def effective_complexity(
    forward_func: Callable,
    inputs: TensorOrTupleOfTensorsGeneric,
    attributions: TensorOrTupleOfTensorsGeneric | list[TensorOrTupleOfTensorsGeneric],
    baselines: BaselineType = None,
    feature_mask: TensorOrTupleOfTensorsGeneric | None = None,
    additional_forward_args: Any = None,
    target: ExplanationTarget | list[ExplanationTarget] = NoTarget(),
    perturb_func: Callable = default_fixed_baseline_perturb_func(),
    n_perturbations_per_feature: int = 10,
    max_features_processed_per_batch: int | None = None,
    percentage_feature_removal_per_step: float = 0.0,
    frozen_features: list[torch.Tensor] | None = None,
    zero_variance_threshold: float = 0.01,
    return_ratio: bool = False,
    multi_target: bool = False,
    show_progress: bool = True,
    return_intermediate_results: bool = False,
    return_dict: bool = False,
) -> dict | tuple | torch.Tensor | list[torch.Tensor]:
    """
    Implementation of Effective complexity metric by Nguyen at el., 2020. This implementation
    reuses the batch-computation ideas from captum and therefore it is fully compatible with the Captum library.
    In addition, the implementation takes some ideas about the implementation of the metric from the python
    Quantus library.

    Effective complexity measures how many attributions in absolute values are exceeding a certain threshold (eps)
    where a value above the specified threshold implies that the features are important and under indicates it is not.
    Effective complexity requires the attributions to be normalized to return reasonable outputs since the original
    attributions may have different scales and effective complexity is sensitive to the scale of the attributions.

    References:
        1) An-phi Nguyen and María Rodríguez Martínez.: "On quantitative aspects of model
        interpretability." arXiv preprint arXiv:2007.07584 (2020).

    Args:
        forward_func (Callable):
                The forward function of the model or any modification of it.

        inputs (Tensor or tuple[Tensor, ...]): Input for which
                attributions are computed. If forward_func takes a single
                tensor as input, a single input tensor should be provided.
                If forward_func takes multiple tensors as input, a tuple
                of the input tensors should be provided. It is assumed
                that for all given input tensors, dimension 0 corresponds
                to the number of examples (aka batch size), and if
                multiple input tensors are provided, the examples must
                be aligned appropriately.


        attributions (Tensor or tuple[Tensor, ...]):
                Attribution scores computed based on an attribution algorithm.
                This attribution scores can be computed using the implementations
                provided in the `captum.attr` package. Some of those attribution
                approaches are so called global methods, which means that
                they factor in model inputs' multiplier, as described in:
                https://arxiv.org/abs/1711.06104
                Many global attribution algorithms can be used in local modes,
                meaning that the inputs multiplier isn't factored in the
                attribution scores.
                This can be done duing the definition of the attribution algorithm
                by passing `multipy_by_inputs=False` flag.
                For example in case of Integrated Gradients (IG) we can obtain
                local attribution scores if we define the constructor of IG as:
                ig = IntegratedGradients(multipy_by_inputs=False)

                Some attribution algorithms are inherently local.
                Examples of inherently local attribution methods include:
                Saliency, Guided GradCam, Guided Backprop and Deconvolution.

                For local attributions we can use real-valued perturbations
                whereas for global attributions that perturbation is binary.
                https://arxiv.org/abs/1901.09392

                If we want to compute the infidelity of global attributions we
                can use a binary perturbation matrix that will allow us to select
                a subset of features from `inputs` or `inputs - baselines` space.
                This will allow us to approximate sensitivity-n for a global
                attribution algorithm.

                `infidelity_perturb_func_decorator` function decorator is a helper
                function that computes perturbations under the hood if perturbed
                inputs are provided.

                For more details about how to use `infidelity_perturb_func_decorator`,
                please, read the documentation about `perturb_func`

                Attributions have the same shape and dimensionality as the inputs.
                If inputs is a single tensor then the attributions is a single
                tensor as well. If inputs is provided as a tuple of tensors
                then attributions will be tuples of tensors as well.

        baselines (scalar, Tensor, tuple of scalar, or Tensor):
                Baselines define reference values against which the completeness is measured which sometimes
                represent ablated values and are used to compare with the actual inputs to compute
                importance scores in attribution algorithms. They can be represented
                as:

                - a single tensor, if inputs is a single tensor, with
                  exactly the same dimensions as inputs or the first
                  dimension is one and the remaining dimensions match
                  with inputs.

                - a single scalar, if inputs is a single tensor, which will
                  be broadcasted for each input value in input tensor.

                - a tuple of tensors or scalars, the baseline corresponding
                  to each tensor in the inputs' tuple can be:

                - either a tensor with matching dimensions to
                  corresponding tensor in the inputs' tuple
                  or the first dimension is one and the remaining
                  dimensions match with the corresponding
                  input tensor.

