class_docstr: Compute `Pearson Correlation Coefficient`_.
  
  .. math::
      P_{corr}(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}
  
  Where :math:`y` is a tensor of target values, and :math:`x` is a tensor of predictions.
  
  As input to ``forward`` and ``update`` the metric accepts the following input:
  
  - ``preds`` (:class:`~torch.Tensor`): either single output float tensor with shape ``(N,)``
    or multioutput float tensor of shape ``(N,d)``
  - ``target`` (:class:`~torch.Tensor`): either single output tensor with shape ``(N,)``
    or multioutput tensor of shape ``(N,d)``
  
  As output of ``forward`` and ``compute`` the metric returns the following output:
  
  - ``pearson`` (:class:`~torch.Tensor`): A tensor with the Pearson Correlation Coefficient
  
  Args:
      num_outputs: Number of outputs in multioutput setting
      kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
  
  Example (single output regression):
      >>> from torchmetrics.regression import PearsonCorrCoef
      >>> target = torch.tensor([3, -0.5, 2, 7])
      >>> preds = torch.tensor([2.5, 0.0, 2, 8])
      >>> pearson = PearsonCorrCoef()
      >>> pearson(preds, target)
      tensor(0.9849)
  
  Example (multi output regression):
      >>> from torchmetrics.regression import PearsonCorrCoef
      >>> target = torch.tensor([[3, -0.5], [2, 7]])
      >>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
      >>> pearson = PearsonCorrCoef(num_outputs=2)
      >>> pearson(preds, target)
      tensor([1., 1.])
docstr: Update state with predictions and targets.
docstr_tok: ["Update","state","with","predictions","and","targets","."]
code: def update(self, preds: Tensor, target: Tensor) -> None:
      """Update state with predictions and targets."""
      (
          self.mean_x,
          self.mean_y,
          self.var_x,
          self.var_y,
          self.corr_xy,
          self.n_total,
      ) = _pearson_corrcoef_update(
          preds,
          target,
          self.mean_x,
          self.mean_y,
          self.var_x,
          self.var_y,
          self.corr_xy,
          self.n_total,
          self.num_outputs,
      )
  
file_path: torchmetrics/src/torchmetrics/regression/pearson.py
imports: from typing import Any, List, Optional, Sequence, Tuple, Union
  import torch
  from torch import Tensor
  from torchmetrics.functional.regression.pearson import _pearson_corrcoef_compute, _pearson_corrcoef_update
  from torchmetrics.metric import Metric
  from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
  from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE
label_desc: Use image node_id 2 for calling the PearsonCorrCoef obj's underlying member method code with example usage: obj.update(preds, target) without return types