Discretely sampled field on a mesh grid from particle catalogues. More...

#include <field.hpp>

Collaboration diagram for trv::MeshField:

Public Member Functions
	MeshField (trv::ParameterSet &params, bool plan_ini=true, const std::string &name="mesh-field")
	Construct the mesh field.

	MeshField (trv::ParameterSet &params, fftw_plan &transform, fftw_plan &inv_transform, const std::string &name="mesh-field")
	Construct the mesh field with external FFTW plans.

	~MeshField ()
	Destruct the mesh field.

void	reset_density_field ()
	(Re-)initialise the complex field (and its shadow) on mesh.

const fftw_complex &	operator[] (long long gid)
	Return mesh field grid cell value.

void	assign_weighted_field_to_mesh (ParticleCatalogue &particles, fftw_complex *weights)
	Assign a weighted field to a mesh by interpolation scheme.

void	compute_unweighted_field (ParticleCatalogue &particles)
	Compute the unweighted field.

void	compute_unweighted_field_fluctuations_insitu (ParticleCatalogue &particles)
	Compute the unweighted field fluctuations.

void	compute_ylm_wgtd_field (ParticleCatalogue &particles_data, ParticleCatalogue &particles_rand, LineOfSight los_data, LineOfSight los_rand, double alpha, int ell, int m)
	Compute the weighted field (fluctuations) further weighted by the reduced spherical harmonics.

void	compute_ylm_wgtd_field (ParticleCatalogue &particles, LineOfSight *los, double alpha, int ell, int m)
	Compute the weighted field further weighted by the reduced spherical harmonics.

void	compute_ylm_wgtd_quad_field (ParticleCatalogue &particles_data, ParticleCatalogue &particles_rand, LineOfSight los_data, LineOfSight los_rand, double alpha, int ell, int m)
	Compute the quadratic weighted field (fluctuations) further weighted by the reduced spherical harmonics.

void	compute_ylm_wgtd_quad_field (ParticleCatalogue &particles, LineOfSight *los, double alpha, int ell, int m)
	Compute the quadratic weighted field (fluctuations) further weighted by the reduced spherical harmonics.

void	fourier_transform ()
	Fourier transform the field.

void	inv_fourier_transform ()
	Inverse Fourier transform the (FFT-transformed) field.

void	apply_wide_angle_pow_law_kernel ()
	Apply wide-angle correction kernel in configuration space.

void	apply_assignment_compensation ()
	Apply compensation needed after Fourier transform for assignment schemes.

void	inv_fourier_transform_ylm_wgtd_field_band_limited (MeshField &field_fourier, std::vector< std::complex< double > > &ylm, double k_band, double dk_band, double &k_eff, int &nmodes)
	Inverse Fourier transform a field \( f \) weighted by the reduced spherical harmonics restricted to a wavenumber band.

void	inv_fourier_transform_sjl_ylm_wgtd_field (MeshField &field_fourier, std::vector< std::complex< double > > &ylm, trvm::SphericalBesselCalculator &sjl, double r)
	Inverse Fourier transform a field \( f \) weighted by the spherical Bessel function and reduced spherical harmonics.

double	calc_grid_based_powlaw_norm (ParticleCatalogue &particles, int order)

Public Attributes
trv::ParameterSet	params
	parameter set

std::string	name
	field name

fftw_complex *	field
	complex field on mesh

double	dr [3]
	grid size in each dimension

double	dk [3]
	fundamental wavenumber in each dimension

double	vol
	mesh volume

double	vol_cell
	mesh grid cell volume

Friends
class	FieldStats

Detailed Description

Discretely sampled field on a mesh grid from particle catalogues.

Definition at line 68 of file field.hpp.

Constructor & Destructor Documentation

◆ MeshField() [1/2]

trv::MeshField::MeshField	(	trv::ParameterSet &	params,
		bool	plan_ini = true,
		const std::string &	name = "mesh-field" )

explicit

Construct the mesh field.

Parameters

params	Parameter set.
plan_ini	Flag for FFTW plan initialisation (default is `true`).
name	Field name (default is "mesh-field").

Definition at line 42 of file field.cpp.

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◆ MeshField() [2/2]

trv::MeshField::MeshField	(	trv::ParameterSet &	params,
		fftw_plan &	transform,
		fftw_plan &	inv_transform,
		const std::string &	name = "mesh-field" )

explicit

Construct the mesh field with external FFTW plans.

