Interpolating Cubic Spline
Computes the natural interpolation cubic spline.
cubicspline(x, y, xi = NULL, endp2nd = FALSE, der = c(0, 0))
x, y |
x- and y-coordinates of points to be interpolated. |
xi |
x-coordinates of points at which the interpolation is to be performed. |
endp2nd |
logical; if true, the derivatives at the endpoints are
prescribed by |
der |
a two-components vector prescribing derivatives at endpoints. |
cubicspline computes the values at xi of the natural
interpolating cubic spline that interpolate the values y at the
nodes x. The derivatives at the endpoints can be prescribed.
Returns either the interpolated values at the points xi or, if
is.null(xi), the piecewise polynomial that represents the spline.
From the piecewise polynomial returned one can easily generate the spline function, see the examples.
Quarteroni, Q., and F. Saleri (2006). Scientific Computing with Matlab and Octave. Springer-Verlag Berlin Heidelberg.
## Example: Average temperatures at different latitudes
x <- seq(-55, 65, by = 10)
y <- c(-3.25, -3.37, -3.35, -3.20, -3.12, -3.02, -3.02,
-3.07, -3.17, -3.32, -3.30, -3.22, -3.10)
xs <- seq(-60, 70, by = 1)
# Generate a function for this
pp <- cubicspline(x, y)
ppfun <- function(xs) ppval(pp, xs)
## Not run:
# Plot with and without endpoint correction
plot(x, y, col = "darkblue",
xlim = c(-60, 70), ylim = c(-3.5, -2.8),
xlab = "Latitude", ylab = "Temp. Difference",
main = "Earth Temperatures per Latitude")
lines(spline(x, y), col = "darkgray")
grid()
ys <- cubicspline(x, y, xs, endp2nd = TRUE) # der = 0 at endpoints
lines(xs, ys, col = "red")
ys <- cubicspline(x, y, xs) # no endpoint condition
lines(xs, ys, col = "darkred")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.