matching_series.py

# Copyright 2020 The HuggingFace Datasets Authors and the current dataset script contributor.
#
# 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.
"""Matching Series is a metric for evaluating time-series generation models. It is based on the idea of matching the generated time-series with the original time-series. The metric calculates the Mean Squared Error (distance) between the generated time-series and the original time-series between matched instances."""

import concurrent.futures
import math
import statistics
from typing import List, Optional, Union

import datasets
import evaluate
import numpy as np

# TODO: Add BibTeX citation
_CITATION = """TBA"""

_DESCRIPTION = """\
Matching Series is a metric for evaluating time-series generation models. It is based on the idea of matching the generated time-series with the original time-series. The metric calculates the Mean Squared Error (distance) between the generated time-series and the original time-series between matched instances. The metric outputs a score greater or equal to 0, where 0 indicates a perfect generation.
"""


_KWARGS_DESCRIPTION = """
Calculates how good are predictions given some references, using certain scores
Args:
    predictions: list of list of list of float or numpy.ndarray: The generated time-series. The shape of the array should be `(num_generation, seq_len, num_features)`.
    references: list of list of list of float or numpy.ndarray: The original time-series. The shape of the array should be `(num_reference, seq_len, num_features)`.
    batch_size: int, optional: The batch size for computing the metric. This affects quadratically. Default is None.
    cuc_n_calculation: int, optional: The number of samples to compute the coverage because sampling exists. Default is 3.
    cuc_n_samples: list of int, optional: The number of samples to compute the coverage. Default is $[2^i \text{for} i \leq \log_2 n] + [n]$.
    metric: str, optional: The metric to measure distance between examples. Default is "mse". Available options are "mse", "mae", "rmse".
    num_processes: int, optional: The number of processes to use for computing the distance. Default is 1.
    instance_normalization: bool, optional: Whether to normalize the instances along the time axis. Default is False.
    return_distance: bool, optional: Whether to return the distance matrix. Default is False.
    return_matching: bool, optional: Whether to return the matching matrix. Default is False.
    return_each_features: bool, optional: Whether to return the results for each feature. Default is False.
    return_coverages: bool, optional: Whether to return the coverages. Default is False.
    return_all: bool, optional: Whether to return all the results. Default is False.
    dtype: str, optional: The data type used for computation. Default is "float32".
    eps: float, optional: The epsilon value to avoid division by zero. Default is 1e-8.
Returns:
    dict: A dictionary containing the following keys:
        precision_distance (float): The precision of the distance.
        recall_distance (float): The recall of the distance.
        mean_distance (float): The mean of the distance.
        index_distance (float): The index of the distance.
        matching_precision (float): The precision of the matching instances.
        matching_recall (float): The recall of the matching instances.
        matching_f1 (float): The F1-score of the matching instances.
        coverages (list of float): The coverages.
        cuc (float): The coverage under the curve.
        macro_.* (float): The macro value of the .*.
        .*_features (list of float): The values computed individually for each feature.
        distance (numpy.ndarray): The distance matrix.
        match (numpy.ndarray): The matching matrix.
        match_inv (numpy.ndarray): The inverse matching matrix.
Examples:
    Examples should be written in doctest format, and should illustrate how
    to use the function.

    >>> num_generation = 100
    >>> num_reference = 10
    >>> seq_len = 100
    >>> num_features = 10
    >>> references = np.random.rand(num_reference, seq_len, num_features)
    >>> predictions = np.random.rand(num_generation, seq_len, num_features)
    >>> metric = evaluate.load("bowdbeg/matching_series")
    >>> results = metric.compute(references=references, predictions=predictions, batch_size=1000, return_all=True)
    >>> print(results)
    {'precision_distance': 0.1573285013437271, 'recall_distance': 0.15106813609600067, 'mean_distance': 0.1541983187198639, 'index_distance': 0.16858606040477753, 'matching_precision': 0.06, 'matching_recall': 1.0, 'matching_f1': 0.11320756503381972, 'cuc': 0.12428571428571429, 'macro_precision_distance': 0.13803552389144896, 'macro_recall_distance': 0.12179495096206665, 'macro_mean_distance': 0.1299152374267578, 'macro_index_distance': 0.16858604848384856, 'macro_matching_precision': 0.094, 'macro_matching_recall': 0.97, 'macro_matching_f1': 0.17132608782381706, 'macro_cuc': 0.11419285714285714, 'distance': array([[[0.20763363, 0.16514072, 0.18695284, ..., 0.15037987,
            0.19424284, 0.15943716],
            [0.17150438, 0.18020014, 0.17024504, ..., 0.18492931,
            0.18814348, 0.204207  ],
            [0.1769202 , 0.15609328, 0.17568389, ..., 0.17731658,
            0.2027854 , 0.13216409],
            ...,
            [0.1838122 , 0.19475608, 0.14176111, ..., 0.1635111 ,
            0.1652672 , 0.17145865],
            [0.16084194, 0.14208058, 0.17567575, ..., 0.15595785,
            0.16614595, 0.17834347],
            [0.16388315, 0.14126392, 0.18021484, ..., 0.16791071,
            0.18403953, 0.16666758]],

