pytorch/torch/testing/_asserts.py

import collections.abc
import functools
import numbers
import sys
from typing import Any, Callable, Dict, List, NamedTuple, Optional, Tuple, Type, TypeVar, Union, cast
from types import SimpleNamespace

import torch
from torch import Tensor

from ._core import _unravel_index

__all__ = ["assert_equal", "assert_close"]


# The UsageError should be raised in case the test function is not used correctly. With this the user is able to
# differentiate between a test failure (there is a bug in the tested code) and a test error (there is a bug in the
# test). If pytest is the test runner, we use the built-in UsageError instead our custom one.

try:
    # The module 'pytest' will be imported if the 'pytest' runner is used. This will only give false-positives in case
    # a previously imported module already directly or indirectly imported 'pytest', but the test is run by another
    # runner such as 'unittest'.
    # 'mypy' is not able to handle this within a type annotation
    # (see https://mypy.readthedocs.io/en/latest/common_issues.html#variables-vs-type-aliases for details). In case
    # 'UsageError' is used in an annotation, add a 'type: ignore[valid-type]' comment.
    UsageError: Type[Exception] = sys.modules["pytest"].UsageError  # type: ignore[attr-defined]
except (KeyError, AttributeError):

    class UsageError(Exception):  # type: ignore[no-redef]
        pass


# This is copy-pasted from torch.testing._internal.common_utils.TestCase.dtype_precisions. With this we avoid a
# dependency on torch.testing._internal at import. See
# https://github.com/pytorch/pytorch/pull/54769#issuecomment-813174256 for details.
# {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),
}


def _get_default_rtol_and_atol(actual: Tensor, expected: Tensor) -> Tuple[float, float]:
    dtype = actual.dtype if actual.dtype == expected.dtype else torch.promote_types(actual.dtype, expected.dtype)
    return _DTYPE_PRECISIONS.get(dtype, (0.0, 0.0))


def _check_complex_components_individually(
    check_tensor_values: Callable[..., Optional[Exception]]
) -> Callable[..., Optional[Exception]]:
    """Decorates real-valued tensor values check functions to handle complex components individually.

    If the inputs are not complex, this decorator is a no-op.

    Args:
        check_tensor_values (Callable[..., Optional[Exception]]): Tensor check function for real-valued tensors.

    Returns:
        Optional[Exception]: Return value of :attr:`check_tensors`.
    """

    @functools.wraps(check_tensor_values)
    def wrapper(actual: Tensor, expected: Tensor, **kwargs: Any) -> Optional[Exception]:
        if "equal_nan" in kwargs:
            if kwargs["equal_nan"] == "relaxed":
                relaxed_complex_nan = True
                kwargs["equal_nan"] = True
            else:
                relaxed_complex_nan = False
                kwargs["equal_nan"] = bool(kwargs["equal_nan"])
        else:
            relaxed_complex_nan = False

        if actual.dtype not in (torch.complex32, torch.complex64, torch.complex128):
            return check_tensor_values(actual, expected, **kwargs,)

        if relaxed_complex_nan:
            actual, expected = [
                t.clone().masked_fill(
                    t.real.isnan() | t.imag.isnan(),
                    complex(float("NaN"), float("NaN")),  # type: ignore[call-overload]
                )
                for t in (actual, expected)
            ]

        exc = check_tensor_values(actual.real, expected.real, **kwargs)
        if exc:
            return _amend_error_message(exc, "{}\n\nThe failure occurred for the real part.")

        exc = check_tensor_values(actual.imag, expected.imag, **kwargs)
        if exc:
            return _amend_error_message(exc, "{}\n\nThe failure occurred for the imaginary part.")

        return None

    return wrapper


def _check_supported_tensor(
    input: Tensor,
) -> Optional[UsageError]:  # type: ignore[valid-type]
    """Checks if the tensors are supported by the current infrastructure.

