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Basic probability simulations in Python 3
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I have been learning Probability from Statistics 110 and trying to simulate problems that have an unintuitive answer
from numpy import cumsum
from statistics import mean
from numpy.random import exponential
from random import randint, sample, uniform
from bisect import bisect_left
def mean_of_experiments(experiment_func, N=100000):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
@mean_of_experiments
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = [randint(1, 365) for _ in range(k)]
return len(rands) != len(set(rands))
@mean_of_experiments
def matching(k=52):
'''Simulates an experiment to permute 'k' cards and check if any jth card's value is j'''
idx_labels = enumerate(sample(range(k), k))
return any(idx == label for idx, label in idx_labels)
@mean_of_experiments
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
def boardings(scale=5.0, N=1_00_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = cumsum([exponential(scale=scale) for _ in range(N)])
@mean_of_experiments
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
Probability Problems:
common_birthday: Given k people, what's the probability that any 2 people share a birthday?matching: Given 52 cards with a unique label in 0...n-1, they are shuffled. What's the probability that there's any j^th card's label is j?dice: Problem posed by a gambler to Newtonboardings: Given that a bus company's buses follow a Poisson process, if a person visits a stop at some random time, what was that inter-arrival time? From Tsitsiklis' lectures
What I wish I could do in my code is dynamically set the value of N in the decorator mean_of_experiments. Is that possible?
python python-3.x statistics simulation
asked 2 hours ago
kamalbanga
1184
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kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |Â
up vote
3
down vote
favorite
I have been learning Probability from Statistics 110 and trying to simulate problems that have an unintuitive answer
from numpy import cumsum
from statistics import mean
from numpy.random import exponential
from random import randint, sample, uniform
from bisect import bisect_left
def mean_of_experiments(experiment_func, N=100000):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
@mean_of_experiments
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = [randint(1, 365) for _ in range(k)]
return len(rands) != len(set(rands))
@mean_of_experiments
def matching(k=52):
'''Simulates an experiment to permute 'k' cards and check if any jth card's value is j'''
idx_labels = enumerate(sample(range(k), k))
return any(idx == label for idx, label in idx_labels)
@mean_of_experiments
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
def boardings(scale=5.0, N=1_00_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = cumsum([exponential(scale=scale) for _ in range(N)])
@mean_of_experiments
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
Probability Problems:
common_birthday: Given k people, what's the probability that any 2 people share a birthday?matching: Given 52 cards with a unique label in 0...n-1, they are shuffled. What's the probability that there's any j^th card's label is j?dice: Problem posed by a gambler to Newtonboardings: Given that a bus company's buses follow a Poisson process, if a person visits a stop at some random time, what was that inter-arrival time? From Tsitsiklis' lectures
What I wish I could do in my code is dynamically set the value of N in the decorator mean_of_experiments. Is that possible?
python python-3.x statistics simulation
asked 2 hours ago
kamalbanga
1184
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kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1
Welcome to Code Review! Thank you for writing a question that's both clear and complete. Could you please add what version of Python you wrote this for?
– Mast
2 hours ago
1
@Mast: Thanks :). Python 3, I edited the question too.
– kamalbanga
2 hours ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I have been learning Probability from Statistics 110 and trying to simulate problems that have an unintuitive answer
from numpy import cumsum
from statistics import mean
from numpy.random import exponential
from random import randint, sample, uniform
from bisect import bisect_left
def mean_of_experiments(experiment_func, N=100000):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
@mean_of_experiments
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = [randint(1, 365) for _ in range(k)]
return len(rands) != len(set(rands))
@mean_of_experiments
def matching(k=52):
'''Simulates an experiment to permute 'k' cards and check if any jth card's value is j'''
idx_labels = enumerate(sample(range(k), k))
return any(idx == label for idx, label in idx_labels)
@mean_of_experiments
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
def boardings(scale=5.0, N=1_00_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = cumsum([exponential(scale=scale) for _ in range(N)])
@mean_of_experiments
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
Probability Problems:
common_birthday: Given k people, what's the probability that any 2 people share a birthday?matching: Given 52 cards with a unique label in 0...n-1, they are shuffled. What's the probability that there's any j^th card's label is j?dice: Problem posed by a gambler to Newtonboardings: Given that a bus company's buses follow a Poisson process, if a person visits a stop at some random time, what was that inter-arrival time? From Tsitsiklis' lectures
What I wish I could do in my code is dynamically set the value of N in the decorator mean_of_experiments. Is that possible?
