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__copyright__ = "Copyright (C) 2009-2013 Andreas Kloeckner"
__license__ = """
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
import operator
import sys
from decorator import decorator
import six
from six.moves import range, zip, intern, input
from functools import reduce
try:
decorator_module = __import__("decorator", level=0)
except TypeError:
# this must be Python 2.4
my_decorator = decorator
except ImportError:
my_decorator = decorator
else:
my_decorator = decorator_module.decorator
# {{{ math --------------------------------------------------------------------
def delta(x, y):
if x == y:
return 1
else:
return 0
def levi_civita(tup):
"""Compute an entry of the Levi-Civita tensor for the indices *tuple*."""
if len(tup) == 2:
i, j = tup
return j-i
if len(tup) == 3:
i, j, k = tup
return (j-i)*(k-i)*(k-j)/2
else:
raise NotImplementedError
def factorial(n):
from operator import mul
assert n == int(n)
return reduce(mul, (i for i in range(1, n+1)), 1)
def perm(n, k):
"""Return P(n, k), the number of permutations of length k drawn from n
choices.
"""
result = 1
assert k > 0
while k:
result *= n
n -= 1
k -= 1
return result
def comb(n, k):
"""Return C(n, k), the number of combinations (subsets)
of length k drawn from n choices.
"""
return perm(n, k)//factorial(k)
def norm_1(iterable):
return sum(abs(x) for x in iterable)
def norm_2(iterable):
return sum(x**2 for x in iterable)**0.5
def norm_inf(iterable):
return max(abs(x) for x in iterable)
def norm_p(iterable, p):
return sum(i**p for i in iterable)**(1/p)
class Norm(object):
def __init__(self, p):
self.p = p
def __call__(self, iterable):
return sum(i**self.p for i in iterable)**(1/self.p)
# }}}
# {{{ data structures
# {{{ record
class RecordWithoutPickling(object):
"""An aggregate of named sub-variables. Assumes that each record sub-type
will be individually derived from this class.
"""
__slots__ = []
def __init__(self, valuedict=None, exclude=["self"], **kwargs):
assert self.__class__ is not Record
try:
fields = self.__class__.fields
except AttributeError:
self.__class__.fields = fields = set()
if valuedict is not None:
kwargs.update(valuedict)
for key, value in six.iteritems(kwargs):
if key not in exclude:
fields.add(key)
setattr(self, key, value)
def get_copy_kwargs(self, **kwargs):
for f in self.__class__.fields:
if f not in kwargs:
try:
kwargs[f] = getattr(self, f)
except AttributeError:
pass
return kwargs
def copy(self, **kwargs):
return self.__class__(**self.get_copy_kwargs(**kwargs))
def __repr__(self):
return "%s(%s)" % (
self.__class__.__name__,
", ".join("%s=%r" % (fld, getattr(self, fld))
for fld in self.__class__.fields
if hasattr(self, fld)))
def register_fields(self, new_fields):
try:
fields = self.__class__.fields
except AttributeError:
self.__class__.fields = fields = set()
fields.update(new_fields)
class Record(RecordWithoutPickling):
__slots__ = []
def __getstate__(self):
return dict(
(key, getattr(self, key))
for key in self.__class__.fields
if hasattr(self, key))
def __setstate__(self, valuedict):
try:
fields = self.__class__.fields
except AttributeError:
self.__class__.fields = fields = set()
for key, value in six.iteritems(valuedict):
fields.add(key)
setattr(self, key, value)
def __eq__(self, other):
return (self.__class__ == other.__class__
and self.__getstate__() == other.__getstate__())
def __ne__(self, other):
return not self.__eq__(other)
class ImmutableRecordWithoutPickling(RecordWithoutPickling):
"Hashable record. Does not explicitly enforce immutability."
def __hash__(self):
return hash(
(type(self),) + tuple(getattr(self, field)
for field in self.__class__.fields))
class ImmutableRecord(ImmutableRecordWithoutPickling, Record):
pass
# }}}
class Reference(object):
def __init__(self, value):
self.value = value
def get(self):
from warnings import warn
warn("Reference.get() is deprecated -- use ref.value instead")
return self.value
def set(self, value):
self.value = value
# {{{ dictionary with default
class DictionaryWithDefault(object):
def __init__(self, default_value_generator, start={}):
self._Dictionary = dict(start)
self._DefaultGenerator = default_value_generator
def __getitem__(self, index):
try:
return self._Dictionary[index]
except KeyError:
value = self._DefaultGenerator(index)
self._Dictionary[index] = value
return value
def __setitem__(self, index, value):
self._Dictionary[index] = value
def __contains__(self, item):
return True
def iterkeys(self):
return six.iterkeys(self._Dictionary)
def __iter__(self):
return self._Dictionary.__iter__()
def iteritems(self):
return six.iteritems(self._Dictionary)
# }}}
class FakeList(object):
def __init__(self, f, length):
self._Length = length
self._Function = f
def __len__(self):
return self._Length
def __getitem__(self, index):
try:
return [self._Function(i)
for i in range(*index.indices(self._Length))]
except AttributeError:
return self._Function(index)
# {{{ dependent dictionary ----------------------------------------------------
class DependentDictionary(object):
def __init__(self, f, start={}):
self._Function = f
self._Dictionary = start.copy()
def copy(self):
return DependentDictionary(self._Function, self._Dictionary)
def __contains__(self, key):
try:
self[key]
return True
except KeyError:
return False
def __getitem__(self, key):
try:
return self._Dictionary[key]
except KeyError:
return self._Function(self._Dictionary, key)
def __setitem__(self, key, value):
self._Dictionary[key] = value
def genuineKeys(self): # noqa
return list(self._Dictionary.keys())
def iteritems(self):
return six.iteritems(self._Dictionary)
def iterkeys(self):
return six.iterkeys(self._Dictionary)
def itervalues(self):
return six.itervalues(self._Dictionary)
# }}}
# }}}
# {{{ assertive accessors
def one(iterable):
"""Return the first entry of *iterable*. Assert that *iterable* has only
that one entry.
