Items for assessing truncation error in spectral methods. More...

Classes
struct	ConvergenceInfo
	Holds convergence rate and pile up modes of a power monitor. More...

Functions
template<typename VectorType, size_t Dim>
std::array< double, Dim >	relative_truncation_error (const VectorType &tensor_component, const Mesh< Dim > &mesh)
	The relative truncation error in each logical direction of the grid.
ConvergenceInfo	convergence_rate_and_number_of_pile_up_modes (const DataVector &power_monitor, size_t number_of_filtered_modes=0)
	Returns the convergence rate and the number of pile up modes of a power monitor as a ConvergenceInfo.
template<typename TensorType>
DataVector	spherical_shell_tensor_radial_power_monitor (const TensorType &tensor, const Mesh< 3 > &mesh)
	Return the RMS radial power monitor across all components of a tensor on a spherical shell.
size_t	spherical_shell_number_of_angular_coefficients (size_t ell, int spin_weight, bool zero_m_is_real, size_t radial_extents)
	Number of independent TensorYlm coefficients contributing to angular degree ell, summed over radial_extents radial points.
template<typename TensorType>
void	accumulate_spherical_shell_tensor_angular_power (const gsl::not_null< DataVector * > weighted_squared_power, const gsl::not_null< std::vector< size_t > * > counts, const TensorType &tensor, const Mesh< 3 > &mesh)
	Accumulate weighted-squared angular TensorYlm power and mode counts for all components of a tensor on a spherical shell.
void	normalize_spherical_shell_angular_power (gsl::not_null< DataVector * > power, const std::vector< size_t > &counts)
	Normalize an angular power monitor accumulator in place.
void	accumulate_b3_tensor_component_sums (gsl::not_null< DataVector * > sum_sq_radial, gsl::not_null< DataVector * > counts_radial, gsl::not_null< DataVector * > sum_sq_angular, gsl::not_null< DataVector * > counts_angular, const double spec_buf, size_t n_r, size_t n_r_max, int spin_weight, const std::vector< std::vector< size_t > > &offsets_by_l, double gathered, double *modal_buf)
	Accumulate squared ZernikeB3 Jacobi spectral coefficients for one TensorYlm component into radial and angular power bins.
template<typename TensorType>
void	accumulate_b3_tensor_sums (gsl::not_null< DataVector * > sum_sq_radial, gsl::not_null< DataVector * > counts_radial, gsl::not_null< DataVector * > sum_sq_angular, gsl::not_null< DataVector * > counts_angular, const TensorType &tensor, size_t n_r, size_t n_r_max, const std::vector< std::vector< size_t > > &offsets_by_l_real, const std::vector< std::vector< size_t > > &offsets_by_l_complex, double gathered, double modal_buf)
	Accumulate squared ZernikeB3 spectral coefficients for all components of a TensorYlm tensor into radial and angular power bins.
void	normalize_b3_power (gsl::not_null< DataVector * > result, const DataVector &sum_sq, const DataVector &counts)
	Normalize a B3 power monitor accumulator in place.

template<typename VectorType, size_t Dim>
void	power_monitors (gsl::not_null< std::array< DataVector, Dim > * > result, const VectorType &u, const Mesh< Dim > &mesh)
	Returns array of power monitors in each spatial dimension.
template<typename VectorType, size_t Dim>
std::array< DataVector, Dim >	power_monitors (const VectorType &u, const Mesh< Dim > &mesh)
	Returns array of power monitors in each spatial dimension.

double	relative_truncation_error (const DataVector &power_monitor, size_t num_modes_to_use)
	Compute the relative truncation error.

template<typename VectorType, size_t Dim>
std::array< double, Dim >	absolute_truncation_error (const VectorType &tensor_component, const Mesh< Dim > &mesh)
	Returns an estimate of the absolute truncation error in each dimension.

void	spherical_shell_radial_power_monitor (gsl::not_null< DataVector * > result, const DataVector &tensor_component, const Mesh< 3 > &mesh)
	Return the radial power monitor for a tensor component on a spherical shell.
DataVector	spherical_shell_radial_power_monitor (const DataVector &tensor_component, const Mesh< 3 > &mesh)
	Return the radial power monitor for a tensor component on a spherical shell.

void	spherical_shell_angular_power_monitor (gsl::not_null< DataVector * > result, const DataVector &tensor_ylm_component, const Mesh< 3 > &mesh, int spin_weight, bool zero_m_is_real)
	Return the angular power monitor for one TensorYlm component on a spherical shell.
DataVector	spherical_shell_angular_power_monitor (const DataVector &tensor_ylm_component, const Mesh< 3 > &mesh, int spin_weight, bool zero_m_is_real)
	Return the angular power monitor for one TensorYlm component on a spherical shell.

