ytBSpline Class Reference

B-Spline routines. More...

#include <math/ytBSpline.h>

Public Member Functions
void	ytBSpline_designMatrix2 (const double *x, const int n, double *B, int *index, const int ndx, const int degree, double *work)
	Generates the design matrix for B-spline nonparametric regression.
void	ytBSpline_designMatrix (const double *x, const int n, const double xl, const double xr, double *B, int *index, const int ndx, const int degree, double *work)
	Generates the design matrix for B-spline nonparametric regression.
void	ytBSpline_Dk (const int m, const int k, double *D)
	Generates k-th order difference matrix.
void	ytBSpline_K (int m, int k, double *K, double *work)
	Calculates Dk' Dk where Dk is the k-th order difference matrix.
double	ytBSpline_det_K_plus (const double *K, const int m)
	Calculates |K|+.
void	ytBSpline_syBtB (const double *B, const int *index, const int n, const int ndx, const int degree, double *BtB)
	Calculates the symmetric matrix of the multiplication B' B using the index vector set by ytBSpline_designMatrix().
void	ytBSpline_dsycopy (const double *X, double *Y, int m)
	Copies an upper symmetric matrix.
void	ytBSpline_dxpy_mask (int n, double *x, const double *y, const char *mask)
	Calculates a vector-vector addition x <- x + y with a mask vector.
void	ytBSpline_dxmy_mask (int n, double *x, const double *y, const char *mask)
	Calculates a vector-vector subtraction x <- x - y with a mask vector.
void	ytBSpline_Mv20 (int n, const double *A, const double *b, double *c)
	A b c (M,n) x (n,1) -> (M,1) M=20.
void	ytBSpline_BM3 (const double *restrict B, const int *index, const double *X, const int n, const int ndx, const int L, double *restrict Y)
	Calculates the design matrix - general matrix multiplication.
void	ytBSpline_printB (FILE *fp, const double *B, const int *index, int n, int ndx, int deg)
	Prints the design matrix.
double	ytBSpline_gamma20 (double x, double xl, double xr, double *gamma)
	Calculates B-splines with its coefficients for a single value.

Detailed Description

B-Spline routines.

The main routine is ytBSpline_designMatrix() that generates the design matrix for the given set of values. By multiplying coeffients to the design matrix, you can obtain a smooth curve made of B-splines. Formaly, the curve can be expressed as a vector Y = B g where B is the n by M design matrix, gamma a M-vector of coefficients, and M the number of B-splines.

Many routines assume that the degree is 3 and M is 20. For example, the above equation can be calculated ytBSpline_Bx3().

Member Function Documentation

ytBSpline_BM3()

void ytBSpline_BM3	(	const double *restrict	B,
		const int *	index,
		const double *	X,
		const int	n,
		const int	ndx,
		const int	L,
		double *restrict	Y
	)

Calculates the design matrix - general matrix multiplication.

This calculates the design matrix - general matrix multiplication B × X where B is the design matrix whose original size is n by ndx where ndx represents the number of the B-spline basis functions, and X, an ndx by L general matrix.

The degree of B-splines is fixed at 3.

Parameters

	B	design matrix returned by ytBSpline_designMatrix().
	index	index vector for the design matrix returned by ytBSpline_designMatrix().
	X	general ndx by L matrix
	n	number of rows of B.
	ndx	number of rows of X.
	L	number of columns of X.
[out]	Y	n by L matrix to return.

ytBSpline_designMatrix()

void ytBSpline_designMatrix	(	const double *	x,
		const int	n,
		const double	xl,
		const double	xr,
		double *	B,
		int *	index,
		const int	ndx,
		const int	degree,
		double *	work
	)

Generates the design matrix for B-spline nonparametric regression.

This generates the design metrix of B-splines.

Because only (degree + 1) B-splines cover a single value in x, the size of the design matrix requires only n by (degree + 1).

NaN values are acceptable in x. If so, NaNs are ignored.

The algorithm is based on Eilers and Marx (1996).

Parameters

[in]	x	vector of size n.
[in]	n	The number of samples.
[in]	xl	minimum value of the input value range.
[in]	xr	maximum value of the input value range.
[out]	B	Row major matrix of size n by (degree + 1), to which the generated design matrix is set.
[out]	index	vector of size n to which values representing the first index of B-splines convering each value in x is set.
[in]	ndx	number of B-splines. The number of intervals for values in x is ndx - degree.
[in]	degree	degree of B-splines.
	work	working area of size ndx + 1 + n * (degree + 1).

ytBSpline_designMatrix2()

void ytBSpline_designMatrix2	(	const double *	x,
		const int	n,
		double *	B,
		int *	index,
		const int	ndx,
		const int	degree,
		double *	work
	)

Generates the design matrix for B-spline nonparametric regression.

