949 lines
32 KiB
Python
949 lines
32 KiB
Python
|
import re
|
||
|
|
from contextlib import contextmanager
|
||
|
|
import functools
|
||
|
|
import operator
|
||
|
|
import warnings
|
||
|
|
import numbers
|
||
|
|
from collections import namedtuple
|
||
|
|
import inspect
|
||
|
|
import math
|
||
|
|
from typing import (
|
||
|
|
Optional,
|
||
|
|
Union,
|
||
|
|
TYPE_CHECKING,
|
||
|
|
TypeVar,
|
||
|
|
)
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy._lib._array_api import array_namespace
|
||
|
|
|
||
|
|
|
||
|
|
AxisError: type[Exception]
|
||
|
|
ComplexWarning: type[Warning]
|
||
|
|
VisibleDeprecationWarning: type[Warning]
|
||
|
|
|
||
|
|
if np.lib.NumpyVersion(np.__version__) >= '1.25.0':
|
||
|
|
from numpy.exceptions import (
|
||
|
|
AxisError, ComplexWarning, VisibleDeprecationWarning,
|
||
|
|
DTypePromotionError
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
from numpy import (
|
||
|
|
AxisError, ComplexWarning, VisibleDeprecationWarning # noqa: F401
|
||
|
|
)
|
||
|
|
DTypePromotionError = TypeError # type: ignore
|
||
|
|
|
||
|
|
np_long: type
|
||
|
|
np_ulong: type
|
||
|
|
|
||
|
|
if np.lib.NumpyVersion(np.__version__) >= "2.0.0.dev0":
|
||
|
|
try:
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.filterwarnings(
|
||
|
|
"ignore",
|
||
|
|
r".*In the future `np\.long` will be defined as.*",
|
||
|
|
FutureWarning,
|
||
|
|
)
|
||
|
|
np_long = np.long # type: ignore[attr-defined]
|
||
|
|
np_ulong = np.ulong # type: ignore[attr-defined]
|
||
|
|
except AttributeError:
|
||
|
|
np_long = np.int_
|
||
|
|
np_ulong = np.uint
|
||
|
|
else:
|
||
|
|
np_long = np.int_
|
||
|
|
np_ulong = np.uint
|
||
|
|
|
||
|
|
IntNumber = Union[int, np.integer]
|
||
|
|
DecimalNumber = Union[float, np.floating, np.integer]
|
||
|
|
|
||
|
|
copy_if_needed: Optional[bool]
|
||
|
|
|
||
|
|
if np.lib.NumpyVersion(np.__version__) >= "2.0.0":
|
||
|
|
copy_if_needed = None
|
||
|
|
elif np.lib.NumpyVersion(np.__version__) < "1.28.0":
|
||
|
|
copy_if_needed = False
|
||
|
|
else:
|
||
|
|
# 2.0.0 dev versions, handle cases where copy may or may not exist
|
||
|
|
try:
|
||
|
|
np.array([1]).__array__(copy=None) # type: ignore[call-overload]
|
||
|
|
copy_if_needed = None
|
||
|
|
except TypeError:
|
||
|
|
copy_if_needed = False
|
||
|
|
|
||
|
|
# Since Generator was introduced in numpy 1.17, the following condition is needed for
|
||
|
|
# backward compatibility
|
||
|
|
if TYPE_CHECKING:
|
||
|
|
SeedType = Optional[Union[IntNumber, np.random.Generator,
|
||
|
|
np.random.RandomState]]
|
||
|
|
GeneratorType = TypeVar("GeneratorType", bound=Union[np.random.Generator,
|
||
|
|
np.random.RandomState])
|
||
|
|
|
||
|
|
try:
|
||
|
|
from numpy.random import Generator as Generator
|
||
|
|
except ImportError:
|
||
|
|
class Generator: # type: ignore[no-redef]
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
def _lazywhere(cond, arrays, f, fillvalue=None, f2=None):
|
||
|
|
"""Return elements chosen from two possibilities depending on a condition
|
||
|
|
|
||
|
|
Equivalent to ``f(*arrays) if cond else fillvalue`` performed elementwise.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
cond : array
|
||
|
|
The condition (expressed as a boolean array).
|
||
|
|
arrays : tuple of array
|
||
|
|
Arguments to `f` (and `f2`). Must be broadcastable with `cond`.
|
||
|
|
f : callable
|
||
|
|
Where `cond` is True, output will be ``f(arr1[cond], arr2[cond], ...)``
|
||
|
|
fillvalue : object
|
||
|
|
If provided, value with which to fill output array where `cond` is
|
||
|
|
not True.
|
||
|
|
f2 : callable
|
||
|
|
If provided, output will be ``f2(arr1[cond], arr2[cond], ...)`` where
|
||
|
|
`cond` is not True.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : array
|
||
|
|
An array with elements from the output of `f` where `cond` is True
|
||
|
|
and `fillvalue` (or elements from the output of `f2`) elsewhere. The
|
||
|
|
returned array has data type determined by Type Promotion Rules
|
||
|
|
with the output of `f` and `fillvalue` (or the output of `f2`).