                - or a scalar, corresponding to a tensor in the
                  inputs' tuple. This scalar value is broadcasted
                  for corresponding input tensor.

                Default: None

        feature_mask (Tensor or tuple[Tensor, ...], optional):
                    feature_mask defines a mask for the input, grouping
                    features which should be perturbed together. feature_mask
                    should contain the same number of tensors as inputs.
                    Each tensor should
                    be the same size as the corresponding input or
                    broadcastable to match the input tensor. Each tensor
                    should contain integers in the range 0 to num_features
                    - 1, and indices corresponding to the same feature should
                    have the same value.
                    Note that features within each input tensor are perturbed
                    independently (not across tensors).
                    If the forward function returns a single scalar per batch,
                    we enforce that the first dimension of each mask must be 1,
                    since attributions are returned batch-wise rather than per
                    example, so the attributions must correspond to the
                    same features (indices) in each input example.
                    If None, then a feature mask is constructed which assigns
                    each scalar within a tensor as a separate feature, which
                    is perturbed independently.
                    Default: None

        additional_forward_args (Any, optional): If the forward function
                requires additional arguments other than the inputs for
                which attributions should not be computed, this argument
                can be provided. It must be either a single additional
                argument of a Tensor or arbitrary (non-tuple) type or a tuple
                containing multiple additional arguments including tensors
                or any arbitrary python types. These arguments are provided to
                forward_func in order, following the arguments in inputs.
                Note that the perturbations are not computed with respect
                to these arguments. This means that these arguments aren't
                being passed to `perturb_func` as an input argument.

                Default: None
        target (int, tuple, Tensor, or list, optional): Indices for selecting
                predictions from output(for classification cases,
                this is usually the target class).
                If the network returns a scalar value per example, no target
                index is necessary.
                For general 2D outputs, targets can be either:

                - A single integer or a tensor containing a single
                  integer, which is applied to all input examples

                - A list of integers or a 1D tensor, with length matching
                  the number of examples in inputs (dim 0). Each integer
                  is applied as the target for the corresponding example.

                  For outputs with > 2 dimensions, targets can be either:

                - A single tuple, which contains #output_dims - 1
                  elements. This target index is applied to all examples.

                - A list of tuples with length equal to the number of
                  examples in inputs (dim 0), and each tuple containing
                  #output_dims - 1 elements. Each tuple is applied as the
                  target for the corresponding example.

                Default: None

        perturb_func (Callable):
                The perturbation function of model inputs. This function takes
                model inputs and the corresponding feature masks to be perturbed.
                Optionally it also takes baselines as input arguments and returns
                a tuple of perturbed inputs. For example:

                >>> def my_perturb_func(inputs, masks, baselines):
                >>>   <MY-LOGIC-HERE>
                >>>   return perturbed_inputs

                If there are more than one inputs passed to this function those
                will be passed to `perturb_func` as tuples in the same order as they
                are passed to the function. In addition the corresponding feature masks
                will also be passed as a tuple in the same order as inputs. See default_perturb_func
                in metrics._utils.perturbation.py for an example of a perturbation function.

                If inputs
                 - is a single tensor, the function needs to return single tensor of perturbed inputs.
                 - is a tuple of tensors, corresponding perturbed
                   inputs must be computed and returned as tuples in the
                   following format:

                   (perturbed_input1, perturbed_input2, ... perturbed_inputN)

                It is important to note that for performance reasons `perturb_func`
                isn't called for each example individually but on a batch of
                input examples that are repeated `max_features_processed_per_batch / batch_size`
                times within the batch.

        n_perturbations_per_feature (int, optional): The number of times each feature is perturbed.
                Each input example in the inputs tensor is expanded `n_perturbations_per_feature`
                times before calling `perturb_func` function for every single feature in the input.
                So if you have an input tensor of shape (N, C, H, W) and you set `n_perturbations_per_feature`,
                then each example in the batch will be handled separately and for each example a total of
                `C * H * W` perturbation steps will be performed and in each perturbation step a single feature
                will be repeated `n_perturbations_per_feature` times. This means that the total number of
                perturbation steps will be `C * H * W * n_perturbations_per_feature` for each example in the batch.

