ibsp: Indefinite integral of B-spline

In bspline: B-Spline Interpolation and Regression

Indefinite integral of B-spline

Description

Indefinite integral of B-spline

Usage

ibsp(f, const = 0, nint = 1L)

Arguments

f	Function, B-spline such as returned by smbsp() or par2bsp()
const	Numeric scalar or vector of length ncol(qw) where qw is weight matrix of f. Defines starting value of weights for indefinite integral (0 by default).
nint	Integer scalar >= 0, defines how many times to take integral (1 by default)

Details

If f is B-spline, then following identity is held: dbsp(ibsp(f)) is identical to f. Generally, it does not work in the other sens: ibsp(dbsp(f)) is not f but not very far. If we can get an appropriate constant C=f(min(x)) then we can assert that ibsp(dbsp(f), const=C) is the same as f.

Value

Function calculating requested integral

bspline documentation built on April 4, 2025, 4:54 a.m.