TransportMaps.Maps.Functionals.FunctionalBase

Module Contents

Classes

Functional

Abstract class for functions \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).

Function

Abstract class for functions \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).

class TransportMaps.Maps.Functionals.FunctionalBase.Functional(dim)[source]

Bases: TransportMaps.Maps.Map

Abstract class for functions \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).

property dim[source]
abstract evaluate(x, precomp=None, idxs_slice=slice(None), cache=None)[source]

[Abstract] Evaluate \(f_{\bf a}\) at x.

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 [\(m,1\)]) – function evaluations

abstract grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)[source]

[Abstract] Evaluate \(\nabla_{\bf x} f_{\bf a}\) at x.

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 [\(m,1,d\)]) –

\(\nabla_{\bf x} f_{\bf a}({\bf x})\)

abstract partial_xd(x, precomp=None, idxs_slice=slice(None), cache=None)[source]

[Abstract] Evaluate \(\partial_{x_d} f_{\bf a}\) at x.

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 [\(m,1\)]) –

\(\partial_{x_d} f_{\bf a}({\bf x})\)

abstract grad_x_partial_xd(x, precomp=None, idxs_slice=slice(None), cache=None)[source]

[Abstract] Evaluate \(\nabla_{\bf x}\partial_{x_d} f_{\bf a}\) at x.

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 [\(m,1,d\)]) –

\(\nabla_{\bf x}\partial_{x_d} f_{\bf a}({\bf x})\)

abstract hess_x_partial_xd(x, precomp=None, idxs_slice=slice(None), cache=None)[source]

[Abstract] Evaluate \(\nabla^2_{\bf x}\partial_{x_d} f_{\bf a}\) at x.

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 [\(m,1,d,d\)]) –

\(\nabla^2_{\bf x}\partial_{x_d} f_{\bf a}({\bf x})\)

abstract partial2_xd(x, precomp=None, idxs_slice=slice(None), cache=None)[source]

[Abstract] Evaluate \(\partial^2_{x_d} f_{\bf a}\) at x.

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 [\(m,1\)]) –

\(\partial^2_{x_d} f_{\bf a}({\bf x})\)

abstract precomp_evaluate(x, precomp=None)[source]

[Abstract] Precompute necessary structures for the evaluation of \(f_{\bf a}\) at x.

Parameters:

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

Returns:

(dict) – data structures

abstract precomp_grad_x(x, precomp=None)[source]

[Abstract] Precompute necessary structures for the evaluation of \(\nabla_{\bf x} f_{\bf a}\) at x

Parameters:

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

Returns:

(dict) – data structures

abstract precomp_partial_xd(x, precomp=None)[source]

[Abstract] Precompute necessary structures for the evaluation of \(\partial_{x_d} f_{\bf a}\) at x.

Parameters:

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

Returns:

(dict) – data structures

abstract precomp_grad_x_partial_xd(x, precomp=None)[source]

[Abstract] Precompute necessary structures for the evaluation of \(\nabla_{\bf x}\partial_{x_d} f_{\bf a}\) at x.

Parameters:

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

Returns:

(dict) – data structures

abstract precomp_partial2_xd(x, precomp=None)[source]

[Abstract] Precompute necessary structures for the evaluation of \(\partial^2_{x_d} f_{\bf a}\) at x.

Parameters:

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

Returns:

(dict) – data structures

class TransportMaps.Maps.Functionals.FunctionalBase.Function(dim)[source]

Bases: Functional

Abstract class for functions \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).