R works with objects. Objects can include vectors, matrices, functions, the results from a function, or a number of other kinds of objects. Objects make working with information easier. This chapter covers assigning names to objects, listing and removing objects, and object operations. Part II (Chapters 4 and 5) covers the possible forms of objects.
Some objects come with the packages in R. Other objects are user created. User-created objects have names that are assigned by the user. Knowing how to create, list, and remove user-created objects is basic to R. In R Studio, the user-created objects are listed in the upper right window under the Environment tab.
Types of Assignment
Names in R must begin with a letter or a period, cannot have breaks, and can contain letters, numeric digits, periods, and underscores. The names that begin with a period are hidden and are used by R for startup defaults, the random seed, and other such things. The indexing symbols [], [[]], $, and @ have special meanings with regard to R names, as explained in the “Subscripting Operators” section of this chapter.
which assigns a to b and brings an assignment in a function up to the workspace level.
which assigns b to a. Using the equal sign for assignment is considered poor practice in R, but we have never had a problem using it. While any of the types of assignment can be used, the use of the equal sign is easiest to type.
When R makes an assignment, the name is automatically saved in the workspace. Note that no warning is given if the assigned name already exists. The assignment will overwrite the object in the workspace with the assigned object.
where the object a is replaced by the original a times two.
For more information about assignment operators, enter ??“Assignment Operators” at the R prompt or in R Studio use the Help tab in the lower right window.
Example of Three Types of Assignment
An example of some of the types of assignment follows. Three objects are created: abc, bcd, and cde. You create the objects by assigning sequences to the objects. The sequences are generated when you put a colon between two integers, which creates a sequence of integers starting with the first integer and ending with the second integer.
As you can see, the assignment operators <- and = give the same result. The assignment operator -> works in the opposite direction.
Listing and Removing Objects in R and R Studio
To see the objects present in the workspace, it is easier to use R Studio rather than R - look under the Environment tab in the right upper window. R has the function ls() to list the workspace objects.
which are the three objects created previously.
Although functions are covered in detail in Part III, one interesting property of functions to note here is they can have arguments that the user enters. Two of the possible arguments for ls() are pattern and all.names.
The argument pattern can be reduced to pat, as in ls(pat=“bc”). The shortening of arguments of functions is a property of R. All arguments in R can be reduced to the shortest unique form, but they are usually given in the full form in manuals.
The [1] refers to “.commander.done” since “.commander.done” is the first element of the vector, and the [5] refers to “abc” since “abc” is the fifth element of the vector. (In R, if the elements of a vector have not been given a name, the convention for listing the elements is to show the index of the first element in each line of the lines of listed elements.)
works. You remove S4 classes by using removeClass().
In R Studio, objects can be removed under the grid option for listing the environmental objects. To the right side of the menu under the Environment tab is an icon that says List. Click on the icon and choose Grid instead of List. In the resulting grid, check the boxes to the left of the objects to be removed. Then, click on the little broom in the middle of the menu. You will be asked if you really want to delete the checked objects.
For more information about ls() or rm(), enter ?ls or ?rm at the R prompt or, in R Studio use the Help tab in the lower right window.
Operators
Operators operate on objects. Operators can be logical, arithmetic, matrix, relational, or subscripting, or they may have a special meaning. Each of the types of operators is described here.
For operators, elementwise refers to performing the operation on each element of an object or paired elements for two objects. If two objects do not have the same dimensions, the operator will often cycle the smaller object against the larger object. The cycling proceeds through each dimension. For example, for matrices, the first dimension is the rows and the second dimension is the columns, so the cycling is down rows starting with the first column.
The letters NA are used to indicate that an element is missing data. Most operators have rules for dealing with missing data and may return an NA if data is missing.
CRAN gives a help page of information about operation precedence. Enter ??“Operator Syntax and Precedence” at the R prompt to see the page or use the Help tab in R Studio.
