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# Source code for torch.testing._comparison

    import abc
    import cmath
    import collections.abc
    import contextlib
    import warnings
    from typing import (
        Any,
        Callable,
        Collection,
        Dict,
        List,
        NoReturn,
        Optional,
        Sequence,
        Tuple,
        Type,
        Union,
    )

    import torch

    try:
        import numpy as np

        NUMPY_AVAILABLE = True
    except ModuleNotFoundError:
        NUMPY_AVAILABLE = False

    class ErrorMeta(Exception):
        """Internal testing exception that makes that carries error metadata."""

        def __init__(
            self, type: Type[Exception], msg: str, *, id: Tuple[Any, ...] = ()
        ) -> None:
            super().__init__(
                "If you are a user and see this message during normal operation "
                "please file an issue at https://github.com/pytorch/pytorch/issues. "
                "If you are a developer and working on the comparison functions, please `raise ErrorMeta().to_error()` "
                "for user facing errors."
            )
            self.type = type
            self.msg = msg
            self.id = id

        def to_error(
            self, msg: Optional[Union[str, Callable[[str], str]]] = None
        ) -> Exception:
            if not isinstance(msg, str):
                generated_msg = self.msg
                if self.id:
                    generated_msg += f"\n\nThe failure occurred for item {''.join(str([item]) for item in self.id)}"

                msg = msg(generated_msg) if callable(msg) else generated_msg

            return self.type(msg)

    # Some analysis of tolerance by logging tests from test_torch.py can be found in
    # https://github.com/pytorch/pytorch/pull/32538.
    # {dtype: (rtol, atol)}
    _DTYPE_PRECISIONS = {
        torch.float16: (0.001, 1e-5),
        torch.bfloat16: (0.016, 1e-5),
        torch.float32: (1.3e-6, 1e-5),
        torch.float64: (1e-7, 1e-7),
        torch.complex32: (0.001, 1e-5),
        torch.complex64: (1.3e-6, 1e-5),
        torch.complex128: (1e-7, 1e-7),
    }
    # The default tolerances of torch.float32 are used for quantized dtypes, because quantized tensors are compared in
    # their dequantized and floating point representation. For more details see `TensorLikePair._compare_quantized_values`
    _DTYPE_PRECISIONS.update(
        {
            dtype: _DTYPE_PRECISIONS[torch.float32]
            for dtype in (
                torch.quint8,
                torch.quint2x4,
                torch.quint4x2,
                torch.qint8,
                torch.qint32,
            )
        }
    )

    def default_tolerances(
        *inputs: Union[torch.Tensor, torch.dtype],
        dtype_precisions: Optional[Dict[torch.dtype, Tuple[float, float]]] = None,
    ) -> Tuple[float, float]:
        """Returns the default absolute and relative testing tolerances for a set of inputs based on the dtype.

        See :func:`assert_close` for a table of the default tolerance for each dtype.

        Returns:
            (Tuple[float, float]): Loosest tolerances of all input dtypes.
        """
        dtypes = []
        for input in inputs:
            if isinstance(input, torch.Tensor):
                dtypes.append(input.dtype)
            elif isinstance(input, torch.dtype):
                dtypes.append(input)
            else:
                raise TypeError(
                    f"Expected a torch.Tensor or a torch.dtype, but got {type(input)} instead."
                )
        dtype_precisions = dtype_precisions or _DTYPE_PRECISIONS
        rtols, atols = zip(*[dtype_precisions.get(dtype, (0.0, 0.0)) for dtype in dtypes])
        return max(rtols), max(atols)

    def get_tolerances(
        *inputs: Union[torch.Tensor, torch.dtype],
        rtol: Optional[float],
        atol: Optional[float],
        id: Tuple[Any, ...] = (),
    ) -> Tuple[float, float]:
        """Gets absolute and relative to be used for numeric comparisons.

        If both ``rtol`` and ``atol`` are specified, this is a no-op. If both are not specified, the return value of
        :func:`default_tolerances` is used.

        Raises:
            ErrorMeta: With :class:`ValueError`, if only ``rtol`` or ``atol`` is specified.

        Returns:
            (Tuple[float, float]): Valid absolute and relative tolerances.
        """
        if (rtol is None) ^ (atol is None):
            # We require both tolerance to be omitted or specified, because specifying only one might lead to surprising
            # results. Imagine setting atol=0.0 and the tensors still match because rtol>0.0.
            raise ErrorMeta(
                ValueError,
                f"Both 'rtol' and 'atol' must be either specified or omitted, "
                f"but got no {'rtol' if rtol is None else 'atol'}.",
                id=id,
            )
        elif rtol is not None and atol is not None:
            return rtol, atol
        else:
            return default_tolerances(*inputs)

    def _make_mismatch_msg(
        *,
        default_identifier: str,
        identifier: Optional[Union[str, Callable[[str], str]]] = None,
        extra: Optional[str] = None,
        abs_diff: float,
        abs_diff_idx: Optional[Union[int, Tuple[int, ...]]] = None,
        atol: float,
        rel_diff: float,
        rel_diff_idx: Optional[Union[int, Tuple[int, ...]]] = None,
        rtol: float,
    ) -> str:
        """Makes a mismatch error message for numeric values.

        Args:
            default_identifier (str): Default description of the compared values, e.g. "Tensor-likes".
            identifier (Optional[Union[str, Callable[[str], str]]]): Optional identifier that overrides
                ``default_identifier``. Can be passed as callable in which case it will be called with
                ``default_identifier`` to create the description at runtime.
            extra (Optional[str]): Extra information to be placed after the message header and the mismatch statistics.
            abs_diff (float): Absolute difference.
            abs_diff_idx (Optional[Union[int, Tuple[int, ...]]]): Optional index of the absolute difference.
            atol (float): Allowed absolute tolerance. Will only be added to mismatch statistics if it or ``rtol`` are
                ``> 0``.
            rel_diff (float): Relative difference.
            rel_diff_idx (Optional[Union[int, Tuple[int, ...]]]): Optional index of the relative difference.
            rtol (float): Allowed relative tolerance. Will only be added to mismatch statistics if it or ``atol`` are
                ``> 0``.
        """
        equality = rtol == 0 and atol == 0

        def make_diff_msg(
            *,
            type: str,
            diff: float,
            idx: Optional[Union[int, Tuple[int, ...]]],
            tol: float,
        ) -> str:
            if idx is None:
                msg = f"{type.title()} difference: {diff}"
            else:
                msg = f"Greatest {type} difference: {diff} at index {idx}"
            if not equality:
                msg += f" (up to {tol} allowed)"
            return msg + "\n"

        if identifier is None:
            identifier = default_identifier
        elif callable(identifier):
            identifier = identifier(default_identifier)

        msg = f"{identifier} are not {'equal' if equality else 'close'}!\n\n"

        if extra:
            msg += f"{extra.strip()}\n"

        msg += make_diff_msg(type="absolute", diff=abs_diff, idx=abs_diff_idx, tol=atol)
        msg += make_diff_msg(type="relative", diff=rel_diff, idx=rel_diff_idx, tol=rtol)

        return msg.strip()

    def make_scalar_mismatch_msg(
        actual: Union[bool, int, float, complex],
        expected: Union[bool, int, float, complex],
        *,
        rtol: float,
        atol: float,
        identifier: Optional[Union[str, Callable[[str], str]]] = None,
    ) -> str:
        """Makes a mismatch error message for scalars.

