# mypy: allow-untyped-defs from __future__ import annotations from collections.abc import Collection from collections.abc import Mapping from collections.abc import Sequence from collections.abc import Sized from decimal import Decimal import math from numbers import Complex import pprint import sys from typing import Any from typing import TYPE_CHECKING if TYPE_CHECKING: from numpy import ndarray def _compare_approx( full_object: object, message_data: Sequence[tuple[str, str, str]], number_of_elements: int, different_ids: Sequence[object], max_abs_diff: float, max_rel_diff: float, ) -> list[str]: message_list = list(message_data) message_list.insert(0, ("Index", "Obtained", "Expected")) max_sizes = [0, 0, 0] for index, obtained, expected in message_list: max_sizes[0] = max(max_sizes[0], len(index)) max_sizes[1] = max(max_sizes[1], len(obtained)) max_sizes[2] = max(max_sizes[2], len(expected)) explanation = [ f"comparison failed. Mismatched elements: {len(different_ids)} / {number_of_elements}:", f"Max absolute difference: {max_abs_diff}", f"Max relative difference: {max_rel_diff}", ] + [ f"{indexes:<{max_sizes[0]}} | {obtained:<{max_sizes[1]}} | {expected:<{max_sizes[2]}}" for indexes, obtained, expected in message_list ] return explanation # builtin pytest.approx helper class ApproxBase: """Provide shared utilities for making approximate comparisons between numbers or sequences of numbers.""" # Tell numpy to use our `__eq__` operator instead of its. __array_ufunc__ = None __array_priority__ = 100 def __init__(self, expected, rel=None, abs=None, nan_ok: bool = False) -> None: __tracebackhide__ = True self.expected = expected self.abs = abs self.rel = rel self.nan_ok = nan_ok self._check_type() def __repr__(self) -> str: raise NotImplementedError def _repr_compare(self, other_side: Any) -> list[str]: return [ "comparison failed", f"Obtained: {other_side}", f"Expected: {self}", ] def __eq__(self, actual) -> bool: return all( a == self._approx_scalar(x) for a, x in self._yield_comparisons(actual) ) def __bool__(self): __tracebackhide__ = True raise AssertionError( "approx() is not supported in a boolean context.\nDid you mean: `assert a == approx(b)`?" ) # Ignore type because of https://github.com/python/mypy/issues/4266. __hash__ = None # type: ignore def __ne__(self, actual) -> bool: return not (actual == self) def _approx_scalar(self, x) -> ApproxScalar: if isinstance(x, Decimal): return ApproxDecimal(x, rel=self.rel, abs=self.abs, nan_ok=self.nan_ok) return ApproxScalar(x, rel=self.rel, abs=self.abs, nan_ok=self.nan_ok) def _yield_comparisons(self, actual): """Yield all the pairs of numbers to be compared. This is used to implement the `__eq__` method. """ raise NotImplementedError def _check_type(self) -> None: """Raise a TypeError if the expected value is not a valid type.""" # This is only a concern if the expected value is a sequence. In every # other case, the approx() function ensures that the expected value has # a numeric type. For this reason, the default is to do nothing. The # classes that deal with sequences should reimplement this method to # raise if there are any non-numeric elements in the sequence. def _recursive_sequence_map(f, x): """Recursively map a function over a sequence of arbitrary depth""" if isinstance(x, (list, tuple)): seq_type = type(x) return seq_type(_recursive_sequence_map(f, xi) for xi in x) elif _is_sequence_like(x): return [_recursive_sequence_map(f, xi) for xi in x] else: return f(x) class ApproxNumpy(ApproxBase): """Perform approximate comparisons where the expected value is numpy array.""" def __repr__(self) -> str: list_scalars = _recursive_sequence_map( self._approx_scalar, self.expected.tolist() ) return f"approx({list_scalars!r})" def _repr_compare(self, other_side: ndarray | list[Any]) -> list[str]: import itertools import math def get_value_from_nested_list( nested_list: list[Any], nd_index: tuple[Any, ...] ) -> Any: """ Helper function to get the value out of a nested list, given an n-dimensional index. This mimics numpy's indexing, but for raw nested python lists. """ value: Any = nested_list for i in nd_index: value = value[i] return value np_array_shape = self.expected.shape approx_side_as_seq = _recursive_sequence_map( self._approx_scalar, self.expected.tolist() ) # convert other_side to numpy array to ensure shape attribute is available other_side_as_array = _as_numpy_array(other_side) assert other_side_as_array is not None if np_array_shape != other_side_as_array.shape: return [ "Impossible to compare arrays with different shapes.", f"Shapes: {np_array_shape} and {other_side_as_array.shape}", ] number_of_elements = self.expected.size max_abs_diff = -math.inf max_rel_diff = -math.inf different_ids = [] for index in itertools.product(*(range(i) for i in np_array_shape)): approx_value = get_value_from_nested_list(approx_side_as_seq, index) other_value = get_value_from_nested_list(other_side_as_array, index) if approx_value != other_value: abs_diff = abs(approx_value.expected - other_value) max_abs_diff = max(max_abs_diff, abs_diff) if other_value == 0.0: max_rel_diff = math.inf else: max_rel_diff = max(max_rel_diff, abs_diff / abs(other_value)) different_ids.append(index) message_data = [ ( str(index), str(get_value_from_nested_list(other_side_as_array, index)), str(get_value_from_nested_list(approx_side_as_seq, index)), ) for index in different_ids ] return _compare_approx( self.expected, message_data, number_of_elements, different_ids, max_abs_diff, max_rel_diff, ) def __eq__(self, actual) -> bool: import numpy as np # self.expected is supposed to always be an array here. if not np.isscalar(actual): try: actual = np.asarray(actual) except Exception as e: raise TypeError(f"cannot compare '{actual}' to numpy.ndarray") from e if not np.isscalar(actual) and actual.shape != self.expected.shape: return False return super().__eq__(actual) def _yield_comparisons(self, actual): import numpy as np # `actual` can either be a numpy array or a scalar, it is treated in # `__eq__` before being passed to `ApproxBase.__eq__`, which is the # only method that calls this one. if np.isscalar(actual): for i in np.ndindex(self.expected.shape): yield actual, self.expected[i].item() else: for i in np.ndindex(self.expected.shape): yield actual[i].item(), self.expected[i].item() class ApproxMapping(ApproxBase): """Perform approximate comparisons where the expected value is a mapping with numeric values (the keys can be anything).""" def __repr__(self) -> str: return f"approx({ ({k: self._approx_scalar(v) for k, v in self.expected.items()})!r})" def _repr_compare(self, other_side: Mapping[object, float]) -> list[str]: import math approx_side_as_map = { k: self._approx_scalar(v) for k, v in self.expected.items() } number_of_elements = len(approx_side_as_map) max_abs_diff = -math.inf max_rel_diff = -math.inf different_ids = [] for (approx_key, approx_value), other_value in zip( approx_side_as_map.items(), other_side.values() ): if approx_value != other_value: if approx_value.expected is not None and other_value is not None: try: max_abs_diff = max( max_abs_diff, abs(approx_value.expected - other_value) ) if approx_value.expected == 0.0: max_rel_diff = math.inf else: max_rel_diff = max( max_rel_diff, abs( (approx_value.expected - other_value) / approx_value.expected ), ) except ZeroDivisionError: pass different_ids.append(approx_key) message_data = [ (str(key), str(other_side[key]), str(approx_side_as_map[key])) for key in different_ids ] return _compare_approx( self.expected, message_data, number_of_elements, different_ids, max_abs_diff, max_rel_diff, ) def __eq__(self, actual) -> bool: try: if set(actual.keys()) != set(self.expected.keys()): return False except AttributeError: return False return super().__eq__(actual) def _yield_comparisons(self, actual): for k in self.expected.keys(): yield actual[k], self.expected[k] def _check_type(self) -> None: __tracebackhide__ = True for key, value in self.expected.items(): if isinstance(value, type(self.expected)): msg = "pytest.approx() does not support nested dictionaries: key={!r} value={!r}\n full mapping={}" raise TypeError(msg.format(key, value, pprint.pformat(self.expected))) class ApproxSequenceLike(ApproxBase): """Perform approximate comparisons where the expected value is a sequence of numbers.""" def __repr__(self) -> str: seq_type = type(self.expected) if seq_type not in (tuple, list): seq_type = list return f"approx({seq_type(self._approx_scalar(x) for x in