Direct and fast summation (convolution). More...

Collaboration diagram for Fast summation:

Topics
	fastsum_matlab
	fastsum_test

Data Structures
struct	fastsum_plan_
	plan for fast summation algorithm More...

Macros
#define	X(name)
	Include header for C99 complex datatype.
#define	NF_KUB
#define	EXACT_NEARFIELD (1U<< 0)
	Constant symbols.
#define	NEARFIELD_BOXES (1U<< 1)
#define	STORE_PERMUTATION_X_ALPHA (1U<< 2)
	If this flag is set, and eps_I > 0.0 and NEARFIELD_BOXES is not set, then the vector permutation_x_alpha is stored.

Typedefs
typedef C(*	kernel) (R, int, const R *)
typedef struct fastsum_plan_	fastsum_plan
	plan for fast summation algorithm

Functions
static int	max_i (int a, int b)
	max
static R	fak (int n)
	factorial
static R	binom (int n, int m)
	binomial coefficient
static R	BasisPoly (int m, int r, R xx)
	basis polynomial for regularized kernel
C	regkern (kernel k, R xx, int p, const R *param, R a, R b)
	regularized kernel with K_I arbitrary and K_B smooth to zero
static C	regkern1 (kernel k, R xx, int p, const R *param, R a, R b)
	regularized kernel with K_I arbitrary and K_B periodized (used in 1D)
static C	regkern3 (kernel k, R xx, int p, const R *param, R a, R b)
	regularized kernel for even kernels with K_I even and K_B mirrored
C	kubintkern (const R x, const C *Add, const int Ad, const R a)
	linear spline interpolation in near field with even kernels
static C	kubintkern1 (const R x, const C *Add, const int Ad, const R a)
	cubic spline interpolation in near field with arbitrary kernels
static void	quicksort (int d, int t, R x, C alpha, int *permutation_x_alpha, int N)
	quicksort algorithm for source knots and associated coefficients
static void	BuildBox (fastsum_plan *ths)
	initialize box-based search data structures
static C	calc_SearchBox (int d, R y, R x, C alpha, int start, int end_lt, const C Add, const int Ad, int p, R a, const kernel k, const R *param, const unsigned flags)
	inner computation function for box-based near field correction
static C	SearchBox (R y, fastsum_plan ths)
	box-based near field correction
static void	BuildTree (int d, int t, R x, C alpha, int *permutation_x_alpha, int N)
	recursive sort of source knots dimension by dimension to get tree structure
static C	SearchTree (const int d, const int t, const R x, const C alpha, const R xmin, const R xmax, const int N, const kernel k, const R param, const int Ad, const C Add, const int p, const unsigned flags)
	fast search in tree of source knots for near field computation
static void	fastsum_precompute_kernel (fastsum_plan *ths)
void	fastsum_init_guru_kernel (fastsum_plan ths, int d, kernel k, R param, unsigned flags, int nn, int p, R eps_I, R eps_B)
	initialize node independent part of fast summation plan
void	fastsum_init_guru_source_nodes (fastsum_plan *ths, int N_total, int nn_oversampled, int m)
	initialize source nodes dependent part of fast summation plan
void	fastsum_init_guru_target_nodes (fastsum_plan *ths, int M_total, int nn_oversampled, int m)
	initialize target nodes dependent part of fast summation plan
void	fastsum_init_guru (fastsum_plan ths, int d, int N_total, int M_total, kernel k, R param, unsigned flags, int nn, int m, int p, R eps_I, R eps_B)
	initialization of fastsum plan
void	fastsum_finalize_source_nodes (fastsum_plan *ths)
	finalization of fastsum plan
void	fastsum_finalize_target_nodes (fastsum_plan *ths)
	finalization of fastsum plan
void	fastsum_finalize_kernel (fastsum_plan *ths)
	finalization of fastsum plan
void	fastsum_finalize (fastsum_plan *ths)
	finalization of fastsum plan
void	fastsum_exact (fastsum_plan *ths)
	direct computation of sums
void	fastsum_precompute_source_nodes (fastsum_plan *ths)
	precomputation for fastsum
void	fastsum_precompute_target_nodes (fastsum_plan *ths)
	precomputation for fastsum
void	fastsum_precompute (fastsum_plan *ths)
	precomputation for fastsum
void	fastsum_trafo (fastsum_plan *ths)
	fast NFFT-based summation
	fastsum_plan_::NFFT (plan) mv1
	source nfft plan
	fastsum_plan_::FFTW (plan) fft_plan
C	gaussian (R x, int der, const R *param)
	K(x)=exp(-x^2/c^2).
C	multiquadric (R x, int der, const R *param)
	K(x)=sqrt(x^2+c^2).
C	inverse_multiquadric (R x, int der, const R *param)
	K(x)=1/sqrt(x^2+c^2).
C	logarithm (R x, int der, const R *param)
	K(x)=log \|x\|.
C	thinplate_spline (R x, int der, const R *param)
	K(x) = x^2 log \|x\|.
C	one_over_square (R x, int der, const R *param)
	K(x) = 1/x^2.
C	one_over_modulus (R x, int der, const R *param)
	K(x) = 1/\|x\|.
C	one_over_x (R x, int der, const R *param)
	K(x) = 1/x.
C	inverse_multiquadric3 (R x, int der, const R *param)
	K(x) = 1/sqrt(x^2+c^2)^3.
C	sinc_kernel (R x, int der, const R *param)
	K(x) = sin(cx)/x.
C	cosc (R x, int der, const R *param)
	K(x) = cos(cx)/x.
C	kcot (R x, int der, const R *param)
	K(x) = cot(cx).
C	one_over_cube (R x, int der, const R *param)
	K(x) = 1/x^3.
C	log_sin (R x, int der, const R *param)
	K(x) = log(\|sin(cx)\|).
C	laplacian_rbf (R x, int der, const R *param)
	K(x) = exp(-\|x\|/c).

