#include <poly_basis.hpp>

Collaboration diagram for PolynomialBasis< Device >:

Public Member Functions
View< double ***, CLayout, Device >	compute_inner_product (const View< double ***, CLayout, Device > &dist_in) const

PolynomialBasisDistribution < Device >	get_coefficients (const View< double ***, CLayout, Device > &inner_prod_matrix) const

template<typename F >
void	add_basis (int &basis_ind, F func)

template<typename... Fs>
	PolynomialBasis (const UniformRange &xrange_in, const UniformRange &yrange_in, Fs...funcs)

PolynomialBasisDistribution < Device >	get_distribution (const View< double ***, CLayout, Device > &dist_in) const

template<typename F >
View< double **, CLayout, Device >	get_moments (const int nnode, F lambda_func) const

View< double ***, CLayout, Device >	get_scaling (const PolynomialBasisDistribution< Device > &polynom, const View< double **, CLayout, Device > &g_mom) const

Private Types
using	exec_space = typename Device::execution_space

Private Attributes
int	n_poly

UniformRange	xrange

UniformRange	yrange

View< double ***, CLayout, Device >	bases

View< double ***, CLayout, HostType >	bases_h

View< double ****, CLayout, Device >	matrix

Member Typedef Documentation

template<class Device>

using PolynomialBasis< Device >::exec_space = typename Device::execution_space

private

Constructor & Destructor Documentation

template<class Device>

template<typename... Fs>

PolynomialBasis< Device >::PolynomialBasis	(	const UniformRange &	xrange_in,
		const UniformRange &	yrange_in,
		Fs...	funcs
	)

inline

Constructor for a polynomial basis with one polynomial per provided function, evaluated with the range and resolution specified by xrange_in and yrange_in. The resulting basis will be able to evaluate all given functions at any point within the specified ranges.

Parameters

[in]	xrange_in	A uniform range object specifying the interval on which the polynomials should have support in the first dimension
[in]	yrange_in	A uniform range object specifying the interval on which the polynomials should have support in the second dimension
[in]	funcs	The desired basis functions on two dimensions

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Member Function Documentation

template<class Device>

template<typename F >

void PolynomialBasis< Device >::add_basis	(	int &	basis_ind,
		F	func
	)

inline

Adds a new basis for the polynomial representation

Parameters

[in,out]	basis_ind	Offset index that is incremented so that the next basis is added to the next index in bases_h
[in]	func	Function representating the new basis on two dimensions (x, y)

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template<class Device>

View<double***, CLayout, Device> PolynomialBasis< Device >::compute_inner_product ( const View< double ***, CLayout, Device > & dist_in ) const

inline

Sets up a moment matrix of the current plasma distribution function and computes orthonormal polynomial basis for scaling of the plasma distribution function Polynomials: lambda_i = sum_[j=1]^4 c_[i,j] gamma_j where gamma_1 = 1, gamma_2 = v_||, gamma_3 = v_pe, gamma_4 = v_||^2, gamma_5 = v_pe^2 Inner product <lambda_i,lambda_j> = int[lambda_i lambda_j f d^3 v] Moment matrix defined by inner products <gamma_i,gamma_j> Gamma = | <1,1> <1 ,v_||> <1 ,v_pe> <1 ,v_||^2> <1 ,v_pe^2> | | <v_||,v_||> <v_||,v_pe> <v_|| ,v_||^2> <v_|| ,v_pe^2> | | <v_pe,v_pe> <v_pe ,v_||^2> <v_pe ,v_pe^2> | | <v_||^2,v_||^2> <v_||^2,v_pe^2> | | <v_pe^2,v_pe^2> | or Gamma = | <1,1> <1 ,v_||> <1 ,v_||^2> <1 ,v_pe^2> | | <v_||,v_||> <v_|| ,v_||^2> <v_|| ,v_pe^2> | | <v_||^2,v_||^2> <v_||^2,v_pe^2> | | <v_pe^2,v_pe^2> |

===> <lambda_i,lambda_j> = sum_[k,l=1]^5 c_[i,k] Gamma_[k,l] c_[j,l] ==> lambda_i^T.A.lambda_k The coefficients c_[i,l] are calculated with Gram-Schmidt process lambda_i = gamma_i - sum_[j=1]^[i-1] <gamma_i,lambda_j>/<lambda_j,lambda_j> lambda_j

The coefficients of the basis polynomials are stored in a 4x4 matrix, The inner products in the matrix A are stored in a 10-element vector starting with the main diagonal, then going through the upper side diagonals.

The moments in the matrix Gamma are evaluated from the global variable storing the distribution function –> f0_f

The coefficients c_[i,j] of the basis polynomials are stored in a PolynomialBasisDistribution struct.

Parameters

[in] dist_in The distribution function to be represented by polynomials return The inner product representation of dist_in

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template<class Device>

PolynomialBasisDistribution<Device> PolynomialBasis< Device >::get_coefficients ( const View< double ***, CLayout, Device > & inner_prod_matrix ) const

inline

Given the inner product matrix built from an input distribution, calculate and return the distribution with polynomial representation

Parameters

[in] inner_prod_matrix The inner product matrix

Returns: The polynomial representation of the distribution used to calculate the inner product matrix

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template<class Device>

PolynomialBasisDistribution<Device> PolynomialBasis< Device >::get_distribution ( const View< double ***, CLayout, Device > & dist_in ) const

inline

Constructs a polynomial representation of the input distribution

Parameters

[in] dist_in The distribution function to be represented by polynomials return The polynomial representation of the distribution used to calculate the inner product matrix

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template<class Device>

template<typename F >

View<double**, CLayout, Device> PolynomialBasis< Device >::get_moments	(	const int	nnode,
		F	lambda_func
	)		const

inline

Computes moments of the distribution using a user-defined kernel function

Parameters

[in]	nnode	Number of mesh nodes to loop over
[in]	lambda_func	User defined kernel function for a single mesh node return The array of new moments

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template<class Device>

View<double***, CLayout, Device> PolynomialBasis< Device >::get_scaling	(	const PolynomialBasisDistribution< Device > &	polynom,
		const View< double **, CLayout, Device > &	g_mom
	)		const

inline

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Member Data Documentation

template<class Device>

View<double***, CLayout, Device> PolynomialBasis< Device >::bases

private

template<class Device>

View<double***, CLayout, HostType> PolynomialBasis< Device >::bases_h

private

template<class Device>

View<double****, CLayout, Device> PolynomialBasis< Device >::matrix

private

template<class Device>

int PolynomialBasis< Device >::n_poly

private

template<class Device>

UniformRange PolynomialBasis< Device >::xrange

private

template<class Device>

UniformRange PolynomialBasis< Device >::yrange

private

The documentation for this class was generated from the following file:

/u/gitlab-xgc/builds/YGMz2TJ8/0/xgc/XGC-Devel/XGC_core/cpp/poly_basis.hpp

Public Member Functions

Private Types

Private Attributes

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation