checks.py

# Copyright The PyTorch Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from time import perf_counter
from typing import Any, Dict, Mapping, Optional, Sequence, Tuple

import torch
from torch import Tensor

from torchmetrics.utilities.data import select_topk, to_onehot
from torchmetrics.utilities.enums import DataType


def _check_for_empty_tensors(preds: Tensor, target: Tensor) -> bool:
    if preds.numel() == target.numel() == 0:
        return True
    return False


def _check_same_shape(preds: Tensor, target: Tensor) -> None:
    """Check that predictions and target have the same shape, else raise error."""
    if preds.shape != target.shape:
        raise RuntimeError("Predictions and targets are expected to have the same shape")


def _basic_input_validation(
    preds: Tensor, target: Tensor, threshold: float, multiclass: Optional[bool], ignore_index: Optional[int]
) -> None:
    """Perform basic validation of inputs that does not require deducing any information of the type of inputs."""
    # Skip all other checks if both preds and target are empty tensors
    if _check_for_empty_tensors(preds, target):
        return

    if target.is_floating_point():
        raise ValueError("The `target` has to be an integer tensor.")

    if ignore_index is None and target.min() < 0:
        raise ValueError("The `target` has to be a non-negative tensor.")
    elif ignore_index is not None and ignore_index >= 0 and target.min() < 0:
        raise ValueError("The `target` has to be a non-negative tensor.")

    preds_float = preds.is_floating_point()
    if not preds_float and preds.min() < 0:
        raise ValueError("If `preds` are integers, they have to be non-negative.")

    if not preds.shape[0] == target.shape[0]:
        raise ValueError("The `preds` and `target` should have the same first dimension.")

    if multiclass is False and target.max() > 1:
        raise ValueError("If you set `multiclass=False`, then `target` should not exceed 1.")

    if multiclass is False and not preds_float and preds.max() > 1:
        raise ValueError("If you set `multiclass=False` and `preds` are integers, then `preds` should not exceed 1.")


def _check_shape_and_type_consistency(preds: Tensor, target: Tensor) -> Tuple[DataType, int]:
    """This checks that the shape and type of inputs are consistent with each other and fall into one of the
    allowed input types (see the documentation of docstring of ``_input_format_classification``). It does not check
    for consistency of number of classes, other functions take care of that.

    It returns the name of the case in which the inputs fall, and the implied number of classes (from the ``C`` dim for
    multi-class data, or extra dim(s) for multi-label data).
    """

    preds_float = preds.is_floating_point()

    if preds.ndim == target.ndim:
        if preds.shape != target.shape:
            raise ValueError(
                "The `preds` and `target` should have the same shape,",
                f" got `preds` with shape={preds.shape} and `target` with shape={target.shape}.",
            )
        if preds_float and target.numel() > 0 and target.max() > 1:
            raise ValueError(
                "If `preds` and `target` are of shape (N, ...) and `preds` are floats, `target` should be binary."
            )

        # Get the case
        if preds.ndim == 1 and preds_float:
            case = DataType.BINARY
        elif preds.ndim == 1 and not preds_float:
            case = DataType.MULTICLASS
        elif preds.ndim > 1 and preds_float:
            case = DataType.MULTILABEL
        else:
            case = DataType.MULTIDIM_MULTICLASS
        implied_classes = preds[0].numel() if preds.numel() > 0 else 0

    elif preds.ndim == target.ndim + 1:
        if not preds_float:
            raise ValueError("If `preds` have one dimension more than `target`, `preds` should be a float tensor.")
        if preds.shape[2:] != target.shape[1:]:
            raise ValueError(
                "If `preds` have one dimension more than `target`, the shape of `preds` should be"
                " (N, C, ...), and the shape of `target` should be (N, ...)."
            )

        implied_classes = preds.shape[1] if preds.numel() > 0 else 0

        if preds.ndim == 2:
            case = DataType.MULTICLASS
        else:
            case = DataType.MULTIDIM_MULTICLASS
    else:
        raise ValueError(
            "Either `preds` and `target` both should have the (same) shape (N, ...), or `target` should be (N, ...)"
            " and `preds` should be (N, C, ...)."
        )

    return case, implied_classes


def _check_num_classes_binary(num_classes: int, multiclass: Optional[bool]) -> None:
    """This checks that the consistency of `num_classes` with the data and `multiclass` param for binary data."""

