Interpolating Cubic Spline

Computes the natural interpolation cubic spline.

cubicspline(x, y, xi = NULL, endp2nd = FALSE, der = c(0, 0))

Arguments

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.

der

a two-components vector prescribing derivatives at endpoints.

Details

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.

Value

Returns either the interpolated values at the points xi or, if is.null(xi), the piecewise polynomial that represents the spline.

Note

From the piecewise polynomial returned one can easily generate the spline function, see the examples.

References

Quarteroni, Q., and F. Saleri (2006). Scientific Computing with Matlab and Octave. Springer-Verlag Berlin Heidelberg.

See also

spline

Examples

##  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)

if (FALSE) { # \dontrun{
# 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")
} # }