# Copyright (c) 2022 The BayesFlow Developers
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# Corresponds to Task T.10 from the paper https://arxiv.org/pdf/2101.04653.pdf
import numpy as np
from scipy.integrate import odeint
bayesflow_benchmark_info = {
"simulator_is_batched": False,
"parameter_names": [r"$\alpha$", r"$\beta$", r"$\gamma$", r"$\delta$"],
"configurator_info": "posterior",
}
[docs]
def prior(rng=None):
"""Generates a random draw from a 4-dimensional (independent) lognormal prior
which represents the four contact parameters of the Lotka-Volterra model.
Parameters
----------
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
theta : np.ndarray of shape (4,)
A single draw from the 4-dimensional prior.
"""
if rng is None:
rng = np.random.default_rng()
theta = rng.lognormal(mean=[-0.125, -3, -0.125, -3], sigma=0.5)
return theta
def _deriv(x, t, alpha, beta, gamma, delta):
"""Helper function for scipy.integrate.odeint."""
X, Y = x
dX = alpha * X - beta * X * Y
dY = -gamma * Y + delta * X * Y
return dX, dY
[docs]
def simulator(theta, X0=30, Y0=1, T=20, subsample=10, flatten=True, obs_noise=0.1, rng=None):
"""Runs a Lotka-Volterra simulation for T time steps and returns `subsample` evenly spaced
points from the simulated trajectory, given contact parameters `theta`.
See https://arxiv.org/pdf/2101.04653.pdf, Benchmark Task T.10.
Parameters
----------
theta : np.ndarray of shape (2,)
The 2-dimensional vector of disease parameters.
X0 : float, optional, default: 30
Initial number of prey species.
Y0 : float, optional, default: 1
Initial number of predator species.
T : T, optional, default: 20
The duration (time horizon) of the simulation.
subsample : int or None, optional, default: 10
The number of evenly spaced time points to return. If None,
no subsampling will be performed and all T timepoints will be returned.
flatten : bool, optional, default: True
A flag to indicate whather a 1D (`flatten=True`) or a 2D (`flatten=False`)
representation of the simulated data is returned.
obs_noise : float, optional, default: 0.1
The standard deviation of the log-normal likelihood.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
x : np.ndarray of shape (subsample, 2) or (subsample*2,) if `subsample is not None`,
otherwise shape (T, 2) or (T*2,) if `subsample is None`.
The time series of simulated predator and pray populations
"""
# Use default RNG, if None specified
if rng is None:
rng = np.random.default_rng()
# Create vector (list) of initial conditions
x0 = X0, Y0
# Unpack parameter vector into scalars
alpha, beta, gamma, delta = theta
# Prepate time vector between 0 and T of length T
t_vec = np.linspace(0, T, T)
# Integrate using scipy and retain only infected (2-nd dimension)
pp = odeint(_deriv, x0, t_vec, args=(alpha, beta, gamma, delta))
# Subsample evenly the specified number of points, if specified
if subsample is not None:
pp = pp[:: (T // subsample)]
# Ensure minimum count is 0, which will later pass by log(0 + 1)
pp[pp < 0] = 0.0
# Add noise, decide whether to flatten and return
x = rng.lognormal(np.log1p(pp), sigma=obs_noise)
if flatten:
return x.flatten()
return x
[docs]
def configurator(forward_dict, mode="posterior", scale_data=1000, as_summary_condition=False):
"""Configures simulator outputs for use in BayesFlow training."""
# Case only posterior configuration
if mode == "posterior":
input_dict = _config_posterior(forward_dict, scale_data, as_summary_condition)
# Case only likelihood configuration
elif mode == "likelihood":
input_dict = _config_likelihood(forward_dict, scale_data)
# Case posterior and likelihood configuration
elif mode == "joint":
input_dict = {}
input_dict["posterior_inputs"] = _config_posterior(forward_dict, scale_data, as_summary_condition)
input_dict["likelihood_inputs"] = _config_likelihood(forward_dict, scale_data)
# Throw otherwise
else:
raise NotImplementedError('For now, only a choice between ["posterior", "likelihood", "joint"] is available!')
return input_dict
def _config_posterior(forward_dict, scale_data, as_summary_condition):
"""Helper function for posterior configuration."""
input_dict = {}
input_dict["parameters"] = forward_dict["prior_draws"].astype(np.float32)
if as_summary_condition:
input_dict["summary_conditions"] = forward_dict["sim_data"].astype(np.float32) / scale_data
else:
input_dict["direct_conditions"] = forward_dict["sim_data"].astype(np.float32) / scale_data
return input_dict
def _config_likelihood(forward_dict, scale_data):
"""Helper function for likelihood configuration."""
input_dict = {}
input_dict["observables"] = forward_dict["sim_data"].astype(np.float32) / scale_data
input_dict["conditions"] = forward_dict["prior_draws"].astype(np.float32)
return input_dict
