# Source code for hypothesis.extra._array_helpers

```
# This file is part of Hypothesis, which may be found at
# https://github.com/HypothesisWorks/hypothesis/
#
# Most of this work is copyright (C) 2013-2021 David R. MacIver
# (david@drmaciver.com), but it contains contributions by others. See
# CONTRIBUTING.rst for a full list of people who may hold copyright, and
# consult the git log if you need to determine who owns an individual
# contribution.
#
# This Source Code Form is subject to the terms of the Mozilla Public License,
# v. 2.0. If a copy of the MPL was not distributed with this file, You can
# obtain one at https://mozilla.org/MPL/2.0/.
#
# END HEADER
import re
from typing import NamedTuple, Optional, Tuple, Union
from hypothesis import assume, strategies as st
from hypothesis.errors import InvalidArgument
from hypothesis.internal.conjecture import utils as cu
from hypothesis.internal.coverage import check_function
from hypothesis.internal.validation import check_type, check_valid_interval
from hypothesis.strategies._internal.utils import defines_strategy
from hypothesis.utils.conventions import UniqueIdentifier, not_set
__all__ = [
"NDIM_MAX",
"Shape",
"BroadcastableShapes",
"BasicIndex",
"check_argument",
"order_check",
"check_valid_dims",
"array_shapes",
"valid_tuple_axes",
"broadcastable_shapes",
"mutually_broadcastable_shapes",
"MutuallyBroadcastableShapesStrategy",
"BasicIndexStrategy",
]
Shape = Tuple[int, ...]
# We silence flake8 here because it disagrees with mypy about `ellipsis` (`type(...)`)
BasicIndex = Tuple[Union[int, slice, None, "ellipsis"], ...] # noqa: F821
class BroadcastableShapes(NamedTuple):
input_shapes: Tuple[Shape, ...]
result_shape: Shape
@check_function
def check_argument(condition, fail_message, *f_args, **f_kwargs):
if not condition:
raise InvalidArgument(fail_message.format(*f_args, **f_kwargs))
@check_function
def order_check(name, floor, min_, max_):
if floor > min_:
raise InvalidArgument(f"min_{name} must be at least {floor} but was {min_}")
if min_ > max_:
raise InvalidArgument(f"min_{name}={min_} is larger than max_{name}={max_}")
# 32 is a dimension limit specific to NumPy, and does not necessarily apply to
# other array/tensor libraries. Historically these strategies were built for the
# NumPy extra, so it's nice to keep these limits, and it's seemingly unlikely
# someone would want to generate >32 dim arrays anyway.
# See https://github.com/HypothesisWorks/hypothesis/pull/3067.
NDIM_MAX = 32
@check_function
def check_valid_dims(dims, name):
if dims > NDIM_MAX:
raise InvalidArgument(
f"{name}={dims}, but Hypothesis does not support arrays with "
f"more than {NDIM_MAX} dimensions"
)
[docs]@defines_strategy()
def array_shapes(
*,
min_dims: int = 1,
max_dims: Optional[int] = None,
min_side: int = 1,
max_side: Optional[int] = None,
) -> st.SearchStrategy[Shape]:
"""Return a strategy for array shapes (tuples of int >= 1).
* ``min_dims`` is the smallest length that the generated shape can possess.
* ``max_dims`` is the largest length that the generated shape can possess,
defaulting to ``min_dims + 2``.
* ``min_side`` is the smallest size that a dimension can possess.
* ``max_side`` is the largest size that a dimension can possess,
defaulting to ``min_side + 5``.
"""
check_type(int, min_dims, "min_dims")
check_type(int, min_side, "min_side")
check_valid_dims(min_dims, "min_dims")
if max_dims is None:
max_dims = min(min_dims + 2, NDIM_MAX)
check_type(int, max_dims, "max_dims")
check_valid_dims(max_dims, "max_dims")
if max_side is None:
max_side = min_side + 5
check_type(int, max_side, "max_side")
order_check("dims", 0, min_dims, max_dims)
order_check("side", 0, min_side, max_side)
return st.lists(
st.integers(min_side, max_side), min_size=min_dims, max_size=max_dims
).map(tuple)
[docs]@defines_strategy()
def valid_tuple_axes(
ndim: int,
*,
min_size: int = 0,
max_size: Optional[int] = None,
) -> st.SearchStrategy[Tuple[int, ...]]:
"""All tuples will have a length >= ``min_size`` and <= ``max_size``. The default
value for ``max_size`` is ``ndim``.
