__(self,
x0: np.ndarray,
F: Callable,
H: np.ndarray,
Q: np.ndarray,
R: np.ndarray,
dt: float,
tau=float('inf'),
eps=1e-3):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.ndim = x0.shape[0]
self.err_hist = []
self.eta_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.n_est = 20
def f(t, state, z_t, err_hist, F_t):
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:3], state[:, 3:]
self.p_t = P_t
z_t = z_t[:, np.newaxis]
eta_t = np.zeros((self.ndim, self.ndim))
if self.history_loaded(): # TODO: warmup case?
H_inv = np.linalg.inv(self.H)
P_inv = np.linalg.solve(P_t.T @ P_t + eps * np.eye(2), P_t.T)
self.p_inv_t = P_inv
tau_n = int(self.tau / self.dt)
d_zz = np.zeros((self.ndim, self.ndim))
for i in range(self.n_est):
err_t, err_tau = err_hist[-1 - i][:, np.newaxis], err_hist[
-tau_n - i][:, np.newaxis]
d_zz += (err_t @ err_t.T - err_tau @ err_tau.T) / self.tau
d_zz /= self.n_est
self.e_zz_t = d_zz
eta_t = H_inv @ d_zz @ H_inv.T @ P_inv / 2
# eta_t = np.clip(eta_t, -10, 10)
self.eta_t = eta_t # TODO fix hack
F_est = F_t - eta_t
K_t = P_t @ self.H @ np.linalg.inv(self.R)
d_x = F_est @ x_t + K_t @ (z_t - self.H @ x_t)
d_P = F_est @ P_t + P_t @ F_est.T + self.Q - K_t @ self.R @ K_t.T
d_eta = np.zeros(
(self.ndim, self.ndim)
) # H_inv@(err_t@err_t.T - err_tau@err_tau.T)@H_inv.T@P_inv / (2*tau)
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
# covariance
P0 = np.eye(self.ndim)
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
iv = np.concatenate((x0, P0, eta0),
axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
def run(self, t_end, dt, max_steps=1000, solver="odeint", output="dataframes",
terminate=False):
"""Run the parcel model.
After initializing the parcel model, it can be immediately run by
calling this function. Before the model is integrated, a routine
:func:`_setup_run()` is performed to equilibrate the initial aerosol
population to the ambient meteorology if it hasn't already been done.
Then, the initial conditions are
passed to a user-specified solver which integrates the system forward
in time. By default, the integrator wraps ODEPACK's LSODA routine through
SciPy's :func:`odeint` method, but extensions to use other solvers can be
written easily (for instance, two methods from :mod:`odespy` are given
below).
The user can specify the timesteps to evaluate the trace of the parcel
in one of two ways:
#. Setting ``dt`` will automatically specify a timestep to use and \
the model will use it to automatically populate the array to \
pass to the solver.
#. Otherwise, the user can specify ``ts`` as a list or array of the \
timesteps where the model should be evaluated.
**Args**:
* *z_top* -- Vertical extent to which the model should be integrated.
* *dt* -- Timestep intervals to report model output.
* *ts* -- Pre-computed array of timestamps where output is requested.
* *max_steps* -- Maximum number of steps allowed by solver to achieve \
tolerance during integration.
* *solver* -- A string indicating which solver to use:
* ``"odeint"``: LSODA implementation from ODEPACK via \
SciPy's ``integrate`` module
* ``"lsoda"``: LSODA implementation from ODEPACK via odespy
* ``"lsode"``: LSODE implementation from ODEPACK via odespy
* *output* -- A string indicating the format in which the output of the run should be returned
**Returns**:
Depending on what was passed to the *output* argument, different
types of data might be returned:
* ``"dataframes"``: (default) will process the output into \
two pandas DataFrames - the first one containing profiles \
of the meteorological quantities tracked in the model, \
and the second a dictionary of DataFrames with one for \
each AerosolSpecies, tracking the growth in each bin \
for those species.
* ``"arrays"``: will return the raw output from the solver \
used internally by the parcel model - the state vector \
``x`` and the evaluated timesteps converted into height \
coordinates.
* ``"smax"``: will only return the maximum supersaturation \
value achieved in the simulation.
A tuple whose first element is a DataFrame containing the profiles
of the meteorological quantities tracked in the parcel model, and
whose second element is a dictionary of DataFrames corresponding to
each aerosol species and their droplet sizes.
