def test_euler_Lambda(self, Lambda):
"""Test the range of valid lambda values for the logistic growth model.
Arguments:
Lambda {float} -- growth factor.
"""
# integration paramters
h = 0.001 # time steps
t_0 = 0.0 # initial time
t_final = 10.0 # final time (limit time interval just to avoid computing time issues)
y_0 = 0.1 # initial condition
times = np.arange(start=t_0, stop=t_final, step=h)
analytic = logistic_growth_dimensionless(times, Lambda=Lambda)
# logistic growth ODE
model = lambda t, x: Lambda * x * (1 - x)
logistic_model = euler.euler(model)
numeric = logistic_model.integrate(h=h,
t_0=t_0,
t_final=t_final,
y_0=y_0)[1, :]
squared_distance = (analytic - numeric)**2
tolerance = 0.01
assert np.all(squared_distance <= tolerance**2)
def test_euler_initial_y(self, y_0):
"""testing the valid realm of y_0. Here the logistic function can only assume values in (0, 1).
Arguments:
y_0 {float} -- initial value of the state variable.
"""
# model parameters
Lambda = 1.0
# integration paramters
h = 0.001 # time steps
t_0 = 0.0 # initial time
t_final = 10.0 # final time (limit time interval just to avoid computing time issues)
y_0 = 0.1 # initial condition
times = np.arange(start=t_0, stop=t_final, step=h)
analytic = logistic_growth_dimensionless(times, Lambda=Lambda)
# logistic growth ODE
model = lambda t, x: Lambda * x * (1 - x)
logistic_model = euler.euler(model)
numeric = logistic_model.integrate(h=h,
t_0=t_0,
t_final=t_final,
y_0=y_0)[1, :]
squared_distance = (analytic - numeric)**2
tolerance = 0.01
assert np.all(squared_distance <= tolerance**2)
def test_euler_intial_time(self, t_0):
"""Testing valid values for t_0. Within the physical limits of the computer any number t_0 shoud work. We just choose a rather
small range [-100, 100] for efficiency of the test.
Arguments:
t_0 {float} -- initial time of integration.
"""
# model parameters
Lambda = 1.0
# integration paramters
h = 0.001 # time steps
t_final = 10.0 # final time (limit time interval just to avoid computing time issues)
y_0 = 0.1 # initial condition
times = np.arange(start=t_0, stop=t_final, step=h)
analytic = logistic_growth_dimensionless(times, t_0=t_0, Lambda=Lambda)
# logistic growth ODE
model = lambda t, x: Lambda * x * (1 - x)
logistic_model = euler.euler(model)
numeric = logistic_model.integrate(h=h,
t_0=t_0,
t_final=t_final,
y_0=y_0)[1, :]
squared_distance = (analytic - numeric)**2
tolerance = 0.01
assert np.all(squared_distance <= tolerance**2)
def test_infer_parameters():
"""test model: logistic growth
"""
### exact parameters
exact_parameters = [1.0, 0.1]
Lambda, x_0 = exact_parameters
### generate data
scale = 0.01
data_time = np.linspace(0, 10, 100)
exact_solution = logistic_growth_dimensionless(times=data_time,
x_0=x_0,
Lambda=Lambda)
gen = DataGenerator()
data_y = gen.generate_data(exact_solution, scale=scale)
data = np.vstack(tup=(data_time, data_y))
ODEmodel = lambda t, x, Lambda: Lambda * x * (1 - x)
problem = InferenceProblem(ODEmodel, data)
initial_parameters = [3.0] # initial lambda
initial_y0 = 0.3
step_size = 0.1
estimated_parameters = problem.infer_parameters(
y_0=initial_y0,
initial_parameters=initial_parameters,
step_size=step_size)
assert np.allclose(a=estimated_parameters, b=exact_parameters, rtol=5.0e-2)
import numpy as np
from PAID.EulerMethod.euler import euler
from PAID.data.generator import DataGenerator
from PAID.InferenceMethod.inference import InferenceProblem
from tests.exact_models.models import logistic_growth_dimensionless
### exact parameters
exact_parameters = [1.0, 0.1]
Lambda, x_0 = exact_parameters
### generate data
scale = 0.05
data_time = np.linspace(0, 10, 100)
exact_solution = logistic_growth_dimensionless(times=data_time,
x_0=x_0,
Lambda=Lambda)
gen = DataGenerator()
data_y = gen.generate_data(exact_solution, scale=scale)
data = np.vstack(tup=(data_time, data_y))
ODEmodel = lambda t, x, Lambda: Lambda * x * (1 - x)
problem = InferenceProblem(ODEmodel, data)
initial_parameters = [3.0] # initial lambda
initial_y0 = 0.3
step_size = 0.1
estimated_parameters = problem.infer_parameters(
y_0=initial_y0, initial_parameters=initial_parameters, step_size=step_size)