| Title: | Integral of B-Spline Functions |
|---|---|
| Description: | Calculate B-spline basis functions with a given set of knots and order, or a B-spline function with a given set of knots and order and set of de Boor points (coefficients), or the integral of a B-spline function. |
| Authors: | Feng Chen |
| Maintainer: | Feng Chen <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.4 |
| Built: | 2025-01-10 05:19:02 UTC |
| Source: | https://github.com/cran/ibs |
Evaluate the integral of a B-spline function, or the B-spline function itself, or the B-spline basis functions.
The function bsbases calculates the values of the B-spline basis
functions defined by knots knots and order ord at sites
x. The function bspline evaluates the B-spline function
defined by knots knots, order ord, and coefficients
coef at sites x. The function ibs calculates the
integrals of the B-spline function defined by knots knots,
order ord, and coefficients coef from the smallest knot
to each of the values in x.
Creator: Feng Chen
Maintainer: Feng Chen <[email protected]>
de Boor, C. (2001) A Practical Guide to Splines. Revised Edition. Springer: New York.
Evaluate the B-spline basis function at the x value(s).
bsbases(x, knots, ord)bsbases(x, knots, ord)
x |
Numerical value or vector. The value(s) at which to evaluate the B spline bases. |
knots |
Numerical vector. The knot positions/sites of the B-spline bases. |
ord |
An integer >=1. The order of the B-spline bases. Equals degree plus 1. |
A numerical matrix of length(x) rows and
length(knots)-ord columns.
In contrast to the implementation based on the splineDesign
function from the splines package, this version of the B-spline
basis functions are left-continuous at the rightmost knot.
Feng Chen <[email protected]>
de Boor, C. (2001) A Practical Guide to Splines. Revised Edition. Springer: New York.
kns <- c(rep(0,4),1:4*0.2,rep(1,4)) round(bsbases(0:5/5,kns,2),10) round(splines::splineDesign(kns,0:5/5,2),10)kns <- c(rep(0,4),1:4*0.2,rep(1,4)) round(bsbases(0:5/5,kns,2),10) round(splines::splineDesign(kns,0:5/5,2),10)
Evaluate the value of the B-spline function with knots knots,
order ord, and coefficients coef at value(s) x.
bspline(x, knots, ord, coef = rep(1, length(knots) - ord))bspline(x, knots, ord, coef = rep(1, length(knots) - ord))
x |
Numerical value or vector. The value(s) at which to evaluate the B-spline. |
knots |
Numerical vector. The knot positions/sites of the B-spline function. |
ord |
An integer >=1. The order of the B-spline function. Equals degree plus 1. |
coef |
A numerical vector. The coefficients (de Boor points) defining the B-spline function. |
A scalar or a vector of length equal to that of x.
In contrast to the implementation based on the splineDesign
function from the splines package, this version of the B-spline
function is left-continuous at the rightmost knot site.
Feng Chen <[email protected]>
de Boor, C. (2001) A Practical Guide to Splines. Revised Edition. Springer: New York.
kns <- c(rep(0,4),1:4*0.2,rep(1,4)) bspline(0:10/10,kns,3,rep(1,length(kns)-3)) splines::splineDesign(kns,0:10/10,3)%*%rep(1,length(kns)-3)kns <- c(rep(0,4),1:4*0.2,rep(1,4)) bspline(0:10/10,kns,3,rep(1,length(kns)-3)) splines::splineDesign(kns,0:10/10,3)%*%rep(1,length(kns)-3)
Calculate the integral of a B-spline function.
ibs(x, knots, ord=4, coef = rep(1, length(knots) - ord))ibs(x, knots, ord=4, coef = rep(1, length(knots) - ord))
x |
Numerical value or vector. The value(s) at which to evaluate the
integral of the B-spline; must be in the interval bewteen the
smallest knot to the |
knots |
Numerical vector. The knot positions/sites of the B-spline function to be integrated. |
ord |
An integer >=1. The order of the B-spline integrand function to be integrated. Equals degree plus 1. |
coef |
A numerical vector. The coefficients (de Boor points) defining the B-spline integrand function. |
The function returns the integral(s) of the B-spline function
specified by knots knots, order ord, and coefficients
coef, from the minimum knot position to each x
value. The evaluation is based on a closed form expression of the
integral in terms of higher order B-splines, given on page 128 of de
Boor (2001).
A numerical equal to the integral(s).
Feng Chen <[email protected]>
de Boor, C (2001) A Practical Guide to Splines. Revised Edition. Springer: New York.
kns <- c(rep(0,4),1:4*0.2,rep(1,4)) co <- rnorm(length(kns)-3) integrate(bspline,knots=kns,ord=3,coef=co,0,0.95) integrate(function(x)bsbases(x,kns,3) %*% co,0,0.95) ibs(0.95,kns,3,co)kns <- c(rep(0,4),1:4*0.2,rep(1,4)) co <- rnorm(length(kns)-3) integrate(bspline,knots=kns,ord=3,coef=co,0,0.95) integrate(function(x)bsbases(x,kns,3) %*% co,0,0.95) ibs(0.95,kns,3,co)