Vectors and assignment
R operates on named data structures. The simplest such structure is the numeric vector, which is a single entity consisting of an ordered collection of numbers. To set up a vector named x, say, consisting of five numbers, namely 10.4, 5.6, 3.1, 6.4 and 21.7, use the R command
> x <- c(10.4, 5.6, 3.1, 6.4, 21.7)
This is an assignment statement using the function c() which in this context can take an arbitrary number of vector arguments and whose value is a vector got by concatenating its arguments end to end.[1] A number occurring by itself in an expression is taken as a vector of length one. Notice that the assignment operator (‘<-’), which consists of the two characters ‘<’ (“less than”) and ‘-’ (“minus”) occurring strictly side-by-side and it ‘points’ to the object receiving the value of the expression. In most contexts the ‘=’ operator can be used as a alternative. Assignment can also be made using the function assign(). An equivalent way of making the same assignment as above is with:
> assign("x", c(10.4, 5.6, 3.1, 6.4, 21.7))
The usual operator, <-, can be thought of as a syntactic short-cut to this. Assignments can also be made in the other direction, using the obvious change in the assignment operator. So the same assignment could be made using
> c(10.4, 5.6, 3.1, 6.4, 21.7) -> x
If an expression is used as a complete command, the value is printed and lost[2]. So now if we were to use the command
> 1/x
the reciprocals of the five values would be printed at the terminal (and the value of x, of course, unchanged). The further assignment
> y <- c(x, 0, x)
would create a vector y with 11 entries consisting of two copies of x with a zero in the middle place.
Vector arithmetic
Vectors can be used in arithmetic expressions, in which case the operations are performed element by element. Vectors occurring in the same expression need not all be of the same length. If they are not, the value of the expression is a vector with the same length as the longest vector which occurs in the expression. Shorter vectors in the expression are recycled as often as need be (perhaps fractionally) until they match the length of the longest vector. In particular a constant is simply repeated. So with the above assignments the command
> v <- 2*x + y + 1
generates a new vector v of length 11 constructed by adding together, element by element, 2*x repeated 2.2 times, y repeated just once, and 1 repeated 11 times. The elementary arithmetic operators are the usual +, -, *, / and ^ for raising to a power. In addition all of the common arithmetic functions are available. log, exp, sin, cos, tan, sqrt, and so on, all have their usual meaning. max and min select the largest and smallest elements of a vector respectively. range is a function whose value is a vector of length two, namely c(min(x), max(x)). length(x) is the number of elements in x, sum(x) gives the total of the elements in x, and prod(x) their product. Two statistical functions are mean(x) which calculates the sample mean, which is the same as sum(x)/length(x), and var(x) which gives
sum((x-mean(x))^2)/(length(x)-1)
or sample variance. If the argument to var() is an n-by-p matrix the value is a p-by-p sample covariance matrix got by regarding the rows as independent p-variate sample vectors. sort(x) returns a vector of the same size as x with the elements arranged in increasing order; however there are other more flexible sorting facilities available (see order() or sort.list() which produce a permutation to do the sorting).
Note that max and min select the largest and smallest values in their arguments, even if they are given several vectors. The parallel maximum and minimum functions pmax and pmin return a vector (of length equal to their longest argument) that contains in each element the largest (smallest) element in that position in any of the input vectors. For most purposes the user will not be concerned if the “numbers” in a numeric vector are integers, reals or even complex. Internally calculations are done as double precision real numbers, or double precision complex numbers if the input data are complex. To work with complex numbers, supply an explicit complex part. Thus
sqrt(-17)
will give NaN and a warning, but
sqrt(-17+0i)
will do the computations as complex numbers.
Generating regular sequences
R has a number of facilities for generating commonly used sequences of numbers. For example 1:30 is the vector c(1, 2, ..., 29, 30). The colon operator has highest priority within an expression, so, for example 2*1:15 is the vector c(2, 4, ..., 28, 30). Put n <- 10 and compare the sequences 1:n-1 and 1:(n-1). The construction 30:1 may be used to generate a sequence backwards. The function seq() is a more general facility for generating sequences. It has five arguments, only some of which may be specified in any one call. The first two arguments, if given, specify the beginning and end of the sequence, and if these are the only two arguments given the result is the same as the colon operator.
That is seq(2,10) is the same vector as 2:10. Parameters to seq(), and to many other R functions, can also be given in named form, in which case the order in which they appear is irrelevant. The first two parameters may be named from=value and to=value; thus seq(1,30), seq(from=1, to=30) and seq(to=30, from=1) are all the same as 1:30. The next two parameters to seq() may be named by=value and length=value, which specify a step size and a length for the sequence respectively. If neither of these is given, the default by=1 is assumed. For example
> seq(-5, 5, by=.2) -> s3
generates in s3 the vector c(-5.0, -4.8, -4.6, ..., 4.6, 4.8, 5.0). Similarly
> s4 <- seq(length=51, from=-5, by=.2)
generates the same vector in s4.
The fifth parameter may be named along=vector, which if used must be the only parameter, and creates a sequence 1, 2, ..., length(vector), or the empty sequence if the vector is empty (as it can be). A related function is rep() which can be used for replicating an object in various complicated ways. The simplest form is
> s5 <- rep(x, times=5)
which will put five copies of x end-to-end in s5. Another useful version is
> s6 <- rep(x, each=5)
which repeats each element of x five times before moving on to the next.
Logical vectors
As well as numerical vectors, R allows manipulation of logical quantities. The elements of a logical vector can have the values TRUE, FALSE, and NA (for “not available”, see below). The first two are often abbreviated as T and F, respectively. Note however that T and F are just variables which are set to TRUE and FALSE by default, but are not reserved words and hence can be overwritten by the user. Hence, you should always use TRUE and FALSE. Logical vectors are generated by conditions. For example
> temp <- x > 13
sets temp as a vector of the same length as x with values FALSE corresponding to elements of x where the condition is not met and TRUE where it is. The logical operators are <, <=, >, >=, == for exact equality and != for inequality. In addition if c1 and c2 are logical expressions, then c1 & c2 is their intersection (“and”), c1 | c2 is their union (“or”), and !c1 is the negation of c1. Logical vectors may be used in ordinary arithmetic, in which case they are coerced into numeric vectors, FALSE becoming 0 and TRUE becoming 1. However there are situations where logical vectors and their coerced numeric counterparts are not equivalent, for example see the next subsection.
1 With other than vector types of argument, such as list mode arguments, the action of c() is rather different.
2 Actually, it is still available as .Last.value before any other statements are executed.
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