python python-3.x statistics simulation
asked 2 hours ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have been learning Probability from Statistics 110 and trying to simulate problems that have an unintuitive answer
from numpy import cumsum
from statistics import mean
from numpy.random import exponential
from random import randint, sample, uniform
from bisect import bisect_left
def mean_of_experiments(experiment_func, N=100000):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
@mean_of_experiments
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = [randint(1, 365) for _ in range(k)]
return len(rands) != len(set(rands))
@mean_of_experiments
def matching(k=52):
'''Simulates an experiment to permute 'k' cards and check if any jth card's value is j'''
idx_labels = enumerate(sample(range(k), k))
return any(idx == label for idx, label in idx_labels)
@mean_of_experiments
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
def boardings(scale=5.0, N=1_00_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = cumsum([exponential(scale=scale) for _ in range(N)])
@mean_of_experiments
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
Probability Problems:
common_birthday: Given k people, what's the probability that any 2 people share a birthday?matching: Given 52 cards with a unique label in 0...n-1, they are shuffled. What's the probability that there's any j^th card's label is j?dice: Problem posed by a gambler to Newtonboardings: Given that a bus company's buses follow a Poisson process, if a person visits a stop at some random time, what was that inter-arrival time? From Tsitsiklis' lectures
What I wish I could do in my code is dynamically set the value of N in the decorator mean_of_experiments. Is that possible?
python python-3.x statistics simulation
python python-3.x statistics simulation
asked 2 hours ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
asked 2 hours ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
kamalbanga
1184
asked 2 hours ago
kamalbanga
1184
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Welcome to Code Review! Thank you for writing a question that's both clear and complete. Could you please add what version of Python you wrote this for?
– Mast
2 hours ago
1
@Mast: Thanks :). Python 3, I edited the question too.
– kamalbanga
2 hours ago
add a comment |Â
1
Welcome to Code Review! Thank you for writing a question that's both clear and complete. Could you please add what version of Python you wrote this for?
– Mast
2 hours ago
1
@Mast: Thanks :). Python 3, I edited the question too.
– kamalbanga
2 hours ago
1
1
Welcome to Code Review! Thank you for writing a question that's both clear and complete. Could you please add what version of Python you wrote this for?
– Mast
2 hours ago
Welcome to Code Review! Thank you for writing a question that's both clear and complete. Could you please add what version of Python you wrote this for?
– Mast
2 hours ago
1
1
@Mast: Thanks :). Python 3, I edited the question too.
– kamalbanga
2 hours ago
@Mast: Thanks :). Python 3, I edited the question too.
– kamalbanga
2 hours ago
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
functools.wraps
Unrelated to your main question, I advice you to use functools.wraps. This way, your methods metadata get transferred to the wrapped method.
For example dice.__doc__ returns None without it, but the doctstring if you include it.
repetitions
It is possible to programatically change the number of repetitions per function. If you look at functools.lru_cache, where you need to specify the size of the cache too, you can see you just need an extra level of wrapper function:
def mean_of_experiments(N=100_000):
def inner_decorator(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
@wraps(experiment_func)
def wrapper(*args, **kwargs):
# print(f"N repititions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
return inner_decorator
where the inner_decorator is the old mean_of_experiments method
Dynamically set repetitions
A decorator is nothing but syntactic sugar for decorator(func), so you can do it by not decorating the functions themselves, but doing the 'decorating' when calling them:
mean_of_experiments(N=100)(dice(100, 20))
Dynamically set repetitions 2:
Another approach is to pass the repetitions on with the kwargs to the experiment_func
def mean_of_experiments_2(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
repetitions = kwargs.pop('repetitions', 100_000)
# print(f"repetitions repetitions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(repetitions)), 3)
return wrapper
@mean_of_experiments_2
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
and then call it like this: dice(6, 4, repetitions=100)
The main caveat here is not to pick repetitions as argument to any of the experiment_funcs
Further remarks
_ in ints
you wrote 100000 in 2 ways: 100000 and 1_00_000. The second way looks incorrect to me (it is syntactically correct, but I would group numbers per 3). The way I would write it is 100_000. You can pick another way, but stay consistent
common_birthday
since the rands as you make it will always contain k elements, it would be more efficient to skip this list, and immediately make the set:
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = randint(1, 365) for _ in range(k)
return len(rands) != k
dice
For large n, this can become a very long list. An alternative approach would be to either use a collections.Counter, or use sum
return sum(randint(1, 6) == 6 for _ in range(n)) >= c
or
return Counter(randint(1, 6) for _ in range(n))[6] >= c
boardings
If, instead of depending on numpy you want a native implementations, you can use itertools.accumulate and random.expovariate.