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
``xp.where(cond, x, fillvalue)`` requires explicitly forming `x` even where
|
||
|
|
`cond` is False. This function evaluates ``f(arr1[cond], arr2[cond], ...)``
|
||
|
|
onle where `cond` ``is True.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> a, b = np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8])
|
||
|
|
>>> def f(a, b):
|
||
|
|
... return a*b
|
||
|
|
>>> _lazywhere(a > 2, (a, b), f, np.nan)
|
||
|
|
array([ nan, nan, 21., 32.])
|
||
|
|
|
||
|
|
"""
|
||
|
|
xp = array_namespace(cond, *arrays)
|
||
|
|
|
||
|
|
if (f2 is fillvalue is None) or (f2 is not None and fillvalue is not None):
|
||
|
|
raise ValueError("Exactly one of `fillvalue` or `f2` must be given.")
|
||
|
|
|
||
|
|
args = xp.broadcast_arrays(cond, *arrays)
|
||
|
|
bool_dtype = xp.asarray([True]).dtype # numpy 1.xx doesn't have `bool`
|
||
|
|
cond, arrays = xp.astype(args[0], bool_dtype, copy=False), args[1:]
|
||
|
|
|
||
|
|
temp1 = xp.asarray(f(*(arr[cond] for arr in arrays)))
|
||
|
|
|
||
|
|
if f2 is None:
|
||
|
|
fillvalue = xp.asarray(fillvalue)
|
||
|
|
dtype = xp.result_type(temp1.dtype, fillvalue.dtype)
|
||
|
|
out = xp.full(cond.shape, fill_value=fillvalue, dtype=dtype)
|
||
|
|
else:
|
||
|
|
ncond = ~cond
|
||
|
|
temp2 = xp.asarray(f2(*(arr[ncond] for arr in arrays)))
|
||
|
|
dtype = xp.result_type(temp1, temp2)
|
||
|
|
out = xp.empty(cond.shape, dtype=dtype)
|
||
|
|
out[ncond] = temp2
|
||
|
|
|
||
|
|
out[cond] = temp1
|
||
|
|
|
||
|
|
return out
|
||
|
|
|
||
|
|
|
||
|
|
def _lazyselect(condlist, choicelist, arrays, default=0):
|
||
|
|
"""
|
||
|
|
Mimic `np.select(condlist, choicelist)`.
|
||
|
|
|
||
|
|
Notice, it assumes that all `arrays` are of the same shape or can be
|
||
|
|
broadcasted together.
|
||
|
|
|
||
|
|
All functions in `choicelist` must accept array arguments in the order
|
||
|
|
given in `arrays` and must return an array of the same shape as broadcasted
|
||
|
|
`arrays`.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> x = np.arange(6)
|
||
|
|
>>> np.select([x <3, x > 3], [x**2, x**3], default=0)
|
||
|
|
array([ 0, 1, 4, 0, 64, 125])
|
||
|
|
|
||
|
|
>>> _lazyselect([x < 3, x > 3], [lambda x: x**2, lambda x: x**3], (x,))
|
||
|
|
array([ 0., 1., 4., 0., 64., 125.])
|
||
|
|
|
||
|
|
>>> a = -np.ones_like(x)
|
||
|
|
>>> _lazyselect([x < 3, x > 3],
|
||
|
|
... [lambda x, a: x**2, lambda x, a: a * x**3],
|
||
|
|
... (x, a), default=np.nan)
|
||
|
|
array([ 0., 1., 4., nan, -64., -125.])
|
||
|
|
|
||
|
|
"""
|
||
|
|
arrays = np.broadcast_arrays(*arrays)
|
||
|
|
tcode = np.mintypecode([a.dtype.char for a in arrays])
|
||
|
|
out = np.full(np.shape(arrays[0]), fill_value=default, dtype=tcode)
|
||
|
|
for func, cond in zip(choicelist, condlist):
|
||
|
|
if np.all(cond is False):
|
||
|
|
continue
|
||
|
|
cond, _ = np.broadcast_arrays(cond, arrays[0])
|
||
|
|
temp = tuple(np.extract(cond, arr) for arr in arrays)
|
||
|
|
np.place(out, cond, func(*temp))
|
||
|
|
return out
|
||
|
|
|
||
|
|
|
||
|
|
def _aligned_zeros(shape, dtype=float, order="C", align=None):
|
||
|
|
"""Allocate a new ndarray with aligned memory.
|
||
|
|
|
||
|
|
Primary use case for this currently is working around a f2py issue
|
||
|
|
in NumPy 1.9.1, where dtype.alignment is such that np.zeros() does
|
||
|
|
not necessarily create arrays aligned up to it.
|
||
|
|
|
||
|
|
"""
|
||
|
|
dtype = np.dtype(dtype)
|
||
|
|
if align is None:
|
||
|
|
align = dtype.alignment
|
||
|
|
if not hasattr(shape, '__len__'):
|
||
|
|
shape = (shape,)
|
||
|
|
size = functools.reduce(operator.mul, shape) * dtype.itemsize
|
||
|
|
buf = np.empty(size + align + 1, np.uint8)
|
||
|
|
offset = buf.__array_interface__['data'][0] % align
|
||
|
|
if offset != 0:
|
||
|
|
offset = align - offset
|
||
|
|
# Note: slices producing 0-size arrays do not necessarily change
|
||
|
|
# data pointer --- so we use and allocate size+1
|
||
|
|
buf = buf[offset:offset+size+1][:-1]
|
||
|
|
data = np.ndarray(shape, dtype, buf, order=order)
|
||
|
|
data.fill(0)
|
||
|
|
return data
|
||
|
|
|
||
|
|
|
||
|
|
def _prune_array(array):
|
||
|
|
"""Return an array equivalent to the input array. If the input
|
||
|
|
array is a view of a much larger array, copy its contents to a
|
||
|
|
newly allocated array. Otherwise, return the input unchanged.