    All checks are temporary and will be relaxed in the future.

    Returns:
        (Optional[UsageError]): If check did not pass.
    """
    if input.is_quantized:
        return UsageError("Comparison for quantized tensors is not supported yet.")
    if input.is_sparse:
        return UsageError("Comparison for sparse tensors is not supported yet.")

    return None


def _check_attributes_equal(
    actual: Tensor,
    expected: Tensor,
    *,
    check_device: bool = True,
    check_dtype: bool = True,
    check_stride: bool = True,
) -> Optional[AssertionError]:
    """Checks if the attributes of two tensors match.

    Always checks the :attr:`~torch.Tensor.shape`. Checks for :attr:`~torch.Tensor.device`,
    :attr:`~torch.Tensor.dtype`, and :meth:`~torch.Tensor.stride` are optional and can be disabled.

    Args:
        actual (Tensor): Actual tensor.
        expected (Tensor): Expected tensor.
        check_device (bool): If ``True`` (default), checks that both :attr:`actual` and :attr:`expected` are on the
            same :attr:`~torch.Tensor.device`.
        check_dtype (bool): If ``True`` (default), checks that both :attr:`actual` and :attr:`expected` have the same
            ``dtype``.
        check_stride (bool): If ``True`` (default), checks that both :attr:`actual` and :attr:`expected` have the same
            stride.

    Returns:
        (Optional[AssertionError]): If checks did not pass.
    """
    msg_fmtstr = "The values for attribute '{}' do not match: {} != {}."

    if actual.shape != expected.shape:
        return AssertionError(msg_fmtstr.format("shape", actual.shape, expected.shape))

    if check_device and actual.device != expected.device:
        return AssertionError(msg_fmtstr.format("device", actual.device, expected.device))

    if check_dtype and actual.dtype != expected.dtype:
        return AssertionError(msg_fmtstr.format("dtype", actual.dtype, expected.dtype))

    if check_stride and actual.stride() != expected.stride():
        return AssertionError(msg_fmtstr.format("stride()", actual.stride(), expected.stride()))

    return None


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

    If :attr:`actual` and :attr:`expected`
    - are not on the same :attr:`~torch.Tensor.device`, they are moved CPU memory, and
    - do not have the same ``dtype``, they are promoted  to a common ``dtype`` (according to
        :func:`torch.promote_types`)

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

    Returns:
        Tuple(Tensor, Tensor): Equalized tensors.
    """
    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)

    return actual, expected


DiagnosticInfo = SimpleNamespace


def _trace_mismatches(actual: Tensor, expected: Tensor, mismatches: Tensor) -> DiagnosticInfo:
    """Traces mismatches and returns diagnostic information.

    Args:
        actual (Tensor): Actual tensor.
        expected (Tensor): Expected tensor.
        mismatches (Tensor): Boolean mask of the same shape as :attr:`actual` and :attr:`expected` that indicates
            the location of mismatches.

    Returns:
        (DiagnosticInfo): Mismatch diagnostics with the following attributes:

            - ``number_of_elements`` (int): Number of elements in each tensor being compared.
            - ``total_mismatches`` (int): Total number of mismatches.
            - ``mismatch_ratio`` (float): Total mismatches divided by number of elements.
            - ``max_abs_diff`` (Union[int, float]): Greatest absolute difference of the inputs.
            - ``max_abs_diff_idx`` (Union[int, Tuple[int, ...]]): Index of greatest absolute difference.
            - ``max_rel_diff`` (Union[int, float]): Greatest relative difference of the inputs.
            - ``max_rel_diff_idx`` (Union[int, Tuple[int, ...]]): Index of greatest relative difference.

