lagrange_weights Struct Reference

This struct contains interpolation weights for 1D Lagrange interpolating polynomials of arbitrary order on a uniform 1D grid. More...

#include <lagrange_weights.hpp>

Public Member Functions
KOKKOS_INLINE_FUNCTION	lagrange_weights ()
KOKKOS_INLINE_FUNCTION	lagrange_weights (double var, double inv_d, int order)
KOKKOS_INLINE_FUNCTION void	set (double var, double inv_d, int order)
KOKKOS_INLINE_FUNCTION void	set_idx (int new_idx)

Public Attributes
int	idx = 0
	The lower cell index on the grid where one cell comprises order+1 grid points. More...
double	w [LAGRANGE_MAX_ORDER] = { 0.0 }
	Stores the Lagrange weights of the grid points i, i+1, i+2, ..., i+order in one cell. More...

Detailed Description

This struct contains interpolation weights for 1D Lagrange interpolating polynomials of arbitrary order on a uniform 1D grid.

The basis functions \(S_k(\xi)\) for \(k=0,1,...,\mathrm{order}\) are given by

\[S_k(\xi)=\prod_{j=0,j{\neq}k}^{\mathrm{order}}\frac{\xi-j\Delta}{k\Delta-j\Delta}\]

for \(\xi\in\left[0,1\right]\) and with \(\Delta=1/\mathrm{order}\). If order is 0 then nearest neighbor interpolation weights are used.

Constructor & Destructor Documentation

lagrange_weights() [1/2]

KOKKOS_INLINE_FUNCTION lagrange_weights::lagrange_weights ( )

inline

lagrange_weights() [2/2]

KOKKOS_INLINE_FUNCTION lagrange_weights::lagrange_weights ( double  var, double  inv_d, int  order  )

inline

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Member Function Documentation

set()

KOKKOS_INLINE_FUNCTION void lagrange_weights::set ( double  var, double  inv_d, int  order  )

inline

Calculates and sets the Lagrange weights

Parameters

[in]	var	is the coordinate on the grid.
[in]	inv_d	is the inverse distance between two neighboring grid points.
[in]	order	is the interpolation order (0 = nearest neighbor), (1 = linear), (2 = quadratic), (3 = cubic), ....

Returns

void

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set_idx()

KOKKOS_INLINE_FUNCTION void lagrange_weights::set_idx ( int  new_idx )

inline

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Member Data Documentation

idx

lagrange_weights::idx = 0

The lower cell index on the grid where one cell comprises order+1 grid points.

member 'idx' contains the lower cell index on the grid where one cell comprises order+1 grid points.

w

lagrange_weights::w = { 0.0 }

Stores the Lagrange weights of the grid points i, i+1, i+2, ..., i+order in one cell.

member 'w' contains the weights used for interpolating to the grid points i, i+1, i+2, ..., i+order in one cell.

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

• /p/test_ssd/builds/t3_84szKM/0/xgc/XGC-Devel/XGC_core/cpp/lagrange_weights.hpp