|
||
|
|
"""
|
||
|
|
if array.base is not None and array.size < array.base.size // 2:
|
||
|
|
return array.copy()
|
||
|
|
return array
|
||
|
|
|
||
|
|
|
||
|
|
def float_factorial(n: int) -> float:
|
||
|
|
"""Compute the factorial and return as a float
|
||
|
|
|
||
|
|
Returns infinity when result is too large for a double
|
||
|
|
"""
|
||
|
|
return float(math.factorial(n)) if n < 171 else np.inf
|
||
|
|
|
||
|
|
|
||
|
|
# copy-pasted from scikit-learn utils/validation.py
|
||
|
|
# change this to scipy.stats._qmc.check_random_state once numpy 1.16 is dropped
|
||
|
|
def check_random_state(seed):
|
||
|
|
"""Turn `seed` into a `np.random.RandomState` instance.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
|
||
|
|
If `seed` is None (or `np.random`), the `numpy.random.RandomState`
|
||
|
|
singleton is used.
|
||
|
|
If `seed` is an int, a new ``RandomState`` instance is used,
|
||
|
|
seeded with `seed`.
|
||
|
|
If `seed` is already a ``Generator`` or ``RandomState`` instance then
|
||
|
|
that instance is used.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
|
||
|
|
Random number generator.
|
||
|
|
|
||
|
|
"""
|
||
|
|
if seed is None or seed is np.random:
|
||
|
|
return np.random.mtrand._rand
|
||
|
|
if isinstance(seed, (numbers.Integral, np.integer)):
|
||
|
|
return np.random.RandomState(seed)
|
||
|
|
if isinstance(seed, (np.random.RandomState, np.random.Generator)):
|
||
|
|
return seed
|
||
|
|
|
||
|
|
raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
|
||
|
|
' instance' % seed)
|
||
|
|
|
||
|
|
|
||
|
|
def _asarray_validated(a, check_finite=True,
|
||
|
|
sparse_ok=False, objects_ok=False, mask_ok=False,
|
||
|
|
as_inexact=False):
|
||
|
|
"""
|
||
|
|
Helper function for SciPy argument validation.
|
||
|
|
|
||
|
|
Many SciPy linear algebra functions do support arbitrary array-like
|
||
|
|
input arguments. Examples of commonly unsupported inputs include
|
||
|
|
matrices containing inf/nan, sparse matrix representations, and
|
||
|
|
matrices with complicated elements.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
a : array_like
|
||
|
|
The array-like input.
|
||
|
|
check_finite : bool, optional
|
||
|
|
Whether to check that the input matrices contain only finite numbers.
|
||
|
|
Disabling may give a performance gain, but may result in problems
|
||
|
|
(crashes, non-termination) if the inputs do contain infinities or NaNs.
|
||
|
|
Default: True
|
||
|
|
sparse_ok : bool, optional
|
||
|
|
True if scipy sparse matrices are allowed.
|
||
|
|
objects_ok : bool, optional
|
||
|
|
True if arrays with dype('O') are allowed.
|
||
|
|
mask_ok : bool, optional
|
||
|
|
True if masked arrays are allowed.
|
||
|
|
as_inexact : bool, optional
|
||
|
|
True to convert the input array to a np.inexact dtype.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
ret : ndarray
|
||
|
|
The converted validated array.
|
||
|
|
|
||
|
|
"""
|
||
|
|
if not sparse_ok:
|
||
|
|
import scipy.sparse
|
||
|
|
if scipy.sparse.issparse(a):
|
||
|
|
msg = ('Sparse matrices are not supported by this function. '
|
||
|
|
'Perhaps one of the scipy.sparse.linalg functions '
|
||
|
|
'would work instead.')
|
||
|
|
raise ValueError(msg)
|
||
|
|
if not mask_ok:
|
||
|
|
if np.ma.isMaskedArray(a):
|
||
|
|
raise ValueError('masked arrays are not supported')
|
||
|
|
toarray = np.asarray_chkfinite if check_finite else np.asarray
|
||
|
|
a = toarray(a)
|
||
|
|
if not objects_ok:
|
||
|
|
if a.dtype is np.dtype('O'):
|
||
|
|
raise ValueError('object arrays are not supported')
|
||
|
|
if as_inexact:
|
||
|
|
if not np.issubdtype(a.dtype, np.inexact):
|
||
|
|
a = toarray(a, dtype=np.float64)
|
||
|
|
return a
|
||
|
|
|
||
|
|
|
||
|
|
def _validate_int(k, name, minimum=None):
|
||
|
|
"""
|
||
|
|
Validate a scalar integer.
|
||
|
|
|
||
|
|
This function can be used to validate an argument to a function
|
||
|
|
that expects the value to be an integer. It uses `operator.index`
|
||
|
|
to validate the value (so, for example, k=2.0 results in a
|
||
|
|
TypeError).
