# Cauchy

Source: https://www.tensorplay.cn/docs/generated/tensorplay.distributions.Cauchy.html

```python
class tensorplay.distributions.Cauchy(loc: Tensor | float, scale: Tensor | float, validate_args: bool | None = None)
```

Samples from a Cauchy (Lorentz) distribution. The distribution of the ratio of
independent normally distributed random variables with means 0 follows a
Cauchy distribution.

Example:

```
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = Cauchy(tensorplay.tensor([0.0]), tensorplay.tensor([1.0]))
>>> m.sample()  # sample from a Cauchy distribution with loc=0 and scale=1
tensor([ 2.3214])
```

Parameters:

- loc ([float](https://docs.python.org/3/builtins/functions.html#float) or [Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – mode or median of the distribution.

- scale ([float](https://docs.python.org/3/builtins/functions.html#float) or [Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – half width at half maximum.

```python
property batch_shape: Size
```

Returns the shape over which parameters are batched.

```python
enumerate_support(expand: bool = True) → Tensor
```

Returns tensor containing all values supported by a discrete
distribution. The result will enumerate over dimension 0, so the shape
of the result will be (cardinality,) + batch_shape + event_shape
(where event_shape = () for univariate distributions).

Note that this enumerates over all batched tensors in lock-step
[[0, 0], [1, 1], …]. With expand=False, enumeration happens
along dim 0, but with the remaining batch dimensions being
singleton dimensions, [[0], [1], ...

To iterate over the full Cartesian product use
itertools.product(m.enumerate_support()).

Parameters:

expand ([bool](https://docs.python.org/3/builtins/functions.html#bool)) – whether to expand the support over the
batch dims to match the distribution’s batch_shape.

Returns:

Tensor iterating over dimension 0.

```python
property event_shape: Size
```

Returns the shape of a single sample (without batching).

```python
perplexity() → Tensor
```

Returns perplexity of distribution, batched over batch_shape.

Returns:

Tensor of shape batch_shape.

```python
sample(sample_shape: Size | Sequence[int] = ()) → Tensor
```

Generates a sample_shape shaped sample or sample_shape shaped batch of
samples if the distribution parameters are batched.

```python
sample_n(n: int) → Tensor
```

Generates n samples or n batches of samples if the distribution
parameters are batched.

```python
static set_default_validate_args(value: bool) → None
```

Sets whether validation is enabled or disabled.

The default behavior mimics Python’s assert statement: validation
is on by default, but is disabled if Python is run in optimized mode
(via python -O). Validation may be expensive, so you may want to
disable it once a model is working.

Parameters:

value ([bool](https://docs.python.org/3/builtins/functions.html#bool)) – Whether to enable validation.

```python
property stddev: Tensor
```

Returns the standard deviation of the distribution.