TransportMaps.Maps.ConditionalTriangularTransportMapBase

Module Contents

Classes

ConditionalTriangularTransportMap

Takes the transport map \(T({\bf x})\) and construct the transport map \(S_{{\bf y}}({\bf x}) := [T({\bf y}, {\bf x})]_{d_y:}\).

class TransportMaps.Maps.ConditionalTriangularTransportMapBase.ConditionalTriangularTransportMap(**kwargs)

Bases: TransportMaps.Maps.SlicedTransportMapBase.SlicedTransportMap

Takes the transport map \(T({\bf x})\) and construct the transport map \(S_{{\bf y}}({\bf x}) := [T({\bf y}, {\bf x})]_{d_y:}\).

log_det_grad_x(x, *args, **kwargs)

[Abstract] Compute: \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\).

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_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 match x.shape[0].

Returns:

(ndarray [\(m\)]) – \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point

grad_x_log_det_grad_x(x, *args, **kwargs)

[Abstract] Compute: \(\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_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 match x.shape[0].

Returns:

(ndarray [\(m,d\)]) – \(\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point

See also

log_det_grad_x().

hess_x_log_det_grad_x(x, *args, **kwargs)

[Abstract] Compute: \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_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 match x.shape[0].

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

log_det_grad_x() and grad_x_log_det_grad_x().

inverse(x, *args, **kwargs)

[Abstract] Evaluate the Moore-Penrose inverse map \(T^\dagger\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_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 match x.shape[0].

Returns:

(ndarray [\(m,d_y\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

log_det_grad_x_inverse(x, precomp=None, idxs_slice=slice(None), **kwargs)

[Abstract] Compute: \(\log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\).

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_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 match x.shape[0].

Returns:

(ndarray [\(m\)]) – \(\log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\) at every evaluation point