Variables
int	fastsum_plan_::d
	api
int	fastsum_plan_::N_total
	number of source knots
int	fastsum_plan_::M_total
	number of target knots
C *	fastsum_plan_::alpha
	source coefficients
C *	fastsum_plan_::f
	target evaluations
R *	fastsum_plan_::x
	source knots in d-ball with radius 1/4-eps_b/2
R *	fastsum_plan_::y
	target knots in d-ball with radius 1/4-eps_b/2
kernel	fastsum_plan_::k
	kernel function
R *	fastsum_plan_::kernel_param
	parameters for kernel function
unsigned	fastsum_plan_::flags
	flags precomp.
C *	fastsum_plan_::pre_K
	internal
int	fastsum_plan_::n
	FS__ - fast summation.
C *	fastsum_plan_::b
	expansion coefficients
C *	fastsum_plan_::f_hat
	Fourier coefficients of nfft plans.
int	fastsum_plan_::p
	degree of smoothness of regularization
R	fastsum_plan_::eps_I
	inner boundary
R	fastsum_plan_::eps_B
	outer boundary
int	fastsum_plan_::Ad
	near field
C *	fastsum_plan_::Add
	spline values
int	fastsum_plan_::box_count
int	fastsum_plan_::box_count_per_dim
int *	fastsum_plan_::box_offset
R *	fastsum_plan_::box_x
C *	fastsum_plan_::box_alpha
int *	fastsum_plan_::permutation_x_alpha
	permutation vector of source nodes if STORE_PERMUTATION_X_ALPHA is set
R	fastsum_plan_::MEASURE_TIME_t [8]
	Measured time for each step if MEASURE_TIME is set.

Detailed Description

Direct and fast summation (convolution).

Computes the sums

$\‍[ f(y_j) = \sum_{k=1}^N \alpha_k K(x_k-y_j),\quad j=1\dots M. \‍]$

Macro Definition Documentation

◆ X

#define X ( name )

Value:

NFFT(name)

Include header for C99 complex datatype.

Include header for utils from NFFT3 library. Include header for NFFT3 library.

Definition at line 57 of file fastsum.h.

Referenced by fpt_init(), fpt_transposed(), main(), nfsft_precompute(), nfsoft_adjoint(), and nfsoft_trafo().

◆ NF_KUB

#define NF_KUB

Definition at line 60 of file fastsum.h.

◆ EXACT_NEARFIELD

#define EXACT_NEARFIELD (1U<< 0)

Constant symbols.

Definition at line 73 of file fastsum.h.

