Fast Gauss transfrom with complex parameter

Data Structures
struct	fgt_plan
	Structure for the Gauss transform. More...

Macros
#define	DGT_PRE_CEXP   (1U<< 0)
	If this flag is set, the whole matrix is precomputed and stored for the discrete Gauss transfrom.
#define	FGT_NDFT   (1U<< 1)
	If this flag is set, the fast Gauss transform uses the discrete instead of the fast Fourier transform.
#define	FGT_APPROX_B   (1U<< 2)
	If this flag is set, the discrete Fourier coefficients of the uniformly sampled Gaussian are used instead of the sampled continuous Fourier transform.

Functions
void	dgt_trafo (fgt_plan *ths)
	Executes the discrete Gauss transform.
void	fgt_trafo (fgt_plan *ths)
	Executes the fast Gauss transform.
void	fgt_init_guru (fgt_plan *ths, int N, int M, double _Complex sigma, int n, double p, int m, unsigned flags)
	Initialisation of a transform plan, guru.
void	fgt_init (fgt_plan *ths, int N, int M, double _Complex sigma, double eps)
	Initialisation of a transform plan, simple.
void	fgt_init_node_dependent (fgt_plan *ths)
	Initialisation of a transform plan, depends on source and target nodes.
void	fgt_finalize (fgt_plan *ths)
	Destroys the transform plan.
void	fgt_test_init_rand (fgt_plan *ths)
	Random initialisation of a fgt plan.
double	fgt_test_measure_time (fgt_plan *ths, unsigned dgt)
	Compares execution times for the fast and discrete Gauss transform.
void	fgt_test_simple (int N, int M, double _Complex sigma, double eps)
	Simple example that computes fast and discrete Gauss transforms.
void	fgt_test_andersson (void)
	Compares accuracy and execution time of the fast Gauss transform with increasing expansion degree.
void	fgt_test_error (void)
	Compares accuracy of the fast Gauss transform with increasing expansion degree.
void	fgt_test_error_p (void)
	Compares accuracy of the fast Gauss transform with increasing expansion degree and different periodisation lengths.
int	main (int argc, char **argv)
	Different tests of the fast Gauss transform.

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Detailed Description

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Macro Definition Documentation

#define DGT_PRE_CEXP   (1U<< 0)

If this flag is set, the whole matrix is precomputed and stored for the discrete Gauss transfrom.

See also:

fgt_init_node_dependent

fgt_init

Author:

Stefan Kunis

Definition at line 48 of file fastgauss.c.

Referenced by dgt_trafo(), fgt_init(), fgt_init_node_dependent(), and fgt_test_andersson().

#define FGT_NDFT   (1U<< 1)

If this flag is set, the fast Gauss transform uses the discrete instead of the fast Fourier transform.

See also:

fgt_init

nfft_trafo_direct

nfft_trafo

Author:

Stefan Kunis

Definition at line 59 of file fastgauss.c.

Referenced by fgt_test_andersson(), and fgt_trafo().

#define FGT_APPROX_B   (1U<< 2)

If this flag is set, the discrete Fourier coefficients of the uniformly sampled Gaussian are used instead of the sampled continuous Fourier transform.

See also:

fgt_init

Author:

Stefan Kunis

Definition at line 69 of file fastgauss.c.

Referenced by fgt_init_guru().

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Function Documentation

void dgt_trafo

(

fgt_plan *

ths

)

Executes the discrete Gauss transform.

• ths The pointer to a fgt plan

Author:

Stefan Kunis

Definition at line 107 of file fastgauss.c.

References fgt_plan::alpha, DGT_PRE_CEXP, fgt_plan::f, fgt_plan::flags, fgt_plan::M, fgt_plan::N, fgt_plan::pre_cexp, fgt_plan::sigma, fgt_plan::x, and fgt_plan::y.

Referenced by fgt_test_error(), fgt_test_error_p(), fgt_test_measure_time(), and fgt_test_simple().

void fgt_trafo

(

fgt_plan *

ths

)

Executes the fast Gauss transform.

• ths The pointer to a fgt plan

Author:

Stefan Kunis

Definition at line 132 of file fastgauss.c.

References fgt_plan::b, nfft_plan::f_hat, FGT_NDFT, fgt_plan::flags, fgt_plan::n, nfft_trafo(), fgt_plan::nplan1, and fgt_plan::nplan2.

Referenced by fgt_test_error(), fgt_test_error_p(), fgt_test_measure_time(), and fgt_test_simple().

void fgt_init_guru	(	fgt_plan *	ths,
		int	N,
		int	M,
		double _Complex	sigma,
		int	n,
		double	p,
		int	m,
		unsigned	flags
	)

Initialisation of a transform plan, guru.

• ths The pointer to a fpt plan
• N The number of source nodes
• M The number of target nodes
• sigma The parameter of the Gaussian
• n The polynomial expansion degree
• p the periodisation length, at least 1
• m The spatial cut-off of the nfft
• flags FGT flags to use

Author:

Stefan Kunis

Definition at line 170 of file fastgauss.c.

References fgt_plan::alpha, fgt_plan::b, fgt_plan::f, nfft_plan::f, nfft_plan::f_hat, FGT_APPROX_B, fgt_plan::flags, fgt_plan::M, fgt_plan::N, fgt_plan::n, nfft_fftshift_complex(), nfft_malloc(), fgt_plan::nplan1, fgt_plan::nplan2, fgt_plan::p, PI, fgt_plan::sigma, fgt_plan::x, and fgt_plan::y.

