BSpline

ok

Basis of N B-splines of order K (degree K-1), defined over [0, xmax].

Constructs and evaluates a B-spline basis using the GSL B-spline library (gsl/gsl_bspline.h). See also: Bachau et al., Rep. Prog. Phys. 64, 1815 (2001).

Knot structure:**

• N - K + 2 breakpoints (internal knots) are placed in [x0, xmax], where x0 is the first non-zero knot. The point 0 is prepended, giving N - K + 2 breakpoints total spanning [0, xmax].
• The full knot vector repeats the endpoints K times.

• Breakpoints may be placed on a logarithmic (default), linear, or log-linear scale; see KnotDistro.

  Compatibility:** Supports GSL v2.x (<2.8), and v2.8+. API differences are handled internally via compile-time version macros. Should also support v1.x, but this is difficult to test.

Copy construction and copy assignment are deleted (GSL workspace is not copyable).

#include <BSpline.hpp>

Public Types
enum class	KnotDistro { logarithmic , linear , loglinear }
	Distribution of internal knot points. More...

Public Member Functions
	BSpline (std::size_t n, std::size_t k, double x0, double xmax, KnotDistro kd=KnotDistro::logarithmic)
	Construct a basis of N B-splines of order K over [0, xmax].
BSpline &	operator= (const BSpline &)=delete
	Copy assignment deleted: GSL workspace is not copyable.
	BSpline (const BSpline &)=delete
	Copy construction deleted: GSL workspace is not copyable.
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 index i0 of the first non-zero spline at x. Spline indices run [0, N); at most K splines are non-zero at any x, occupying indices [i0, min(i0+K-1, N-1)].
std::vector< double >	get (double x)
	Returns all N spline values {b_0(x), b_1(x), ..., b_{N-1}(x)}. Returns a vector of zeros if x is outside [0, xmax].
std::pair< std::size_t, LinAlg::Matrix< double > >	get_nonzero (double x, std::size_t n_deriv)
	Returns the non-zero splines and their derivatives at x.
void	print_knots () const
	Prints the full knot vector to stdout (N+K values).

Member Enumeration Documentation

KnotDistro

enum class BSpline::KnotDistro

strong

Distribution of internal knot points.

Enumerator
logarithmic	Knots on a logarithmic scale (default; suits bound-state grids)
linear	Knots evenly spaced.
loglinear	Log-linear blend; midpoint at xmax/2.

Constructor & Destructor Documentation

BSpline() [1/2]

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

inline

Construct a basis of N B-splines of order K over [0, xmax].

Parameters

n	Number of splines N. Must satisfy N > K.
k	Order K (degree K-1). E.g. K=4 gives cubic splines.
x0	First non-zero (internal) knot; must satisfy 0 < x0 < xmax.
xmax	Upper bound of the spline domain.
kd	Knot distribution: logarithmic (default), linear, or loglinear.

BSpline() [2/2]

BSpline::BSpline ( const BSpline &  )

delete

Copy construction deleted: GSL workspace is not copyable.

Member Function Documentation

operator=()

BSpline & BSpline::operator= ( const BSpline &  )

delete

Copy assignment deleted: GSL workspace is not copyable.

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 index i0 of the first non-zero spline at x. Spline indices run [0, N); at most K splines are non-zero at any x, occupying indices [i0, min(i0+K-1, N-1)].

get()

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

inline

Returns all N spline values {b_0(x), b_1(x), ..., b_{N-1}(x)}. Returns a vector of zeros if x is outside [0, xmax].

get_nonzero()

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

inline

Returns the non-zero splines and their derivatives at x.

Returns {i0, M}, where:

• i0 is the index of the first non-zero spline,
• M is a K (n_deriv+1) matrix; M(i, j) is the j-th derivative of spline b[i0 + i] evaluated at x.

At most K splines are non-zero at any x. This is more efficient than get() when only the non-zero splines are needed.

If x > xmax, returns a zero matrix with i0+K > N. If x = xmax, only the last spline is non-zero (lower derivatives may not be zero).

Parameters

x	Evaluation point.
n_deriv	Maximum derivative order to compute (inclusive).

Returns

Pair {i0, M}.

print_knots()

void BSpline::print_knots ( ) const

inline

Prints the full knot vector to stdout (N+K values).

---

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

• Maths/BSpline.hpp