self.expected)!r})" def _repr_compare(self, other_side: Sequence[float]) -> list[str]: import math if len(self.expected) != len(other_side): return [ "Impossible to compare lists with different sizes.", f"Lengths: {len(self.expected)} and {len(other_side)}", ] approx_side_as_map = _recursive_sequence_map(self._approx_scalar, self.expected) number_of_elements = len(approx_side_as_map) max_abs_diff = -math.inf max_rel_diff = -math.inf different_ids = [] for i, (approx_value, other_value) in enumerate( zip(approx_side_as_map, other_side) ): if approx_value != other_value: try: abs_diff = abs(approx_value.expected - other_value) max_abs_diff = max(max_abs_diff, abs_diff) # Ignore non-numbers for the diff calculations (#13012). except TypeError: pass else: if other_value == 0.0: max_rel_diff = math.inf else: max_rel_diff = max(max_rel_diff, abs_diff / abs(other_value)) different_ids.append(i) message_data = [ (str(i), str(other_side[i]), str(approx_side_as_map[i])) for i in different_ids ] return _compare_approx( self.expected, message_data, number_of_elements, different_ids, max_abs_diff, max_rel_diff, ) def __eq__(self, actual) -> bool: try: if len(actual) != len(self.expected): return False except TypeError: return False return super().__eq__(actual) def _yield_comparisons(self, actual): return zip(actual, self.expected) def _check_type(self) -> None: __tracebackhide__ = True for index, x in enumerate(self.expected): if isinstance(x, type(self.expected)): msg = "pytest.approx() does not support nested data structures: {!r} at index {}\n full sequence: {}" raise TypeError(msg.format(x, index, pprint.pformat(self.expected))) class ApproxScalar(ApproxBase): """Perform approximate comparisons where the expected value is a single number.""" # Using Real should be better than this Union, but not possible yet: # https://github.com/python/typeshed/pull/3108 DEFAULT_ABSOLUTE_TOLERANCE: float | Decimal = 1e-12 DEFAULT_RELATIVE_TOLERANCE: float | Decimal = 1e-6 def __repr__(self) -> str: """Return a string communicating both the expected value and the tolerance for the comparison being made. For example, ``1.0 ± 1e-6``, ``(3+4j) ± 5e-6 ∠ ±180°``. """ # Don't show a tolerance for values that aren't compared using # tolerances, i.e. non-numerics and infinities. Need to call abs to # handle complex numbers, e.g. (inf + 1j). if ( isinstance(self.expected, bool) or (not isinstance(self.expected, (Complex, Decimal))) or math.isinf(abs(self.expected) or isinstance(self.expected, bool)) ): return str(self.expected) # If a sensible tolerance can't be calculated, self.tolerance will # raise a ValueError. In this case, display '???'. try: if 1e-3 <= self.tolerance < 1e3: vetted_tolerance = f"{self.tolerance:n}" else: vetted_tolerance = f"{self.tolerance:.1e}" if ( isinstance(self.expected, Complex) and self.expected.imag and not math.isinf(self.tolerance) ): vetted_tolerance += " ∠ ±180°" except ValueError: vetted_tolerance = "???" return f"{self.expected} ± {vetted_tolerance}" def __eq__(self, actual) -> bool: """Return whether the given value is equal to the expected value within the pre-specified tolerance.""" def is_bool(val: Any) -> bool: # Check if `val` is a native bool or numpy bool. if isinstance(val, bool): return True if np := sys.modules.get("numpy"): return isinstance(val, np.bool_) return False asarray = _as_numpy_array(actual) if asarray is not None: # Call ``__eq__()`` manually to prevent infinite-recursion with # numpy<1.13. See #3748. return all(self.__eq__(a) for a in asarray.flat) # Short-circuit exact equality, except for bool and np.bool_ if is_bool(self.expected) and not is_bool(actual): return False elif actual == self.expected: return True # If either type is non-numeric, fall back to strict equality. # NB: we need Complex, rather than just Number, to ensure that __abs__, # __sub__, and __float__ are defined. Also, consider bool to be # non-numeric, even though it has the required arithmetic. if is_bool(self.expected) or not ( isinstance(self.expected, (Complex, Decimal)) and isinstance(actual, (Complex, Decimal)) ): return False # Allow the user to control whether NaNs are considered equal to each # other or not. The abs() calls are for compatibility with complex # numbers. if