def boardings_native(scale=5.0, N=100_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = list(accumulate(expovariate(lambd=1/scale) for _ in range(N)))
@mean_of_experiments(3)
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
If I look at the performance, it is even faster than the numpy implementation, but that is probably because generating the arrivals is an iteration instead of a vectorised operation
%timeit boardings_native()
52 ms ± 1.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit boardings()
143 ms ± 713 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
answered 1 hour ago
Maarten Fabré
3,734215
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,common_birthdayI could set the value forN. So if I am okay with low-confidence answer I setN=100and if I want answer with high confidence, I could setN=1000000.
– kamalbanga
1 hour ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
add a comment |Â
up vote
0
down vote
There is a function choices in random library that returns a list of elements chosen from the population with replacement. It could simplify the methods common_birthday and dice. Though, I believe, this decreases readability by a little.
from random import choices
def common_birthday(k):
return len(set(choices(range(1, 366), k=k))) != k
def dice(n, c):
return choices(range(1, 7), k=n).count(6) >= c
I removed the docstring and decorator for exposition of business logic.
answered 32 mins ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
functools.wraps
Unrelated to your main question, I advice you to use functools.wraps. This way, your methods metadata get transferred to the wrapped method.
For example dice.__doc__ returns None without it, but the doctstring if you include it.
repetitions
It is possible to programatically change the number of repetitions per function. If you look at functools.lru_cache, where you need to specify the size of the cache too, you can see you just need an extra level of wrapper function:
def mean_of_experiments(N=100_000):
def inner_decorator(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
@wraps(experiment_func)
def wrapper(*args, **kwargs):
# print(f"N repititions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
return inner_decorator
where the inner_decorator is the old mean_of_experiments method
Dynamically set repetitions
A decorator is nothing but syntactic sugar for decorator(func), so you can do it by not decorating the functions themselves, but doing the 'decorating' when calling them:
mean_of_experiments(N=100)(dice(100, 20))
Dynamically set repetitions 2:
Another approach is to pass the repetitions on with the kwargs to the experiment_func
def mean_of_experiments_2(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
repetitions = kwargs.pop('repetitions', 100_000)
# print(f"repetitions repetitions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(repetitions)), 3)
return wrapper
@mean_of_experiments_2
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
and then call it like this: dice(6, 4, repetitions=100)
The main caveat here is not to pick repetitions as argument to any of the experiment_funcs
Further remarks
_ in ints
you wrote 100000 in 2 ways: 100000 and 1_00_000. The second way looks incorrect to me (it is syntactically correct, but I would group numbers per 3). The way I would write it is 100_000. You can pick another way, but stay consistent
common_birthday
since the rands as you make it will always contain k elements, it would be more efficient to skip this list, and immediately make the set:
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = randint(1, 365) for _ in range(k)
return len(rands) != k
dice
For large n, this can become a very long list. An alternative approach would be to either use a collections.Counter, or use sum
return sum(randint(1, 6) == 6 for _ in range(n)) >= c
or
return Counter(randint(1, 6) for _ in range(n))[6] >= c
boardings
If, instead of depending on numpy you want a native implementations, you can use itertools.accumulate and random.expovariate.
def boardings_native(scale=5.0, N=100_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = list(accumulate(expovariate(lambd=1/scale) for _ in range(N)))
@mean_of_experiments(3)
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
If I look at the performance, it is even faster than the numpy implementation, but that is probably because generating the arrivals is an iteration instead of a vectorised operation
%timeit boardings_native()
52 ms ± 1.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit boardings()
143 ms ± 713 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
answered 1 hour ago
Maarten Fabré
3,734215
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,common_birthdayI could set the value forN. So if I am okay with low-confidence answer I setN=100and if I want answer with high confidence, I could setN=1000000.
