Analysis on Monte Carlo Data Sampling

By: Roth In

This notebook will re-creating the example of Monte Carlo data simpling within a circle.
After the simpling, each data point will be assigned its quadrant.
Counting the quadrants will show how the data are spreading throughout the circle.

Import the libraries:

import matplotlib.pyplot as plt
import numpy as np
import math
import random
import pandas as pd

Given (x, y) coordinant, within_circle will return TRUE if the point is inside the cirle. Otherwise, the function will return FALSE.

def within_circle(x, y, radius=1, c_x=0, c_y=0):
    dis = math.sqrt(((x-c_x)**2) + ((y-c_y)**2))
    return dis < radius

generate_data will take size as the number of sample data that will be generate.

def generate_data(size, center_x=0, center_y=0, radius=1):
    count = 0
    x = []
    y = []
    while(count < size):
        x_var = random.uniform(center_x - radius,center_x + radius)
        y_var = random.uniform(center_y-radius, center_y + radius)
        if(within_circle(x_var, y_var,radius, center_x, center_y)):
            x.append(x_var)
            y.append(y_var)
            count+=1
    return x, y

Generate 500 data points centered at (0, 0) with radius of 1

x, y = generate_data(1000, 0, 0, 1)

Plot the 500 data generated from generate_data function above.

plt.scatter(x, y, marker='o', color="red", s=5)
plt.xlim(-1.5, 1.5)
plt.ylim(-1.5, 1.5)
plt.gca().set_aspect('equal', adjustable='box')

data = {'x': x, 'y':y}

Loop through to check and assign quandrant to each point in data

q = []
for i, j in zip(x, y):
    if(i > 0):
        if(j>0):
            q.append("I")
        else:
            q.append("IV")
    else:
        if(j>0):
            q.append("II")
        else:
            q.append("III")

data["Quadrants"] = q

Creat pandas dataframe from with the (x, y) coordinate and its respective quadrant.

df = pd.DataFrame(data)

df

	x	y	Quadrants
0	0.804789	-0.344615	IV
1	0.194384	-0.449343	IV
2	0.692455	0.293018	I
3	-0.654444	-0.585161	III
4	0.294066	-0.822927	IV
...	...	...	...
995	0.618112	-0.044275	IV
996	0.671554	-0.059373	IV
997	-0.739402	-0.244411	III
998	0.253110	-0.586791	IV
999	-0.663163	0.144050	II

1000 rows × 3 columns

Count the values of each quadrant, and then plot into piechart.

spreadness = df['Quadrants'].value_counts()
pie_data = np.array([spreadness["I"],spreadness["II"],spreadness["III"],spreadness["IV"]])
mylabels = ["Quadrant I", " Quadrant II", "Quadrant III", "Quadrant IV"]
plt.pie(pie_data, labels = mylabels, autopct='%.1f%%',)

([<matplotlib.patches.Wedge at 0x11ba52fa0>,
  <matplotlib.patches.Wedge at 0x11ba5e700>,
  <matplotlib.patches.Wedge at 0x11ba5ed90>,
  <matplotlib.patches.Wedge at 0x11ba69460>],
 [Text(0.7802572074659874, 0.7753700343689969, 'Quadrant I'),
  Text(-0.7899389160720414, 0.765504088085053, ' Quadrant II'),
  Text(-0.7530018405458982, -0.8018654676031945, 'Quadrant III'),
  Text(0.7875301149299792, -0.7679819777041478, 'Quadrant IV')],
 [Text(0.42559484043599305, 0.4229291096558165, '24.9%'),
  Text(-0.4308757724029316, 0.4175476844100289, '25.7%'),
  Text(-0.41072827666139905, -0.43738116414719697, '24.8%'),
  Text(0.4295618808708977, -0.4188992605658987, '24.6%')])