Examples from this strategy shrink towards an empty tuple, which render most
sequential functions as no-ops.
The following are some examples drawn from this strategy.
.. code-block:: pycon
>>> [valid_tuple_axes(3).example() for i in range(4)]
[(-3, 1), (0, 1, -1), (0, 2), (0, -2, 2)]
``valid_tuple_axes`` can be joined with other strategies to generate
any type of valid axis object, i.e. integers, tuples, and ``None``:
.. code-block:: python
any_axis_strategy = none() | integers(-ndim, ndim - 1) | valid_tuple_axes(ndim)
"""
check_type(int, ndim, "ndim")
check_type(int, min_size, "min_size")
if max_size is None:
max_size = ndim
check_type(int, max_size, "max_size")
order_check("size", 0, min_size, max_size)
check_valid_interval(max_size, ndim, "max_size", "ndim")
axes = st.integers(0, max(0, 2 * ndim - 1)).map(
lambda x: x if x < ndim else x - 2 * ndim
)
return st.lists(
axes, min_size=min_size, max_size=max_size, unique_by=lambda x: x % ndim
).map(tuple)
[docs]@defines_strategy()
def broadcastable_shapes(
shape: Shape,
*,
min_dims: int = 0,
max_dims: Optional[int] = None,
min_side: int = 1,
max_side: Optional[int] = None,
) -> st.SearchStrategy[Shape]:
"""Return a strategy for shapes that are broadcast-compatible with the
provided shape.
Examples from this strategy shrink towards a shape with length ``min_dims``.
The size of an aligned dimension shrinks towards size ``1``. The size of an
unaligned dimension shrink towards ``min_side``.
* ``shape`` is a tuple of integers.
* ``min_dims`` is the smallest length that the generated shape can possess.
* ``max_dims`` is the largest length that the generated shape can possess,
defaulting to ``max(len(shape), min_dims) + 2``.
* ``min_side`` is the smallest size that an unaligned dimension can possess.
* ``max_side`` is the largest size that an unaligned dimension can possess,
defaulting to 2 plus the size of the largest aligned dimension.
The following are some examples drawn from this strategy.
.. code-block:: pycon
>>> [broadcastable_shapes(shape=(2, 3)).example() for i in range(5)]
[(1, 3), (), (2, 3), (2, 1), (4, 1, 3), (3, )]
"""
check_type(tuple, shape, "shape")
check_type(int, min_side, "min_side")
check_type(int, min_dims, "min_dims")
check_valid_dims(min_dims, "min_dims")
strict_check = max_side is None or max_dims is None
if max_dims is None:
max_dims = min(max(len(shape), min_dims) + 2, NDIM_MAX)
check_type(int, max_dims, "max_dims")
check_valid_dims(max_dims, "max_dims")
if max_side is None:
max_side = max(shape[-max_dims:] + (min_side,)) + 2
check_type(int, max_side, "max_side")
order_check("dims", 0, min_dims, max_dims)
order_check("side", 0, min_side, max_side)
if strict_check:
dims = max_dims
bound_name = "max_dims"
else:
dims = min_dims
bound_name = "min_dims"
# check for unsatisfiable min_side
if not all(min_side <= s for s in shape[::-1][:dims] if s != 1):
raise InvalidArgument(
f"Given shape={shape}, there are no broadcast-compatible "
f"shapes that satisfy: {bound_name}={dims} and min_side={min_side}"
)
# check for unsatisfiable [min_side, max_side]
if not (
min_side <= 1 <= max_side or all(s <= max_side for s in shape[::-1][:dims])
):
raise InvalidArgument(
f"Given base_shape={shape}, there are no broadcast-compatible "
f"shapes that satisfy all of {bound_name}={dims}, "
f"min_side={min_side}, and max_side={max_side}"
)
if not strict_check:
# reduce max_dims to exclude unsatisfiable dimensions
for n, s in zip(range(max_dims), shape[::-1]):
if s < min_side and s != 1:
max_dims = n
break
elif not (min_side <= 1 <= max_side or s <= max_side):
max_dims = n
break
return MutuallyBroadcastableShapesStrategy(
num_shapes=1,
base_shape=shape,
min_dims=min_dims,
max_dims=max_dims,
min_side=min_side,
max_side=max_side,
).map(lambda x: x.input_shapes[0])
