smint (version 0.4.0)

cardinalBasis_natSpline: 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.

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.

Details

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

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")