"""
it = iter(iterable)
try:
v = next(it)
except StopIteration:
raise ValueError("empty iterable passed to 'one()'")
def no_more():
try:
next(it)
raise ValueError("iterable with more than one entry passed to 'one()'")
except StopIteration:
return True
assert no_more()
return v
def is_single_valued(iterable, equality_pred=operator.eq):
it = iter(iterable)
try:
first_item = next(it)
except StopIteration:
raise ValueError("empty iterable passed to 'single_valued()'")
for other_item in it:
if not equality_pred(other_item, first_item):
return False
return True
all_equal = is_single_valued
def all_roughly_equal(iterable, threshold):
return is_single_valued(iterable,
equality_pred=lambda a, b: abs(a-b) < threshold)
def single_valued(iterable, equality_pred=operator.eq):
"""Return the first entry of *iterable*; Assert that other entries
are the same with the first entry of *iterable*.
"""
it = iter(iterable)
try:
first_item = next(it)
except StopIteration:
raise ValueError("empty iterable passed to 'single_valued()'")
def others_same():
for other_item in it:
if not equality_pred(other_item, first_item):
return False
return True
assert others_same()
return first_item
# }}}
# {{{ memoization / attribute storage
def memoize(*args, **kwargs):
"""Stores previously computed function values in a cache.
Two keyword-only arguments are supported:
:arg use_kwargs: Allows the caller to use keyword arguments. Defaults to
``False``. Setting this to ``True`` has a non-negligible performance
impact.
:arg key: A function receiving the same arguments as the decorated function
which computes and returns the cache key.
"""
use_kw = bool(kwargs.pop('use_kwargs', False))
if use_kw:
def default_key_func(*inner_args, **inner_kwargs):
return inner_args, frozenset(six.iteritems(inner_kwargs))
else:
default_key_func = None
key_func = kwargs.pop("key", default_key_func)
if kwargs:
raise TypeError(
"memoize received unexpected keyword arguments: %s"
% ", ".join(list(kwargs.keys())))
if key_func is not None:
@my_decorator
def _deco(func, *args, **kwargs):
# by Michele Simionato
# http://www.phyast.pitt.edu/~micheles/python/
key = key_func(*args, **kwargs)
try:
return func._memoize_dic[key]
except AttributeError:
# _memoize_dic doesn't exist yet.
result = func(*args, **kwargs)
func._memoize_dic = {key: result}
return result
except KeyError:
result = func(*args, **kwargs)
func._memoize_dic[key] = result
return result
else:
@my_decorator
def _deco(func, *args):
# by Michele Simionato
# http://www.phyast.pitt.edu/~micheles/python/
try:
return func._memoize_dic[args]
except AttributeError:
# _memoize_dic doesn't exist yet.
result = func(*args)
func._memoize_dic = {args: result}
return result
except KeyError:
result = func(*args)
func._memoize_dic[args] = result
return result
if not args:
return _deco
if callable(args[0]) and len(args) == 1:
return _deco(args[0])
raise TypeError(
"memoize received unexpected position arguments: %s" % args)
FunctionValueCache = memoize
class _HasKwargs(object):
pass
def memoize_on_first_arg(function, cache_dict_name=None):
"""Like :func:`memoize_method`, but for functions that take the object
to do memoization as first argument.
Supports cache deletion via ``function_name.clear_cache(self)``.
.. note::
*clear_cache* support requires Python 2.5 or newer.
"""
if cache_dict_name is None:
cache_dict_name = intern("_memoize_dic_"
+ function.__module__ + function.__name__)
def wrapper(obj, *args, **kwargs):
if kwargs:
key = (_HasKwargs, frozenset(six.iteritems(kwargs))) + args
else:
key = args
try:
return getattr(obj, cache_dict_name)[key]
except AttributeError:
result = function(obj, *args, **kwargs)
setattr(obj, cache_dict_name, {key: result})
return result
except KeyError:
result = function(obj, *args, **kwargs)
getattr(obj, cache_dict_name)[key] = result
return result
def clear_cache(obj):
delattr(obj, cache_dict_name)
if sys.version_info >= (2, 5):
from functools import update_wrapper
new_wrapper = update_wrapper(wrapper, function)
new_wrapper.clear_cache = clear_cache
return new_wrapper
def memoize_method(method):
"""Supports cache deletion via ``method_name.clear_cache(self)``.