# See https://numpy.org/doc/stable/reference/c-api/generalized-ufuncs.html
# Implementation based on numpy.lib.function_base._parse_gufunc_signature
# with minor upgrades to handle numeric and optional dimensions. Examples:
#
# add (),()->() binary ufunc
# sum1d (i)->() reduction
# inner1d (i),(i)->() vector-vector multiplication
# matmat (m,n),(n,p)->(m,p) matrix multiplication
# vecmat (n),(n,p)->(p) vector-matrix multiplication
# matvec (m,n),(n)->(m) matrix-vector multiplication
# matmul (m?,n),(n,p?)->(m?,p?) combination of the four above
# cross1d (3),(3)->(3) cross product with frozen dimensions
#
# Note that while no examples of such usage are given, Numpy does allow
# generalised ufuncs that have *multiple output arrays*. This is not
# currently supported by Hypothesis - please contact us if you would use it!
#
# We are unsure if gufuncs allow frozen dimensions to be optional, but it's
# easy enough to support here - and so we will unless we learn otherwise.
_DIMENSION = r"\w+\??" # Note that \w permits digits too!
_SHAPE = r"\((?:{0}(?:,{0})".format(_DIMENSION) + r"{0,31})?\)"
_ARGUMENT_LIST = "{0}(?:,{0})*".format(_SHAPE)
_SIGNATURE = fr"^{_ARGUMENT_LIST}->{_SHAPE}$"
_SIGNATURE_MULTIPLE_OUTPUT = r"^{0}->{0}$".format(_ARGUMENT_LIST)
class _GUfuncSig(NamedTuple):
input_shapes: Tuple[Shape, ...]
result_shape: Shape
def _hypothesis_parse_gufunc_signature(signature, all_checks=True):
# Disable all_checks to better match the Numpy version, for testing
if not re.match(_SIGNATURE, signature):
if re.match(_SIGNATURE_MULTIPLE_OUTPUT, signature):
raise InvalidArgument(
"Hypothesis does not yet support generalised ufunc signatures "
"with multiple output arrays - mostly because we don't know of "
"anyone who uses them! Please get in touch with us to fix that."
f"\n (signature={signature!r})"
)
if re.match(
(
# Taken from np.lib.function_base._SIGNATURE
r"^\((?:\w+(?:,\w+)*)?\)(?:,\((?:\w+(?:,\w+)*)?\))*->"
r"\((?:\w+(?:,\w+)*)?\)(?:,\((?:\w+(?:,\w+)*)?\))*$"
),
signature,
):
raise InvalidArgument(
f"signature={signature!r} matches Numpy's regex for gufunc signatures, "
f"but contains shapes with more than {NDIM_MAX} dimensions and is thus invalid."
)
raise InvalidArgument(f"{signature!r} is not a valid gufunc signature")
input_shapes, output_shapes = (
tuple(tuple(re.findall(_DIMENSION, a)) for a in re.findall(_SHAPE, arg_list))
for arg_list in signature.split("->")
)
assert len(output_shapes) == 1
result_shape = output_shapes[0]
if all_checks:
# Check that there are no names in output shape that do not appear in inputs.
# (kept out of parser function for easier generation of test values)
# We also disallow frozen optional dimensions - this is ambiguous as there is
# no way to share an un-named dimension between shapes. Maybe just padding?
# Anyway, we disallow it pending clarification from upstream.
frozen_optional_err = (
"Got dimension %r, but handling of frozen optional dimensions "
"is ambiguous. If you known how this should work, please "
"contact us to get this fixed and documented (signature=%r)."
)
only_out_err = (
"The %r dimension only appears in the output shape, and is "
"not frozen, so the size is not determined (signature=%r)."