        [[0.16838932, 0.18878576, 0.17654441, ..., 0.1747057 ,
            0.16590554, 0.16901629],
            [0.16553226, 0.1882645 , 0.17863466, ..., 0.19269662,
            0.20451452, 0.19941731],
            [0.16502398, 0.16619626, 0.18069996, ..., 0.16124909,
            0.18933088, 0.1495165 ],
            ...,
            [0.15946846, 0.19988221, 0.17965002, ..., 0.12951666,
            0.2067793 , 0.13811146],
            [0.16227122, 0.17736743, 0.18641905, ..., 0.15038314,
            0.20186146, 0.17849396],
            [0.16410898, 0.18323919, 0.16945514, ..., 0.15783694,
            0.21556957, 0.17172968]],

        [[0.18094379, 0.1364854 , 0.18436092, ..., 0.187335  ,
            0.16240291, 0.13713893],
            [0.18005298, 0.15323727, 0.15788248, ..., 0.19451861,
            0.12822135, 0.14064161],
            [0.1564556 , 0.17312287, 0.1856657 , ..., 0.17237219,
            0.1596888 , 0.16547912],
            ...,
            [0.15611127, 0.16121496, 0.15533476, ..., 0.16520709,
            0.1427248 , 0.19455005],
            [0.17268528, 0.17360437, 0.15962966, ..., 0.18134868,
            0.15509704, 0.20222983],
            [0.18704675, 0.15934442, 0.14928888, ..., 0.18904984,
            0.16192877, 0.18576236]],

        ...,

        [[0.13717972, 0.15645625, 0.16123378, ..., 0.19453087,
            0.14441733, 0.1487963 ],
            [0.1454296 , 0.13368016, 0.18665504, ..., 0.16096605,
            0.15130125, 0.18332979],
            [0.14654924, 0.19097947, 0.19629759, ..., 0.15887487,
            0.19266474, 0.17430782],
            ...,
            [0.161704  , 0.16357127, 0.18512094, ..., 0.16441964,
            0.13961458, 0.17298506],
            [0.1366249 , 0.15852758, 0.1982772 , ..., 0.18822236,
            0.16153064, 0.19617072],
            [0.14570995, 0.15005183, 0.19667573, ..., 0.1856473 ,
            0.18603194, 0.19179863]],

        [[0.17813908, 0.176182  , 0.16847256, ..., 0.16903524,
            0.17150073, 0.15068175],
            [0.17632519, 0.1404587 , 0.16388708, ..., 0.16873878,
            0.15744762, 0.198475  ],
            [0.14986345, 0.1517829 , 0.17624639, ..., 0.18365957,
            0.17399347, 0.15581599],
            ...,
            [0.16128553, 0.1974935 , 0.13766351, ..., 0.14026196,
            0.15450196, 0.16110381],
            [0.16281141, 0.14699166, 0.16935429, ..., 0.1394466 ,
            0.1717883 , 0.16191883],
            [0.14886455, 0.1603608 , 0.15172943, ..., 0.12851712,
            0.19859877, 0.15576601]],

