splinefun {stats} | R Documentation |
Perform cubic (or Hermite) spline interpolation of given data points, returning either a list of points obtained by the interpolation or a function performing the interpolation.
splinefun(x, y = NULL, method = c("fmm", "periodic", "natural", "monoH.FC"),
ties = mean)
spline(x, y = NULL, n = 3*length(x), method = "fmm",
xmin = min(x), xmax = max(x), xout, ties = mean)
splinefunH(x, y, m)
x , y |
vectors giving the coordinates of the points to be
interpolated. Alternatively a single plotting structure can be
specified: see |
m |
(for |
method |
specifies the type of spline to be used. Possible
values are |
n |
if |
xmin , xmax |
left-hand and right-hand endpoint of the
interpolation interval (when |
xout |
an optional set of values specifying where interpolation is to take place. |
ties |
Handling of tied |
The inputs can contain missing values which are deleted, so at least
one complete (x, y)
pair is required.
If method = "fmm"
, the spline used is that of Forsythe, Malcolm
and Moler (an exact cubic is fitted through the four points at each
end of the data, and this is used to determine the end conditions).
Natural splines are used when method = "natural"
, and periodic
splines when method = "periodic"
.
The new (R 2.8.0) method "monoH.FC"
computes a monotone
Hermite spline according to the method of Fritsch and Carlson. It
does so by determining slopes such that the Hermite spline, determined
by (x_i,y_i,m_i)
, is monotone (increasing or
decreasing) iff the data are.
These interpolation splines can also be used for extrapolation, that is
prediction at points outside the range of x
. Extrapolation
makes little sense for method = "fmm"
; for natural splines it
is linear using the slope of the interpolating curve at the nearest
data point.
spline
returns a list containing components x
and
y
which give the ordinates where interpolation took place and
the interpolated values.
splinefun
returns a function with formal arguments x
and
deriv
, the latter defaulting to zero. This function
can be used to evaluate the interpolating cubic spline
(deriv
=0), or its derivatives (deriv
=1,2,3) at the
points x
, where the spline function interpolates the data
points originally specified. This is often more useful than
spline
.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Forsythe, G. E., Malcolm, M. A. and Moler, C. B. (1977) Computer Methods for Mathematical Computations.
Fritsch, F. N. and Carlson, R. E. (1980) Monotone piecewise cubic interpolation, SIAM Journal on Numerical Analysis 17, 238–246.
approx
and approxfun
for constant and
linear interpolation.
Package splines, especially interpSpline
and periodicSpline
for interpolation splines.
That package also generates spline bases that can be used for
regression splines.
smooth.spline
for smoothing splines.
require(graphics)
op <- par(mfrow = c(2,1), mgp = c(2,.8,0), mar = .1+c(3,3,3,1))
n <- 9
x <- 1:n
y <- rnorm(n)
plot(x, y, main = paste("spline[fun](.) through", n, "points"))
lines(spline(x, y))
lines(spline(x, y, n = 201), col = 2)
y <- (x-6)^2
plot(x, y, main = "spline(.) -- 3 methods")
lines(spline(x, y, n = 201), col = 2)
lines(spline(x, y, n = 201, method = "natural"), col = 3)
lines(spline(x, y, n = 201, method = "periodic"), col = 4)
legend(6,25, c("fmm","natural","periodic"), col=2:4, lty=1)
y <- sin((x-0.5)*pi)
f <- splinefun(x, y)
ls(envir = environment(f))
splinecoef <- get("z", envir = environment(f))
curve(f(x), 1, 10, col = "green", lwd = 1.5)
points(splinecoef, col = "purple", cex = 2)
curve(f(x, deriv=1), 1, 10, col = 2, lwd = 1.5)
curve(f(x, deriv=2), 1, 10, col = 2, lwd = 1.5, n = 401)
curve(f(x, deriv=3), 1, 10, col = 2, lwd = 1.5, n = 401)
par(op)
## Manual spline evaluation --- demo the coefficients :
.x <- splinecoef$x
u <- seq(3,6, by = 0.25)
(ii <- findInterval(u, .x))
dx <- u - .x[ii]
f.u <- with(splinecoef,
y[ii] + dx*(b[ii] + dx*(c[ii] + dx* d[ii])))
stopifnot(all.equal(f(u), f.u))
## An example with ties (non-unique x values):
set.seed(1); x <- round(rnorm(30), 1); y <- sin(pi * x) + rnorm(30)/10
plot(x,y, main="spline(x,y) when x has ties")
lines(spline(x,y, n= 201), col = 2)
## visualizes the non-unique ones:
tx <- table(x); mx <- as.numeric(names(tx[tx > 1]))
ry <- matrix(unlist(tapply(y, match(x,mx), range, simplify=FALSE)),
ncol=2, byrow=TRUE)
segments(mx, ry[,1], mx, ry[,2], col = "blue", lwd = 2)
## An example of monotone interpolation
n <- 20
set.seed(11)
x. <- sort(runif(n)) ; y. <- cumsum(abs(rnorm(n)))
plot(x.,y.)
curve(splinefun(x.,y.)(x), add=TRUE, col=2, n=1001)
curve(splinefun(x.,y., method="mono")(x), add=TRUE, col=3, n=1001)
legend("topleft", paste("splinefun( \"", c("fmm", "monoH.CS"), "\" )", sep=''),
col=2:3, lty=1)