            For ``max_abs_diff`` and ``max_rel_diff`` the type depends on the :attr:`~torch.Tensor.dtype` of the inputs.
    """
    number_of_elements = mismatches.numel()
    total_mismatches = torch.sum(mismatches).item()
    mismatch_ratio = total_mismatches / number_of_elements

    dtype = torch.float64 if actual.dtype.is_floating_point else torch.int64
    a_flat = actual.flatten().to(dtype)
    b_flat = expected.flatten().to(dtype)
    matches_flat = ~mismatches.flatten()

    abs_diff = torch.abs(a_flat - b_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(b_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 SimpleNamespace(
        number_of_elements=number_of_elements,
        total_mismatches=cast(int, total_mismatches),
        mismatch_ratio=mismatch_ratio,
        max_abs_diff=max_abs_diff.item(),
        max_abs_diff_idx=_unravel_index(max_abs_diff_flat_idx.item(), mismatches.shape),
        max_rel_diff=max_rel_diff.item(),
        max_rel_diff_idx=_unravel_index(max_rel_diff_flat_idx.item(), mismatches.shape),
    )


@_check_complex_components_individually
def _check_values_equal(
    actual: Tensor,
    expected: Tensor,
    *,
    msg: Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]] = None,
) -> Optional[AssertionError]:
    """Checks if the values of two tensors are bitwise equal.

    Args:
        actual (Tensor): Actual tensor.
        expected (Tensor): Expected tensor.
        msg (Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]]): Optional error message. Can be
            passed as callable in which case it will be called with the inputs and the result of
            :func:`_trace_mismatches`.

    Returns:
        (Optional[AssertionError]): If check did not pass.
    """
    mismatches = torch.ne(actual, expected)
    if not torch.any(mismatches):
        return None

    trace = _trace_mismatches(actual, expected, mismatches)

    if msg is None:
        msg = (
            f"Tensors are not equal!\n\n"
            f"Mismatched elements: {trace.total_mismatches} / {trace.number_of_elements} ({trace.mismatch_ratio:.1%})\n"
            f"Greatest absolute difference: {trace.max_abs_diff} at {trace.max_abs_diff_idx}\n"
            f"Greatest relative difference: {trace.max_rel_diff} at {trace.max_rel_diff_idx}"
        )
    elif callable(msg):
        msg = msg(actual, expected, trace)
    return AssertionError(msg)


@_check_complex_components_individually
def _check_values_close(
    actual: Tensor,
    expected: Tensor,
    *,
    rtol: float,
    atol: float,
    equal_nan: bool,
    msg: Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]],
) -> Optional[AssertionError]:
    """Checks if the values of two tensors are close up to a desired tolerance.

    Args:
        actual (Tensor): Actual tensor.
        expected (Tensor): Expected tensor.
        rtol (float): Relative tolerance.
        atol (float): Absolute tolerance.
        equal_nan (bool): If ``True``, two ``NaN`` values will be considered equal.
        msg (Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]]): Optional error message. Can be
            passed as callable in which case it will be called with the inputs and the result of
            :func:`_trace_mismatches`.

    Returns:
        (Optional[AssertionError]): If check did not pass.
    """

    mismatches = ~torch.isclose(actual, expected, rtol=rtol, atol=atol, equal_nan=equal_nan)
    if not torch.any(mismatches):
        return None

    trace = _trace_mismatches(actual, expected, mismatches)
    if msg is None:
        msg = (
            f"Tensors are not close!\n\n"
            f"Mismatched elements: {trace.total_mismatches} / {trace.number_of_elements} ({trace.mismatch_ratio:.1%})\n"
            f"Greatest absolute difference: {trace.max_abs_diff} at {trace.max_abs_diff_idx} (up to {atol} allowed)\n"
            f"Greatest relative difference: {trace.max_rel_diff} at {trace.max_rel_diff_idx} (up to {rtol} allowed)"
        )
    elif callable(msg):
        msg = msg(actual, expected, trace)
    return AssertionError(msg)


def _check_tensors_equal(
    actual: Tensor,
    expected: Tensor,
    *,
    check_device: bool = True,
    check_dtype: bool = True,
    check_stride: bool = True,
    msg: Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]] = None,
) -> Optional[Exception]:
    """Checks that the values of two tensors are bitwise equal.

