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Fast summation
[Applications]


Modules

 fastsum_matlab
 fastsum_test

Data Structures

struct  fastsum_plan_
 plan for fast summation algorithm More...

Defines

#define EXACT_NEARFIELD   (1U<< 0)
 Constant symbols.

Typedefs

typedef fastsum_plan_ fastsum_plan
 plan for fast summation algorithm

Functions

double fak (int n)
 factorial
double binom (int n, int m)
 binomial coefficient
double BasisPoly (int m, int r, double xx)
 basis polynomial for regularized kernel
double regkern (complex double(*kernel)(double, int, const double *), double xx, int p, const double *param, double a, double b)
 regularized kernel with K_I arbitrary and K_B smooth to zero
double regkern1 (complex double(*kernel)(double, int, const double *), double xx, int p, const double *param, double a, double b)
 regularized kernel with K_I arbitrary and K_B periodized (used in 1D)
double regkern2 (complex double(*kernel)(double, int, const double *), double xx, int p, const double *param, double a, double b)
 regularized kernel for even kernels with K_I even and K_B mirrored
double regkern3 (complex double(*kernel)(double, int, const double *), double xx, int p, const double *param, double a, double b)
 regularized kernel for even kernels with K_I even and K_B mirrored smooth to K(1/2) (used in dD, d>1)
double kubintkern (double x, double *Add, int Ad, double a)
 cubic spline interpolation in near field with even kernels
double kubintkern1 (double x, double *Add, int Ad, double a)
 cubic spline interpolation in near field with arbitrary kernels
void quicksort (int d, int t, double *x, complex double *alpha, int N)
 quicksort algorithm for source knots and associated coefficients
void BuildTree (int d, int t, double *x, complex double *alpha, int N)
 recursive sort of source knots dimension by dimension to get tree structure
complex double SearchTree (int d, int t, double *x, complex double *alpha, double *xmin, double *xmax, int N, complex double(*kernel)(double, int, const double *), const double *param, int Ad, double *Add, int p, 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, complex double(*kernel)(), double *param, unsigned flags, int nn, int m, int p, double eps_I, double eps_B)
 initialization 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 (fastsum_plan *ths)
 precomputation for fastsum
void fastsum_trafo (fastsum_plan *ths)
 fast NFFT-based summation
complex double gaussian (double x, int der, const double *param)
complex double multiquadric (double x, int der, const double *param)
complex double inverse_multiquadric (double x, int der, const double *param)
complex double logarithm (double x, int der, const double *param)
complex double thinplate_spline (double x, int der, const double *param)
complex double one_over_square (double x, int der, const double *param)
complex double one_over_modulus (double x, int der, const double *param)
complex double one_over_x (double x, int der, const double *param)
complex double inverse_multiquadric3 (double x, int der, const double *param)
complex double sinc_kernel (double x, int der, const double *param)
complex double cosc (double x, int der, const double *param)
complex double cot (double x, int der, const double *param)
complex one_over_cube (double x, int der, const double *param)

Function Documentation

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

initialization of fastsum 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 370 of file fastsum.c.

References EXACT_NEARFIELD, FFT_OUT_OF_PLACE, FFTW_INIT, MALLOC_F, MALLOC_F_HAT, MALLOC_X, nfft_init_guru(), PRE_PHI_HUT, and PRE_PSI.

Referenced by fields_fastsum_init().

void fastsum_finalize fastsum_plan ths  ) 
 

finalization of fastsum plan

Parameters:
ths The pointer to a fastsum plan.

Definition at line 436 of file fastsum.c.

References EXACT_NEARFIELD, and nfft_finalize().

Referenced by fields_fastsum_finalize().

void fastsum_exact fastsum_plan ths  ) 
 

direct computation of sums

Parameters:
ths The pointer to a fastsum plan.

Definition at line 454 of file fastsum.c.

void fastsum_precompute fastsum_plan ths  ) 
 

precomputation for fastsum

Parameters:
ths The pointer to a fastsum plan.

Definition at line 480 of file fastsum.c.

References BuildTree(), EXACT_NEARFIELD, nfft_fftshift_complex(), nfft_precompute_full_psi(), nfft_precompute_lin_psi(), nfft_precompute_psi(), PRE_FULL_PSI, PRE_LIN_PSI, PRE_PSI, regkern1(), and regkern3().

Referenced by fields_fastsum_precompute(), and fields_fastsum_simple().

void fastsum_trafo fastsum_plan ths  ) 
 

fast NFFT-based summation

Parameters:
ths The pointer to a fastsum plan.

Definition at line 563 of file fastsum.c.

References nfft_adjoint(), nfft_trafo(), and SearchTree().

Referenced by fields_fastsum_simple().


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