TransportMaps.Maps.Functionals.TensorizedParametricFunctionalBase

Module Contents

Classes

TensorizedParametricFunctional

[Abstract] Class for approximations using tensorization of unidimensional basis

TensorizedFunctionApproximation

[Abstract] Class for approximations using tensorization of unidimensional basis

class TransportMaps.Maps.Functionals.TensorizedParametricFunctionalBase.TensorizedParametricFunctional(basis_list, full_basis_list=None)[source]

Bases: TransportMaps.Maps.Functionals.ParametricFunctionalBase.ParametricFunctional

[Abstract] Class for approximations using tensorization of unidimensional basis

Parameters:
  • basis_list (list) – list of \(d\) Basis

  • full_basis_list (list) – full list of Basis. basis_list is a subset of full_basis_list. This may be used to automatically increase the input dimension of the approximation.

precomp_evaluate(x, precomp=None, precomp_type='uni')[source]

Precompute the uni-variate Vandermonde matrices for the evaluation of \(f_{\bf a}\) at x.

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with list

[\(d\)] of ndarray [\(m,n_i\)]) – dictionary containing the list of Vandermonde matrices

precomp_grad_x(x, precomp=None)[source]

Precompute the uni-variate Vandermonde matrices for the evaluation of \(\nabla_{\bf x} f_{\bf a}\) at x

Letting \(\Phi^{(i)}(x_i)\) being the uni-variate Vandermonde in \(x_i\), the i-th element of the returned list is \(\partial_{x_i}\Phi^{(i)}(x_i)\).

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with list

[\(d\)] of ndarray [\(m,n_i\)]) – dictionary containing the list of Vandermonde matrices

precomp_hess_x(x, precomp=None)[source]

Precompute the uni-variate Vandermonde matrices for the evaluation of \(\nabla^2_{\bf x} f_{\bf a}\) at x

Letting \(\Phi^{(i)}(x_i)\) being the uni-variate Vandermonde in \(x_i\), the i-th element of the returned list is \(\partial^2_{x_i}\Phi^{(i)}(x_i)\).

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with list

[\(d\)] of ndarray [\(m,n_i\)]) – dictionary containing the list of Vandermonde matrices

precomp_partial_xd(x, precomp=None, precomp_type='uni')[source]

Precompute uni-variate Vandermonde matrix for the evaluation of \(\partial_{x_d} f_{\bf a}\) at x.

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with ndarray [\(m,n_d\)]) –

dictionary with Vandermonde matrix

precomp_partial2_xd(x, precomp=None)[source]

Precompute uni-variate Vandermonde matrix for the evaluation of \(\partial^2_{x_d} f_{\bf a}\) at x.

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with ndarray [\(m,n_d\)]) –

dictionary with Vandermonde matrix

precomp_grad_x_partial_xd(x, precomp=None)[source]

Precompute uni-variate Vandermonde matrices for the evaluation of \(\nabla_{\bf x}\partial_{x_d} f_{\bf a}\) at x.

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with list [d]

ndarray [\(m,N\)]) – dictionary containing the list of uni-variate Vandermonde matrices.

precomp_partial3_xd(x, precomp=None)[source]

Precompute uni-variate Vandermonde matrix for the evaluation of \(\partial^3_{x_d} f_{\bf a}\) at x.

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with ndarray [\(m,n_d\)]) –

dictionary with Vandermonde matrix

precomp_hess_x_partial_xd(x, precomp=None)[source]

Precompute uni-variate Vandermonde matrices for the evaluation of \(\nabla_{\bf x}\partial_{x_d} f_{\bf a}\) at x.

Enriches the precomp dictionary if necessary.

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

  • precomp (dict) – dictionary of precomputed values

Returns:

(dict with list [d]

ndarray [\(m,N\)]) – dictionary containing the list of uni-variate Vandermonde matrices.

class TransportMaps.Maps.Functionals.TensorizedParametricFunctionalBase.TensorizedFunctionApproximation(dim)[source]

Bases: TensorizedParametricFunctional

[Abstract] Class for approximations using tensorization of unidimensional basis

Parameters:
  • basis_list (list) – list of \(d\) Basis

  • full_basis_list (list) – full list of Basis. basis_list is a subset of full_basis_list. This may be used to automatically increase the input dimension of the approximation.