        Args:
            actual (Union[bool, int, float, complex]): Actual scalar.
            expected (Union[bool, int, float, complex]): Expected scalar.
            rtol (float): Relative tolerance.
            atol (float): Absolute tolerance.
            identifier (Optional[Union[str, Callable[[str], str]]]): Optional description for the scalars. Can be passed
                as callable in which case it will be called by the default value to create the description at runtime.
                Defaults to "Scalars".
        """
        abs_diff = abs(actual - expected)
        rel_diff = float("inf") if expected == 0 else abs_diff / abs(expected)
        return _make_mismatch_msg(
            default_identifier="Scalars",
            identifier=identifier,
            extra=f"Expected {expected} but got {actual}.",
            abs_diff=abs_diff,
            atol=atol,
            rel_diff=rel_diff,
            rtol=rtol,
        )

    def make_tensor_mismatch_msg(
        actual: torch.Tensor,
        expected: torch.Tensor,
        matches: torch.Tensor,
        *,
        rtol: float,
        atol: float,
        identifier: Optional[Union[str, Callable[[str], str]]] = None,
    ):
        """Makes a mismatch error message for tensors.

        Args:
            actual (torch.Tensor): Actual tensor.
            expected (torch.Tensor): Expected tensor.
            matches (torch.Tensor): Boolean mask of the same shape as ``actual`` and ``expected`` that indicates the
                location of matches.
            rtol (float): Relative tolerance.
            atol (float): Absolute tolerance.
            identifier (Optional[Union[str, Callable[[str], str]]]): Optional description for the tensors. Can be passed
                as callable in which case it will be called by the default value to create the description at runtime.
                Defaults to "Tensor-likes".
        """

        def unravel_flat_index(flat_index: int) -> Tuple[int, ...]:
            if not matches.shape:
                return ()

            inverse_index = []
            for size in matches.shape[::-1]:
                div, mod = divmod(flat_index, size)
                flat_index = div
                inverse_index.append(mod)

            return tuple(inverse_index[::-1])

        number_of_elements = matches.numel()
        total_mismatches = number_of_elements - int(torch.sum(matches))
        extra = (
            f"Mismatched elements: {total_mismatches} / {number_of_elements} "
            f"({total_mismatches / number_of_elements:.1%})"
        )

        actual_flat = actual.flatten()
        expected_flat = expected.flatten()
        matches_flat = matches.flatten()

        if not actual.dtype.is_floating_point and not actual.dtype.is_complex:
            # TODO: Instead of always upcasting to int64, it would be sufficient to cast to the next higher dtype to avoid
            #  overflow
            actual_flat = actual_flat.to(torch.int64)
            expected_flat = expected_flat.to(torch.int64)

        abs_diff = torch.abs(actual_flat - expected_flat)
        # Ensure that only mismatches are used for the max_abs_diff computation
        abs_diff[matches_flat] = 0
        max_abs_diff, max_abs_diff_flat_idx = torch.max(abs_diff, 0)

        rel_diff = abs_diff / torch.abs(expected_flat)
        # Ensure that only mismatches are used for the max_rel_diff computation
        rel_diff[matches_flat] = 0
        max_rel_diff, max_rel_diff_flat_idx = torch.max(rel_diff, 0)
        return _make_mismatch_msg(
            default_identifier="Tensor-likes",
            identifier=identifier,
            extra=extra,
            abs_diff=max_abs_diff.item(),
            abs_diff_idx=unravel_flat_index(int(max_abs_diff_flat_idx)),
            atol=atol,
            rel_diff=max_rel_diff.item(),
            rel_diff_idx=unravel_flat_index(int(max_rel_diff_flat_idx)),
            rtol=rtol,
        )

    class UnsupportedInputs(Exception):  # noqa: B903
        """Exception to be raised during the construction of a :class:`Pair` in case it doesn't support the inputs."""

    class Pair(abc.ABC):
        """ABC for all comparison pairs to be used in conjunction with :func:`assert_equal`.

        Each subclass needs to overwrite :meth:`Pair.compare` that performs the actual comparison.

        Each pair receives **all** options, so select the ones applicable for the subclass and forward the rest to the
        super class. Raising an :class:`UnsupportedInputs` during constructions indicates that the pair is not able to
        handle the inputs and the next pair type will be tried.

        All other errors should be raised as :class:`ErrorMeta`. After the instantiation, :meth:`Pair._make_error_meta` can
        be used to automatically handle overwriting the message with a user supplied one and id handling.
        """

        def __init__(
            self,
            actual: Any,
            expected: Any,
            *,
            id: Tuple[Any, ...] = (),
            **unknown_parameters: Any,
        ) -> None:
            self.actual = actual
            self.expected = expected
            self.id = id
            self._unknown_parameters = unknown_parameters

        @staticmethod
        def _inputs_not_supported() -> NoReturn:
            raise UnsupportedInputs()

        @staticmethod
        def _check_inputs_isinstance(*inputs: Any, cls: Union[Type, Tuple[Type, ...]]):
            """Checks if all inputs are instances of a given class and raise :class:`UnsupportedInputs` otherwise."""
            if not all(isinstance(input, cls) for input in inputs):
                Pair._inputs_not_supported()

        def _fail(
            self, type: Type[Exception], msg: str, *, id: Tuple[Any, ...] = ()
        ) -> NoReturn:
            """Raises an :class:`ErrorMeta` from a given exception type and message and the stored id.

            .. warning::

                If you use this before the ``super().__init__(...)`` call in the constructor, you have to pass the ``id``
                explicitly.
            """
            raise ErrorMeta(type, msg, id=self.id if not id and hasattr(self, "id") else id)

        @abc.abstractmethod
        def compare(self) -> None:
            """Compares the inputs and raises an :class`ErrorMeta` in case they mismatch."""

        def extra_repr(self) -> Sequence[Union[str, Tuple[str, Any]]]:
            """Returns extra information that will be included in the representation.

            Should be overwritten by all subclasses that use additional options. The representation of the object will only
            be surfaced in case we encounter an unexpected error and thus should help debug the issue. Can be a sequence of
            key-value-pairs or attribute names.
            """
            return []

        def __repr__(self) -> str:
            head = f"{type(self).__name__}("
            tail = ")"
            body = [
                f"    {name}={value!s},"
                for name, value in [
                    ("id", self.id),
                    ("actual", self.actual),
                    ("expected", self.expected),
                    *[
                        (extra, getattr(self, extra)) if isinstance(extra, str) else extra
                        for extra in self.extra_repr()
                    ],
                ]
            ]
            return "\n".join((head, *body, *tail))

    class ObjectPair(Pair):
        """Pair for any type of inputs that will be compared with the `==` operator.

        .. note::

            Since this will instantiate for any kind of inputs, it should only be used as fallback after all other pairs
            couldn't handle the inputs.

