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experiments.py
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experiments.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# ----------------------------------------------------------------------------
# Created By: Sjoerd Terpstra
# Created Date: 19/03/2022
# ---------------------------------------------------------------------------
""" experiments.py
Functions to perform the experiments. These functions are called from ms.py
"""
# ---------------------------------------------------------------------------
import copy
from timeit import default_timer as timer
import matplotlib.pyplot as plt
from matplotlib.patches import Patch
import numpy as np
from tqdm import tqdm
import pollcomm as pc
from cycler import cycler
line_cycler = (cycler(color=["#E69F00", "#56B4E9", "#009E73", "#0072B2", "#D55E00", "#CC79A7", "#F0E442"]) +
cycler(linestyle=["-", "--", "-.", ":", "-", "--", "-."]))
marker_cycler = (cycler(color=["#E69F00", "#56B4E9", "#009E73", "#0072B2", "#D55E00", "#CC79A7", "#F0E442"]) +
cycler(linestyle=["none", "none", "none", "none", "none", "none", "none"]) +
cycler(marker=["4", "2", "3", "1", "+", "x", "."]))
plt.rc("axes", prop_cycle=line_cycler)
# plt.rc("axes", prop_cycle=marker_cycler)
plt.rc("font", family="serif", size=18.)
plt.rc("savefig", dpi=200)
plt.rc("legend", loc="best", fontsize="medium", fancybox=True, framealpha=0.5)
plt.rc("lines", linewidth=2.5, markersize=10, markeredgewidth=2.5)
MODELS = {
"BM": pc.BaseModel,
"AM": pc.AdaptiveModel
}
def state_space_rate_dA(fname, AM, rates=None, dAs_init=None, A_init=None):
if rates is None:
rates = np.linspace(0.0001, 0.1, 11)
if dAs_init is None:
dAs_init = np.linspace(0, 4, 11)
if A_init is None:
A_init = 1
def dA_rate(t, r, dA_init):
return dA_init + r * t
t_end = int(1e5)
n_steps = int(1e6) # number of interpolated time steps
extinct_threshold = 0.01
dAs_critical = np.zeros((len(rates), len(dAs_init)))
curr_iter = 0
total_iter = len(rates) * len(dAs_init)
for i, rate in enumerate(rates):
for j, dA_init in enumerate(dAs_init):
print(f"Iteration {curr_iter + 1} out of {total_iter}")
# initial conditions
y0 = np.full(AM.N, A_init, dtype=float)
y0 = np.concatenate((y0, copy.deepcopy(AM.alpha.flatten())))
# drivers of decline
dA = {
"func": dA_rate,
"args": (rate, dA_init)
}
sol = AM.solve(
t_end, dA=dA, n_steps=n_steps, y0=y0, stop_on_collapse=True,
extinct_threshold=extinct_threshold
)
# check if point of collapse has been found:
if sol.status == 1:
# find point of collapse
A = AM.y[AM.N_p:AM.N]
# put default at -1 if no population went extinct
try:
ind = (A < extinct_threshold).all(axis=0).nonzero()[0][0]
t_extinct = AM.t[ind]
dAs_critical[i, j] = dA["func"](t_extinct, rate, dA_init)
except IndexError:
dAs_critical[i, j] = -1
else:
dAs_critical[i, j] = -1
curr_iter += 1
np.savez(
fname, rates=rates, dAs_init=dAs_init, A_init=A_init,
dAs_critical=dAs_critical,
)
def state_space_abundance_dA(fname, AM, dAs_init=None, A_init=None):
if dAs_init is None:
dAs_init = np.linspace(0, 4, 41)
if A_init is None:
A_init = np.linspace(0, 1, 11)
t_end = int(1e5)
n_steps = int(1e4) # number of interpolated time steps
final_abundance = np.zeros((len(dAs_init), len(A_init)))
curr_iter = 0
total_iter = len(dAs_init) * len(A_init)
for i, dA in enumerate(dAs_init):
for j, abundance in enumerate(A_init):
print(f"Iteration {curr_iter + 1} out of {total_iter}")
