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fastsum.c File Reference

Fast NFFT-based summation algorithm. More...

#include <stdlib.h>
#include <complex.h>
#include <math.h>
#include "util.h"
#include "nfft3.h"
#include "fastsum.h"

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(*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(*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(*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(*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 *alpha, int N)
 quicksort algorithm for source knots and associated coefficients
void BuildTree (int d, int t, double *x, complex *alpha, int N)
 recursive sort of source knots dimension by dimension to get tree structure
complex SearchTree (int d, int t, double *x, complex *alpha, double *xmin, double *xmax, int N, complex(*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(*kernel)(), double *param, unsigned flags, int nn, int m, int p, double eps_I, double eps_B)
 initialize fast summation plan
void fastsum_finalize (fastsum_plan *ths)
 finalize plan
void fastsum_exact (fastsum_plan *ths)
 direct summation
void fastsum_precompute (fastsum_plan *ths)
 sort source nodes, precompute Fourier coefficients, etc.
void fastsum_trafo (fastsum_plan *ths)
 fast NFFT-based summation algorithm


Detailed Description

Fast NFFT-based summation algorithm.

Author:
Markus Fenn
Date:
2003-2006

Function Documentation

void fastsum_exact fastsum_plan ths  ) 
 

direct summation

Parameters:
ths The pointer to a fastsum plan.

void fastsum_finalize fastsum_plan ths  ) 
 

finalize plan

Parameters:
ths The pointer to a fastsum plan.

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

initialize fast summation plan

inner boundary

outer boundary

init spline for near field computation

init d-dimensional NFFT plan

init d-dimensional FFTW plan

void fastsum_precompute fastsum_plan ths  ) 
 

sort source nodes, precompute Fourier coefficients, etc.

sort source knots

precompute spline values for near field

init NFFT plan for transposed transform in first step

precompute psi, the entries of the matrix B

init Fourier coefficients

init NFFT plan for transform in third step

precompute psi, the entries of the matrix B

precompute Fourier coefficients of regularised kernel

void fastsum_trafo fastsum_plan ths  ) 
 

fast NFFT-based summation algorithm

limits for d-dimensional near field box

first step of algorithm

second step of algorithm

third step of algorithm

add near field


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