TransportMaps.Maps.ListCompositeTransportMapBase
¶
Module Contents¶
Classes¶
Composition of transport maps \(T({\bf x}) := T_1 \circ T_2 \circ \ldots \circ T_k({\bf x})\). |
|
Composition of two transport maps \(T({\bf x}) := T_1 \circ T_2\). |
- class TransportMaps.Maps.ListCompositeTransportMapBase.ListCompositeTransportMap(**kwargs)[source]¶
Bases:
TransportMaps.Maps.ListCompositeMapBase.ListCompositeMap
,TransportMaps.Maps.TransportMapBase.TransportMap
Composition of transport maps \(T({\bf x}) := T_1 \circ T_2 \circ \ldots \circ T_k({\bf x})\).
- hess_x_inverse(x, *args, **kwargs)[source]¶
Compute \(\nabla^2_{\bf x} T^{-1}({\bf x})\).
- Parameters:
- Returns:
(
ndarray
[\(m,d,d,d\)]) – Hessian matrices for every evaluation point and every dimension.- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
- action_hess_x_inverse(x, dx, *args, **kwargs)[source]¶
Compute \(\langle\nabla^2_{\bf x} T^{-1}({\bf x}), \delta{\bf x}\rangle\).
- Parameters:
- Returns:
(
ndarray
[\(m,d,d,d\)]) – action of the Hessian matrices for every evaluation point and every dimension.- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
- log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
Compute: \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\).
For the transport maps \(T_1,T_2\),
\[\log \det \nabla_{\bf x} (T_1 \circ T_2)({\bf x}) = \log \det \nabla_{\bf x} T_1 ({\bf y}) + \log \det \nabla_{\bf x} T_2({\bf x})\]where \({\bf y} = T_2({\bf x})\).
- grad_x_log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
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- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
See also
- log_det_grad_x_inverse(x, precomp=None, *args, **kwargs)[source]¶
Compute: \(\log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\).
- class TransportMaps.Maps.ListCompositeTransportMapBase.CompositeTransportMap(t1, t2)[source]¶
Bases:
ListCompositeTransportMap
Composition of two transport maps \(T({\bf x}) := T_1 \circ T_2\).
- hess_x_log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
Compute: \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x})\)
For the transport maps \(T_1,T_2\),
\[\nabla^2_{\bf x} \log \det \nabla_{\bf x} (T_1 \circ T_2) = \left[ \nabla^2_{\bf x} \log \det (\nabla_{\bf x} T_1 \circ T_2) \cdot \nabla_{\bf x} T_2 + \nabla_{\bf x} \log \det \nabla_{\bf x} T_2 \right] \cdot (\nabla_{\bf x} T_2) + \nabla_{\bf x} \log \det (\nabla_{\bf x} T_1 \circ T_2) \cdot \nabla^2_{\bf x} T_2 + \nabla^2_{\bf x} \log \det \nabla_{\bf x} T_2\]- Parameters:
- Returns:
(
ndarray
[\(m,d,d\)]) – \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x})\) at every evaluation point- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
See also
log_det_grad_x()
andgrad_x_log_det_grad_x()
.
- action_hess_x_log_det_grad_x(x, dx, precomp=None, idxs_slice=slice(None), cache=None)[source]¶
Compute: \(\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}), \delta{\bf x}\rangle\)
- Parameters:
- Returns:
- (
ndarray
[\(m,d\)]) – \(\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}), \delta{\bf x}\rangle\) at every evaluation point
- (
- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
See also
- hess_x_log_det_grad_x_inverse(x, precomp=None, *args, **kwargs)[source]¶
Compute: \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x})\)
- Parameters:
- Returns:
(
ndarray
[\(m,d,d\)]) – \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x})\) at every evaluation point- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
See also
log_det_grad_x()
andgrad_x_log_det_grad_x()
.
- action_hess_x_log_det_grad_x_inverse(x, dx, precomp=None, *args, **kwargs)[source]¶
Compute: \(\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}), \delta{\bf x}\rangle\)
- Parameters:
- Returns:
(
ndarray
[\(m,d,d\)]) – \(\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}), \delta{\bf x}\rangle\) at every evaluation point- Raises:
ValueError – if \(d\) does not match the dimension of the transport map.
See also
log_det_grad_x()
andgrad_x_log_det_grad_x()
.