"""Provides some utilities widely used by other modules."""
import bisect
import collections
import collections.abc
import heapq
import operator
import os.path
import random
import math
import functools
from statistics import mean
import numpy as np
from itertools import chain, combinations
inf = float('inf')
# ______________________________________________________________________________
# Functions on Sequences and Iterables
def sequence(iterable):
"""Converts iterable to sequence, if it is not already one."""
return iterable if isinstance(iterable, collections.abc.Sequence) else tuple([iterable])
def remove_all(item, seq):
"""Return a copy of seq (or string) with all occurrences of item removed."""
if isinstance(seq, str):
return seq.replace(item, '')
elif isinstance(seq, set):
rest = seq.copy()
rest.remove(item)
return rest
else:
return [x for x in seq if x != item]
def unique(seq):
"""Remove duplicate elements from seq. Assumes hashable elements."""
return list(set(seq))
def count(seq):
"""Count the number of items in sequence that are interpreted as true."""
return sum(map(bool, seq))
def multimap(items):
"""Given (key, val) pairs, return {key: [val, ....], ...}."""
result = collections.defaultdict(list)
for (key, val) in items:
result[key].append(val)
return dict(result)
def multimap_items(mmap):
"""Yield all (key, val) pairs stored in the multimap."""
for (key, vals) in mmap.items():
for val in vals:
yield key, val
def product(numbers):
"""Return the product of the numbers, e.g. product([2, 3, 10]) == 60"""
result = 1
for x in numbers:
result *= x
return result
def first(iterable, default=None):
"""Return the first element of an iterable; or default."""
return next(iter(iterable), default)
def is_in(elt, seq):
"""Similar to (elt in seq), but compares with 'is', not '=='."""
return any(x is elt for x in seq)
def mode(data):
"""Return the most common data item. If there are ties, return any one of them."""
[(item, count)] = collections.Counter(data).most_common(1)
return item
def powerset(iterable):
"""powerset([1,2,3]) --> (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"""
s = list(iterable)
return list(chain.from_iterable(combinations(s, r) for r in range(len(s) + 1)))[1:]
def extend(s, var, val):
"""Copy dict s and extend it by setting var to val; return copy."""
s2 = s.copy()
s2[var] = val
return s2
# ______________________________________________________________________________
# argmin and argmax
identity = lambda x: x
argmin = min
argmax = max
def argmin_random_tie(seq, key=identity):
"""Return a minimum element of seq; break ties at random."""
return argmin(shuffled(seq), key=key)
def argmax_random_tie(seq, key=identity):
"""Return an element with highest fn(seq[i]) score; break ties at random."""
return argmax(shuffled(seq), key=key)
def shuffled(iterable):
"""Randomly shuffle a copy of iterable."""
items = list(iterable)
random.shuffle(items)
return items
# ______________________________________________________________________________
# Statistical and mathematical functions
def histogram(values, mode=0, bin_function=None):
"""Return a list of (value, count) pairs, summarizing the input values.
Sorted by increasing value, or if mode=1, by decreasing count.
If bin_function is given, map it over values first."""
if bin_function:
values = map(bin_function, values)
bins = {}
for val in values:
bins[val] = bins.get(val, 0) + 1
if mode:
return sorted(list(bins.items()), key=lambda x: (x[1], x[0]), reverse=True)
else:
return sorted(bins.items())
def dot_product(X, Y):
"""Return the sum of the element-wise product of vectors X and Y."""
return sum(x * y for x, y in zip(X, Y))
def element_wise_product(X, Y):
"""Return vector as an element-wise product of vectors X and Y"""
assert len(X) == len(Y)
return [x * y for x, y in zip(X, Y)]
def matrix_multiplication(X_M, *Y_M):
"""Return a matrix as a matrix-multiplication of X_M and arbitrary number of matrices *Y_M"""
def _mat_mult(X_M, Y_M):
"""Return a matrix as a matrix-multiplication of two matrices X_M and Y_M
>>> matrix_multiplication([[1, 2, 3], [2, 3, 4]], [[3, 4], [1, 2], [1, 0]])
[[8, 8],[13, 14]]
"""
assert len(X_M[0]) == len(Y_M)
result = [[0 for i in range(len(Y_M[0]))] for _ in range(len(X_M))]
for i in range(len(X_M)):
for j in range(len(Y_M[0])):
for k in range(len(Y_M)):
result[i][j] += X_M[i][k] * Y_M[k][j]
return result
result = X_M
for Y in Y_M:
result = _mat_mult(result, Y)
return result
def vector_to_diagonal(v):
"""Converts a vector to a diagonal matrix with vector elements
as the diagonal elements of the matrix"""
diag_matrix = [[0 for i in range(len(v))] for _ in range(len(v))]
for i in range(len(v)):
diag_matrix[i][i] = v[i]
return diag_matrix
def vector_add(a, b):
"""Component-wise addition of two vectors."""
