|---|
| [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/tangent_spaces/symmetric_matrix.py#L26-L73) |
Tangent space of M the space of `n x n` symmetric matrices.
Inherits From: [`TangentSpace`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/TangentSpace)
## Methods
### `compute_basis`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/tangent_spaces/symmetric_matrix.py#L29-L46)
compute_basis(
x
)
Compute basis of symmetric matrices.
### `transform_coordinatewise`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/tangent_spaces/spaces.py#L172-L193)
transform_coordinatewise(
x, f, **kwargs
)
Same as `transform_dimension_preserving`, for a coordinatewise f.
Default falls back to `transform_dimension_preserving`, which may
be overridden in subclasses.
| Args ||
|---|---|
| `x` | same as in `transform_dimension_preserving`. |
| `f` | same as in `transform_dimension_preserving`. |
| `**kwargs` | same as in `transform_dimension_preserving`. |
| Returns ||
|---|---|
| `log_density` | A `Tensor` representing the log density correction of f at x |
| `space` | A `TangentSpace` representing the tangent to fM at f(x) |
| Raises ||
|---|---|
| `NotImplementedError` | if the `TangentSpace` subclass does not implement `transform_dimension_preserving`. |
### `transform_dimension_preserving`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/tangent_spaces/spaces.py#L123-L143)
transform_dimension_preserving(
x, f, **kwargs
)
Same as `transform_general`, assuming f goes from R\^n to R\^n.
Default falls back to `transform_general`, which may be overridden
in subclasses.
| Args ||
|---|---|
| `x` | same as in `transform_general`. |
| `f` | same as in `transform_general`. |
| `**kwargs` | same as in `transform_general`. |
| Returns ||
|---|---|
| `log_density` | A `Tensor` representing the log density correction of f at x |
| `space` | A `TangentSpace` representing the tangent to fM at f(x) |
| Raises ||
|---|---|
| `NotImplementedError` | if the `TangentSpace` subclass does not implement `transform_general`. |
### `transform_general`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/tangent_spaces/spaces.py#L98-L118)
transform_general(
x, f, **kwargs
)
Returns the density correction, in log space, corresponding to f at x.
Also returns a new `TangentSpace` representing the tangent to fM at f(x).
| Args ||
|---|---|
| `x` | `Tensor` (structure). The point at which to calculate the density. |
| `f` | `Bijector` or one of its subclasses. The transformation that requires a density correction based on this tangent space. |
| `**kwargs` | Optional keyword arguments as part of the Bijector. |
| Returns ||
|---|---|
| `log_density` | A `Tensor` representing the log density correction of f at x |
| `space` | A `TangentSpace` representing the tangent to fM at f(x) |
| Raises ||
|---|---|
| `NotImplementedError` | if the `TangentSpace` subclass does not implement this method. |
### `transform_projection`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/tangent_spaces/spaces.py#L148-L167)
transform_projection(
x, f, **kwargs
)
Same as `transform_general`, with f a projection (or its inverse).
Default falls back to `transform_general`, which may be overridden
in subclasses.
| Args ||
|---|---|
| `x` | same as in `transform_general`. |
| `f` | same as in `transform_general`. |
| `**kwargs` | same as in `transform_general`. |
| Returns ||
|---|---|
| `log_density` | A `Tensor` representing the log density correction of f at x |
| `space` | A `TangentSpace` representing the tangent to fM at f(x) |
| Raises ||
|---|---|
| `NotImplementedError` | if the `TangentSpace` subclass does not implement `transform_general`. |