        """

        def compare(self) -> None:
            try:
                equal = self.actual == self.expected
            except Exception as error:
                # We are not using `self._raise_error_meta` here since we need the exception chaining
                raise ErrorMeta(
                    ValueError,
                    f"{self.actual} == {self.expected} failed with:\n{error}.",
                    id=self.id,
                ) from error

            if not equal:
                self._fail(AssertionError, f"{self.actual} != {self.expected}")

    class NonePair(Pair):
        """Pair for ``None`` inputs."""

        def __init__(self, actual: Any, expected: Any, **other_parameters: Any) -> None:
            if not (actual is None or expected is None):
                self._inputs_not_supported()

            super().__init__(actual, expected, **other_parameters)

        def compare(self) -> None:
            if not (self.actual is None and self.expected is None):
                self._fail(
                    AssertionError, f"None mismatch: {self.actual} is not {self.expected}"
                )

    class BooleanPair(Pair):
        """Pair for :class:`bool` inputs.

        .. note::

            If ``numpy`` is available, also handles :class:`numpy.bool_` inputs.

        """

        def __init__(
            self,
            actual: Any,
            expected: Any,
            *,
            id: Tuple[Any, ...],
            **other_parameters: Any,
        ) -> None:
            actual, expected = self._process_inputs(actual, expected, id=id)
            super().__init__(actual, expected, **other_parameters)

        @property
        def _supported_types(self) -> Tuple[Type, ...]:
            cls: List[Type] = [bool]
            if NUMPY_AVAILABLE:
                cls.append(np.bool_)
            return tuple(cls)

        def _process_inputs(
            self, actual: Any, expected: Any, *, id: Tuple[Any, ...]
        ) -> Tuple[bool, bool]:
            self._check_inputs_isinstance(actual, expected, cls=self._supported_types)
            actual, expected = (
                self._to_bool(bool_like, id=id) for bool_like in (actual, expected)
            )
            return actual, expected

        def _to_bool(self, bool_like: Any, *, id: Tuple[Any, ...]) -> bool:
            if isinstance(bool_like, bool):
                return bool_like
            elif isinstance(bool_like, np.bool_):
                return bool_like.item()
            else:
                raise ErrorMeta(
                    TypeError, f"Unknown boolean type {type(bool_like)}.", id=id
                )

        def compare(self) -> None:
            if self.actual is not self.expected:
                self._fail(
                    AssertionError,
                    f"Booleans mismatch: {self.actual} is not {self.expected}",
                )

    class NumberPair(Pair):
        """Pair for Python number (:class:`int`, :class:`float`, and :class:`complex`) inputs.

        .. note::

            If ``numpy`` is available, also handles :class:`numpy.number` inputs.

        Kwargs:
            rtol (Optional[float]): Relative tolerance. If specified ``atol`` must also be specified. If omitted, default
                values based on the type are selected with the below table.
            atol (Optional[float]): Absolute tolerance. If specified ``rtol`` must also be specified. If omitted, default
                values based on the type are selected with the below table.
            equal_nan (bool): If ``True``, two ``NaN`` values are considered equal. Defaults to ``False``.
            check_dtype (bool): If ``True``, the type of the inputs will be checked for equality. Defaults to ``False``.

        The following table displays correspondence between Python number type and the ``torch.dtype``'s. See
        :func:`assert_close` for the corresponding tolerances.

        +------------------+-------------------------------+
        | ``type``         | corresponding ``torch.dtype`` |
        +==================+===============================+
        | :class:`int`     | :attr:`~torch.int64`          |
        +------------------+-------------------------------+
        | :class:`float`   | :attr:`~torch.float64`        |
        +------------------+-------------------------------+
        | :class:`complex` | :attr:`~torch.complex64`      |
        +------------------+-------------------------------+
        """

        _TYPE_TO_DTYPE = {
            int: torch.int64,
            float: torch.float64,
            complex: torch.complex128,
        }
        _NUMBER_TYPES = tuple(_TYPE_TO_DTYPE.keys())

        def __init__(
            self,
            actual: Any,
            expected: Any,
            *,
            id: Tuple[Any, ...] = (),
            rtol: Optional[float] = None,
            atol: Optional[float] = None,
            equal_nan: bool = False,
            check_dtype: bool = False,
            **other_parameters: Any,
        ) -> None:
            actual, expected = self._process_inputs(actual, expected, id=id)
            super().__init__(actual, expected, id=id, **other_parameters)

            self.rtol, self.atol = get_tolerances(
                *[self._TYPE_TO_DTYPE[type(input)] for input in (actual, expected)],
                rtol=rtol,
                atol=atol,
                id=id,
            )
            self.equal_nan = equal_nan
            self.check_dtype = check_dtype

        @property
        def _supported_types(self) -> Tuple[Type, ...]:
            cls = list(self._NUMBER_TYPES)
            if NUMPY_AVAILABLE:
                cls.append(np.number)
            return tuple(cls)

        def _process_inputs(
            self, actual: Any, expected: Any, *, id: Tuple[Any, ...]
        ) -> Tuple[Union[int, float, complex], Union[int, float, complex]]:
            self._check_inputs_isinstance(actual, expected, cls=self._supported_types)
            actual, expected = (
                self._to_number(number_like, id=id) for number_like in (actual, expected)
            )
            return actual, expected

        def _to_number(
            self, number_like: Any, *, id: Tuple[Any, ...]
        ) -> Union[int, float, complex]:
            if NUMPY_AVAILABLE and isinstance(number_like, np.number):
                return number_like.item()
            elif isinstance(number_like, self._NUMBER_TYPES):
                return number_like
            else:
                raise ErrorMeta(
                    TypeError, f"Unknown number type {type(number_like)}.", id=id
                )

        def compare(self) -> None:
            if self.check_dtype and type(self.actual) is not type(self.expected):
                self._fail(
                    AssertionError,
                    f"The (d)types do not match: {type(self.actual)} != {type(self.expected)}.",
                )

            if self.actual == self.expected:
                return

            if self.equal_nan and cmath.isnan(self.actual) and cmath.isnan(self.expected):
                return

            abs_diff = abs(self.actual - self.expected)
            tolerance = self.atol + self.rtol * abs(self.expected)

            if cmath.isfinite(abs_diff) and abs_diff <= tolerance:
                return

            self._fail(
                AssertionError,
                make_scalar_mismatch_msg(
                    self.actual, self.expected, rtol=self.rtol, atol=self.atol
                ),
            )

        def extra_repr(self) -> Sequence[str]:
            return (
                "rtol",
                "atol",
                "equal_nan",
                "check_dtype",
            )

    class TensorLikePair(Pair):
        """Pair for :class:`torch.Tensor`-like inputs.

