Create monte_carlo_integration_univariate.py

maths/monte_carlo_integration_univariate.py

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+"""
+This program finds the approximate integration value/area under the curve of
+a specified function within specified limits using Monte Carlo integration method.
+
+Further, a graph of the individal areas under the curve considered for the calculation
+is also plotted. (PLOT SECTION -> Optional implementation)
+"""
+
+import doctest
+
+# importing the modules
+import random
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+# function to calculate the sin of a particular value of x
+# define your function
+def function_to_be_integrated(x : int) -> float:
+
+ # Doctest
+ """
+ :param x: int
+ :return: float
+
+ >>> round(function_to_be_integrated(0))
+ 0
+ """
+
+ return np.sin(x) # example function
+
+
+def monte_carlo(lower_limit : int, upper_limit : int, n : int) -> float:
+
+ # Doctest
+ """
+ :param lower_limit: int
+ :param upper_limit: int
+ :param N: int
+ :return: float
+
+ >>> round(monte_carlo(0, np.pi, 1000))
+ 2
+ """
+
+ # list to store all the values for plotting
+ plt_vals = []
+
+ # array of zeros of length N
+ ar = np.zeros(n)
+
+ # we iterate through all the values to generate
+ # multiple results and show whose intensity is
+ # the most.
+ for i in range(n):
+
+ # iterating over each Value of ar and filling it
+ # with a random value between the limits a and b
+ for i in range(len(ar)):
+ ar[i] = random.uniform(lower_limit, upper_limit)
+
+ # variable to store sum of the functions of different
+ # values of x
+ integral = 0.0
+
+ # iterates and sums up values of different functions
+ # of x
+ for i in ar:
+ integral += function_to_be_integrated(i)
+
+ # we get the answer by the formula derived adobe
+ ans = (upper_limit - lower_limit) / float(n) * integral
+ # appends the solution to a list for plotting the graph
+ plt_vals.append(ans)
+
+ """
+ #--------PLOT SECTION (OPTIONAL)----------#
+
+ # details of the plot to be generated
+ # sets the title of the plot
+ plt.title("Distributions of areas calculated")
+
+ # 3 parameters (array on which histogram needs
+ plt.hist(plt_vals, bins=30, ec="black")
+
+ # sets the label of the x-axis of the plot
+ plt.xlabel("Areas")
+ plt.show() # shows the plot
+
+ #-----END OF PLOT SECTION (OPTIONAL)------#
+ """
+
+ return sum(plt_vals) / N # takinf the average value
+
+
+doctest.testmod()
+
+
+# define parameters
+# limits of integration (specify limits)
+# example limits
+lower_limit = 0
+upper_limit = np.pi # gets the value of pi
+
+n = 1000 # Number of individual ares to be considered
+
+# function call
+# the final area under the curve(integration) value is considered as the average
+# of all the individual areas calculated
+print(f"\nThe value calculated by monte carlo integration is {monte_carlo(lower_limit, upper_limit, n)}.")