)
names_in = {n.strip("?") for shp in input_shapes for n in shp}
names_out = {n.strip("?") for n in result_shape}
for shape in input_shapes + (result_shape,):
for name in shape:
try:
int(name.strip("?"))
if "?" in name:
raise InvalidArgument(frozen_optional_err % (name, signature))
except ValueError:
if name.strip("?") in (names_out - names_in):
raise InvalidArgument(
only_out_err % (name, signature)
) from None
return _GUfuncSig(input_shapes=input_shapes, result_shape=result_shape)
[docs]@defines_strategy()
def mutually_broadcastable_shapes(
*,
num_shapes: Union[UniqueIdentifier, int] = not_set,
signature: Union[UniqueIdentifier, str] = not_set,
base_shape: Shape = (),
min_dims: int = 0,
max_dims: Optional[int] = None,
min_side: int = 1,
max_side: Optional[int] = None,
) -> st.SearchStrategy[BroadcastableShapes]:
"""Return a strategy for a specified number of shapes N that are
mutually-broadcastable with one another and with the provided base shape.
* ``num_shapes`` is the number of mutually broadcast-compatible shapes to generate.
* ``base_shape`` is the shape against which all generated shapes can broadcast.
The default shape is empty, which corresponds to a scalar and thus does
not constrain broadcasting at all.
* ``shape`` is a tuple of integers.
* ``min_dims`` is the smallest length that the generated shape can possess.
* ``max_dims`` is the largest length that the generated shape can possess,
defaulting to ``max(len(shape), min_dims) + 2``.
* ``min_side`` is the smallest size that an unaligned dimension can possess.
* ``max_side`` is the largest size that an unaligned dimension can possess,
defaulting to 2 plus the size of the largest aligned dimension.
The strategy will generate a :obj:`python:typing.NamedTuple` containing:
* ``input_shapes`` as a tuple of the N generated shapes.
* ``result_shape`` as the resulting shape produced by broadcasting the N shapes
with the base shape.
The following are some examples drawn from this strategy.
.. code-block:: pycon
>>> # Draw three shapes where each shape is broadcast-compatible with (2, 3)
... strat = mutually_broadcastable_shapes(num_shapes=3, base_shape=(2, 3))
>>> for _ in range(5):
... print(strat.example())
BroadcastableShapes(input_shapes=((4, 1, 3), (4, 2, 3), ()), result_shape=(4, 2, 3))
BroadcastableShapes(input_shapes=((3,), (1, 3), (2, 3)), result_shape=(2, 3))
BroadcastableShapes(input_shapes=((), (), ()), result_shape=(2, 3))
BroadcastableShapes(input_shapes=((3,), (), (3,)), result_shape=(2, 3))
BroadcastableShapes(input_shapes=((1, 2, 3), (3,), ()), result_shape=(1, 2, 3))
"""
arg_msg = "Pass either the `num_shapes` or the `signature` argument, but not both."
if num_shapes is not not_set:
check_argument(signature is not_set, arg_msg)
check_type(int, num_shapes, "num_shapes")
assert isinstance(num_shapes, int) # for mypy
parsed_signature = None
sig_dims = 0
else:
check_argument(signature is not not_set, arg_msg)
if signature is None:
raise InvalidArgument(
"Expected a string, but got invalid signature=None. "
"(maybe .signature attribute of an element-wise ufunc?)"
