BSpline

#include <BSpline.hpp>

Public Types
enum class	KnotDistro { logarithmic , linear , loglinear }

Public Member Functions
	BSpline (std::size_t n, std::size_t k, double x0, double xmax, KnotDistro kd=KnotDistro::logarithmic)
	Constructs basis of n splines of order k, defined over [0,xmax]. x0 is first non-zero knot. kd = { logarithmic, linear, loglinear }.
BSpline &	operator= (const BSpline &)=delete
	BSpline (const BSpline &)=delete
std::size_t	K ()
	Order of the splines, K.
std::size_t	d ()
	Degree of the splines, d:=K-1.
std::size_t	N ()
	Number of splines, N.
std::size_t	find_i0 (double x)
	Returns the first nonzero spline index i0; Note that i runs [0,N). The last non-zero index is min(i0+K-1, N-1).
std::vector< double >	get (double x)
	Returns a std::vector of all splines {b0, b1, ..., b_N-1} evaluated at x.
std::pair< std::size_t, LinAlg::Matrix< double > >	get_nonzero (double x, std::size_t n_deriv)
	Returns a pair {i0, M}, where i0 is spline index of first non-zero spline, and M is a matrix of non-zero splines and their derivatives. M_ij contains the jth derivative of the spline b[i+i0] evaulated at x.
void	print_knots () const

Detailed Description

Calculates basis of N B-splines of order K (degree K-1), defined over range [0, xmax]. x0 is first non-zero ("internal") knot point.

N - K + 2 break-points "internal knots" placed between [x0,xmax]. By default: on a logarithmic scale May also be placed on a linear or log-linear scale If log-linear scale, b=(xmax/2) (see qip::loglinear_range) knots are the same as breakpoints, but the ends are repeated K times. Uses the GSL Bspline library, gsl/gsl_bspline.h https://www.gnu.org/software/gsl/doc/html/bspline.html See also: Bachau et al., Reports Prog. Phys. 64, 1815 (2001).

Constructor & Destructor Documentation

BSpline()

BSpline::BSpline ( std::size_t  n, std::size_t  k, double  x0, double  xmax, KnotDistro  kd = KnotDistro::logarithmic  )

inline

Constructs basis of n splines of order k, defined over [0,xmax]. x0 is first non-zero knot. kd = { logarithmic, linear, loglinear }.

Member Function Documentation

K()

std::size_t BSpline::K ( )

inline

Order of the splines, K.

d()

std::size_t BSpline::d ( )

inline

Degree of the splines, d:=K-1.

N()

std::size_t BSpline::N ( )

inline

Number of splines, N.

find_i0()

std::size_t BSpline::find_i0 ( double  x )

inline

Returns the first nonzero spline index i0; Note that i runs [0,N). The last non-zero index is min(i0+K-1, N-1).

get()

std::vector< double > BSpline::get ( double  x )

inline

Returns a std::vector of all splines {b0, b1, ..., b_N-1} evaluated at x.

get_nonzero()

std::pair< std::size_t, LinAlg::Matrix< double > > BSpline::get_nonzero ( double  x, std::size_t  n_deriv  )

inline

Returns a pair {i0, M}, where i0 is spline index of first non-zero spline, and M is a matrix of non-zero splines and their derivatives. M_ij contains the jth derivative of the spline b[i+i0] evaulated at x.

• n_deriv is the maximum derivative calculated (inclusive).
• Matrix M is has K rows, and (n_deriv+1) columns.
• If x>xmax, will return a matrix of zeros, and i0+K will be >N
• If x=xmax, only last spline is nonzero, still i0+K=N [lower derivs may be non-zero]

---

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

• Maths/BSpline.hpp