# initial conditions
y0 = np.full(AM.N, abundance, dtype=float)
y0 = np.concatenate((y0, copy.deepcopy(AM.alpha.flatten())))
sol = AM.solve(
t_end, dA=dA, n_steps=n_steps, y0=y0, stop_on_collapse=False,
stop_on_equilibrium=True
)
A_mean = AM.y[AM.N_p:AM.N].mean(axis=0)
# final abundace is the mean abundace at the final time point
final_abundance[i, j] = A_mean[-1]
curr_iter += 1
np.savez(
fname, dAs_init=dAs_init, A_init=A_init, final_abundance=final_abundance,
)
def state_space_abundance_rate_critical_dA(fname, AM, rates=None, A_init=None):
if rates is None:
rates = np.linspace(0.0001, 0.1, 11)
if A_init is None:
A_init = np.linspace(0, 1, 11)
def dA_rate(t, r):
return r * t
t_end = int(1e5)
n_steps = int(1e4) # number of interpolated time steps
extinct_threshold = 0.01
dAs_critical = np.zeros((len(rates), len(A_init)))
curr_iter = 0
total_iter = len(rates) * len(A_init)
for i, rate in enumerate(rates):
for j, abundance in enumerate(A_init):
print(f"Iteration {curr_iter + 1} out of {total_iter}")
# initial conditions
y0 = np.full(AM.N, abundance, dtype=float)
y0 = np.concatenate((y0, copy.deepcopy(AM.alpha.flatten())))
# drivers of decline
dA = {
"func": dA_rate,
"args": (rate, )
}
sol = AM.solve(
t_end, dA=dA, n_steps=n_steps, y0=y0, stop_on_collapse=True,
extinct_threshold=extinct_threshold
)
# check if point of collapse has been found:
if sol.status == 1:
# find point of collapse
A_mean = AM.y[AM.N_p:AM.N].mean(axis=0)
# put default at -1 if no population went extinct
try:
ind = (A_mean < extinct_threshold).nonzero()[0][0]
t_extinct = AM.t[ind]
dAs_critical[i, j] = dA["func"](t_extinct, rate)
except IndexError:
dAs_critical[i, j] = -1
else:
dAs_critical[i, j] = -1
curr_iter += 1
np.savez(
fname, rates=rates, A_init=A_init, dAs_critical=dAs_critical,
)
def state_space_abundance_rate_critical_dA_all(fname, AM, rates=None, A_init=None):
if rates is None:
rates = np.linspace(0.0001, 0.1, 11)
if A_init is None:
A_init = np.linspace(0, 1, 11)
def dA_rate(t, r):
return r * t
t_end = int(1e5)
n_steps = int(1e6) # number of interpolated time steps
extinct_threshold = 0.01
dAs_critical = np.zeros((len(rates), len(A_init)))
curr_iter = 0
total_iter = len(rates) * len(A_init)
for i, rate in enumerate(rates):
for j, abundance in enumerate(A_init):
print(f"Iteration {curr_iter + 1} out of {total_iter}")
# initial conditions
y0 = np.full(AM.N, abundance, dtype=float)
y0 = np.concatenate((y0, copy.deepcopy(AM.alpha.flatten())))
# drivers of decline
dA = {
"func": dA_rate,
"args": (rate, )
}
sol = AM.solve(
t_end, dA=dA, n_steps=n_steps, y0=y0, stop_on_collapse=True,
extinct_threshold=extinct_threshold
)
# check if point of collapse has been found:
if sol.status == 1:
# find point of collapse
A = AM.y[AM.N_p:AM.N]
# print((A[:, -1] < extinct_threshold).all())
# print((A < extinct_threshold).all(axis=0))
# if not (A[:, -1] < extinct_threshold).all():
# print(A[:, -1])
# print(AM.t[-1])
# put default at -1 if no population went extinct
try:
ind = (A < extinct_threshold).all(axis=0).nonzero()[0][0]
t_extinct = AM.t[ind]
dAs_critical[i, j] = dA["func"](t_extinct, rate)
except IndexError:
dAs_critical[i, j] = -1
else:
dAs_critical[i, j] = -1
curr_iter += 1
np.savez(
fname, rates=rates, A_init=A_init, dAs_critical=dAs_critical,
)
def state_space_rate_critical_dA(fname, AM, rates=None, A_init=None):
if rates is None:
rates = np.linspace(0.0001, 0.1, 11)
if A_init is None:
A_init = [0.2]
def dA_rate(t, r):
return r * t
t_end = int(1e5)
