smint (version 0.4.2)

interp_ceschino: Ceschino cubic interpolation

Description

Cubic Ceschino interpolation.

Usage

interp_ceschino(x, y = NULL, xout, deriv = 0)

Arguments

x

Numeric vector of design abscissas.

y

Numeric vector of ordinates.

xout

Numeric vector of new points where interpolation must be done.

deriv

Logical or binary integer. Compute the (first order) derivative?

Value

A list with the following elements.

x, y

Coordinates of interpolated points, thus x is a copy of the input xout.

CB

A matrix with length(xout) rows and length(x) columns as returned by cardinalBasis_ceschino. The columns are the values or xout of the $n$ Cardinal Basis functions where $n$ is the length of x.

deriv

Derivation order used.

knots

The knots used in the interpolation. This is a sorted copy of the input x.

Details

Cubic Ceschino interpolation

References

A. Hebert (2013) Revisiting the Ceschino Interpolation Method. link.

Examples

set.seed(12345)
n <- 6; nout <- 300L
x <- sort(runif(n))
xout <- sort(runif(nout, min = x[1], max = x[n]))
y <- sin(2 * pi * x)
cI0 <- interp_ceschino(x = x, xout = xout, y = y)

## compare with a natural spline
require(splines)
spI <- interpSpline(x, y)
spPred0 <- predict(spI, xout)

plot(xout, sin(2 * pi * xout), type = "l", col = "black", lwd = 2,
     xlab = "x", ylab = "f(x)", main = "Interpolations")
abline(v = x, col = "gray")
lines(cI0, type = "l", col = "SpringGreen3", lty = 2, lwd = 2)
lines(spPred0, type = "l", col = "SteelBlue2", lty = 3, lwd = 2)
points(x, y, type = "p", pch = 21, col = "red",
       bg = "yellow", lwd = 2)
legend("topright", legend = c("true", "Ceschino", "nat. spline"),
        col = c("black", "SpringGreen3", "SteelBlue2"),
        lty = 1:3, lwd = rep(2, 3))

## derivative estimation
cI1 <- interp_ceschino(x =x, xout = xout, y = y, deriv = 1)
spPred1 <- predict(spI, xout, deriv = 1)

plot(xout, 2 * pi * cos(2 * pi * xout), type = "l", col = "black", lwd = 2,
     xlab = "x", ylab = "fprime(x)", main = "Derivatives")
abline(v = x, col = "gray")
lines(cI1, type = "l", col = "SpringGreen3", lty = 2, lwd = 2)
lines(spPred1, type = "l", col = "SteelBlue2", lty = 3, lwd = 2)
points(x, 2 * pi * cos(2 * pi * x), type = "p", pch = 21,
       col = "red", bg = "yellow", lwd = 2)
legend("bottomright", legend = c("true", "Ceschino", "nat. spline"),
       col = c("black", "SpringGreen3", "SteelBlue2"),
       lty = 1:3, lwd = rep(2, 3))