    For complex tensors the check is performed on the real and imaginary component separately. Optionally, checks that
    some attributes of tensor pairs are equal.

    For a description of the parameters see :func:`assert_equal`.

    Returns:
        Optional[Exception]: If checks did not pass.
    """
    exc: Optional[Exception] = _check_attributes_equal(
        actual, expected, check_device=check_device, check_dtype=check_dtype, check_stride=check_stride
    )
    if exc:
        return exc
    actual, expected = _equalize_attributes(actual, expected)

    exc = _check_values_equal(actual, expected, msg=msg)
    if exc:
        return exc

    return None


def _check_tensors_close(
    actual: Tensor,
    expected: Tensor,
    *,
    rtol: Optional[float] = None,
    atol: Optional[float] = None,
    equal_nan: bool = False,
    check_device: bool = True,
    check_dtype: bool = True,
    check_stride: bool = True,
    msg: Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]] = None,
) -> Optional[Exception]:
    r"""Checks that the values of :attr:`actual` and :attr:`expected` are close.

    If :attr:`actual` and :attr:`expected` are real-valued and finite, they are considered close if

    .. code::

        torch.abs(actual - expected) <= (atol + rtol * expected)

    and they have the same device (if :attr:`check_device` is ``True``), same dtype (if :attr:`check_dtype` is
    ``True``), and the same stride (if :attr:`check_stride` is ``True``). 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
    :attr:`equal_nan` is ``True``.

    For a description of the parameters see :func:`assert_equal`.

    Returns:
        Optional[Exception]: If checks did not pass.
    """
    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.
        return UsageError(
            f"Both 'rtol' and 'atol' must be omitted or specified, but got rtol={rtol} and atol={atol} instead."
        )
    elif rtol is None or atol is None:
        rtol, atol = _get_default_rtol_and_atol(actual, expected)

    exc: Optional[Exception] = _check_attributes_equal(
        actual, expected, check_device=check_device, check_dtype=check_dtype, check_stride=check_stride
    )
    if exc:
        raise exc
    actual, expected = _equalize_attributes(actual, expected)

    if (rtol == 0.0) and (atol == 0.0):
        exc = _check_values_equal(actual, expected, msg=msg)
    else:
        exc = _check_values_close(actual, expected, rtol=rtol, atol=atol, equal_nan=equal_nan, msg=msg)
    if exc:
        return exc

    return None


E = TypeVar("E", bound=Exception)


def _amend_error_message(exc: E, msg_fmtstr: str) -> E:
    """Amends an exception message.

    Args:
        exc (E): Exception.
        msg_fmtstr: Format string for the amended message.

    Returns:
        (E): New exception with amended error message.
    """
    return type(exc)(msg_fmtstr.format(str(exc)))


class _TensorPair(NamedTuple):
    actual: Tensor
    expected: Tensor


_SEQUENCE_MSG_FMTSTR = "The failure occurred at index {} of the sequences."
_MAPPING_MSG_FMTSTR = "The failure occurred for key '{}' of the mappings."


def _check_pair(
    pair: Union[_TensorPair, List, Dict],
    check_tensors: Callable[[Any, Any], Optional[Exception]],
) -> Optional[Exception]:
    """Checks input pairs.

    :class:`list`'s or :class:`dict`'s are checked elementwise. Checking is performed recursively and thus nested
    containers are supported.

    Args:
        pair (Union[_TensorPair, List, Dict]): Input pair.
        check_tensors (Callable[[Any, Any], Optional[Exception]]): Callable used to check if a tensor pair matches.
            In case it mismatches should return an :class:`Exception` with an expressive error message.