.. note::
*clear_cache* support requires Python 2.5 or newer.
"""
return memoize_on_first_arg(method, intern("_memoize_dic_"+method.__name__))
def memoize_method_with_uncached(uncached_args=[], uncached_kwargs=set()):
"""Supports cache deletion via ``method_name.clear_cache(self)``.
:arg uncached_args: a list of argument numbers
(0-based, not counting 'self' argument)
"""
# delete starting from the end
uncached_args = sorted(uncached_args, reverse=True)
uncached_kwargs = list(uncached_kwargs)
def parametrized_decorator(method):
cache_dict_name = intern("_memoize_dic_"+method.__name__)
def wrapper(self, *args, **kwargs):
cache_args = list(args)
cache_kwargs = kwargs.copy()
for i in uncached_args:
if i < len(cache_args):
cache_args.pop(i)
cache_args = tuple(cache_args)
if kwargs:
for name in uncached_kwargs:
cache_kwargs.pop(name, None)
key = (
(_HasKwargs, frozenset(six.iteritems(cache_kwargs)))
+ cache_args)
else:
key = cache_args
try:
return getattr(self, cache_dict_name)[key]
except AttributeError:
result = method(self, *args, **kwargs)
setattr(self, cache_dict_name, {key: result})
return result
except KeyError:
result = method(self, *args, **kwargs)
getattr(self, cache_dict_name)[key] = result
return result
def clear_cache(self):
delattr(self, cache_dict_name)
if sys.version_info >= (2, 5):
from functools import update_wrapper
new_wrapper = update_wrapper(wrapper, method)
new_wrapper.clear_cache = clear_cache
return new_wrapper
return parametrized_decorator
def memoize_method_nested(inner):
"""Adds a cache to a function nested inside a method. The cache is attached
to *memoize_cache_context* (if it exists) or *self* in the outer (method)
namespace.
Requires Python 2.5 or newer.
"""
from warnings import warn
warn("memoize_method_nested is deprecated. Use @memoize_in(self, 'identifier') "
"instead", DeprecationWarning, stacklevel=2)
from functools import wraps
cache_dict_name = intern("_memoize_inner_dic_%s_%s_%d"
% (inner.__name__, inner.__code__.co_filename,
inner.__code__.co_firstlineno))
from inspect import currentframe
outer_frame = currentframe().f_back
cache_context = outer_frame.f_locals.get("memoize_cache_context")
if cache_context is None:
cache_context = outer_frame.f_locals.get("self")
try:
cache_dict = getattr(cache_context, cache_dict_name)
except AttributeError:
cache_dict = {}
setattr(cache_context, cache_dict_name, cache_dict)
@wraps(inner)
def new_inner(*args):
try:
return cache_dict[args]
except KeyError:
result = inner(*args)
cache_dict[args] = result
return result
return new_inner
class memoize_in(object): # noqa
"""Adds a cache to a function nested inside a method. The cache is attached
to *object*.
Requires Python 2.5 or newer.
"""
def __init__(self, container, identifier):
key = "_pytools_memoize_in_dict_for_"+identifier
try:
self.cache_dict = getattr(container, key)
except AttributeError:
self.cache_dict = {}
setattr(container, key, self.cache_dict)
def __call__(self, inner):
from functools import wraps
@wraps(inner)
def new_inner(*args):
try:
return self.cache_dict[args]
except KeyError:
result = inner(*args)
self.cache_dict[args] = result
return result
return new_inner
# }}}
# {{{ syntactical sugar
class InfixOperator:
"""Pseudo-infix operators that allow syntax of the kind `op1 <<operator>> op2'.
Following a recipe from
http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/384122
"""
def __init__(self, function):
self.function = function
def __rlshift__(self, other):
return InfixOperator(lambda x: self.function(other, x))
def __rshift__(self, other):
return self.function(other)
def call(self, a, b):
return self.function(a, b)
def monkeypatch_method(cls):
# from GvR, http://mail.python.org/pipermail/python-dev/2008-January/076194.html
def decorator(func):
setattr(cls, func.__name__, func)
return func
return decorator
def monkeypatch_class(name, bases, namespace):
# from GvR, http://mail.python.org/pipermail/python-dev/2008-January/076194.html
assert len(bases) == 1, "Exactly one base class required"
base = bases[0]
for name, value in six.iteritems(namespace):
if name != "__metaclass__":
setattr(base, name, value)
return base
# }}}
# {{{ generic utilities
def add_tuples(t1, t2):
return tuple([t1v + t2v for t1v, t2v in zip(t1, t2)])
def negate_tuple(t1):
return tuple([-t1v for t1v in t1])
def shift(vec, dist):
"""Return a copy of C{vec} shifted by C{dist}.
