Calculating area under the curve using Monte Carlo method for any given function.
Python, 38 lines
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | # Calculating area under the curve using Monte Carlo method
# FB - 201006137
import math
import random
# define any function here!
def f(x):
return math.sqrt(1.0 - x * x)
# define any xmin-xmax interval here! (xmin < xmax)
xmin = -1.0
xmax = 1.0
# find ymin-ymax
numSteps = 1000000 # bigger the better but slower!
ymin = f(xmin)
ymax = ymin
for i in range(numSteps):
x = xmin + (xmax - xmin) * float(i) / numSteps
y = f(x)
if y < ymin: ymin = y
if y > ymax: ymax = y
# Monte Carlo
rectArea = (xmax - xmin) * (ymax - ymin)
numPoints = 1000000 # bigger the better but slower!
ctr = 0
for j in range(numPoints):
x = xmin + (xmax - xmin) * random.random()
y = ymin + (ymax - ymin) * random.random()
if f(x) > 0 and y > 0 and y <= f(x):
ctr += 1
if f(x) < 0 and y < 0 and y >= f(x):
ctr += 1
fnArea = rectArea * float(ctr) / numPoints
print "Area under the curve = " + str(fnArea)
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In the given example, it would calculate pi/2 because the given function defines a half-circle.
Given that the code is already evaluating the function at a huge number of points (lines 19--23), conventional numerical integration would be far better. Also, the kind of rejection sampling proposed here is very inefficient, and requires knowing the minimum and maximum of the function.
I certainly did not write this code for any practical purpose. Monte Carlo is probably the most inefficient solution method for almost any problem. I only put it here thinking some people may find it interesting, that's all.