TransportMaps.Maps.TriangularListStackedTransportMapBase

Module Contents

Classes

TriangularListStackedTransportMap

Defines the transport map \(T\) obtained by stacking \(T_1, T_2, \ldots\).

class TransportMaps.Maps.TriangularListStackedTransportMapBase.TriangularListStackedTransportMap(**kwargs)

Bases: TransportMaps.Maps.ListStackedTransportMapBase.ListStackedTransportMap

Defines the transport map \(T\) obtained by stacking \(T_1, T_2, \ldots\).

log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)

[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, precomp=None, idxs_slice=slice(None), cache=None)

[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, precomp=None, idxs_slice=slice(None), cache=None)

[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().

action_hess_x_log_det_grad_x(x, dx, precomp=None, idxs_slice=slice(None), cache=None)

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

Parameters:

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

• dx (ndarray [\(m,d\)]) – directions on which to evaluate the Hessian

• 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 [\(m,d\)]) – \(\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}), \delta{\bf x}\rangle\) at every evaluation point

See also

log_det_grad_x() and grad_x_log_det_grad_x().

log_det_grad_x_inverse(x, dx, precomp=None, idxs_slice=slice(None), cache=None)

[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