One-dimensional Interpolation

One-dimensional interpolation of points.

interp1(x, y, xi = x,
        method = c("linear", "constant", "nearest", "spline", "cubic"))

Arguments

x

Numeric vector; points on the x-axis; at least two points require; will be sorted if necessary.

y

Numeric vector; values of the assumed underlying function; x and y must be of the same length.

xi

Numeric vector; points at which to compute the interpolation; all points must lie between min(x) and max(x).

method

One of “constant", “linear", “nearest", “spline", or “cubic"; default is “linear"

Details

Interpolation to find yi, the values of the underlying function at the points in the vector xi.

Methods can be:

linearlinear interpolation (default)
constantconstant between points
nearestnearest neighbor interpolation
splinecubic spline interpolation
cubiccubic Hermite interpolation

Value

Numeric vector representing values at points xi.

Note

Method `spline' uses the spline approach by Moler et al., and is identical with the Matlab option of the same name, but slightly different from R's spline function.

The Matlab option “cubic” seems to have no direct correspondence in R. Therefore, we simply use pchip here.

See also

approx, spline

Examples

x <- c(0.8, 0.3, 0.1, 0.6, 0.9, 0.5, 0.2, 0.0, 0.7, 1.0, 0.4)
y <- x^2
xi <- seq(0, 1, len = 81)
yl <- interp1(x, y, xi, method = "linear")
#> Warning: Points in argument in 'x' unsorted; will be sorted.
yn <- interp1(x, y, xi, method = "nearest")
#> Warning: Points in argument in 'x' unsorted; will be sorted.
ys <- interp1(x, y, xi, method = "spline")
#> Warning: Points in argument in 'x' unsorted; will be sorted.

if (FALSE) { # \dontrun{
plot(x, y); grid()
lines(xi, yl, col="blue", lwd = 2)
lines(xi, yn, col="black", lty = 2)
lines(xi, ys, col="red")
  } # }

## Difference between spline (Matlab) and spline (R).
x <- 1:6
y <- c(16, 18, 21, 17, 15, 12)
xs <- linspace(1, 6, 51)
ys <- interp1(x, y, xs, method = "spline")
sp <- spline(x, y, n = 51, method = "fmm")

if (FALSE) { # \dontrun{
plot(x, y, main = "Matlab and R splines")
grid()
lines(xs, ys, col = "red")
lines(sp$x, sp$y, col = "blue")
legend(4, 20, c("Matlab spline", "R spline"), 
              col = c("red", "blue"), lty = 1)
  } # }