| interp {akima} | R Documentation |
These functions implement bivariate interpolation onto a grid for irregularly spaced input data. Bilinear or bicubic spline interpolation is applied using different versions of algorithms from Akima.
interp(x, y, z, xo=seq(min(x), max(x), length = 40),
yo=seq(min(y), max(y), length = 40),
linear = TRUE, extrap=FALSE, duplicate = "error", dupfun = NULL, ncp = NULL)
interp.old(x, y, z, xo= seq(min(x), max(x), length = 40),
yo=seq(min(y), max(y), length = 40), ncp = 0,
extrap=FALSE, duplicate = "error", dupfun = NULL)
interp.new(x, y, z, xo = seq(min(x), max(x), length = 40),
yo = seq(min(y), max(y), length = 40), linear = FALSE,
ncp = NULL, extrap=FALSE, duplicate = "error", dupfun = NULL)
x |
vector of x-coordinates of data points. Missing values are not accepted. |
y |
vector of y-coordinates of data points. Missing values are not accepted. |
z |
vector of z-coordinates of data points.
Missing values are not accepted.
x, y, and z must be the same length and may
contain no fewer than four points. The points of x and
y cannot be collinear, i.e, they cannot fall on the same line
(two vectors x and y such that y = ax + b for
some a, b will not be accepted). interp is
meant for cases in which you have x, y values
scattered over a plane and a z value for each. If, instead,
you are trying to evaluate a mathematical function, or get a
graphical interpretation of relationships that can be described by a
polynomial, try outer().
|
xo |
vector of x-coordinates of output grid. The default is 40 points
evenly spaced over the range of x. If extrapolation is not being
used (extrap=FALSE, the default), xo should have a
range that is close to or inside of the range of x for the
results to be meaningful.
|
yo |
vector of y-coordinates of output grid; analogous to
xo, see above. |
linear |
logical – indicating wether linear or spline
interpolation should be used. supersedes old ncp parameter |
ncp |
deprecated, use parameter linear. Now only used by
interp.old().
meaning was: number of additional points to be used in computing partial derivatives at each data point. ncp must be either 0 (partial derivatives are not used), or at
least 2 but smaller than the number of data points (and smaller than
25).
|
extrap |
logical flag: should extrapolation be used outside of the convex hull determined by the data points? |
duplicate |
character string indicating how to handle duplicate
data points. Possible values are
|
dupfun |
a function, applied to duplicate points if
duplicate= "user". |
If linear is TRUE (default), linear
interpolation is used in the triangles bounded by data points.
Cubic interpolation is done if linear is set to FALSE.
If extrap is FALSE, z-values for points outside the
convex hull are returned as NA.
No extrapolation can be performed for the linear case.
The interp function handles duplicate (x,y) points
in different ways. As default it will stop with an error message. But
it can give duplicate points an unique z value according to the
parameter duplicate (mean,median or any other
user defined function).
The triangulation scheme used by interp works well if x
and y have similar scales but will appear stretched if they have
very different scales. The spreads of x and y must be
within four orders of magnitude of each other for interp to work.
list with 3 components:
x,y |
vectors of x- and y- coordinates of output grid, the same as the input
argument xo, or yo, if present. Otherwise, their
default, a vector 40 points evenly spaced over the range of the
input x. |
z |
matrix of fitted z-values. The value z[i,j] is computed
at the x,y point xo[i], yo[j]. z has
dimensions length(xo) times length(yo). |
interp is a wrapper for the two versions interp.old (it
uses (almost) the same Fortran code from Akima 1978 as the S-Plus version) and
interp.new
(it is based on new Fortran code from Akima 1996). For linear
interpolation the old version is choosen, but spline interpolation is
done by the new version.
Earlier versions (pre 0.5-1) of interp used the parameter
ncp to choose between linear and cubic interpolation, this is now done
by setting the logical parameter linear. Use of ncp is still
possible, but is deprecated.
