ShuaiGuo16

# Load trajectory data
traj_X = np.genfromtxt('./Dataset/traj_X.csv', delimiter=',')
traj_Y = np.genfromtxt('./Dataset/traj_Y.csv', delimiter=',')

# Display a single trajectory
fig, ax = plt.subplots(figsize=(8,3))

pick_traj = 5
ax.plot(traj_X[pick_traj,:],traj_Y[pick_traj,:],
       color='b', lw=2, linestyle='--')

ShuaiGuo16

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation
from IPython.display import HTML
from celluloid import Camera
%matplotlib inline

# Animate a single trajectory
pick_traj = 5      # Select a trajectory to simulate

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# Create individual frames
for i in range(0,30):
    for j in range(1,traj_X.shape[1]+1):
    
        # Projectile's trajectory
        x = traj_X[i][0:j]
        y = traj_Y[i][0:j]
    
        # Show Projectile's location
        ax.plot(x[-1], y[-1], marker='o', markersize=12, 

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# Extract range data
Range = traj_X[:,-1]

# Extract bins
n, bins, patches = plt.hist(Range, bins=10, edgecolor='black')
plt.close()

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# Set up the histogram axis
ax_hist = ax.twinx()        # Make an identical copy
ax_hist.set_ylim(0, 10.2)
ax_hist.set_yticks(list(range(0,10,2)))
ax_hist.set_ylabel('Count', fontsize=15)

# Initiate camera
camera = Camera(fig)

# A list of range values

ShuaiGuo16

# Data analysis
import pandas as pd
import numpy as np

# Simulate SIR model
from scipy.integrate import odeint

# Sampling
from pyDOE import lhs
from scipy.stats.distributions import norm

ShuaiGuo16

def SIR_model(beta, gamma, t, N, I0, R0):
    """The function solves the SIR model to simulate 
    the disease spreading"""
    
    S0 = N - I0 - R0
    
    def deriv(y, t, N, beta, gamma):
        S, I, R = y
        dSdt = -beta * S * I / N
        dIdt = beta * S * I / N - gamma * I

ShuaiGuo16

# Assign infection and recovery rate parameters
beta, gamma = 0.22, 0.1

# Grid of time points (in days)
t = np.arange(0, 101, 2)

# Run SIR model to predict epidemic evolution
S, I, R = SIR_model(beta, gamma, t, I0=8, N=1000, R0=0)

# Extract output of interest

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# Specify random sample number
sample_num = 1000

# Using Latin Hypercube method to generate uniform distribution
uni_samples = lhs(n=2, samples=sample_num, criterion='maximin')

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# Transforming to standard normal distribution
std_norm_samples = np.zeros_like(uni_samples)
for i in range(2):
    std_norm_samples[:,i] = norm(loc=0, scale=1).ppf(uni_samples[:,i])