**Raises**:
``ParcelModelError``: The parcel model failed to complete successfully or failed to initialize.
"""
if not output in ["dataframes", "arrays", "smax"]:
raise ParcelModelError("Invalid value ('%s') specified for output format." % output)
if not self._model_set:
_ = self._setup_run()
y0 = self.y0
r_drys = self._r_drys
kappas = self._kappas
Nis = self._Nis
nr = self._nr
## Setup run time conditions
t = np.arange(0., t_end+dt, dt)
if self.console:
print "\n"+"n_steps = %d" % (len(t))+"\n"
## Setup/run integrator
try:
from parcel_aux import der as der_fcn
except ImportError:
print "Could not load Cython derivative; using Python version."
from parcel import der as der_fcn
args = (nr, r_drys, Nis, self.V, kappas)
integrator = Integrator.solver(solver)
## Is the updraft speed a function?
v_is_func = hasattr(self.V, '__call__')
if v_is_func: # Re-wrap the function to correctly figure out V
orig_der_fcn = der_fcn
def der_fcn(y, t, nr, r_drys, Nis, V, kappas):
V_t = self.V(t)
return orig_der_fcn(y, t, nr, r_drys, Nis, V_t, kappas)
try:
x, t, success = integrator(der_fcn, t, y0, args, self.console, max_steps, terminate)
except ValueError, e:
raise ParcelModelError("Something failed during model integration: %r" % e)
if __name__ == '__main__':
if len(sys.argv) == 3:
dt = 0.01
bodies = [[], []]
interactions = [[], [], [], [], []]
app = QtGui.QApplication(sys.argv)
init_system(sys.argv[1], bodies, interactions)
integrator = Integrator(bodies, interactions)
viewer = GridViewer(integrator, dt, k_list)
configure_system(sys.argv[2], integrator)
integrator.integrate(dt)
integrator.max_energy = integrator.normalize(integrator.get_max_energy())
viewer.prepare_color_key()
timer = QTimer()
timer.timeout.connect(run)
timer.start(10)
sys.exit(app.exec_())
else:
def setUp(self):
self.integrator = Integrator()
def test_create_plot():
"""Just creating the plot"""
f = lambda x: x**3 / 3
a, b, N = 0, 1, 10
Integrator.plot_dat(f, a, b, N)
def run(self, t_end,
output_dt=1., solver_dt=None,
max_steps=1000, solver="odeint", output="dataframes",
terminate=False, terminate_depth=100., **solver_args):
""" Run the parcel model simulation.
Once the model has been instantiated, a simulation can immediately be
performed by invoking this method. The numerical details underlying the
simulation and the times over which to integrate can be flexibly set
here.
**Time** -- The user must specify two timesteps: `output_dt`, which is the
timestep between output snapshots of the state of the parcel model, and
`solver_dt`, which is the the interval of time before the ODE integrator
is paused and re-started. It's usually okay to use a very large `solver_dt`,
as `output_dt` can be interpolated from the simulation. In some cases though
a small `solver_dt` could be useful to force the solver to use smaller
internal timesteps.
**Numerical Solver** -- By default, the model will use the `odeint` wrapper
of LSODA shipped by default with scipy. Some fine-tuning of the solver tolerances
is afforded here through the `max_steps`. For other solvers, a set of optional
arguments `solver_args` can be passed.
**Solution Output** -- Several different output formats are available by default.
Additionally, the output arrays are saved with the `ParcelModel` instance so they
can be used later.
Parameters
----------
t_end : float
Total time over interval over which the model should be integrated
output_dt : float
Timestep intervals to report model output.
solver_dt : float
Timestep interval for calling solver integration routine.
max_steps : int
Maximum number of steps allowed by solver to satisfy error tolerances
per timestep.
solver : {'odeint', 'lsoda', 'lsode', 'vode', cvode'}
Choose which numerical solver to use:
* `'odeint'`: LSODA implementation from ODEPACK via
SciPy's integrate module
* `'lsoda'`: LSODA implementation from ODEPACK via odespy
* `'lsode'`: LSODE implementation from ODEPACK via odespy
* `'vode'` : VODE implementation from ODEPACK via odespy
* `'cvode'` : CVODE implementation from Sundials via Assimulo
* `'lsodar'` : LSODAR implementation from Sundials via Assimulo
output : {'dataframes', 'arrays', 'smax'}
Choose format of solution output.
terminate : boolean
End simulation at or shortly after a maximum supersaturation has been achieved
terminate_depth : float, optional (default=100.)