    if num_classes > 2:
        raise ValueError("Your data is binary, but `num_classes` is larger than 2.")
    if num_classes == 2 and not multiclass:
        raise ValueError(
            "Your data is binary and `num_classes=2`, but `multiclass` is not True."
            " Set it to True if you want to transform binary data to multi-class format."
        )
    if num_classes == 1 and multiclass:
        raise ValueError(
            "You have binary data and have set `multiclass=True`, but `num_classes` is 1."
            " Either set `multiclass=None`(default) or set `num_classes=2`"
            " to transform binary data to multi-class format."
        )


def _check_num_classes_mc(
    preds: Tensor,
    target: Tensor,
    num_classes: int,
    multiclass: Optional[bool],
    implied_classes: int,
) -> None:
    """This checks that the consistency of `num_classes` with the data and `multiclass` param for (multi-
    dimensional) multi-class data."""

    if num_classes == 1 and multiclass is not False:
        raise ValueError(
            "You have set `num_classes=1`, but predictions are integers."
            " If you want to convert (multi-dimensional) multi-class data with 2 classes"
            " to binary/multi-label, set `multiclass=False`."
        )
    if num_classes > 1:
        if multiclass is False and implied_classes != num_classes:
            raise ValueError(
                "You have set `multiclass=False`, but the implied number of classes "
                " (from shape of inputs) does not match `num_classes`. If you are trying to"
                " transform multi-dim multi-class data with 2 classes to multi-label, `num_classes`"
                " should be either None or the product of the size of extra dimensions (...)."
                " See Input Types in Metrics documentation."
            )
        if target.numel() > 0 and num_classes <= target.max():
            raise ValueError("The highest label in `target` should be smaller than `num_classes`.")
        if preds.shape != target.shape and num_classes != implied_classes:
            raise ValueError("The size of C dimension of `preds` does not match `num_classes`.")


def _check_num_classes_ml(num_classes: int, multiclass: Optional[bool], implied_classes: int) -> None:
    """This checks that the consistency of ``num_classes`` with the data and ``multiclass`` param for multi-label
    data."""

    if multiclass and num_classes != 2:
        raise ValueError(
            "Your have set `multiclass=True`, but `num_classes` is not equal to 2."
            " If you are trying to transform multi-label data to 2 class multi-dimensional"
            " multi-class, you should set `num_classes` to either 2 or None."
        )
    if not multiclass and num_classes != implied_classes:
        raise ValueError("The implied number of classes (from shape of inputs) does not match num_classes.")


def _check_top_k(top_k: int, case: str, implied_classes: int, multiclass: Optional[bool], preds_float: bool) -> None:
    if case == DataType.BINARY:
        raise ValueError("You can not use `top_k` parameter with binary data.")
    if not isinstance(top_k, int) or top_k <= 0:
        raise ValueError("The `top_k` has to be an integer larger than 0.")
    if not preds_float:
        raise ValueError("You have set `top_k`, but you do not have probability predictions.")
    if multiclass is False:
        raise ValueError("If you set `multiclass=False`, you can not set `top_k`.")
    if case == DataType.MULTILABEL and multiclass:
        raise ValueError(
            "If you want to transform multi-label data to 2 class multi-dimensional"
            "multi-class data using `multiclass=True`, you can not use `top_k`."
        )
    if top_k >= implied_classes:
        raise ValueError("The `top_k` has to be strictly smaller than the `C` dimension of `preds`.")


def _check_classification_inputs(
    preds: Tensor,
    target: Tensor,
    threshold: float,
    num_classes: Optional[int],
    multiclass: Optional[bool],
    top_k: Optional[int],
    ignore_index: Optional[int] = None,
) -> DataType:
    """Performs error checking on inputs for classification.