return tuple(map(operator.add, a, b))
def scalar_vector_product(X, Y):
"""Return vector as a product of a scalar and a vector"""
return [X * y for y in Y]
def scalar_matrix_product(X, Y):
"""Return matrix as a product of a scalar and a matrix"""
return [scalar_vector_product(X, y) for y in Y]
def inverse_matrix(X):
"""Inverse a given square matrix of size 2x2"""
assert len(X) == 2
assert len(X[0]) == 2
det = X[0][0] * X[1][1] - X[0][1] * X[1][0]
assert det != 0
inv_mat = scalar_matrix_product(1.0 / det, [[X[1][1], -X[0][1]], [-X[1][0], X[0][0]]])
return inv_mat
def probability(p):
"""Return true with probability p."""
return p > random.uniform(0.0, 1.0)
def weighted_sample_with_replacement(n, seq, weights):
"""Pick n samples from seq at random, with replacement, with the
probability of each element in proportion to its corresponding
weight."""
sample = weighted_sampler(seq, weights)
return [sample() for _ in range(n)]
def weighted_sampler(seq, weights):
"""Return a random-sample function that picks from seq weighted by weights."""
totals = []
for w in weights:
totals.append(w + totals[-1] if totals else w)
return lambda: seq[bisect.bisect(totals, random.uniform(0, totals[-1]))]
def weighted_choice(choices):
"""A weighted version of random.choice"""
# NOTE: should be replaced by random.choices if we port to Python 3.6
total = sum(w for _, w in choices)
r = random.uniform(0, total)
upto = 0
for c, w in choices:
if upto + w >= r:
return c, w
upto += w
def rounder(numbers, d=4):
"""Round a single number, or sequence of numbers, to d decimal places."""
if isinstance(numbers, (int, float)):
return round(numbers, d)
else:
constructor = type(numbers) # Can be list, set, tuple, etc.
return constructor(rounder(n, d) for n in numbers)
def num_or_str(x): # TODO: rename as `atom`
"""The argument is a string; convert to a number if possible, or strip it."""
try:
return int(x)
except ValueError:
try:
return float(x)
except ValueError:
return str(x).strip()
def euclidean_distance(X, Y):
return math.sqrt(sum((x - y) ** 2 for x, y in zip(X, Y)))
def cross_entropy_loss(X, Y):
n = len(X)
return (-1.0 / n) * sum(x * math.log(y) + (1 - x) * math.log(1 - y) for x, y in zip(X, Y))
def rms_error(X, Y):
return math.sqrt(ms_error(X, Y))
def ms_error(X, Y):
return mean((x - y) ** 2 for x, y in zip(X, Y))
def mean_error(X, Y):
return mean(abs(x - y) for x, y in zip(X, Y))
def manhattan_distance(X, Y):
return sum(abs(x - y) for x, y in zip(X, Y))
def mean_boolean_error(X, Y):
return mean(x != y for x, y in zip(X, Y))
def hamming_distance(X, Y):
return sum(x != y for x, y in zip(X, Y))
def normalize(dist):
"""Multiply each number by a constant such that the sum is 1.0"""
if isinstance(dist, dict):
total = sum(dist.values())
for key in dist:
dist[key] = dist[key] / total
assert 0 0 else alpha * (math.exp(x) - 1)
def elu_derivative(value, alpha=0.01):
return 1 if value > 0 else alpha * math.exp(value)
def tanh(x):
return np.tanh(x)
def tanh_derivative(value):
return 1 - (value ** 2)
def leaky_relu(x, alpha=0.01):
return x if x > 0 else alpha * x
def leaky_relu_derivative(value, alpha=0.01):
return 1 if value > 0 else alpha
def relu(x):
return max(0, x)
def relu_derivative(value):
return 1 if value > 0 else 0
def step(x):
"""Return activation value of x with sign function"""
return 1 if x >= 0 else 0
def gaussian(mean, st_dev, x):
"""Given the mean and standard deviation of a distribution, it returns the probability of x."""
return 1 / (math.sqrt(2 * math.pi) * st_dev) * math.e ** (-0.5 * (float(x - mean) / st_dev) ** 2)
try: # math.isclose was added in Python 3.5; but we might be in 3.4
from math import isclose
except ImportError:
def isclose(a, b, rel_tol=1e-09, abs_tol=0.0):
"""Return true if numbers a and b are close to each other."""
return abs(a - b)