We have seen this example to subset multiple values from a vector:
# values to subset
numbers <- c(-4, 6, -3, 5, -2, 4, -1, 3)
# subscript indices
indices <- c(2, 4, 6, 8)
# The subsetting
numbers[indices]
[1] 6 5 4 3
The idea of vectorization
This solution is achieved via the concept of array programming, or vectorization (as it is referred to in R). Vectorization allows us the simplification of an expression of repeated operations (such as the subsetting above) and makes it easy express them without explicitly using iterations such as for and while loops. This is possible because of the homogeneity of vectors: we can safely assume that if a calculation can be done with one element of the vector, we can do it with all of them - and just automatically repeat every operation that you can do with one value, with all elements of a vector.
This simplification is so profoud that we typically do not even think about concepts of repetition when we use these instructions. You either do one thing with the whole vector, org just rather think about objects that morph into each other.
Most basic functions that work with single values are vectorized out of the box. For instance consider the abs() function that calculates the absolute value of a value.
a <- abs(-3.5)
a
3.5
Or with a positive value:
b<- abs(7)
b
7
If we could do this only one-by-one, then repeating the process on an arbitrary vector of values, such as this:
vals <- c(-3, 5, 1, 1, -7, 9, -1.7, 4)
Requires iteration:
# store the results somewhere else
res <- rep(NA, length(vals))
# iterate for every value of vals
for(i in 1:length(vals)) res[i] <- abs(vals[i])
# the result (floating point numbers)
res
[1] 3.0 5.0 1.0 1.0 7.0 9.0 1.7 4.0
Vectorization allows us the implementation of this simple, perfectly equivalent solution
abs(vals)
[1] 3.0 5.0 1.0 1.0 7.0 9.0 1.7 4.0
All mathematical functions are vectorized and so are the operations, such as the logical NOT (!), which will invert every logical value i n a vector:
logVec <- c(TRUE, FALSE, TRUE)
!logVec
[1] FALSE TRUE FALSE