@postcondition: C{shift(a, i)[j] == a[(i+j) % len(a)]}
"""
result = vec[:]
N = len(vec) # noqa
dist = dist % N
# modulo only returns positive distances!
if dist > 0:
result[dist:] = vec[:N-dist]
result[:dist] = vec[N-dist:]
return result
def len_iterable(iterable):
return sum(1 for i in iterable)
def flatten(list):
"""For an iterable of sub-iterables, generate each member of each
sub-iterable in turn, i.e. a flattened version of that super-iterable.
Example: Turn [[a,b,c],[d,e,f]] into [a,b,c,d,e,f].
"""
for sublist in list:
for j in sublist:
yield j
def general_sum(sequence):
return reduce(operator.add, sequence)
def linear_combination(coefficients, vectors):
result = coefficients[0] * vectors[0]
for c, v in zip(coefficients, vectors)[1:]:
result += c*v
return result
def common_prefix(iterable, empty=None):
it = iter(iterable)
try:
pfx = next(it)
except StopIteration:
return empty
for v in it:
for j in range(len(pfx)):
if pfx[j] != v[j]:
pfx = pfx[:j]
if j == 0:
return pfx
break
return pfx
def decorate(function, list):
return [(x, function(x)) for x in list]
def partition(criterion, list):
part_true = []
part_false = []
for i in list:
if criterion(i):
part_true.append(i)
else:
part_false.append(i)
return part_true, part_false
def partition2(iterable):
part_true = []
part_false = []
for pred, i in iterable:
if pred:
part_true.append(i)
else:
part_false.append(i)
return part_true, part_false
def product(iterable):
from operator import mul
return reduce(mul, iterable, 1)
all = six.moves.builtins.all
any = six.moves.builtins.any
def reverse_dictionary(the_dict):
result = {}
for key, value in six.iteritems(the_dict):
if value in result:
raise RuntimeError(
"non-reversible mapping, duplicate key '%s'" % value)
result[value] = key
return result
def set_sum(set_iterable):
from operator import or_
return reduce(or_, set_iterable, set())
def div_ceil(nr, dr):
return -(-nr // dr)
def uniform_interval_splitting(n, granularity, max_intervals):
""" Return *(interval_size, num_intervals)* such that::
num_intervals * interval_size >= n
and::
(num_intervals - 1) * interval_size < n
and *interval_size* is a multiple of *granularity*.
"""
# ported from Thrust
grains = div_ceil(n, granularity)
# one grain per interval
if grains <= max_intervals:
return granularity, grains
grains_per_interval = div_ceil(grains, max_intervals)
interval_size = grains_per_interval * granularity
num_intervals = div_ceil(n, interval_size)
return interval_size, num_intervals
def find_max_where(predicate, prec=1e-5, initial_guess=1, fail_bound=1e38):
"""Find the largest value for which a predicate is true,
along a half-line. 0 is assumed to be the lower bound."""
# {{{ establish bracket
mag = 1
if predicate(mag):
mag *= 2
while predicate(mag):
mag *= 2
if mag > fail_bound:
raise RuntimeError("predicate appears to be true "
"everywhere, up to %g" % fail_bound)
lower_true = mag/2
upper_false = mag
else:
mag /= 2
while not predicate(mag):
mag /= 2
if mag < prec:
return mag
lower_true = mag
upper_false = mag*2
# }}}
# {{{ refine
# Refine a bracket between *lower_true*, where the predicate is true,
# and *upper_false*, where it is false, until *prec* is satisfied.
assert predicate(lower_true)
assert not predicate(upper_false)
while abs(lower_true-upper_false) > prec:
mid = (lower_true+upper_false)/2
if predicate(mid):
lower_true = mid
else:
upper_false = mid
else:
return lower_true
# }}}
# }}}
# {{{ argmin, argmax
def argmin2(iterable, return_value=False):
it = iter(iterable)
try:
current_argmin, current_min = next(it)
except StopIteration:
raise ValueError("argmin of empty iterable")
for arg, item in it:
if item < current_min:
current_argmin = arg
current_min = item
if return_value:
return current_argmin, current_min
else:
return current_argmin
def argmax2(iterable, return_value=False):
it = iter(iterable)
try:
current_argmax, current_max = next(it)
except StopIteration:
raise ValueError("argmax of empty iterable")
for arg, item in it:
if item > current_max:
current_argmax = arg
current_max = item
if return_value:
return current_argmax, current_max
else:
return current_argmax
def argmin(iterable):
return argmin2(enumerate(iterable))
def argmax(iterable):
return argmax2(enumerate(iterable))
# }}}
# {{{ cartesian products etc.
def cartesian_product(list1, list2):
for i in list1:
for j in list2:
yield (i, j)
def distinct_pairs(list1, list2):
for i, xi in enumerate(list1):
for j, yj in enumerate(list2):
if i != j:
yield (xi, yj)
def cartesian_product_sum(list1, list2):
"""This routine returns a list of sums of each element of
list1 with each element of list2. Also works with lists.