Parameters

params	Parameter set.
transform	External FFTW plan for Fourier transform.
inv_transform	External FFTW plan for inverse Fourier transform.
name	Field name (default is "mesh-field").

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 273 of file field.cpp.

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◆ ~MeshField()

trv::MeshField::~MeshField ( )

Destruct the mesh field.

Definition at line 329 of file field.cpp.

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Member Function Documentation

◆ reset_density_field()

void trv::MeshField::reset_density_field ( )

(Re-)initialise the complex field (and its shadow) on mesh.

This is an explicit method to reset values of trv::MeshField::field (and its interlaced counterpart) to zeros.

Definition at line 358 of file field.cpp.

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◆ operator[]()

const fftw_complex & trv::MeshField::operator[] ( long long gid )

Return mesh field grid cell value.

Parameters

gid	Grid index.

Returns: Field value.

Definition at line 382 of file field.cpp.

◆ assign_weighted_field_to_mesh()

void trv::MeshField::assign_weighted_field_to_mesh	(	ParticleCatalogue &	particles,
		fftw_complex *	weights )

Assign a weighted field to a mesh by interpolation scheme.

Parameters

particles	Particle catalogue.
weights	Weight field.

Definition at line 427 of file field.cpp.

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◆ compute_unweighted_field()

void trv::MeshField::compute_unweighted_field ( ParticleCatalogue & particles )

Compute the unweighted field.

This is is the number density field

\[ n(\vec{x}) = \sum_i \delta^{(\mathrm{D})}(\vec{x} - \vec{x}_i) \,. \]

Parameters

particles Particle catalogue.

Definition at line 1066 of file field.cpp.

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◆ compute_unweighted_field_fluctuations_insitu()

void trv::MeshField::compute_unweighted_field_fluctuations_insitu ( ParticleCatalogue & particles )

Compute the unweighted field fluctuations.

This is typically used for the number density fluctuations in a simulation snapshot in a periodic box, with a global field value calculated from the particle number and box volume subtracted to compute the fluctuations, i.e.

\[ \delta{n}(\vec{x}) = \sum_i \delta^{(\mathrm{D})}(\vec{x} - \vec{x}_i) - N / V \,, \]

where \( N \) is the total number of particles and \( V \) the box volume.

Parameters

particles Particle catalogue.

Definition at line 1089 of file field.cpp.

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◆ compute_ylm_wgtd_field() [1/2]

void trv::MeshField::compute_ylm_wgtd_field	(	ParticleCatalogue &	particles_data,
		ParticleCatalogue &	particles_rand,
		LineOfSight *	los_data,
		LineOfSight *	los_rand,
		double	alpha,
		int	ell,
		int	m )

Compute the weighted field (fluctuations) further weighted by the reduced spherical harmonics.

For a field (or its fluctuations) \( f \), this is

\[ f_{LM}(\vec{x}) = {\sum_i}{\vphantom{\sum}}' y_{LM}^*(\hat{\vec{x}}) w(\vec{x}) \delta^{(\mathrm{D})}(\vec{x} - \vec{x}_i) \,, \]

where if a pair of catalogues are provided,

\[ {\sum_i}{\vphantom{\sum}}' = \sum_{i \in \mathrm{data}} - \alpha \sum_{i \in \mathrm{rand}} \]

with \( f \equiv \delta{n} \), and otherwise

\[ {\sum_i}{\vphantom{\sum}}' = \sum_{i \in \mathrm{data\ or\ rand}} \]

with \( f \equiv n \).

See also: Eq. (34) in Sugiyama et al. (2019) [1803.02132].

Parameters

particles_data	(Data-source) particle catalogue.
particles_rand	(Random-source) particle catalogue.
los_data	(Data-source) particle lines of sight.
los_rand	(Random-source) particle lines of sight.
alpha	Alpha contrast.
ell	Degree of the spherical harmonic.
m	Order of the spherical harmonic.

Definition at line 1106 of file field.cpp.

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◆ compute_ylm_wgtd_field() [2/2]

void trv::MeshField::compute_ylm_wgtd_field	(	ParticleCatalogue &	particles,
		LineOfSight *	los,
		double	alpha,
		int	ell,
		int	m )

Compute the weighted field further weighted by the reduced spherical harmonics.

Parameters

particles	Particle catalogue.
los	Particle lines of sight.
alpha	Alpha contrast.
ell	Degree of the spherical harmonic.
m	Order of the spherical harmonic.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 1188 of file field.cpp.

