In fzao/interpn: n dimensional linear interpolation

knitr::opts_chunk$set(echo = TRUE)

Short Description

interpn is a N-dimensional linear interpolant based on the original Scilab function linear_interpln

Download the package from GitHub and then install and load it.

library(interpn)

Test functions

1D

Let's play with a simple sinus function:

x <- matrix(0:10, ncol = 11)
y <- sin(x)

We want intermediate values of the function based on the linear interpolation:

xguess <- matrix(1.5:10.5, ncol = 10)
yguess <- interpn(outmode = 2, y, x, xguess)

Note that the point (10.5) is out of bounds, see the value of the argument 'outmode' for some information on the possible extrapolation choices. Here value 4 is for 'by_NaN'.

print(c(sin(10.5), yguess[10]))

Plot the results:

plot(x, y, main = "interpn in 1D", type = "l")
points(xguess, yguess, col = "red")

2D

Let's define two variables now and a summation function:

x1 <- matrix(1:5, ncol = 5)
x2 <- matrix(1:7, ncol = 7)
y <- as.vector(outer(x1, x2, "+"))

Interpolate for three query points:

xguess1 <- c(1.5, 1.6, 1.7)  # dimension 1
xguess2 <- c(2.5, 4.6, 6.7)  # dimension 2
yguess <- interpn(outmode = 2, y, x1, x2, xguess1, xguess2)

print(yguess)

3D

Finally let's see a 3D case with a multiplication function:

nx1 <- 4  # number of points in dimension 1
nx2 <- 7  # number of points in dimension 2
nx3 <- 10  # number of points in dimension 3
ny <- nx1 * nx2 * nx3 # dimension of the output vector y
y <- double(ny)  # size 
x1 <- as.double(seq(1, nx1))  # grid definition
x2 <- as.double(seq(1, nx2))
x3 <- as.double(seq(1, nx3))

The multiplication is done with nested loops:

# function values
a <- 1
for(i in 1:nx3){
    for(j in 1:nx2){
        for(k in 1:nx1){
           y[a] <- x1[k] * x2[j] * x3[i]
           a <- a + 1
        }
    }
 }

Approximating the multiplication...

# two query points
xguess1 <- c(1.5, 2.5)
xguess2 <- c(2.5, 3.5)
xguess3 <- c(5, 10)
yguess <- interpn(0, y, x1, x2, x3, xguess1, xguess2, xguess3)
print(yguess)