Referenced by fgt_init(), fgt_test_andersson(), fgt_test_error(), and fgt_test_error_p().

void fgt_init	(	fgt_plan *	ths,
		int	N,
		int	M,
		double _Complex	sigma,
		double	eps
	)

Initialisation of a transform plan, simple.

• ths The pointer to a fpt plan
• N The number of source nodes
• M The number of target nodes
• sigma The parameter of the Gaussian
• eps The target accuracy

Author:

Stefan Kunis

Definition at line 240 of file fastgauss.c.

References DGT_PRE_CEXP, fgt_init_guru(), and PI.

Referenced by fgt_test_simple().

void fgt_init_node_dependent

(

fgt_plan *

ths

)

Initialisation of a transform plan, depends on source and target nodes.

• ths The pointer to a fpt plan

  Author:

  Stefan Kunis

Definition at line 263 of file fastgauss.c.

References DGT_PRE_CEXP, fgt_plan::flags, fgt_plan::M, nfft_plan::M_total, fgt_plan::N, nfft_plan::nfft_flags, nfft_malloc(), fgt_plan::nplan1, fgt_plan::nplan2, fgt_plan::p, fgt_plan::pre_cexp, fgt_plan::sigma, fgt_plan::x, nfft_plan::x, and fgt_plan::y.

Referenced by fgt_test_andersson(), fgt_test_error(), fgt_test_error_p(), and fgt_test_simple().

void fgt_finalize

(

fgt_plan *

ths

)

Destroys the transform plan.

• ths The pointer to the fgt plan

  Author:

  Stefan Kunis

Definition at line 295 of file fastgauss.c.

References fgt_plan::alpha, fgt_plan::b, fgt_plan::f, nfft_free(), fgt_plan::nplan1, fgt_plan::nplan2, fgt_plan::x, and fgt_plan::y.

Referenced by fgt_test_andersson(), fgt_test_error(), fgt_test_error_p(), and fgt_test_simple().

void fgt_test_init_rand

(

fgt_plan *

ths

)

Random initialisation of a fgt plan.

• ths The pointer to the fgt plan

  Author:

  Stefan Kunis

Definition at line 318 of file fastgauss.c.

References fgt_plan::alpha, fgt_plan::M, fgt_plan::N, fgt_plan::x, and fgt_plan::y.

Referenced by fgt_test_andersson(), fgt_test_error(), fgt_test_error_p(), and fgt_test_simple().

double fgt_test_measure_time	(	fgt_plan *	ths,
		unsigned	dgt
	)

Compares execution times for the fast and discrete Gauss transform.

• ths The pointer to the fgt plan
• dgt If this parameter is set dgt_trafo is called as well

Author:

Stefan Kunis

Definition at line 341 of file fastgauss.c.

References dgt_trafo(), and fgt_trafo().

Referenced by fgt_test_andersson().

void fgt_test_simple	(	int	N,
		int	M,
		double _Complex	sigma,
		double	eps
	)

Simple example that computes fast and discrete Gauss transforms.

• ths The pointer to the fgt plan
• sigma The parameter of the Gaussian
• eps The target accuracy

Author:

Stefan Kunis

Definition at line 375 of file fastgauss.c.

References fgt_plan::alpha, dgt_trafo(), fgt_plan::f, fgt_finalize(), fgt_init(), fgt_init_node_dependent(), fgt_test_init_rand(), fgt_trafo(), fgt_plan::M, fgt_plan::N, nfft_free(), nfft_malloc(), NFFT_SWAP_complex, and nfft_vpr_complex().

Referenced by main().

void fgt_test_andersson

(

void

)

Compares accuracy and execution time of the fast Gauss transform with increasing expansion degree.

Similar to the test in F. Andersson and G. Beylkin. The fast Gauss transform with double _Complex parameters. J. Comput. Physics 203 (2005) 274-286

Author:

Stefan Kunis

Definition at line 410 of file fastgauss.c.

References fgt_plan::alpha, DGT_PRE_CEXP, fgt_plan::f, fgt_finalize(), fgt_init_guru(), fgt_init_node_dependent(), FGT_NDFT, fgt_test_init_rand(), fgt_test_measure_time(), fgt_plan::flags, fgt_plan::M, fgt_plan::N, nfft_free(), nfft_malloc(), and NFFT_SWAP_complex.

Referenced by main().

void fgt_test_error

(

void

)

Compares accuracy of the fast Gauss transform with increasing expansion degree.

Author:

Stefan Kunis

Definition at line 481 of file fastgauss.c.

References fgt_plan::alpha, dgt_trafo(), fgt_plan::f, fgt_finalize(), fgt_init_guru(), fgt_init_node_dependent(), fgt_test_init_rand(), fgt_trafo(), fgt_plan::M, fgt_plan::N, nfft_free(), nfft_malloc(), and NFFT_SWAP_complex.

Referenced by main().

void fgt_test_error_p

(

void

)

Compares accuracy of the fast Gauss transform with increasing expansion degree and different periodisation lengths.

Author:

Stefan Kunis

Definition at line 532 of file fastgauss.c.

References fgt_plan::alpha, dgt_trafo(), fgt_plan::f, fgt_finalize(), fgt_init_guru(), fgt_init_node_dependent(), fgt_test_init_rand(), fgt_trafo(), fgt_plan::M, fgt_plan::N, nfft_malloc(), and NFFT_SWAP_complex.

Referenced by main().

int main	(	int	argc,
		char **	argv
	)

Different tests of the fast Gauss transform.

Author:

Stefan Kunis

Definition at line 580 of file fastgauss.c.

References fgt_test_andersson(), fgt_test_error(), fgt_test_error_p(), and fgt_test_simple().