R Basic Operations

This chapter introduces simple operations in the R language.

Assignment

Generally, assignment in programming languages is = symbol, but since R is a mathematical language, the assignment symbol is very similar to the pseudocode in our mathematical books, which is a left arrow <- ：

a　<-　123
b　<-　456
print(a　+　b)

The result of executing the above code:

[1]　579

This assignment symbol is a formal advantage and an operational disadvantage of the R language: formally more suitable for mathematicians, after all, not all mathematicians are accustomed to using = as an assignment symbol.

In terms of operation, the < symbol and - The symbols are not very easy to type characters, which will make many programmers feel uncomfortable. Therefore, the relatively new version of the R language also supports = as an assignment operator:

a　=　123
b　=　456
print(a　+　b)

This is also a valid R program.

Note:It is difficult to verify from which version of R support was added = Assignment, but the R version used in this tutorial is 4.0.0.

Mathematical operators

The table below lists the main mathematical operators and their order of operations:

The following examples demonstrate simple mathematical operations:

>　1　+　2　*　3
[1]　7
> (1　+　2)　*　3
[1]　9
>　3　/　4
[1] 0.75
>　3.4　-　1.2
[1]　2.2
>　1　-　4　*　0.5^3
[1] 0.5
>　8　/　3　%%　2
[1]　8
>　8　/　4　%%　2
[1Inf
>　3　%%　2^2
[1]　3
>　10　/　3　%/%　2
[1]　10

Relational operators

The following table lists the relational operators supported by R language, which compare two vectors, compare each element of the first vector with the corresponding element of the second vector, and return a boolean value as the result.

v　<-　c(2,4,6,9)
t　<-　c(1,4,7,9)
print(v>t)
print(v < t)
print(v == t)
print(v!=t)
print(v>=t)
print(v<=t)

The output of the above code is:

[1TRUE FALSE FALSE FALSE
[1FALSE FALSE  TRUE FALSE
[1FALSE TRUE FALSE TRUE
[1TRUE FALSE  TRUE FALSE
[1]　　TRUE　　TRUE　FALSE　　TRUE
[1FALSE  TRUE  TRUE  TRUE

Logical operators

The following table lists the logical operators supported by R language, which can be used for vectors of numeric, logical, and complex types.

greater than 1 numbers are all TRUE.

Logical operators compare two vectors, comparing each element of the first vector with the corresponding element of the second vector, and returning a boolean value as the result.

v　<-　c(3,1,TRUE,2+3i)
t　<-　c(4,1,FALSE,2+3i)
print(v&t)
print(v|t)
print(!v)
#　&&、|| only compare the first element of the two vectors
v　<-　c(3,0,TRUE,2+2i)
t　<-　c(1,3,TRUE,2+3i)
print(v&&t)
v　<-　c(0,0,TRUE,2+2i)
t　<-　c(0,3,TRUE,2+3i)
print(v||t)

The output of the above code is:

[1]　　TRUE　　TRUE　FALSE　　TRUE
[1]　TRUE　TRUE　TRUE　TRUE
[1]　FALSE　FALSE　FALSE　FALSE
[1]　TRUE
[1]　FALSE

Assignment operators

R language variables can use left, right, or equal operators to assign values.

The table below lists the assignment operators supported by R language.

#　Left assignment
v1　<-　c(3,1,TRUE,"w3codebox")
v2　<<-　c(3,1,TRUE,"w3codebox")
v3　=　c(3,1,TRUE,"w3codebox")
print(v1)
print(v2)
print(v3)
#　Right assignment
c(3,1,TRUE,"w3codebox")　->　v1
c(3,1,TRUE,"w3codebox")　->>　v2　
print(v1)
print(v2)

The output of the above code is:

[1]　"3"　　　　　　"1"　　　　　　"TRUE"　　　"w3codebox"
[1]　"3"　　　　　　"1"　　　　　　"TRUE"　　　"w3codebox"
[1]　"3"　　　　　　"1"　　　　　　"TRUE"　　　"w3codebox"
[1]　"3"　　　　　　"1"　　　　　　"TRUE"　　　"w3codebox"
[1]　"3"　　　　　　"1"　　　　　　"TRUE"　　　"w3codebox"

Other operators

R language also includes some special operators.

#　1　to　10　The vector
v　<-　1:10
print(v)　
#　Determine if a number is in the vector v
v1　<-　3
v2　<-　15
print(v1　%in%　v)　
print(v2　%in%　v)　
#　Matrix multiplication with its transpose
M　=　matrix(　c(2,6,5,1,10,4),　nrow　=　2,ncol　=　3,byrow　=　TRUE)
t　=　M　%*%　t(M)
print(t)

The output of the above code is:

[1]　　1　　2　　3　　4　　5　　6　　7　　8　　9　10
[1]　TRUE
[1]　FALSE
　　　　　[,1]　[,2]
[1,]　　　65　　　82
[2,]　　　82　　117

Mathematical functions

Common for some mathematical functions are:

The following examples demonstrate the application of mathematical functions:

>　sqrt(4)
[1]　2
>  exp(1)
[1]　2.718282
>  exp(2)
[1]　7.389056
>  log(2,4)
[1] 0.5
>  log10(10000)
[1]　4

Rounding Functions:

)

>  round(1.5)
[1]　2
>  round(2.5)
[1]　2
>  round(3.5)
[1]　4
>  round(4.5)
[1]　4

AttentionNote that the round function in R may 'discard the five' in some cases.

When the integer part is even, the five will also be discarded, which is different from C language.

R's trigonometric functions are in radians:

>  sin(pi/6)
[1] 0.5
>  cos(pi/4)
[1] 0.7071068
>  tan(pi/3)
[1]　1.732051

Inverse Trigonometric Functions:

>  asin(0.5)
[1] 0.5235988
>  acos(0.7071068)
[1] 0.7853981
>  atan(1.732051)
[1]　1.047198

If you have studied probability theory and statistics, you should be familiar with the following probability distribution functions because R language is designed for mathematicians and is often used:

>  dnorm(0)
[1] 0.3989423
>  pnorm(0)
[1] 0.5
>  qnorm(0.95)
[1]　1.644854
>  rnorm(3,　5,　2)  # Generate　3　average of　5, standard deviation of　2　normal random numbers
[1]　4.177589　6.413927　4.206032

These four are all used to calculate normal distributions. Their names end with 'norm', representing 'normal distribution'.

There are four prefixes for the names of distribution functions:

• d - Probability Density Function

• p - Probability Density Integral Function (integral from infinitesimal to x)

• q - Quantile Functions

• r - Random Number Functions (often used in probability simulation)

NoteSince this tutorial does not elaborate on the mathematical theory of probability distribution, a detailed explanation of the mathematical theory related to probability distribution is not provided. R language, in addition to containing normal distribution functions, also has common distribution functions such as Poisson distribution (pois, Poisson). If you want to learn more, you can study "Probability Theory and Mathematical Statistics".