"""
for i in list1:
for j in list2:
yield i+j
# }}}
# {{{ elementary statistics
def average(iterable):
"""Return the average of the values in iterable.
iterable may not be empty.
"""
it = iterable.__iter__()
try:
sum = next(it)
count = 1
except StopIteration:
raise ValueError("empty average")
for value in it:
sum = sum + value
count += 1
return sum/count
class VarianceAggregator:
"""Online variance calculator.
See http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
Adheres to pysqlite's aggregate interface.
"""
def __init__(self, entire_pop):
self.n = 0
self.mean = 0
self.m2 = 0
self.entire_pop = entire_pop
def step(self, x):
self.n += 1
delta = x - self.mean
self.mean += delta/self.n
self.m2 += delta*(x - self.mean)
def finalize(self):
if self.entire_pop:
if self.n == 0:
return None
else:
return self.m2/self.n
else:
if self.n <= 1:
return None
else:
return self.m2/(self.n - 1)
def variance(iterable, entire_pop):
v_comp = VarianceAggregator(entire_pop)
for x in iterable:
v_comp.step(x)
return v_comp.finalize()
def std_deviation(iterable, finite_pop):
from math import sqrt
return sqrt(variance(iterable, finite_pop))
# }}}
# {{{ permutations, tuples, integer sequences
def wandering_element(length, wanderer=1, landscape=0):
for i in range(length):
yield i*(landscape,) + (wanderer,) + (length-1-i)*(landscape,)
def indices_in_shape(shape):
if isinstance(shape, int):
shape = (shape,)
if len(shape) == 0:
yield ()
elif len(shape) == 1:
for i in range(0, shape[0]):
yield (i,)
else:
remainder = shape[1:]
for i in range(0, shape[0]):
for rest in indices_in_shape(remainder):
yield (i,)+rest
def generate_nonnegative_integer_tuples_below(n, length=None, least=0):
"""n may be a sequence, in which case length must be None."""
if length is None:
if len(n) == 0:
yield ()
return
my_n = n[0]
n = n[1:]
next_length = None
else:
my_n = n
assert length >= 0
if length == 0:
yield ()
return
next_length = length-1
for i in range(least, my_n):
my_part = (i,)
for base in generate_nonnegative_integer_tuples_below(n, next_length, least):
yield my_part + base
def generate_decreasing_nonnegative_tuples_summing_to(n, length, min=0, max=None):
if length == 0:
yield ()
elif length == 1:
if n <= max:
#print "MX", n, max
yield (n,)
else:
return
else:
if max is None or n < max:
max = n
for i in range(min, max+1):
#print "SIG", sig, i
for remainder in generate_decreasing_nonnegative_tuples_summing_to(
n-i, length-1, min, i):
yield (i,) + remainder
def generate_nonnegative_integer_tuples_summing_to_at_most(n, length):
"""Enumerate all non-negative integer tuples summing to at most n,
exhausting the search space by varying the first entry fastest,
and the last entry the slowest.
"""
assert length >= 0
if length == 0:
yield ()
else:
for i in range(n+1):
for remainder in generate_nonnegative_integer_tuples_summing_to_at_most(
n-i, length-1):
yield remainder + (i,)
def generate_all_nonnegative_integer_tuples(length, least=0):
assert length >= 0
current_max = least
while True:
for max_pos in range(length):
for prebase in generate_nonnegative_integer_tuples_below(
current_max, max_pos, least):
for postbase in generate_nonnegative_integer_tuples_below(
current_max+1, length-max_pos-1, least):
yield prebase + [current_max] + postbase
current_max += 1
# backwards compatibility
generate_positive_integer_tuples_below = generate_nonnegative_integer_tuples_below
generate_all_positive_integer_tuples = generate_all_nonnegative_integer_tuples
def _pos_and_neg_adaptor(tuple_iter):
for tup in tuple_iter:
nonzero_indices = [i for i in range(len(tup)) if tup[i] != 0]
for do_neg_tup in generate_nonnegative_integer_tuples_below(
2, len(nonzero_indices)):
this_result = list(tup)
for index, do_neg in enumerate(do_neg_tup):
if do_neg:
this_result[nonzero_indices[index]] *= -1
yield tuple(this_result)
def generate_all_integer_tuples_below(n, length, least_abs=0):
return _pos_and_neg_adaptor(generate_nonnegative_integer_tuples_below(
n, length, least_abs))
def generate_all_integer_tuples(length, least_abs=0):
return _pos_and_neg_adaptor(generate_all_nonnegative_integer_tuples(
length, least_abs))
def generate_permutations(original):
"""Generate all permutations of the list `original'.
Nicked from http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/252178
"""
if len(original) <= 1:
yield original
else:
for perm in generate_permutations(original[1:]):
for i in range(len(perm)+1):
#nb str[0:1] works in both string and list contexts
yield perm[:i] + original[0:1] + perm[i:]
def generate_unique_permutations(original):
"""Generate all unique permutations of the list `original'.
"""
had_those = set()
for perm in generate_permutations(original):
if perm not in had_those:
had_those.add(perm)
yield perm
def enumerate_basic_directions(dimensions):
coordinate_list = [[0], [1], [-1]]
return reduce(cartesian_product_sum, [coordinate_list] * dimensions)[1:]
# }}}
# {{{ index mangling
def get_read_from_map_from_permutation(original, permuted):
"""With a permutation given by C{original} and C{permuted},
generate a list C{rfm} of indices such that
C{permuted[i] == original[rfm[i]]}.
Requires that the permutation can be inferred from
C{original} and C{permuted}.
>>> for p1 in generate_permutations(range(5)):
... for p2 in generate_permutations(range(5)):
... rfm = get_read_from_map_from_permutation(p1, p2)
... p2a = [p1[rfm[i]] for i in range(len(p1))]
... assert p2 == p2a
"""
assert len(original) == len(permuted)
where_in_original = dict(
(original[i], i) for i in range(len(original)))
assert len(where_in_original) == len(original)
return tuple(where_in_original[pi] for pi in permuted)
def get_write_to_map_from_permutation(original, permuted):
"""With a permutation given by C{original} and C{permuted},
generate a list C{wtm} of indices such that
C{permuted[wtm[i]] == original[i]}.
Requires that the permutation can be inferred from
C{original} and C{permuted}.
>>> for p1 in generate_permutations(range(5)):
... for p2 in generate_permutations(range(5)):
... wtm = get_write_to_map_from_permutation(p1, p2)
... p2a = [0] * len(p2)
... for i, oi in enumerate(p1):
... p2a[wtm[i]] = oi
... assert p2 == p2a
"""
assert len(original) == len(permuted)
where_in_permuted = dict(
(permuted[i], i) for i in range(len(permuted)))
assert len(where_in_permuted) == len(permuted)
return tuple(where_in_permuted[oi] for oi in original)
# }}}
# {{{ graph algorithms
def a_star(initial_state, goal_state, neighbor_map,
estimate_remaining_cost=None,
get_step_cost=lambda x, y: 1):
"""
With the default cost and heuristic, this amounts to Dijkstra's algorithm.
"""
from heapq import heappop, heappush
if estimate_remaining_cost is None:
def estimate_remaining_cost(x):
if x != goal_state:
return 1
else:
return 0
class AStarNode(object):
__slots__ = ["state", "parent", "path_cost"]
def __init__(self, state, parent, path_cost):
self.state = state
self.parent = parent
self.path_cost = path_cost
inf = float("inf")
init_remcost = estimate_remaining_cost(initial_state)
assert init_remcost != inf
queue = [(init_remcost, AStarNode(initial_state, parent=None, path_cost=0))]
visited_states = set()
while len(queue):
_, top = heappop(queue)
visited_states.add(top.state)
if top.state == goal_state:
result = []
it = top
while it is not None:
result.append(it.state)
it = it.parent
return result[::-1]
for state in neighbor_map[top.state]:
if state in visited_states:
continue
remaining_cost = estimate_remaining_cost(state)
if remaining_cost == inf:
continue
step_cost = get_step_cost(top, state)
estimated_path_cost = top.path_cost+step_cost+remaining_cost
heappush(queue,
(estimated_path_cost,
AStarNode(state, top, path_cost=top.path_cost + step_cost)))
raise RuntimeError("no solution")
# }}}
# {{{ formatting
# {{{ table formatting
class Table:
"""An ASCII table generator."""
def __init__(self):
self.rows = []
def add_row(self, row):
self.rows.append([str(i) for i in row])
def __str__(self):
columns = len(self.rows[0])
col_widths = [max(len(row[i]) for row in self.rows)
for i in range(columns)]
lines = [
"|".join([cell.ljust(col_width)
for cell, col_width in zip(row, col_widths)])
for row in self.rows]
lines[1:1] = ["+".join("-"*col_width
for col_width in col_widths)]
return "\n".join(lines)
def latex(self, skip_lines=0, hline_after=[]):
lines = []
for row_nr, row in list(enumerate(self.rows))[skip_lines:]:
lines.append(" & ".join(row)+r" \\")
if row_nr in hline_after:
lines.append(r"\hline")
return "\n".join(lines)
# }}}
# {{{ histogram formatting
def string_histogram(iterable, min_value=None, max_value=None,
bin_count=20, width=70, bin_starts=None, use_unicode=True):
if bin_starts is None:
if min_value is None or max_value is None:
iterable = list(iterable)
min_value = min(iterable)
max_value = max(iterable)
bin_width = (max_value - min_value)/bin_count
bin_starts = [min_value+bin_width*i for i in range(bin_count)]
bins = [0 for i in range(len(bin_starts))]
from bisect import bisect
for value in iterable:
if max_value is not None and value > max_value or value < bin_starts[0]:
from warnings import warn
warn("string_histogram: out-of-bounds value ignored")
else:
bin_nr = bisect(bin_starts, value)-1
try:
bins[bin_nr] += 1
except:
print(value, bin_nr, bin_starts)
raise
from math import floor, ceil
if use_unicode:
def format_bar(cnt):
scaled = cnt*width/max_count
full = int(floor(scaled))
eighths = int(ceil((scaled-full)*8))
if eighths:
return full*six.unichr(0x2588) + six.unichr(0x2588+(8-eighths))
else:
return full*six.unichr(0x2588)
else:
def format_bar(cnt):
return int(ceil(cnt*width/max_count))*"#"
max_count = max(bins)
total_count = sum(bins)
return "\n".join("%9g |%9d | %3.0f %% | %s" % (
bin_start,
bin_value,
bin_value/total_count*100,
format_bar(bin_value))
for bin_start, bin_value in zip(bin_starts, bins))
# }}}
def word_wrap(text, width, wrap_using="\n"):
# http://code.activestate.com/recipes/148061-one-liner-word-wrap-function/
"""
A word-wrap function that preserves existing line breaks
and most spaces in the text. Expects that existing line
breaks are posix newlines (\n).
"""
space_or_break = [" ", wrap_using]
return reduce(lambda line, word, width=width: '%s%s%s' %
(line,
space_or_break[(len(line)-line.rfind('\n')-1
+ len(word.split('\n', 1)[0])
>= width)],
word),
text.split(' ')
)
# }}}
# {{{ command line interfaces -------------------------------------------------
def _exec_arg(arg, execenv):
import os
if os.access(arg, os.F_OK):
exec(compile(open(arg, "r"), arg, 'exec'), execenv)
else:
exec(compile(arg, "<command line>", 'exec'), execenv)
class CPyUserInterface(object):
class Parameters(Record):
pass
def __init__(self, variables, constants={}, doc={}):
self.variables = variables
self.constants = constants
self.doc = doc
def show_usage(self, progname):
print("usage: %s <FILE-OR-STATEMENTS>" % progname)
print()
print("FILE-OR-STATEMENTS may either be Python statements of the form")
print("'variable1 = value1; variable2 = value2' or the name of a file")
print("containing such statements. Any valid Python code may be used")
print("on the command line or in a command file. If new variables are")
print("used, they must start with 'user_' or just '_'.")
print()
print("The following variables are recognized:")
for v in sorted(self.variables):
print(" %s = %s" % (v, self.variables[v]))
if v in self.doc:
print(" %s" % self.doc[v])
print()
print("The following constants are supplied:")
for c in sorted(self.constants):
print(" %s = %s" % (c, self.constants[c]))
if c in self.doc:
print(" %s" % self.doc[c])
def gather(self, argv=None):
import sys
if argv is None:
argv = sys.argv
if len(argv) == 1 or (
("-h" in argv) or
("help" in argv) or
("-help" in argv) or
("--help" in argv)):
self.show_usage(argv[0])
sys.exit(2)
execenv = self.variables.copy()
execenv.update(self.constants)
for arg in argv[1:]:
_exec_arg(arg, execenv)
# check if the user set invalid keys
for added_key in (
set(execenv.keys())
- set(self.variables.keys())
- set(self.constants.keys())):
if not (added_key.startswith("user_") or added_key.startswith("_")):
raise ValueError(
"invalid setup key: '%s' "
"(user variables must start with 'user_' or '_')"
% added_key)
result = self.Parameters(dict((key, execenv[key]) for key in self.variables))
self.validate(result)
return result
def validate(self, setup):
pass
# }}}
# {{{ code maintenance
class MovedFunctionDeprecationWrapper:
def __init__(self, f):
self.f = f
def __call__(self, *args, **kwargs):
from warnings import warn
warn("This function is deprecated. Use %s.%s instead." % (
self.f.__module__, self.f.__name__),
DeprecationWarning, stacklevel=2)
return self.f(*args, **kwargs)
# }}}
# {{{ debugging
class StderrToStdout(object):
def __enter__(self):
import sys
self.stderr_backup = sys.stderr
sys.stderr = sys.stdout
def __exit__(self, exc_type, exc_val, exc_tb):
import sys
sys.stderr = self.stderr_backup
del self.stderr_backup
def typedump(val, max_seq=5, special_handlers={}):
try:
hdlr = special_handlers[type(val)]
except KeyError:
pass
else:
return hdlr(val)
try:
len(val)
except TypeError:
return type(val).__name__
else:
if isinstance(val, dict):
return "{%s}" % (
", ".join(
"%r: %s" % (str(k), typedump(v))
for k, v in six.iteritems(val)))
try:
if len(val) > max_seq:
return "%s(%s,...)" % (
type(val).__name__,
",".join(typedump(x, max_seq, special_handlers)
for x in val[:max_seq]))
else:
return "%s(%s)" % (
type(val).__name__,
",".join(typedump(x, max_seq, special_handlers)
for x in val))
except TypeError:
return val.__class__.__name__
def invoke_editor(s, filename="edit.txt", descr="the file"):
from tempfile import mkdtemp
tempdir = mkdtemp()
from os.path import join
full_name = join(tempdir, filename)
outf = open(full_name, "w")
outf.write(str(s))
outf.close()
import os
if "EDITOR" in os.environ:
from subprocess import Popen
p = Popen([os.environ["EDITOR"], full_name])
os.waitpid(p.pid, 0)[1]
else:
print("(Set the EDITOR environment variable to be "
"dropped directly into an editor next time.)")