– kamalbanga
1 hour ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
add a comment |Â
up vote
1
down vote
accepted
functools.wraps
Unrelated to your main question, I advice you to use functools.wraps. This way, your methods metadata get transferred to the wrapped method.
For example dice.__doc__ returns None without it, but the doctstring if you include it.
repetitions
It is possible to programatically change the number of repetitions per function. If you look at functools.lru_cache, where you need to specify the size of the cache too, you can see you just need an extra level of wrapper function:
def mean_of_experiments(N=100_000):
def inner_decorator(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
@wraps(experiment_func)
def wrapper(*args, **kwargs):
# print(f"N repititions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
return inner_decorator
where the inner_decorator is the old mean_of_experiments method
Dynamically set repetitions
A decorator is nothing but syntactic sugar for decorator(func), so you can do it by not decorating the functions themselves, but doing the 'decorating' when calling them:
mean_of_experiments(N=100)(dice(100, 20))
Dynamically set repetitions 2:
Another approach is to pass the repetitions on with the kwargs to the experiment_func
def mean_of_experiments_2(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
repetitions = kwargs.pop('repetitions', 100_000)
# print(f"repetitions repetitions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(repetitions)), 3)
return wrapper
@mean_of_experiments_2
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
and then call it like this: dice(6, 4, repetitions=100)
The main caveat here is not to pick repetitions as argument to any of the experiment_funcs
Further remarks
_ in ints
you wrote 100000 in 2 ways: 100000 and 1_00_000. The second way looks incorrect to me (it is syntactically correct, but I would group numbers per 3). The way I would write it is 100_000. You can pick another way, but stay consistent
common_birthday
since the rands as you make it will always contain k elements, it would be more efficient to skip this list, and immediately make the set:
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = randint(1, 365) for _ in range(k)
return len(rands) != k
dice
For large n, this can become a very long list. An alternative approach would be to either use a collections.Counter, or use sum
return sum(randint(1, 6) == 6 for _ in range(n)) >= c
or
return Counter(randint(1, 6) for _ in range(n))[6] >= c
boardings
If, instead of depending on numpy you want a native implementations, you can use itertools.accumulate and random.expovariate.
def boardings_native(scale=5.0, N=100_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = list(accumulate(expovariate(lambd=1/scale) for _ in range(N)))
@mean_of_experiments(3)
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
If I look at the performance, it is even faster than the numpy implementation, but that is probably because generating the arrivals is an iteration instead of a vectorised operation
%timeit boardings_native()
52 ms ± 1.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit boardings()
143 ms ± 713 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
answered 1 hour ago
Maarten Fabré
3,734215
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,common_birthdayI could set the value forN. So if I am okay with low-confidence answer I setN=100and if I want answer with high confidence, I could setN=1000000.
– kamalbanga
1 hour ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
functools.wraps
Unrelated to your main question, I advice you to use functools.wraps. This way, your methods metadata get transferred to the wrapped method.
For example dice.__doc__ returns None without it, but the doctstring if you include it.
repetitions
It is possible to programatically change the number of repetitions per function. If you look at functools.lru_cache, where you need to specify the size of the cache too, you can see you just need an extra level of wrapper function:
def mean_of_experiments(N=100_000):
def inner_decorator(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
@wraps(experiment_func)
def wrapper(*args, **kwargs):
# print(f"N repititions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
return inner_decorator
where the inner_decorator is the old mean_of_experiments method
Dynamically set repetitions
A decorator is nothing but syntactic sugar for decorator(func), so you can do it by not decorating the functions themselves, but doing the 'decorating' when calling them:
mean_of_experiments(N=100)(dice(100, 20))
Dynamically set repetitions 2:
Another approach is to pass the repetitions on with the kwargs to the experiment_func
def mean_of_experiments_2(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
repetitions = kwargs.pop('repetitions', 100_000)
# print(f"repetitions repetitions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(repetitions)), 3)
return wrapper
@mean_of_experiments_2
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
and then call it like this: dice(6, 4, repetitions=100)
The main caveat here is not to pick repetitions as argument to any of the experiment_funcs
Further remarks
_ in ints
you wrote 100000 in 2 ways: 100000 and 1_00_000. The second way looks incorrect to me (it is syntactically correct, but I would group numbers per 3). The way I would write it is 100_000. You can pick another way, but stay consistent
common_birthday
since the rands as you make it will always contain k elements, it would be more efficient to skip this list, and immediately make the set:
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = randint(1, 365) for _ in range(k)
return len(rands) != k
dice
For large n, this can become a very long list. An alternative approach would be to either use a collections.Counter, or use sum
return sum(randint(1, 6) == 6 for _ in range(n)) >= c
or
return Counter(randint(1, 6) for _ in range(n))[6] >= c
boardings
If, instead of depending on numpy you want a native implementations, you can use itertools.accumulate and random.expovariate.