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
k : int
|
||
|
|
The value to be validated.
|
||
|
|
name : str
|
||
|
|
The name of the parameter.
|
||
|
|
minimum : int, optional
|
||
|
|
An optional lower bound.
|
||
|
|
"""
|
||
|
|
try:
|
||
|
|
k = operator.index(k)
|
||
|
|
except TypeError:
|
||
|
|
raise TypeError(f'{name} must be an integer.') from None
|
||
|
|
if minimum is not None and k < minimum:
|
||
|
|
raise ValueError(f'{name} must be an integer not less '
|
||
|
|
f'than {minimum}') from None
|
||
|
|
return k
|
||
|
|
|
||
|
|
|
||
|
|
# Add a replacement for inspect.getfullargspec()/
|
||
|
|
# The version below is borrowed from Django,
|
||
|
|
# https://github.com/django/django/pull/4846.
|
||
|
|
|
||
|
|
# Note an inconsistency between inspect.getfullargspec(func) and
|
||
|
|
# inspect.signature(func). If `func` is a bound method, the latter does *not*
|
||
|
|
# list `self` as a first argument, while the former *does*.
|
||
|
|
# Hence, cook up a common ground replacement: `getfullargspec_no_self` which
|
||
|
|
# mimics `inspect.getfullargspec` but does not list `self`.
|
||
|
|
#
|
||
|
|
# This way, the caller code does not need to know whether it uses a legacy
|
||
|
|
# .getfullargspec or a bright and shiny .signature.
|
||
|
|
|
||
|
|
FullArgSpec = namedtuple('FullArgSpec',
|
||
|
|
['args', 'varargs', 'varkw', 'defaults',
|
||
|
|
'kwonlyargs', 'kwonlydefaults', 'annotations'])
|
||
|
|
|
||
|
|
|
||
|
|
def getfullargspec_no_self(func):
|
||
|
|
"""inspect.getfullargspec replacement using inspect.signature.
|
||
|
|
|
||
|
|
If func is a bound method, do not list the 'self' parameter.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
func : callable
|
||
|
|
A callable to inspect
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
fullargspec : FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
|
||
|
|
kwonlydefaults, annotations)
|
||
|
|
|
||
|
|
NOTE: if the first argument of `func` is self, it is *not*, I repeat
|
||
|
|
*not*, included in fullargspec.args.
|
||
|
|
This is done for consistency between inspect.getargspec() under
|
||
|
|
Python 2.x, and inspect.signature() under Python 3.x.
|
||
|
|
|
||
|
|
"""
|
||
|
|
sig = inspect.signature(func)
|
||
|
|
args = [
|
||
|
|
p.name for p in sig.parameters.values()
|
||
|
|
if p.kind in [inspect.Parameter.POSITIONAL_OR_KEYWORD,
|
||
|
|
inspect.Parameter.POSITIONAL_ONLY]
|
||
|
|
]
|
||
|
|
varargs = [
|
||
|
|
p.name for p in sig.parameters.values()
|
||
|
|
if p.kind == inspect.Parameter.VAR_POSITIONAL
|
||
|
|
]
|
||
|
|
varargs = varargs[0] if varargs else None
|
||
|
|
varkw = [
|
||
|
|
p.name for p in sig.parameters.values()
|
||
|
|
if p.kind == inspect.Parameter.VAR_KEYWORD
|
||
|
|
]
|
||
|
|
varkw = varkw[0] if varkw else None
|
||
|
|
defaults = tuple(
|
||
|
|
p.default for p in sig.parameters.values()
|
||
|
|
if (p.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD and
|
||
|
|
p.default is not p.empty)
|
||
|
|
) or None
|
||
|
|
kwonlyargs = [
|
||
|
|
p.name for p in sig.parameters.values()
|
||
|
|
if p.kind == inspect.Parameter.KEYWORD_ONLY
|
||
|
|
]
|
||
|
|
kwdefaults = {p.name: p.default for p in sig.parameters.values()
|
||
|
|
if p.kind == inspect.Parameter.KEYWORD_ONLY and
|
||
|
|
p.default is not p.empty}
|
||
|
|
annotations = {p.name: p.annotation for p in sig.parameters.values()
|
||
|
|
if p.annotation is not p.empty}
|
||
|
|
return FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
|
||
|
|
kwdefaults or None, annotations)
|
||
|
|
|
||
|
|
|
||
|
|
class _FunctionWrapper:
|
||
|
|
"""
|
||
|
|
Object to wrap user's function, allowing picklability
|
||
|
|
"""
|
||
|
|
def __init__(self, f, args):
|
||
|
|
self.f = f
|
||
|
|
self.args = [] if args is None else args
|
||
|
|
|
||
|
|
def __call__(self, x):
|
||
|
|
return self.f(x, *self.args)
|
||
|
|
|
||
|
|
|
||
|
|
class MapWrapper:
|
||
|
|
"""
|
||
|
|
Parallelisation wrapper for working with map-like callables, such as
|
||
|
|
`multiprocessing.Pool.map`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
pool : int or map-like callable
|
||
|
|
If `pool` is an integer, then it specifies the number of threads to
|
||
|
|
use for parallelization. If ``int(pool) == 1``, then no parallel
|
||
|
|
processing is used and the map builtin is used.
|
||
|
|
If ``pool == -1``, then the pool will utilize all available CPUs.
|
||
|
|
If `pool` is a map-like callable that follows the same
|
||
|
|
calling sequence as the built-in map function, then this callable is
|
||
|
|
used for parallelization.
