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Added doctests for monte_carlo.py

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Pablito 2024-12-07 16:11:56 +01:00
parent 27c1840095
commit 9b229ed229
1 changed files with 23 additions and 2 deletions
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maths/monte_carlo.py
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@ -18,6 +18,10 @@ def pi_estimator(iterations: int):
4. After all the dots are placed, divide the dots in the circle by the total.
5. Multiply this value by 4 to get your estimate of pi.
6. Print the estimated and numpy value of pi
>>> pi_estimator(1000)
The estimated value of pi is 3.145
The numpy value of pi is 3.141592653589793
The total error is 0.003
"""
# A local function to see if a dot lands in the circle.
@ -61,8 +65,11 @@ def area_under_curve_estimator(
c. Expected value = average of the function evaluations
4. Estimated value of integral = Expected value * (max_value - min_value)
5. Returns estimated value
>>> def test_function(x):
>>> return x * x
>>> area_under_curve_estimator(1000, test_function)
0.334 (estimated value should be close to 1/3)
"""
return mean(
function_to_integrate(uniform(min_value, max_value)) for _ in range(iterations)
) * (max_value - min_value)
@ -77,12 +84,19 @@ def area_under_line_estimator_check(
1. Calls "area_under_curve_estimator" function
2. Compares with the expected value
3. Prints estimated, expected and error value
>>> area_under_line_estimator_check(1000)
******************
Estimating area under y=x where x varies from 0.0 to 1.0
Estimated value is 0.332
Expected value is 0.5
Total error is 0.168
******************
"""
def identity_function(x: float) -> float:
"""
Represents identity function
>>> [function_to_integrate(x) for x in [-2.0, -1.0, 0.0, 1.0, 2.0]]
>>> [identity_function(x) for x in [-2.0, -1.0, 0.0, 1.0, 2.0]]
[-2.0, -1.0, 0.0, 1.0, 2.0]
"""
return x
@ -103,6 +117,13 @@ def area_under_line_estimator_check(
def pi_estimator_using_area_under_curve(iterations: int) -> None:
"""
Area under curve y = sqrt(4 - x^2) where x lies in 0 to 2 is equal to pi
>>> pi_estimator_using_area_under_curve(1000)
******************
Estimating pi using area_under_curve_estimator
Estimated value is 3.141
Expected value is 3.141592653589793
Total error is 0.0004
******************
"""
def function_to_integrate(x: float) -> float: