ModuleBase::Bspline Class Reference

A class to treat Cardinal B-spline interpolation. More...

#include <math_bspline.h>

Collaboration diagram for ModuleBase::Bspline:

Public Member Functions
	Bspline ()
	~Bspline ()
void	init (int norderin, double Dxin, double xiin)
void	getbspline (double x)
double	bezier_ele (int n)

Private Attributes
int	norder
double	Dx
double	xi
double *	bezier

Detailed Description

A class to treat Cardinal B-spline interpolation.

Author

qianrui created 2021-09-14

see: J. Chem. Phys. 103, 8577 (1995). Math: Only uniform nodes are considered: xm-x[m-1]=Dx(>= 0) for control node: X={x0,x1,...,xm}; Any function p(x) can be written by p(x)=\sum_i{ci*M_ik(x)} (k->infinity), where M_ik is the i-th k-order Cardinal B-spline base function and ci is undetermined coefficient. M_i0 = H(x-xi)-H(x-x[i+1]), H(x): step function x-xi x[i+k+1]-x M_ik(x)= ------—*M_i(k-1)(x)+ -------------—*M_[i+1][k-1](x) ( xi <= x <= x[i+1] ) x[i+k]-xi x[i+k+1]-x[i+1] For uniform nodes: M_[i+1]k(x+Dx)=M_ik(x) If we define Bk[n] stores M_ik(x+n*Dx) for x in (xi,xi+Dx): x+n*Dx-xi xi+(k-n+1)*Dx-x Bk[n] = --------—*B(k-1)[n] + --------------—*B(k-1)[n-1] k*Dx k*Dx USAGE: ModuleBase::Bspline bp; bp.init(10,0.7,2); //Dx = 0.7, xi = 2 bp.getbslpine(0.5); //x = 0.5 cout<<bp.bezier_ele(3)<<endl; //print M_ik[xi+3*Dx+x]: M_i10

Constructor & Destructor Documentation

Bspline()

ModuleBase::Bspline::Bspline

(

)

~Bspline()

ModuleBase::Bspline::~Bspline

(

)

Member Function Documentation

bezier_ele()

double ModuleBase::Bspline::bezier_ele

(

int

n

)

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getbspline()

void ModuleBase::Bspline::getbspline

(

double

x

)

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init()

void ModuleBase::Bspline::init	(	int	norderin,
		double	Dxin,
		double	xiin
	)

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Member Data Documentation

bezier

double* ModuleBase::Bspline::bezier

private

Dx

double ModuleBase::Bspline::Dx

private

norder

int ModuleBase::Bspline::norder

private

xi

double ModuleBase::Bspline::xi

private

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

• /home/runner/work/abacus-develop/abacus-develop/source/source_base/math_bspline.h
• /home/runner/work/abacus-develop/abacus-develop/source/source_base/math_bspline.cpp