|
||
|
|
"""
|
||
|
|
def __init__(self, pool=1):
|
||
|
|
self.pool = None
|
||
|
|
self._mapfunc = map
|
||
|
|
self._own_pool = False
|
||
|
|
|
||
|
|
if callable(pool):
|
||
|
|
self.pool = pool
|
||
|
|
self._mapfunc = self.pool
|
||
|
|
else:
|
||
|
|
from multiprocessing import Pool
|
||
|
|
# user supplies a number
|
||
|
|
if int(pool) == -1:
|
||
|
|
# use as many processors as possible
|
||
|
|
self.pool = Pool()
|
||
|
|
self._mapfunc = self.pool.map
|
||
|
|
self._own_pool = True
|
||
|
|
elif int(pool) == 1:
|
||
|
|
pass
|
||
|
|
elif int(pool) > 1:
|
||
|
|
# use the number of processors requested
|
||
|
|
self.pool = Pool(processes=int(pool))
|
||
|
|
self._mapfunc = self.pool.map
|
||
|
|
self._own_pool = True
|
||
|
|
else:
|
||
|
|
raise RuntimeError("Number of workers specified must be -1,"
|
||
|
|
" an int >= 1, or an object with a 'map' "
|
||
|
|
"method")
|
||
|
|
|
||
|
|
def __enter__(self):
|
||
|
|
return self
|
||
|
|
|
||
|
|
def terminate(self):
|
||
|
|
if self._own_pool:
|
||
|
|
self.pool.terminate()
|
||
|
|
|
||
|
|
def join(self):
|
||
|
|
if self._own_pool:
|
||
|
|
self.pool.join()
|
||
|
|
|
||
|
|
def close(self):
|
||
|
|
if self._own_pool:
|
||
|
|
self.pool.close()
|
||
|
|
|
||
|
|
def __exit__(self, exc_type, exc_value, traceback):
|
||
|
|
if self._own_pool:
|
||
|
|
self.pool.close()
|
||
|
|
self.pool.terminate()
|
||
|
|
|
||
|
|
def __call__(self, func, iterable):
|
||
|
|
# only accept one iterable because that's all Pool.map accepts
|
||
|
|
try:
|
||
|
|
return self._mapfunc(func, iterable)
|
||
|
|
except TypeError as e:
|
||
|
|
# wrong number of arguments
|
||
|
|
raise TypeError("The map-like callable must be of the"
|
||
|
|
" form f(func, iterable)") from e
|
||
|
|
|
||
|
|
|
||
|
|
def rng_integers(gen, low, high=None, size=None, dtype='int64',
|
||
|
|
endpoint=False):
|
||
|
|
"""
|
||
|
|
Return random integers from low (inclusive) to high (exclusive), or if
|
||
|
|
endpoint=True, low (inclusive) to high (inclusive). Replaces
|
||
|
|
`RandomState.randint` (with endpoint=False) and
|
||
|
|
`RandomState.random_integers` (with endpoint=True).
|
||
|
|
|
||
|
|
Return random integers from the "discrete uniform" distribution of the
|
||
|
|
specified dtype. If high is None (the default), then results are from
|
||
|
|
0 to low.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
gen : {None, np.random.RandomState, np.random.Generator}
|
||
|
|
Random number generator. If None, then the np.random.RandomState
|
||
|
|
singleton is used.
|
||
|
|
low : int or array-like of ints
|
||
|
|
Lowest (signed) integers to be drawn from the distribution (unless
|
||
|
|
high=None, in which case this parameter is 0 and this value is used
|
||
|
|
for high).
|
||
|
|
high : int or array-like of ints
|
||
|
|
If provided, one above the largest (signed) integer to be drawn from
|
||
|
|
the distribution (see above for behavior if high=None). If array-like,
|
||
|
|
must contain integer values.
|
||
|
|
size : array-like of ints, optional
|
||
|
|
Output shape. If the given shape is, e.g., (m, n, k), then m * n * k
|
||
|
|
samples are drawn. Default is None, in which case a single value is
|
||
|
|
returned.
|
||
|
|
dtype : {str, dtype}, optional
|
||
|
|
Desired dtype of the result. All dtypes are determined by their name,
|
||
|
|
i.e., 'int64', 'int', etc, so byteorder is not available and a specific
|
||
|
|
precision may have different C types depending on the platform.
|
||
|
|
The default value is 'int64'.
|
||
|
|
endpoint : bool, optional
|
||
|
|
If True, sample from the interval [low, high] instead of the default
|
||
|
|
[low, high) Defaults to False.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out: int or ndarray of ints
|
||
|
|
size-shaped array of random integers from the appropriate distribution,
|
||
|
|
or a single such random int if size not provided.
|
||
|
|
"""
|
||
|
|
if isinstance(gen, Generator):
|
||
|
|
return gen.integers(low, high=high, size=size, dtype=dtype,
|
||
|
|
endpoint=endpoint)
|
||
|
|
else:
|
||
|
|
if gen is None:
|
||
|
|
# default is RandomState singleton used by np.random.
|
||
|
|
gen = np.random.mtrand._rand
|
||
|
|
if endpoint:
|
||
|
|
# inclusive of endpoint
|
||
|
|
# remember that low and high can be arrays, so don't modify in
|
||
|
|
# place
|
||
|
|
if high is None:
|
||
|
|
return gen.randint(low + 1, size=size, dtype=dtype)
|
||
|
|
if high is not None:
|
||
|
|
return gen.randint(low, high=high + 1, size=size, dtype=dtype)
|
||
|
|
|
||
|
|
# exclusive
|
||
|
|
return gen.randint(low, high=high, size=size, dtype=dtype)
|
||
|
|
|
||
|
|
|
||
|
|
@contextmanager
|
||
|
|
def _fixed_default_rng(seed=1638083107694713882823079058616272161):
|
||
|
|
"""Context with a fixed np.random.default_rng seed."""
|
||
|
|
orig_fun = np.random.default_rng
|
||
|
|
np.random.default_rng = lambda seed=seed: orig_fun(seed)
|
||
|
|
try:
|
||
|
|
yield
|
||
|
|
finally:
|
||
|
|
np.random.default_rng = orig_fun
|
||
|
|
|
||
|
|
|
||
|
|
def _rng_html_rewrite(func):
|
||
|
|
"""Rewrite the HTML rendering of ``np.random.default_rng``.