    This ensures that preds and target take one of the shape/type combinations that are
    specified in ``_input_format_classification`` docstring. It also checks the cases of
    over-rides with ``multiclass`` by checking (for multi-class and multi-dim multi-class
    cases) that there are only up to 2 distinct labels.

    In case where preds are floats (probabilities), it is checked whether they are in ``[0,1]`` interval.

    When ``num_classes`` is given, it is checked that it is consistent with input cases (binary,
    multi-label, ...), and that, if available, the implied number of classes in the ``C``
    dimension is consistent with it (as well as that max label in target is smaller than it).

    When ``num_classes`` is not specified in these cases, consistency of the highest target
    value against ``C`` dimension is checked for (multi-dimensional) multi-class cases.

    If ``top_k`` is set (not None) for inputs that do not have probability predictions (and
    are not binary), an error is raised. Similarly, if ``top_k`` is set to a number that
    is higher than or equal to the ``C`` dimension of ``preds``, an error is raised.

    Preds and target tensors are expected to be squeezed already - all dimensions should be
    greater than 1, except perhaps the first one (``N``).

    Args:
        preds: Tensor with predictions (labels or probabilities)
        target: Tensor with ground truth labels, always integers (labels)
        threshold:
            Threshold value for transforming probability/logit predictions to binary
            (0,1) predictions, in the case of binary or multi-label inputs.
        num_classes:
            Number of classes. If not explicitly set, the number of classes will be inferred
            either from the shape of inputs, or the maximum label in the ``target`` and ``preds``
            tensor, where applicable.
        top_k:
            Number of the highest probability entries for each sample to convert to 1s - relevant
            only for inputs with probability predictions. The default value (``None``) will be
            interpreted as 1 for these inputs. If this parameter is set for multi-label inputs,
            it will take precedence over threshold.

            Should be left unset (``None``) for inputs with label predictions.
        multiclass:
            Used only in certain special cases, where you want to treat inputs as a different type
            than what they appear to be. See the parameter's
            :ref:`documentation section <pages/overview:using the multiclass parameter>`
            for a more detailed explanation and examples.


    Return:
        case: The case the inputs fall in, one of 'binary', 'multi-class', 'multi-label' or
            'multi-dim multi-class'
    """

    # Basic validation (that does not need case/type information)
    _basic_input_validation(preds, target, threshold, multiclass, ignore_index)

    # Check that shape/types fall into one of the cases
    case, implied_classes = _check_shape_and_type_consistency(preds, target)

    # Check consistency with the `C` dimension in case of multi-class data
    if preds.shape != target.shape:
        if multiclass is False and implied_classes != 2:
            raise ValueError(
                "You have set `multiclass=False`, but have more than 2 classes in your data,"
                " based on the C dimension of `preds`."
            )
        if target.max() >= implied_classes:
            raise ValueError(
                "The highest label in `target` should be smaller than the size of the `C` dimension of `preds`."
            )

    # Check that num_classes is consistent
    if num_classes:
        if case == DataType.BINARY:
            _check_num_classes_binary(num_classes, multiclass)
        elif case in (DataType.MULTICLASS, DataType.MULTIDIM_MULTICLASS):
            _check_num_classes_mc(preds, target, num_classes, multiclass, implied_classes)
        elif case.MULTILABEL:
            _check_num_classes_ml(num_classes, multiclass, implied_classes)

    # Check that top_k is consistent
    if top_k is not None:
        _check_top_k(top_k, case, implied_classes, multiclass, preds.is_floating_point())

    return case


def _input_squeeze(
    preds: Tensor,
    target: Tensor,
) -> Tuple[Tensor, Tensor]:
    """Remove excess dimensions."""
    if preds.shape[0] == 1:
        preds, target = preds.squeeze().unsqueeze(0), target.squeeze().unsqueeze(0)
    else:
        preds, target = preds.squeeze(), target.squeeze()
    return preds, target


def _input_format_classification(
    preds: Tensor,
    target: Tensor,
    threshold: float = 0.5,
    top_k: Optional[int] = None,
    num_classes: Optional[int] = None,
    multiclass: Optional[bool] = None,
    ignore_index: Optional[int] = None,
) -> Tuple[Tensor, Tensor, DataType]:
    """Convert preds and target tensors into common format.