def boardings_native(scale=5.0, N=100_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = list(accumulate(expovariate(lambd=1/scale) for _ in range(N)))
@mean_of_experiments(3)
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
If I look at the performance, it is even faster than the numpy implementation, but that is probably because generating the arrivals is an iteration instead of a vectorised operation
%timeit boardings_native()
52 ms ± 1.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit boardings()
143 ms ± 713 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
answered 1 hour ago
Maarten Fabré
3,734215
functools.wraps
Unrelated to your main question, I advice you to use functools.wraps. This way, your methods metadata get transferred to the wrapped method.
For example dice.__doc__ returns None without it, but the doctstring if you include it.
repetitions
It is possible to programatically change the number of repetitions per function. If you look at functools.lru_cache, where you need to specify the size of the cache too, you can see you just need an extra level of wrapper function:
def mean_of_experiments(N=100_000):
def inner_decorator(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
@wraps(experiment_func)
def wrapper(*args, **kwargs):
# print(f"N repititions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(N)), 3)
return wrapper
return inner_decorator
where the inner_decorator is the old mean_of_experiments method
Dynamically set repetitions
A decorator is nothing but syntactic sugar for decorator(func), so you can do it by not decorating the functions themselves, but doing the 'decorating' when calling them:
mean_of_experiments(N=100)(dice(100, 20))
Dynamically set repetitions 2:
Another approach is to pass the repetitions on with the kwargs to the experiment_func
def mean_of_experiments_2(experiment_func):
'''Decorator to repeat any Bernoulli trial N times and return probability of success'''
def wrapper(*args, **kwargs):
repetitions = kwargs.pop('repetitions', 100_000)
# print(f"repetitions repetitions")
return round(mean(experiment_func(*args, **kwargs) for _ in range(repetitions)), 3)
return wrapper
@mean_of_experiments_2
def dice(n, c):
'''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''
return [randint(1, 6) for _ in range(n)].count(6) >= c
and then call it like this: dice(6, 4, repetitions=100)
The main caveat here is not to pick repetitions as argument to any of the experiment_funcs
Further remarks
_ in ints
you wrote 100000 in 2 ways: 100000 and 1_00_000. The second way looks incorrect to me (it is syntactically correct, but I would group numbers per 3). The way I would write it is 100_000. You can pick another way, but stay consistent
common_birthday
since the rands as you make it will always contain k elements, it would be more efficient to skip this list, and immediately make the set:
def common_birthday(k):
'''Simulates an experiment to generate k independent uniformly random birthdays and check if there are any repeat birthdays'''
rands = randint(1, 365) for _ in range(k)
return len(rands) != k
dice
For large n, this can become a very long list. An alternative approach would be to either use a collections.Counter, or use sum
return sum(randint(1, 6) == 6 for _ in range(n)) >= c
or
return Counter(randint(1, 6) for _ in range(n))[6] >= c
boardings
If, instead of depending on numpy you want a native implementations, you can use itertools.accumulate and random.expovariate.
