Interpolators namespace. More...

Classes
class	BaseParticleContainer
	BaseParticleContainer abstract class definition. More...

class	ParticleIterator

class	ParticlesContainer
	ParticlesContainer class definition. More...

struct	PhotonsData
	Struct to managing null geodesic particles. More...

Functions
template<int N>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	barycentric_cubic_1d (CCTK_REAL &value, const int(&points)[N], const CCTK_REAL *weights, const CCTK_REAL(&values)[N], const CCTK_REAL &x, const CCTK_REAL &plo, const CCTK_REAL &dx)
	Do a Barycentric interpolation in one direction. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE CCTK_REAL	barycentric_cubic_3d (const amrex::Array4< CCTK_REAL const > &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo, const int &comp)
	Do a Barycentric interpolation in three direction for a vectorial function. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE CCTK_REAL	barycentric_cubic_3d (const amrex::Array4< CCTK_REAL const > &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo)
	Do a Barycentric interpolation in three direction for a scalar function. More...

template<int N>
AMREX_GPU_DEVICE AMREX_GPU_HOST AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	der_barycentric_cubic_1d (CCTK_REAL &f_x, CCTK_REAL &d_f_x, const int(&points)[N], const CCTK_REAL *weights, const CCTK_REAL(&values)[N], const CCTK_REAL &x, const CCTK_REAL &plo, const CCTK_REAL &dx)
	Do a Barycentric interpolation and its derivative in one direction. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	barycentric_derivative_and_interpolate (CCTK_REAL &f_xyz, CCTK_REAL &df_xyz_0, CCTK_REAL &df_xyz_1, CCTK_REAL &df_xyz_2, amrex::Array4< CCTK_REAL const > const &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo, const int &comp)
	Do a Barycentric interpolation and its derivatives in three directions. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	interpolate_array (amrex::GpuArray< CCTK_REAL, 6 > &array6, const amrex::Array4< CCTK_REAL const > &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo)
	Do the barycentric interpolation for a 3 dimensional and symmetric matrix. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	d_interpolate_array (amrex::GpuArray< CCTK_REAL, 6 > &array6, amrex::GpuArray< amrex::GpuArray< CCTK_REAL, 6 >, 3 > &d_array6, const amrex::Array4< CCTK_REAL const > &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo)
	Do the barycentric interpolation for a 3 dimensional and symmetric matrix and its derivatives. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	d_interpolate_array (amrex::GpuArray< CCTK_REAL, 3 > &array3, amrex::GpuArray< amrex::GpuArray< CCTK_REAL, 3 >, 3 > &d_array3, const amrex::Array4< CCTK_REAL const > &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo)
	Do the barycentric interpolation for a 3 dimensional and symmetric vector and its derivatives. More...

template<int INTERPOLATION_ORDER>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void	d_interpolate_array (CCTK_REAL &array, amrex::GpuArray< CCTK_REAL, 3 > &d_array, const amrex::Array4< CCTK_REAL const > &f, const long int &i0, const long int &j0, const long int &k0, const CCTK_REAL &x, const CCTK_REAL &y, const CCTK_REAL &z, const amrex::GpuArray< double, 3 > &dx, const amrex::GpuArray< double, 3 > &plo)
	Do the barycentric interpolation for a scalar function its derivatives. More...

Detailed Description

Interpolators namespace.

Function Documentation

◆ barycentric_cubic_1d()

template<int N>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::barycentric_cubic_1d	(	CCTK_REAL &	value,
		const int(&)	points[N],
		const CCTK_REAL *	weights,
		const CCTK_REAL(&)	values[N],
		const CCTK_REAL &	x,
		const CCTK_REAL &	plo,
		const CCTK_REAL &	dx
	)

Do a Barycentric interpolation in one direction.

This function computes the interpolation of a function on just one direction using a barycentric Lagrange interpolation by doing:

\[ f(x) = \frac{\sum\limits_{i = 0}^N \frac{w_i}{x - x_i}f(x_i)}{\sum\limits_{l = 0}^N \frac{w_l}{x - x_l}} \]

where \(N\) is the order of interpolation.

Parameters

value	The interpolated value reference.
points	Vector containing the coordinates of each point.
weights	The weights of each datapoint.
x	The value where we are interpolating.
dx	Vector \(\Delta x\) on the particular direction.
plo	Lower coordinates in the box domain.

