---
title: Pearson Corr. Coef.
description: Compute Pearson Correlation Coefficient.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/regression/pearson_corr_coef'
---
# Pearson Corr. Coef. {#pearson-corr-coef}

## Module Interface {#module-interface}

### `class torchmetrics.PearsonCorrCoef(num_outputs=1, **kwargs)` {#torchmetrics.PearsonCorrCoef}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/pearson.py#L100-L264)

Compute [Pearson Correlation Coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient).

```math
P_{corr}(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}
```

Where $`y`$ is a tensor of target values, and $`x`$ is a tensor of predictions.

As input to `forward` and `update` the metric accepts the following input:

*   `preds` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): either single output float tensor with shape `(N,)` or multioutput float tensor of shape `(N,d)`
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor with the Pearson Correlation Coefficient
    

Parameters:

*   **num\_outputs** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of outputs in multioutput setting
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example (single output regression):

```python
>>> 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):

```python
>>> 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.])
```

#### `plot(val=None, ax=None)` {#torchmetrics.PearsonCorrCoef.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/pearson.py#L224-L264)

Plot a single or multiple values from the metric.

Parameters:

*   **val** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import PearsonCorrCoef
>>> metric = PearsonCorrCoef()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/pearson\_corr\_coef-1.png](/docs/torchmetrics/1.9.0/static/_images/pearson_corr_coef-1.png)](/docs/torchmetrics/1.9.0/static/_images/pearson_corr_coef-1.png)

```python
>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import PearsonCorrCoef
>>> metric = PearsonCorrCoef()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)
```

[![../../\_images/pearson\_corr\_coef-2.png](/docs/torchmetrics/1.9.0/static/_images/pearson_corr_coef-2.png)](/docs/torchmetrics/1.9.0/static/_images/pearson_corr_coef-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.pearson_corrcoef(preds, target)` {#torchmetrics.functional.pearson_corrcoef}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/regression/pearson.py#L149-L189)

Compute pearson correlation coefficient.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – estimated scores
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – ground truth scores
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")

Example (single output regression):

```python
>>> from torchmetrics.functional.regression import pearson_corrcoef
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> pearson_corrcoef(preds, target)
tensor(0.9849)
```

Example (multi output regression):

```python
>>> from torchmetrics.functional.regression import pearson_corrcoef
>>> target = torch.tensor([[3, -0.5], [2, 7]])
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> pearson_corrcoef(preds, target)
tensor([1., 1.])
```

---

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- Parent: [Regression](/docs/torchmetrics/1.9.0/regression.md)