Referenced by calc_SearchBox(), fastsum_finalize_kernel(), fastsum_init_guru_kernel(), and SearchTree().

◆ NEARFIELD_BOXES

#define NEARFIELD_BOXES (1U<< 1)

Definition at line 75 of file fastsum.h.

◆ STORE_PERMUTATION_X_ALPHA

#define STORE_PERMUTATION_X_ALPHA (1U<< 2)

If this flag is set, and eps_I > 0.0 and NEARFIELD_BOXES is not set, then the vector permutation_x_alpha is stored.

Definition at line 79 of file fastsum.h.

Referenced by fastsum_init_guru_source_nodes().

Typedef Documentation

◆ kernel

typedef C(* kernel) (R, int, const R *)

Definition at line 68 of file fastsum.h.

Function Documentation

◆ max_i()

int max_i	(	int	a,
		int	b )

static

max

Definition at line 46 of file fastsum.c.

Referenced by fastsum_init_guru_kernel(), and SearchBox().

◆ fak()

R fak ( int n )

static

factorial

Definition at line 52 of file fastsum.c.

References fak().

Referenced by BasisPoly(), binom(), and fak().

◆ binom()

R binom	(	int	n,
		int	m )

static

binomial coefficient

Definition at line 61 of file fastsum.c.

References fak().

Referenced by BasisPoly().

◆ BasisPoly()

R BasisPoly	(	int	m,
		int	r,
		R	xx )

static

basis polynomial for regularized kernel

Definition at line 67 of file fastsum.c.

References binom(), and fak().

Referenced by regkern(), regkern1(), and regkern3().

◆ regkern()

C regkern	(	kernel	k,
		R	xx,
		int	p,
		const R *	param,
		R	a,
		R	b )

regularized kernel with K_I arbitrary and K_B smooth to zero

Definition at line 81 of file fastsum.c.

References BasisPoly().

Referenced by calc_SearchBox(), and SearchTree().

◆ regkern1()

C regkern1	(	kernel	k,
		R	xx,
		int	p,
		const R *	param,
		R	a,
		R	b )

static

regularized kernel with K_I arbitrary and K_B periodized (used in 1D)

Definition at line 134 of file fastsum.c.

References BasisPoly().

Referenced by calc_SearchBox(), and SearchTree().

◆ regkern3()

C regkern3	(	kernel	k,
		R	xx,
		int	p,
		const R *	param,
		R	a,
		R	b )

static

regularized kernel for even kernels with K_I even and K_B mirrored

regularized kernel for even kernels with K_I even and K_B mirrored smooth to K(1/2) (used in dD, d>1)

Definition at line 230 of file fastsum.c.

References BasisPoly().

◆ kubintkern()

C kubintkern	(	const R	x,
		const C *	Add,
		const int	Ad,
		const R	a )

linear spline interpolation in near field with even kernels

cubic spline interpolation in near field with even kernels

Definition at line 318 of file fastsum.c.

Referenced by calc_SearchBox(), and SearchTree().

◆ kubintkern1()

C kubintkern1	(	const R	x,
		const C *	Add,
		const int	Ad,
		const R	a )

static

cubic spline interpolation in near field with arbitrary kernels

Definition at line 352 of file fastsum.c.

Referenced by calc_SearchBox(), and SearchTree().

◆ quicksort()

void quicksort	(	int	d,
		int	t,
		R *	x,
		C *	alpha,
		int *	permutation_x_alpha,
		int	N )

static

quicksort algorithm for source knots and associated coefficients

Definition at line 381 of file fastsum.c.

References quicksort().

Referenced by BuildTree(), and quicksort().

◆ BuildBox()

void BuildBox ( fastsum_plan * ths )

static

initialize box-based search data structures

Definition at line 429 of file fastsum.c.

References fastsum_plan_::alpha, fastsum_plan_::d, fastsum_plan_::eps_B, fastsum_plan_::eps_I, fastsum_plan_::N_total, and fastsum_plan_::x.

Referenced by fastsum_precompute_source_nodes().

◆ calc_SearchBox()

C calc_SearchBox	(	int	d,
		R *	y,
		R *	x,
		C *	alpha,
		int	start,
		int	end_lt,
		const C *	Add,
		const int	Ad,
		int	p,
		R	a,
		const kernel	k,
		const R *	param,
		const unsigned	flags )

inlinestatic

inner computation function for box-based near field correction

Definition at line 480 of file fastsum.c.

