R: interpolate a value from dataframe based on two inputs

Question

I have a data frame that looks like this:

  Teff logg M_div_H       U       B      V      R      I     J     H     K     L Lprime     M
1 2000  4.0    -0.1 -13.443 -11.390 -7.895 -4.464 -1.831 1.666 3.511 2.701 4.345  4.765 5.680
2 2000  4.5    -0.1 -13.402 -11.416 -7.896 -4.454 -1.794 1.664 3.503 2.728 4.352  4.772 5.687
3 2000  5.0    -0.1 -13.358 -11.428 -7.888 -4.431 -1.738 1.664 3.488 2.753 4.361  4.779 5.685
4 2000  5.5    -0.1 -13.220 -11.079 -7.377 -4.136 -1.483 1.656 3.418 2.759 4.355  4.753 5.638
5 2200  3.5    -0.1 -11.866  -9.557 -6.378 -3.612 -1.185 1.892 3.294 2.608 3.929  4.289 4.842
6 2200  4.5    -0.1 -11.845  -9.643 -6.348 -3.589 -1.132 1.874 3.310 2.648 3.947  4.305 4.939
...

Let's say I have two values:

input_Teff = 4.8529282904170595E+003
input_log_g = 1.9241934741026787E+000

Notice how every V value has a unique Teff, logg combination. From the input values, I would like to interpolate a value for V. Is there a way to do this in R?

Edit 1: Here is the link to the full data frame: https://www.dropbox.com/s/prbceabxmd25etx/lcb98cor.dat?dl=0

Answer 1

Building on Ian Campbell's observation that you can consider your data as points on a two-dimensional plane, you can use spatial interpolation methods. The simplest approach is inverse-distance weighting, which you can implement like this

library(data.table) 
d <- fread("https://www.dropbox.com/s/prbceabxmd25etx/lcb98cor.dat?dl=1")
setnames(d,"#Teff","Teff")

First rescale the data as appropriate (not shown here, see Ian's answer)

library(gstat)
# fit model
idw <- gstat(id="V", formula = V~1, locations = ~Teff+logg, data=d, nmax=7, set=list(idp = .5))

# new "points" to predict to 
newd <- data.frame(Teff=c(4100, 4852.928), logg=c(1.5, 1.9241934741026787))

p <- predict(idw, newd)
#[inverse distance weighted interpolation]
p$V.pred
#[1] -0.9818571 -0.3602857

For higher dimensions you could use fields::Tps (I think you can force that to be an exact method, that is, exactly honor the observations, by making each observation a node)

Answer 2

We can imagine that Teff and logg exist in a 2-dimensional plane. We can see that your input point exists in that same space:

library(tidyverse)
ggplot(data,aes(x = Teff, y = logg)) +
  geom_point() +
  geom_point(data = data.frame(Teff = 4.8529282904170595e3, logg = 1.9241934741026787),
             color = "orange")

However, we can see the scale of Teff and logg are not the same. Simply taking log(Teff) gets us pretty close, but not quite. So we can rescale between 0 and 1 instead. We can create a custom rescale function. It will become clear why we can't use scales::rescale in a moment.

rescale = function(x,y){(x - min(y))/(max(y)-min(y))}

We can now rescale the data:

data %>% 
  mutate(Teff.scale = rescale(Teff,Teff),
         logg.scale = rescale(logg,logg)) -> data

From here, we might use raster::pointDistance to calculate the distance from the input point to all of the scaled values:

raster::pointDistance(cbind(rescale(input_Teff,data$Teff),rescale(input_log_g,data$logg)),
                      data[,c("Teff.scale","logg.scale")],
                      lonlat = FALSE)

We can use which.min to find the row with the minimum distance:

data[which.min(raster::pointDistance(cbind(rescale(input_Teff,data$Teff),rescale(input_log_g,data$logg)),
                                     data[,c("Teff.scale","logg.scale")],
                                     lonlat = FALSE)),]
   Teff logg M_div_H      U      B      V     R     I     J     H     K     L Lprime     M Teff.scale logg.scale
1: 4750    2    -0.1 -2.447 -1.438 -0.355 0.159 0.589 1.384 1.976 1.881 2.079  2.083 2.489 0.05729167  0.4631902

Here we can visualize the result:

ggplot(data,aes(x = Teff.scale, y = logg.scale)) +
  geom_point() +
  geom_point(data = data[which.min(raster::pointDistance(cbind(rescale(input_Teff,data$Teff),rescale(input_log_g,data$logg)),data[,c("Teff.scale","logg.scale")], FALSE)),],
             color = "blue") +
  geom_point(data = data.frame(Teff.scale = rescale(input_Teff,data$Teff),logg.scale = rescale(input_log_g,data$logg)),
             color = "orange")

And access the appropriate value for V:

data[which.min(raster::pointDistance(cbind(rescale(input_Teff,data$Teff),rescale(input_log_g,data$logg)),data[,c("Teff.scale","logg.scale")], FALSE)),"V"]
        V
1: -0.355

Data:

library(data.table)
data <- fread("https://www.dropbox.com/s/prbceabxmd25etx/lcb98cor.dat?dl=1")
setnames(data,"#Teff","Teff")
input_Teff = 4.8529282904170595E+003
input_log_g = 1.9241934741026787E+000