# LowRankMultivariateNormal

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

```python
class tensorplay.distributions.LowRankMultivariateNormal(loc: Tensor, cov_factor: Tensor, cov_diag: Tensor, validate_args: bool | None = None)
```

Creates a multivariate normal distribution with covariance matrix having a low-rank form
parameterized by cov_factor and cov_diag:

```
covariance_matrix = cov_factor @ cov_factor.T + cov_diag
```

Example

```
>>> # xdoctest: +REQUIRES(env:TENSORPLAY_DOCTEST_LAPACK)
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = LowRankMultivariateNormal(
...     tensorplay.zeros(2), tensorplay.tensor([[1.0], [0.0]]), tensorplay.ones(2)
... )
>>> m.sample()  # normally distributed with mean=`[0,0]`, cov_factor=`[[1],[0]]`, cov_diag=`[1,1]`
tensor([-0.2102, -0.5429])
```

Parameters:

- loc ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – mean of the distribution with shape batch_shape + event_shape

- cov_factor ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – factor part of low-rank form of covariance matrix with shape batch_shape + event_shape + (rank,)

- cov_diag ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – diagonal part of low-rank form of covariance matrix with shape batch_shape + event_shape

> **Note**
>
> The computation for determinant and inverse of covariance matrix is avoided when cov_factor.shape[1] @@TPBLOCK_2@@

```python
property batch_shape: Size
```

Returns the shape over which parameters are batched.

```python
cdf(value: Tensor) → Tensor
```

Returns the cumulative density/mass function evaluated at
value.

Parameters:

value ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor))

```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
icdf(value: Tensor) → Tensor
```

Returns the inverse cumulative density/mass function evaluated at
value.

Parameters:

value ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor))

```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.