|
||
|
|
|
||
|
|
This is intended to decorate
|
||
|
|
``numpydoc.docscrape_sphinx.SphinxDocString._str_examples``.
|
||
|
|
|
||
|
|
Examples are only run by Sphinx when there are plot involved. Even so,
|
||
|
|
it does not change the result values getting printed.
|
||
|
|
"""
|
||
|
|
# hexadecimal or number seed, case-insensitive
|
||
|
|
pattern = re.compile(r'np.random.default_rng\((0x[0-9A-F]+|\d+)\)', re.I)
|
||
|
|
|
||
|
|
def _wrapped(*args, **kwargs):
|
||
|
|
res = func(*args, **kwargs)
|
||
|
|
lines = [
|
||
|
|
re.sub(pattern, 'np.random.default_rng()', line)
|
||
|
|
for line in res
|
||
|
|
]
|
||
|
|
return lines
|
||
|
|
|
||
|
|
return _wrapped
|
||
|
|
|
||
|
|
|
||
|
|
def _argmin(a, keepdims=False, axis=None):
|
||
|
|
"""
|
||
|
|
argmin with a `keepdims` parameter.
|
||
|
|
|
||
|
|
See https://github.com/numpy/numpy/issues/8710
|
||
|
|
|
||
|
|
If axis is not None, a.shape[axis] must be greater than 0.
|
||
|
|
"""
|
||
|
|
res = np.argmin(a, axis=axis)
|
||
|
|
if keepdims and axis is not None:
|
||
|
|
res = np.expand_dims(res, axis=axis)
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def _first_nonnan(a, axis):
|
||
|
|
"""
|
||
|
|
Return the first non-nan value along the given axis.
|
||
|
|
|
||
|
|
If a slice is all nan, nan is returned for that slice.
|
||
|
|
|
||
|
|
The shape of the return value corresponds to ``keepdims=True``.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> nan = np.nan
|
||
|
|
>>> a = np.array([[ 3., 3., nan, 3.],
|
||
|
|
[ 1., nan, 2., 4.],
|
||
|
|
[nan, nan, 9., -1.],
|
||
|
|
[nan, 5., 4., 3.],
|
||
|
|
[ 2., 2., 2., 2.],
|
||
|
|
[nan, nan, nan, nan]])
|
||
|
|
>>> _first_nonnan(a, axis=0)
|
||
|
|
array([[3., 3., 2., 3.]])
|
||
|
|
>>> _first_nonnan(a, axis=1)
|
||
|
|
array([[ 3.],
|
||
|
|
[ 1.],
|
||
|
|
[ 9.],
|
||
|
|
[ 5.],
|
||
|
|
[ 2.],
|
||
|
|
[nan]])
|
||
|
|
"""
|
||
|
|
k = _argmin(np.isnan(a), axis=axis, keepdims=True)
|
||
|
|
return np.take_along_axis(a, k, axis=axis)
|
||
|
|
|
||
|
|
|
||
|
|
def _nan_allsame(a, axis, keepdims=False):
|
||
|
|
"""
|
||
|
|
Determine if the values along an axis are all the same.
|
||
|
|
|
||
|
|
nan values are ignored.
|
||
|
|
|
||
|
|
`a` must be a numpy array.
|
||
|
|
|
||
|
|
`axis` is assumed to be normalized; that is, 0 <= axis < a.ndim.
|
||
|
|
|
||
|
|
For an axis of length 0, the result is True. That is, we adopt the
|
||
|
|
convention that ``allsame([])`` is True. (There are no values in the
|
||
|
|
input that are different.)
|
||
|
|
|
||
|
|
`True` is returned for slices that are all nan--not because all the
|
||
|
|
values are the same, but because this is equivalent to ``allsame([])``.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from numpy import nan, array
|
||
|
|
>>> a = array([[ 3., 3., nan, 3.],
|
||
|
|
... [ 1., nan, 2., 4.],
|
||
|
|
... [nan, nan, 9., -1.],
|
||
|
|
... [nan, 5., 4., 3.],
|
||
|
|
... [ 2., 2., 2., 2.],
|
||
|
|
... [nan, nan, nan, nan]])
|
||
|
|
>>> _nan_allsame(a, axis=1, keepdims=True)
|
||
|
|
array([[ True],
|
||
|
|
[False],
|
||
|
|
[False],
|
||
|
|
[False],
|
||
|
|
[ True],
|
||
|
|
[ True]])
|
||
|
|
"""
|
||
|
|
if axis is None:
|
||
|
|
if a.size == 0:
|
||
|
|
return True
|
||
|
|
a = a.ravel()
|
||
|
|
axis = 0
|
||
|
|
else:
|
||
|
|
shp = a.shape
|
||
|
|
if shp[axis] == 0:
|
||
|
|
shp = shp[:axis] + (1,)*keepdims + shp[axis + 1:]
|
||
|
|
return np.full(shp, fill_value=True, dtype=bool)
|
||
|
|
a0 = _first_nonnan(a, axis=axis)
|
||
|
|
return ((a0 == a) | np.isnan(a)).all(axis=axis, keepdims=keepdims)
|
||
|
|
|
||
|
|
|
||
|
|
def _contains_nan(a, nan_policy='propagate', use_summation=True,
|
||
|
|
policies=None):
|
||
|
|
if not isinstance(a, np.ndarray):
|
||
|
|
use_summation = False # some array_likes ignore nans (e.g. pandas)
|
||
|
|
if policies is None:
|
||
|
|
policies = ['propagate', 'raise', 'omit']
|
||
|
|
if nan_policy not in policies:
|
||
|
|
raise ValueError("nan_policy must be one of {%s}" %
|
||
|
|
', '.join("'%s'" % s for s in policies))
|
||
|
|
|
||
|
|
if np.issubdtype(a.dtype, np.inexact):