Additional depth (in meters) to integrate after termination criterion
eached.
Returns
-------
DataFrames, array, or float
Depending on what was passed to the *output* argument, different
types of data might be returned:
- `dataframes': (default) will process the output into
two pandas DataFrames - the first one containing profiles
of the meteorological quantities tracked in the model,
and the second a dictionary of DataFrames with one for
each AerosolSpecies, tracking the growth in each bin
for those species.
- 'arrays': will return the raw output from the solver
used internally by the parcel model - the state vector
`y` and the evaluated timesteps converted into height
coordinates.
- 'smax': will only return the maximum supersaturation
value achieved in the simulation.
Raises
------
ParcelModelError
The parcel model failed to complete successfully or failed to initialize.
See Also
--------
der : right-hand side derivative evaluated during model integration.
"""
if not output in ["dataframes", "arrays", "smax"]:
raise ParcelModelError("Invalid value ('%s') specified for output format." % output)
if solver_dt is None:
solver_dt = 10.*output_dt
if not self._model_set:
self._setup_run()
y0 = self.y0
r_drys = self._r_drys
kappas = self._kappas
Nis = self._Nis
nr = self._nr
## Setup/run integrator
try:
from parcel_aux import der as der_fcn
except ImportError:
print "Could not load Cython derivative; using Python version."
from parcel import der as der_fcn
## Is the updraft speed a function of time?
v_is_func = hasattr(self.V, '__call__')
if v_is_func: # Re-wrap the function to correctly figure out V
orig_der_fcn = der_fcn
def der_fcn(y, t, *args):
V_t = self.V(t)
args[3] = V_t
return orig_der_fcn(y, t, *args)
## Will the simulation terminate early?
if not terminate:
terminate_depth = 0.
else:
if terminate_depth <= 0.:
raise ParcelModelError("`terminate_depth` must be greater than 0!")
if self.console:
print
print "Integration control"
print "----------------------------"
print " output dt: ", output_dt
print " max solver dt: ", solver_dt
print " solver int steps: ", int(solver_dt/output_dt )
print " termination: %r (%5dm)" % (terminate, terminate_depth)
args = [nr, r_drys, Nis, self.V, kappas, self.accom]
integrator_type = Integrator.solver(solver)
integrator = integrator_type(der_fcn, output_dt, solver_dt, y0, args,
terminate=terminate, terminate_depth=terminate_depth,
console=self.console,
**solver_args)
try:
## Pack args as tuple for solvers
args = tuple(args)
if self.console: print "\nBEGIN INTEGRATION ->\n"
x, t, success = integrator.integrate(t_end)
except ValueError, e:
raise ParcelModelError("Something failed during model integration: %r" % e)
class LKF(LSProcess):
def __init__(self, x0: np.ndarray, F: Callable, H: np.ndarray, Q: np.ndarray, R: np.ndarray, dt: float, tau: float = float('inf'), eta_mu: float = 0., eta_var: float = 1., eps=1e-2):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.eta_mu = eta_mu
self.eta_var = eta_var
self.ndim = x0.shape[0]
self.err_hist = []
self.eta_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.zz_tau = np.zeros((self.ndim, self.ndim)) # temp var..
alpha = 0.05
def f(t, state, z_t, err_hist, F_t):
# TODO fix all stateful references in this body
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:1+self.ndim], state[:, 1+self.ndim:]
z_t = z_t[:, np.newaxis]
K_t = [email protected]@np.linalg.inv(self.R)
self.p_t = P_t
eta_t = np.zeros((self.ndim, self.ndim)) # TODO warmup case?
