Spatial statistics problem

Template for spatial statistics problems. More...

Collaboration diagram for Spatial statistics problem:

Modules
	Kernels
	Set of kernels for spatial statistics problems.

Data Structures
struct	starsh_ssdata
	Structure for Spatial Statistics problems. More...

Typedefs
typedef struct starsh_ssdata	STARSH_ssdata
	Structure for Spatial Statistics problems.

Enumerations
enum	STARSH_SPATIAL_KERNEL {   STARSH_SPATIAL_EXP = 1, STARSH_SPATIAL_SQREXP = 2, STARSH_SPATIAL_MATERN = 3, STARSH_SPATIAL_MATERN2 = 4,   STARSH_SPATIAL_EXP_SIMD = 11, STARSH_SPATIAL_SQREXP_SIMD = 12, STARSH_SPATIAL_MATERN_SIMD = 13, STARSH_SPATIAL_MATERN2_SIMD = 14,   STARSH_SPATIAL_EXP_GCD = 15, STARSH_SPATIAL_SQREXP_GCD = 16, STARSH_SPATIAL_MATERN_GCD = 17, STARSH_SPATIAL_MATERN2_GCD = 18,   STARSH_SPATIAL_PARSIMONIOUS_GCD = 19, STARSH_SPATIAL_PARSIMONIOUS2_GCD = 20, STARSH_SPATIAL_PARSIMONIOUS_SIMD = 21, STARSH_SPATIAL_PARSIMONIOUS2_SIMD = 22 }
	List of built-in kernels for starsh_ssdata_get_kernel(). More...
enum	STARSH_SPATIAL_PARAM {   STARSH_SPATIAL_NDIM = 1, STARSH_SPATIAL_BETA = 2, STARSH_SPATIAL_NU = 3, STARSH_SPATIAL_NOISE = 4,   STARSH_SPATIAL_PLACE = 5, STARSH_SPATIAL_SIGMA = 6, STARSH_SPATIAL_SIGMA2 = 7, STARSH_SPATIAL_NU2 = 8,   STARSH_SPATIAL_CORR = 9 }
	List of parameters for starsh_application(). More...
enum	STARSH_CAUCHY_PARAM { STARSH_CAUCHY_POINT = 1, STARSH_CAUCHY_DIAG = 2 }
	List of parameters for starsh_application(). More...

Functions
int	starsh_ssdata_new (STARSH_ssdata **data, STARSH_int count, int ndim)
	Allocate memory for STARSH_ssdata object. More...
int	starsh_ssdata_init (STARSH_ssdata **data, STARSH_int count, int ndim, double *point, double beta, double nu, double noise, double sigma)
	Initialize STARSH_ssdata object by given data. More...
int	starsh_ssdata_init_parsimonious (STARSH_ssdata **data, STARSH_int count, int ndim, double *point, double sigma1, double sigma2, double beta, double nu1, double nu2, double corr, double noise)
	Initialize STARSH_ssdata object by given data. More...
int	starsh_ssdata_generate (STARSH_ssdata **data, STARSH_int count, int ndim, double beta, double nu, double noise, enum STARSH_PARTICLES_PLACEMENT place, double sigma)
	Generate STARSH_ssdata object by given distribution. More...
int	starsh_ssdata_generate_parsimonious (STARSH_ssdata **data, STARSH_int count, int ndim, double beta, double nu, double noise, enum STARSH_PARTICLES_PLACEMENT place, double sigma, double sigma2, double nu2, double corr)
	Generate STARSH_ssdata object by given distribution. More...
int	starsh_ssdata_generate_va (STARSH_ssdata **data, STARSH_int count, va_list args)
	Generate STARSH_ssdata object with incomplete set of parameters. More...
int	starsh_ssdata_generate_el (STARSH_ssdata **data, STARSH_int count,...)
	Generate STARSH_ssdata object with incomplete set of parameters. More...
void	starsh_ssdata_free (STARSH_ssdata *data)
	Free memory of STARSH_ssdata object. More...
int	starsh_ssdata_get_kernel (STARSH_kernel **kernel, STARSH_ssdata *data, enum STARSH_SPATIAL_KERNEL type)
	Get kernel for spatial statistics problem. More...
int	starsh_esdata_get_kernel (STARSH_kernel **kernel, STARSH_esdata *data, enum STARSH_ELECTROSTATICS_KERNEL type)
	Get kernel for electrostatics problem. More...
void	starsh_mddata_free (STARSH_mddata *data)
	Free memory of STARSH_mddata object. More...