math.isnan(abs(self.expected)): return self.nan_ok and math.isnan(abs(actual)) # Infinity shouldn't be approximately equal to anything but itself, but # if there's a relative tolerance, it will be infinite and infinity # will seem approximately equal to everything. The equal-to-itself # case would have been short circuited above, so here we can just # return false if the expected value is infinite. The abs() call is # for compatibility with complex numbers. if math.isinf(abs(self.expected)): return False # Return true if the two numbers are within the tolerance. result: bool = abs(self.expected - actual) <= self.tolerance return result __hash__ = None @property def tolerance(self): """Return the tolerance for the comparison. This could be either an absolute tolerance or a relative tolerance, depending on what the user specified or which would be larger. """ def set_default(x, default): return x if x is not None else default # Figure out what the absolute tolerance should be. ``self.abs`` is # either None or a value specified by the user. absolute_tolerance = set_default(self.abs, self.DEFAULT_ABSOLUTE_TOLERANCE) if absolute_tolerance < 0: raise ValueError( f"absolute tolerance can't be negative: {absolute_tolerance}" ) if math.isnan(absolute_tolerance): raise ValueError("absolute tolerance can't be NaN.") # If the user specified an absolute tolerance but not a relative one, # just return the absolute tolerance. if self.rel is None: if self.abs is not None: return absolute_tolerance # Figure out what the relative tolerance should be. ``self.rel`` is # either None or a value specified by the user. This is done after # we've made sure the user didn't ask for an absolute tolerance only, # because we don't want to raise errors about the relative tolerance if # we aren't even going to use it. relative_tolerance = set_default( self.rel, self.DEFAULT_RELATIVE_TOLERANCE ) * abs(self.expected) if relative_tolerance < 0: raise ValueError( f"relative tolerance can't be negative: {relative_tolerance}" ) if math.isnan(relative_tolerance): raise ValueError("relative tolerance can't be NaN.") # Return the larger of the relative and absolute tolerances. return max(relative_tolerance, absolute_tolerance) class ApproxDecimal(ApproxScalar): """Perform approximate comparisons where the expected value is a Decimal.""" DEFAULT_ABSOLUTE_TOLERANCE = Decimal("1e-12") DEFAULT_RELATIVE_TOLERANCE = Decimal("1e-6") def __repr__(self) -> str: if isinstance(self.rel, float): rel = Decimal.from_float(self.rel) else: rel = self.rel if isinstance(self.abs, float): abs_ = Decimal.from_float(self.abs) else: abs_ = self.abs tol_str = "???" if rel is not None and Decimal("1e-3") <= rel <= Decimal("1e3"): tol_str = f"{rel:.1e}" elif abs_ is not None: tol_str = f"{abs_:.1e}" return f"{self.expected} ± {tol_str}" [docs] def approx(expected, rel=None, abs=None, nan_ok: bool = False) -> ApproxBase: """Assert that two numbers (or two ordered sequences of numbers) are equal to each other within some tolerance. Due to the :doc:`python:tutorial/floatingpoint`, numbers that we would intuitively expect to be equal are not always so:: >>> 0.1 + 0.2 == 0.3 False This problem is commonly encountered when writing tests, e.g. when making sure that floating-point values are what you expect them to be. One way to deal with this problem is to assert that two floating-point numbers are equal to within some appropriate tolerance:: >>> abs((0.1 + 0.2) - 0.3) < 1e-6 True However, comparisons like this are tedious to write and difficult to understand. Furthermore, absolute comparisons like the one above are usually discouraged because there's no tolerance that works well for all situations. ``1e-6`` is good for numbers around ``1``, but too small for very big numbers and too big for very small ones. It's better to express the tolerance as a fraction of the expected value, but relative comparisons like that are even more difficult to write correctly and concisely. The ``approx`` class performs floating-point comparisons using a syntax that's as intuitive as possible:: >>> from pytest import approx >>> 0.1 + 0.2 == approx(0.3) True The same syntax also works for ordered sequences of numbers:: >>> (0.1 + 0.2, 0.2 + 0.4) == approx((0.3, 