---
title: Minkowski Distance
description: Compute Minkowski Distance.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/regression/minkowski_distance'
---
# Minkowski Distance {#minkowski-distance}

## Module Interface {#module-interface}

### `class torchmetrics.MinkowskiDistance(p, **kwargs)` {#torchmetrics.MinkowskiDistance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/minkowski.py#L30-L122)

Compute [Minkowski Distance](https://en.wikipedia.org/wiki/Minkowski_distance).

```math
d_{\text{Minkowski}} = \sum_{i}^N (| y_i - \hat{y_i} |^p)^\frac{1}{p}
```

where

math:

y is a tensor of target values,

math:

hat{y} is a tensor of predictions,

math:

p is a non-negative integer or floating-point number

This metric can be seen as generalized version of the standard euclidean distance which corresponds to minkowski distance with p=2.

Parameters:

*   **p** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – int or float larger than 1, exponent to which the difference between preds and target is to be raised
    
*   **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

```python
>>> from torchmetrics.regression import MinkowskiDistance
>>> target = tensor([1.0, 2.8, 3.5, 4.5])
>>> preds = tensor([6.1, 2.11, 3.1, 5.6])
>>> minkowski_distance = MinkowskiDistance(3)
>>> minkowski_distance(preds, target)
tensor(5.1220)
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/minkowski.py#L82-L122)

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 MinkowskiDistance
>>> metric = MinkowskiDistance(p=3)
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/minkowski\_distance-1.png](/docs/torchmetrics/1.9.0/static/_images/minkowski_distance-1.png)](/docs/torchmetrics/1.9.0/static/_images/minkowski_distance-1.png)

```python
>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import MinkowskiDistance
>>> metric = MinkowskiDistance(p=3)
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)
```

[![../../\_images/minkowski\_distance-2.png](/docs/torchmetrics/1.9.0/static/_images/minkowski_distance-2.png)](/docs/torchmetrics/1.9.0/static/_images/minkowski_distance-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.minkowski_distance(preds, targets, p)` {#torchmetrics.functional.minkowski_distance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/regression/minkowski.py#L59-L84)

Compute the [Minkowski distance](https://en.wikipedia.org/wiki/Minkowski_distance).

```math
\begin{split}d_{\text{Minkowski}} = \\sum_{i}^N (| y_i - \\hat{y_i} |^p)^\frac{1}{p}\end{split}
```

This metric can be seen as generalized version of the standard euclidean distance which corresponds to minkowski distance with p=2.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – estimated labels of type Tensor
    
*   **targets** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – ground truth labels of type Tensor
    
*   **p** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – int or float larger than 1, exponent to which the difference between preds and target is to be raised
    

Return type:

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

Returns:

Tensor with the Minkowski distance

Example

```python
>>> from torchmetrics.functional.regression import minkowski_distance
>>> x = torch.tensor([1.0, 2.8, 3.5, 4.5])
>>> y = torch.tensor([6.1, 2.11, 3.1, 5.6])
>>> minkowski_distance(x, y, p=3)
tensor(5.1220)
```

---

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