        Kwargs:
            allow_subclasses (bool):
            rtol (Optional[float]): Relative tolerance. If specified ``atol`` must also be specified. If omitted, default
                values based on the type are selected. See :func:assert_close: for details.
            atol (Optional[float]): Absolute tolerance. If specified ``rtol`` must also be specified. If omitted, default
                values based on the type are selected. See :func:assert_close: for details.
            equal_nan (bool): If ``True``, two ``NaN`` values are considered equal. Defaults to ``False``.
            check_device (bool): If ``True`` (default), asserts that corresponding tensors are on the same
                :attr:`~torch.Tensor.device`. If this check is disabled, tensors on different
                :attr:`~torch.Tensor.device`'s are moved to the CPU before being compared.
            check_dtype (bool): If ``True`` (default), asserts that corresponding tensors have the same ``dtype``. If this
                check is disabled, tensors with different ``dtype``'s are promoted  to a common ``dtype`` (according to
                :func:`torch.promote_types`) before being compared.
            check_layout (bool): If ``True`` (default), asserts that corresponding tensors have the same ``layout``. If this
                check is disabled, tensors with different ``layout``'s are converted to strided tensors before being
                compared.
            check_stride (bool): If ``True`` and corresponding tensors are strided, asserts that they have the same stride.
        """

        def __init__(
            self,
            actual: Any,
            expected: Any,
            *,
            id: Tuple[Any, ...] = (),
            allow_subclasses: bool = True,
            rtol: Optional[float] = None,
            atol: Optional[float] = None,
            equal_nan: bool = False,
            check_device: bool = True,
            check_dtype: bool = True,
            check_layout: bool = True,
            check_stride: bool = False,
            **other_parameters: Any,
        ):
            actual, expected = self._process_inputs(
                actual, expected, id=id, allow_subclasses=allow_subclasses
            )
            super().__init__(actual, expected, id=id, **other_parameters)

            self.rtol, self.atol = get_tolerances(
                actual, expected, rtol=rtol, atol=atol, id=self.id
            )
            self.equal_nan = equal_nan
            self.check_device = check_device
            self.check_dtype = check_dtype
            self.check_layout = check_layout
            self.check_stride = check_stride

        def _process_inputs(
            self, actual: Any, expected: Any, *, id: Tuple[Any, ...], allow_subclasses: bool
        ) -> Tuple[torch.Tensor, torch.Tensor]:
            directly_related = isinstance(actual, type(expected)) or isinstance(
                expected, type(actual)
            )
            if not directly_related:
                self._inputs_not_supported()

            if not allow_subclasses and type(actual) is not type(expected):
                self._inputs_not_supported()

            actual, expected = (self._to_tensor(input) for input in (actual, expected))
            for tensor in (actual, expected):
                self._check_supported(tensor, id=id)
            return actual, expected

        def _to_tensor(self, tensor_like: Any) -> torch.Tensor:
            if isinstance(tensor_like, torch.Tensor):
                return tensor_like

            try:
                return torch.as_tensor(tensor_like)
            except Exception:
                self._inputs_not_supported()

        def _check_supported(self, tensor: torch.Tensor, *, id: Tuple[Any, ...]) -> None:
            if tensor.layout not in {
                torch.strided,
                torch.sparse_coo,
                torch.sparse_csr,
                torch.sparse_csc,
                torch.sparse_bsr,
                torch.sparse_bsc,
            }:
                raise ErrorMeta(
                    ValueError, f"Unsupported tensor layout {tensor.layout}", id=id
                )

        def compare(self) -> None:
            actual, expected = self.actual, self.expected

            self._compare_attributes(actual, expected)
            if any(input.device.type == "meta" for input in (actual, expected)):
                return

            actual, expected = self._equalize_attributes(actual, expected)
            self._compare_values(actual, expected)

        def _compare_attributes(
            self,
            actual: torch.Tensor,
            expected: torch.Tensor,
        ) -> None:
            """Checks if the attributes of two tensors match.

            Always checks

            - the :attr:`~torch.Tensor.shape`,
            - whether both inputs are quantized or not,
            - and if they use the same quantization scheme.

            Checks for

            - :attr:`~torch.Tensor.layout`,
            - :meth:`~torch.Tensor.stride`,
            - :attr:`~torch.Tensor.device`, and
            - :attr:`~torch.Tensor.dtype`

            are optional and can be disabled through the corresponding ``check_*`` flag during construction of the pair.
            """

            def raise_mismatch_error(
                attribute_name: str, actual_value: Any, expected_value: Any
            ) -> NoReturn:
                self._fail(
                    AssertionError,
                    f"The values for attribute '{attribute_name}' do not match: {actual_value} != {expected_value}.",
                )

            if actual.shape != expected.shape:
                raise_mismatch_error("shape", actual.shape, expected.shape)

            if actual.is_quantized != expected.is_quantized:
                raise_mismatch_error(
                    "is_quantized", actual.is_quantized, expected.is_quantized
                )
            elif actual.is_quantized and actual.qscheme() != expected.qscheme():
                raise_mismatch_error("qscheme()", actual.qscheme(), expected.qscheme())

            if actual.layout != expected.layout:
                if self.check_layout:
                    raise_mismatch_error("layout", actual.layout, expected.layout)
            elif (
                actual.layout == torch.strided
                and self.check_stride
                and actual.stride() != expected.stride()
            ):
                raise_mismatch_error("stride()", actual.stride(), expected.stride())

            if self.check_device and actual.device != expected.device:
                raise_mismatch_error("device", actual.device, expected.device)

            if self.check_dtype and actual.dtype != expected.dtype:
                raise_mismatch_error("dtype", actual.dtype, expected.dtype)

        def _equalize_attributes(
            self, actual: torch.Tensor, expected: torch.Tensor
        ) -> Tuple[torch.Tensor, torch.Tensor]:
            """Equalizes some attributes of two tensors for value comparison.

            If ``actual`` and ``expected`` are ...

            - ... not on the same :attr:`~torch.Tensor.device`, they are moved CPU memory.
            - ... not of the same ``dtype``, they are promoted  to a common ``dtype`` (according to
                :func:`torch.promote_types`).
            - ... not of the same ``layout``, they are converted to strided tensors.

            Args:
                actual (Tensor): Actual tensor.
                expected (Tensor): Expected tensor.

            Returns:
                (Tuple[Tensor, Tensor]): Equalized tensors.
            """
            # The comparison logic uses operators currently not supported by the MPS backends.
            #  See https://github.com/pytorch/pytorch/issues/77144 for details.
            # TODO: Remove this conversion as soon as all operations are supported natively by the MPS backend
            if actual.is_mps or expected.is_mps:  # type: ignore[attr-defined]
                actual = actual.cpu()
                expected = expected.cpu()

            if actual.device != expected.device:
                actual = actual.cpu()
                expected = expected.cpu()

            if actual.dtype != expected.dtype:
                dtype = torch.promote_types(actual.dtype, expected.dtype)
                actual = actual.to(dtype)
                expected = expected.to(dtype)

            if actual.layout != expected.layout:
                # These checks are needed, since Tensor.to_dense() fails on tensors that are already strided
                actual = actual.to_dense() if actual.layout != torch.strided else actual
                expected = (
                    expected.to_dense() if expected.layout != torch.strided else expected
                )

            return actual, expected

        def _compare_values(self, actual: torch.Tensor, expected: torch.Tensor) -> None:
            if actual.is_quantized:
                compare_fn = self._compare_quantized_values
            elif actual.is_sparse:
                compare_fn = self._compare_sparse_coo_values
            elif actual.layout in {
                torch.sparse_csr,
                torch.sparse_csc,
                torch.sparse_bsr,
                torch.sparse_bsc,
            }:
                compare_fn = self._compare_sparse_compressed_values
            else:
                compare_fn = self._compare_regular_values_close

            compare_fn(
                actual, expected, rtol=self.rtol, atol=self.atol, equal_nan=self.equal_nan
            )

        def _compare_quantized_values(
            self,
            actual: torch.Tensor,
            expected: torch.Tensor,
            *,
            rtol: float,
            atol: float,
            equal_nan: bool,
        ) -> None:
            """Compares quantized tensors by comparing the :meth:`~torch.Tensor.dequantize`'d variants for closeness.