0.6)) True ``numpy`` arrays:: >>> import numpy as np # doctest: +SKIP >>> np.array([0.1, 0.2]) + np.array([0.2, 0.4]) == approx(np.array([0.3, 0.6])) # doctest: +SKIP True And for a ``numpy`` array against a scalar:: >>> import numpy as np # doctest: +SKIP >>> np.array([0.1, 0.2]) + np.array([0.2, 0.1]) == approx(0.3) # doctest: +SKIP True Only ordered sequences are supported, because ``approx`` needs to infer the relative position of the sequences without ambiguity. This means ``sets`` and other unordered sequences are not supported. Finally, dictionary *values* can also be compared:: >>> {'a': 0.1 + 0.2, 'b': 0.2 + 0.4} == approx({'a': 0.3, 'b': 0.6}) True The comparison will be true if both mappings have the same keys and their respective values match the expected tolerances. **Tolerances** By default, ``approx`` considers numbers within a relative tolerance of ``1e-6`` (i.e. one part in a million) of its expected value to be equal. This treatment would lead to surprising results if the expected value was ``0.0``, because nothing but ``0.0`` itself is relatively close to ``0.0``. To handle this case less surprisingly, ``approx`` also considers numbers within an absolute tolerance of ``1e-12`` of its expected value to be equal. Infinity and NaN are special cases. Infinity is only considered equal to itself, regardless of the relative tolerance. NaN is not considered equal to anything by default, but you can make it be equal to itself by setting the ``nan_ok`` argument to True. (This is meant to facilitate comparing arrays that use NaN to mean "no data".) Both the relative and absolute tolerances can be changed by passing arguments to the ``approx`` constructor:: >>> 1.0001 == approx(1) False >>> 1.0001 == approx(1, rel=1e-3) True >>> 1.0001 == approx(1, abs=1e-3) True If you specify ``abs`` but not ``rel``, the comparison will not consider the relative tolerance at all. In other words, two numbers that are within the default relative tolerance of ``1e-6`` will still be considered unequal if they exceed the specified absolute tolerance. If you specify both ``abs`` and ``rel``, the numbers will be considered equal if either tolerance is met:: >>> 1 + 1e-8 == approx(1) True >>> 1 + 1e-8 == approx(1, abs=1e-12) False >>> 1 + 1e-8 == approx(1, rel=1e-6, abs=1e-12) True **Non-numeric types** You can also use ``approx`` to compare non-numeric types, or dicts and sequences containing non-numeric types, in which case it falls back to strict equality. This can be useful for comparing dicts and sequences that can contain optional values:: >>> {"required": 1.0000005, "optional": None} == approx({"required": 1, "optional": None}) True >>> [None, 1.0000005] == approx([None,1]) True >>> ["foo", 1.0000005] == approx([None,1]) False If you're thinking about using ``approx``, then you might want to know how it compares to other good ways of comparing floating-point numbers. All of these algorithms are based on relative and absolute tolerances and should agree for the most part, but they do have meaningful differences: - ``math.isclose(a, b, rel_tol=1e-9, abs_tol=0.0)``: True if the relative tolerance is met w.r.t. either ``a`` or ``b`` or if the absolute tolerance is met. Because the relative tolerance is calculated w.r.t. both ``a`` and ``b``, this test is symmetric (i.e. neither ``a`` nor ``b`` is a "reference value"). You have to specify an absolute tolerance if you want to compare to ``0.0`` because there is no tolerance by default. More information: :py:func:`math.isclose`. - ``numpy.isclose(a, b, rtol=1e-5, atol=1e-8)``: True if the difference between ``a`` and ``b`` is less that the sum of the relative tolerance w.r.t. ``b`` and the absolute tolerance. Because the relative tolerance is only calculated w.r.t. ``b``, this test is asymmetric and you can think of ``b`` as the reference value. Support for comparing sequences is provided by :py:func:`numpy.allclose`. More information: :std:doc:`numpy:reference/generated/numpy.isclose`. - ``unittest.TestCase.assertAlmostEqual(a, b)``: True if ``a`` and ``b`` are within an absolute tolerance of ``1e-7``. No relative tolerance is considered , so this function is not appropriate for very large or very small numbers. Also, it's only available