File Describing useful mathematical functions. More...

#include <ddc/ddc.hpp>
#include "quadrature.hpp"

Functions
template<class... Tags>
KOKKOS_FUNCTION double	norm_inf (ddc::Coordinate< Tags... > coord)
	Compute the infinity norm. More...

KOKKOS_INLINE_FUNCTION double	norm_inf (double const coord)
	Compute the infinity norm. More...

template<class ExecSpace , class ElementType , class IdxRange >
double	norm_inf (ExecSpace exec_space, ConstField< ElementType, IdxRange, typename ExecSpace::memory_space > function)
	Compute the infinity norm for a Field. More...

template<class ExecSpace , class ElementType , class IdxRange , class NDTag >
double	norm_inf (ExecSpace exec_space, VectorConstField< ElementType, IdxRange, NDTag, typename ExecSpace::memory_space > function)
	Compute the infinity norm for a VectorField. More...

template<class ExecSpace , class ElementType , class IdxRange >
double	error_norm_inf (ExecSpace exec_space, ConstField< ElementType, IdxRange, typename ExecSpace::memory_space > function, ConstField< ElementType, IdxRange, typename ExecSpace::memory_space > exact_function)
	Compute the infinity norm of the error between 2 Fields. More...

template<class ExecSpace , class ElementType , class IdxRange , class NDTag >
double	error_norm_inf (ExecSpace exec_space, VectorConstField< ElementType, IdxRange, NDTag, typename ExecSpace::memory_space > function, VectorConstField< ElementType, IdxRange, NDTag, typename ExecSpace::memory_space > exact_function)
	Compute the infinity norm of the error between 2 VectorFields. More...

template<class IdxRangeQuad , class ExecSpace >
double	norm_L1 (ExecSpace exec_space, Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space > quadrature, DField< IdxRangeQuad, typename ExecSpace::memory_space > function)
	Compute L1 norm of a function with a given quadrature. More...

template<class IdxRangeQuad , class ExecSpace >
double	error_norm_L1 (ExecSpace exec_space, Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space > quadrature, DField< IdxRangeQuad, typename ExecSpace::memory_space > function, DField< IdxRangeQuad, typename ExecSpace::memory_space > exact_function)
	Compute the L1 norm of the error between 2 Fields. More...

template<class IdxRangeQuad , class ExecSpace >
double	norm_L2 (ExecSpace exec_space, Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space > quadrature, DField< IdxRangeQuad, typename ExecSpace::memory_space > function)
	Compute L2 norm of a function with a given quadrature. More...

template<class IdxRangeQuad , class ExecSpace >
double	error_norm_L2 (ExecSpace exec_space, Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space > quadrature, DField< IdxRangeQuad, typename ExecSpace::memory_space > function, DField< IdxRangeQuad, typename ExecSpace::memory_space > exact_function)
	Compute the L2 norm of the error between 2 Fields. More...

Detailed Description

File Describing useful mathematical functions.

Function Documentation

◆ norm_inf() [1/4]

template<class... Tags>

KOKKOS_FUNCTION double norm_inf ( ddc::Coordinate< Tags... > coord )

Compute the infinity norm.

For a given vector \( x \) , compute \(|Vert x |Vert_{\infty} = \sup_n |x_n| \).

Parameters

[in] coord The given vector.

Returns: A double containing the value of the infinty norm.

◆ norm_inf() [2/4]

KOKKOS_INLINE_FUNCTION double norm_inf ( double const coord )

Compute the infinity norm.

In case of scalar, the infinity norm returns the scalar.

Parameters

[in] coord The given double.

Returns: A double containing the value of the infinty norm.

◆ norm_inf() [3/4]

template<class ExecSpace , class ElementType , class IdxRange >

double norm_inf	(	ExecSpace	exec_space,
		ConstField< ElementType, IdxRange, typename ExecSpace::memory_space >	function
	)

inline

Compute the infinity norm for a Field.

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	function	The function whose norm is calcuated.

Returns: A double containing the value of the infinty norm.

◆ norm_inf() [4/4]

template<class ExecSpace , class ElementType , class IdxRange , class NDTag >

double norm_inf	(	ExecSpace	exec_space,
		VectorConstField< ElementType, IdxRange, NDTag, typename ExecSpace::memory_space >	function
	)

inline

Compute the infinity norm for a VectorField.

