"""Contains an implementation of the Lotka Volterra model.
An implementation of a Lotka Volterra example model.
"""
import numpy as np
import pandas as pd
from scipy.integrate import solve_ivp
from ..base import ExampleModelBase
# Refer to https://www.pymc.io/projects/examples/en/latest/samplers/SMC-ABC_Lotka-Volterra_example.html
[docs]
class LotkaVolterraModel(ExampleModelBase):
"""Lotka Volterra simulation model."""
def __init__(self) -> None:
"""LotkaVolterraModel constructor."""
super().__init__()
self.GROUND_TRUTH = dict(
alpha=0.52,
beta=0.024,
h0=34.0,
l0=5.9,
t=np.arange(1900.0, 1921.0, 1),
gamma=0.84,
delta=0.026,
)
self.OUTPUT_LABELS = ["lynx", "hare"]
[docs]
def get_observed_data(self) -> np.ndarray | pd.DataFrame:
"""Retrieve observed data.
Returns:
np.ndarray | pd.DataFrame: The observed data.
"""
observed_df = pd.DataFrame(
dict(
year=np.arange(1900.0, 1921.0, 1),
lynx=np.array(
[
4.0,
6.1,
9.8,
35.2,
59.4,
41.7,
19.0,
13.0,
8.3,
9.1,
7.4,
8.0,
12.3,
19.5,
45.7,
51.1,
29.7,
15.8,
9.7,
10.1,
8.6,
]
),
hare=np.array(
[
30.0,
47.2,
70.2,
77.4,
36.3,
20.6,
18.1,
21.4,
22.0,
25.4,
27.1,
40.3,
57.0,
76.6,
52.3,
19.5,
11.2,
7.6,
14.6,
16.2,
24.7,
]
),
)
)
return observed_df
[docs]
def simulate(self, parameters: dict) -> np.ndarray | pd.DataFrame:
"""Run the simulation.
Args:
parameters (dict): The simulation parameters.
Returns:
np.ndarray | pd.DataFrame: The simulated data.
"""
def dX_dt(_: np.ndarray, X: np.ndarray) -> np.ndarray:
x, y = X
dx_dt = parameters["alpha"] * x - parameters["beta"] * x * y
dy_dt = -parameters["gamma"] * y + parameters["delta"] * x * y
return np.array([dx_dt, dy_dt])
X0 = [parameters["h0"], parameters["l0"]]
t = (parameters["t"].min(), parameters["t"].max())
x_y = solve_ivp(fun=dX_dt, y0=X0, t_span=t, t_eval=parameters["t"].values).y
df = pd.DataFrame(dict(lynx=x_y[1, :], hare=x_y[0, :]))
return df