Pearsoncorrcoef

---
name: pearsoncorrcoef
description: Compute the PearsonCorrCoef metric — provided by torchmetrics. Use when the user has predictions and ground-truth and needs to compute PearsonCorrCoef, or asks how to score with PearsonCorrCoef.
metadata:
  skill_kind: metric
  source_lib: torchmetrics
  import_path: torchmetrics.PearsonCorrCoef
  source: library_introspection
---

# pearsoncorrcoef

> Metric `PearsonCorrCoef` from `torchmetrics` (torchmetrics.PearsonCorrCoef)

## When to invoke this skill

The user has predictions + ground truth and asks to evaluate with PearsonCorrCoef, or
mentions `torchmetrics.PearsonCorrCoef` directly, or wants the standard torchmetrics implementation.

## Reference signature

```python
from torchmetrics import PearsonCorrCoef

# PearsonCorrCoef(num_outputs: int = 1, **kwargs: Any) -> None
```

## Library docstring

```
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.])
```

## Quick recipe

```python
import torchmetrics as _m
score = _m.PearsonCorrCoef(y_true, y_pred)
```

## Don'ts

- Don't reimplement when the library version handles edge cases (NaN, ties, empty inputs) better than a hand-rolled formula.
- Always check the library version's argument order — sklearn is `(y_true, y_pred)` while torchmetrics is `(preds, target)`.