    Returns:
        (Optional[Exception]): Return value of :attr:`check_tensors`.
    """
    if isinstance(pair, list):
        for idx, pair_item in enumerate(pair):
            exc = _check_pair(pair_item, check_tensors)
            if exc:
                return _amend_error_message(exc, f"{{}}\n\n{_SEQUENCE_MSG_FMTSTR.format(idx)}")
        else:
            return None
    elif isinstance(pair, dict):
        for key, pair_item in pair.items():
            exc = _check_pair(pair_item, check_tensors)
            if exc:
                return _amend_error_message(exc, f"{{}}\n\n{_MAPPING_MSG_FMTSTR.format(key)}")
        else:
            return None
    else:  # isinstance(pair, TensorPair)
        return check_tensors(pair.actual, pair.expected)


def _to_tensor(array_or_scalar_like: Any) -> Tuple[Optional[Exception], Optional[Tensor]]:
    """Converts a scalar-or-array-like to a :class:`~torch.Tensor`.
    Args:
        array_or_scalar_like (Any): Scalar-or-array-like.
    Returns:
        (Tuple[Optional[Exception], Optional[Tensor]]): The two elements are orthogonal, i.e. if the first ``is None``
            the second will be valid and vice versa. Returns a :class:`UsageError` if no tensor can be constructed from
            :attr:`actual` or :attr:`expected`. Additionally, returns any exception from
            :func:`_check_supported_tensor`.
    """
    exc: Optional[Exception]

    if isinstance(array_or_scalar_like, Tensor):
        tensor = array_or_scalar_like
    else:
        try:
            tensor = torch.as_tensor(array_or_scalar_like)
        except Exception:
            exc = UsageError(f"No tensor can be constructed from type {type(array_or_scalar_like)}.")
            return exc, None

    exc = _check_supported_tensor(tensor)
    if exc:
        return exc, None

    return None, tensor


def _to_tensor_pair(actual: Any, expected: Any) -> Tuple[Optional[Exception], Optional[_TensorPair]]:
    """Converts a scalar-or-array-like pair to a :class:`_TensorPair`.

    Args:
        actual (Any): Actual array-or-scalar-like.
        expected (Any): Expected array-or-scalar-like.

    (Optional[Exception], Optional[_TensorPair]): The two elements are orthogonal, i.e. if the first ``is None``
            the second will not and vice versa. Returns a :class:`AssertionError` if :attr:`actual` and
            :attr:`expected` are not scalars and do not have the same type. Additionally, returns any exception from
            :func:`_to_tensor`.
    """
    exc: Optional[Exception]

    # We exclude numbers here, since numbers of different type, e.g. int vs. float, should be treated the same as
    # tensors with different dtypes. Without user input, passing numbers of different types will still fail, but this
    # can be disabled by setting `check_dtype=False`.
    if type(actual) is not type(expected) and not (
        isinstance(actual, numbers.Number) and isinstance(expected, numbers.Number)
    ):
        exc = AssertionError(
            f"Except for scalars, type equality is required, but got {type(actual)} and {type(expected)} instead."
        )
        return exc, None

    exc, actual = _to_tensor(actual)
    if exc:
        return exc, None

    exc, expected = _to_tensor(expected)
    if exc:
        return exc, None

    return None, _TensorPair(actual, expected)


def _parse_inputs(actual: Any, expected: Any) -> Tuple[Optional[Exception], Optional[Union[_TensorPair, List, Dict]]]:
    """Parses the positional inputs by constructing :class:`_TensorPairs` from corresponding array-or-scalar-likes.

    :class:`~collections.abc.Sequence`'s or :class:`~collections.abc.Mapping`'s are parsed elementwise. Parsing is
    performed recursively and thus nested containers are supported. The hierarchy of the containers is preserved, but
    sequences are returned as :class:`list` and mappings as :class:`dict`.

    Args:
        actual (Any): Actual input.
        expected (Any): Expected input.