if t > self.tau:
H_inv = np.linalg.inv(self.H)
P_inv = np.linalg.solve(P_t.T@P_t + self.eps*np.eye(self.ndim), P_t.T)
self.p_inv_t = P_inv
err_t, err_tau = err_hist[-1][:,np.newaxis], err_hist[0][:,np.newaxis]
self.zz_t = (1 - alpha)*self.zz_t + alpha*err_t@err_t.T
self.zz_tau = (1 - alpha)*self.zz_tau + alpha*err_tau@err_tau.T
d_zz = (self.zz_t - self.zz_tau) / self.tau
# if np.linalg.norm(d_zz) >= 1.0:
# d_zz = np.zeros((self.ndim, self.ndim))
self.e_zz_t = d_zz
# E_z = sum(err_hist)[:,np.newaxis] / len(err_hist)
# d_uu = ((err_t - err_tau)/self.tau)@(E_z.T) + E_z@(((err_t - err_tau)/self.tau).T)
eta_t = H_inv@d_zz@H_inv.T@P_inv / 2
self.propose_eta(eta_t)
F_est = F_t - self.eta_t
d_x = F_est@x_t + K_t@(z_t - self.H@x_t)
d_P = F_est@P_t + P_t@F_est.T + self.Q - [email protected]@K_t.T
d_eta = np.zeros((self.ndim, self.ndim))
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
# covariance
P0 = np.eye(self.ndim)
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
iv = np.concatenate((x0, P0, eta0), axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
def __call__(self, z_t: np.ndarray):
''' Observe through filter '''
self.r.set_f_params(z_t, self.err_hist, self.F(self.t))
self.r.integrate(self.t + self.dt)
x_t = np.squeeze(self.r.y.reshape(self.ode_shape)[:, :1])
err_t = z_t - [email protected]
self.err_hist.append(err_t)
if self.t > self.tau:
self.err_hist = self.err_hist[1:]
return x_t.copy(), err_t # x_t variable gets reused somewhere...
@property
def ode_shape(self):
return (self.ndim, 1 + 2*self.ndim) # representational dimension: x_t, P_t, eta_t
@property
def ode_ndim(self):
return self.ode_shape[0] * self.ode_shape[1] # for raveled representation
def propose_eta(self, eta_new: np.ndarray):
""" Metropolis-Hastings on variation """
# alpha = self.f_eta(eta_new) / self.f_eta(self.eta_mu)
# # pdb.set_trace()
# if stats.uniform.rvs() <= alpha:
# self.eta_t = eta_new
# eta_new = np.clip(eta_new, -.2, .2)
self.eta_t = eta_new
def f_eta(self, eta: np.ndarray):
""" density function of variations """
return stats.multivariate_normal.pdf(eta.ravel(), mean=self.eta_mu.ravel(), cov=self.eta_var.ravel())
XSIM = np.zeros((nsim + 1, 2, n_scenarios))
XSIMEXACT = np.zeros((nsim + 1, 2, n_scenarios))
USIM = np.zeros((nsim, 1, n_scenarios))
VSIMSQRT = np.zeros((nsim, 1, n_scenarios))
ZSIM = np.zeros((nsim, 1, n_scenarios))
DELTAZSIM = np.zeros((nsim, 1, n_scenarios))
VSOSIM = np.zeros((nsim, 1, n_scenarios))
for j in range(len(par.x0_v)):
x0 = par.x0_v[j]
XSIM[0, :, j] = x0
XSIMEXACT[0, :, j] = x0
# closed loop simulation
integrator = Integrator(par.ode)
ocp_solver = OcpSolver()
ocp_solver.rti_eval()
ocp_solver.nlp_eval()
if LQR_INIT:
if FLIP_LQR_INIT:
x0_lqr = -par.x0_v[j]
else:
x0_lqr = par.x0_v[j]
lqr_solver.update_x0(x0_lqr)
lqr_solver.lqr_eval()
lqr_sol = lqr_solver.get_lqr_sol()
def __init__(self, x_lin=[0, 0], u_lin=0):
Td = par.Tp / par.N
# linearize model
X_lin = ca.MX.sym('X_lin', 2, 1)
U_lin = ca.MX.sym('U_lin', 1, 1)
A_c = ca.Function('A_c', \
[X_lin, U_lin], [ca.jacobian(par.ode(X_lin, U_lin), X_lin)])
A_c = A_c([0, 0], 0).full()
B_c = ca.Function('B_c', \
[X_lin, U_lin], [ca.jacobian(par.ode(X_lin, U_lin), U_lin)])
B_c = B_c([0, 0], 0).full()
# solve continuous-time Riccati equation
Qt, e, K = cn.care(A_c, B_c, par.Q, par.R)
self.integrator = Integrator(par.ode)
self.x = self.integrator.x
self.u = self.integrator.u
self.Td = Td
# start with an empty NLP
w = []
w0 = []
w_lin = []
lbw = []
ubw = []
g = []
lbg = []
ubg = []
Xk = ca.MX.sym('X0', 2, 1)
w += [Xk]
lbw += [0, 0]
ubw += [0, 0]
w0 += [0, 0]
w_lin += x_lin
f = 0
# formulate the NLP
for k in range(par.N):
