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fastsumS2_matlab
[Fast summation of radial functions on the sphere]


Defines

#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 double innerProduct (const double phi1, const double theta1, const double phi2, const double theta2)
 Computes the $\mathbb{R}^3$ standard inner product between two vectors on the unit sphere $\mathbb{S}^2$ given in spherical coordinates.
static double poissonKernel (const double x, const double h)
 Evaluates the Poisson kernel $Q_h: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.
static double singularityKernel (const double x, const double h)
 Evaluates the singularity kernel $S_h: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.
static double locallySupportedKernel (const double x, const double h, const double lambda)
 Evaluates the locally supported kernel $L_{h,\lambda}: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.
static double gaussianKernel (const double x, const double sigma)
 Evaluates the spherical Gaussian kernel $G_\sigma: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.
int main (int argc, char **argv)
 The main program.

Enumeration Type Documentation

enum pvalue

Enumeration type for yes/no/both-type parameters.

Enumerator:
NO 
YES 
BOTH 

Definition at line 58 of file fastsumS2.c.


Function Documentation

static double innerProduct ( const double  phi1,
const double  theta1,
const double  phi2,
const double  theta2 
) [inline, static]

Computes the $\mathbb{R}^3$ standard inner product between two vectors on the unit sphere $\mathbb{S}^2$ given in spherical coordinates.

Returns:
The inner product $\cos \vartheta_1 \cos \vartheta_2 + \sin \vartheta_1 \sin(\vartheta_2 \cos(\varphi_1 - \varphi_2)$
Author:
Jens Keiner

Definition at line 74 of file fastsumS2.c.

References PI2.

Referenced by main().

static double poissonKernel ( const double  x,
const double  h 
) [inline, static]

Evaluates the Poisson kernel $Q_h: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.

Returns:
The value of the Poisson kernel $Q_h(x)$ at the node $x$
Author:
Jens Keiner

Definition at line 93 of file fastsumS2.c.

References PI4.

Referenced by main().

static double singularityKernel ( const double  x,
const double  h 
) [inline, static]

Evaluates the singularity kernel $S_h: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.

Returns:
The value of the Poisson kernel $S_h(x)$ at the node $x$
Author:
Jens Keiner

Definition at line 109 of file fastsumS2.c.

References PI2.

Referenced by main().

static double locallySupportedKernel ( const double  x,
const double  h,
const double  lambda 
) [inline, static]

Evaluates the locally supported kernel $L_{h,\lambda}: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.

Returns:
The value of the locally supported kernel $L_{h,\lambda}(x)$ at the node $x$
Author:
Jens Keiner

Definition at line 127 of file fastsumS2.c.

Referenced by main().

static double gaussianKernel ( const double  x,
const double  sigma 
) [inline, static]

Evaluates the spherical Gaussian kernel $G_\sigma: [-1,1] \rightarrow \mathbb{R}$ at a node $x \in [-1,1]$.

Returns:
The value of the pherical Gaussian kernel $G_\sigma(x)$ at the node $x$
Author:
Jens Keiner

Definition at line 145 of file fastsumS2.c.

Referenced by main().

int main ( int  argc,
char **  argv 
)

The main program.

Parameters:
argc The number of arguments
argv An array containing the arguments as C-strings
Returns:
Exit code
Author:
Jens Keiner

Definition at line 160 of file fastsumS2.c.

References BOTH, nfsft_plan::f, nfsft_plan::f_hat, FFT_OUT_OF_PLACE, FFTW_INIT, gaussianKernel(), innerProduct(), KT_ABEL_POISSON, KT_GAUSSIAN, KT_LOC_SUPP, KT_SINGULARITY, locallySupportedKernel(), ndsft_adjoint(), ndsft_trafo(), nfft_error_l_infty_1_complex(), nfft_free(), nfft_malloc(), NFFT_MAX, nfft_second(), nfft_smbi(), nfsft_adjoint(), NFSFT_F_HAT_SIZE, nfsft_finalize(), nfsft_forget(), NFSFT_INDEX, nfsft_init_guru(), NFSFT_NO_FAST_ALGORITHM, nfsft_precompute(), nfsft_precompute_x(), nfsft_trafo(), NFSFT_USE_DPT, NFSFT_USE_NDFT, NO, PI, PI2, PI4, poissonKernel(), PRE_PHI_HUT, PRE_PSI, singularityKernel(), SYMBOL_ABEL_POISSON, SYMBOL_SINGULARITY, nfsft_plan::x, and YES.


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