Kernels

Set of kernels for spatial statistics problems. More...

Collaboration diagram for Kernels:

Functions
void	starsh_ssdata_block_exp_kernel_2d_simd_gcd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_2d_simd_gcd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_2d_simd_gcd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_2d_simd_gcd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_parsimonious_kernel_2d_simd_gcd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_parsimonious_kernel_2d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_parsimonious2_kernel_2d_simd_gcd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_parsimonious2_kernel_2d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for -dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_nd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_nd_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_1d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_1d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_2d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_2d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_3d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_3d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_4d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_exp_kernel_4d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Exponential kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_nd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_nd_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_1d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_1d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_2d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_2d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_3d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_3d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_4d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_sqrexp_kernel_4d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Square exponential kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_nd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_nd_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_1d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_1d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_2d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_2d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_3d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_3d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_4d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern_kernel_4d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_nd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_nd_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for n-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_1d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_1d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 1-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_2d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_2d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 2-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_3d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_3d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 3-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_4d (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 4-dimensional spatial statistics problem. More...
void	starsh_ssdata_block_matern2_kernel_4d_simd (int nrows, int ncols, STARSH_int *irow, STARSH_int *icol, void *row_data, void *col_data, void *result, int ld)
	Matérn kernel for 4-dimensional spatial statistics problem. More...

Detailed Description

Set of kernels for spatial statistics problems.

Click on functions to view implemented equations.

Function Documentation

starsh_ssdata_block_exp_kernel_1d()

void starsh_ssdata_block_exp_kernel_1d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d(), starsh_ssdata_block_exp_kernel_2d(), starsh_ssdata_block_exp_kernel_3d(), starsh_ssdata_block_exp_kernel_4d(), starsh_ssdata_block_exp_kernel_nd().

starsh_ssdata_block_exp_kernel_1d_simd()

void starsh_ssdata_block_exp_kernel_1d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d_simd(), starsh_ssdata_block_exp_kernel_2d_simd(), starsh_ssdata_block_exp_kernel_3d_simd(), starsh_ssdata_block_exp_kernel_4d_simd(), starsh_ssdata_block_exp_kernel_nd_simd().

starsh_ssdata_block_exp_kernel_2d()

void starsh_ssdata_block_exp_kernel_2d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d(), starsh_ssdata_block_exp_kernel_2d(), starsh_ssdata_block_exp_kernel_3d(), starsh_ssdata_block_exp_kernel_4d(), starsh_ssdata_block_exp_kernel_nd().

starsh_ssdata_block_exp_kernel_2d_simd()

void starsh_ssdata_block_exp_kernel_2d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d_simd(), starsh_ssdata_block_exp_kernel_2d_simd(), starsh_ssdata_block_exp_kernel_3d_simd(), starsh_ssdata_block_exp_kernel_4d_simd(), starsh_ssdata_block_exp_kernel_nd_simd().

starsh_ssdata_block_exp_kernel_2d_simd_gcd()

void starsh_ssdata_block_exp_kernel_2d_simd_gcd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points, measured by arc on sphere, and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d_simd(), starsh_ssdata_block_exp_kernel_2d_simd(), starsh_ssdata_block_exp_kernel_3d_simd(), starsh_ssdata_block_exp_kernel_4d_simd(), starsh_ssdata_block_exp_kernel_nd_simd().

starsh_ssdata_block_exp_kernel_3d()

void starsh_ssdata_block_exp_kernel_3d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d(), starsh_ssdata_block_exp_kernel_2d(), starsh_ssdata_block_exp_kernel_3d(), starsh_ssdata_block_exp_kernel_4d(), starsh_ssdata_block_exp_kernel_nd().

starsh_ssdata_block_exp_kernel_3d_simd()

void starsh_ssdata_block_exp_kernel_3d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d_simd(), starsh_ssdata_block_exp_kernel_2d_simd(), starsh_ssdata_block_exp_kernel_3d_simd(), starsh_ssdata_block_exp_kernel_4d_simd(), starsh_ssdata_block_exp_kernel_nd_simd().

starsh_ssdata_block_exp_kernel_4d()

void starsh_ssdata_block_exp_kernel_4d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d(), starsh_ssdata_block_exp_kernel_2d(), starsh_ssdata_block_exp_kernel_3d(), starsh_ssdata_block_exp_kernel_4d(), starsh_ssdata_block_exp_kernel_nd().

starsh_ssdata_block_exp_kernel_4d_simd()

void starsh_ssdata_block_exp_kernel_4d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d_simd(), starsh_ssdata_block_exp_kernel_2d_simd(), starsh_ssdata_block_exp_kernel_3d_simd(), starsh_ssdata_block_exp_kernel_4d_simd(), starsh_ssdata_block_exp_kernel_nd_simd().

starsh_ssdata_block_exp_kernel_nd()

void starsh_ssdata_block_exp_kernel_nd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d(), starsh_ssdata_block_exp_kernel_2d(), starsh_ssdata_block_exp_kernel_3d(), starsh_ssdata_block_exp_kernel_4d(), starsh_ssdata_block_exp_kernel_nd().

