from typing import Optional
import math
import numpy as np

from overrides import overrides
import torch

from allennlp.training.metrics.covariance import Covariance
from allennlp.training.metrics.metric import Metric


@Metric.register("pearson_correlation")
class PearsonCorrelation(Metric):
    """
    This `Metric` calculates the sample Pearson correlation coefficient (r)
    between two tensors. Each element in the two tensors is assumed to be
    a different observation of the variable (i.e., the input tensors are
    implicitly flattened into vectors and the correlation is calculated
    between the vectors).

    This implementation is mostly modeled after the streaming_pearson_correlation function in Tensorflow. See
    https://github.com/tensorflow/tensorflow/blob/v1.10.1/tensorflow/contrib/metrics/python/ops/metric_ops.py#L3267

    This metric delegates to the Covariance metric the tracking of three [co]variances:

    - `covariance(predictions, labels)`, i.e. covariance
    - `covariance(predictions, predictions)`, i.e. variance of `predictions`
    - `covariance(labels, labels)`, i.e. variance of `labels`

    If we have these values, the sample Pearson correlation coefficient is simply:

    r = covariance / (sqrt(predictions_variance) * sqrt(labels_variance))

    if predictions_variance or labels_variance is 0, r is 0
    """

    def __init__(self) -> None:
        self._predictions_labels_covariance = Covariance()
        self._predictions_variance = Covariance()
        self._labels_variance = Covariance()

    def __call__(
        self,
        predictions: torch.Tensor,
        gold_labels: torch.Tensor,
        mask: Optional[torch.BoolTensor] = None,
    ):
        """
        # Parameters

        predictions : `torch.Tensor`, required.
            A tensor of predictions of shape (batch_size, ...).
        gold_labels : `torch.Tensor`, required.
            A tensor of the same shape as `predictions`.
        mask : `torch.BoolTensor`, optional (default = None).
            A tensor of the same shape as `predictions`.
        """
        predictions, gold_labels, mask = self.detach_tensors(predictions, gold_labels, mask)
        self._predictions_labels_covariance(predictions, gold_labels, mask)
        self._predictions_variance(predictions, predictions, mask)
        self._labels_variance(gold_labels, gold_labels, mask)

    def get_metric(self, reset: bool = False):
        """
        # Returns

        The accumulated sample Pearson correlation.
        """
        covariance = self._predictions_labels_covariance.get_metric(reset=reset)
        predictions_variance = self._predictions_variance.get_metric(reset=reset)
        labels_variance = self._labels_variance.get_metric(reset=reset)
        if reset:
            self.reset()
        denominator = math.sqrt(predictions_variance) * math.sqrt(labels_variance)
        if np.around(denominator, decimals=5) == 0:
            pearson_r = 0
        else:
            pearson_r = covariance / denominator
        return pearson_r

    @overrides
    def reset(self):
        self._predictions_labels_covariance.reset()
        self._predictions_variance.reset()
        self._labels_variance.reset()