◆ barycentric_cubic_3d() [1/2]

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE CCTK_REAL GInX::barycentric_cubic_3d	(	const amrex::Array4< CCTK_REAL const > &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo
	)

Do a Barycentric interpolation in three direction for a scalar function.

This function computes the interpolation of a function on three directions using a barycentric Lagrange interpolation by doing:

\[ f(x, y, z) = \frac{\sum\limits_{i,j,k = 0}^N \frac{u_i}{z - z_i}\frac{v_j}{y - y_j}\frac{w_k}{x - x_k}f(x_k, y_j, x_i)}{\sum\limits_{i,j,k = 0}^N \frac{u_i}{z - z_i}\frac{v_j}{y - y_j}\frac{w_k}{x - x_k}} = \frac{\sum\limits_{i=0}^N\frac{u_i}{z - z_i}\left(\frac{\sum\limits_{j=0}^N\frac{v_j}{y-y_j}\left(\frac{\sum\limits_{k=0}^N \frac{w_k}{x - x_k}f(x_k, y_j, x_i)}{\sum\limits_{k= 0}^N \frac{w_k}{x - x_k}}\right)}{\sum\limits_{j= 0}^N \frac{v_j}{y - y_j}}\right)}{\sum\limits_{i= 0}^N \frac{u_i}{z - z_i}} \]

where \(N\) is the order of interpolation.

See also: barycentric_cubic_1d

Parameters

f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector \(\Delta x\) with the space steps value.
plo	Lower values of the entire domain.

Returns: The interpolated value.

◆ barycentric_cubic_3d() [2/2]

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE CCTK_REAL GInX::barycentric_cubic_3d	(	const amrex::Array4< CCTK_REAL const > &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo,
		const int &	comp
	)

Do a Barycentric interpolation in three direction for a vectorial function.

Parameters

f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector with the \(\Delta x\) on each direction.
plo	Lower coordinates in the domain.
comp	Function's component to compute.

Returns: The interpolated value.

◆ barycentric_derivative_and_interpolate()

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::barycentric_derivative_and_interpolate	(	CCTK_REAL &	f_xyz,
		CCTK_REAL &	df_xyz_0,
		CCTK_REAL &	df_xyz_1,
		CCTK_REAL &	df_xyz_2,
		amrex::Array4< CCTK_REAL const > const &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo,
		const int &	comp
	)

Do a Barycentric interpolation and its derivatives in three directions.

This function computes the interpolation of a function on three directions using a barycentric Lagrange interpolation by doing:

\[ f(x, y, z) = \frac{\sum\limits_{i,j,k = 0}^N \frac{u_i}{z - z_i}\frac{v_j}{y - y_j}\frac{w_k}{x - x_k}f(x_k, y_j, x_i)}{\sum\limits_{i,j,k = 0}^N \frac{u_i}{z - z_i}\frac{v_j}{y - y_j}\frac{w_k}{x - x_k}} = \frac{\sum\limits_{i=0}^N\frac{u_i}{z - z_i}\left(\frac{\sum\limits_{j=0}^N\frac{v_j}{y-y_j}\left(\frac{\sum\limits_{k=0}^N \frac{w_k}{x - x_k}f(x_k, y_j, x_i)}{\sum\limits_{k= 0}^N \frac{w_k}{x - x_k}}\right)}{\sum\limits_{j= 0}^N \frac{v_j}{y - y_j}}\right)}{\sum\limits_{i= 0}^N \frac{u_i}{z - z_i}} \]

where \(N\) is the order of interpolation.

But at the same time computes the gradient of the same function by doing:

\[ \frac{\partial}{\partial x}f(x, y, z) = \frac{\sum\limits_{i,j,k = 0}^N \frac{u_i}{z - z_i}\frac{v_j}{y - y_j}\frac{d}{dx}\left(\frac{\frac{w_k}{x - x_k}}{\sum\limits_{l = 0}^N\frac{w_l}{x - x_l}}\right)f(x_k, y_j, x_i)}{\sum\limits_{i,j = 0}^N \frac{u_i}{z - z_i}\frac{v_j}{y - y_j}}, \]