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◆ compute_ylm_wgtd_quad_field() [1/2]

void trv::MeshField::compute_ylm_wgtd_quad_field	(	ParticleCatalogue &	particles_data,
		ParticleCatalogue &	particles_rand,
		LineOfSight *	los_data,
		LineOfSight *	los_rand,
		double	alpha,
		int	ell,
		int	m )

Compute the quadratic weighted field (fluctuations) further weighted by the reduced spherical harmonics.

For a quadratic field (of fluctuations) \( f \), this is

\[ f_{LM}(\vec{x}) = {\sum_i}{\vphantom{\sum}}' y_{LM}^*(\hat{\vec{x}}) w(\vec{x})^2 \delta^{(\mathrm{D})}(\vec{x} - \vec{x}_i) \,, \]

where if a pair of catalogues are provided,

\[ {\sum_i}{\vphantom{\sum}}' = \sum_{i \in \mathrm{data}} + \alpha^2 \sum_{i \in \mathrm{rand}} \,, \]

and otherwise

\[ {\sum_i}{\vphantom{\sum}}' = \sum_{i \in \mathrm{data\ or\ rand}} \,. \]

See also: Eq. (46) in Sugiyama et al. (2019) [1803.02132].

Parameters

particles_data	(Data-source) particle catalogue.
particles_rand	(Random-source) particle catalogue.
los_data	(Data-source) particle lines of sight.
los_rand	(Random-source) particle lines of sight.
alpha	Alpha contrast.
ell	Degree of the spherical harmonic.
m	Order of the spherical harmonic.

Definition at line 1229 of file field.cpp.

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◆ compute_ylm_wgtd_quad_field() [2/2]

void trv::MeshField::compute_ylm_wgtd_quad_field	(	ParticleCatalogue &	particles,
		LineOfSight *	los,
		double	alpha,
		int	ell,
		int	m )

Compute the quadratic weighted field (fluctuations) further weighted by the reduced spherical harmonics.

Parameters

particles	Particle catalogue.
los	Particle lines of sight.
alpha	Alpha contrast.
ell	Degree of the spherical harmonic.
m	Order of the spherical harmonic.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 1316 of file field.cpp.

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◆ fourier_transform()

void trv::MeshField::fourier_transform ( )

Fourier transform the field.

If trv::MeshField.params.interlace is set to "true", interlacing is performed where a phase factor is multiplied into the 'shadow' complex field before the average of the complex field and its shadow is taken.

Definition at line 1365 of file field.cpp.

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◆ inv_fourier_transform()

void trv::MeshField::inv_fourier_transform ( )

Inverse Fourier transform the (FFT-transformed) field.

Definition at line 1448 of file field.cpp.

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◆ apply_wide_angle_pow_law_kernel()

void trv::MeshField::apply_wide_angle_pow_law_kernel ( )

Apply wide-angle correction kernel in configuration space.

This multiplies the field by a power law \( r^{- i - j} \) at order \( (i, j) \) where \( r \) is the grid cell radial distance.

Definition at line 1479 of file field.cpp.

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◆ apply_assignment_compensation()

void trv::MeshField::apply_assignment_compensation ( )

Apply compensation needed after Fourier transform for assignment schemes.

Definition at line 1516 of file field.cpp.

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◆ inv_fourier_transform_ylm_wgtd_field_band_limited()

void trv::MeshField::inv_fourier_transform_ylm_wgtd_field_band_limited	(	MeshField &	field_fourier,
		std::vector< std::complex< double > > &	ylm,
		double	k_band,
		double	dk_band,
		double &	k_eff,
		int &	nmodes )

Inverse Fourier transform a field \( f \) weighted by the reduced spherical harmonics restricted to a wavenumber band.

This method computes the quantity

\[ F_{LM}(\vec{x}; k) = \frac{(2\pi)^3}{4\pi k^2} \int \frac{\mathrm{d}^3\,\vec{k}'}{(2\pi)^3} \mathrm{e}^{\mathrm{i} \vec{k}' \cdot \vec{x}} \delta^{(\mathrm{D})}(k' - k) y_{LM}(\hat{\vec{k}}) f(\vec{k}) \,. \]

See also: Eq. (42) in Sugiyama et al. (2019) [1803.02132].

