aima-python/utils.py at aima3python2 · 773173224/aima-python · GitHub

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"""Provides some utilities widely used by other modules"""

import bisect

import collections

import collections.abc

import operator

import os.path

import random

import math

import functools

# ______________________________________________________________________________

# Functions on Sequences and Iterables

def sequence(iterable):

"""Coerce iterable to sequence, if it is not already one."""

return (iterable if isinstance(iterable, collections.abc.Sequence)

else tuple(iterable))

def removeall(item, seq):

"""Return a copy of seq (or string) with all occurences of item removed."""

if isinstance(seq, str):

return seq.replace(item, '')

else:

return [x for x in seq if x != item]

def unique(seq): # TODO: replace with set

"""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(bool(x) for x in seq)

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 the next element of a generator; or default."""

try:

return iterable[0]

except IndexError:

return default

except TypeError:

return next(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

# ______________________________________________________________________________

# 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 dotproduct(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 arbitary 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 j 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 j 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 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):

"""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 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 <= dist[key] <= 1, "Probabilities must be between 0 and 1."

return dist

total = sum(dist)

return [(n / total) for n in dist]

def clip(x, lowest, highest):

"""Return x clipped to the range [lowest..highest]."""

return max(lowest, min(x, highest))

def sigmoid_derivative(value):

return value * (1 - value)

def sigmoid(x):

"""Return activation value of x with sigmoid function"""

return 1/(1 + math.exp(-x))

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) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)

# ______________________________________________________________________________

# Misc Functions

def memoize(fn, slot=None, maxsize=32):

"""Memoize fn: make it remember the computed value for any argument list.

If slot is specified, store result in that slot of first argument.

If slot is false, use lru_cache for caching the values."""

if slot:

def memoized_fn(obj, *args):

if hasattr(obj, slot):

return getattr(obj, slot)

else:

val = fn(obj, *args)

setattr(obj, slot, val)

return val

else:

@functools.lru_cache(maxsize=maxsize)

def memoized_fn(*args):

return fn(*args)

return memoized_fn

def name(obj):

"""Try to find some reasonable name for the object."""

return (getattr(obj, 'name', 0) or getattr(obj, '__name__', 0) or

getattr(getattr(obj, '__class__', 0), '__name__', 0) or

str(obj))

def isnumber(x):

"""Is x a number?"""

return hasattr(x, '__int__')

def issequence(x):

"""Is x a sequence?"""

return isinstance(x, collections.abc.Sequence)

def print_table(table, header=None, sep=' ', numfmt='{}'):

"""Print a list of lists as a table, so that columns line up nicely.

header, if specified, will be printed as the first row.

numfmt is the format for all numbers; you might want e.g. '{:.2f}'.

(If you want different formats in different columns,

don't use print_table.) sep is the separator between columns."""

justs = ['rjust' if isnumber(x) else 'ljust' for x in table[0]]

if header:

table.insert(0, header)

table = [[numfmt.format(x) if isnumber(x) else x for x in row]

for row in table]

sizes = list(

map(lambda seq: max(map(len, seq)),

list(zip(*[map(str, row) for row in table]))))

for row in table:

print(sep.join(getattr(

str(x), j)(size) for (j, size, x) in zip(justs, sizes, row)))

def AIMAFile(components, mode='r'):

"""Open a file based at the AIMA root directory."""

aima_root = os.path.dirname(__file__)

aima_file = os.path.join(aima_root, *components)

return open(aima_file)

def DataFile(name, mode='r'):

"Return a file in the AIMA /aima-data directory."

return AIMAFile(['aima-data', name], mode)

# ______________________________________________________________________________

# Expressions

# See https://docs.python.org/3/reference/expressions.html#operator-precedence

# See https://docs.python.org/3/reference/datamodel.html#special-method-names

class Expr(object):

"""A mathematical expression with an operator and 0 or more arguments.

op is a str like '+' or 'sin'; args are Expressions.

Expr('x') or Symbol('x') creates a symbol (a nullary Expr).