|
||
|
|
# The summation method avoids creating a (potentially huge) array.
|
||
|
|
if use_summation:
|
||
|
|
with np.errstate(invalid='ignore', over='ignore'):
|
||
|
|
contains_nan = np.isnan(np.sum(a))
|
||
|
|
else:
|
||
|
|
contains_nan = np.isnan(a).any()
|
||
|
|
elif np.issubdtype(a.dtype, object):
|
||
|
|
contains_nan = False
|
||
|
|
for el in a.ravel():
|
||
|
|
# isnan doesn't work on non-numeric elements
|
||
|
|
if np.issubdtype(type(el), np.number) and np.isnan(el):
|
||
|
|
contains_nan = True
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
# Only `object` and `inexact` arrays can have NaNs
|
||
|
|
contains_nan = False
|
||
|
|
|
||
|
|
if contains_nan and nan_policy == 'raise':
|
||
|
|
raise ValueError("The input contains nan values")
|
||
|
|
|
||
|
|
return contains_nan, nan_policy
|
||
|
|
|
||
|
|
|
||
|
|
def _rename_parameter(old_name, new_name, dep_version=None):
|
||
|
|
"""
|
||
|
|
Generate decorator for backward-compatible keyword renaming.
|
||
|
|
|
||
|
|
Apply the decorator generated by `_rename_parameter` to functions with a
|
||
|
|
recently renamed parameter to maintain backward-compatibility.
|
||
|
|
|
||
|
|
After decoration, the function behaves as follows:
|
||
|
|
If only the new parameter is passed into the function, behave as usual.
|
||
|
|
If only the old parameter is passed into the function (as a keyword), raise
|
||
|
|
a DeprecationWarning if `dep_version` is provided, and behave as usual
|
||
|
|
otherwise.
|
||
|
|
If both old and new parameters are passed into the function, raise a
|
||
|
|
DeprecationWarning if `dep_version` is provided, and raise the appropriate
|
||
|
|
TypeError (function got multiple values for argument).
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
old_name : str
|
||
|
|
Old name of parameter
|
||
|
|
new_name : str
|
||
|
|
New name of parameter
|
||
|
|
dep_version : str, optional
|
||
|
|
Version of SciPy in which old parameter was deprecated in the format
|
||
|
|
'X.Y.Z'. If supplied, the deprecation message will indicate that
|
||
|
|
support for the old parameter will be removed in version 'X.Y+2.Z'
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Untested with functions that accept *args. Probably won't work as written.
|
||
|
|
|
||
|
|
"""
|
||
|
|
def decorator(fun):
|
||
|
|
@functools.wraps(fun)
|
||
|
|
def wrapper(*args, **kwargs):
|
||
|
|
if old_name in kwargs:
|
||
|
|
if dep_version:
|
||
|
|
end_version = dep_version.split('.')
|
||
|
|
end_version[1] = str(int(end_version[1]) + 2)
|
||
|
|
end_version = '.'.join(end_version)
|
||
|
|
message = (f"Use of keyword argument `{old_name}` is "
|
||
|
|
f"deprecated and replaced by `{new_name}`. "
|
||
|
|
f"Support for `{old_name}` will be removed "
|
||
|
|
f"in SciPy {end_version}.")
|
||
|
|
warnings.warn(message, DeprecationWarning, stacklevel=2)
|
||
|
|
if new_name in kwargs:
|
||
|
|
message = (f"{fun.__name__}() got multiple values for "
|
||
|
|
f"argument now known as `{new_name}`")
|
||
|
|
raise TypeError(message)
|
||
|
|
kwargs[new_name] = kwargs.pop(old_name)
|
||
|
|
return fun(*args, **kwargs)
|
||
|
|
return wrapper
|
||
|
|
return decorator
|
||
|
|
|
||
|
|
|
||
|
|
def _rng_spawn(rng, n_children):
|
||
|
|
# spawns independent RNGs from a parent RNG
|
||
|
|
bg = rng._bit_generator
|
||
|
|
ss = bg._seed_seq
|
||
|
|
child_rngs = [np.random.Generator(type(bg)(child_ss))
|
||
|
|
for child_ss in ss.spawn(n_children)]
|
||
|
|
return child_rngs
|
||
|
|
|
||
|
|
|
||
|
|
def _get_nan(*data):
|
||
|
|
# Get NaN of appropriate dtype for data
|
||
|
|
data = [np.asarray(item) for item in data]
|
||
|
|
try:
|
||
|
|
dtype = np.result_type(*data, np.half) # must be a float16 at least
|
||
|
|
except DTypePromotionError:
|
||
|
|
# fallback to float64
|
||
|
|
return np.array(np.nan, dtype=np.float64)[()]
|
||
|
|
return np.array(np.nan, dtype=dtype)[()]
|
||
|
|
|
||
|
|
|
||
|
|
def normalize_axis_index(axis, ndim):
|
||
|
|
# Check if `axis` is in the correct range and normalize it
|
||
|
|
if axis < -ndim or axis >= ndim:
|
||
|
|
msg = f"axis {axis} is out of bounds for array of dimension {ndim}"
|
||
|
|
raise AxisError(msg)
|
||
|
|
|
||
|
|
if axis < 0:
|
||
|
|
