TransportMaps.Maps.ListCompositeMapBase

Module Contents

Classes

ListCompositeMap	Construct the composite map \(T_1 \circ T_2 \circ \cdots \circ T_n\)
CompositeMap	Given maps \(T_1,T_2\), define map \(T=T_1 \circ T_2\).

class TransportMaps.Maps.ListCompositeMapBase.ListCompositeMap(**kwargs)

Bases: TransportMaps.Maps.MapBase.Map

Construct the composite map \(T_1 \circ T_2 \circ \cdots \circ T_n\)

property map_list

property dim_in

property dim_out

property n_maps

append(mp)

Append one map to the composition.

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), cache=None)

Evaluate the transport map 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, precomp=None, idxs_slice=slice(None), cache=None)

Compute \(\nabla_{\bf x} T({\bf x})\).

Apply chain rule.

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.

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

[Abstract] Evaluate the action of the gradient \(\langle\delta{\bf x},\nabla_{\bf x}T({\bf x})\rangle\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\) on the vector \(\delta{\bf x}\).

Parameters:

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

• dx (ndarray [\(m,d_x,...\)]) – vector \(\delta{\bf x}\)

• 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

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

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

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

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

Apply chain rule.

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

Compute \(\langle\nabla^2_{\bf x} T({\bf x}), \delta{\bf x}\rangle\).

Apply chain rule.

Parameters:

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

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

• precomp (dict) – dictionary of precomputed values

Returns:

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

Raises:

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

inverse(x, *args, **kwargs)

Compute: \(T^{\dagger}({\bf y})\)

Parameters:

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

Returns:

(ndarray [\(m,d\)]) – \(T^{-1}({\bf y})\) for every evaluation point

grad_x_inverse(x, *args, **kwargs)

Compute \(\nabla_{\bf x} T^{\dagger}({\bf x})\).

Parameters:

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

Returns:

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

hess_x_inverse(x, *args, **kwargs)

Compute \(\nabla^2_{\bf x} T^{\dagger}({\bf x})\).

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, dx, *args, **kwargs)

Compute \(\langle\nabla^2_{\bf x} T^{\dagger}({\bf x}), \delta{\bf x}\rangle\).

Parameters:

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

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

• precomp (dict) – dictionary of precomputed values

Returns:

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

Raises:

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

class TransportMaps.Maps.ListCompositeMapBase.CompositeMap(t1, t2)

Bases: ListCompositeMap

Given maps \(T_1,T_2\), define map \(T=T_1 \circ T_2\).

Parameters:

• t1 (Map) – map \(T_1\)

• t2 (Map) – map \(T_2\)