Expr('-', x) creates a unary; Expr('+', x, 1) creates a binary."""

def __init__(self, op, *args):

self.op = str(op)

self.args = args

# Operator overloads

def __neg__(self):

return Expr('-', self)

def __pos__(self):

return Expr('+', self)

def __invert__(self):

return Expr('~', self)

def __add__(self, rhs):

return Expr('+', self, rhs)

def __sub__(self, rhs):

return Expr('-', self, rhs)

def __mul__(self, rhs):

return Expr('*', self, rhs)

def __pow__(self, rhs):

return Expr('**', self, rhs)

def __mod__(self, rhs):

return Expr('%', self, rhs)

def __and__(self, rhs):

return Expr('&', self, rhs)

def __xor__(self, rhs):

return Expr('^', self, rhs)

def __rshift__(self, rhs):

return Expr('>>', self, rhs)

def __lshift__(self, rhs):

return Expr('<<', self, rhs)

def __truediv__(self, rhs):

return Expr('/', self, rhs)

def __floordiv__(self, rhs):

return Expr('//', self, rhs)

def __matmul__(self, rhs):

return Expr('@', self, rhs)

def __or__(self, rhs):

"""Allow both P | Q, and P |'==>'| Q."""

if isinstance(rhs, Expression):

return Expr('|', self, rhs)

else:

return PartialExpr(rhs, self)

# Reverse operator overloads

def __radd__(self, lhs):

return Expr('+', lhs, self)

def __rsub__(self, lhs):

return Expr('-', lhs, self)

def __rmul__(self, lhs):

return Expr('*', lhs, self)

def __rdiv__(self, lhs):

return Expr('/', lhs, self)

def __rpow__(self, lhs):

return Expr('**', lhs, self)

def __rmod__(self, lhs):

return Expr('%', lhs, self)

def __rand__(self, lhs):

return Expr('&', lhs, self)

def __rxor__(self, lhs):

return Expr('^', lhs, self)

def __ror__(self, lhs):

return Expr('|', lhs, self)

def __rrshift__(self, lhs):

return Expr('>>', lhs, self)

def __rlshift__(self, lhs):

return Expr('<<', lhs, self)

def __rtruediv__(self, lhs):

return Expr('/', lhs, self)

def __rfloordiv__(self, lhs):

return Expr('//', lhs, self)

def __rmatmul__(self, lhs):

return Expr('@', lhs, self)

def __call__(self, *args):

"Call: if 'f' is a Symbol, then f(0) == Expr('f', 0)."

if self.args:

raise ValueError('can only do a call for a Symbol, not an Expr')

else:

return Expr(self.op, *args)

# Equality and repr

def __eq__(self, other):

"'x == y' evaluates to True or False; does not build an Expr."

return (isinstance(other, Expr)

and self.op == other.op

and self.args == other.args)

def __hash__(self): return hash(self.op) ^ hash(self.args)

def __repr__(self):

op = self.op

args = [str(arg) for arg in self.args]

if op.isidentifier(): # f(x) or f(x, y)

return '{}({})'.format(op, ', '.join(args)) if args else op

elif len(args) == 1: # -x or -(x + 1)

return op + args[0]

else: # (x - y)

opp = (' ' + op + ' ')

return '(' + opp.join(args) + ')'

# An 'Expression' is either an Expr or a Number.

# Symbol is not an explicit type; it is any Expr with 0 args.

Number = (int, float, complex)

Expression = (Expr, Number)

def Symbol(name):

"""A Symbol is just an Expr with no args."""

return Expr(name)

def symbols(names):

"""Return a tuple of Symbols; names is a comma/whitespace delimited str."""

return tuple(Symbol(name) for name in names.replace(',', ' ').split())

def subexpressions(x):

"""Yield the subexpressions of an Expression (including x itself)."""

yield x

if isinstance(x, Expr):

for arg in x.args:

yield from subexpressions(arg)

def arity(expression):

"""The number of sub-expressions in this expression."""

if isinstance(expression, Expr):

return len(expression.args)

else: # expression is a number

return 0

# For operators that are not defined in Python, we allow new InfixOps:

class PartialExpr:

"""Given 'P |'==>'| Q, first form PartialExpr('==>', P), then combine with Q."""

def __init__(self, op, lhs):

self.op, self.lhs = op, lhs

def __or__(self, rhs):

return Expr(self.op, self.lhs, rhs)

def __repr__(self):

return "PartialExpr('{}', {})".format(self.op, self.lhs)

def expr(x):

"""Shortcut to create an Expression. x is a str in which:

- identifiers are automatically defined as Symbols.

- ==> is treated as an infix |'==>'|, as are <== and <=>.

If x is already an Expression, it is returned unchanged. Example:

>>> expr('P & Q ==> Q')

((P & Q) ==> Q)

"""

if isinstance(x, str):

return eval(expr_handle_infix_ops(x), defaultkeydict(Symbol))

else:

return x

infix_ops = '==> <== <=>'.split()

def expr_handle_infix_ops(x):

"""Given a str, return a new str with ==> replaced by |'==>'|, etc.