starsh_ssdata_block_exp_kernel_nd_simd()

void starsh_ssdata_block_exp_kernel_nd_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Exponential kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{r_{ij}}{\beta}} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_exp_kernel_1d_simd(), starsh_ssdata_block_exp_kernel_2d_simd(), starsh_ssdata_block_exp_kernel_3d_simd(), starsh_ssdata_block_exp_kernel_4d_simd(), starsh_ssdata_block_exp_kernel_nd_simd().

starsh_ssdata_block_matern2_kernel_1d()

void starsh_ssdata_block_matern2_kernel_1d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d(), starsh_ssdata_block_matern2_kernel_2d(), starsh_ssdata_block_matern2_kernel_3d(), starsh_ssdata_block_matern2_kernel_4d(), starsh_ssdata_block_matern2_kernel_nd().

starsh_ssdata_block_matern2_kernel_1d_simd()

void starsh_ssdata_block_matern2_kernel_1d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_matern2_kernel_2d()

void starsh_ssdata_block_matern2_kernel_2d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d(), starsh_ssdata_block_matern2_kernel_2d(), starsh_ssdata_block_matern2_kernel_3d(), starsh_ssdata_block_matern2_kernel_4d(), starsh_ssdata_block_matern2_kernel_nd().

starsh_ssdata_block_matern2_kernel_2d_simd()

void starsh_ssdata_block_matern2_kernel_2d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_matern2_kernel_2d_simd_gcd()

void starsh_ssdata_block_matern2_kernel_2d_simd_gcd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_matern2_kernel_3d()

void starsh_ssdata_block_matern2_kernel_3d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d(), starsh_ssdata_block_matern2_kernel_2d(), starsh_ssdata_block_matern2_kernel_3d(), starsh_ssdata_block_matern2_kernel_4d(), starsh_ssdata_block_matern2_kernel_nd().

starsh_ssdata_block_matern2_kernel_3d_simd()

void starsh_ssdata_block_matern2_kernel_3d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_matern2_kernel_4d()

void starsh_ssdata_block_matern2_kernel_4d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d(), starsh_ssdata_block_matern2_kernel_2d(), starsh_ssdata_block_matern2_kernel_3d(), starsh_ssdata_block_matern2_kernel_4d(), starsh_ssdata_block_matern2_kernel_nd().

starsh_ssdata_block_matern2_kernel_4d_simd()

void starsh_ssdata_block_matern2_kernel_4d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_matern2_kernel_nd()

void starsh_ssdata_block_matern2_kernel_nd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d(), starsh_ssdata_block_matern2_kernel_2d(), starsh_ssdata_block_matern2_kernel_3d(), starsh_ssdata_block_matern2_kernel_4d(), starsh_ssdata_block_matern2_kernel_nd().

starsh_ssdata_block_matern2_kernel_nd_simd()

void starsh_ssdata_block_matern2_kernel_nd_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_matern_kernel_1d()

void starsh_ssdata_block_matern_kernel_1d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d(), starsh_ssdata_block_matern_kernel_3d(), starsh_ssdata_block_matern_kernel_4d(), starsh_ssdata_block_matern_kernel_nd().

starsh_ssdata_block_matern_kernel_1d_simd()

void starsh_ssdata_block_matern_kernel_1d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d_simd(), starsh_ssdata_block_matern_kernel_3d_simd(), starsh_ssdata_block_matern_kernel_4d_simd(), starsh_ssdata_block_matern_kernel_nd_simd().

starsh_ssdata_block_matern_kernel_2d()

void starsh_ssdata_block_matern_kernel_2d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d(), starsh_ssdata_block_matern_kernel_3d(), starsh_ssdata_block_matern_kernel_4d(), starsh_ssdata_block_matern_kernel_nd().

starsh_ssdata_block_matern_kernel_2d_simd()

void starsh_ssdata_block_matern_kernel_2d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d_simd(), starsh_ssdata_block_matern_kernel_3d_simd(), starsh_ssdata_block_matern_kernel_4d_simd(), starsh_ssdata_block_matern_kernel_nd_simd().

starsh_ssdata_block_matern_kernel_2d_simd_gcd()

void starsh_ssdata_block_matern_kernel_2d_simd_gcd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d_simd(), starsh_ssdata_block_matern_kernel_3d_simd(), starsh_ssdata_block_matern_kernel_4d_simd(), starsh_ssdata_block_matern_kernel_nd_simd().

starsh_ssdata_block_matern_kernel_3d()

void starsh_ssdata_block_matern_kernel_3d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d(), starsh_ssdata_block_matern_kernel_3d(), starsh_ssdata_block_matern_kernel_4d(), starsh_ssdata_block_matern_kernel_nd().

starsh_ssdata_block_matern_kernel_3d_simd()

void starsh_ssdata_block_matern_kernel_3d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d_simd(), starsh_ssdata_block_matern_kernel_3d_simd(), starsh_ssdata_block_matern_kernel_4d_simd(), starsh_ssdata_block_matern_kernel_nd_simd().

starsh_ssdata_block_matern_kernel_4d()

void starsh_ssdata_block_matern_kernel_4d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d(), starsh_ssdata_block_matern_kernel_3d(), starsh_ssdata_block_matern_kernel_4d(), starsh_ssdata_block_matern_kernel_nd().