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	function	The function whose norm is calcuated.

Returns: A double containing the value of the infinty norm.

◆ error_norm_inf() [1/2]

template<class ExecSpace , class ElementType , class IdxRange >

double error_norm_inf	(	ExecSpace	exec_space,
		ConstField< ElementType, IdxRange, typename ExecSpace::memory_space >	function,
		ConstField< ElementType, IdxRange, typename ExecSpace::memory_space >	exact_function
	)

inline

Compute the infinity norm of the error between 2 Fields.

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	function	The calculated function.
[in]	exact_function	The exact function with which the calculated function is compared.

Returns: A double containing the value of the infinty norm.

◆ error_norm_inf() [2/2]

template<class ExecSpace , class ElementType , class IdxRange , class NDTag >

double error_norm_inf	(	ExecSpace	exec_space,
		VectorConstField< ElementType, IdxRange, NDTag, typename ExecSpace::memory_space >	function,
		VectorConstField< ElementType, IdxRange, NDTag, typename ExecSpace::memory_space >	exact_function
	)

inline

Compute the infinity norm of the error between 2 VectorFields.

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	function	The calculated function.
[in]	exact_function	The exact function with which the calculated function is compared.

Returns: A double containing the value of the infinty norm.

◆ norm_L1()

template<class IdxRangeQuad , class ExecSpace >

double norm_L1	(	ExecSpace	exec_space,
		Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space >	quadrature,
		DField< IdxRangeQuad, typename ExecSpace::memory_space >	function
	)

Compute L1 norm of a function with a given quadrature.

\( \int_{\Omega} |f(X)| dX \)

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	quadrature	The quadrature used to compute the integral.
[in]	function	A Field to the value of the function on the quadrature grid.

Returns: A double containing the L1 norm of the function.

◆ error_norm_L1()

template<class IdxRangeQuad , class ExecSpace >

double error_norm_L1	(	ExecSpace	exec_space,
		Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space >	quadrature,
		DField< IdxRangeQuad, typename ExecSpace::memory_space >	function,
		DField< IdxRangeQuad, typename ExecSpace::memory_space >	exact_function
	)

Compute the L1 norm of the error between 2 Fields.

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	quadrature	The quadrature used to compute the integral.
[in]	function	The calculated function.
[in]	exact_function	The exact function with which the calculated function is compared.

Returns: A double containing the value of the infinty norm.

◆ norm_L2()

template<class IdxRangeQuad , class ExecSpace >

double norm_L2	(	ExecSpace	exec_space,
		Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space >	quadrature,
		DField< IdxRangeQuad, typename ExecSpace::memory_space >	function
	)

Compute L2 norm of a function with a given quadrature.

\( \sqrt{\int_{\Omega} |f(X)|^2 dX} \)

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	quadrature	The quadrature used to compute the integral.
[in]	function	A Field to the value of the function on the quadrature grid.

Returns: A double containing the L2 norm of the function.

◆ error_norm_L2()

template<class IdxRangeQuad , class ExecSpace >

double error_norm_L2	(	ExecSpace	exec_space,
		Quadrature< IdxRangeQuad, IdxRangeQuad, typename ExecSpace::memory_space >	quadrature,
		DField< IdxRangeQuad, typename ExecSpace::memory_space >	function,
		DField< IdxRangeQuad, typename ExecSpace::memory_space >	exact_function
	)

Compute the L2 norm of the error between 2 Fields.

Parameters

[in]	exec_space	The space on which the function is executed (CPU/GPU).
[in]	quadrature	The quadrature used to compute the integral.
[in]	function	The calculated function.
[in]	exact_function	The exact function with which the calculated function is compared.

Returns: A double containing the value of the infinty norm.

Functions

Detailed Description

Function Documentation

◆ norm_inf() [1/4]

◆ norm_inf() [2/4]

◆ norm_inf() [3/4]

◆ norm_inf() [4/4]

◆ error_norm_inf() [1/2]

◆ error_norm_inf() [2/2]

◆ norm_L1()

◆ error_norm_L1()

◆ norm_L2()

◆ error_norm_L2()