)
check_type(str, signature, "signature")
parsed_signature = _hypothesis_parse_gufunc_signature(signature)
all_shapes = parsed_signature.input_shapes + (parsed_signature.result_shape,)
sig_dims = min(len(s) for s in all_shapes)
num_shapes = len(parsed_signature.input_shapes)
if num_shapes < 1:
raise InvalidArgument(f"num_shapes={num_shapes} must be at least 1")
check_type(tuple, base_shape, "base_shape")
check_type(int, min_side, "min_side")
check_type(int, min_dims, "min_dims")
check_valid_dims(min_dims, "min_dims")
strict_check = max_dims is not None
if max_dims is None:
max_dims = min(max(len(base_shape), min_dims) + 2, NDIM_MAX - sig_dims)
check_type(int, max_dims, "max_dims")
check_valid_dims(max_dims, "max_dims")
if max_side is None:
max_side = max(base_shape[-max_dims:] + (min_side,)) + 2
check_type(int, max_side, "max_side")
order_check("dims", 0, min_dims, max_dims)
order_check("side", 0, min_side, max_side)
if signature is not None and max_dims > NDIM_MAX - sig_dims:
raise InvalidArgument(
f"max_dims={signature!r} would exceed the {NDIM_MAX}-dimension"
"limit Hypothesis imposes on array shapes, "
f"given signature={parsed_signature!r}"
)
if strict_check:
dims = max_dims
bound_name = "max_dims"
else:
dims = min_dims
bound_name = "min_dims"
# check for unsatisfiable min_side
if not all(min_side <= s for s in base_shape[::-1][:dims] if s != 1):
raise InvalidArgument(
f"Given base_shape={base_shape}, there are no broadcast-compatible "
f"shapes that satisfy: {bound_name}={dims} and min_side={min_side}"
)
# check for unsatisfiable [min_side, max_side]
if not (
min_side <= 1 <= max_side or all(s <= max_side for s in base_shape[::-1][:dims])
):
raise InvalidArgument(
f"Given base_shape={base_shape}, there are no broadcast-compatible "
f"shapes that satisfy all of {bound_name}={dims}, "
f"min_side={min_side}, and max_side={max_side}"
)
if not strict_check:
# reduce max_dims to exclude unsatisfiable dimensions
for n, s in zip(range(max_dims), base_shape[::-1]):
if s < min_side and s != 1:
max_dims = n
break
elif not (min_side <= 1 <= max_side or s <= max_side):
max_dims = n
break
return MutuallyBroadcastableShapesStrategy(
num_shapes=num_shapes,
signature=parsed_signature,
base_shape=base_shape,
min_dims=min_dims,
max_dims=max_dims,
min_side=min_side,
max_side=max_side,
)
class MutuallyBroadcastableShapesStrategy(st.SearchStrategy):
def __init__(
self,
num_shapes,
signature=None,
base_shape=(),
min_dims=0,
max_dims=None,
min_side=1,
max_side=None,
):
super().__init__()
self.base_shape = base_shape
self.side_strat = st.integers(min_side, max_side)
self.num_shapes = num_shapes
self.signature = signature
self.min_dims = min_dims
self.max_dims = max_dims
self.min_side = min_side
self.max_side = max_side
self.size_one_allowed = self.min_side <= 1 <= self.max_side
def do_draw(self, data):
# We don't usually have a gufunc signature; do the common case first & fast.
if self.signature is None:
return self._draw_loop_dimensions(data)
# When we *do*, draw the core dims, then draw loop dims, and finally combine.
core_in, core_res = self._draw_core_dimensions(data)
# If some core shape has omitted optional dimensions, it's an error to add
# loop dimensions to it. We never omit core dims if min_dims >= 1.
# This ensures that we respect Numpy's gufunc broadcasting semantics and user
# constraints without needing to check whether the loop dims will be
# interpreted as an invalid substitute for the omitted core dims.
# We may implement this check later!
use = [None not in shp for shp in core_in]
loop_in, loop_res = self._draw_loop_dimensions(data, use=use)
def add_shape(loop, core):
return tuple(x for x in (loop + core)[-NDIM_MAX:] if x is not None)
return BroadcastableShapes(
input_shapes=tuple(add_shape(l_in, c) for l_in, c in zip(loop_in, core_in)),
result_shape=add_shape(loop_res, core_res),
)
def _draw_core_dimensions(self, data):
# Draw gufunc core dimensions, with None standing for optional dimensions
# that will not be present in the final shape. We track omitted dims so
# that we can do an accurate per-shape length cap.
dims = {}
shapes = []
for shape in self.signature.input_shapes + (self.signature.result_shape,):
shapes.append([])
for name in shape:
if name.isdigit():
shapes[-1].append(int(name))
continue
if name not in dims:
dim = name.strip("?")