        [[0.20230632, 0.19680001, 0.17143433, ..., 0.18601838,
            0.15998998, 0.16043548],
            [0.19753966, 0.19073424, 0.15046756, ..., 0.18833323,
            0.16755773, 0.20127842],
            [0.16012056, 0.16638812, 0.16493171, ..., 0.15849902,
            0.20269662, 0.1857642 ],
            ...,
            [0.16341361, 0.19168772, 0.16597596, ..., 0.15715535,
            0.18122095, 0.17266828],
            [0.1570099 , 0.18294124, 0.16713732, ..., 0.17442709,
            0.17020254, 0.18804537],
            [0.16752282, 0.1295177 , 0.18792175, ..., 0.13976808,
            0.21054329, 0.18118018]]], dtype=float32), 'match': array([4, 7, 3, 9, 4, 0, 7, 5, 4, 7, 9, 7, 7, 5, 7, 0, 0, 7, 4, 3, 3, 2,
        8, 9, 4, 4, 5, 1, 4, 9, 0, 2, 7, 3, 6, 5, 6, 3, 2, 2, 2, 6, 9, 4,
        4, 9, 1, 6, 0, 6, 9, 2, 0, 6, 7, 2, 0, 4, 5, 2, 3, 9, 2, 3, 9, 1,
        6, 4, 8, 9, 7, 4, 6, 5, 5, 6, 9, 5, 6, 2, 9, 4, 9, 3, 2, 9, 9, 7,
        9, 5, 9, 1, 7, 6, 4, 4, 5, 4, 7, 5]), 'match_inv': array([15, 91, 79,  4,  4,  4, 49,  4, 49, 45]), 'coverages': [0.10000000000000002, 0.16666666666666666, 0.3666666666666667, 0.6333333333333333, 0.8333333333333334, 0.9, 1.0], 'precision_distance_features': [0.1383965164422989, 0.13804036378860474, 0.1388234943151474, 0.1392393559217453, 0.1357768476009369, 0.1364508718252182, 0.14039862155914307, 0.13417008519172668, 0.1368638128042221, 0.14219526946544647], 'recall_distance_features': [0.11730053275823593, 0.12232911586761475, 0.12200610339641571, 0.12571024894714355, 0.12081331014633179, 0.11693283170461655, 0.12660981714725494, 0.12248671054840088, 0.11726576089859009, 0.12649507820606232], 'mean_distance_features': [0.1278485246002674, 0.13018473982810974, 0.13041479885578156, 0.13247480243444443, 0.12829507887363434, 0.12669185176491737, 0.133504219353199, 0.12832839787006378, 0.1270647868514061, 0.1343451738357544], 'index_distance_features': [0.17064405977725983, 0.17019756138324738, 0.17373089492321014, 0.17575454711914062, 0.15942324697971344, 0.1615942418575287, 0.16519878804683685, 0.1714271903038025, 0.17072594165802002, 0.16716401278972626], 'matching_precision_features': [0.1, 0.09, 0.1, 0.1, 0.09, 0.09, 0.1, 0.08, 0.09, 0.1], 'matching_recall_features': [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9, 0.9, 0.9, 1.0], 'matching_f1_features': [0.18181819851239656, 0.16513763164885095, 0.18181819851239656, 0.18181819851239656, 0.16513763164885095, 0.16513763164885095, 0.18000001639999985, 0.14693879251145342, 0.16363638033057834, 0.18181819851239656], 'cuc_features': [0.11935714285714286, 0.11578571428571431, 0.11814285714285715, 0.12407142857142857, 0.11207142857142856, 0.11821428571428572, 0.10807142857142855, 0.09635714285714285, 0.10700000000000001, 0.12285714285714286], 'coverages_features': [[0.10000000000000002, 0.20000000000000004, 0.26666666666666666, 0.4666666666666666, 0.7666666666666666, 0.8666666666666667, 1.0], [0.10000000000000002, 0.20000000000000004, 0.3666666666666667, 0.5666666666666668, 0.6, 0.8333333333333334, 1.0], [0.10000000000000002, 0.16666666666666666, 0.26666666666666666, 0.4666666666666666, 0.6999999999999998, 0.8666666666666667, 1.0], [0.10000000000000002, 0.20000000000000004, 0.3, 0.6, 0.7333333333333333, 0.9333333333333332, 1.0], [0.10000000000000002, 0.20000000000000004, 0.3, 0.5, 0.6666666666666666, 0.7666666666666666, 1.0], [0.10000000000000002, 0.20000000000000004, 0.3333333333333333, 0.5333333333333333, 0.7666666666666666, 0.8333333333333334, 1.0], [0.10000000000000002, 0.20000000000000004, 0.3, 0.5333333333333333, 0.6999999999999998, 0.7666666666666666, 0.9], [0.10000000000000002, 0.20000000000000004, 0.2333333333333333, 0.4666666666666666, 0.5333333333333333, 0.6333333333333333, 0.9], [0.10000000000000002, 0.16666666666666666, 0.26666666666666666, 0.4666666666666666, 0.5666666666666667, 0.8000000000000002, 0.9], [0.10000000000000002, 0.16666666666666666, 0.30000000000000004, 0.5666666666666667, 0.7999999999999999, 0.9, 1.0]]}
"""