n_steps = int(1e6) # number of interpolated time steps
extinct_threshold = 0.01
dAs_critical = np.zeros((len(rates), len(A_init)))
curr_iter = 0
total_iter = len(rates) * len(A_init)
for i, rate in enumerate(rates):
for j, abundance in enumerate(A_init):
print(f"Iteration {curr_iter + 1} out of {total_iter}")
# initial conditions
y0 = np.full(AM.N, abundance, dtype=float)
y0 = np.concatenate((y0, copy.deepcopy(AM.alpha.flatten())))
# drivers of decline
dA = {
"func": dA_rate,
"args": (rate, )
}
sol = AM.solve(
t_end, dA=dA, n_steps=n_steps, y0=y0, stop_on_collapse=True,
extinct_threshold=extinct_threshold
)
# check if point of collapse has been found:
if sol.status == 1:
# find point of collapse
A = AM.y[AM.N_p:AM.N]
# print((A[:, -1] < extinct_threshold).all())
# print((A < extinct_threshold).all(axis=0))
# if not (A[:, -1] < extinct_threshold).all():
# print(A[:, -1])
# print(AM.t[-1])
# put default at -1 if no population went extinct
try:
ind = (A < extinct_threshold).all(axis=0).nonzero()[0][0]
t_extinct = AM.t[ind]
dAs_critical[i, j] = dA["func"](t_extinct, rate)
except IndexError:
dAs_critical[i, j] = -1
else:
dAs_critical[i, j] = -1
curr_iter += 1
np.savez(
fname, rates=rates, A_init=A_init, dAs_critical=dAs_critical,
)
def hysteresis_q(AM, dAs=None, qs=None, seed=None, fnumber=0):
"""Calculate hysteresis as function of dA for different q. """
if dAs is None:
dAs = np.linspace(0, 4, 21)
if qs is None:
qs = np.linspace(0, 1, 11)
if seed is None:
seed = np.random.SeedSequence().generate_state(1)[0]
rng = np.random.default_rng(seed)
for i, q in enumerate(qs):
print(f"\nCalculating q: {i+1} out of {len(qs)}...")
# set q parameter, set seed and rng
AM.q = q
AM.rng = rng
fname = f"output/hysteresis_G{AM.G}_nu{AM.nu}_q{AM.q}_{fnumber}"
hysteresis(fname, AM, dAs=dAs)
def find_dA_collapse_recovery(fname, AM, dA_step=0.02):
"""Calculate hysteresis as function of dA. """
# maximum simulation time
t_end = int(1e4)
t_step = int(1e4)
extinct_threshold = 0.01
# obtain initial solution
y0 = AM.equilibrium()
if AM.is_all_alive()[-1]:
is_feasible = True
else:
is_feasible = False
# calculate solution for increasing dA
print("\nCalculating hysteresis forward...")
dA = 0
while (AM.y[AM.N_p:AM.N, -1] > extinct_threshold).any():
dA += dA_step
AM.solve(t_step, dA=dA, y0=y0, save_period=0, stop_on_equilibrium=True)
y0 = AM.y[:, -1]
y0 = np.concatenate((y0, AM.y_partial[:, -1]))
dA_collapse = dA
# calculate solution for decreasing dA
print("\nCalculating hysteresis backward...")
while not (AM.y[AM.N_p:AM.N, -1] > extinct_threshold).any():
dA -= dA_step
AM.solve(t_step, dA=dA, y0=y0, save_period=0, stop_on_equilibrium=True)
y0 = AM.y[:, -1]
y0 = np.concatenate((y0, AM.y_partial[:, -1]))
dA_recover = dA
np.savez(
fname, dA_collapse=dA_collapse, dA_recover=dA_recover, is_feasible=is_feasible
)
def hysteresis(fname, AM, dAs=None):
"""Calculate hysteresis as function of dA. """
# maximum simulation time
t_end = 1000
t_step = 100
if dAs is None:
dAs = np.linspace(0, 4, 21)
# save only steady state solutions
P_sol_forward = np.zeros((len(dAs), AM.N_p))
A_sol_forward = np.zeros((len(dAs), AM.N_a))
P_sol_backward = np.zeros((len(dAs), AM.N_p))
A_sol_backward = np.zeros((len(dAs), AM.N_a))
# obtain initial solution
AM.solve(t_end, dA=0, save_period=0, stop_on_equilibrium=True)
if AM.is_all_alive()[-1]:
is_feasible = True
else:
is_feasible = False
# calculate solution for increasing dA
print("\nCalculating hysteresis forward...")