starsh_ssdata_block_matern_kernel_4d_simd()

void starsh_ssdata_block_matern_kernel_4d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d_simd(), starsh_ssdata_block_matern_kernel_3d_simd(), starsh_ssdata_block_matern_kernel_4d_simd(), starsh_ssdata_block_matern_kernel_nd_simd().

starsh_ssdata_block_matern_kernel_nd()

void starsh_ssdata_block_matern_kernel_nd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d(), starsh_ssdata_block_matern_kernel_3d(), starsh_ssdata_block_matern_kernel_4d(), starsh_ssdata_block_matern_kernel_nd().

starsh_ssdata_block_matern_kernel_nd_simd()

void starsh_ssdata_block_matern_kernel_nd_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right)^{\nu} K_{\nu} \left( \sqrt{2 \nu} \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern_kernel_1d(), starsh_ssdata_block_matern_kernel_2d_simd(), starsh_ssdata_block_matern_kernel_3d_simd(), starsh_ssdata_block_matern_kernel_4d_simd(), starsh_ssdata_block_matern_kernel_nd_simd().

starsh_ssdata_block_parsimonious2_kernel_2d_simd()

void starsh_ssdata_block_parsimonious2_kernel_2d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_parsimonious2_kernel_2d_simd_gcd()

void starsh_ssdata_block_parsimonious2_kernel_2d_simd_gcd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_parsimonious_kernel_2d_simd()

void starsh_ssdata_block_parsimonious_kernel_2d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_parsimonious_kernel_2d_simd_gcd()

void starsh_ssdata_block_parsimonious_kernel_2d_simd_gcd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Matérn kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{r_{ij}} {\beta} \right)^{\nu} K_{\nu} \left( \frac{r_{ij}}{\beta} \right) + \mu \delta(r_{ij}), \]

where \( \Gamma \) is the Gamma function, \( K_{\nu} \) is the modified Bessel function of the second kind, \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \), smoothing parameter \( \nu \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_matern2_kernel_1d_simd(), starsh_ssdata_block_matern2_kernel_2d_simd(), starsh_ssdata_block_matern2_kernel_3d_simd(), starsh_ssdata_block_matern2_kernel_4d_simd(), starsh_ssdata_block_matern2_kernel_nd_simd().

starsh_ssdata_block_sqrexp_kernel_1d()

void starsh_ssdata_block_sqrexp_kernel_1d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_1d_simd()

void starsh_ssdata_block_sqrexp_kernel_1d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 1-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_2d()

void starsh_ssdata_block_sqrexp_kernel_2d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_2d_simd()

void starsh_ssdata_block_sqrexp_kernel_2d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 2-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_2d_simd_gcd()

void starsh_ssdata_block_sqrexp_kernel_2d_simd_gcd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for -dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_3d()

void starsh_ssdata_block_sqrexp_kernel_3d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_3d_simd()

void starsh_ssdata_block_sqrexp_kernel_3d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 3-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_4d()

void starsh_ssdata_block_sqrexp_kernel_4d	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_4d_simd()

void starsh_ssdata_block_sqrexp_kernel_4d_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for 4-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_nd()

void starsh_ssdata_block_sqrexp_kernel_nd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().

starsh_ssdata_block_sqrexp_kernel_nd_simd()

void starsh_ssdata_block_sqrexp_kernel_nd_simd	(	int	nrows,
		int	ncols,
		STARSH_int *	irow,
		STARSH_int *	icol,
		void *	row_data,
		void *	col_data,
		void *	result,
		int	ld
	)

Square exponential kernel for n-dimensional spatial statistics problem.

Fills matrix \( A \) with values

\[ A_{ij} = \sigma^2 e^{-\frac{1}{2} \left( \frac{r_{ij}}{\beta} \right)^2} + \mu \delta(r_{ij}), \]

where \( \delta \) is the delta function

\[ \delta(x) = \left\{ \begin{array}{ll} 0, & x \ne 0\\ 1, & x = 0 \end{array} \right., \]

\( r_{ij} \) is a distance between \(i\)-th and \(j\)-th spatial points and variance \( \sigma \), correlation length \( \beta \) and noise \( \mu \) come from row_data (STARSH_ssdata object). No memory is allocated in this function!

Uses SIMD instructions.

Parameters

[in]	nrows	Number of rows of \( A \).
[in]	ncols	Number of columns of \( A \).
[in]	irow	Array of row indexes.
[in]	icol	Array of column indexes.
[in]	row_data	Pointer to physical data (STARSH_ssdata object).
[in]	col_data	Pointer to physical data (STARSH_ssdata object).
[out]	result	Pointer to memory of \( A \).
[in]	ld	Leading dimension of result.

See also

starsh_ssdata_block_sqrexp_kernel_1d(), starsh_ssdata_block_sqrexp_kernel_2d(), starsh_ssdata_block_sqrexp_kernel_3d(), starsh_ssdata_block_sqrexp_kernel_4d(), starsh_ssdata_block_sqrexp_kernel_nd().