Logical Operators and Functions
The Logical Operators and Functions
Operator | Operation | Description |
|---|---|---|
! | not | negation operator—e.g., !a |
| | or | elementwise or operator—e.g., a|b |
|| | Or | or operator, just evaluates the first elements in the objects—e.g., a||b |
& | and | elementwise and operator—e.g., a&b |
&& | And | and operator, just evaluates the first elements in the objects—e.g., a&&b |
xor( ) | exclusive or | exclusive or function—e.g., xor(a,b) |
isTRUE( ) | logical test | returns TRUE if the argument contains only one value and the value is true, otherwise returns FALSE—e.g., isTRUE(a) |
isFALSE( ) | logical test | returns TRUE if the argument contains only one value and the value is false, otherwise returns FALSE—e.g., isFALSE(a), |
any( ) | logical test | returns TRUE if TRUE is present in a logical object— e.g., any(a) |
all( ) | logical test | returns TRUE if TRUE is the only value in a logical object— e.g., all(a) |
The logical operators operate on objects that are logical, numeric, or raw. When a numeric object is coerced to logical, all of the nonzero values are set to TRUE, and the zero values are set to FALSE. For raw vectors, the operators are applied bitwise.
The negation operator changes TRUE to FALSE and FALSE to TRUE in a logical object. An NA remains an NA.
The operator | compares the two objects elementwise and, for each pair of elements, returns TRUE if TRUE is present, FALSE if no TRUE or NA is present, and NA if any NA is present. The operator || compares the first element of the first object to the first element of the second object and returns TRUE if both elements are TRUE, FALSE if both are FALSE and NA if either element is NA.
The operator & compares two objects elementwise and, for each pair of elements, returns TRUE if both elements are TRUE, FALSE if FALSE is present, and NA if both elements are NA. The operator && compares the first element of the first object to the first element of the second object and returns TRUE if the first elements are both TRUE, FALSE if FALSE is present, and NA if both elements are NA.
The xor() function compares objects elementwise and returns TRUE if the paired elements are different and FALSE if the paired elements are the same, unless an NA is present. If an NA is present, the test returns NA.
For a logical vector or a vector that can be coerced to logical, the function any() will return TRUE if any of the elements are TRUE, FALSE if no TRUE or NA is present, and NA if no TRUE is present but an NA is.
For a logical vector or a vector that can be coerced to logical, the function all() will return TRUE if all of the elements are TRUE, otherwise FALSE if a FALSE is present and NA if not.
The functions isTRUE() and isFALSE() only evaluate single element objects or expressions. If more than one element is present, the function will give an error. The function isTRUE() returns TRUE if the value is TRUE and FALSE if otherwise. The function isFALSE() returns TRUE if the value is FALSE and FALSE otherwise.
For more information about the logical operators and the functions isTRUE() and isFALSE(), the CRAN help pages for logical operators can be found by entering ??“logical operators” at the R prompt or by using the Help tab in R Studio. The help page for any() and all() can be accessed by entering ?any or ?all at the R prompt or by using the Help tab in R Studio.
Arithmetic Operators
Arithmetic operators can have numeric operands or operands that can be coerced to numeric. For example, for logical objects, TRUE coerces to 1 and FALSE coerces to 0. For some types of objects, specific operators have a different meaning, but those types of objects will not be covered in this chapter.
Arithmetic expressions are evaluated elementwise. If the number of elements is not the same between the objects in an expression, the smaller object cycles through the larger one until the end of the larger one. The numbers of elements in the larger object do not have to be a multiple of the smaller object for cycling. Expressions are evaluated from left to right, under the rules of precedence.
Arithmetic Operators
Operator | Operation | Example |
|---|---|---|
* | multiplication | a*b |
/ | division | a/b |
+ | addition | a+b |
- | subtraction | a-b |
^ | exponentiation | a^b |
%% | modulus | a%%b |
%/% | integer division | a%/%b |
For more information, the CRAN help pages for arithmetic operators can be found by entering ??“arithmetic operators” at the R prompt or by using the Help tab in R Studio. (At the time of writing, this help page was not available using the above but can be brought up by using ?“+” at the R prompt or + in the R Studio Help tab search box.)