    Preds and targets are supposed to fall into one of these categories (and are
    validated to make sure this is the case):

    * Both preds and target are of shape ``(N,)``, and both are integers (multi-class)
    * Both preds and target are of shape ``(N,)``, and target is binary, while preds
      are a float (binary)
    * preds are of shape ``(N, C)`` and are floats, and target is of shape ``(N,)`` and
      is integer (multi-class)
    * preds and target are of shape ``(N, ...)``, target is binary and preds is a float
      (multi-label)
    * preds are of shape ``(N, C, ...)`` and are floats, target is of shape ``(N, ...)``
      and is integer (multi-dimensional multi-class)
    * preds and target are of shape ``(N, ...)`` both are integers (multi-dimensional
      multi-class)

    To avoid ambiguities, all dimensions of size 1, except the first one, are squeezed out.

    The returned output tensors will be binary tensors of the same shape, either ``(N, C)``
    of ``(N, C, X)``, the details for each case are described below. The function also returns
    a ``case`` string, which describes which of the above cases the inputs belonged to - regardless
    of whether this was "overridden" by other settings (like ``multiclass``).

    In binary case, targets are normally returned as ``(N,1)`` tensor, while preds are transformed
    into a binary tensor (elements become 1 if the probability is greater than or equal to
    ``threshold`` or 0 otherwise). If ``multiclass=True``, then both targets are preds
    become ``(N, 2)`` tensors by a one-hot transformation; with the thresholding being applied to
    preds first.

    In multi-class case, normally both preds and targets become ``(N, C)`` binary tensors; targets
    by a one-hot transformation and preds by selecting ``top_k`` largest entries (if their original
    shape was ``(N,C)``). However, if ``multiclass=False``, then targets and preds will be
    returned as ``(N,1)`` tensor.

    In multi-label case, normally targets and preds are returned as ``(N, C)`` binary tensors, with
    preds being binarized as in the binary case. Here the ``C`` dimension is obtained by flattening
    all dimensions after the first one. However, if ``multiclass=True``, then both are returned as
    ``(N, 2, C)``, by an equivalent transformation as in the binary case.

    In multi-dimensional multi-class case, normally both target and preds are returned as
    ``(N, C, X)`` tensors, with ``X`` resulting from flattening of all dimensions except ``N`` and
    ``C``. The transformations performed here are equivalent to the multi-class case. However, if
    ``multiclass=False`` (and there are up to two classes), then the data is returned as
    ``(N, X)`` binary tensors (multi-label).

    Note:
        Where a one-hot transformation needs to be performed and the number of classes
        is not implicitly given by a ``C`` dimension, the new ``C`` dimension will either be
        equal to ``num_classes``, if it is given, or the maximum label value in preds and
        target.

    Args:
        preds: Tensor with predictions (labels or probabilities)
        target: Tensor with ground truth labels, always integers (labels)
        threshold:
            Threshold value for transforming probability/logit predictions to binary
            (0 or 1) predictions, in the case of binary or multi-label inputs.
        num_classes:
            Number of classes. If not explicitly set, the number of classes will be inferred
            either from the shape of inputs, or the maximum label in the ``target`` and ``preds``
            tensor, where applicable.
        top_k:
            Number of the highest probability entries for each sample to convert to 1s - relevant
            only for (multi-dimensional) multi-class inputs with probability predictions. The
            default value (``None``) will be interpreted as 1 for these inputs.

            Should be left unset (``None``) for all other types of inputs.
        multiclass:
            Used only in certain special cases, where you want to treat inputs as a different type
            than what they appear to be. See the parameter's
            :ref:`documentation section <pages/overview:using the multiclass parameter>`
            for a more detailed explanation and examples.

