TransportMaps.Maps.IdentityEmbeddedTransportMapBase
¶
Module Contents¶
Classes¶
Transport map \(T({\bf x},{\bf a}): \mathbb{R}^d \rightarrow \mathbb{R}^d\). |
- class TransportMaps.Maps.IdentityEmbeddedTransportMapBase.IdentityEmbeddedTransportMap(**kwargs)[source]¶
Bases:
TransportMaps.Maps.TransportMapBase.TransportMap
Transport map \(T({\bf x},{\bf a}): \mathbb{R}^d \rightarrow \mathbb{R}^d\).
- evaluate(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- inverse(x, precomp=None, idxs_slice=slice(None))[source]¶
[Abstract] Compute: \(T^{-1}({\bf x})\)
- Parameters:
- Returns:
(
ndarray
[\(m,d\)]) – \(T^{-1}({\bf x})\) for every evaluation point
- grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y,d_x\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- action_grad_x(x, dx, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the action of the gradient \(\langle\nabla_{\bf x}T({\bf x}),\delta{\bf x}\rangle\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\) on the vector \(\delta{\bf x}\).
- Parameters:
x (
ndarray
[\(m,d_x\)]) – evaluation pointsdx (
ndarray
[\(m,d_x,...\)]) – vector \(\delta{\bf x}\)precomp (
dict
) – dictionary of precomputed valuesidxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by
idxs_slice
must matchx.shape[0]
.
- Returns:
(
ndarray
[\(m,d_y,...\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- action_adjoint_grad_x(x, dx, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the action of the gradient \(\langle\delta{\bf x},\nabla_{\bf x}T({\bf x})\rangle\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\) on the vector \(\delta{\bf x}\).
- Parameters:
x (
ndarray
[\(m,d_x\)]) – evaluation pointsdx (
ndarray
[\(m,d_x,...\)]) – vector \(\delta{\bf x}\)precomp (
dict
) – dictionary of precomputed valuesidxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by
idxs_slice
must matchx.shape[0]
.
- Returns:
(
ndarray
[\(m,d_y,...\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- tuple_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the function and gradient.
- Parameters:
- Returns:
(
tuple
) – function and gradient evaluation- Raises:
NotImplementedError – to be implemented in sub-classes
- action_tuple_grad_x(x, dx, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the function and action of the gradient.
- Parameters:
x (
ndarray
[\(m,d_x\)]) – evaluation pointsdx (
ndarray
[\(m,d_x,...\)]) – vector \(\delta{\bf x}\)precomp (
dict
) – dictionary of precomputed valuesidxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by
idxs_slice
must matchx.shape[0]
.
- Returns:
(
tuple
) – function and action of the gradient evaluation- Raises:
NotImplementedError – to be implemented in sub-classes
- hess_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Evaluate the Hessian \(\nabla^2_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y,d_x,d_x\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Compute: \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\).
- Parameters:
- Returns:
(
ndarray
[\(m\)]) – \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point
- grad_x_log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Compute: \(\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\)
- Parameters:
- Returns:
(
ndarray
[\(m,d\)]) – \(\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point
See also
- hess_x_log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
[Abstract] Compute: \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\)
- Parameters:
- Returns:
(
ndarray
[\(m,d,d\)]) – \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point
See also