Entropy of the distribution as a function of time

AI Thread Summary
The discussion revolves around a programming issue related to calculating entropy in a distribution over time. The user has shared a code snippet that implements a Monte Carlo method to estimate the area of an N-dimensional unit circle but is struggling to integrate the concept of entropy into their program. Key points of feedback highlight a misunderstanding in the mathematical expression used for the integral calculation. Specifically, the expression (1 - (-1)) is noted to always evaluate to 2, which raises questions about its intended use. Additionally, the precedence of the exponentiation operator (**) is emphasized, indicating that the current structure of the expression may not yield the desired results. The conversation suggests that the user needs to clarify their approach to both the mathematical formulation and the implementation of entropy within their code.
alex steve
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I am having an issue with finding the entropy in my program. I was asked to the find the entropy of the distribution as a function of time but i do not know where to start with entropy.

I understand entropy but putting it in my program is where I am stuck

Here is my code:

Python:
# -*- coding: utf-8 -*-
"""
Created on Thu Nov 12 11:15:44 2015"""import matplotlib.pyplot as plt

import random
def Function(D):    #D = dimensions
    sumOfSquare = 0.0
    for i in range(0, len(D)):
        sumOfSquare += D[i]**2
    if sumOfSquare <=1:
        return 1
    else:
        return 0
       
def MonteCarlo(f_n,dim):
    intervalsForSphere = 1000000
    integral = 0.0
    for i in range(0, intervalsForSphere):
        for j in range(0,len(dim)):
            dim[j] = random.random()
        integral += f_n(dim)
    integral = (1-(-1))**len(dim)/intervalsForSphere * integral
    return integral
   
print("10 dimensional unit circle ")
Ten_Dim= list(range(1,10+1))
ten_D_circle = MonteCarlo(Function,Ten_Dim)
print("area:",ten_D_circle)

AreaofCircle = []
x = []

for i in range(1,13):
    D = list(range(1,i+1))
    AreaofCircle.append(MonteCarlo(Function, D))
    x.append(i)

plt.plot(x,AreaofCircle)
plt.xlim([0,13])
plt.xlabel("Dimensions")
plt.ylabel("area")
plt.title("Area of N-dimensional Unit Circle")
plt.show()
 
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alex steve said:
integral = (1-(-1))**len(dim)/intervalsForSphere * integral

Not really about entropy, but are you certain about this expression? It is always evaluated to 2 between the parentheses. Shouldn't it be (1 - (-1)**len(dim)…) or something similar? I'll look further into the code and try to help, but the quoted code above made me scratch my head.
 
In addition to what DevacDave said about (1 - (-1)) always evaluating to 2, the expression after '**' probably isn't what you want.
Python:
integral = (1-(-1))**len(dim)/intervalsForSphere * integral

The ** operator is higher in precedence than any of the arithmetic operators, so the expression on the right above is raising 2 to the power len(dim), and is then dividing that result by intervalsForSphere, and finally, multiplying by integral.
 
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