def boardings_native(scale=5.0, N=100_000):
'''Simulates an experiment where arrival of buses at stop follows a Poisson process and finds avg. inter-arrival time at a random instant'''
arrivals = list(accumulate(expovariate(lambd=1/scale) for _ in range(N)))
@mean_of_experiments(3)
def wait():
boarding_idx = bisect_left(arrivals, uniform(0, arrivals[-1]))
missed_bus = 0 if boarding_idx == 0 else arrivals[boarding_idx - 1]
return arrivals[boarding_idx] - missed_bus
return wait()
If I look at the performance, it is even faster than the numpy implementation, but that is probably because generating the arrivals is an iteration instead of a vectorised operation
%timeit boardings_native()
52 ms ± 1.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit boardings()
143 ms ± 713 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
answered 1 hour ago
Maarten Fabré
3,734215
edited 53 mins ago
answered 1 hour ago
Maarten Fabré
3,734215
answered 1 hour ago
Maarten Fabré
3,734215
answered 1 hour ago
Maarten Fabré
3,734215
3,734215
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,common_birthdayI could set the value forN. So if I am okay with low-confidence answer I setN=100and if I want answer with high confidence, I could setN=1000000.
– kamalbanga
1 hour ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
add a comment |Â
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,common_birthdayI could set the value forN. So if I am okay with low-confidence answer I setN=100and if I want answer with high confidence, I could setN=1000000.
– kamalbanga
1 hour ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,
common_birthday I could set the value for N. So if I am okay with low-confidence answer I set N=100 and if I want answer with high confidence, I could set N=1000000.– kamalbanga
1 hour ago
Wow! All these seem great suggestions. Regarding that decorator, what I meant is that moving beyond decorators, is there some construct in which while calling a function, say,
common_birthday I could set the value for N. So if I am okay with low-confidence answer I set N=100 and if I want answer with high confidence, I could set N=1000000.– kamalbanga
1 hour ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I added 2 approaches to do this dynamically
– Maarten Fabré
53 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
I am amazed again! I like the second approach so much! Exactly what I wished for, since it can keep a default value; in case I want to set it to some other value, I could do that too. Thanks :)
– kamalbanga
43 mins ago
add a comment |Â
up vote
0
down vote
There is a function choices in random library that returns a list of elements chosen from the population with replacement. It could simplify the methods common_birthday and dice. Though, I believe, this decreases readability by a little.
from random import choices
def common_birthday(k):
return len(set(choices(range(1, 366), k=k))) != k
def dice(n, c):
return choices(range(1, 7), k=n).count(6) >= c
I removed the docstring and decorator for exposition of business logic.
answered 32 mins ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
There is a function choices in random library that returns a list of elements chosen from the population with replacement. It could simplify the methods common_birthday and dice. Though, I believe, this decreases readability by a little.
from random import choices
def common_birthday(k):
return len(set(choices(range(1, 366), k=k))) != k
def dice(n, c):
return choices(range(1, 7), k=n).count(6) >= c
I removed the docstring and decorator for exposition of business logic.
answered 32 mins ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
There is a function choices in random library that returns a list of elements chosen from the population with replacement. It could simplify the methods common_birthday and dice. Though, I believe, this decreases readability by a little.
from random import choices
def common_birthday(k):
return len(set(choices(range(1, 366), k=k))) != k
def dice(n, c):
return choices(range(1, 7), k=n).count(6) >= c
I removed the docstring and decorator for exposition of business logic.
answered 32 mins ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
There is a function choices in random library that returns a list of elements chosen from the population with replacement. It could simplify the methods common_birthday and dice. Though, I believe, this decreases readability by a little.
from random import choices
def common_birthday(k):
return len(set(choices(range(1, 366), k=k))) != k
def dice(n, c):
return choices(range(1, 7), k=n).count(6) >= c
I removed the docstring and decorator for exposition of business logic.
answered 32 mins ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 32 mins ago
kamalbanga
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 32 mins ago
kamalbanga
1184
answered 32 mins ago
kamalbanga
1184
1184
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
kamalbanga is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
kamalbanga is a new contributor. Be nice, and check out our Code of Conduct.
kamalbanga is a new contributor. Be nice, and check out our Code of Conduct.
kamalbanga is a new contributor. Be nice, and check out our Code of Conduct.
kamalbanga is a new contributor. Be nice, and check out our Code of Conduct.
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1
Welcome to Code Review! Thank you for writing a question that's both clear and complete. Could you please add what version of Python you wrote this for?
– Mast
2 hours ago
1
@Mast: Thanks :). Python 3, I edited the question too.
– kamalbanga
2 hours ago