utils.py

"""Provide some widely useful utilities. Safe for "from utils import *".

TODO[COMPLETED]: Let's take the >>> doctest examples out of the docstrings, and put them in utils_test.py
TODO: count_if and the like are leftovers from COmmon Lisp; let's make replace thenm with Pythonic alternatives.
TODO: Create a separate grid.py file for 2D grid environments; move headings, etc there.
TODO: Priority queues may not belong here -- see treatment in search.py
"""

import operator
import math
import random
import os.path
import bisect
import re
from functools import reduce

#______________________________________________________________________________
# Simple Data Structures: infinity, Dict, Struct

infinity = float('inf')

class Struct:
    """Create an instance with argument=value slots.
    This is for making a lightweight object whose class doesn't matter."""
    def __init__(self, **entries):
        self.__dict__.update(entries)

    def __cmp__(self, other):
        if isinstance(other, Struct):
            return self.__dict__ == other.__dict__
        else:
            return self.__dict__ == other

    def __repr__(self):
        args = ['{!s}={!s}'.format(k, repr(v))
                    for (k, v) in vars(self).items()]

def update(x, **entries):
    """Update a dict or an object with slots according to entries."""
    if isinstance(x, dict):
        x.update(entries)
    else:
        x.__dict__.update(entries)

    return x

#______________________________________________________________________________
# Functions on Sequences (mostly inspired by Common Lisp)
# NOTE: Sequence functions (count_if, find_if, every, some) take function
# argument first (like reduce, filter, and map).

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 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 count_if(predicate, seq):
    """Count the number of elements of seq for which the predicate is true."""
    return sum(map(lambda x: bool(predicate(x)), seq))

def find_if(predicate, seq):
    """If there is an element of seq that satisfies predicate; return it."""
    for x in seq:
        if predicate(x):
            return x

    return None

def every(predicate, seq):
    """True if every element of seq satisfies predicate."""

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

def some(predicate, seq):
    """If some element x of seq satisfies predicate(x), return predicate(x)."""
    elem = find_if(predicate,seq)

    return predicate(elem) or False

# TODO: rename to is_in or possibily add 'identity' to function name to clarify intent
def isin(elt, seq):
    """Like (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 = len(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 = len(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_gen(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 = len(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 = len(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 = map(bin_function, values)

    bins = {}
    for val in values:
        bins[val] = bins.get(val, 0) + 1

    if mode:
        return sorted(bins.items(), key=lambda x: (x[1],x[0]), reverse=True)
    else:
        return sorted(bins.items())

from math import log2
from statistics import mode, median, mean, stdev

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 vector_add(a, b):
    """Component-wise addition of two vectors."""
    return tuple(map(operator.add, a, b))

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 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))

#______________________________________________________________________________
## OK, the following are not as widely useful utilities as some of the other
## functions here, but they do show up wherever we have 2D grids: Wumpus and
## Vacuum worlds, TicTacToe and Checkers, and markov decision Processes.

orientations = [(1, 0), (0, 1), (-1, 0), (0, -1)]

def turn_heading(heading, inc, headings=orientations):
    return headings[(headings.index(heading) + inc) % len(headings)]

def turn_right(heading):
    return turn_heading(heading, -1)

def turn_left(heading):
    return turn_heading(heading, +1)

def Point(x, y):
    return (x, y)

def point_x(point):
    return point[0]

def point_y(point):
    return point[1]

def distance(a, b):
    "The distance between two (x, y) points."
    ax, ay = a
    bx, by = b
    return math.hypot((ax - bx), (ay - by))

def distance2(a, b):
    "The square of the distance between two (x, y) points."
    ax, ay = a
    bx, by = b
    return (ax - bx)**2 + (ay - by)**2

def vector_clip(vector, lowest, highest):
    """Return vector, except if any element is less than the corresponding
    value of lowest or more than the corresponding value of highest, clip to
    those values.
    """
    return type(vector)(map(clip, vector, lowest, highest))

#______________________________________________________________________________
# 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 not memoized_fn.cache.has_key(args):
                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]

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

    sizes = map(maxlen, 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."
    import utils
    aima_root = os.path.dirname(utils.__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(['..', '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):
        update(self, A=[], order=order, 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 some(lambda _, x: x == item, 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 = {}