@evaluate.utils.file_utils.add_start_docstrings(_DESCRIPTION, _KWARGS_DESCRIPTION)
class matching_series(evaluate.Metric):
    """TODO: Short description of my evaluation module."""

    def _info(self):
        # TODO: Specifies the evaluate.EvaluationModuleInfo object
        return evaluate.MetricInfo(
            # This is the description that will appear on the modules page.
            module_type="metric",
            description=_DESCRIPTION,
            citation=_CITATION,
            inputs_description=_KWARGS_DESCRIPTION,
            # This defines the format of each prediction and reference
            features=datasets.Features(
                {
                    "predictions": datasets.Sequence(datasets.Sequence(datasets.Value("float"))),
                    "references": datasets.Sequence(datasets.Sequence(datasets.Value("float"))),
                }
            ),
            # Homepage of the module for documentation
            homepage="https://huggingface.co/spaces/bowdbeg/matching_series",
            # Additional links to the codebase or references
            codebase_urls=["http://github.com/path/to/codebase/of/new_module"],
            reference_urls=["http://path.to.reference.url/new_module"],
        )

    def _download_and_prepare(self, dl_manager):
        """Optional: download external resources useful to compute the scores"""
        pass

    def compute(self, *, predictions=None, references=None, **kwargs) -> Optional[dict]:
        """"""
        all_kwargs = {"predictions": predictions, "references": references, **kwargs}
        if predictions is None and references is None:
            missing_kwargs = {k: None for k in self._feature_names() if k not in all_kwargs}
            all_kwargs.update(missing_kwargs)
        else:
            missing_inputs = [k for k in self._feature_names() if k not in all_kwargs]
            if missing_inputs:
                raise ValueError(
                    f"Evaluation module inputs are missing: {missing_inputs}. All required inputs are {list(self._feature_names())}"
                )
        inputs = {input_name: all_kwargs[input_name] for input_name in self._feature_names()}
        compute_kwargs = {k: kwargs[k] for k in kwargs if k not in self._feature_names()}
        return self._compute(**inputs, **compute_kwargs)

    def _compute(
        self,
        predictions: Union[List, np.ndarray],
        references: Union[List, np.ndarray],
        batch_size: Optional[int] = None,
        cuc_n_calculation: int = 3,
        cuc_n_samples: Union[List[int], str] = "auto",
        metric: str = "mse",
        num_processes: int = 1,
        instance_normalization: bool = False,
        return_distance: bool = False,
        return_matching: bool = False,
        return_each_features: bool = False,
        return_coverages: bool = False,
        return_all: bool = False,
        dtype=np.float32,
        eps: float = 1e-8,
    ):
        """
        Compute the Matching Series metric

        Args:
            predictions: list of list of list of float or numpy.ndarray: The generated time-series. The shape of the array should be `(num_generation, seq_len, num_features)`.
            references: list of list of list of float or numpy.ndarray: The original time-series. The shape of the array should be `(num_reference, seq_len, num_features)`.
            batch_size: int, optional: The batch size for computing the metric. This affects quadratically. Default is None.
            cuc_n_calculation: int, optional: The number of samples to compute the coverage because sampling exists. Default is 3.
            cuc_n_samples: list of int, optional: The number of samples to compute the coverage. Default is $[2^i \text{for} i \leq \log_2 n] + [n]$.
            metric: str, optional: The metric to measure distance between examples. Default is "mse". Available options are "mse", "mae", "rmse".
            num_processes: int, optional: The number of processes to use for computing the distance. Default is 1.
            instance_normalization: bool, optional: Whether to normalize the instances along the time axis. Default is False.
            return_distance: bool, optional: Whether to return the distance matrix. Default is False.
            return_matching: bool, optional: Whether to return the matching matrix. Default is False.
            return_each_features: bool, optional: Whether to return the results for each feature. Default is False.
            return_coverages: bool, optional: Whether to return the coverages. Default is False.
            return_matching_indices: bool, optional: Whether to return the indices of matching. Default is False.
            return_all: bool, optional: Whether to return all the results. Default is False.
            dtype: str, optional: The data type used for computation. Default is "float32".
            eps: float, optional: The epsilon value to avoid division by zero. Default is 1e-8.
        Returns:
            dict: A dictionary containing the following keys:
                precision_distance (float): The precision of the distance.
                recall_distance (float): The recall of the distance.
                mean_distance (float): The mean of the distance.
                index_distance (float): The index of the distance.
                matching_precision (float): The precision of the matching instances.
                matching_recall (float): The recall of the matching instances.
                matching_f1 (float): The F1-score of the matching instances.
                coverages (list of float): The coverages.
                cuc (float): The coverage under the curve.
                macro_.* (float): The macro value of the .*.
                .*_features (list of float): The values computed individually for each feature.
                distance (numpy.ndarray): The distance matrix.
                match (numpy.ndarray): The matching matrix.
                match_inv (numpy.ndarray): The inverse matching matrix.
                match_features (list of numpy.ndarray): The matching matrix for each feature.
                match_inv_features (list of numpy.ndarray): The inverse matching matrix for each feature.
        """
        if return_all:
            return_distance = True
            return_matching = True
            return_each_features = True
            return_coverages = True
        predictions = np.array(predictions).astype(dtype)
        references = np.array(references).astype(dtype)