Parameters

[in]	field_fourier	A Fourier-space field.
[in]	ylm	Reduced spherical harmonic on a mesh.
[in]	k_band	Band wavenumber.
[in]	dk_band	Band wavenumber width.
[out]	k_eff	Effective band wavenumber.
[out]	nmodes	Number of wavevector modes in band.

Definition at line 1544 of file field.cpp.

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◆ inv_fourier_transform_sjl_ylm_wgtd_field()

void trv::MeshField::inv_fourier_transform_sjl_ylm_wgtd_field	(	MeshField &	field_fourier,
		std::vector< std::complex< double > > &	ylm,
		trvm::SphericalBesselCalculator &	sjl,
		double	r )

Inverse Fourier transform a field \( f \) weighted by the spherical Bessel function and reduced spherical harmonics.

This method computes the quantity

\[ F_{LM}(\vec{x}; r) = \mathrm{i}^L \int \frac{\mathrm{d}^3\,\vec{k}}{(2\pi)^3} \mathrm{e}^{\mathrm{i} \vec{k} \cdot \vec{x}} j_L(kr) y_{LM}(\hat{\vec{k}}) f(\vec{k}) \,. \]

See also: Eq. (49) in Sugiyama et al. (2019) [1803.02132].

Parameters

field_fourier	A Fourier-space field.
ylm	Reduced spherical harmonic on a mesh.
sjl	Spherical Bessel function interpolator.
r	Separation in configuration space.

Definition at line 1627 of file field.cpp.

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◆ calc_grid_based_powlaw_norm()

double trv::MeshField::calc_grid_based_powlaw_norm	(	ParticleCatalogue &	particles,
		int	order )

Calculate the normalisation factor \( 1/I_N \) for N-point (for two-point statistics), where

\[ I_N = \int\mathrm{d}^3\,\vec{x} w(\vec{x})^N \bar{n}(\vec{x})^N \,. \]

Parameters

particles	(Typically random-source) particle catalogue.
order	Order \( N \) of the N-point statistics.

Returns: norm_factor Normalisation factor.

Definition at line 1702 of file field.cpp.

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Friends And Related Symbol Documentation

◆ FieldStats

friend class FieldStats

friend

Definition at line 430 of file field.hpp.

Member Data Documentation

◆ params

trv::ParameterSet trv::MeshField::params

parameter set

Definition at line 70 of file field.hpp.

◆ name

std::string trv::MeshField::name

field name

Definition at line 71 of file field.hpp.

◆ field

fftw_complex* trv::MeshField::field

complex field on mesh

Definition at line 72 of file field.hpp.

◆ dr

double trv::MeshField::dr[3]

grid size in each dimension

Definition at line 73 of file field.hpp.

◆ dk

double trv::MeshField::dk[3]

fundamental wavenumber in each dimension

Definition at line 74 of file field.hpp.

◆ vol

double trv::MeshField::vol

mesh volume

Definition at line 75 of file field.hpp.

◆ vol_cell

double trv::MeshField::vol_cell

mesh grid cell volume

Definition at line 76 of file field.hpp.

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

/home/docs/checkouts/readthedocs.org/user_builds/triumvirate/checkouts/stable/src/triumvirate/include/field.hpp
/home/docs/checkouts/readthedocs.org/user_builds/triumvirate/checkouts/stable/src/triumvirate/src/field.cpp

Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ MeshField() [1/2]

◆ MeshField() [2/2]

◆ ~MeshField()

Member Function Documentation

◆ reset_density_field()

◆ operator[]()

◆ assign_weighted_field_to_mesh()

◆ compute_unweighted_field()

◆ compute_unweighted_field_fluctuations_insitu()

◆ compute_ylm_wgtd_field() [1/2]

◆ compute_ylm_wgtd_field() [2/2]

◆ compute_ylm_wgtd_quad_field() [1/2]

◆ compute_ylm_wgtd_quad_field() [2/2]

◆ fourier_transform()

◆ inv_fourier_transform()

◆ apply_wide_angle_pow_law_kernel()

◆ apply_assignment_compensation()

◆ inv_fourier_transform_ylm_wgtd_field_band_limited()

◆ inv_fourier_transform_sjl_ylm_wgtd_field()

◆ calc_grid_based_powlaw_norm()

Friends And Related Symbol Documentation

◆ FieldStats

Member Data Documentation

◆ params

◆ name

◆ field

◆ dr

◆ dk

◆ vol

◆ vol_cell