            .. note::

                A detailed discussion about why only the dequantized variant is checked for closeness rather than checking
                the individual quantization parameters for closeness and the integer representation for equality can be
                found in https://github.com/pytorch/pytorch/issues/68548.
            """
            return self._compare_regular_values_close(
                actual.dequantize(),
                expected.dequantize(),
                rtol=rtol,
                atol=atol,
                equal_nan=equal_nan,
                identifier=lambda default_identifier: f"Quantized {default_identifier.lower()}",
            )

        def _compare_sparse_coo_values(
            self,
            actual: torch.Tensor,
            expected: torch.Tensor,
            *,
            rtol: float,
            atol: float,
            equal_nan: bool,
        ) -> None:
            """Compares sparse COO tensors by comparing

            - the number of sparse dimensions,
            - the number of non-zero elements (nnz) for equality,
            - the indices for equality, and
            - the values for closeness.
            """
            if actual.sparse_dim() != expected.sparse_dim():
                self._fail(
                    AssertionError,
                    (
                        f"The number of sparse dimensions in sparse COO tensors does not match: "
                        f"{actual.sparse_dim()} != {expected.sparse_dim()}"
                    ),
                )

            if actual._nnz() != expected._nnz():
                self._fail(
                    AssertionError,
                    (
                        f"The number of specified values in sparse COO tensors does not match: "
                        f"{actual._nnz()} != {expected._nnz()}"
                    ),
                )

            self._compare_regular_values_equal(
                actual._indices(),
                expected._indices(),
                identifier="Sparse COO indices",
            )
            self._compare_regular_values_close(
                actual._values(),
                expected._values(),
                rtol=rtol,
                atol=atol,
                equal_nan=equal_nan,
                identifier="Sparse COO values",
            )

        def _compare_sparse_compressed_values(
            self,
            actual: torch.Tensor,
            expected: torch.Tensor,
            *,
            rtol: float,
            atol: float,
            equal_nan: bool,
        ) -> None:
            """Compares sparse compressed tensors by comparing

            - the number of non-zero elements (nnz) for equality,
            - the plain indices for equality,
            - the compressed indices for equality, and
            - the values for closeness.
            """
            format_name, compressed_indices_method, plain_indices_method = {
                torch.sparse_csr: (
                    "CSR",
                    torch.Tensor.crow_indices,
                    torch.Tensor.col_indices,
                ),
                torch.sparse_csc: (
                    "CSC",
                    torch.Tensor.ccol_indices,
                    torch.Tensor.row_indices,
                ),
                torch.sparse_bsr: (
                    "BSR",
                    torch.Tensor.crow_indices,
                    torch.Tensor.col_indices,
                ),
                torch.sparse_bsc: (
                    "BSC",
                    torch.Tensor.ccol_indices,
                    torch.Tensor.row_indices,
                ),
            }[actual.layout]

            if actual._nnz() != expected._nnz():
                self._fail(
                    AssertionError,
                    (
                        f"The number of specified values in sparse {format_name} tensors does not match: "
                        f"{actual._nnz()} != {expected._nnz()}"
                    ),
                )

            # Compressed and plain indices in the CSR / CSC / BSR / BSC sparse formates can be `torch.int32` _or_
            # `torch.int64`. While the same dtype is enforced for the compressed and plain indices of a single tensor, it
            # can be different between two tensors. Thus, we need to convert them to the same dtype, or the comparison will
            # fail.
            actual_compressed_indices = compressed_indices_method(actual)
            expected_compressed_indices = compressed_indices_method(expected)
            indices_dtype = torch.promote_types(
                actual_compressed_indices.dtype, expected_compressed_indices.dtype
            )

            self._compare_regular_values_equal(
                actual_compressed_indices.to(indices_dtype),
                expected_compressed_indices.to(indices_dtype),
                identifier=f"Sparse {format_name} {compressed_indices_method.__name__}",
            )
            self._compare_regular_values_equal(
                plain_indices_method(actual).to(indices_dtype),
                plain_indices_method(expected).to(indices_dtype),
                identifier=f"Sparse {format_name} {plain_indices_method.__name__}",
            )
            self._compare_regular_values_close(
                actual.values(),
                expected.values(),
                rtol=rtol,
                atol=atol,
                equal_nan=equal_nan,
                identifier=f"Sparse {format_name} values",
            )

        def _compare_regular_values_equal(
            self,
            actual: torch.Tensor,
            expected: torch.Tensor,
            *,
            equal_nan: bool = False,
            identifier: Optional[Union[str, Callable[[str], str]]] = None,
        ) -> None:
            """Checks if the values of two tensors are equal."""
            self._compare_regular_values_close(
                actual, expected, rtol=0, atol=0, equal_nan=equal_nan, identifier=identifier
            )

        def _compare_regular_values_close(
            self,
            actual: torch.Tensor,
            expected: torch.Tensor,
            *,
            rtol: float,
            atol: float,
            equal_nan: bool,
            identifier: Optional[Union[str, Callable[[str], str]]] = None,
        ) -> None:
            """Checks if the values of two tensors are close up to a desired tolerance."""
            matches = torch.isclose(
                actual, expected, rtol=rtol, atol=atol, equal_nan=equal_nan
            )
            if torch.all(matches):
                return

            if actual.shape == torch.Size([]):
                msg = make_scalar_mismatch_msg(
                    actual.item(),
                    expected.item(),
                    rtol=rtol,
                    atol=atol,
                    identifier=identifier,
                )
            else:
                msg = make_tensor_mismatch_msg(
                    actual, expected, matches, rtol=rtol, atol=atol, identifier=identifier
                )
            self._fail(AssertionError, msg)

        def extra_repr(self) -> Sequence[str]:
            return (
                "rtol",
                "atol",
                "equal_nan",
                "check_device",
                "check_dtype",
                "check_layout",
                "check_stride",
            )

    def originate_pairs(
        actual: Any,
        expected: Any,
        *,
        pair_types: Sequence[Type[Pair]],
        sequence_types: Tuple[Type, ...] = (collections.abc.Sequence,),
        mapping_types: Tuple[Type, ...] = (collections.abc.Mapping,),
        id: Tuple[Any, ...] = (),
        **options: Any,
    ) -> List[Pair]:
        """Originates pairs from the individual inputs.