Detailed Description

Items for assessing truncation error in spectral methods.

Function Documentation

◆ accumulate_b3_tensor_component_sums()

void PowerMonitors::accumulate_b3_tensor_component_sums	(	gsl::not_null< DataVector * >	sum_sq_radial,
		gsl::not_null< DataVector * >	counts_radial,
		gsl::not_null< DataVector * >	sum_sq_angular,
		gsl::not_null< DataVector * >	counts_angular,
		const double *	spec_buf,
		size_t	n_r,
		size_t	n_r_max,
		int	spin_weight,
		const std::vector< std::vector< size_t > > &	offsets_by_l,
		double *	gathered,
		double *	modal_buf )

Accumulate squared ZernikeB3 Jacobi spectral coefficients for one TensorYlm component into radial and angular power bins.

spec_buf has layout spec_buf[s * n_r + i_r] where s is the SPHEREPACK offset and i_r is the radial collocation index. Modes are binned radially via radial_mode = (n_total + 1) / 2 where n_total = l + 2 * k_spec, and angularly by degree \(\ell\). Modes with l < |spin_weight| are skipped.

offsets_by_l must be pre-computed for the correct zero_m_is_real value of this component. gathered and modal_buf are caller-owned scratch buffers of size max_n_modes_l * n_r each, where max_n_modes_l = 2 * (l_max + 1).

◆ accumulate_b3_tensor_sums()

template<typename TensorType>

void PowerMonitors::accumulate_b3_tensor_sums	(	gsl::not_null< DataVector * >	sum_sq_radial,
		gsl::not_null< DataVector * >	counts_radial,
		gsl::not_null< DataVector * >	sum_sq_angular,
		gsl::not_null< DataVector * >	counts_angular,
		const TensorType &	tensor,
		size_t	n_r,
		size_t	n_r_max,
		const std::vector< std::vector< size_t > > &	offsets_by_l_real,
		const std::vector< std::vector< size_t > > &	offsets_by_l_complex,
		double *	gathered,
		double *	modal_buf )

Accumulate squared ZernikeB3 spectral coefficients for all components of a TensorYlm tensor into radial and angular power bins.

Selects offsets_by_l_real for rank-0 (scalar) tensors and offsets_by_l_complex for all higher-rank tensors. The spin weight for each component is determined from the tensor structure.

◆ accumulate_spherical_shell_tensor_angular_power()

template<typename TensorType>

void PowerMonitors::accumulate_spherical_shell_tensor_angular_power	(	const gsl::not_null< DataVector * >	weighted_squared_power,
		const gsl::not_null< std::vector< size_t > * >	counts,
		const TensorType &	tensor,
		const Mesh< 3 > &	mesh )

Accumulate weighted-squared angular TensorYlm power and mode counts for all components of a tensor on a spherical shell.

Adds to weighted_squared_power and counts in place, so this can be called repeatedly to combine several tensors into the same angular power monitor before calling normalize_spherical_shell_angular_power.

◆ normalize_b3_power()

void PowerMonitors::normalize_b3_power	(	gsl::not_null< DataVector * >	result,
		const DataVector &	sum_sq,
		const DataVector &	counts )

Normalize a B3 power monitor accumulator in place.

Sets result[i] = sqrt(sum_sq[i] / counts[i]), or 0 when counts[i] == 0.

◆ normalize_spherical_shell_angular_power()

void PowerMonitors::normalize_spherical_shell_angular_power	(	gsl::not_null< DataVector * >	power,
		const std::vector< size_t > &	counts )

Normalize an angular power monitor accumulator in place.

Sets power[ell] = sqrt(power[ell] / counts[ell]), or 0 when counts[ell] == 0.