References EXACT_NEARFIELD, kubintkern(), kubintkern1(), regkern(), and regkern1().

Referenced by SearchBox().

◆ SearchBox()

C SearchBox	(	R *	y,
		fastsum_plan *	ths )

static

box-based near field correction

Definition at line 533 of file fastsum.c.

References fastsum_plan_::Ad, fastsum_plan_::Add, calc_SearchBox(), fastsum_plan_::d, fastsum_plan_::eps_B, fastsum_plan_::eps_I, fastsum_plan_::flags, fastsum_plan_::k, fastsum_plan_::kernel_param, max_i(), and fastsum_plan_::p.

Referenced by fastsum_trafo().

◆ BuildTree()

void BuildTree	(	int	d,
		int	t,
		R *	x,
		C *	alpha,
		int *	permutation_x_alpha,
		int	N )

static

recursive sort of source knots dimension by dimension to get tree structure

Definition at line 599 of file fastsum.c.

References BuildTree(), and quicksort().

Referenced by BuildTree(), and fastsum_precompute_source_nodes().

◆ SearchTree()

C SearchTree	(	const int	d,
		const int	t,
		const R *	x,
		const C *	alpha,
		const R *	xmin,
		const R *	xmax,
		const int	N,
		const kernel	k,
		const R *	param,
		const int	Ad,
		const C *	Add,
		const int	p,
		const unsigned	flags )

static

fast search in tree of source knots for near field computation

Definition at line 613 of file fastsum.c.

References EXACT_NEARFIELD, kubintkern(), kubintkern1(), regkern(), regkern1(), and SearchTree().

Referenced by fastsum_trafo(), and SearchTree().

◆ fastsum_precompute_kernel()

void fastsum_precompute_kernel ( fastsum_plan * ths )

static

Definition at line 698 of file fastsum.c.

◆ fastsum_init_guru_kernel()

void fastsum_init_guru_kernel	(	fastsum_plan *	ths,
		int	d,
		kernel	k,
		R *	param,
		unsigned	flags,
		int	nn,
		int	p,
		R	eps_I,
		R	eps_B )

initialize node independent part of fast summation plan

Parameters

ths	The pointer to a fastsum plan.
d	The dimension of the problem.
kernel	The kernel function.
param	The parameters for the kernel function.
flags	Fastsum flags.
nn	The expansion degree.
p	The degree of smoothness.
eps_I	The inner boundary.
eps_B	the outer boundary.

Definition at line 779 of file fastsum.c.

References fastsum_plan_::Ad, fastsum_plan_::Add, fastsum_plan_::b, fastsum_plan_::d, fastsum_plan_::eps_B, fastsum_plan_::eps_I, EXACT_NEARFIELD, fastsum_plan_::f_hat, fastsum_plan_::flags, fastsum_plan_::k, fastsum_plan_::kernel_param, max_i(), fastsum_plan_::n, one_over_x(), and fastsum_plan_::p.

Referenced by fastsum_init_guru().

◆ fastsum_init_guru_source_nodes()

void fastsum_init_guru_source_nodes	(	fastsum_plan *	ths,
		int	N_total,
		int	nn_oversampled,
		int	m )

initialize source nodes dependent part of fast summation plan

Parameters

ths	The pointer to a fastsum plan.
N_total	The number of source knots x.
nn_oversampled	The oversampled expansion degree for nfft.
m	The cut-off parameter for the NFFT.

Definition at line 887 of file fastsum.c.

References fastsum_plan_::alpha, fastsum_plan_::d, fastsum_plan_::eps_B, fastsum_plan_::eps_I, fastsum_plan_::f, fastsum_plan_::f_hat, FFT_OUT_OF_PLACE, FFTW_INIT, fastsum_plan_::flags, fastsum_plan_::n, fastsum_plan_::N_total, fastsum_plan_::permutation_x_alpha, PRE_PHI_HUT, PRE_PSI, STORE_PERMUTATION_X_ALPHA, and fastsum_plan_::x.

Referenced by fastsum_init_guru().