Detailed Description

Template for spatial statistics problems.

STARSH_ssdata holds all the necessary data.

Enumeration Type Documentation

STARSH_CAUCHY_PARAM

enum STARSH_CAUCHY_PARAM

List of parameters for starsh_application().

In the table below each constant corresponds to a given argument and type for starsh_cauchy_new(). These constants are used to generate problem with incomplete set of parameters via starsh_application() or starsh_cauchy_new_va().

See also

starsh_application(), starsh_cauchy_new(), starsh_cauchy_init(), starsh_cauchy_new_va().

Enumerator
STARSH_CAUCHY_POINT	Values of X_i for Cauchy matrix.
STARSH_CAUCHY_DIAG	Diagonal values of Cauchy matrix.

STARSH_SPATIAL_KERNEL

enum STARSH_SPATIAL_KERNEL

List of built-in kernels for starsh_ssdata_get_kernel().

For more info on exact formulas inside kernels, take a look at functions starsh_ssdata_block_exp_kernel_nd(), starsh_ssdata_block_sqrexp_kernel_nd(), starsh_ssdata_block_matern_kernel_nd(), starsh_ssdata_block_matern2_kernel_nd(), starsh_ssdata_block_exp_kernel_nd_simd(), starsh_ssdata_block_sqrexp_kernel_nd_simd(), starsh_ssdata_block_matern_kernel_nd_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

Enumerator
STARSH_SPATIAL_EXP	Exponential kernel. See also starsh_ssdata_block_exp_kernel_nd().
STARSH_SPATIAL_SQREXP	Square exponential kernel. See also starsh_ssdata_block_sqrexp_kernel_nd().
STARSH_SPATIAL_MATERN	Matérn kernel. See also starsh_ssdata_block_matern_kernel_nd().
STARSH_SPATIAL_MATERN2	Modified Matérn kernel. See also starsh_ssdata_block_matern2_kernel_nd().
STARSH_SPATIAL_EXP_SIMD	Exponential kernel with SIMD. See also starsh_ssdata_block_exp_kernel_nd_simd().
STARSH_SPATIAL_SQREXP_SIMD	Exponential kernel with SIMD. See also starsh_ssdata_block_sqrexp_kernel_nd_simd().
STARSH_SPATIAL_MATERN_SIMD	Matérn kernel with SIMD. See also starsh_ssdata_block_matern_kernel_nd().
STARSH_SPATIAL_MATERN2_SIMD	Modified Matérn kernel with SIMD. See also starsh_ssdata_block_matern2_kernel_nd_simd().
STARSH_SPATIAL_EXP_GCD	Exponential kernel. See also starsh_ssdata_block_exp_kernel_nd_simd_gcd().
STARSH_SPATIAL_SQREXP_GCD	Square exponential kernel. See also starsh_ssdata_block_sqrexp_kernel_nd_simd_gcd().
STARSH_SPATIAL_MATERN_GCD	Matérn kernel with SIMD. See also starsh_ssdata_block_matern_kernel_nd_simd_gcd().
STARSH_SPATIAL_MATERN2_GCD	Modified Matérn kernel with SIMD. See also starsh_ssdata_block_matern2_kernel_nd_simd_gcd().
STARSH_SPATIAL_PARSIMONIOUS_GCD	Bivariate Modified parsimonious Matérn kernel with GCD. See also starsh_ssdata_block_parsimonious_kernel_nd_simd_gcd().
STARSH_SPATIAL_PARSIMONIOUS2_GCD	Bivariate Modified parsimonious2 Matérn kernel with GCD. See also starsh_ssdata_block_parsimonious_kernel_nd_simd_gcd().
STARSH_SPATIAL_PARSIMONIOUS_SIMD	Bivariate Modified parsimonious Matérn kernel with SIMD. See also starsh_ssdata_block_parsimonious_kernel_nd_simd().
STARSH_SPATIAL_PARSIMONIOUS2_SIMD	Bivariate Modified parsimonious2 Matérnkernel with SIMD. See also starsh_ssdata_block_parsimonious_kernel_nd_simd().