                Default: 10
        max_features_processed_per_batch (int, optional): The number of maximum input
                features that are processed together for every example. In case the number of
                features in each example (`C * H * W`) exceeds
                `max_features_processed_per_batch`, they will be sliced
                into batches of `max_features_processed_per_batch` examples and processed
                sequentially.
        percentage_feature_removal_per_step (int, optional): The number of steps to process the features in a single batch.
                This is useful for reducing the computation time for large models. This allows 'percentage_feature_removal_per_step'
                ascending features to be removed together in each step instead of removing all the features.
                Therefore, if percentage_feature_removal_per_step=10, instead of removing the features X1, <X2, <X3... in each step, we
                will remove the features <X1-10, <X10-X20, <X20-X30 ...
                Default: 1
        frozen_features (List[torch.Tensor], optional): A list of frozen features that are not perturbed.
                This can be useful for ignoring the input structure features like padding, etc. Default: None
                In case CLS,PAD,SEP tokens are present in the input, they can be frozen by passing the indices
                of feature masks that correspond to these tokens.
        zero_variance_threshold (float, optional): A small value that is used to threshold the output variance
        return_ratio (bool, optional): A boolean flag that indicates whether the effective complexity is returned as a ratio
                of the number of important features to the total number of features. Default: False
        multi_target (bool, optional): A boolean flag that indicates whether the metric computation is for
                multi-target explanations. if set to true, the targets are required to be a list of integers
                each corresponding to a required target class in the output. The corresponding metric outputs
                are then returned as a list of metric outputs corresponding to each target class.
                Default is False.
        show_progress (bool, optional): Displays the progress of the computation. Default: True
        return_intermediate_results (bool, optional): A boolean flag that indicates whether the intermediate
                results are returned. Default: False
        return_dict (bool, optional): A boolean flag that indicates whether the metric outputs are returned as a dictionary
    Returns:
        A tuple of tensors:
            effective_complexity_batch (Tensor): A tensor of scalar effective_complexity scores per
                    input example. The first dimension is equal to the
                    number of examples in the input batch and the second
                    dimension is one.
            non_sensitivity_batch (Tensor): A tensor of scalar non_sensitivity scores per
                    input example. The first dimension is equal to the
                    number of examples in the input batch and the second
                    dimension is one.
            n_features_batch (Tensor): A tensor of scalar values that represent the total number of
                    features that are processed in the input batch. The first dimension is equal to the
                    number of examples in the input batch and the second dimension is one.
    Examples::
        >>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
        >>> # and returns an Nx10 tensor of class probabilities.
        >>> net = ImageClassifier()
        >>> saliency = Saliency(net)
        >>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
        >>> baselines = torch.zeros(2, 3, 32, 32)
        >>> # Computes saliency maps for class 3.
        >>> attribution = saliency.attribute(input, target=3)
        >>> # define a perturbation function for the input

        >>> # Computes the effective complexity for saliency maps
        >>> effective_complexity, non_sens, n_features = effective_complexity(net, input, attribution, baselines)
    """
    is_attributions_list = isinstance(attributions, list)
    is_targets_list = isinstance(target, list)
    if multi_target:
        assert is_attributions_list, (
            "attributions must be a list of tensors or list of tuples of tensors"
        )
        assert is_targets_list, "targets must be a list of targets"
        assert len(target) == len(
            attributions
        ), f"""The number of targets in the targets_list and
            attributions_list must match. Found number of targets in the targets_list is: {len(target)} and in the
            attributions_list: {len(attributions)}"""

    if not is_attributions_list:
        attributions = [attributions]
    if not is_targets_list:
        target = [target]

    effective_complexity_batch_list = []
    perturbed_fwd_diffs_relative_vars_batch_list = []
    n_features_batch_list = []
    for a, t in tqdm.tqdm(
        zip(attributions, target, strict=True), disable=not show_progress
    ):
        (
            effective_complexity_batch,
            perturbed_fwd_diffs_relative_vars_batch,
            n_features_batch,
        ) = _effective_complexity(
            forward_func=forward_func,
            inputs=inputs,
            attributions=a,
            baselines=baselines,
            feature_mask=feature_mask,
            additional_forward_args=additional_forward_args,
            target=t.value,
            perturb_func=perturb_func,
            n_perturbations_per_feature=n_perturbations_per_feature,
            max_features_processed_per_batch=max_features_processed_per_batch,
            percentage_feature_removal_per_step=percentage_feature_removal_per_step,
            frozen_features=frozen_features,
            zero_variance_threshold=zero_variance_threshold,
            return_ratio=return_ratio,
            show_progress=show_progress,
        )
        effective_complexity_batch_list.append(effective_complexity_batch)
        perturbed_fwd_diffs_relative_vars_batch_list.append(
            perturbed_fwd_diffs_relative_vars_batch
        )
        n_features_batch_list.append(n_features_batch)

    if not is_attributions_list:
        effective_complexity_batch_list = effective_complexity_batch_list[0]
        perturbed_fwd_diffs_relative_vars_batch_list = (
            perturbed_fwd_diffs_relative_vars_batch_list[0]
        )
        n_features_batch_list = n_features_batch_list[0]

    if return_intermediate_results:
        if return_dict:
            return {
                "score": effective_complexity_batch_list,
                "perturbed_fwd_diffs_relative_vars_batch": perturbed_fwd_diffs_relative_vars_batch_list,
                "n_features_batch": n_features_batch_list,
            }
        else:
            return (
                effective_complexity_batch_list,
                perturbed_fwd_diffs_relative_vars_batch_list,
                n_features_batch_list,
            )
    else:
        if return_dict:
            return {"score": effective_complexity_batch_list}
        return effective_complexity_batch_list