# new NLP variable for the control
Uk = ca.MX.sym('U_' + str(k), 1, 1)
f = f + Td*ca.mtimes(ca.mtimes(Xk.T, par.Q), Xk) \
+ Td*ca.mtimes(ca.mtimes(Uk.T, par.R), Uk)
w += [Uk]
lbw += [-np.inf]
ubw += [np.inf]
w0 += [0.0]
w_lin += [u_lin]
# integrate till the end of the interval
Xk_end = self.integrator.eval(Td, Xk, Uk)
# new NLP variable for state at end of interval
Xk = ca.MX.sym('X_' + str(k + 1), 2, 1)
w += [Xk]
lbw += [-np.inf, -np.inf]
ubw += [np.inf, np.inf]
w0 += [0, 0]
w_lin += x_lin
# add equality constraint
g += [Xk_end - Xk]
lbg += [0, 0]
ubg += [0, 0]
f = f + ca.mtimes(ca.mtimes(Xk_end.T, Qt), Xk_end)
g = ca.vertcat(*g)
w = ca.vertcat(*w)
# create an NLP solver
self.__lbw = lbw
self.__ubw = ubw
self.__lbg = lbg
self.__ubg = ubg
self.__w0 = np.array(w0)
self.__lqr_sol = []
# create QP solver
nw = len(w0)
# define linearization point
# w_lin = ca.MX.sym('w_lin', nw, 1)
w_qp = ca.MX.sym('w_qp', nw, 1)
# linearized objective = original LLS objective
f_lin = ca.substitute(f, w, w_qp)
nabla_g = ca.jacobian(g, w).T
g_lin = ca.substitute(g, w, w_lin) + \
ca.mtimes(ca.substitute(nabla_g, w, w_lin).T, w_qp - w_lin)
# create a QP solver
prob = {'f': f_lin, 'x': w_qp, 'g': g_lin}
self.__lqr_solver = ca.nlpsol('solver', 'ipopt', prob)
def __init__(self, x0: np.ndarray, F: Callable, H: np.ndarray, Q: np.ndarray, R: np.ndarray, dt: float, tau: float = float('inf'), eta_mu: float = 0., eta_var: float = 1., eps=1e-2):
self.F = F
self.H = H
self.Q = Q
self.R = R
self.dt = dt
self.tau = tau
self.eps = eps
self.eta_mu = eta_mu
self.eta_var = eta_var
self.ndim = x0.shape[0]
self.err_hist = []
self.eta_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.e_zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_inv_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.p_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.zz_t = np.zeros((self.ndim, self.ndim)) # temp var..
self.zz_tau = np.zeros((self.ndim, self.ndim)) # temp var..
alpha = 0.05
def f(t, state, z_t, err_hist, F_t):
# TODO fix all stateful references in this body
state = state.reshape(self.ode_shape)
x_t, P_t, eta_t = state[:, :1], state[:, 1:1+self.ndim], state[:, 1+self.ndim:]
z_t = z_t[:, np.newaxis]
K_t = [email protected]@np.linalg.inv(self.R)
self.p_t = P_t
eta_t = np.zeros((self.ndim, self.ndim)) # TODO warmup case?
if t > self.tau:
H_inv = np.linalg.inv(self.H)
P_inv = np.linalg.solve(P_t.T@P_t + self.eps*np.eye(self.ndim), P_t.T)
self.p_inv_t = P_inv
err_t, err_tau = err_hist[-1][:,np.newaxis], err_hist[0][:,np.newaxis]
self.zz_t = (1 - alpha)*self.zz_t + alpha*err_t@err_t.T
self.zz_tau = (1 - alpha)*self.zz_tau + alpha*err_tau@err_tau.T
d_zz = (self.zz_t - self.zz_tau) / self.tau
# if np.linalg.norm(d_zz) >= 1.0:
# d_zz = np.zeros((self.ndim, self.ndim))
self.e_zz_t = d_zz
# E_z = sum(err_hist)[:,np.newaxis] / len(err_hist)
# d_uu = ((err_t - err_tau)/self.tau)@(E_z.T) + E_z@(((err_t - err_tau)/self.tau).T)
eta_t = H_inv@d_zz@H_inv.T@P_inv / 2
self.propose_eta(eta_t)
F_est = F_t - self.eta_t
d_x = F_est@x_t + K_t@(z_t - self.H@x_t)
d_P = F_est@P_t + P_t@F_est.T + self.Q - [email protected]@K_t.T
d_eta = np.zeros((self.ndim, self.ndim))
d_state = np.concatenate((d_x, d_P, d_eta), axis=1)
return d_state.ravel() # Flatten for integrator
def g(t, state):
return np.zeros((self.ode_ndim, self.ode_ndim))
# state
x0 = x0[:, np.newaxis]
# covariance
P0 = np.eye(self.ndim)
# model variation
eta0 = np.zeros((self.ndim, self.ndim))
iv = np.concatenate((x0, P0, eta0), axis=1).ravel() # Flatten for integrator
self.r = Integrator(f, g, self.ode_ndim)
self.r.set_initial_value(iv, 0.)