for i, dA in enumerate(dAs):
print(f"{i+1} out of {len(dAs)}...")
y0 = AM.y[:, -1]
y0 = np.concatenate((y0, AM.y_partial[:, -1]))
AM.solve(t_step, dA=dA, y0=y0, save_period=0, stop_on_equilibrium=True)
P_sol_forward[i] = AM.y[:AM.N_p, -1]
A_sol_forward[i] = AM.y[AM.N_p:AM.N, -1]
# calculate solution for decreasing dA
print("\nCalculating hysteresis backward...")
for i, dA in enumerate(np.flip(dAs)):
print(f"{i+1} out of {len(dAs)}...")
y0 = AM.y[:, -1]
y0 = np.concatenate((y0, AM.y_partial[:, -1]))
AM.solve(t_step, dA=dA, y0=y0, save_period=0, stop_on_equilibrium=True)
P_sol_backward[i] = AM.y[:AM.N_p, -1]
A_sol_backward[i] = AM.y[AM.N_p:AM.N, -1]
np.savez(
fname, dAs=dAs, P_sol_forward=P_sol_forward, A_sol_forward=A_sol_forward,
P_sol_backward=P_sol_backward, A_sol_backward=A_sol_backward,
is_feasible=is_feasible
)
def hysteresis_rate(fname, AM, rate=0.001, dA_max=3):
# maximum simulation time
t_equilibrium = 1000
# time needed to reach dA_max for given rate
t_end = dA_max / rate
n_steps = 1000
# save only steady state solutions
P_sol_forward = np.zeros((n_steps, AM.N_p))
A_sol_forward = np.zeros((n_steps, AM.N_a))
P_sol_backward = np.zeros((n_steps, AM.N_p))
A_sol_backward = np.zeros((n_steps, AM.N_a))
if AM.is_all_alive()[-1]:
is_feasible = True
else:
is_feasible = False
# obtain initial solution
AM.solve(
t_equilibrium, n_steps=1000, dA=0, save_period=0, stop_on_equilibrium=True
)
# calculate solution for increasing dA
print("\nCalculating hysteresis forward...")
dA_rate = {
"func": lambda t, rate: rate * t,
"args": (rate, )
}
y0 = AM.y[:, -1]
y0 = np.concatenate((y0, AM.y_partial[:, -1]))
AM.solve(
t_end, y0=y0, n_steps=n_steps, dA=dA_rate, save_period=0
)
P_sol_forward = AM.y[:AM.N_p].T
A_sol_forward = AM.y[AM.N_p:AM.N].T
dAs_forward = rate * AM.t
# calculate solution for decreasing dA
print("\nCalculating hysteresis backward...\n")
def func(t, rate, dA_max):
if dA_max - rate * t < 0:
return 0
else:
return dA_max - rate * t
dA_rate = {
"func": func,
"args": (rate, dA_max)
}
y0 = AM.y[:, -1]
y0 = np.concatenate((y0, AM.y_partial[:, -1]))
# make sure system ends up in final equilibrium
AM.solve(
t_end*10, y0=y0, n_steps=n_steps, dA=dA_rate, save_period=0,
stop_on_equilibrium=True
)
P_sol_backward = AM.y[:AM.N_p].T
A_sol_backward = AM.y[AM.N_p:AM.N].T
dAs_backward = [func(t, rate, dA_max) for t in AM.t]
np.savez(
fname, dAs_forward=dAs_forward, dAs_backward=dAs_backward,
P_sol_forward=P_sol_forward, A_sol_forward=A_sol_forward,
P_sol_backward=P_sol_backward, A_sol_backward=A_sol_backward,
is_feasible=is_feasible, rate=rate
)