axis = axis + ndim
|
||
|
|
return axis
|
||
|
|
|
||
|
|
|
||
|
|
def _call_callback_maybe_halt(callback, res):
|
||
|
|
"""Call wrapped callback; return True if algorithm should stop.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
callback : callable or None
|
||
|
|
A user-provided callback wrapped with `_wrap_callback`
|
||
|
|
res : OptimizeResult
|
||
|
|
Information about the current iterate
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
halt : bool
|
||
|
|
True if minimization should stop
|
||
|
|
|
||
|
|
"""
|
||
|
|
if callback is None:
|
||
|
|
return False
|
||
|
|
try:
|
||
|
|
callback(res)
|
||
|
|
return False
|
||
|
|
except StopIteration:
|
||
|
|
callback.stop_iteration = True
|
||
|
|
return True
|
||
|
|
|
||
|
|
|
||
|
|
class _RichResult(dict):
|
||
|
|
""" Container for multiple outputs with pretty-printing """
|
||
|
|
def __getattr__(self, name):
|
||
|
|
try:
|
||
|
|
return self[name]
|
||
|
|
except KeyError as e:
|
||
|
|
raise AttributeError(name) from e
|
||
|
|
|
||
|
|
__setattr__ = dict.__setitem__
|
||
|
|
__delattr__ = dict.__delitem__
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
order_keys = ['message', 'success', 'status', 'fun', 'funl', 'x', 'xl',
|
||
|
|
'col_ind', 'nit', 'lower', 'upper', 'eqlin', 'ineqlin',
|
||
|
|
'converged', 'flag', 'function_calls', 'iterations',
|
||
|
|
'root']
|
||
|
|
order_keys = getattr(self, '_order_keys', order_keys)
|
||
|
|
# 'slack', 'con' are redundant with residuals
|
||
|
|
# 'crossover_nit' is probably not interesting to most users
|
||
|
|
omit_keys = {'slack', 'con', 'crossover_nit', '_order_keys'}
|
||
|
|
|
||
|
|
def key(item):
|
||
|
|
try:
|
||
|
|
return order_keys.index(item[0].lower())
|
||
|
|
except ValueError: # item not in list
|
||
|
|
return np.inf
|
||
|
|
|
||
|
|
def omit_redundant(items):
|
||
|
|
for item in items:
|
||
|
|
if item[0] in omit_keys:
|
||
|
|
continue
|
||
|
|
yield item
|
||
|
|
|
||
|
|
def item_sorter(d):
|
||
|
|
return sorted(omit_redundant(d.items()), key=key)
|
||
|
|
|
||
|
|
if self.keys():
|
||
|
|
return _dict_formatter(self, sorter=item_sorter)
|
||
|
|
else:
|
||
|
|
return self.__class__.__name__ + "()"
|
||
|
|
|
||
|
|
def __dir__(self):
|
||
|
|
return list(self.keys())
|
||
|
|
|
||
|
|
|
||
|
|
def _indenter(s, n=0):
|
||
|
|
"""
|
||
|
|
Ensures that lines after the first are indented by the specified amount
|
||
|
|
"""
|
||
|
|
split = s.split("\n")
|
||
|
|
indent = " "*n
|
||
|
|
return ("\n" + indent).join(split)
|
||
|
|
|
||
|
|
|
||
|
|
def _float_formatter_10(x):
|
||
|
|
"""
|
||
|
|
Returns a string representation of a float with exactly ten characters
|
||
|
|
"""
|
||
|
|
if np.isposinf(x):
|
||
|
|
return " inf"
|
||
|
|
elif np.isneginf(x):
|
||
|
|
return " -inf"
|
||
|
|
elif np.isnan(x):
|
||
|
|
return " nan"
|
||
|
|
return np.format_float_scientific(x, precision=3, pad_left=2, unique=False)
|
||
|
|
|
||
|
|
|
||
|
|
def _dict_formatter(d, n=0, mplus=1, sorter=None):
|
||
|
|
"""
|
||
|
|
Pretty printer for dictionaries
|
||
|
|
|
||
|
|
`n` keeps track of the starting indentation;
|
||
|
|
lines are indented by this much after a line break.
|
||
|
|
`mplus` is additional left padding applied to keys
|
||
|
|
"""
|
||
|
|
if isinstance(d, dict):
|
||
|
|
m = max(map(len, list(d.keys()))) + mplus # width to print keys
|
||
|
|
s = '\n'.join([k.rjust(m) + ': ' + # right justified, width m
|
||
|
|
_indenter(_dict_formatter(v, m+n+2, 0, sorter), m+2)
|
||
|
|
for k, v in sorter(d)]) # +2 for ': '
|
||
|
|
else:
|
||
|
|
# By default, NumPy arrays print with linewidth=76. `n` is
|
||
|
|
# the indent at which a line begins printing, so it is subtracted
|
||
|
|
# from the default to avoid exceeding 76 characters total.
|
||
|
|
# `edgeitems` is the number of elements to include before and after
|
||
|
|
# ellipses when arrays are not shown in full.
|
||
|
|
# `threshold` is the maximum number of elements for which an
|
||
|
|
# array is shown in full.
|
||
|
|
# These values tend to work well for use with OptimizeResult.
|
||
|
|
with np.printoptions(linewidth=76-n, edgeitems=2, threshold=12,
|
||
|
|
formatter={'float_kind': _float_formatter_10}):
|
||
|
|
s = str(d)
|
||
|
|
return s
|