approxfun {stats} | R Documentation |
Interpolation Functions
Description
Return a list of points which linearly interpolate given data points, or a function performing the linear (or constant) interpolation.
Usage
approx (x, y = NULL, xout, method = "linear", n = 50,
yleft, yright, rule = 1, f = 0, ties = mean, na.rm = TRUE)
approxfun(x, y = NULL, method = "linear",
yleft, yright, rule = 1, f = 0, ties = mean, na.rm = TRUE)
Arguments
x , y |
numeric vectors giving the coordinates of the points to be
interpolated. Alternatively a single plotting structure can be
specified: see |
xout |
an optional set of numeric values specifying where interpolation is to take place. |
method |
specifies the interpolation method to be used. Choices
are |
n |
If |
yleft |
the value to be returned when input |
yright |
the value to be returned when input |
rule |
an integer (of length 1 or 2) describing how interpolation
is to take place outside the interval [ |
f |
for |
ties |
handling of tied |
na.rm |
logical specifying how missing values ( |
Details
The inputs can contain missing values which are deleted (if na.rm
is true, i.e., by default), so at least
two complete (x, y)
pairs are required (for method =
"linear"
, one otherwise). If there are duplicated (tied) x
values and ties
contains a function it is applied to the y
values for each distinct x
value to produce (x,y)
pairs
with unique x
.
Useful functions in this context include mean
,
min
, and max
.
If ties = "ordered"
the x
values are assumed to be already
ordered (and unique) and ties are not checked but kept if present.
This is the fastest option for large length(x)
.
If ties
is a list
of length two, ties[[2]]
must be a function to be applied to ties, see above, but if
ties[[1]]
is identical to "ordered"
, the x
values
are assumed to be sorted and are only checked for ties. Consequently,
ties = list("ordered", mean)
will be slightly more efficient than
the default ties = mean
in such a case.
The first y
value will be used for interpolation to the left and the last
one for interpolation to the right.
Value
approx
returns a list with components x
and y
,
containing n
coordinates which interpolate the given data
points according to the method
(and rule
) desired.
The function approxfun
returns a function performing (linear or
constant) interpolation of the given data points. For a given set of
x
values, this function will return the corresponding
interpolated values. It uses data stored in its environment when it
was created, the details of which are subject to change.
Warning
The value returned by approxfun
contains references to the code
in the current version of R: it is not intended to be saved and
loaded into a different R session. This is safer for R >= 3.0.0.
References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
See Also
spline
and splinefun
for spline
interpolation.
Examples
require(graphics)
x <- 1:10
y <- rnorm(10)
par(mfrow = c(2,1))
plot(x, y, main = "approx(.) and approxfun(.)")
points(approx(x, y), col = 2, pch = "*")
points(approx(x, y, method = "constant"), col = 4, pch = "*")
f <- approxfun(x, y)
curve(f(x), 0, 11, col = "green2")
points(x, y)
is.function(fc <- approxfun(x, y, method = "const")) # TRUE
curve(fc(x), 0, 10, col = "darkblue", add = TRUE)
## different extrapolation on left and right side :
plot(approxfun(x, y, rule = 2:1), 0, 11,
col = "tomato", add = TRUE, lty = 3, lwd = 2)
### Treatment of 'NA's -- are kept if na.rm=FALSE :
xn <- 1:4
yn <- c(1,NA,3:4)
xout <- (1:9)/2
## Default behavior (na.rm = TRUE): NA's omitted; extrapolation gives NA
data.frame(approx(xn,yn, xout))
data.frame(approx(xn,yn, xout, rule = 2))# -> *constant* extrapolation
## New (2019-2020) na.rm = FALSE: NA's are "kept"
data.frame(approx(xn,yn, xout, na.rm=FALSE, rule = 2))
data.frame(approx(xn,yn, xout, na.rm=FALSE, rule = 2, method="constant"))
## NA's in x[] are not allowed:
stopifnot(inherits( try( approx(yn,yn, na.rm=FALSE) ), "try-error"))
## Give a nice overview of all possibilities rule * method * na.rm :
## ----------------------------- ==== ====== =====
## extrapolations "N":= NA; "C":= Constant :
rules <- list(N=1, C=2, NC=1:2, CN=2:1)
methods <- c("constant","linear")
ry <- sapply(rules, function(R) {
sapply(methods, function(M)
sapply(setNames(,c(TRUE,FALSE)), function(na.)
approx(xn, yn, xout=xout, method=M, rule=R, na.rm=na.)$y),
simplify="array")
}, simplify="array")
names(dimnames(ry)) <- c("x = ", "na.rm", "method", "rule")
dimnames(ry)[[1]] <- format(xout)
ftable(aperm(ry, 4:1)) # --> (4 * 2 * 2) x length(xout) = 16 x 9 matrix
## Show treatment of 'ties' :
x <- c(2,2:4,4,4,5,5,7,7,7)
y <- c(1:6, 5:4, 3:1)
(amy <- approx(x, y, xout = x)$y) # warning, can be avoided by specifying 'ties=':
op <- options(warn=2) # warnings would be error
stopifnot(identical(amy, approx(x, y, xout = x, ties=mean)$y))
(ay <- approx(x, y, xout = x, ties = "ordered")$y)
stopifnot(amy == c(1.5,1.5, 3, 5,5,5, 4.5,4.5, 2,2,2),
ay == c(2, 2, 3, 6,6,6, 4, 4, 1,1,1))
approx(x, y, xout = x, ties = min)$y
approx(x, y, xout = x, ties = max)$y
options(op) # revert 'warn'ing level