I am searching for a solution that implements the following simple growth-rate formula by applying vectorization in R:
gr <- function(x){
a <- matrix(,nrow=nrow(x),ncol=ncol(x))
for (j in 1:ncol(x)){
for (i in 2:nrow(x)){
if (!is.na(x[i,j]) & !is.na(x[i-1,j]) & x[i-1,j] != 0){
result[i,j] <- x[i,j]/x[i-1,j]-1
}
}
}
return(a)
}
I found the xts package to generate lags of time-series, but in the end I always ended up having to compare to many values (see above), so I cannot simply use ifelse. One possible problem is when the time-series (e.g. a price index) has zeros in between. This would create NaNs in the result, which I am trying to avoid and which cannot simply be removed afterwards (edit: apparently they can, see the answers below!)
In short: I'd like to produce a table of correct growth rates for a given table of values. Here is an example:
m <- matrix(c(1:3,NA,2.4,2.8,3.9,0,1,3,0,2,1.3,2,NA,7,3.9,2.4),6,3)
generates:
[,1] [,2] [,3]
[1,] 1.0 3.9 1.3
[2,] 2.0 0.0 2.0
[3,] 3.0 1.0 NA
[4,] NA 3.0 7.0
[5,] 2.4 0.0 3.9
[6,] 2.8 2.0 2.4
correct result, produced by gr(m):
[,1] [,2] [,3]
[1,] NA NA NA
[2,] 1.0000000 -1 0.5384615
[3,] 0.5000000 NA NA
[4,] NA 2 NA
[5,] NA -1 -0.4428571
[6,] 0.1666667 NA -0.3846154
But this takes forever with large tables. Is there any way to use conditions without looping so extensively?
You can speed this up by performing the entire calculation in a single vectorized operation (with one additional operation to fix up the results whenever you divide by 0):
out <- rbind(NA, tail(m, -1) / head(m, -1) - 1)
out[!is.finite(out)] <- NA
out
# [,1] [,2] [,3]
# NA NA NA
# [2,] 1.0000000 -1 0.5384615
# [3,] 0.5000000 NA NA
# [4,] NA 2 NA
# [5,] NA -1 -0.4428571
# [6,] 0.1666667 NA -0.3846154
This is much faster than a looping solution, as demonstrated on a 1000 x 1000 example:
set.seed(144)
m <- matrix(rnorm(10000000), 10000, 1000)
system.time(j <- josilber(m))
# user system elapsed
# 1.425 0.030 1.446
system.time(g <- gr(m))
# user system elapsed
# 34.551 0.263 36.581
The vectorized solution provides a 25x speedup.