STARSH_SPATIAL_PARAM

enum STARSH_SPATIAL_PARAM

List of parameters for starsh_application().

In the table below each constant corresponds to a given argument and type for starsh_ssdata_generate(). These constants are used to generate problem with incomplete set of parameters via starsh_application(), starsh_ssdata_generate_va() or starsh_ssdata_generate_el().

See also

starsh_application(), starsh_ssdata_generate(), starsh_ssdata_generate_va(), starsh_ssdata_generate_el().

Enumerator
STARSH_SPATIAL_NDIM	Dimensionality of space (ndim, integer).
STARSH_SPATIAL_BETA	Correlation length (beta, double).
STARSH_SPATIAL_NU	Smoothing parameter for Matérn kernel (nu, double).
STARSH_SPATIAL_NOISE	Noise or what to add to diagonal elements (noise, double).
STARSH_SPATIAL_PLACE	Distribution of particles (place, STARSH_PARTICLES_PLACEMENT).
STARSH_SPATIAL_SIGMA	Variance parameter (sigma, double).
STARSH_SPATIAL_SIGMA2	Variance for the second variable (in the parsimonious bivariate case).
STARSH_SPATIAL_NU2	Order of Matérn kernel for the second variable (in the parsimonious bivariate case).
STARSH_SPATIAL_CORR	spatial range parameter (define the correlation between the two variables in the parsimonious bivariate case).

Function Documentation

starsh_esdata_get_kernel()

int starsh_esdata_get_kernel	(	STARSH_kernel **	kernel,
		STARSH_esdata *	data,
		enum STARSH_ELECTROSTATICS_KERNEL	type
	)

Get kernel for electrostatics problem.

Kernel can be selected with this call or manually. To select kernel manually look into Kernels.

Parameters

[out]	kernel	Address of pointer to STARSH_kernel function.
[in]	data	Pointer to STARSH_esdata object.
[in]	type	Type of kernel. For more info look at STARSH_ELECTROSTATICS_KERNEL.

Returns

Error code STARSH_ERRNO.

See also

starsh_esdata_block_coulomb_potential_kernel_nd(), starsh_esdata_block_coulomb_potential_kernel_nd_simd().

starsh_mddata_free()

void starsh_mddata_free

(

STARSH_mddata *

data

)

Free memory of STARSH_mddata object.

See also

starsh_mddata_new(), starsh_mddata_init(), starsh_mddata_generate().

starsh_ssdata_free()

void starsh_ssdata_free

(

STARSH_ssdata *

data

)

Free memory of STARSH_ssdata object.

See also

starsh_ssdata_new(), starsh_ssdata_init(), starsh_ssdata_generate().

starsh_ssdata_generate()

int starsh_ssdata_generate	(	STARSH_ssdata **	data,
		STARSH_int	count,
		int	ndim,
		double	beta,
		double	nu,
		double	noise,
		enum STARSH_PARTICLES_PLACEMENT	place,
		double	sigma
	)

Generate STARSH_ssdata object by given distribution.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	ndim	Dimensionality of space.
[in]	beta	Correlation length.
[in]	nu	Smoothing parameter for Matérn kernel.
[in]	noise	Value to add to diagonal elements.
[in]	place	Placement strategy for spatial points.
[in]	sigma	Square of variance.

Returns

Error code STARSH_ERRNO.

See also

starsh_ssdata_generate_va(), starsh_ssdata_generate_el().

starsh_ssdata_generate_el()

int starsh_ssdata_generate_el	(	STARSH_ssdata **	data,
		STARSH_int	count,
			...
	)

Generate STARSH_ssdata object with incomplete set of parameters.

