Question

I have a vector containing simple time series data (extracted from a deSolve matrix), which for testing purposes can be:

x <- c(1, 2, 3, 4, 5)

and would like to apply the nonlinear filter

x[n]*x[n]-x[n-1]*x[n+1]

to all elements of the vector except the first and last elements because the filter can’t be applied to these two elements (e.g., when the x[n-1] term meets the first element or the x[n+1] term meets the last element). Therein lies my problem.

Things I’ve tried:
1) The filter() command expects a linear filter (i.e., without multiplication of filter coefficients).
2) lapply() requires that the function applies to all elements of the list.

Is a loop the only alternative?

Thanks for your help,
Carey

Answer 1

Can do it with loop or apply or vectorized.

> x <- c(1, 2, 3, 4, 5)
> r <- NA
> for (n in 2:length(x)) r[n] <- x[n]*x[n]-x[n-1]*x[n+1]
> (r)
[1] NA  1  1  1 NA
> 
> r <- NA
> lapply(2:length(x),function(n) r[n] <<- x[n]*x[n]-x[n-1]*x[n+1])
[[1]]
[1] 1

[[2]]
[1] 1

[[3]]
[1] 1

[[4]]
[1] NA

> (r)
[1] NA  1  1  1 NA

> r <- NA
> r <- x^2 - c(NA,x[1:(length(x)-1)]) * c(x[2:length(x)],NA)
> (r)
[1] NA  1  1  1 NA

vectorization is the most efficient but code is harder to decipher

> x <- runif(50000)
> 
> r <- NA
> system.time(for (n in 2:length(x)) r[n] <- x[n]*x[n]-x[n-1]*x[n+1])
   user  system elapsed 
   8.55    0.01    8.58 
> 
> r <- NA
> system.time(lapply(2:length(x),function(n) r[n] <<- x[n]*x[n]-x[n-1]*x[n+1]))
   user  system elapsed 
  11.36    0.00   11.39 
> 
> r <- NA
> system.time(r <- x^2 - c(NA,x[1:(length(x)-1)]) * c(x[2:length(x)],NA))
   user  system elapsed 
   0.01    0.00    0.01