    Returns:
        preds: binary tensor of shape ``(N, C)`` or ``(N, C, X)``
        target: binary tensor of shape ``(N, C)`` or ``(N, C, X)``
        case: The case the inputs fall in, one of ``'binary'``, ``'multi-class'``, ``'multi-label'`` or
            ``'multi-dim multi-class'``
    """
    # Remove excess dimensions
    preds, target = _input_squeeze(preds, target)

    # Convert half precision tensors to full precision, as not all ops are supported
    # for example, min() is not supported
    if preds.dtype == torch.float16:
        preds = preds.float()

    case = _check_classification_inputs(
        preds,
        target,
        threshold=threshold,
        num_classes=num_classes,
        multiclass=multiclass,
        top_k=top_k,
        ignore_index=ignore_index,
    )

    if case in (DataType.BINARY, DataType.MULTILABEL) and not top_k:
        preds = (preds >= threshold).int()
        num_classes = num_classes if not multiclass else 2

    if case == DataType.MULTILABEL and top_k:
        preds = select_topk(preds, top_k)

    if case in (DataType.MULTICLASS, DataType.MULTIDIM_MULTICLASS) or multiclass:
        if preds.is_floating_point():
            num_classes = preds.shape[1]
            preds = select_topk(preds, top_k or 1)
        else:
            num_classes = num_classes if num_classes else max(preds.max(), target.max()) + 1
            preds = to_onehot(preds, max(2, num_classes))

        target = to_onehot(target, max(2, num_classes))  # type: ignore

        if multiclass is False:
            preds, target = preds[:, 1, ...], target[:, 1, ...]

    if not _check_for_empty_tensors(preds, target):
        if (case in (DataType.MULTICLASS, DataType.MULTIDIM_MULTICLASS) and multiclass is not False) or multiclass:
            target = target.reshape(target.shape[0], target.shape[1], -1)
            preds = preds.reshape(preds.shape[0], preds.shape[1], -1)
        else:
            target = target.reshape(target.shape[0], -1)
            preds = preds.reshape(preds.shape[0], -1)

    # Some operations above create an extra dimension for MC/binary case - this removes it
    if preds.ndim > 2:
        preds, target = preds.squeeze(-1), target.squeeze(-1)

    return preds.int(), target.int(), case


def _input_format_classification_one_hot(
    num_classes: int,
    preds: Tensor,
    target: Tensor,
    threshold: float = 0.5,
    multilabel: bool = False,
) -> Tuple[Tensor, Tensor]:
    """Convert preds and target tensors into one hot spare label tensors.

    Args:
        num_classes: number of classes
        preds: either tensor with labels, tensor with probabilities/logits or multilabel tensor
        target: tensor with ground-true labels
        threshold: float used for thresholding multilabel input
        multilabel: boolean flag indicating if input is multilabel

    Raises:
        ValueError:
            If ``preds`` and ``target`` don't have the same number of dimensions
            or one additional dimension for ``preds``.

    Returns:
        preds: one hot tensor of shape [num_classes, -1] with predicted labels
        target: one hot tensors of shape [num_classes, -1] with true labels
    """
    if preds.ndim not in (target.ndim, target.ndim + 1):
        raise ValueError("preds and target must have same number of dimensions, or one additional dimension for preds")

    if preds.ndim == target.ndim + 1:
        # multi class probabilities
        preds = torch.argmax(preds, dim=1)

    if preds.ndim == target.ndim and preds.dtype in (torch.long, torch.int) and num_classes > 1 and not multilabel:
        # multi-class
        preds = to_onehot(preds, num_classes=num_classes)
        target = to_onehot(target, num_classes=num_classes)

    elif preds.ndim == target.ndim and preds.is_floating_point():
        # binary or multilabel probabilities
        preds = (preds >= threshold).long()

    # transpose class as first dim and reshape
    if preds.ndim > 1:
        preds = preds.transpose(1, 0)
        target = target.transpose(1, 0)

    return preds.reshape(num_classes, -1), target.reshape(num_classes, -1)


def _check_retrieval_functional_inputs(
    preds: Tensor,
    target: Tensor,
    allow_non_binary_target: bool = False,
) -> Tuple[Tensor, Tensor]:
    """Check ``preds`` and ``target`` tensors are of the same shape and of the correct data type.