        if instance_normalization:
            predictions = (predictions - predictions.mean(axis=1, keepdims=True)) / predictions.std(
                axis=1, keepdims=True
            )
            references = (references - references.mean(axis=1, keepdims=True)) / references.std(axis=1, keepdims=True)

        assert isinstance(predictions, np.ndarray) and isinstance(references, np.ndarray)
        if predictions.shape[1:] != references.shape[1:]:
            raise ValueError(
                "The number of features in the predictions and references should be the same. predictions: {}, references: {}".format(
                    predictions.shape[1:], references.shape[1:]
                )
            )

        # at first, convert the inputs to numpy arrays
        distance = self.compute_distance(
            predictions=predictions,
            references=references,
            metric=metric,
            batch_size=batch_size,
            num_processes=num_processes,
            dtype=dtype,
        )

        distance_mean = distance.mean(axis=-1)
        metrics = self._compute_metrics(
            distance=distance_mean,
            eps=eps,
            cuc_n_calculation=cuc_n_calculation,
            cuc_n_samples=cuc_n_samples,
        )
        metrics_feature = [
            self._compute_metrics(distance[:, :, f], eps, cuc_n_calculation, cuc_n_samples)
            for f in range(predictions.shape[-1])
        ]
        macro_metrics = {
            "macro_" + k: statistics.mean([m[k] for m in metrics_feature])  # type: ignore
            for k in metrics_feature[0].keys()
            if isinstance(metrics_feature[0][k], (int, float))
        }

        out = {}
        out.update({k: v for k, v in metrics.items() if isinstance(v, (int, float))})
        out.update(macro_metrics)

        if return_distance:
            out["distance"] = distance
        if return_matching:
            out.update({k: v for k, v in metrics.items() if "match" in k})

            g2r_index = distance.argmin(axis=1)
            r2g_index = distance.argmin(axis=0)
            out["match_features"] = g2r_index
            out["match_inv_features"] = r2g_index

        if return_coverages:
            out["coverages"] = metrics["coverages"]
        if return_each_features:
            out.update(
                {
                    k + "_features": [m[k] for m in metrics_feature]
                    for k in metrics_feature[0].keys()
                    if isinstance(metrics_feature[0][k], (int, float))
                }
            )
            if return_coverages:
                out.update(
                    {
                        "coverages_features": [m["coverages"] for m in metrics_feature],
                    }
                )

        return out

    def compute_cuc(
        self,
        match: np.ndarray,
        n_reference: int,
        n_calculation: int,
        n_samples: Union[List[int], str],
    ):
        """
        Compute Coverage Under Curve
        Args:
            match: best match for each generated time series
            n_reference: number of reference time series
            n_calculation: number of Coverage Under Curve calculate times
            n_samples: number of samples to use for Coverage Under Curve calculation. If "auto", it uses the number of samples of the predictions.
        Returns:
        """
        n_generaiton = len(match)
        if n_samples == "auto":
            exp = int(math.log2(n_generaiton))
            n_samples = [int(2**i) for i in range(exp)]
            n_samples.append(n_generaiton)
        assert isinstance(n_samples, list) and all(isinstance(n, int) for n in n_samples)

        coverages = []
        for n_sample in n_samples:
            coverage = 0
            for _ in range(n_calculation):
                sample = np.random.choice(match, size=n_sample, replace=False)  # type: ignore
                coverage += len(np.unique(sample)) / n_reference
            coverages.append(coverage / n_calculation)
        cuc = (np.trapz(coverages, n_samples) / len(n_samples) / max(n_samples)).item()
        return coverages, cuc