◆ fastsum_init_guru_target_nodes()

void fastsum_init_guru_target_nodes	(	fastsum_plan *	ths,
		int	M_total,
		int	nn_oversampled,
		int	m )

initialize target nodes dependent part of fast summation plan

Parameters

ths	The pointer to a fastsum plan.
M_total	The number of target knots y.
nn_oversampled	The oversampled expansion degree for nfft.
m	The cut-off parameter for the NFFT.

Definition at line 955 of file fastsum.c.

References fastsum_plan_::d, fastsum_plan_::f, fastsum_plan_::f_hat, FFT_OUT_OF_PLACE, FFTW_INIT, fastsum_plan_::M_total, fastsum_plan_::n, PRE_PHI_HUT, PRE_PSI, fastsum_plan_::x, and fastsum_plan_::y.

Referenced by fastsum_init_guru().

◆ fastsum_init_guru()

void fastsum_init_guru	(	fastsum_plan *	ths,
		int	d,
		int	N_total,
		int	M_total,
		kernel	k,
		R *	param,
		unsigned	flags,
		int	nn,
		int	m,
		int	p,
		R	eps_I,
		R	eps_B )

initialization of fastsum plan

initialize fast summation plan

Parameters

ths	The pointer to a fastsum plan.
d	The dimension of the problem.
N_total	The number of source knots x.
M_total	The number of target knots y.
kernel	The kernel function.
param	The parameters for the kernel function.
flags	Fastsum flags.
nn	The expansion degree.
m	The cut-off parameter for the NFFT.
p	The degree of smoothness.
eps_I	The inner boundary.
eps_B	the outer boundary.

Definition at line 987 of file fastsum.c.

References fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), and fastsum_init_guru_target_nodes().

◆ fastsum_finalize_source_nodes()

void fastsum_finalize_source_nodes ( fastsum_plan * ths )

finalization of fastsum plan

finalize source nodes dependent part of plan

Parameters

ths	The pointer to a fastsum plan.

Definition at line 996 of file fastsum.c.

References fastsum_plan_::alpha, fastsum_plan_::eps_I, fastsum_plan_::flags, fastsum_plan_::permutation_x_alpha, and fastsum_plan_::x.

Referenced by fastsum_finalize().

◆ fastsum_finalize_target_nodes()

void fastsum_finalize_target_nodes ( fastsum_plan * ths )

finalization of fastsum plan

finalize target nodes dependent part of plan

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1020 of file fastsum.c.

References fastsum_plan_::f, and fastsum_plan_::y.

Referenced by fastsum_finalize().

◆ fastsum_finalize_kernel()

void fastsum_finalize_kernel ( fastsum_plan * ths )

finalization of fastsum plan

finalize node independent part of plan

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1029 of file fastsum.c.

References fastsum_plan_::Add, fastsum_plan_::b, fastsum_plan_::eps_I, EXACT_NEARFIELD, fastsum_plan_::f_hat, and fastsum_plan_::flags.

Referenced by fastsum_finalize().

◆ fastsum_finalize()

void fastsum_finalize ( fastsum_plan * ths )

finalization of fastsum plan

finalize plan

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1048 of file fastsum.c.

References fastsum_finalize_kernel(), fastsum_finalize_source_nodes(), and fastsum_finalize_target_nodes().

◆ fastsum_exact()

void fastsum_exact ( fastsum_plan * ths )

direct computation of sums

direct summation

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1056 of file fastsum.c.

References fastsum_plan_::alpha, fastsum_plan_::d, fastsum_plan_::f, fastsum_plan_::k, fastsum_plan_::kernel_param, fastsum_plan_::M_total, fastsum_plan_::N_total, fastsum_plan_::x, and fastsum_plan_::y.

◆ fastsum_precompute_source_nodes()

void fastsum_precompute_source_nodes ( fastsum_plan * ths )

precomputation for fastsum

sort source nodes, precompute nfft source plan.

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1086 of file fastsum.c.

References fastsum_plan_::alpha, BuildBox(), BuildTree(), fastsum_plan_::d, fastsum_plan_::eps_I, fastsum_plan_::flags, fastsum_plan_::MEASURE_TIME_t, fastsum_plan_::N_total, nfft_elapsed_seconds(), fastsum_plan_::permutation_x_alpha, PRE_FULL_PSI, PRE_LIN_PSI, PRE_PSI, and fastsum_plan_::x.

