integral.dierckx: Spline Integration
In DierckxSpline: R companion to "Curve and Surface Fitting with Splines"

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates the integral of a spline function s(x) of degree k, which is given in its normalized b-spline representation

1 2	## S3 method for class 'dierckx' integral(expr, from = NULL, to = NULL, ...)

`expr`	An object of class `dierckx`.
`from`	Lower integration bound. If `NULL`, the minimum knot value is used.
`to`	Upper integration bound. If `NULL`, the maximum knot value is used.
`...`	ignored

s(x) is considered to be identically zero outside the interval (t(k+1),t(n-k)), where t are the knot values. For this reason, from and to are forced to be in or on the boundaries of the knots.

The value of the integral.

Sundar Dorai-Raj with help from William Venables on how to eliminate a conflict between the generic integral functions in the PolynomF and DierckxSpline packages.

Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications.

integral, curfit, deriv.dierckx, spline, smooth.spline

x <- seq(0, 1, 0.1)
y <- (1 - x)^3
z <- curfit(x, y, knots = seq(0, 1, 0.2))

plot(x, y, type = "p")
lines(x, fitted(z), col = "blue")

(answer <- integrate(function(x) (1 - x)^3, 0, 1))
#0.25 with absolute error < 2.8e-15
integral(z)-answer$value
# 0

(ans2 <- integrate(function(x) (1 - x)^3, 0.5, 0.6))
#0.009225 with absolute error < 1.0e-16
integral(z, 0.5, 0.6)-ans2$value
# 6e-9