    Returns:
        (Tuple[Optional[Exception], Optional[Union[_TensorPair, List, Dict]]]): The two elements are orthogonal, i.e.
            if the first ``is None`` the second will be valid and vice versa. Returns an :class:`AssertionError` if the
            length of two sequences or the keys of two mappings do not match. Additionally, returns any exception from
            :func:`_to_tensor_pair`.
    """
    exc: Optional[Exception]

    # 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, collections.abc.Sequence)
        and not isinstance(actual, str)
        and isinstance(expected, collections.abc.Sequence)
        and not isinstance(expected, str)
    ):
        actual_len = len(actual)
        expected_len = len(expected)
        if actual_len != expected_len:
            exc = AssertionError(f"The length of the sequences mismatch: {actual_len} != {expected_len}")
            return exc, None

        pair_list = []
        for idx in range(actual_len):
            exc, pair = _parse_inputs(actual[idx], expected[idx])
            if exc:
                exc = _amend_error_message(exc, f"{{}}\n\n{_SEQUENCE_MSG_FMTSTR.format(idx)}")
                return exc, None

            pair_list.append(pair)
        else:
            return None, pair_list

    elif isinstance(actual, collections.abc.Mapping) and isinstance(expected, collections.abc.Mapping):
        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
            exc = 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)}"
            )
            return exc, None

        pair_dict = {}
        for key in sorted(actual_keys):
            exc, pair = _parse_inputs(actual[key], expected[key])
            if exc:
                exc = _amend_error_message(exc, f"{{}}\n\n{_MAPPING_MSG_FMTSTR.format(key)}")
                return exc, None

            pair_dict[key] = pair
        else:
            return None, pair_dict

    else:
        return _to_tensor_pair(actual, expected)


def assert_equal(
    actual: Any,
    expected: Any,
    *,
    check_device: bool = True,
    check_dtype: bool = True,
    check_stride: bool = True,
    msg: Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]] = None,
) -> None:
    """Asserts that the values of tensor pairs are bitwise equal.

    For complex tensors the check is performed on the real and imaginary component separately. Optionally, checks that
    some attributes of tensor pairs are equal.

    Also supports array-or-scalar-like inputs from which a :class:`torch.Tensor` can be constructed with
    :func:`torch.as_tensor`. Still, requires type equality, i.e. comparing a :class:`torch.Tensor` and a
    :class:`numpy.ndarray` is not supported.

    In case both inputs are :class:`~collections.abc.Sequence`'s or :class:`~collections.abc.Mapping`'s the checks are
    performed elementwise.

    Args:
        actual (Any): Actual input.
        expected (Any): Expected input.
        check_device (bool): If ``True`` (default), asserts that each tensor pair is on the same
            :attr:`~torch.Tensor.device` memory. If this check is disabled **and** it is not on the same
            :attr:`~torch.Tensor.device` memory, it is moved CPU memory before the values are compared.
        check_dtype (bool): If ``True`` (default), asserts that each tensor pair has the same
            :attr:`~torch.Tensor.dtype`. If this check is disabled it does not have the same
            :attr:`~torch.Tensor.dtype`, it is copied to the :class:`~torch.dtype` returned by
            :func:`torch.promote_types` before the values are compared.
        check_stride (bool): If ``True`` (default), asserts that each tensor pair has the same stride.
        msg (Optional[Union[str, Callable[[Tensor, Tensor, SimpleNamespace], str]]]): Optional error message to use if
            the values of a tensor pair mismatch. Can be passed as callable in which case it will be called with the
            tensor pair and a namespace of diagnostic info about the mismatches. See below for details.