The resulting structure is suitable for input to the
functions contour and image. Check
the requirements of these functions when choosing values for
xo and yo.
Akima, H. (1978). A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points. ACM Transactions on Mathematical Software 4, 148-164.
Akima, H. (1996). Algorithm 761: scattered-data surface fitting that has the accuracy of a cubic polynomial. ACM Transactions on Mathematical Software 22, 362–371.
contour, image,
approx, spline,
aspline,
outer, expand.grid.
data(akima)
plot(y ~ x, data = akima, main = "akima example data")
with(akima, text(x, y, formatC(z,dig=2), adj = -0.1))
## linear interpolation
akima.li <- interp(akima$x, akima$y, akima$z)
image (akima.li, add=TRUE)
contour(akima.li, add=TRUE)
points (akima, pch = 3)
## increase smoothness (using finer grid):
akima.smooth <-
with(akima, interp(x, y, z, xo=seq(0,25, length=100),
yo=seq(0,20, length=100)))
image (akima.smooth, main = "interp(<akima data>, *) on finer grid")
contour(akima.smooth, add = TRUE, col = "thistle")
points(akima, pch = 3, cex = 2, col = "blue")
# use triangulation package to show underlying triangulation:
if(library(tripack, logical.return=TRUE))
plot(tri.mesh(akima), add=TRUE, lty="dashed")
# use only 15 points (interpolation only within convex hull!)
akima.part <- with(akima, interp(x[1:15], y[1:15], z[1:15]))
image(akima.part)
title("interp() on subset of only 15 points")
contour(akima.part, add=TRUE)
points(akima$x[1:15],akima$y[1:15], col = "blue")
## spline interpolation, two variants (AMS 526 "Old", AMS 761 "New")
## -----------------------------------------------------------------
## "Old": use 5 points to calculate derivatives -> many NAs
akima.sO <- interp.old(akima$x, akima$y, akima$z,
xo=seq(0,25, length=100), yo=seq(0,20, length=100), ncp=5)
table(is.na(akima.sO$z)) ## 3990 NA's; = 40 %
akima.sO <- with(akima,
interp.old(x,y,z, xo=seq(0,25, length=100), yo=seq(0,20, len=100), ncp = 4))
sum(is.na(akima.sO$z)) ## still 3429
image (akima.sO, main = "interp.old(*, ncp = 4) [almost useless]")
contour(akima.sO, add = TRUE)
## "New:"
akima.spl <- with(akima, interp.new(x,y,z, xo=seq(0,25, length=100),
yo=seq(0,20, length=100)))
## equivalent call via setting linear=FALSE in interp():
akima.spl <- with(akima, interp(x,y,z, xo=seq(0,25, length=100),
yo=seq(0,20, length=100),
linear=FALSE))
contour(akima.spl, main = "smooth interp(*, linear = FALSE)")
points(akima)
full.pal <- function(n) hcl(h = seq(340, 20, length = n))
cool.pal <- function(n) hcl(h = seq(120, 0, length = n) + 150)
warm.pal <- function(n) hcl(h = seq(120, 0, length = n) - 30)
filled.contour(akima.spl, color.palette = full.pal,
plot.axes = { axis(1); axis(2);
title("smooth interp(*, linear = FALSE)");
points(akima, pch = 3, col= hcl(c=100, l = 20))})
# no extrapolation!
## example with duplicate points :
data(airquality)
air <- subset(airquality,
!is.na(Temp) & !is.na(Ozone) & !is.na(Solar.R))
# gives an error {duplicate ..}:
try( air.ip <- interp(air$Temp,air$Solar.R,air$Ozone, linear=FALSE) )
# use mean of duplicate points:
air.ip <- with(air, interp(Temp, Solar.R, log(Ozone), duplicate = "mean",
linear = FALSE))
image(air.ip, main = "Airquality: Ozone vs. Temp and Solar.R")
with(air, points(Temp, Solar.R))