TransportMaps.Maps.InverseMapBase

Module Contents

Classes

InverseMap

Defines the map \(S := T^{\dagger}\)

class TransportMaps.Maps.InverseMapBase.InverseMap(**kwargs)

Bases: TransportMaps.Maps.MapBase.Map

Defines the map \(S := T^{\dagger}\)

property base_map

get_ncalls_tree(indent='')

get_nevals_tree(indent='')

get_teval_tree(indent='')

update_ncalls_tree(obj)

update_nevals_tree(obj)

update_teval_tree(obj)

reset_counters()

evaluate(x, precomp=None, idxs_slice=slice(None), *args, **kwargs)

Evaluate the map \(T^{-1}\) at the points \({\bf x} \in \mathbb{R}^{m \times d}\).

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 [\(m,d\)]) – transformed points

Raises:

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

grad_x(x, *args, **kwargs)

[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

tuple_grad_x(x, *args, **kwargs)

[Abstract] Evaluate the function and gradient.

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:

(tuple) – function and gradient evaluation

Raises:

NotImplementedError – to be implemented in sub-classes

hess_x(x, *args, **kwargs)

[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, *args, **kwargs)

[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

inverse(x, *args, **kwargs)

Evaluates \(T\)

Parameters:

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

Returns:

(ndarray [\(m,d\)]) – \(T({\bf x})\) for every evaluation point

grad_x_inverse(x, *args, **kwargs)

Evaluates \(\nabla_{\bf x}T\)

Parameters:

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

• precomp (dict) – dictionary of precomputed values

Returns:

(ndarray [\(m,d,d\)]) – gradient matrices for every evaluation point.

Raises:

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

tuple_grad_x_inverse(x, *args, **kwargs)

[Abstract] Evaluate the Moore-Penrose inverse function and gradient.

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:

(tuple) – function and gradient evaluation

Raises:

NotImplementedError – to be implemented in sub-classes

hess_x_inverse(x, *args, **kwargs)

Evaluates \(\nabla^2_{\bf x}T\)

Parameters:

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

• precomp (dict) – dictionary of precomputed values

Returns:

(ndarray [\(m,d,d,d\)]) – Hessian matrices for every evaluation point and every dimension.

Raises:

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

action_hess_x_inverse(x, *args, **kwargs)

[Abstract] Evaluate the action of the Hessian of the Moore-Penrose inverse \(\langle\nabla^2_{\bf x}T^\dagger,\delta{\bf x}\rangle\) 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