Basis Evaluators#

enum mpart::BasisHomogeneity#

Flags for controlling how “homogeneous/heterogeneous” a real-valued multivariate basis function is.

Assuming you want create a function \(f_{\vec{\alpha}}:\mathbb{R}^{d+1}\to\mathbb{R}\) which has multi-index \(\vec{\alpha}\), there are a few possibilities:

All diagonal and offdiagonal univariate functions are identical, i.e. \(f(x_1,\ldots,x_d,y)=\psi_{\alpha_{d+1}}(y)\prod_{j=1}^d\psi_{\alpha_j}(x_j)\), which is Homogeneous
All offdiagonal univariate functions are identical, i.e. \(f(x_1,\ldots,x_d,y)=\psi^{diag}_{\alpha_{d+1}}(y)\prod_{j=1}^d\psi^{offdiag}_{\alpha_j}(x_j)\), which is OffdiagHomogeneous.
All univariate basis functions may be different, i.e. \(f(x_1,\ldots,x_d,y)=\psi^{d+1}_{\alpha_{d+1}}(y)\prod_{j=1}^d\psi^{j}_{\alpha_j}(x_j)\) which is Heterogeneous

Values:

enumerator Homogeneous#

enumerator OffdiagHomogeneous#

enumerator Heterogeneous#

template<BasisHomogeneity HowHomogeneous, typename BasisEvaluatorType, typename RectifierType = Identity> class BasisEvaluator#

Class to represent all elements of a multivariate function basis.

See BasisHomogeneity for information on options for HowHomogeneous . The form of template parameter BasisEvaluatorType will depend on HowHomogeneous See the documentation of each implementation for details on what’s necessary. We give the option to “rectify” the function if it depends on y (i.e. make the part dependent on x positive)

Any univariate basis function used here must have the following functions:

EvaluateAll
EvaluateDerivatives
EvaluateSecondDerivatives

See OrthogonalPolynomial as an example that implements the required functions

Template Parameters:

HowHomogeneous – What level of homogeneity the basis has (see BasisHomogeneity for more info)
BasisEvaluatorType – The type we need to evaluate when evaluating the basis
RectifierType – The rectification operator for diag/offdiag cross-terms

Public Functions

inline BasisEvaluator(unsigned int dim, BasisEvaluatorType basis1d)#

Construct a new Basis Evaluator object.

Parameters:

dim – input dimension of the multivariate basis
basis1d – object(s) used to evaluate the basis

inline void EvaluateAll(unsigned int dim, double *output_eval, int maxOrder, double point) const#

Evaluate the functions for the multivariate basis.

Parameters:

dim – Which input dimension to evaluate
output_eval – Memory to store output (should be size maxOrder + 1)
maxOrder – Maximum basis order to evaluate
point – Input point to evaluate the dim th basis functions at

inline void EvaluateDerivatives(unsigned int dim, double *output_eval, double *output_diff, int maxOrder, double point) const#

Evaluate the functions for the multivariate basis.

Parameters:

dim – Which input dimension to evaluate
output_eval – Memory to store eval output (size maxOrder + 1)
output_diff – Memory to store 1st deriv output (size maxOrder + 1)
maxOrder – Maximum basis order to evaluate
point – Input point to evaluate the dim th basis functions at

inline void EvaluateSecondDerivatives(unsigned int dim, double *output_eval, double *output_diff, double *output_diff_2, int maxOrder, double point) const#

Evaluate the functions for the multivariate basis.

Parameters:

dim – Which input dimension to evaluate
output_eval – Memory to store eval output (size maxOrder + 1)
output_diff – Memory to store 1st deriv output (size maxOrder + 1)
output_diff_2 – Memory to store 2nd deriv output (size maxOrder + 1)
maxOrder – Maximum basis order to evaluate
point – Input point to evaluate the dim th basis functions at

template<typename BasisEvaluatorType> class BasisEvaluator<BasisHomogeneity::Homogeneous, BasisEvaluatorType>#

Basis evaluator when all univariate basis fcns are identical.