\[ \frac{\partial}{\partial y}f(x, y, z) = \frac{\sum\limits_{i,j,k = 0}^N \frac{u_i}{z - z_i}\frac{d}{dy}\left(\frac{\frac{v_j}{y - y_j}}{\sum\limits_{l = 0}^N\frac{v_l}{y - y_l}}\right)\frac{w_k}{x - x_k}f(x_k, y_j, x_i)}{\sum\limits_{i,k = 0}^N \frac{u_i}{z - z_i}\frac{w_k}{x - x_k}}, \]

\[ \frac{\partial}{\partial z}f(x, y, z) = \frac{\sum\limits_{i,j,k = 0}^N \frac{d}{dz}\left(\frac{\frac{u_i}{z - z_i}}{\sum\limits_{l = 0}^N\frac{u_l}{z - z_l}}\right)\frac{v_j}{y - y_j}\frac{w_k}{x - x_k}f(x_k, y_j, x_i)}{\sum\limits_{i,k = 0}^N \frac{v_j}{y - y_j}\frac{w_k}{x - x_k}}. \]

by calling the function der_barycentric_cubic_1d().

See also: der_barycentric_cubic_1d

Parameters

f_xyz	Reference to the interpolated value, i.e., \(f(x,y,z)\).
df_xyz_0	Reference to the interpolated derivative value on the direction 0, i.e., \(\partial_xf(x,y,z)\).
df_xyz_1	Reference to the interpolated derivative value on the direction 1, i.e., \(\partial_yf(x,y,z)\).
df_xyz_2	Reference to the interpolated derivative value on the direction 2, i.e., \(\partial_zf(x,y,z)\).
f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector \(\Delta x\) with the space steps value.
plo	Lower values of the entire domain.
comp	Function's component to compute.

◆ d_interpolate_array() [1/3]

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::d_interpolate_array	(	amrex::GpuArray< CCTK_REAL, 3 > &	array3,
		amrex::GpuArray< amrex::GpuArray< CCTK_REAL, 3 >, 3 > &	d_array3,
		const amrex::Array4< CCTK_REAL const > &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo
	)

Do the barycentric interpolation for a 3 dimensional and symmetric vector and its derivatives.

This function computes the interpolation for a 3 dimensional and symmetric vector and its derivatives, such as the induced shift vector in just one call using the der_barycentric_cubic_1d function similarly to the barycentric_derivative_and_interpolate function.

See also: barycentric_derivative_and_interpolate; der_barycentric_cubic_1d

Parameters

array6	Reference to the GpuArray of size 3 that is going to store the interpolated values.
d_array6	Reference to GpuArray of size 3 x 3 that stores all the derivatives values.
f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector \(\Delta x\) with the space steps value.
plo	Lower values of the entire domain.

◆ d_interpolate_array() [2/3]

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::d_interpolate_array	(	amrex::GpuArray< CCTK_REAL, 6 > &	array6,
		amrex::GpuArray< amrex::GpuArray< CCTK_REAL, 6 >, 3 > &	d_array6,
		const amrex::Array4< CCTK_REAL const > &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo
	)

Do the barycentric interpolation for a 3 dimensional and symmetric matrix and its derivatives.

This function computes the interpolation for a 3 dimensional and symmetric matrix and its derivatives, such as the induced metric and the extrinsic curvature tensor in just one call using the der_barycentric_cubic_1d function similarly to the barycentric_derivative_and_interpolate function.

See also: barycentric_derivative_and_interpolate; der_barycentric_cubic_1d

Parameters

array6	Reference to the GpuArray of size 6 that is going to store the interpolated values.
d_array6	Reference to the GpuArray of size 6 x 3 that stores all the derivatives values.
f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector \(\Delta x\) with the space steps value.
plo	Lower values of the entire domain.

◆ d_interpolate_array() [3/3]

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::d_interpolate_array	(	CCTK_REAL &	array,
		amrex::GpuArray< CCTK_REAL, 3 > &	d_array,
		const amrex::Array4< CCTK_REAL const > &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo
	)

Do the barycentric interpolation for a scalar function its derivatives.

This function computes the interpolation for scalar function and its derivatives, such as the lapse function in just one call using the der_barycentric_cubic_1d function similar to the barycentric_derivative_and_interpolate function.

See also: barycentric_derivative_and_interpolate; der_barycentric_cubic_1d

Parameters

array6	reference to the CCTK_REAL variable that is going to store the interpolated value.
d_array6	Reference to the GpuArray of size 3 that stores all the derivatives values.
f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector \(\Delta x\) with the space steps value.
plo	Lower values of the entire domain.