Parse possibly incomplete set of parameters for starsh_ssdata_generate(). If argument is not in the ..., then its default value is used:

Argument	Default value	Type –
ndim	2	int
beta	0.1	double
nu	0.5	double
noise	0.0	double
place	STARSH_PARTICLES_UNIFORM	STARSH_PARTICLES_PLACEMENT
sigma	1.0	double

List of arguments in ... should look as pairs (Arg.constant, Value) with 0 as a last argument. For correspondance of arguments and arg.constants take a look at STARSH_SPATIAL_PARAM.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	...	Variable amount of arguments.

Returns

Error code STARSH_ERRNO.

Examples

• starsh_ssdata_generate_el(&data, count,
      STARSH_SPATIAL_PLACE, STARSH_PARTICLES_RAND,
      STARSH_SPATIAL_NOISE, 0.1,
      STARSH_SPATIAL_SIGMA, 0.9,
      0).

• starsh_ssdata_generate_el(&data, count,
      STARSH_SPATIAL_NDIM, 3,
      STARSH_SPATIAL_BETA, 0.2,
      STARSH_SPATIAL_NU, 1.5,
      STARSH_SPATIAL_NOISE, 0.1,
      STARSH_SPATIAL_PLACE, STARSH_PARTICLES_RAND,
      STARSH_SPATIAL_SIGMA, 0.9,
      0).

See also

starsh_ssdata_generate(), starsh_ssdata_generate_va().

starsh_ssdata_generate_parsimonious()

int starsh_ssdata_generate_parsimonious	(	STARSH_ssdata **	data,
		STARSH_int	count,
		int	ndim,
		double	beta,
		double	nu,
		double	noise,
		enum STARSH_PARTICLES_PLACEMENT	place,
		double	sigma,
		double	sigma2,
		double	nu2,
		double	corr
	)

Generate STARSH_ssdata object by given distribution.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	ndim	Dimensionality of space.
[in]	beta	Correlation length.
[in]	nu	Smoothing parameter for Matérn kernel.
[in]	noise	Value to add to diagonal elements.
[in]	place	Placement strategy for spatial points.
[in]	sigma	Square of variance.
[in]	sigma2	Square of variance2.
[in]	nu2	Smoothing parameter for Matérn kernel.
[in]	corr	Corr parameter for Matérn kernel.

Returns

Error code STARSH_ERRNO.

See also

starsh_ssdata_generate_va(), starsh_ssdata_generate_el().

starsh_ssdata_generate_va()

int starsh_ssdata_generate_va	(	STARSH_ssdata **	data,
		STARSH_int	count,
		va_list	args
	)

Generate STARSH_ssdata object with incomplete set of parameters.

Parse possibly incomplete set of parameters for starsh_ssdata_generate(). If argument is not in the args, then its default value is used:

Argument	Default value	Type –
ndim	2	int
beta	0.1	double
nu	0.5	double
noise	0.0	double
place	STARSH_PARTICLES_UNIFORM	STARSH_PARTICLES_PLACEMENT
sigma	1.0	double
nu2	0.5	double
`sigma2	1.0	double
corr	0.5	double

List of arguments args should look as pairs (Arg.constant, Value) with 0 as a last argument. For correspondance of arguments and arg.constants take a look at STARSH_SPATIAL_PARAM.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	args	Arguments, packed into va_args.

Returns

Error code STARSH_ERRNO.

Examples

• void generate(size_t count, ...)
  {
      STARSH_ssdata *data;
      va_list args;
      va_start(args, count);
      starsh_ssdata_generate_va(&data, count, args);
      va_end(args);
  }

See also

starsh_ssdata_generate(), starsh_ssdata_generate_el().

starsh_ssdata_get_kernel()

int starsh_ssdata_get_kernel	(	STARSH_kernel **	kernel,
		STARSH_ssdata *	data,
		enum STARSH_SPATIAL_KERNEL	type
	)

Get kernel for spatial statistics problem.

