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NFFT 3.5.3alpha
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Macros | |
#define | SYMBOL_ABEL_POISSON(k, h) (pow(h,k)) |
#define | SYMBOL_SINGULARITY(k, h) ((2.0/(2*k+1))*pow(h,k)) |
#define | KT_ABEL_POISSON (0) |
Abel-Poisson kernel. | |
#define | KT_SINGULARITY (1) |
Singularity kernel. | |
#define | KT_LOC_SUPP (2) |
Locally supported kernel. | |
#define | KT_GAUSSIAN (3) |
Gaussian kernel. | |
Enumerations | |
enum | pvalue { NO = 0 , YES = 1 , BOTH = 2 } |
Enumeration type for yes/no/both-type parameters. More... | |
Functions | |
static int | scaled_modified_bessel_i_series (const R x, const R alpha, const int nb, const int ize, R *b) |
static void | scaled_modified_bessel_i_normalize (const R x, const R alpha, const int nb, const int ize, R *b, const R sum_) |
static int | smbi (const R x, const R alpha, const int nb, const int ize, R *b) |
Calculates the modified bessel function ![]() ![]() ![]() ![]() ![]() | |
static double | innerProduct (const double phi1, const double theta1, const double phi2, const double theta2) |
Computes the ![]() ![]() | |
static double | poissonKernel (const double x, const double h) |
Evaluates the Poisson kernel ![]() ![]() | |
static double | singularityKernel (const double x, const double h) |
Evaluates the singularity kernel ![]() ![]() | |
static double | locallySupportedKernel (const double x, const double h, const double lambda) |
Evaluates the locally supported kernel ![]() ![]() | |
static double | gaussianKernel (const double x, const double sigma) |
Evaluates the spherical Gaussian kernel ![]() ![]() | |
int | main (int argc, char **argv) |
The main program. | |
#define SYMBOL_ABEL_POISSON | ( | k, | |
h | |||
) | (pow(h,k)) |
Definition at line 42 of file fastsumS2.c.
#define SYMBOL_SINGULARITY | ( | k, | |
h | |||
) | ((2.0/(2*k+1))*pow(h,k)) |
Definition at line 45 of file fastsumS2.c.
#define KT_ABEL_POISSON (0) |
Abel-Poisson kernel.
Definition at line 50 of file fastsumS2.c.
#define KT_SINGULARITY (1) |
Singularity kernel.
Definition at line 52 of file fastsumS2.c.
#define KT_LOC_SUPP (2) |
Locally supported kernel.
Definition at line 54 of file fastsumS2.c.
#define KT_GAUSSIAN (3) |
Gaussian kernel.
Definition at line 56 of file fastsumS2.c.
enum pvalue |
Enumeration type for yes/no/both-type parameters.
Definition at line 59 of file fastsumS2.c.
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inlinestatic |
Definition at line 61 of file fastsumS2.c.
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inlinestatic |
Definition at line 117 of file fastsumS2.c.
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static |
Calculates the modified bessel function
x
non-negative real number in alpha
non-negative real number with nb
number of functions to be calculated ize
switch between no scaling (ize
= 1) and exponential scaling (ize
= 2) b
real output vector to contain nb
, then all values in b
have been calculated to full accuracy. If not, errors are indicated using the following scheme:ncalc
is set to This program is based on a program written by David J. Sookne [2] that computes values of the Bessel functions
References: [1] F. W. J. Olver and D. J. Sookne, A note on backward recurrence algorithms", Math. Comput. (26), 1972, pp 125 -- 132. [2] D. J. Sookne, "Bessel functions of real argument and int order", NBS Jour. of Res. B. (77B), 1973, pp. 125 – 132.
Modified by W. J. Cody, Applied Mathematics Division, Argonne National Laboratory, Argonne, IL, 60439, USA
Modified by Jens Keiner, Institute of Mathematics, University of Lübeck, 23560 Lübeck, Germany
Definition at line 192 of file fastsumS2.c.
Referenced by main().
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inlinestatic |
Computes the
Definition at line 449 of file fastsumS2.c.
Referenced by main().
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inlinestatic |
Evaluates the Poisson kernel
Definition at line 468 of file fastsumS2.c.
Referenced by main().
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inlinestatic |
Evaluates the singularity kernel
Definition at line 484 of file fastsumS2.c.
Referenced by main().
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inlinestatic |
Evaluates the locally supported kernel
Definition at line 502 of file fastsumS2.c.
Referenced by main().
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inlinestatic |
Evaluates the spherical Gaussian kernel
Definition at line 520 of file fastsumS2.c.
Referenced by main().
int main | ( | int | argc, |
char ** | argv | ||
) |
The main program.
argc | The number of arguments |
argv | An array containing the arguments as C-strings |
Definition at line 535 of file fastsumS2.c.
References nfsft_plan::f, nfsft_plan::f_hat, FFTW_INIT, gaussianKernel(), innerProduct(), KT_ABEL_POISSON, KT_GAUSSIAN, KT_LOC_SUPP, KT_SINGULARITY, locallySupportedKernel(), nfft_elapsed_seconds(), nfft_free(), nfft_malloc(), nfsft_adjoint(), NFSFT_F_HAT_SIZE, nfsft_finalize(), nfsft_forget(), NFSFT_INDEX, NFSFT_NO_FAST_ALGORITHM, nfsft_precompute(), nfsft_trafo(), NFSFT_USE_DPT, NFSFT_USE_NDFT, poissonKernel(), PRE_PHI_HUT, PRE_PSI, singularityKernel(), smbi(), and nfsft_plan::x.