        ``actual`` and ``expected`` can be possibly nested :class:`~collections.abc.Sequence`'s or
        :class:`~collections.abc.Mapping`'s. In this case the pairs are originated by recursing through them.

        Args:
            actual (Any): Actual input.
            expected (Any): Expected input.
            pair_types (Sequence[Type[Pair]]): Sequence of pair types that will be tried to construct with the inputs.
                First successful pair will be used.
            sequence_types (Tuple[Type, ...]): Optional types treated as sequences that will be checked elementwise.
            mapping_types (Tuple[Type, ...]): Optional types treated as mappings that will be checked elementwise.
            id (Tuple[Any, ...]): Optional id of a pair that will be included in an error message.
            **options (Any): Options passed to each pair during construction.

        Raises:
            ErrorMeta: With :class`AssertionError`, if the inputs are :class:`~collections.abc.Sequence`'s, but their
                length does not match.
            ErrorMeta: With :class`AssertionError`, if the inputs are :class:`~collections.abc.Mapping`'s, but their set of
                keys do not match.
            ErrorMeta: With :class`TypeError`, if no pair is able to handle the inputs.
            ErrorMeta: With any expected exception that happens during the construction of a pair.

        Returns:
            (List[Pair]): Originated pairs.
        """
        # We explicitly exclude str's here since they are self-referential and would cause an infinite recursion loop:
        # "a" == "a"[0][0]...
        if (
            isinstance(actual, sequence_types)
            and not isinstance(actual, str)
            and isinstance(expected, sequence_types)
            and not isinstance(expected, str)
        ):
            actual_len = len(actual)
            expected_len = len(expected)
            if actual_len != expected_len:
                raise ErrorMeta(
                    AssertionError,
                    f"The length of the sequences mismatch: {actual_len} != {expected_len}",
                    id=id,
                )

            pairs = []
            for idx in range(actual_len):
                pairs.extend(
                    originate_pairs(
                        actual[idx],
                        expected[idx],
                        pair_types=pair_types,
                        sequence_types=sequence_types,
                        mapping_types=mapping_types,
                        id=(*id, idx),
                        **options,
                    )
                )
            return pairs

        elif isinstance(actual, mapping_types) and isinstance(expected, mapping_types):
            actual_keys = set(actual.keys())
            expected_keys = set(expected.keys())
            if actual_keys != expected_keys:
                missing_keys = expected_keys - actual_keys
                additional_keys = actual_keys - expected_keys
                raise ErrorMeta(
                    AssertionError,
                    (
                        f"The keys of the mappings do not match:\n"
                        f"Missing keys in the actual mapping: {sorted(missing_keys)}\n"
                        f"Additional keys in the actual mapping: {sorted(additional_keys)}"
                    ),
                    id=id,
                )

            keys: Collection = actual_keys
            # Since the origination aborts after the first failure, we try to be deterministic
            with contextlib.suppress(Exception):
                keys = sorted(keys)

            pairs = []
            for key in keys:
                pairs.extend(
                    originate_pairs(
                        actual[key],
                        expected[key],
                        pair_types=pair_types,
                        sequence_types=sequence_types,
                        mapping_types=mapping_types,
                        id=(*id, key),
                        **options,
                    )
                )
            return pairs

        else:
            for pair_type in pair_types:
                try:
                    return [pair_type(actual, expected, id=id, **options)]
                # Raising an `UnsupportedInputs` during origination indicates that the pair type is not able to handle the
                # inputs. Thus, we try the next pair type.
                except UnsupportedInputs:
                    continue
                # Raising an `ErrorMeta` during origination is the orderly way to abort and so we simply re-raise it. This
                # is only in a separate branch, because the one below would also except it.
                except ErrorMeta:
                    raise
                # Raising any other exception during origination is unexpected and will give some extra information about
                # what happened. If applicable, the exception should be expected in the future.
                except Exception as error:
                    raise RuntimeError(
                        f"Originating a {pair_type.__name__}() at item {''.join(str([item]) for item in id)} with\n\n"
                        f"{type(actual).__name__}(): {actual}\n\n"
                        f"and\n\n"
                        f"{type(expected).__name__}(): {expected}\n\n"
                        f"resulted in the unexpected exception above. "
                        f"If you are a user and see this message during normal operation "
                        "please file an issue at https://github.com/pytorch/pytorch/issues. "
                        "If you are a developer and working on the comparison functions, "
                        "please except the previous error and raise an expressive `ErrorMeta` instead."
                    ) from error
            else:
                raise ErrorMeta(
                    TypeError,
                    f"No comparison pair was able to handle inputs of type {type(actual)} and {type(expected)}.",
                    id=id,
                )

    def not_close_error_metas(
        actual: Any,
        expected: Any,
        *,
        pair_types: Sequence[Type[Pair]] = (ObjectPair,),
        sequence_types: Tuple[Type, ...] = (collections.abc.Sequence,),
        mapping_types: Tuple[Type, ...] = (collections.abc.Mapping,),
        **options: Any,
    ) -> List[ErrorMeta]:
        """Asserts that inputs are equal.

        ``actual`` and ``expected`` can be possibly nested :class:`~collections.abc.Sequence`'s or
        :class:`~collections.abc.Mapping`'s. In this case the comparison happens elementwise by recursing through them.

        Args:
            actual (Any): Actual input.
            expected (Any): Expected input.
            pair_types (Sequence[Type[Pair]]): Sequence of :class:`Pair` types that will be tried to construct with the
                inputs. First successful pair will be used. Defaults to only using :class:`ObjectPair`.
            sequence_types (Tuple[Type, ...]): Optional types treated as sequences that will be checked elementwise.
            mapping_types (Tuple[Type, ...]): Optional types treated as mappings that will be checked elementwise.
            **options (Any): Options passed to each pair during construction.
        """
        # Hide this function from `pytest`'s traceback
        __tracebackhide__ = True

        try:
            pairs = originate_pairs(
                actual,
                expected,
                pair_types=pair_types,
                sequence_types=sequence_types,
                mapping_types=mapping_types,
                **options,
            )
        except ErrorMeta as error_meta:
            # Explicitly raising from None to hide the internal traceback
            raise error_meta.to_error() from None

        error_metas: List[ErrorMeta] = []
        for pair in pairs:
            try:
                pair.compare()
            except ErrorMeta as error_meta:
                error_metas.append(error_meta)
            # Raising any exception besides `ErrorMeta` while comparing is unexpected and will give some extra information
            # about what happened. If applicable, the exception should be expected in the future.
            except Exception as error:
                raise RuntimeError(
                    f"Comparing\n\n"
                    f"{pair}\n\n"
                    f"resulted in the unexpected exception above. "
                    f"If you are a user and see this message during normal operation "
                    "please file an issue at https://github.com/pytorch/pytorch/issues. "
                    "If you are a developer and working on the comparison functions, "
                    "please except the previous error and raise an expressive `ErrorMeta` instead."
                ) from error

        # [ErrorMeta Cycles]
        # ErrorMeta objects in this list capture
        # tracebacks that refer to the frame of this function.
        # The local variable `error_metas` refers to the error meta
        # objects, creating a reference cycle. Frames in the traceback
        # would not get freed until cycle collection, leaking cuda memory in tests.
        # We break the cycle by removing the reference to the error_meta objects
        # from this frame as it returns.
        error_metas = [error_metas]
        return error_metas.pop()

    def assert_close(
        actual: Any,
        expected: Any,
        *,
        allow_subclasses: bool = True,
        rtol: Optional[float] = None,
        atol: Optional[float] = None,
        equal_nan: bool = False,
        check_device: bool = True,
        check_dtype: bool = True,
        check_layout: bool = True,
        check_stride: bool = False,
        msg: Optional[Union[str, Callable[[str], str]]] = None,
    ):
        r"""Asserts that ``actual`` and ``expected`` are close.