Referenced by fastsum_precompute().

◆ fastsum_precompute_target_nodes()

void fastsum_precompute_target_nodes ( fastsum_plan * ths )

precomputation for fastsum

precompute nfft target plan.

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1141 of file fastsum.c.

References fastsum_plan_::flags, fastsum_plan_::MEASURE_TIME_t, PRE_FULL_PSI, PRE_LIN_PSI, and PRE_PSI.

Referenced by fastsum_precompute().

◆ fastsum_precompute()

void fastsum_precompute ( fastsum_plan * ths )

precomputation for fastsum

sort source nodes, precompute nfft plans etc.

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1173 of file fastsum.c.

References fastsum_precompute_source_nodes(), and fastsum_precompute_target_nodes().

◆ fastsum_trafo()

void fastsum_trafo ( fastsum_plan * ths )

fast NFFT-based summation

fast NFFT-based summation algorithm

Parameters

ths	The pointer to a fastsum plan.

Definition at line 1180 of file fastsum.c.

References fastsum_plan_::Ad, fastsum_plan_::Add, fastsum_plan_::alpha, fastsum_plan_::b, fastsum_plan_::d, fastsum_plan_::eps_I, fastsum_plan_::f, fastsum_plan_::f_hat, fastsum_plan_::flags, fastsum_plan_::k, fastsum_plan_::kernel_param, fastsum_plan_::M_total, fastsum_plan_::MEASURE_TIME_t, fastsum_plan_::N_total, nfft_elapsed_seconds(), fastsum_plan_::p, SearchBox(), SearchTree(), fastsum_plan_::x, and fastsum_plan_::y.

◆ gaussian()

C gaussian	(	R	x,
		int	der,
		const R *	param )

K(x)=exp(-x^2/c^2).

Definition at line 38 of file kernels.c.

◆ multiquadric()

C multiquadric	(	R	x,
		int	der,
		const R *	param )

K(x)=sqrt(x^2+c^2).

Definition at line 64 of file kernels.c.

◆ inverse_multiquadric()

C inverse_multiquadric	(	R	x,
		int	der,
		const R *	param )

K(x)=1/sqrt(x^2+c^2).

Definition at line 90 of file kernels.c.

◆ logarithm()

C logarithm	(	R	x,
		int	der,
		const R *	param )

K(x)=log |x|.

Definition at line 116 of file kernels.c.

◆ thinplate_spline()

C thinplate_spline	(	R	x,
		int	der,
		const R *	param )

K(x) = x^2 log |x|.

Definition at line 149 of file kernels.c.

◆ one_over_square()

C one_over_square	(	R	x,
		int	der,
		const R *	param )

K(x) = 1/x^2.

Definition at line 177 of file kernels.c.

◆ one_over_modulus()

C one_over_modulus	(	R	x,
		int	der,
		const R *	param )

K(x) = 1/|x|.

Definition at line 205 of file kernels.c.

◆ one_over_x()

C one_over_x	(	R	x,
		int	der,
		const R *	param )

K(x) = 1/x.

Definition at line 233 of file kernels.c.

Referenced by fastsum_init_guru_kernel().

◆ inverse_multiquadric3()

C inverse_multiquadric3	(	R	x,
		int	der,
		const R *	param )

K(x) = 1/sqrt(x^2+c^2)^3.

Definition at line 261 of file kernels.c.

◆ sinc_kernel()

C sinc_kernel	(	R	x,
		int	der,
		const R *	param )

K(x) = sin(cx)/x.

Definition at line 287 of file kernels.c.

◆ cosc()

C cosc	(	R	x,
		int	der,
		const R *	param )

K(x) = cos(cx)/x.

Definition at line 314 of file kernels.c.

◆ kcot()

C kcot	(	R	x,
		int	der,
		const R *	param )

K(x) = cot(cx).

Definition at line 346 of file kernels.c.

Referenced by log_sin().

◆ one_over_cube()

C one_over_cube	(	R	x,
		int	der,
		const R *	param )

K(x) = 1/x^3.

Definition at line 374 of file kernels.c.

References UNUSED.

◆ log_sin()

C log_sin	(	R	x,
		int	der,
		const R *	param )

K(x) = log(|sin(cx)|).

