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plots.py
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plots.py
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import os
import numpy as np
import pandas as pd
from matplotlib import colors
from matplotlib import pyplot as plt
def delaycontourplot(file, tau_file, nu_file):
"""Countour plot (Fig. 2a) of in-rate vs. delay from Mathematica generated csv files. Run
Mathematica notebook to generate csv files or load delivered csv files
from disk.
Parameters
-----------
file : str
path to csv file containing stability information
tau_file : str
path to csv file containing the delay times tau
nu_file : str
path to csv file containing the in-rate values
Returns
-------
"""
data = pd.read_csv(file, header=None)
tau_data = pd.read_csv(tau_file, header=None)
nu_data = pd.read_csv(nu_file, header=None)
time_vals = data.to_numpy()
tau_tvals = tau_data.to_numpy()
nu_tvals = nu_data.to_numpy()
bool_times = time_vals <= 0
bool_times = np.ma.masked_where(~bool_times, bool_times)
tau_vals = np.arange(0, 20.5, 0.5)
nu_in_vals = np.arange(1, 1.31, 0.01)
_, ax = plt.subplots()
cmap = colors.ListedColormap(["white"])
cmap.set_bad(color="darkgrey")
ax.imshow(
bool_times,
extent=[tau_vals[0], tau_vals[-1], nu_in_vals[0], nu_in_vals[-1]],
origin="lower",
cmap=cmap,
aspect="auto",
)
ax.plot(tau_tvals, nu_tvals)
markers = [(0.0, 1.1), (4, 1.1), (8, 1.1)]
x, y = zip(*markers)
ax.plot(x, y, "o", c="red")
ax.set_yticks(np.arange(1, 1.4, 0.1))
ax.set_xticks(np.arange(0, 25, 5))
ax.set_yticklabels(np.array([1, 1.1, 1.2, 1.3]), fontsize=14)
ax.set_xticklabels(np.arange(0, 25, 5), fontsize=14)
ax.set_xlabel("delay", fontsize=14)
ax.set_ylabel("in-rate", fontsize=14)
def combinedcontourplot(file, avfile, tau_file, nu_file, av_taufile, av_nufile):
"""Plot contourplot for delay vs. in-rate for the case with time-averaged informatin (Fig. 3a).
Use Mathematica generated csv files.
Parameters
-----------
file : str
Path to csv file containing stability information for non-averaged case
avfile : str
Path to csv file containing stability information for averaged case
tau_file : str
Path to csv file containing the delay times tau for non-averaged case
nu_file : str
Path to csv file containing the in-rate values for non-averaged case
av_taufile : str
Path to csv file containing the delay times tau for averaged case
av_nufile : str
Path to csv file containing the in-rate values for averaged case
Returns
-------
"""
av_tau_vals = pd.read_csv(av_taufile, header=None).to_numpy()
av_stab_vals = pd.read_csv(av_nufile, header=None).to_numpy()
tau_vals = pd.read_csv(tau_file, header=None).to_numpy()
stab_vals = pd.read_csv(nu_file, header=None).to_numpy()
av_time_vals = pd.read_csv(avfile, header=None).to_numpy()
time_vals = pd.read_csv(file, header=None).to_numpy()
colorarray = np.zeros((32, 41))
for i in range(0, 32):
for j in range(0, 41):
av_md = av_time_vals[i, j]
md = time_vals[i, j]
if av_md > 0 and md > 0:
colorarray[i, j] = 1
if av_md > 0 and md < 0:
colorarray[i, j] = 0.25
if av_md < 0 and md > 0:
colorarray[i, j] = 0.6
if av_md < 0 and md < 0:
colorarray[i, j] = 0
_, ax = plt.subplots()
cmap = colors.ListedColormap(["white", "red", "blue", "darkgrey"])
ax.imshow(
colorarray,
extent=[0, 20, 1, 1.31],
origin="lower",
aspect="auto",
cmap=cmap,
)
ax.plot(tau_vals, stab_vals, "-", color="black")
ax.plot(av_tau_vals, av_stab_vals, "--", color="green")
ax.set_yticks(np.arange(1, 1.4, 0.1))
ax.set_xticks(np.arange(0, 25, 5))
ax.set_yticklabels(np.array([1, 1.1, 1.2, 1.3]), fontsize=14)
ax.set_xticklabels(np.arange(0, 25, 5), fontsize=14)
ax.set_xlabel("delay", fontsize=14)
ax.set_ylabel("in-rate", fontsize=14)
def plot_crit_inrates_time_averaging(tau1file, tau5file, tau10file):
"""Plot critical in-rates vs. averaging time window at which congestion occurs for different
time delays. Uses Mathematica generate csv files. Run
Parameters
----------
tau1file : str
Path to csv file containing data for time delay 1
tau5file : str
Path to csv file containing data for time delay 5
tau10file : str
Path to csv file containing data for time delay 10
"""
time_vals = np.arange(1, 51, 1)
nu_vals = np.arange(1, 1.301, 0.001)
def stab_line_finder(file, time_vals, nu_vals):
"""Find the critical in-rates for each averaging time from Mathematica calculation results.
Parameters
----------
file : str
Path to csv file containing stability information
time_vals : array-like
averaging time values
nu_vals : array-like
in-rate values
Returns
-------
array-like
"""
tau_vals = pd.read_csv(file, header=None)
tau_vals = tau_vals.to_numpy()
instab_bound = []
for time_idx in range(0, len(time_vals)):
nu_idx = np.where(tau_vals[:, time_idx] > 0)[0][0]
instab_bound.append(nu_vals[nu_idx])
return instab_bound
instab_bound_10 = stab_line_finder(tau10file, time_vals, nu_vals)
instab_bound_5 = stab_line_finder(tau5file, time_vals, nu_vals)
instab_bound_1 = stab_line_finder(tau1file, time_vals, nu_vals)
_, ax = plt.subplots()
ax.plot(time_vals, instab_bound_10, label=r"delay $\tau=10$")
ax.plot(time_vals, instab_bound_5, label=r"delay $\tau=5$")
ax.plot(time_vals, instab_bound_1, label=r"delay $\tau=1$")
ax.axhline(instab_bound_10[0], linestyle="dotted")
ax.axhline(instab_bound_5[0], linestyle="dotted")
ax.axhline(instab_bound_1[0], linestyle="dotted")
ax.set_xlabel(r"averaging time $T_{\mathrm{av}}$", fontsize=14)
ax.set_ylabel(r"critical in-rate $\nu_{\mathrm{in}}^{\mathrm{crit}}$", fontsize=14)
ax.set_yticks(np.arange(1, 1.4, 0.1))
ax.set_xticks(np.arange(0, 60, 10))
ax.set_yticklabels(np.array([1, 1.1, 1.2, 1.3]), fontsize=14)
ax.set_xticklabels(np.arange(0, 60, 10), fontsize=14)
ax.set_xlim((0, 50))
ax.legend(loc="lower right")