tmax = 2e3 # ms
dt = 0.0005 # ms
#init = np.array([18, # V, mvolt
#0.1, # h
#0.7, # n
#0.07, # z
#0.1, # s_ampa
#0.1, # x_nmda
#0.8])# s_nmda
init = np.array([-50, # V, mvolt
0.83, # h
0.11, # n
0.002, # z
0.0, # s_ampa
0.0, # x_nmda
0.0])# s_nmda
#init = np.zeros(7)
m = SGY_neuron()
m.set_parameters(**reference_set)
# unstable parameters
m.par.g_ampa = 0
m.par.g_nmda = 0.09
m.par.w = 1.0
i = Integrator(m, tmax, dt)
i.set_initial_conditions(init)
def main():
H = Hamiltonian()
locator = Locator(H)
integrator = Integrator(H)
J = get_metric_mat(2)
locate_po = True
x = np.array([0.7,1.0,0.3,-0.3])
# print ("Locate minimum by minimum search of Hamiltonian")
# mini = locator.find_min(x,method='SLSQP',bounds=((0,2),(0,2),(-1,1),(-1,1)))
# if mini.success:
# print("found minimum at : {}".format(mini.x))
# else:
# print("couldn't find minimum : {}".format(mini.message))
print ("Locate minimum by root finding of Hamiltonian gradient")
mini = locator.find_saddle(x,root_method='hybr')
if mini.success:
print("found critical pt at : {}\n".format(mini.x))
# analyse stability of critical pt
eig, eigv, periods = analyse_equilibrium(H, 0.0, mini.x)
else:
print("couldn't find minimum : {}".format(mini.message))
# just to get options for specific solver
# show_options(solver='root', method='broyden1', disp=True)
if locate_po and mini.success:
print ("\n\n########################\nTrying to locate PO...")
period = periods[0] + periods[0]*0.05
dev = np.array([0.5,0,0.1,0])
xini = mini.x + dev #0.1*eigv[:,0]
# variational_0 = np.array(np.identity(2*H.dof)).flatten()
# xstart = np.concatenate((xini, variational_0))
# print("xstart:\n{}".format(xstart))
# traj = integrator.integrate_variational_plot(x=xstart, tstart=0., tend=period, npts=50)
# # traj = integrator.integrate_plot(x=xini, tstart=0., tend=period, npts=50)
# print("trajectory:\n{}".format(traj[-1]))
# plot_traj(traj,H.dof,'traj.pdf')
PO_sol = locator.locatePO(xini,period,root_method='broyden1',integration_method="dop853")
if PO_sol.success:
print("success : {}".format(PO_sol.success))
print("PO initial conditions {}".format(PO_sol.x))
# compute monodromy matrix
variational_0 = np.array(np.identity(2*H.dof)).flatten()
xstart = np.concatenate((PO_sol.x, variational_0))
print("xstart:\n{}".format(xstart))
traj = integrator.integrate_variational(x=xstart, tstart=0., tend=period,method="dop853")
# last = traj[-1]
monod = np.reshape(traj[2*H.dof:], (2*H.dof, 2*H.dof))
print("monodromy matrix:\n{}".format(monod))
eig, eigenvec = compute_eigenval_mat(monod)
for i in range(eig.size):
print("eigenvalue: {}".format(eig[i]))
# PO = integrator.integrate_plot(PO_sol.x,0,period,'dop853',100)
# print("PO:\n{}".format(PO))
# plot_traj(traj,H.dof,'PO.pdf')
else:
print("Couldn't find PO : {}".format(PO_sol.message))