in subclasses of ``unittest.TestCase`` and it's ugly because it doesn't follow PEP8. More information: :py:meth:`unittest.TestCase.assertAlmostEqual`. - ``a == pytest.approx(b, rel=1e-6, abs=1e-12)``: True if the relative tolerance is met w.r.t. ``b`` or if the absolute tolerance is met. Because the relative tolerance is only calculated w.r.t. ``b``, this test is asymmetric and you can think of ``b`` as the reference value. In the special case that you explicitly specify an absolute tolerance but not a relative tolerance, only the absolute tolerance is considered. .. note:: ``approx`` can handle numpy arrays, but we recommend the specialised test helpers in :std:doc:`numpy:reference/routines.testing` if you need support for comparisons, NaNs, or ULP-based tolerances. To match strings using regex, you can use `Matches <https://github.com/asottile/re-assert#re_assertmatchespattern-str-args-kwargs>`_ from the `re_assert package <https://github.com/asottile/re-assert>`_. .. note:: Unlike built-in equality, this function considers booleans unequal to numeric zero or one. For example:: >>> 1 == approx(True) False .. warning:: .. versionchanged:: 3.2 In order to avoid inconsistent behavior, :py:exc:`TypeError` is raised for ``>``, ``>=``, ``<`` and ``<=`` comparisons. The example below illustrates the problem:: assert approx(0.1) > 0.1 + 1e-10 # calls approx(0.1).__gt__(0.1 + 1e-10) assert 0.1 + 1e-10 > approx(0.1) # calls approx(0.1).__lt__(0.1 + 1e-10) In the second example one expects ``approx(0.1).__le__(0.1 + 1e-10)`` to be called. But instead, ``approx(0.1).__lt__(0.1 + 1e-10)`` is used to comparison. This is because the call hierarchy of rich comparisons follows a fixed behavior. More information: :py:meth:`object.__ge__` .. versionchanged:: 3.7.1 ``approx`` raises ``TypeError`` when it encounters a dict value or sequence element of non-numeric type. .. versionchanged:: 6.1.0 ``approx`` falls back to strict equality for non-numeric types instead of raising ``TypeError``. """ # Delegate the comparison to a class that knows how to deal with the type # of the expected value (e.g. int, float, list, dict, numpy.array, etc). # # The primary responsibility of these classes is to implement ``__eq__()`` # and ``__repr__()``. The former is used to actually check if some # "actual" value is equivalent to the given expected value within the # allowed tolerance. The latter is used to show the user the expected # value and tolerance, in the case that a test failed. # # The actual logic for making approximate comparisons can be found in # ApproxScalar, which is used to compare individual numbers. All of the # other Approx classes eventually delegate to this class. The ApproxBase # class provides some convenient methods and overloads, but isn't really # essential. __tracebackhide__ = True if isinstance(expected, Decimal): cls: type[ApproxBase] = ApproxDecimal elif isinstance(expected, Mapping): cls = ApproxMapping elif _is_numpy_array(expected): expected = _as_numpy_array(expected) cls = ApproxNumpy elif _is_sequence_like(expected): cls = ApproxSequenceLike elif isinstance(expected, Collection) and not isinstance(expected, (str, bytes)): msg = f"pytest.approx() only supports ordered sequences, but got: {expected!r}" raise TypeError(msg) else: cls = ApproxScalar return cls(expected, rel, abs, nan_ok) def _is_sequence_like(expected: object) -> bool: return ( hasattr(expected, "__getitem__") and isinstance(expected, Sized) and not isinstance(expected, (str, bytes)) ) def _is_numpy_array(obj: object) -> bool: """ Return true if the given object is implicitly convertible to ndarray, and numpy is already imported. """ return _as_numpy_array(obj) is not None def _as_numpy_array(obj: object) -> ndarray | None: """ Return an ndarray if the given object is implicitly convertible to ndarray, and numpy is already imported, otherwise None. """ np: Any = sys.modules.get("numpy") if np is not None: # avoid infinite recursion on numpy scalars, which have __array__ if np.isscalar(obj): return None elif isinstance(obj, np.ndarray): return obj elif hasattr(obj, "__array__") or hasattr("obj", "__array_interface__"): return np.asarray(obj) return None
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