# TransportMaps.Maps.SlicedMapBase¶

## Module Contents¶

### Classes¶

 SlicedMap Takes the map $$T({\bf x})$$ and construct the map $$S_{\bf y}({\bf x}) := [T({\bf y}_{\bf i} \cup {\bf x}_{\neg{\bf i}})]_{\bf j}$$, where $$S_{\bf y}:\mathbb{R}^{\sharp(\neg{\bf i})}\rightarrow\mathbb{R}^{\sharp{\bf j}}$$.
class TransportMaps.Maps.SlicedMapBase.SlicedMap(**kwargs)[source]

Takes the map $$T({\bf x})$$ and construct the map $$S_{\bf y}({\bf x}) := [T({\bf y}_{\bf i} \cup {\bf x}_{\neg{\bf i}})]_{\bf j}$$, where $$S_{\bf y}:\mathbb{R}^{\sharp(\neg{\bf i})}\rightarrow\mathbb{R}^{\sharp{\bf j}}$$.

_xin(x)[source]
evaluate(x, **kwargs)[source]

[Abstract] Evaluate the map $$T$$ 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

[Abstract] Evaluate the gradient $$\nabla_{\bf x}T$$ 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 [$$m,d_y,d_x$$]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

hess_x(x, **kwargs)[source]

[Abstract] Evaluate the Hessian $$\nabla^2_{\bf x}T$$ 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 [$$m,d_y,d_x,d_x$$]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

action_hess_x(x, dx, **kwargs)[source]

[Abstract] Evaluate the action of the Hessian $$\langle\nabla^2_{\bf x}T,\delta{\bf x}\rangle$$ at the points $${\bf x} \in \mathbb{R}^{m \times d_x}$$.

Parameters:
• x (ndarray [$$m,d_x$$]) – evaluation points

• dx (ndarray [$$m,d_x$$]) – direction 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 [$$m,d_y,d_x$$]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes