Referring to previous row in calculation - r

Question

I'm new to R and can't seem to get to grips with how to call a previous value of "self", in this case previous "b" b[-1].
b <- ( ( 1 / 14 ) * MyData$High + (( 13 / 14 )*b[-1]))
Obviously I need a NA somewhere in there for the first calculation, but I just couldn't figure this out on my own.
Adding example of what the sought after result should be (A=MyData$High):
A b
1 5 NA
2 10 0.7142...
3 15 3.0393...
4 20 4.6079...

Answer 1

1) for loop Normally one would just use a simple loop for this:
MyData <- data.frame(A = c(5, 10, 15, 20))
MyData$b <- 0
n <- nrow(MyData)
if (n > 1) for(i in 2:n) MyData$b[i] <- ( MyData$A[i] + 13 * MyData$b[i-1] )/ 14
MyData$b[1] <- NA
giving:
> MyData
A b
1 5 NA
2 10 0.7142857
3 15 1.7346939
4 20 3.0393586
2) Reduce It would also be possible to use Reduce. One first defines a function f that carries out the body of the loop and then we have Reduce invoke it repeatedly like this:
f <- function(b, A) (A + 13 * b) / 14
MyData$b <- Reduce(f, MyData$A[-1], 0, acc = TRUE)
MyData$b[1] <- NA
giving the same result.
This gives the appearance of being vectorized but in fact if you look at the source of Reduce it does a for loop itself.
3) filter Noting that the form of the problem is a recursive filter with coefficient 13/14 operating on A/14 (but with A[1] replaced with 0) we can write the following. Since filter returns a time series we use c(...) to convert it back to an ordinary vector. This approach actually is vectorized as the filter operation is performed in C.
MyData$b <- c(filter(replace(MyData$A, 1, 0)/14, 13/14, method = "recursive"))
MyData$b[1] <- NA
again giving the same result.
Note: All solutions assume that MyData has at least 1 row.

Answer 2

There are a couple of ways you could do this.
The first method is a simple loop
df <- data.frame(A = seq(5, 25, 5))
df$b <- 0
for(i in 2:nrow(df)){
df$b[i] <- (1/14)*df$A[i]+(13/14)*df$b[i-1]
}
df
A b
1 5 0.0000000
2 10 0.7142857
3 15 1.7346939
4 20 3.0393586
5 25 4.6079758
This doesn't give the exact values given in the expected answer, but it's close enough that I've assumed you made a transcription mistake. Note that we have to assume that we can take the NA in df$b[1] as being zero or we get NA all the way down.
If you have heaps of data or need to do this a bunch of time the speed could be improved by implementing the code in C++ and calling it from R.
The second method uses the R function sapply
The form you present the problem in
is recursive, which makes it impossible to vectorise, however we can do some maths and find that it is equivalent to
We can then write a function which calculates b_i and use sapply to calculate each element
calc_b <- function(n,A){
(1/14)*sum((13/14)^(n-1:n)*A[1:n])
}
df2 <- data.frame(A = seq(10,25,5))
df2$b <- sapply(seq_along(df2$A), calc_b, df2$A)
df2
A b
1 10 0.7142857
2 15 1.7346939
3 20 3.0393586
4 25 4.6079758
Note: We need to drop the first row (where A = 5) in order for the calculation to perform correctly.