This generates the design metrix of B-splines.

Because only (degree + 1) B-splines cover a single value in x, the size of the design matrix requires only n by (degree + 1).

NaN values are acceptable in x. If so, NaNs are ignored.

The algorithm is based on Eilers and Marx (1996).

Parameters

[in]	x	vector of size n.
[in]	n	The number of samples.
[out]	B	Row major matrix of size n by (degree + 1), to which the generated design matrix is set.
[out]	index	vector of size n to which values representing the first index of B-splines convering each value in x is set.
[in]	ndx	number of B-splines. The number of intervals for values in x is ndx - degree.
[in]	degree	degree of B-splines.
	work	working area of size ndx + 1 + n * (degree + 1).

ytBSpline_det_K_plus()

double ytBSpline_det_K_plus	(	const double *	K,
		const int	m
	)

Calculates |K|₊.

Parameters

[in]	K	Matrix calculated by BSpline_K().
[in]	m	size of K.

Returns

|K|₊.

ytBSpline_Dk()

void ytBSpline_Dk	(	const int	m,
		const int	k,
		double *	D
	)

Generates k-th order difference matrix.

Parameters

[in]	m	the size of matrix to generate.
[in]	k	the order of the difference matrix to generate.
[out]	D	(m - k) x m difference matrix.

ytBSpline_dsycopy()

void ytBSpline_dsycopy	(	const double *	X,
		double *	Y,
		int	m
	)

Copies an upper symmetric matrix.

Parameters

[in]	X
[out]	Y
[in]	m	size (the number of rows) of the matrix.

ytBSpline_dxmy_mask()

void ytBSpline_dxmy_mask	(	int	n,
		double *	x,
		const double *	y,
		const char *	mask
	)

Calculates a vector-vector subtraction x <- x - y with a mask vector.

Parameters

	n
[in,out]	x
[in]	y
[in]	mask

ytBSpline_dxpy_mask()

void ytBSpline_dxpy_mask	(	int	n,
		double *	x,
		const double *	y,
		const char *	mask
	)

Calculates a vector-vector addition x <- x + y with a mask vector.

The i-th elements where mask has 0 are ignored.

Parameters

	n
[in,out]	x
[in]	y
[in]	mask

ytBSpline_gamma20()

double ytBSpline_gamma20	(	double	x,
		double	xl,
		double	xr,
		double *	gamma
	)

Calculates B-splines with its coefficients for a single value.

This assumes the fixed 20 B-splines for the range from xl to xr.

Parameters

x
xl	left most (minimum) value of the range.
xr	right most (maximum) value of the range.
gamma	20 length array of coefficients.

ytBSpline_K()

void ytBSpline_K	(	int	m,
		int	k,
		double *	K,
		double *	work
	)

Calculates Dk' Dk where Dk is the k-th order difference matrix.

Parameters

m	size of the matrix.
k	degree (order) of the difference matrix.
K	m x m matrix.
work	At least (m - k) x m size working area. NULL is acceptable. If so, this function allocates dynamically the working area and frees it on exit.

ytBSpline_printB()

void ytBSpline_printB	(	FILE *	fp,
		const double *	B,
		const int *	index,
		int	n,
		int	ndx,
		int	deg
	)

Prints the design matrix.

Parameters

fp	file stream pointer to output.
B	row-major n by deg + 1 - design matrix returned by ytBSpline_designMatrix().
index	index vector returned by ytBSpline_designMatrix().
n	the number of samples.
ndx	the number of B-splines.
deg	degree of B-splines.

ytBSpline_syBtB()

void ytBSpline_syBtB	(	const double *	B,
		const int *	index,
		const int	n,
		const int	ndx,
		const int	degree,
		double *	BtB
	)

Calculates the symmetric matrix of the multiplication B' B using the index vector set by ytBSpline_designMatrix().

Note: only upper triangle elements are filled.

Parameters

[in]	B	design matrix of size n x degree + 1, calculated by BSpline_design_matrix().
[in]	index	index vector of size n, calculated by BSpline_design_matrix().
[in]	n	number of samples
[in]	ndx	number of B-splines.
[in]	degree	degree of B-splines.
[out]	BtB	matrix of size ndx x ndx used to put the results.

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The documentation for this class was generated from the following file:

• math/ytBSpline.c