# 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)[source]

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

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.