TransportMaps.Maps.LinearSpanParametricTriangularComponentwiseMapBase

Module Contents

Classes

LinearSpanParametricTriangularComponentwiseMap	Triangular map \(T[{\bf a}_{1:d_y}]({\bf x})= [T_1[{\bf a}_1],\ldots,T_{d_y}[{\bf a}_{d_y}]]^\top\) where :math:`T_i[{bf a}_i](x_{1:i}) := {bf a}_i^top , Phi(x_{1:i}) `.
CommonBasisLinearSpanParametricTriangularComponentwiseMap	Triangular map \(T[{\bf a}_{1:d_y}]({\bf x})= [T_1[{\bf a}_1],\ldots,T_{d_y}[{\bf a}_{d_y}]]^\top\) where \(T_i[{\bf a}_i](x_{1:i}) := {\bf a}_i^\top \, \Phi(x_{1:i})\), and for each dimension \(i\), every component \(T_k\) share the same basis type.

class TransportMaps.Maps.LinearSpanParametricTriangularComponentwiseMapBase.LinearSpanParametricTriangularComponentwiseMap(**kwargs)

Bases: TransportMaps.Maps.ParametricTriangularComponentwiseMapBase.ParametricTriangularComponentwiseMap

Triangular map \(T[{\bf a}_{1:d_y}]({\bf x})= [T_1[{\bf a}_1],\ldots,T_{d_y}[{\bf a}_{d_y}]]^\top\) where :math:`T_i[{bf a}_i](x_{1:i}) := {bf a}_i^top , Phi(x_{1:i}) `.

get_identity_coeffs()

Returns the coefficients corresponding to the identity map

Returns:

coefficients

Return type:

(ndarray [\(N\)])

class TransportMaps.Maps.LinearSpanParametricTriangularComponentwiseMapBase.CommonBasisLinearSpanParametricTriangularComponentwiseMap(**kwargs)

Bases: LinearSpanParametricTriangularComponentwiseMap

Triangular map \(T[{\bf a}_{1:d_y}]({\bf x})= [T_1[{\bf a}_1],\ldots,T_{d_y}[{\bf a}_{d_y}]]^\top\) where \(T_i[{\bf a}_i](x_{1:i}) := {\bf a}_i^\top \, \Phi(x_{1:i})\), and for each dimension \(i\), every component \(T_k\) share the same basis type.

This is leads to some more efficient evaluation operations.

precomp_evaluate(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(T({\bf x},{\bf a})\)

This returns a list of uni-variate Vandermonde matrices with order maximum among the components \(T_i\).

Enriches the dictionaries in the precomp list if necessary.

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

ndarray) – necessary structures

precomp_grad_x(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(\nabla_{\bf x}T({\bf x},{\bf a})\)

Enriches the dictionaries in the precomp list if necessary.

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

ndarray) – necessary structures

precomp_hess_x(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(\nabla^2_{\bf x}T({\bf x},{\bf a})\)

Enriches the dictionaries in the precomp list if necessary.

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

ndarray) – necessary structures

precomp_nabla3_x(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(\nabla^3_{\bf x}T({\bf x},{\bf a})\)

Enriches the dictionaries in the precomp list if necessary.

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

ndarray) – necessary structures

precomp_partial_xd(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(\partial_{x_k}T_k({\bf x},{\bf a})\) for \(k=1,\ldots,d\)

Enriches the dictionaries in the precomp list if necessary.

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

ndarray) – necessary structures

precomp_grad_x_partial_xd(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(\nabla_{\bf x}\partial_{x_k}T_k({\bf x},{\bf a})\) for \(k=1,\ldots,d\)

Enriches the dictionaries in the precomp list if necessary.

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

dict) – necessary structures

precomp_hess_x_partial_xd(x, precomp=None, precomp_type='uni')

Precompute necessary structures for the evaluation of \(\nabla^2_{\bf x}\partial_{x_k}T_k({\bf x},{\bf a})\) for \(k=1,\ldots,d\)

Parameters:

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

• precomp (dict) – list of dictionaries of precomputed values

• precomp_type (str) – only option ‘uni’ is allowed for this TransportMap

Returns:

(dict of list [\(d\)]

dict) – necessary structures