Definition at line 402 of file kernels.c.

References kcot().

◆ laplacian_rbf()

C laplacian_rbf	(	R	x,
		int	der,
		const R *	param )

K(x) = exp(-|x|/c).

Definition at line 417 of file kernels.c.

Variable Documentation

◆ d

int fastsum_plan_::d

api

number of dimensions

Definition at line 86 of file fastsum.h.

Referenced by BuildBox(), fastsum_exact(), fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), fastsum_init_guru_target_nodes(), fastsum_precompute_source_nodes(), fastsum_trafo(), and SearchBox().

◆ N_total

int fastsum_plan_::N_total

number of source knots

Definition at line 88 of file fastsum.h.

Referenced by BuildBox(), fastsum_exact(), fastsum_init_guru_source_nodes(), fastsum_precompute_source_nodes(), and fastsum_trafo().

◆ M_total

int fastsum_plan_::M_total

number of target knots

Definition at line 89 of file fastsum.h.

Referenced by fastsum_exact(), fastsum_init_guru_target_nodes(), and fastsum_trafo().

◆ alpha

C* fastsum_plan_::alpha

source coefficients

Definition at line 91 of file fastsum.h.

Referenced by BuildBox(), fastsum_exact(), fastsum_finalize_source_nodes(), fastsum_init_guru_source_nodes(), fastsum_precompute_source_nodes(), and fastsum_trafo().

◆ f

C* fastsum_plan_::f

target evaluations

Definition at line 92 of file fastsum.h.

Referenced by fastsum_exact(), fastsum_finalize_target_nodes(), fastsum_init_guru_source_nodes(), fastsum_init_guru_target_nodes(), and fastsum_trafo().

◆ x

R* fastsum_plan_::x

source knots in d-ball with radius 1/4-eps_b/2

Definition at line 94 of file fastsum.h.

Referenced by BuildBox(), fastsum_exact(), fastsum_finalize_source_nodes(), fastsum_init_guru_source_nodes(), fastsum_init_guru_target_nodes(), fastsum_precompute_source_nodes(), and fastsum_trafo().

◆ y

R* fastsum_plan_::y

target knots in d-ball with radius 1/4-eps_b/2

Definition at line 95 of file fastsum.h.

Referenced by fastsum_exact(), fastsum_finalize_target_nodes(), fastsum_init_guru_target_nodes(), and fastsum_trafo().

◆ k

kernel fastsum_plan_::k

kernel function

Definition at line 97 of file fastsum.h.

Referenced by fastsum_exact(), fastsum_init_guru_kernel(), fastsum_trafo(), and SearchBox().

◆ kernel_param

R* fastsum_plan_::kernel_param

parameters for kernel function

Definition at line 98 of file fastsum.h.

Referenced by fastsum_exact(), fastsum_init_guru_kernel(), fastsum_trafo(), and SearchBox().

◆ flags

unsigned fastsum_plan_::flags

flags precomp.

and approx.type

Definition at line 100 of file fastsum.h.

Referenced by fastsum_finalize_kernel(), fastsum_finalize_source_nodes(), fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), fastsum_precompute_source_nodes(), fastsum_precompute_target_nodes(), fastsum_trafo(), and SearchBox().

◆ pre_K

C* fastsum_plan_::pre_K

internal

DS_PRE - direct summation precomputed K(x_j-y_l)

Definition at line 105 of file fastsum.h.

◆ n

int fastsum_plan_::n

FS__ - fast summation.

expansion degree

Definition at line 108 of file fastsum.h.

Referenced by fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), and fastsum_init_guru_target_nodes().

◆ b

C* fastsum_plan_::b

expansion coefficients

Definition at line 109 of file fastsum.h.

Referenced by fastsum_finalize_kernel(), fastsum_init_guru_kernel(), and fastsum_trafo().

◆ f_hat

C* fastsum_plan_::f_hat

Fourier coefficients of nfft plans.

Definition at line 110 of file fastsum.h.

Referenced by fastsum_finalize_kernel(), fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), fastsum_init_guru_target_nodes(), and fastsum_trafo().

◆ p

int fastsum_plan_::p

degree of smoothness of regularization

Definition at line 112 of file fastsum.h.

Referenced by fastsum_init_guru_kernel(), fastsum_trafo(), and SearchBox().