dims[dim] = data.draw(self.side_strat)
if self.min_dims == 0 and not data.draw_bits(3):
dims[dim + "?"] = None
else:
dims[dim + "?"] = dims[dim]
shapes[-1].append(dims[name])
return tuple(tuple(s) for s in shapes[:-1]), tuple(shapes[-1])
def _draw_loop_dimensions(self, data, use=None):
# All shapes are handled in column-major order; i.e. they are reversed
base_shape = self.base_shape[::-1]
result_shape = list(base_shape)
shapes = [[] for _ in range(self.num_shapes)]
if use is None:
use = [True for _ in range(self.num_shapes)]
else:
assert len(use) == self.num_shapes
assert all(isinstance(x, bool) for x in use)
for dim_count in range(1, self.max_dims + 1):
dim = dim_count - 1
# We begin by drawing a valid dimension-size for the given
# dimension. This restricts the variability across the shapes
# at this dimension such that they can only choose between
# this size and a singleton dimension.
if len(base_shape) < dim_count or base_shape[dim] == 1:
# dim is unrestricted by the base-shape: shrink to min_side
dim_side = data.draw(self.side_strat)
elif base_shape[dim] <= self.max_side:
# dim is aligned with non-singleton base-dim
dim_side = base_shape[dim]
else:
# only a singleton is valid in alignment with the base-dim
dim_side = 1
for shape_id, shape in enumerate(shapes):
# Populating this dimension-size for each shape, either
# the drawn size is used or, if permitted, a singleton
# dimension.
if dim_count <= len(base_shape) and self.size_one_allowed:
# aligned: shrink towards size 1
side = data.draw(st.sampled_from([1, dim_side]))
else:
side = dim_side
# Use a trick where where a biased coin is queried to see
# if the given shape-tuple will continue to be grown. All
# of the relevant draws will still be made for the given
# shape-tuple even if it is no longer being added to.
# This helps to ensure more stable shrinking behavior.
if self.min_dims < dim_count:
use[shape_id] &= cu.biased_coin(
data, 1 - 1 / (1 + self.max_dims - dim)
)
if use[shape_id]:
shape.append(side)
if len(result_shape) < len(shape):
result_shape.append(shape[-1])
elif shape[-1] != 1 and result_shape[dim] == 1:
result_shape[dim] = shape[-1]
if not any(use):
break
result_shape = result_shape[: max(map(len, [self.base_shape] + shapes))]
assert len(shapes) == self.num_shapes
assert all(self.min_dims <= len(s) <= self.max_dims for s in shapes)
assert all(self.min_side <= s <= self.max_side for side in shapes for s in side)
return BroadcastableShapes(
input_shapes=tuple(tuple(reversed(shape)) for shape in shapes),
result_shape=tuple(reversed(result_shape)),
)
class BasicIndexStrategy(st.SearchStrategy):
def __init__(self, shape, min_dims, max_dims, allow_ellipsis, allow_newaxis):
self.shape = shape
self.min_dims = min_dims
self.max_dims = max_dims
self.allow_ellipsis = allow_ellipsis
self.allow_newaxis = allow_newaxis
def do_draw(self, data):
# General plan: determine the actual selection up front with a straightforward
# approach that shrinks well, then complicate it by inserting other things.
result = []
for dim_size in self.shape:
if dim_size == 0:
result.append(slice(None))
continue
strategy = st.integers(-dim_size, dim_size - 1) | st.slices(dim_size)
result.append(data.draw(strategy))
# Insert some number of new size-one dimensions if allowed
result_dims = sum(isinstance(idx, slice) for idx in result)
while (
self.allow_newaxis
and result_dims < self.max_dims
and (result_dims < self.min_dims or data.draw(st.booleans()))
):
i = data.draw(st.integers(0, len(result)))
result.insert(i, None) # Note that `np.newaxis is None`
result_dims += 1
# Check that we'll have the right number of dimensions; reject if not.
# It's easy to do this by construction if you don't care about shrinking,
# which is really important for array shapes. So we filter instead.
assume(self.min_dims <= result_dims <= self.max_dims)
# This is a quick-and-dirty way to insert ..., xor shorten the indexer,
# but it means we don't have to do any structural analysis.
if self.allow_ellipsis and data.draw(st.booleans()):
# Choose an index; then replace all adjacent whole-dimension slices.
i = j = data.draw(st.integers(0, len(result)))
while i > 0 and result[i - 1] == slice(None):
i -= 1
while j < len(result) and result[j] == slice(None):
j += 1
result[i:j] = [Ellipsis]
else:
while result[-1:] == [slice(None, None)] and data.draw(st.integers(0, 7)):
result.pop()
if len(result) == 1 and data.draw(st.booleans()):
# Sometimes generate bare element equivalent to a length-one tuple
return result[0]
return tuple(result)
```