>>> expr_handle_infix_ops('P ==> Q')

"P |'==>'| Q"

"""

for op in infix_ops:

x = x.replace(op, '|' + repr(op) + '|')

return x

class defaultkeydict(collections.defaultdict):

"""Like defaultdict, but the default_factory is a function of the key.

>>> d = defaultkeydict(len); d['four']

"""

def __missing__(self, key):

self[key] = result = self.default_factory(key)

return result

class hashabledict(dict):

"""Allows hashing by representing a dictionary as tuple of key:value pairs

May cause problems as the hash value may change during runtime

"""

def __tuplify__(self):

return tuple(sorted(self.items()))

def __hash__(self):

return hash(self.__tuplify__())

def __lt__(self, odict):

assert isinstance(odict, hashabledict)

return self.__tuplify__() < odict.__tuplify__()

def __gt__(self, odict):

assert isinstance(odict, hashabledict)

return self.__tuplify__() > odict.__tuplify__()

def __le__(self, odict):

assert isinstance(odict, hashabledict)

return self.__tuplify__() <= odict.__tuplify__()

def __ge__(self, odict):

assert isinstance(odict, hashabledict)

return self.__tuplify__() >= odict.__tuplify__()

# ______________________________________________________________________________

# Queues: Stack, FIFOQueue, PriorityQueue

# TODO: queue.PriorityQueue

# TODO: Priority queues may not belong here -- see treatment in search.py

class Queue:

"""Queue is an abstract class/interface. There are three types:

Stack(): A Last In First Out Queue.

FIFOQueue(): A First In First Out Queue.

PriorityQueue(order, f): Queue in sorted order (default min-first).

Each type supports the following methods and functions:

q.append(item) -- add an item to the queue

q.extend(items) -- equivalent to: for item in items: q.append(item)

q.pop() -- return the top item from the queue

len(q) -- number of items in q (also q.__len())

item in q -- does q contain item?

Note that isinstance(Stack(), Queue) is false, because we implement stacks

as lists. If Python ever gets interfaces, Queue will be an interface."""

def __init__(self):

raise NotImplementedError

def extend(self, items):

for item in items:

self.append(item)

def Stack():

"""Return an empty list, suitable as a Last-In-First-Out Queue."""

return []

class FIFOQueue(Queue):

"""A First-In-First-Out Queue."""

def __init__(self, maxlen=None, items=[]):

self.queue = collections.deque(items, maxlen)

def append(self, item):

if not self.queue.maxlen or len(self.queue) < self.queue.maxlen:

self.queue.append(item)

else:

raise Exception('FIFOQueue is full')

def extend(self, items):

if not self.queue.maxlen or len(self.queue) + len(items) <= self.queue.maxlen:

self.queue.extend(items)

else:

raise Exception('FIFOQueue max length exceeded')

def pop(self):

if len(self.queue) > 0:

return self.queue.popleft()

else:

raise Exception('FIFOQueue is empty')

def __len__(self):

return len(self.queue)

def __contains__(self, item):

return item in self.queue

class PriorityQueue(Queue):

"""A queue in which the minimum (or maximum) element (as determined by f and

order) is returned first. If order is min, the item with minimum f(x) is

returned first; if order is max, then it is the item with maximum f(x).

Also supports dict-like lookup."""

def __init__(self, order=min, f=lambda x: x):

self.A = []

self.order = order

self.f = f

def append(self, item):

bisect.insort(self.A, (self.f(item), item))

def __len__(self):

return len(self.A)

def pop(self):

if self.order == min:

return self.A.pop(0)[1]

else:

return self.A.pop()[1]

def __contains__(self, item):

return any(item == pair[1] for pair in self.A)

def __getitem__(self, key):

for _, item in self.A:

if item == key:

return item

def __delitem__(self, key):

for i, (value, item) in enumerate(self.A):

if item == key:

self.A.pop(i)

# ______________________________________________________________________________

# Useful Shorthands

class Bool(int):

"""Just like `bool`, except values display as 'T' and 'F' instead of 'True' and 'False'"""

__str__ = __repr__ = lambda self: 'T' if self else 'F'

T = Bool(True)

F = Bool(False)

aima-python/utils.py at aima3python2 · 773173224/aima-python · GitHub

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