        If ``actual`` and ``expected`` are strided, non-quantized, real-valued, and finite, they are considered close if

        .. math::

            \lvert \text{actual} - \text{expected} \rvert \le \texttt{atol} + \texttt{rtol} \cdot \lvert \text{expected} \rvert

        Non-finite values (``-inf`` and ``inf``) are only considered close if and only if they are equal. ``NaN``'s are
        only considered equal to each other if ``equal_nan`` is ``True``.

        In addition, they are only considered close if they have the same

        - :attr:`~torch.Tensor.device` (if ``check_device`` is ``True``),
        - ``dtype`` (if ``check_dtype`` is ``True``),
        - ``layout`` (if ``check_layout`` is ``True``), and
        - stride (if ``check_stride`` is ``True``).

        If either ``actual`` or ``expected`` is a meta tensor, only the attribute checks will be performed.

        If ``actual`` and ``expected`` are sparse (either having COO, CSR, CSC, BSR, or BSC layout), their strided members are
        checked individually. Indices, namely ``indices`` for COO, ``crow_indices`` and ``col_indices`` for CSR and BSR,
        or ``ccol_indices``  and ``row_indices`` for CSC and BSC layouts, respectively,
        are always checked for equality whereas the values are checked for closeness according to the definition above.

        If ``actual`` and ``expected`` are quantized, they are considered close if they have the same
        :meth:`~torch.Tensor.qscheme` and the result of :meth:`~torch.Tensor.dequantize` is close according to the
        definition above.

        ``actual`` and ``expected`` can be :class:`~torch.Tensor`'s or any tensor-or-scalar-likes from which
        :class:`torch.Tensor`'s can be constructed with :func:`torch.as_tensor`. Except for Python scalars the input types
        have to be directly related. In addition, ``actual`` and ``expected`` can be :class:`~collections.abc.Sequence`'s
        or :class:`~collections.abc.Mapping`'s in which case they are considered close if their structure matches and all
        their elements are considered close according to the above definition.

        .. note::

            Python scalars are an exception to the type relation requirement, because their :func:`type`, i.e.
            :class:`int`, :class:`float`, and :class:`complex`, is equivalent to the ``dtype`` of a tensor-like. Thus,
            Python scalars of different types can be checked, but require ``check_dtype=False``.

        Args:
            actual (Any): Actual input.
            expected (Any): Expected input.
            allow_subclasses (bool): If ``True`` (default) and except for Python scalars, inputs of directly related types
                are allowed. Otherwise type equality is required.
            rtol (Optional[float]): Relative tolerance. If specified ``atol`` must also be specified. If omitted, default
                values based on the :attr:`~torch.Tensor.dtype` are selected with the below table.
            atol (Optional[float]): Absolute tolerance. If specified ``rtol`` must also be specified. If omitted, default
                values based on the :attr:`~torch.Tensor.dtype` are selected with the below table.
            equal_nan (Union[bool, str]): If ``True``, two ``NaN`` values will be considered equal.
            check_device (bool): If ``True`` (default), asserts that corresponding tensors are on the same
                :attr:`~torch.Tensor.device`. If this check is disabled, tensors on different
                :attr:`~torch.Tensor.device`'s are moved to the CPU before being compared.
            check_dtype (bool): If ``True`` (default), asserts that corresponding tensors have the same ``dtype``. If this
                check is disabled, tensors with different ``dtype``'s are promoted  to a common ``dtype`` (according to
                :func:`torch.promote_types`) before being compared.
            check_layout (bool): If ``True`` (default), asserts that corresponding tensors have the same ``layout``. If this
                check is disabled, tensors with different ``layout``'s are converted to strided tensors before being
                compared.
            check_stride (bool): If ``True`` and corresponding tensors are strided, asserts that they have the same stride.
            msg (Optional[Union[str, Callable[[str], str]]]): Optional error message to use in case a failure occurs during
                the comparison. Can also passed as callable in which case it will be called with the generated message and
                should return the new message.

        Raises:
            ValueError: If no :class:`torch.Tensor` can be constructed from an input.
            ValueError: If only ``rtol`` or ``atol`` is specified.
            AssertionError: If corresponding inputs are not Python scalars and are not directly related.
            AssertionError: If ``allow_subclasses`` is ``False``, but corresponding inputs are not Python scalars and have
                different types.
            AssertionError: If the inputs are :class:`~collections.abc.Sequence`'s, but their length does not match.
            AssertionError: If the inputs are :class:`~collections.abc.Mapping`'s, but their set of keys do not match.
            AssertionError: If corresponding tensors do not have the same :attr:`~torch.Tensor.shape`.
            AssertionError: If ``check_layout`` is ``True``, but corresponding tensors do not have the same
                :attr:`~torch.Tensor.layout`.
            AssertionError: If only one of corresponding tensors is quantized.
            AssertionError: If corresponding tensors are quantized, but have different :meth:`~torch.Tensor.qscheme`'s.
            AssertionError: If ``check_device`` is ``True``, but corresponding tensors are not on the same
                :attr:`~torch.Tensor.device`.
            AssertionError: If ``check_dtype`` is ``True``, but corresponding tensors do not have the same ``dtype``.
            AssertionError: If ``check_stride`` is ``True``, but corresponding strided tensors do not have the same stride.
            AssertionError: If the values of corresponding tensors are not close according to the definition above.

        The following table displays the default ``rtol`` and ``atol`` for different ``dtype``'s. In case of mismatching
        ``dtype``'s, the maximum of both tolerances is used.

        +---------------------------+------------+----------+
        | ``dtype``                 | ``rtol``   | ``atol`` |
        +===========================+============+==========+
        | :attr:`~torch.float16`    | ``1e-3``   | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.bfloat16`   | ``1.6e-2`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.float32`    | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.float64`    | ``1e-7``   | ``1e-7`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.complex32`  | ``1e-3``   | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.complex64`  | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.complex128` | ``1e-7``   | ``1e-7`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.quint8`     | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.quint2x4`   | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.quint4x2`   | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.qint8`      | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | :attr:`~torch.qint32`     | ``1.3e-6`` | ``1e-5`` |
        +---------------------------+------------+----------+
        | other                     | ``0.0``    | ``0.0``  |
        +---------------------------+------------+----------+

        .. note::

            :func:`~torch.testing.assert_close` is highly configurable with strict default settings. Users are encouraged
            to :func:`~functools.partial` it to fit their use case. For example, if an equality check is needed, one might
            define an ``assert_equal`` that uses zero tolerances for every ``dtype`` by default:

            >>> import functools
            >>> assert_equal = functools.partial(torch.testing.assert_close, rtol=0, atol=0)
            >>> assert_equal(1e-9, 1e-10)
            Traceback (most recent call last):
            ...
            AssertionError: Scalars are not equal!
            <BLANKLINE>
            Expected 1e-10 but got 1e-09.
            Absolute difference: 9.000000000000001e-10
            Relative difference: 9.0

        Examples:
            >>> # tensor to tensor comparison
            >>> expected = torch.tensor([1e0, 1e-1, 1e-2])
            >>> actual = torch.acos(torch.cos(expected))
            >>> torch.testing.assert_close(actual, expected)

            >>> # scalar to scalar comparison
            >>> import math
            >>> expected = math.sqrt(2.0)
            >>> actual = 2.0 / math.sqrt(2.0)
            >>> torch.testing.assert_close(actual, expected)

            >>> # numpy array to numpy array comparison
            >>> import numpy as np
            >>> expected = np.array([1e0, 1e-1, 1e-2])
            >>> actual = np.arccos(np.cos(expected))
            >>> torch.testing.assert_close(actual, expected)

            >>> # sequence to sequence comparison
            >>> import numpy as np
            >>> # The types of the sequences do not have to match. They only have to have the same
            >>> # length and their elements have to match.
            >>> expected = [torch.tensor([1.0]), 2.0, np.array(3.0)]
            >>> actual = tuple(expected)
            >>> torch.testing.assert_close(actual, expected)

            >>> # mapping to mapping comparison
            >>> from collections import OrderedDict
            >>> import numpy as np
            >>> foo = torch.tensor(1.0)
            >>> bar = 2.0
            >>> baz = np.array(3.0)
            >>> # The types and a possible ordering of mappings do not have to match. They only
            >>> # have to have the same set of keys and their elements have to match.
            >>> expected = OrderedDict([("foo", foo), ("bar", bar), ("baz", baz)])
            >>> actual = {"baz": baz, "bar": bar, "foo": foo}
            >>> torch.testing.assert_close(actual, expected)

            >>> expected = torch.tensor([1.0, 2.0, 3.0])
            >>> actual = expected.clone()
            >>> # By default, directly related instances can be compared
            >>> torch.testing.assert_close(torch.nn.Parameter(actual), expected)
            >>> # This check can be made more strict with allow_subclasses=False
            >>> torch.testing.assert_close(
            ...     torch.nn.Parameter(actual), expected, allow_subclasses=False
            ... )
            Traceback (most recent call last):
            ...
            TypeError: No comparison pair was able to handle inputs of type
            <class 'torch.nn.parameter.Parameter'> and <class 'torch.Tensor'>.
            >>> # If the inputs are not directly related, they are never considered close
            >>> torch.testing.assert_close(actual.numpy(), expected)
            Traceback (most recent call last):
            ...
            TypeError: No comparison pair was able to handle inputs of type <class 'numpy.ndarray'>
            and <class 'torch.Tensor'>.
            >>> # Exceptions to these rules are Python scalars. They can be checked regardless of
            >>> # their type if check_dtype=False.
            >>> torch.testing.assert_close(1.0, 1, check_dtype=False)

            >>> # NaN != NaN by default.
            >>> expected = torch.tensor(float("Nan"))
            >>> actual = expected.clone()
            >>> torch.testing.assert_close(actual, expected)
            Traceback (most recent call last):
            ...
            AssertionError: Scalars are not close!
            <BLANKLINE>
            Expected nan but got nan.
            Absolute difference: nan (up to 1e-05 allowed)
            Relative difference: nan (up to 1.3e-06 allowed)
            >>> torch.testing.assert_close(actual, expected, equal_nan=True)

            >>> expected = torch.tensor([1.0, 2.0, 3.0])
            >>> actual = torch.tensor([1.0, 4.0, 5.0])
            >>> # The default error message can be overwritten.
            >>> torch.testing.assert_close(actual, expected, msg="Argh, the tensors are not close!")
            Traceback (most recent call last):
            ...
            AssertionError: Argh, the tensors are not close!
            >>> # If msg is a callable, it can be used to augment the generated message with
            >>> # extra information
            >>> torch.testing.assert_close(
            ...     actual, expected, msg=lambda msg: f"Header\n\n{msg}\n\nFooter"
            ... )
            Traceback (most recent call last):
            ...
            AssertionError: Header
            <BLANKLINE>
            Tensor-likes are not close!
            <BLANKLINE>
            Mismatched elements: 2 / 3 (66.7%)
            Greatest absolute difference: 2.0 at index (1,) (up to 1e-05 allowed)
            Greatest relative difference: 1.0 at index (1,) (up to 1.3e-06 allowed)
            <BLANKLINE>
            Footer
        """
        # Hide this function from `pytest`'s traceback
        __tracebackhide__ = True

        error_metas = not_close_error_metas(
            actual,
            expected,
            pair_types=(
                NonePair,
                BooleanPair,
                NumberPair,
                TensorLikePair,
            ),
            allow_subclasses=allow_subclasses,
            rtol=rtol,
            atol=atol,
            equal_nan=equal_nan,
            check_device=check_device,
            check_dtype=check_dtype,
            check_layout=check_layout,
            check_stride=check_stride,
            msg=msg,
        )

        if error_metas:
            # TODO: compose all metas into one AssertionError
            raise error_metas[0].to_error(msg)

    def assert_allclose(
        actual: Any,
        expected: Any,
        rtol: Optional[float] = None,
        atol: Optional[float] = None,
        equal_nan: bool = True,
        msg: str = "",
    ) -> None:
        """
        .. warning::

           :func:`torch.testing.assert_allclose` is deprecated since ``1.12`` and will be removed in a future release.
           Please use :func:`torch.testing.assert_close` instead. You can find detailed upgrade instructions
           `here <https://github.com/pytorch/pytorch/issues/61844>`_.
        """
        warnings.warn(
            "`torch.testing.assert_allclose()` is deprecated since 1.12 and will be removed in a future release. "
            "Please use `torch.testing.assert_close()` instead. "
            "You can find detailed upgrade instructions in https://github.com/pytorch/pytorch/issues/61844.",
            FutureWarning,
            stacklevel=2,
        )

        if not isinstance(actual, torch.Tensor):
            actual = torch.tensor(actual)
        if not isinstance(expected, torch.Tensor):
            expected = torch.tensor(expected, dtype=actual.dtype)

        if rtol is None and atol is None:
            rtol, atol = default_tolerances(
                actual,
                expected,
                dtype_precisions={
                    torch.float16: (1e-3, 1e-3),
                    torch.float32: (1e-4, 1e-5),
                    torch.float64: (1e-5, 1e-8),
                },
            )

        torch.testing.assert_close(
            actual,
            expected,
            rtol=rtol,
            atol=atol,
            equal_nan=equal_nan,
            check_device=True,
            check_dtype=False,
            check_stride=False,
            msg=msg or None,
        )

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