Kernel can be selected with this call or manually. To select kernel manually look into Kernels.

Parameters

[out]	kernel	Address of pointer to STARSH_kernel function.
[in]	data	Pointer to STARSH_ssdata object.
[in]	type	Type of kernel. For more info look at STARSH_SPATIAL_KERNEL.

Returns

Error code STARSH_ERRNO.

See also

starsh_ssdata_block_exp_kernel_nd(), starsh_ssdata_block_exp_kernel_nd_simd(), starsh_ssdata_block_sqrexp_kernel_nd(), starsh_ssdata_block_sqrexp_kernel_nd_simd(), starsh_ssdata_block_matern_kernel_nd(), starsh_ssdata_block_matern_kernel_nd_simd(), starsh_ssdata_block_matern2_kernel_nd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_init()

int starsh_ssdata_init	(	STARSH_ssdata **	data,
		STARSH_int	count,
		int	ndim,
		double *	point,
		double	beta,
		double	nu,
		double	noise,
		double	sigma
	)

Initialize STARSH_ssdata object by given data.

Array point should be stored in a special way: x_1 x_2 ... x_count y_1 y_2 ... y_count z_1 z_2 .... This function does not allocate memory for coordinates and uses provided pointer point. Do not free memory of point until you finish using returned STARSH_ssdata object. Do not forget to sort data->particles by starsh_particles_zsort_inplace() to take advantage of low-rank submatrices.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	ndim	Dimensionality of space.
[in]	point	Pointer to array of coordinates of particles.
[in]	beta	Correlation length.
[in]	nu	Smoothing parameter for Matérn kernel.
[in]	noise	Value to add to diagonal elements.
[in]	sigma	Square of variance.

Returns

Error code STARSH_ERRNO.

See also

starsh_ssdata_new(), starsh_ssdata_free(), starsh_ssdata_generate(), starsh_ssdata_read_from_file(), starsh_particles_zsort_inplace().

starsh_ssdata_init_parsimonious()

int starsh_ssdata_init_parsimonious	(	STARSH_ssdata **	data,
		STARSH_int	count,
		int	ndim,
		double *	point,
		double	sigma1,
		double	sigma2,
		double	beta,
		double	nu1,
		double	nu2,
		double	corr,
		double	noise
	)

Initialize STARSH_ssdata object by given data.

Array point should be stored in a special way: x_1 x_2 ... x_count y_1 y_2 ... y_count z_1 z_2 .... This function does not allocate memory for coordinates and uses provided pointer point. Do not free memory of point until you finish using returned STARSH_ssdata object. Do not forget to sort data->particles by starsh_particles_zsort_inplace() to take advantage of low-rank submatrices.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	ndim	Dimensionality of space.
[in]	point	Pointer to array of coordinates of particles.
[in]	beta	Correlation length.
[in]	nu	Smoothing parameter for Matérn kernel.
[in]	noise	Value to add to diagonal elements.
[in]	sigma	Square of variance.

Returns

Error code STARSH_ERRNO.

See also

starsh_ssdata_new(), starsh_ssdata_free(), starsh_ssdata_generate(), starsh_ssdata_read_from_file(), starsh_particles_zsort_inplace().

starsh_ssdata_new()

int starsh_ssdata_new	(	STARSH_ssdata **	data,
		STARSH_int	count,
		int	ndim
	)

Allocate memory for STARSH_ssdata object.

This functions only allocates memory for particles without setting coordinates to any value. Do not forget to sort data->particles by starsh_particles_zsort_inplace() to take advantage of low-rank submatrices.

Parameters

[out]	data	Address of pointer to STARSH_ssdata object.
[in]	count	Number of particles.
[in]	ndim	Dimensionality of space.

Returns

Error code STARSH_ERRNO.

See also

starsh_ssdata_init(), starsh_ssdata_free(), starsh_ssdata_generate(), starsh_ssdata_read_from_file(), starsh_particles_zsort_inplace(), STARSH_particles.