◆ eps_I

R fastsum_plan_::eps_I

inner boundary

Definition at line 113 of file fastsum.h.

Referenced by BuildBox(), fastsum_finalize_kernel(), fastsum_finalize_source_nodes(), fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), fastsum_precompute_source_nodes(), fastsum_trafo(), and SearchBox().

◆ eps_B

R fastsum_plan_::eps_B

outer boundary

Definition at line 114 of file fastsum.h.

Referenced by BuildBox(), fastsum_init_guru_kernel(), fastsum_init_guru_source_nodes(), and SearchBox().

◆ Ad

int fastsum_plan_::Ad

near field

number of spline knots for nearfield computation of regularized kernel

Definition at line 120 of file fastsum.h.

Referenced by fastsum_init_guru_kernel(), fastsum_trafo(), and SearchBox().

◆ Add

C* fastsum_plan_::Add

spline values

Definition at line 121 of file fastsum.h.

Referenced by fastsum_finalize_kernel(), fastsum_init_guru_kernel(), fastsum_trafo(), and SearchBox().

◆ box_count

int fastsum_plan_::box_count

Definition at line 126 of file fastsum.h.

◆ box_count_per_dim

int fastsum_plan_::box_count_per_dim

Definition at line 127 of file fastsum.h.

◆ box_offset

int* fastsum_plan_::box_offset

Definition at line 128 of file fastsum.h.

◆ box_x

R* fastsum_plan_::box_x

Definition at line 129 of file fastsum.h.

◆ box_alpha

C* fastsum_plan_::box_alpha

Definition at line 130 of file fastsum.h.

◆ permutation_x_alpha

int* fastsum_plan_::permutation_x_alpha

permutation vector of source nodes if STORE_PERMUTATION_X_ALPHA is set

Definition at line 132 of file fastsum.h.

Referenced by fastsum_finalize_source_nodes(), fastsum_init_guru_source_nodes(), and fastsum_precompute_source_nodes().

◆ MEASURE_TIME_t

R fastsum_plan_::MEASURE_TIME_t[8]

Measured time for each step if MEASURE_TIME is set.

Definition at line 134 of file fastsum.h.

Referenced by fastsum_precompute_source_nodes(), fastsum_precompute_target_nodes(), and fastsum_trafo().

Topics

Data Structures

Macros

Typedefs

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ X

◆ NF_KUB

◆ EXACT_NEARFIELD

◆ NEARFIELD_BOXES

◆ STORE_PERMUTATION_X_ALPHA

Typedef Documentation

◆ kernel

Function Documentation

◆ max_i()

◆ fak()

◆ binom()

◆ BasisPoly()

◆ regkern()

◆ regkern1()

◆ regkern3()

◆ kubintkern()

◆ kubintkern1()

◆ quicksort()

◆ BuildBox()

◆ calc_SearchBox()

◆ SearchBox()

◆ BuildTree()

◆ SearchTree()

◆ fastsum_precompute_kernel()

◆ fastsum_init_guru_kernel()

◆ fastsum_init_guru_source_nodes()

◆ fastsum_init_guru_target_nodes()

◆ fastsum_init_guru()

◆ fastsum_finalize_source_nodes()

◆ fastsum_finalize_target_nodes()

◆ fastsum_finalize_kernel()

◆ fastsum_finalize()

◆ fastsum_exact()

◆ fastsum_precompute_source_nodes()

◆ fastsum_precompute_target_nodes()

◆ fastsum_precompute()

◆ fastsum_trafo()

◆ gaussian()

◆ multiquadric()

◆ inverse_multiquadric()

◆ logarithm()

◆ thinplate_spline()

◆ one_over_square()

◆ one_over_modulus()

◆ one_over_x()

◆ inverse_multiquadric3()

◆ sinc_kernel()

◆ cosc()

◆ kcot()

◆ one_over_cube()

◆ log_sin()

◆ laplacian_rbf()

Variable Documentation

◆ d

◆ N_total

◆ M_total

◆ alpha

◆ f

◆ x

◆ y

◆ k

◆ kernel_param

◆ flags

◆ pre_K

◆ n

◆ b

◆ f_hat

◆ p

◆ eps_I

◆ eps_B

◆ Ad

◆ Add