◆ der_barycentric_cubic_1d()

template<int N>

AMREX_GPU_DEVICE AMREX_GPU_HOST AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::der_barycentric_cubic_1d	(	CCTK_REAL &	f_x,
		CCTK_REAL &	d_f_x,
		const int(&)	points[N],
		const CCTK_REAL *	weights,
		const CCTK_REAL(&)	values[N],
		const CCTK_REAL &	x,
		const CCTK_REAL &	plo,
		const CCTK_REAL &	dx
	)

Do a Barycentric interpolation and its derivative in one direction.

This function computes the interpolation of a function on just one direction using a barycentric Lagrange interpolation by doing:

\[ f(x) = \frac{\sum\limits_{i = 0}^N \frac{w_i}{x - x_i}f(x_i)}{\sum\limits_{i = 0}^N \frac{w_i}{x - x_i}} \]

where \(N\) is the order of interpolation.

And at the same time computes the derivative on the desired direction by doing:

\[ f'(x) = \sum\limits_{i = 0}^N f(x_i)\frac{d}{dx}\left(\frac{\frac{w_i}{x - x_i}}{\sum\limits_{i = 0}^N \frac{w_i}{x - x_i}}\right) = \frac{\sum\limits_{j = 0}^N f(x_j)\frac{w_j}{(x-x_j)}\sum\limits_{m = 0}^N\frac{w_m}{(x-x_m)^2} - \sum\limits_{j = 0}^N f(x_j)\frac{w_j}{(x-x_j)^2}\sum\limits_{m = 0}^N \frac{w_m}{x - x_m}}{\left(\sum\limits_{l = 0}^N \frac{w_l}{x - x_l}\right)^2} \]

In the case \(x = x_i\), one of the nodes, we have the expression

\[ f'(x) = \sum\limits_{j=0}^{N}\frac{w_j}{w_i}\frac{f(x_i)}{x_i-x_j}. \]

See also: barycentric_cubic_3d; barycentric_cubic_1d

Parameters

f_x	Reference to the final interpolated function value.
d_f_x	Reference to the final interpolated derivative function value.
points	Vector containing the coordinates of each point.
weights	The weights of each datapoint.
x	The value where we are interpolating.
plo	Lower values of the entire domain.
dx	Vector \(\Delta x\) with the space steps value.

◆ interpolate_array()

template<int INTERPOLATION_ORDER>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE CCTK_ATTRIBUTE_ALWAYS_INLINE void GInX::interpolate_array	(	amrex::GpuArray< CCTK_REAL, 6 > &	array6,
		const amrex::Array4< CCTK_REAL const > &	f,
		const long int &	i0,
		const long int &	j0,
		const long int &	k0,
		const CCTK_REAL &	x,
		const CCTK_REAL &	y,
		const CCTK_REAL &	z,
		const amrex::GpuArray< double, 3 > &	dx,
		const amrex::GpuArray< double, 3 > &	plo
	)

Do the barycentric interpolation for a 3 dimensional and symmetric matrix.

This function computes the interpolation for a 3 dimensional and symmetric matrix, such as the induced metric and the extrinsic curvature tensor in just one call using the barycentric_cubic_1d function similar to the barycentric_cubic_3d function.

See also: barycentric_cubic_3d; barycentric_cubic_1d

Parameters

array6	Reference to GpuArray of size 6 that is going to store the interpolated values.
f	Array containing the function values.
i0	Basis cell index accordingly to x.
j0	Basis cell index accordingly to y.
k0	Basis cell index accordingly to z.
x	Coordinate x value to interpolate.
y	Coordinate y value to interpolate.
z	Coordinate z value to interpolate.
dx	Vector \(\Delta x\) with the space steps value.
plo	Lower values of the entire domain.

Classes

Functions

Detailed Description

Function Documentation

◆ barycentric_cubic_1d()

◆ barycentric_cubic_3d() [1/2]

◆ barycentric_cubic_3d() [2/2]

◆ barycentric_derivative_and_interpolate()

◆ d_interpolate_array() [1/3]

◆ d_interpolate_array() [2/3]

◆ d_interpolate_array() [3/3]

◆ der_barycentric_cubic_1d()

◆ interpolate_array()