    @staticmethod
    def _compute_distance(x, y, metric: str = "mse", axis: int = -1):
        if metric.lower() == "mse":
            return np.mean((x - y) ** 2, axis=axis)
        elif metric.lower() == "mae":
            return np.mean(np.abs(x - y), axis=axis)
        elif metric.lower() == "rmse":
            return np.sqrt(np.mean((x - y) ** 2, axis=axis))
        else:
            raise ValueError("Unknown metric: {}".format(metric))

    def compute_distance(
        self,
        predictions: np.ndarray,
        references: np.ndarray,
        metric: str,
        batch_size: Optional[int] = None,
        num_processes: int = 1,
        dtype=np.float32,
    ):
        # distance between predictions and references for all example combinations for each features
        # shape: (num_generation, num_reference, num_features)
        if batch_size is not None:
            if num_processes > 1:
                distance = np.zeros((len(predictions), len(references), predictions.shape[-1]), dtype=dtype)
                idxs = [
                    (i, j)
                    for i in range(0, len(predictions) + batch_size, batch_size)
                    for j in range(0, len(references) + batch_size, batch_size)
                ]
                args = [
                    (predictions[i : i + batch_size, None], references[None, j : j + batch_size], metric, -2)
                    for i, j in idxs
                ]
                with concurrent.futures.ProcessPoolExecutor(max_workers=num_processes) as executor:
                    results = executor.map(
                        self._compute_distance,
                        *zip(*args),
                    )
                    for (i, j), d in zip(idxs, results):
                        distance[i : i + batch_size, j : j + batch_size] = d

            else:
                distance = np.zeros((len(predictions), len(references), predictions.shape[-1]), dtype=dtype)
                # iterate over the predictions and references in batches
                for i in range(0, len(predictions) + batch_size, batch_size):
                    for j in range(0, len(references) + batch_size, batch_size):
                        d = self._compute_distance(
                            predictions[i : i + batch_size, None],
                            references[None, j : j + batch_size],
                            metric=metric,
                            axis=-2,
                        )
                        distance[i : i + batch_size, j : j + batch_size] = d
        else:
            distance = self._compute_distance(predictions[:, None], references[None, :], metric=metric, axis=-2)
        return distance

    def _compute_metrics(
        self,
        distance: np.ndarray,
        eps: float = 1e-8,
        cuc_n_calculation: int = 3,
        cuc_n_samples: Union[List[int], str] = "auto",
    ) -> dict[str, float | list[float]]:
        """
        Compute metrics from the distance matrix
        Args:
            distance: distance matrix. shape: (num_generation, num_reference)
        Returns:
        """
        index_distance = distance.diagonal(axis1=0, axis2=1).mean().item()

        # matching scores
        # best match for each generated time series
        # shape: (num_generation,)
        best_match = np.argmin(distance, axis=-1)
        precision_distance = distance[np.arange(len(best_match)), best_match].mean().item()

        # best match for each reference time series
        # shape: (num_reference,)
        best_match_inv = np.argmin(distance, axis=0)
        recall_distance = distance[best_match_inv, np.arange(len(best_match_inv))].mean().item()

        mean_distance = (precision_distance + recall_distance) / 2

        # matching precision, recall and f1
        matching_precision = np.unique(best_match_inv).size / len(best_match)
        matching_recall = np.unique(best_match).size / len(best_match_inv)
        matching_f1 = 2 / (1 / (matching_precision + eps) + 1 / (matching_recall + eps))

        # cuc
        coverages, cuc = self.compute_cuc(best_match, len(best_match_inv), cuc_n_calculation, cuc_n_samples)
        return {
            "precision_distance": precision_distance,
            "recall_distance": recall_distance,
            "mean_distance": mean_distance,
            "index_distance": index_distance,
            "matching_precision": matching_precision,
            "matching_recall": matching_recall,
            "matching_f1": matching_f1,
            "cuc": cuc,
            "coverages": coverages,
            "match": best_match,
            "match_inv": best_match_inv,
        }