    Args:
        preds: either tensor with scores/logits
        target: tensor with ground true labels
        allow_non_binary_target: whether to allow target to contain non-binary values

    Raises:
        ValueError:
            If ``preds`` and ``target`` don't have the same shape, if they are empty
            or not of the correct ``dtypes``.

    Returns:
        preds: as torch.float32
        target: as torch.long if not floating point else torch.float32
    """
    if preds.shape != target.shape:
        raise ValueError("`preds` and `target` must be of the same shape")

    if not preds.numel() or not preds.size():
        raise ValueError("`preds` and `target` must be non-empty and non-scalar tensors")

    return _check_retrieval_target_and_prediction_types(preds, target, allow_non_binary_target=allow_non_binary_target)


def _check_retrieval_inputs(
    indexes: Tensor,
    preds: Tensor,
    target: Tensor,
    allow_non_binary_target: bool = False,
    ignore_index: Optional[int] = None,
) -> Tuple[Tensor, Tensor, Tensor]:
    """Check ``indexes``, ``preds`` and ``target`` tensors are of the same shape and of the correct data type.

    Args:
        indexes: tensor with queries indexes
        preds: tensor with scores/logits
        target: tensor with ground true labels
        ignore_index: ignore predictions where targets are equal to this number

    Raises:
        ValueError:
            If ``preds`` and ``target`` don't have the same shape, if they are empty or not of the correct ``dtypes``.

    Returns:
        indexes: as ``torch.long``
        preds: as ``torch.float32``
        target: as ``torch.long``
    """
    if indexes.shape != preds.shape or preds.shape != target.shape:
        raise ValueError("`indexes`, `preds` and `target` must be of the same shape")

    if indexes.dtype is not torch.long:
        raise ValueError("`indexes` must be a tensor of long integers")

    # remove predictions where target is equal to `ignore_index`
    if ignore_index is not None:
        valid_positions = target != ignore_index
        indexes, preds, target = indexes[valid_positions], preds[valid_positions], target[valid_positions]

    if not indexes.numel() or not indexes.size():
        raise ValueError(
            "`indexes`, `preds` and `target` must be non-empty and non-scalar tensors",
        )

    preds, target = _check_retrieval_target_and_prediction_types(
        preds, target, allow_non_binary_target=allow_non_binary_target
    )

    return indexes.long().flatten(), preds, target


def _check_retrieval_target_and_prediction_types(
    preds: Tensor,
    target: Tensor,
    allow_non_binary_target: bool = False,
) -> Tuple[Tensor, Tensor]:
    """Check ``preds`` and ``target`` tensors are of the same shape and of the correct data type.

    Args:
        preds: either tensor with scores/logits
        target: tensor with ground true labels
        allow_non_binary_target: whether to allow target to contain non-binary values

    Raises:
        ValueError:
            If ``preds`` and ``target`` don't have the same shape, if they are empty or not of the correct ``dtypes``.
    """
    if target.dtype not in (torch.bool, torch.long, torch.int) and not torch.is_floating_point(target):
        raise ValueError("`target` must be a tensor of booleans, integers or floats")

    if not preds.is_floating_point():
        raise ValueError("`preds` must be a tensor of floats")

    if not allow_non_binary_target and (target.max() > 1 or target.min() < 0):
        raise ValueError("`target` must contain `binary` values")

    target = target.float() if target.is_floating_point() else target.long()
    preds = preds.float()

    return preds.flatten(), target.flatten()


def _allclose_recursive(res1: Any, res2: Any, atol: float = 1e-8) -> bool:
    """Utility function for recursively asserting that two results are within a certain tolerance."""
    # single output compare
    if isinstance(res1, Tensor):
        return torch.allclose(res1, res2, atol=atol)
    elif isinstance(res1, str):
        return res1 == res2
    elif isinstance(res1, Sequence):
        return all(_allclose_recursive(r1, r2) for r1, r2 in zip(res1, res2))
    elif isinstance(res1, Mapping):
        return all(_allclose_recursive(res1[k], res2[k]) for k in res1.keys())
    else:
        return res1 == res2


