Concordancecorrcoef

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

# concordancecorrcoef

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

## When to invoke this skill

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

## Reference signature

```python
from torchmetrics import ConcordanceCorrCoef

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

## Library docstring

```
Compute concordance correlation coefficient that measures the agreement between two variables.

.. math::
    \rho_c = \frac{2 \rho \sigma_x \sigma_y}{\sigma_x^2 + \sigma_y^2 + (\mu_x - \mu_y)^2}

where :math:`\mu_x, \mu_y` is the means for the two variables, :math:`\sigma_x^2, \sigma_y^2` are the corresponding
variances and \rho is the pearson correlation coefficient between the two variables.

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 float tensor with shape ``(N,)`` or multioutput
  float tensor of shape ``(N,d)``

As output of ``forward`` and ``compute`` the metric returns the following output:

- ``concordance`` (:class:`~torch.Tensor`): A scalar float tensor with the concordance coefficient(s) for
  non-multioutput input or a float tensor with shape ``(d,)`` for multioutput input

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 ConcordanceCorrCoef
    >>> from torch import tensor
    >>> target = tensor([3, -0.5, 2, 7])
    >>> preds = tensor([2.5, 0.0, 2, 8])
    >>> concordance = ConcordanceCorrCoef()
    >>> concordance(preds, target)
    tensor(0.9777)

Example (multi output regression):
    >>> from torchmetrics.regression import ConcordanceCorrCoef
    >>> target = tensor([[3, -0.5], [2, 7]])
    >>> preds = tensor([[2.5, 0.0], [2, 8]])
    >>> concordance = ConcordanceCorrCoef(num_outputs=2)
    >>> concordance(preds, target)
    tensor([0.7273, 0.9887])
```

## Quick recipe

```python
import torchmetrics as _m
score = _m.ConcordanceCorrCoef(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)`.