def test_accumulate():
assert list(accumulate(add, [1, 2, 3, 4, 5])) == [1, 3, 6, 10, 15]
assert list(accumulate(mul, [1, 2, 3, 4, 5])) == [1, 2, 6, 24, 120]
assert list(accumulate(add, [1, 2, 3, 4, 5], -1)) == [-1, 0, 2, 5, 9, 14]
def binop(a, b):
raise AssertionError('binop should not be called')
start = object()
assert list(accumulate(binop, [], start)) == [start]
def test_accumulate():
assert list(accumulate(add, [1, 2, 3, 4, 5])) == [1, 3, 6, 10, 15]
assert list(accumulate(mul, [1, 2, 3, 4, 5])) == [1, 2, 6, 24, 120]
assert list(accumulate(add, [1, 2, 3, 4, 5], -1)) == [-1, 0, 2, 5, 9, 14]
def binop(a, b):
raise AssertionError('binop should not be called')
start = object()
assert list(accumulate(binop, [], start)) == [start]
def sequential_p_values(
data: np.ndarray,
null_probabilities: np.ndarray,
dirichlet_probability=None,
dirichlet_concentration=10000,
) -> np.ndarray:
"""
Accumulates sequential p-values after every datapoint
Parameters
----------
data : np.ndarray
Data i.e. [[0, 1], [1, 0], ...] or [[10, 12], [14, 3], ...]
null_probabilities : np.ndarray
The expected traffic allocation probability, where the values must sum to 1.
Note the order must match the order of data.
dirichlet_probability : np.ndarray
The mean of the dirichlet distribution, subject to elements summing to 1.
dirichlet_concentration : float
How tightly the prior concentrates around the mean.
Returns
-------
np.ndarray
Sequential p-value after every datapoint.
"""
data = np.array(data)
if not _validate_data(data):
raise TypeError("Data is supposed to be an array of integer arrays")
bayes_factors = sequential_bayes_factors(data, null_probabilities,
dirichlet_probability,
dirichlet_concentration)
inverse_bayes_factors = 1 / bayes_factors
return list(accumulate(min, inverse_bayes_factors, 1))
def sequential_posteriors(
data: np.ndarray,
null_probabilities: np.ndarray,
dirichlet_probability=None,
dirichlet_concentration=10000,
prior_odds=1,
) -> List[dict]:
"""
Accumulates the posteriors and marginal likelihoods for each datapoint.
Parameters
----------
data : List[tuple]
Data.
null_probabilities : np.ndarray
The expected traffic allocation probability, where the values must sum to 1.
Note the order must match the order of data.
dirichlet_probability : np.ndarray
The mean of the dirichlet distribution, subject to elements summing to 1.
dirichlet_concentration : float
How tightly the prior concentrates around the mean.
Returns
-------
List[dict]
Posterior distribution and marginal likelihoods at every datapoint.
Examples
--------
For unit-level data, we can use sequential_posteriors like so:
>>> data = np.array([[1, 0, 0], [0, 1, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> null_probabilities = [0.4, 0.4, 0.2]
>>> list_dict = sequential_posteriors(data, null_probabilities)
For time-aggregated data, we can pass in tuples that represent the
aggregated count during that time:
>>> data = np.array([[20, 17, 9], [18, 21, 8], [4, 6, 4], [18, 19, 11]])
>>> null_probabilities = [0.4, 0.4, 0.2]
>>> list_dict = sequential_posteriors(data, null_probabilities)
"""
data = np.array(data)
if not _validate_data(data):
raise TypeError("Data is supposed to be an array of integer arrays")
null_probabilities = np.array(null_probabilities)
if dirichlet_probability is None:
dirichlet_probability = null_probabilities
dirichlet_alpha = dirichlet_probability * dirichlet_concentration
acc = {
const.LOG_POSTERIOR_ODDS: np.log(prior_odds),
const.POSTERIOR_ODDS: prior_odds,
const.LOG_BAYES_FACTOR: 0,
const.BAYES_FACTOR: 1,
const.P_VALUE: 1,
const.POSTERIOR_PROBABILITY: posterior_probability(prior_odds),
const.LOG_MARGINAL_LIKELIHOOD_M1: 0,
const.LOG_MARGINAL_LIKELIHOOD_M0: 0,
const.POSTERIOR_M1: dirichlet_alpha,
const.POSTERIOR_M0: null_probabilities,
}
return list(accumulate(accumulator, data, acc))[1:]
def test_accumulate_works_on_consumable_iterables():
assert list(accumulate(add, iter((1, 2, 3)))) == [1, 3, 6]
def test_accumulate():
assert list(accumulate(add, [1, 2, 3, 4, 5])) == [1, 3, 6, 10, 15]
assert list(accumulate(mul, [1, 2, 3, 4, 5])) == [1, 2, 6, 24, 120]
#!/usr/bin/env python3
from toolz.itertoolz import accumulate, frequencies
with open('input', 'r') as f:
inp = f.readline().strip().split(',')
def total_movement(counts):
straight = counts['nw'] - counts['se']
left = counts['sw'] - counts['ne']
right = counts['n'] - counts['s']
straight += left
right -= left
return abs(straight + right)
print(total_movement(frequencies(inp)))
counts = {dir: 0 for dir in ['n', 'nw', 'ne', 's', 'sw', 'se']}
def single_count(counts, direction):
counts[direction] += 1
return counts.copy()
print(max(map(total_movement, accumulate(single_count, inp, counts))))