input("Edit %s at %s now, then hit [Enter]:"
% (descr, full_name))
inf = open(full_name, "r")
result = inf.read()
inf.close()
return result
# }}}
# {{{ progress bars
class ProgressBar:
def __init__(self, descr, total, initial=0, length=40):
import time
self.description = descr
self.total = total
self.done = initial
self.length = length
self.last_squares = -1
self.start_time = time.time()
self.last_update_time = self.start_time
self.speed_meas_start_time = self.start_time
self.speed_meas_start_done = initial
self.time_per_step = None
def draw(self):
import time
now = time.time()
squares = int(self.done/self.total*self.length)
if squares != self.last_squares or now-self.last_update_time > 0.5:
if (self.done != self.speed_meas_start_done
and now-self.speed_meas_start_time > 3):
new_time_per_step = (now-self.speed_meas_start_time) \
/ (self.done-self.speed_meas_start_done)
if self.time_per_step is not None:
self.time_per_step = (new_time_per_step + self.time_per_step)/2
else:
self.time_per_step = new_time_per_step
self.speed_meas_start_time = now
self.speed_meas_start_done = self.done
if self.time_per_step is not None:
eta_str = "%7.1fs " % max(
0, (self.total-self.done) * self.time_per_step)
else:
eta_str = "?"
import sys
sys.stderr.write("%-20s [%s] ETA %s\r" % (
self.description,
squares*"#"+(self.length-squares)*" ",
eta_str))
self.last_squares = squares
self.last_update_time = now
def progress(self, steps=1):
self.set_progress(self.done + steps)
def set_progress(self, done):
self.done = done
self.draw()
def finished(self):
import sys
self.set_progress(self.total)
sys.stderr.write("\n")
def __enter__(self):
self.draw()
def __exit__(self, exc_type, exc_val, exc_tb):
self.finished()
# }}}
# {{{ file system related
def assert_not_a_file(name):
import os
if os.access(name, os.F_OK):
raise IOError("file `%s' already exists" % name)
def add_python_path_relative_to_script(rel_path):
import sys
from os.path import dirname, join, abspath
script_name = sys.argv[0]
rel_script_dir = dirname(script_name)
sys.path.append(abspath(join(rel_script_dir, rel_path)))
# }}}
# {{{ numpy dtype mangling
def common_dtype(dtypes, default=None):
dtypes = list(dtypes)
if dtypes:
return argmax2((dtype, dtype.num) for dtype in dtypes)
else:
if default is not None:
return default
else:
raise ValueError(
"cannot find common dtype of empty dtype list")
def to_uncomplex_dtype(dtype):
import numpy
if dtype == numpy.complex64:
return numpy.float32
elif dtype == numpy.complex128:
return numpy.float64
if dtype == numpy.float32:
return numpy.float32
elif dtype == numpy.float64:
return numpy.float64
else:
raise TypeError("unrecgonized dtype '%s'" % dtype)
def match_precision(dtype, dtype_to_match):
import numpy
tgt_is_double = dtype_to_match in [
numpy.float64, numpy.complex128]
dtype_is_complex = dtype.kind == "c"
if dtype_is_complex:
if tgt_is_double:
return numpy.dtype(numpy.complex128)
else:
return numpy.dtype(numpy.complex64)
else:
if tgt_is_double:
return numpy.dtype(numpy.float64)
else:
return numpy.dtype(numpy.float32)
# }}}
# {{{ unique name generation
def generate_unique_names(prefix):
yield prefix
try_num = 0
while True:
yield "%s_%d" % (prefix, try_num)
try_num += 1
generate_unique_possibilities = MovedFunctionDeprecationWrapper(
generate_unique_names)
class UniqueNameGenerator:
def __init__(self, existing_names=set(), forced_prefix=""):
self.existing_names = existing_names.copy()
self.forced_prefix = forced_prefix
def is_name_conflicting(self, name):
return name in self.existing_names
def add_name(self, name):
if self.is_name_conflicting(name):
raise ValueError("name '%s' conflicts with existing names")
if not name.startswith(self.forced_prefix):
raise ValueError("name '%s' does not start with required prefix")
self.existing_names.add(name)
def add_names(self, names):
for name in names:
self.add_name(name)
def __call__(self, based_on="id"):
based_on = self.forced_prefix + based_on
for var_name in generate_unique_names(based_on):
if not self.is_name_conflicting(var_name):
break
var_name = intern(var_name)
self.existing_names.add(var_name)
return var_name
# }}}
def _test():
import doctest
doctest.testmod()
if __name__ == "__main__":
_test()
# vim: foldmethod=marker
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