NFFT  3.3.0
Modules | Data Structures | Macros | Typedefs | Functions
Fast summation

Modules

 fastsum_matlab
 
 fastsum_test
 

Data Structures

struct  fastsum_plan_
 plan for fast summation algorithm More...
 

Macros

#define X(name)   NFFT(name)
 Include header for C99 complex datatype. More...
 
#define NF_KUB
 
#define EXACT_NEARFIELD   (1U<< 0)
 Constant symbols.
 
#define NEARFIELD_BOXES   (1U<< 1)
 

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
 
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 More...
 
kubintkern (const R x, const C *Add, const int Ad, const R a)
 linear spline interpolation in near field with even kernels More...
 
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 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 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
 
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 More...
 
void fastsum_finalize (fastsum_plan *ths)
 finalization of fastsum plan More...
 
void fastsum_exact (fastsum_plan *ths)
 direct computation of sums More...
 
void fastsum_precompute (fastsum_plan *ths)
 precomputation for fastsum More...
 
void fastsum_trafo (fastsum_plan *ths)
 fast NFFT-based summation More...
 
gaussian (R x, int der, const R *param)
 
multiquadric (R x, int der, const R *param)
 
inverse_multiquadric (R x, int der, const R *param)
 
logarithm (R x, int der, const R *param)
 
thinplate_spline (R x, int der, const R *param)
 
one_over_square (R x, int der, const R *param)
 
one_over_modulus (R x, int der, const R *param)
 
one_over_x (R x, int der, const R *param)
 
inverse_multiquadric3 (R x, int der, const R *param)
 
sinc_kernel (R x, int der, const R *param)
 
cosc (R x, int der, const R *param)
 
kcot (R x, int der, const R *param)
 
one_over_cube (R x, int der, const R *param)
 

Detailed Description

Macro Definition Documentation

#define X (   name)    NFFT(name)

Include header for C99 complex datatype.

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

Definition at line 53 of file fastsum.h.

Referenced by c2e_transposed(), CONCAT(), eval_sum_clenshaw_transposed(), and main().

Function Documentation

static C regkern3 ( kernel  k,
xx,
int  p,
const R *  param,
a,
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 232 of file fastsum.c.

References BasisPoly().

Referenced by fastsum_precompute().

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 320 of file fastsum.c.

Referenced by calc_SearchBox(), and SearchTree().

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,
eps_I,
eps_B 
)

initialization of fastsum plan

initialize fast summation plan

Parameters
thsThe pointer to a fastsum plan.
dThe dimension of the problem.
N_totalThe number of source knots x.
M_totalThe number of target knots y.
kernelThe kernel function.
paramThe parameters for the kernel function.
flagsFastsum flags.
nnThe expansion degree.
mThe cut-off parameter for the NFFT.
pThe degree of smoothness.
eps_IThe inner boundary.
eps_Bthe outer boundary.

Definition at line 693 of file fastsum.c.

References fastsum_plan_::Ad, fastsum_plan_::Add, fastsum_plan_::alpha, fastsum_plan_::b, fastsum_plan_::d, fastsum_plan_::eps_B, fastsum_plan_::eps_I, EXACT_NEARFIELD, fastsum_plan_::f, fastsum_plan_::flags, fastsum_plan_::k, fastsum_plan_::kernel_param, fastsum_plan_::M_total, max_i(), fastsum_plan_::n, fastsum_plan_::N_total, fastsum_plan_::p, fastsum_plan_::x, and fastsum_plan_::y.

void fastsum_finalize ( fastsum_plan ths)

finalization of fastsum plan

finalize plan

Parameters
thsThe pointer to a fastsum plan.

Definition at line 846 of file fastsum.c.

References fastsum_plan_::Add, fastsum_plan_::alpha, fastsum_plan_::b, EXACT_NEARFIELD, fastsum_plan_::f, fastsum_plan_::flags, fastsum_plan_::x, and fastsum_plan_::y.

void fastsum_exact ( fastsum_plan ths)

direct computation of sums

direct summation

Parameters
thsThe pointer to a fastsum plan.

Definition at line 879 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.

void fastsum_precompute ( fastsum_plan ths)
void fastsum_trafo ( fastsum_plan ths)