aima-python/utils.py at master · lap089/aima-python · GitHub

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

# This module is safe for: from utils import *

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

import operator

import random

import os.path

import bisect

from grid import * # noqa

# ______________________________________________________________________________

# Functions on Sequences (mostly inspired by Common Lisp)

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):

"""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 every(predicate, seq):

"""True if every element of seq satisfies predicate."""

return all(predicate(x) for x in seq)

def is_in(elt, seq):

"""Similar to (elt in seq), but compares with 'is', not '=='."""

return any(x is elt for x in seq)

# ______________________________________________________________________________

# Functions on sequences of numbers

# NOTE: these take the sequence argument first, like min and max,

# and like standard math notation: \sigma (i = 1..n) fn(i)

# A lot of programing is finding the best value that satisfies some condition;

# so there are three versions of argmin/argmax, depending on what you want to

# do with ties: return the first one, return them all, or pick at random.

def argmin(seq, fn):

return min(seq, key=fn)

def argmin_list(seq, fn):

"""Return a list of elements of seq[i] with

the lowest fn(seq[i]) scores.’

"""

smallest_score = fn(min(seq, key=fn))

return [elem for elem in seq if fn(elem) == smallest_score]

def argmin_gen(seq, fn):

"""Return a generator of elements of seq[i] with the

lowest fn(seq[i]) scores.

"""

smallest_score = fn(min(seq, key=fn))

yield from (elem for elem in seq if fn(elem) == smallest_score)

def argmin_random_tie(seq, fn):

"""Return an element with lowest fn(seq[i]) score; break ties at random.

Thus, for all s,f: argmin_random_tie(s, f) in argmin_list(s, f)"""

return random.choice(argmin_list(seq, fn))

def argmax(seq, fn):

"""Return an element with highest fn(seq[i]) score;

tie goes to first one.

"""

return max(seq, key=fn)

def argmax_list(seq, fn):

"""Return a list of elements of seq[i] with the highest fn(seq[i]) scores.

Not good to use 'argmin_list(seq, lambda x: -fn(x))' as method

breaks if fn is len

"""

largest_score = fn(max(seq, key=fn))

return [elem for elem in seq if fn(elem) == largest_score]

def argmax_gen(seq, fn):

"""Return a generator of elements of seq[i] with

the highest fn(seq[i]) scores.

"""

largest_score = fn(min(seq, key=fn))

yield from (elem for elem in seq if fn(elem) == largest_score)

def argmax_random_tie(seq, fn):

"Return an element with highest fn(seq[i]) score; break ties at random."

return argmin_random_tie(seq, lambda x: -fn(x))

# ______________________________________________________________________________

# 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 = list(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([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(seq, weights, n):

"""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 truncate(x, n = 4):

"""Truncates floats, vectors, matrices to n decimal values"""

if isinstance(x, float):

return(float("{0:.{1}f}".format(x, n)))

elif isinstance(x, list) and isinstance(x[0], float):

return([float("{0:.{1}f}".format(i, n)) for i in x])

elif isinstance(x, list) and isinstance(x[0], list) and isinstance(x[0][0], float):

return([[float("{0:.{1}f}".format(i, n)) for i in row] for row in x])

else:

return x

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(numbers):

"""Multiply each number by a constant such that the sum is 1.0"""

total = float(sum(numbers))

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

def clip(x, lowest, highest):

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

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

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

try: # math.isclose was added in Python 3.5

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 printf(format_str, *args):

"""Format args with the first argument as format string, and write.

Return the last arg, or format itself if there are no args."""

print(str(format_str).format(*args, end=''))

return args[-1] if args else format_str

def caller(n=1):

"""Return the name of the calling function n levels up

in the frame stack.

"""

import inspect

return inspect.getouterframes(inspect.currentframe())[n][3]

# TODO: Use functools.lru_cache memoization decorator

def memoize(fn, slot=None):

"""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, store results in a dictionary."""

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:

def memoized_fn(*args):

if args not in memoized_fn.cache:

memoized_fn.cache[args] = fn(*args)

return memoized_fn.cache[args]

memoized_fn.cache = {}

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? We say it is if it has a __int__ method."

return hasattr(x, '__int__')

def issequence(x):

"Is x a sequence? We say it is if it has a __getitem__ method."

return hasattr(x, '__getitem__')

def print_table(table, header=None, sep=' ', numfmt='%g'):

"""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. '%6.2f'.

(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(list(map(len, seq))),

list(zip(*[list(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 /data directory."

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

def unimplemented():

"Use this as a stub for not-yet-implemented functions."

raise NotImplementedError

# ______________________________________________________________________________

# Queues: Stack, FIFOQueue, PriorityQueue

# TODO: Use queue.Queue

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):

self.A = []

self.start = 0

def append(self, item):

self.A.append(item)

def __len__(self):

return len(self.A) - self.start

def extend(self, items):

self.A.extend(items)

def pop(self):

e = self.A[self.start]

self.start += 1

if self.start > 5 and self.start > len(self.A)/2:

self.A = self.A[self.start:]

self.start = 0

return e

def __contains__(self, item):

return item in self.A[self.start:]

# TODO: Use queue.PriorityQueue

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)

# Fig: The idea is we can define things like Fig[3,10] later.

# Alas, it is Fig[3,10] not Fig[3.10], because that would be the same

# as Fig[3.1]

Fig = {}

aima-python/utils.py at master · lap089/aima-python · GitHub

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