◆ relative_truncation_error()

template<typename VectorType, size_t Dim>

std::array< double, Dim > PowerMonitors::relative_truncation_error	(	const VectorType &	tensor_component,
		const Mesh< Dim > &	mesh )

The relative truncation error in each logical direction of the grid.

This overload is intended for visualization purposes only. It takes a tensor component as input, so it can be used as a kernel to post-process volume data with Python bindings (see TransformVolumeData.py).

◆ spherical_shell_angular_power_monitor() [1/2]

DataVector PowerMonitors::spherical_shell_angular_power_monitor	(	const DataVector &	tensor_ylm_component,
		const Mesh< 3 > &	mesh,
		int	spin_weight,
		bool	zero_m_is_real )

Return the angular power monitor for one TensorYlm component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi), with l_max == m_max. TensorYlm coefficients use the radial dimension as the fastest-moving extent. As reviewed in Sec. II of [31], spin-weighted spherical harmonics with l < |spin_weight| vanish, so these modes are omitted from both the sum and its normalization. Set zero_m_is_real for real scalar coefficients, which have no imaginary m=0 coefficients in Spherepack storage.

◆ spherical_shell_angular_power_monitor() [2/2]

void PowerMonitors::spherical_shell_angular_power_monitor	(	gsl::not_null< DataVector * >	result,
		const DataVector &	tensor_ylm_component,
		const Mesh< 3 > &	mesh,
		int	spin_weight,
		bool	zero_m_is_real )

Return the angular power monitor for one TensorYlm component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi), with l_max == m_max. TensorYlm coefficients use the radial dimension as the fastest-moving extent. As reviewed in Sec. II of [31], spin-weighted spherical harmonics with l < |spin_weight| vanish, so these modes are omitted from both the sum and its normalization. Set zero_m_is_real for real scalar coefficients, which have no imaginary m=0 coefficients in Spherepack storage.

◆ spherical_shell_number_of_angular_coefficients()

size_t PowerMonitors::spherical_shell_number_of_angular_coefficients	(	size_t	ell,
		int	spin_weight,
		bool	zero_m_is_real,
		size_t	radial_extents )

Number of independent TensorYlm coefficients contributing to angular degree ell, summed over radial_extents radial points.

Returns 0 when ell < |spin_weight|, since spin-weighted spherical harmonics vanish there (such terms are then excluded from accumulate_spherical_shell_tensor_angular_power()'s sum and normalization). See SpherepackIterator for the meaning of zero_m_is_real.

◆ spherical_shell_radial_power_monitor() [1/2]

DataVector PowerMonitors::spherical_shell_radial_power_monitor	(	const DataVector &	tensor_component,
		const Mesh< 3 > &	mesh )

Return the radial power monitor for a tensor component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi). The radial grid points are contiguous, so each angular point supplies one radial slice to the one-dimensional modal transform.

◆ spherical_shell_radial_power_monitor() [2/2]

void PowerMonitors::spherical_shell_radial_power_monitor	(	gsl::not_null< DataVector * >	result,
		const DataVector &	tensor_component,
		const Mesh< 3 > &	mesh )

Return the radial power monitor for a tensor component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi). The radial grid points are contiguous, so each angular point supplies one radial slice to the one-dimensional modal transform.

◆ spherical_shell_tensor_radial_power_monitor()

template<typename TensorType>

DataVector PowerMonitors::spherical_shell_tensor_radial_power_monitor	(	const TensorType &	tensor,
		const Mesh< 3 > &	mesh )

Return the RMS radial power monitor across all components of a tensor on a spherical shell.

Combines spherical_shell_radial_power_monitor for each of tensor.size() components in quadrature, normalized by the number of components.

Classes

Functions

Detailed Description

Function Documentation

◆ accumulate_b3_tensor_component_sums()

◆ accumulate_b3_tensor_sums()

◆ accumulate_spherical_shell_tensor_angular_power()

◆ normalize_b3_power()

◆ normalize_spherical_shell_angular_power()

◆ relative_truncation_error()

◆ spherical_shell_angular_power_monitor() [1/2]

◆ spherical_shell_angular_power_monitor() [2/2]

◆ spherical_shell_number_of_angular_coefficients()

◆ spherical_shell_radial_power_monitor() [1/2]

◆ spherical_shell_radial_power_monitor() [2/2]

◆ spherical_shell_tensor_radial_power_monitor()