TransportMaps.Maps.Functionals.ParametricFunctionalBase

Module Contents

Classes

ParametricFunctional	Abstract class for parametric approximation \(f_{\bf a}:\mathbb{R}^d\rightarrow\mathbb{R}\) of \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).
ParametricFunctionApproximation	Abstract class for parametric approximation \(f_{\bf a}:\mathbb{R}^d\rightarrow\mathbb{R}\) of \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).

class TransportMaps.Maps.Functionals.ParametricFunctionalBase.ParametricFunctional(dim)

Bases: TransportMaps.Maps.Functionals.FunctionalBase.Functional

Abstract class for parametric approximation \(f_{\bf a}:\mathbb{R}^d\rightarrow\mathbb{R}\) of \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).

Parameters:

dim (int) – number of dimensions

abstract property n_coeffs

[Abstract] Get the number \(N\) of coefficients \({\bf a}\)

Returns:

(int) – number of coefficients

abstract property coeffs

[Abstract] Get the coefficients \({\bf a}\)

Returns:

(ndarray [\(N\)]) – coefficients

abstract get_identity_coeffs()

abstract get_default_init_values_regression()

regression_callback(xk)

regression_nominal_coeffs()

abstract init_coeffs()

[Abstract] Initialize the coefficients \({\bf a}\)

get_n_coeffs()

get_coeffs()

_set_coeffs(coeffs)

set_coeffs(coeffs)

abstract grad_a(x, precomp=None, idxs_slice=slice(None))

[Abstract] Evaluate \(\nabla_{\bf a} f_{\bf a}\) 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 [\(m,1,N\)]) –

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

abstract hess_a(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Evaluate \(\nabla^2_{\bf a} f_{\bf a}\) 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 [\(m,1,N,N\)]) –

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

abstract grad_a_partial_xd(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Evaluate \(\nabla_{\bf a}\partial_{x_d} f_{\bf a}\) 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 [\(m,1,N\)]) –

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

abstract hess_a_partial_xd(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Evaluate \(\nabla^2_{\bf a}\partial_{x_d} f_{\bf a}\) 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 [\(m,1,N,N\)]) –

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

class TransportMaps.Maps.Functionals.ParametricFunctionalBase.ParametricFunctionApproximation(dim)

Bases: ParametricFunctional

Abstract class for parametric approximation \(f_{\bf a}:\mathbb{R}^d\rightarrow\mathbb{R}\) of \(f:\mathbb{R}^d\rightarrow\mathbb{R}\).

Parameters:

dim (int) – number of dimensions