    Raises:
        UsageError: If an array-or-scalar-like pair has different types.
        UsageError: If a :class:`torch.Tensor` can't be constructed from an array-or-scalar-like.
        UsageError: If any tensor is quantized or sparse. This is a temporary restriction and will be relaxed in the
            future.
        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 a tensor pair does not have the same :attr:`~torch.Tensor.shape`.
        AssertionError: If :attr:`check_device`, but a tensor pair is not on the same :attr:`~torch.Tensor.device`
            memory.
        AssertionError: If :attr:`check_dtype`, but a tensor pair does not have the same :attr:`~torch.Tensor.dtype`.
        AssertionError: If :attr:`check_stride`, but a tensor pair does not have the same stride.
        AssertionError: If the values of a tensor pair are not bitwise equal.

    The namespace that will be passed to :attr:`msg` if its a callable comprises the following attributes:

    - total_elements (int): Total number of values.
    - total_mismatches (int): Total number of mismatches.
    - mismatch_ratio (float): Quotient of total mismatches and total elements.
    - max_abs_diff (Union[int, float]): Greatest absolute difference of the inputs.
    - max_abs_diff_idx (Union[int, Tuple[int, ...]]): Index of greatest absolute difference.
    - max_rel_diff (Union[int, float]): Greatest relative difference of the inputs.
    - max_rel_diff_idx (Union[int, Tuple[int, ...]]): Index of greatest relative difference.

    For ``max_abs_diff`` and ``max_rel_diff`` the type depends on the :attr:`~torch.Tensor.dtype` of the inputs.

    .. seealso::

        To assert that the values of a tensor pair are close but are not required to be bitwise equal, use
        :func:`assert_close` instead.
    """
    exc, pair = _parse_inputs(actual, expected)
    if exc:
        raise exc
    else:
        pair = cast(Union[_TensorPair, List, Dict], pair)

    check_tensors = functools.partial(
        _check_tensors_equal,
        check_device=check_device,
        check_dtype=check_dtype,
        check_stride=check_stride,
        msg=msg,
    )
    exc = _check_pair(pair, check_tensors)
    if exc:
        raise exc


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

    If :attr:`actual` and :attr:`expected` are 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

    and they have the same :attr:`~torch.Tensor.device` (if :attr:`check_device` is ``True``), same ``dtype`` (if
    :attr:`check_dtype` is ``True``), and the same stride (if :attr:`check_stride` is ``True``). 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 :attr:`equal_nan` is ``True``.

    If :attr:`actual` and :attr:`expected` are complex-valued, they are considered close if both their real and
    imaginary components are considered close according to the definition above.

    :attr:`actual` and :attr:`expected` can be :class:`~torch.Tensor`'s or any array-or-scalar-like of the same type,
    from which :class:`torch.Tensor`'s can be constructed with :func:`torch.as_tensor`. In addition, :attr:`actual` and
    :attr:`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.

    Args:
        actual (Any): Actual input.
        expected (Any): Expected input.
        rtol (Optional[float]): Relative tolerance. If specified :attr:`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 :attr:`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. If ``"relaxed"``,
            complex values are considered as ``NaN`` if either the real **or** imaginary component is ``NaN``.
        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_stride (bool): If ``True`` (default), asserts that corresponding tensors have the same stride.
        msg (Optional[Union[str, Callable[[Tensor, Tensor, DiagnosticInfo], str]]]): Optional error message to use if
            the values of corresponding tensors mismatch. Can be passed as callable in which case it will be called
            with the mismatching tensors and a namespace of diagnostic info about the mismatches. See below for details.

    Raises:
        UsageError: If a :class:`torch.Tensor` can't be constructed from an array-or-scalar-like.
        UsageError: If any tensor is quantized or sparse. This is a temporary restriction and will be relaxed in the
            future.
        UsageError: If only :attr:`rtol` or :attr:`atol` is specified.
        AssertionError: If corresponding array-likes 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 :attr:`check_device`, but corresponding tensors are not on the same
            :attr:`~torch.Tensor.device`.
        AssertionError: If :attr:`check_dtype`, but corresponding tensors do not have the same ``dtype``.
        AssertionError: If :attr:`check_stride`, but corresponding tensors do not have the same stride.
        AssertionError: If the values of corresponding tensors are not close.

