cardinalBasis_natSpline: Cardinal Basis for natural cubic spline interpolation

In IRSN/smint: Smooth Multivariate Interpolation for Gridded and Scattered Data

Cardinal Basis for natural cubic spline interpolation

Description

Cardinal Basis for natural cubic spline interpolation.

Usage

cardinalBasis_natSpline(x, xout, deriv = 0)

Arguments

x	Numeric vector of design points.
xout	Numeric vector of new points.
deriv	Integer. Order of derivation. Can be 0, 1 or 2.

Details

This is a simple and raw interface to splinterp Fortran subroutine.

Value

A list with several elements

x	Numeric vector of abscissas at which the basis is evaluated. This is a copy of xout.
CB	Matrix of the Cardinal Basis function values.
deriv	Order of derivation as given on input.
method	Character description of the method involved in the CB determination.

Author(s)

Yves Deville

Examples

set.seed(123)
n <- 16; nout <- 360
x <- sort(runif(n))

## let 'xout' contain n + nout points including nodes 
xout <- sort(c(x, seq(from =  x[1] + 1e-8, to = x[n] - 1e-8, length.out = nout)))
res  <- cardinalBasis_natSpline(x, xout = xout)

matplot(res$x, res$CB, type = "n", main = "Cardinal Basis")
abline(v = x, h = 1.0, col = "gray")
points(x = x, y = rep(0, n), pch = 21, col = "black", lwd = 2, bg = "white")
matlines(res$x, res$CB, type = "l")

## compare with 'splines'
require(splines)
y <- sin(2* pi * x)
sp <- interpSpline(x, y)
test <- rep(NA, 3)
der <- 0:2
names(test) <- nms <- paste("deriv. ", der, sep = "")
for (i in seq(along = der)) {
   resDer <- cardinalBasis_natSpline(x, xout = xout, deriv = der[i])
   test[nms[i]] = max(abs(predict(sp, xout, deriv = der[i])$y - resDer$CB %*% y))
}
test
## Lebesgue's function
plot(x = xout, y = apply(res$CB, 1, function(x) sum(abs(x))), type = "l",
     lwd = 2, col = "orangered", main = "Lebesgue\'s function", log = "y",
     xlab = "x", ylab = "L(x)")
points(x = x, y = rep(1, n), pch = 21, col = "black", lwd = 2, bg = "white")

IRSN/smint documentation built on Dec. 9, 2023, 9:53 p.m.