TransportMaps.Maps.ParametricTriangularComponentwiseMapBase

Module Contents

Classes

ParametricTriangularComponentwiseMap

Map \(T[{\bf a}_{1:d_y}]({\bf x})= [T_1[{\bf a}_1],\ldots,T_{d_y}[{\bf a}_{d_y}]]^\top\), where \(T_i[{\bf a}_i](x_{1:i}):\mathbb{R}^{n_i}\times\mathbb{R}^{i}\rightarrow\mathbb{R}\).

class TransportMaps.Maps.ParametricTriangularComponentwiseMapBase.ParametricTriangularComponentwiseMap(**kwargs)

Bases: TransportMaps.Maps.ParametricComponentwiseMapBase.ParametricComponentwiseMap, TransportMaps.Maps.TriangularComponentwiseMapBase.TriangularComponentwiseMap

Map \(T[{\bf a}_{1:d_y}]({\bf x})= [T_1[{\bf a}_1],\ldots,T_{d_y}[{\bf a}_{d_y}]]^\top\), where \(T_i[{\bf a}_i](x_{1:i}):\mathbb{R}^{n_i}\times\mathbb{R}^{i}\rightarrow\mathbb{R}\).

Parameters:

• active_vars (list [\(d\)] of list) – for each dimension lists the active variables.

• approx_list (list [\(d\)] of FunctionalApproximations.MonotonicFunctionApproximation) – list of monotonic functional approximations for each dimension

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

Compute: \([\nabla_{\bf a}\partial_{{\bf x}_k} T_k]_k\)

This is

\[\begin{split}\left[ \begin{array}{ccccc} \nabla_{{\bf a}_1}\partial_{{\bf x}_1}T_1 & 0 & \cdots & & 0 \\ 0 \nabla_{{\bf a}_2}\partial_{{\bf x}_2}T_2 & 0 & \cdots & 0 \\ \vdots & \ddots & & & \\ 0 & & \cdots & 0 & \nabla_{{\bf a}_d}\partial_{{\bf x}_d}T_d \end{array} \right]\end{split}\]

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].

• cache (dict) – cache

Returns:

(ndarray [\(m,d\)]) – \([\partial_{{\bf x}_1}T_1({\bf x}_1,{\bf a}^{(1)}),\ldots,\partial_{{\bf x}_d}T_d({\bf x}_{1:d},{\bf a}^{(d)})]\) at every evaluation point

Raises:

ValueError – if \(d\) does not match the dimension of the transport map.