    The following table displays the default ``rtol`` and ``atol`` for different ``dtype``'s. Note that the ``dtype``
    refers to the promoted type in case :attr:`actual` and :attr:`expected` do not have the same ``dtype``.

    +---------------------------+------------+----------+
    | ``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`` |
    +---------------------------+------------+----------+
    | other                     | ``0.0``    | ``0.0``  |
    +---------------------------+------------+----------+

    The namespace of diagnostic information that will be passed to :attr:`msg` if its a callable has the following
    attributes:

    - ``number_of_elements`` (int): Number of elements in each tensor being compared.
    - ``total_mismatches`` (int): Total number of mismatches.
    - ``mismatch_ratio`` (float): Total mismatches divided by number of elements.
    - ``max_abs_diff`` (Union[int, float]): Greatest absolute difference of the inputs.
    - ``max_abs_diff_idx`` (Union[int, Tuple[int, ...]]): Index of greatest absolute difference.
    - ``max_rel_diff`` (Union[int, float]): Greatest relative difference of the inputs.
    - ``max_rel_diff_idx`` (Union[int, Tuple[int, ...]]): Index of greatest relative difference.

    For ``max_abs_diff`` and ``max_rel_diff`` the type depends on the :attr:`~torch.Tensor.dtype` of the inputs.

    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)

        >>> # Different input types are never considered close.
        >>> expected = torch.tensor([1.0, 2.0, 3.0])
        >>> actual = expected.numpy()
        >>> torch.testing.assert_close(actual, expected)
        AssertionError: Except for scalars, type equality is required, but got
        <class 'numpy.ndarray'> and <class 'torch.Tensor'> instead.
        >>> # Scalars of different types are an exception and can be compared with
        >>> # 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)
        AssertionError: Tensors are not close!
        >>> torch.testing.assert_close(actual, expected, equal_nan=True)

        >>> # If equal_nan=True, the real and imaginary NaN's of complex inputs have to match.
        >>> expected = torch.tensor(complex(float("NaN"), 0))
        >>> actual = torch.tensor(complex(0, float("NaN")))
        >>> torch.testing.assert_close(actual, expected, equal_nan=True)
        AssertionError: Tensors are not close!
        >>> # If equal_nan="relaxed", however, then complex numbers are treated as NaN if any
        >>> # of the real or imaginary component is NaN.
        >>> torch.testing.assert_close(actual, expected, equal_nan="relaxed")

        >>> expected = torch.tensor([1.0, 2.0, 3.0])
        >>> actual = torch.tensor([1.0, 4.0, 5.0])
        >>> # The default mismatch message can be overwritten.
        >>> torch.testing.assert_close(actual, expected, msg="Argh, the tensors are not close!")
        AssertionError: Argh, the tensors are not close!
        >>> # The error message can also created at runtime by passing a callable.
        >>> def custom_msg(actual, expected, diagnostic_info):
        ...     return (
        ...         f"Argh, we found {diagnostic_info.total_mismatches} mismatches! "
        ...         f"That is {diagnostic_info.mismatch_ratio:.1%}!"
        ...     )
        >>> torch.testing.assert_close(actual, expected, msg=custom_msg)
        AssertionError: Argh, we found 2 mismatches! That is 66.7%!
    """
    exc, pair = _parse_inputs(actual, expected)
    if exc:
        raise exc
    else:
        pair = cast(Union[_TensorPair, List, Dict], pair)

    check_tensors = functools.partial(
        _check_tensors_close,
        rtol=rtol,
        atol=atol,
        equal_nan=equal_nan,
        check_device=check_device,
        check_dtype=check_dtype,
        check_stride=check_stride,
        msg=msg,
    )
    exc = _check_pair(pair, check_tensors)
    if exc:
        raise exc