def check_forward_no_full_state(
    metric_class,  # type: ignore
    init_args: Dict[str, Any] = {},
    input_args: Dict[str, Any] = {},
    num_update_to_compare: Sequence[int] = [10, 100, 1000],
    reps: int = 5,
) -> bool:
    """Utility function for checking if the new ``full_state_update`` property can safely be set to ``False`` which
    will for most metrics results in a speedup when using ``forward``.

    Args:
        metric_class: metric class object that should be checked
        init_args: dict containing arguments for initializing the metric class
        input_args: dict containing arguments to pass to ``forward``
        num_update_to_compare: if we successfully detech that the flag is safe to set to ``False``
            we will run some speedup test. This arg should be a list of integers for how many
            steps to compare over.
        reps: number of repetitions of speedup test

    Example (states in ``update`` are independent, save to set ``full_state_update=False``)
        >>> from torchmetrics import ConfusionMatrix
        >>> check_forward_no_full_state(
        ...     ConfusionMatrix,
        ...     init_args = {'num_classes': 3},
        ...     input_args = {'preds': torch.randint(3, (10,)), 'target': torch.randint(3, (10,))},
        ... )  # doctest: +ELLIPSIS
        Full state for 10 steps took: ...
        Partial state for 10 steps took: ...
        Full state for 100 steps took: ...
        Partial state for 100 steps took: ...
        Full state for 1000 steps took: ...
        Partial state for 1000 steps took: ...
        True

    Example (states in ``update`` are dependend meaning that ``full_state_update=True``):
        >>> from torchmetrics import ConfusionMatrix
        >>> class MyMetric(ConfusionMatrix):
        ...     def update(self, preds, target):
        ...         super().update(preds, target)
        ...         # by construction make future states dependent on prior states
        ...         if self.confmat.sum() > 20:
        ...             self.reset()
        >>> check_forward_no_full_state(
        ...     MyMetric,
        ...     init_args = {'num_classes': 3},
        ...     input_args = {'preds': torch.randint(3, (10,)), 'target': torch.randint(3, (10,))},
        ... )
        False
    """

    class FullState(metric_class):
        full_state_update = True

    class PartState(metric_class):
        full_state_update = False

    fullstate = FullState(**init_args)
    partstate = PartState(**init_args)

    equal = True
    for _ in range(num_update_to_compare[0]):
        out1 = fullstate(**input_args)
        try:  # if it fails, the code most likely need access to the full state
            out2 = partstate(**input_args)
        except RuntimeError:
            equal = False
            break
        equal = equal & _allclose_recursive(out1, out2)

    res1 = fullstate.compute()
    try:  # if it fails, the code most likely need access to the full state
        res2 = partstate.compute()
    except RuntimeError:
        equal = False
    equal = equal & _allclose_recursive(res1, res2)

    if not equal:  # we can stop early because the results did not match
        return False

    # Do timings
    res = torch.zeros(2, len(num_update_to_compare), reps)
    for i, metric in enumerate([fullstate, partstate]):
        for j, t in enumerate(num_update_to_compare):
            for r in range(reps):
                start = perf_counter()
                for _ in range(t):
                    _ = metric(**input_args)
                end = perf_counter()
                res[i, j, r] = end - start
                metric.reset()

    mean = torch.mean(res, -1)
    std = torch.std(res, -1)

    for t in range(len(num_update_to_compare)):
        print(f"Full state for {num_update_to_compare[t]} steps took: {mean[0, t]}+-{std[0, t]:0.3f}")
        print(f"Partial state for {num_update_to_compare[t]} steps took: {mean[1, t]:0.3f}+-{std[1, t]:0.3f}")

    return (mean[1, -1] < mean[0, -1]).item()  # if faster on average, we recommend upgrading