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13-Monte_carlo_integral_area_under_curve.py
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# -*- coding: utf-8 -*-
"""SM_Assignment-3-2.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/1md3eJMmKNeM-nw4w2ZDGCYSe3vCL3kaW
"""
import math
import random
import matplotlib.pyplot as plt
trials=[100,1000,5000,10000]
#f(x)=x*e^x 0-5
error_list=[]
error_list2=[]
for i in trials:
a=0
b=4
#print("Trials",i)
print("--------")
func_value=0
func_sum=0
func_squre_sum=0
func_avg=0
func_squard_avg=0
integral_value=0
error=0
for j in range(i):
x=random.uniform(a, b)
func_value=2*math.sqrt(x)
func_sum=func_sum+func_value
func_squre=func_value**2
func_squre_sum=func_squre_sum+func_squre
func_avg=func_sum/i
func_squard_avg=func_squre_sum/i
integral_value=(b-a)*func_avg
error= ((b-a)/math.sqrt(i))*(math.sqrt(func_squard_avg-(func_avg**2)))
error_list.append(error)
print("For Points",i)
print("Integral Value",integral_value)
print("Error",error)
print("Error",error_list)
a=4
b=8
#print("Trials",i)
print("--------")
func_value2=0
func_sum2=0
func_squre_sum2=0
func_avg2=0
func_squard_avg2=0
integral_value2=0
error2=0
for j in range(i):
x=random.uniform(a, b)
func_value2=8-x
func_sum2=func_sum2+func_value2
func_squre2=func_value2**2
func_squre_sum2=func_squre_sum2+func_squre2
func_avg2=func_sum2/i
func_squard_avg2=func_squre_sum2/i
integral_value2=(b-a)*func_avg2
error2= ((b-a)/math.sqrt(i))*(math.sqrt(func_squard_avg2-(func_avg2**2)))
error_list2.append(error2)
final_area=integral_value+integral_value2
print("For Points2",i)
print("Integral Value2",integral_value2)
print("Error2",error2)
print("Error2",error_list2)
print("Total Area",final_area)
plt.figure(figsize=(8, 6))
x=["100","1000","5000","10000"]
#plt.ylim(0, 100)
plt.bar(x,error_list, tick_label = x, width = 0.2, color = ['steelblue'])
plt.xlabel('Number of trials')
plt.ylabel('Error for part 1 (0-4)')
plt.title('Error for part 1 (0-4) vs Number of trials')
plt.show()
plt.figure(figsize=(8, 6))
x=["100","1000","5000","10000"]
#plt.ylim(0, 2)
plt.bar(x,error_list2, tick_label = x, width = 0.2, color = ['steelblue'])
plt.xlabel('Number of trials')
plt.ylabel('Error for part 1 (4-8)')
plt.title('Error for part 1 (4-8) vs Number of trials')
plt.show()