Matrix Operators and Functions
Matrix Operators and Functions
Operator / Function | Operation | Example |
|---|---|---|
%*% | matrix multiplication | a%*%b |
%o% or outer( ) | outer product of two vectors, matrices, or arrays | a%*%b, outer(a,b) |
%x% or kronecker( ) | kronecker product of a matrix (or array) | a%x%b, kronecker(a,b) |
t( ) | transpose of a matrix | t(a) |
crossprod( ) or tcrossprod( ) | crossproduct of a matrix or two matrices | crossprod(a) or crossprod(a,b) or tcrossprod(a) or tcrossprod(a,b) |
diag( ) | diagonal of a matrix or a diagonal matrix | diag(a), a is a matrix or diag(a), a is a vector |
solve( ) | inverse of a matrix or solution to Xa=b | solve(a), solve(X,b) |
det( ) | determinant of a square matrix | det(a) |
The matrix multiplication operator is %*%. R will return an error if the two matrices do not conform.
For two arrays (arrays include vectors and matrices), %o%, or outer(), gives the outer product of the arrays.
For two arrays, %x%, or kronecker(), gives the kronecker product of the arrays.
To transpose a matrix, use the function t(), for example, t(a).
for a, where X is a nonsingular square matrix and b has the same number of rows as X. The syntax is solve(X,b).
To find the determinant of a square matrix use det(X), where X is a square matrix.
For more information, the CRAN help page for matrix multiplication can be found by entering ??“matrix multiplication” at the R prompt. For the six functions, entering ?name, where name is the name of the function, brings up the help page for the function. You can also use the R Studio Help tab. Enter ?“%” at the R prompt or % in The R Studio Help tab to see the % operators.
Relational Operators
Logical Operators
Operator | Operation | Example |
|---|---|---|
== | equals | a==9 |
!= | not equal | a!=9 |
> | greater than | a>9 |
>= | greater than or equal to | a>=9 |
< | less than | a<9 |
<= | less than or equal to | a<=9 |
Note that the equal to relational operator is ==, not =. A common mistake is to enter = for == in a logical expression. R will return an error for =.
is a logical expression and can be assigned a name.
The CRAN help page for relational operators can be found by entering ??“ relational operators ” at the R prompt or == in the Help tab search box in R Studio.
Subscripting Operators
Many objects in R have more than one element. Subscripting is used to access specific elements of an object. Vectors, matrices, arrays, lists, and slots can be subscripted. In S3, single square brackets ([]), double square brackets ([[]]), and dollar signs ($) are used. For S4 objects, the at symbol (@) is used for subscripting. None are used elsewhere.
Vectors
The first expression results in the third through seventh elements of a. The second expression results in those elements of a that are greater than three.
would return the object a with elements two through six removed.
where the length of a is greater than or equal to ten, and b is of length ten. The expression would return those elements of the first ten elements of a for which the corresponding element of b is greater than three. The subsetting can be continued with more sets of square brackets. Each set will operate on the result of all previous subsetting.
Matrices
For matrices, both kinds of square brackets are also used. For single square brackets, the selection instructions for the rows are separated from the selection instructions for the columns by a comma. Or, by not using the comma, the matrix is treated like a vector, going down the rows starting with the first column. Like the subsetting for vectors, for single square brackets, indices or a logical expression may be used to subset a matrix. To reference all rows of a matrix, put nothing to the left of the comma inside the brackets. To reference all columns of a matrix, put nothing to the right of the comma inside the brackets.
Double square brackets return just one value. If subsetted with a row and a column index separated by a comma, the value in the cell is returned. If just one index value is entered within double square brackets, R treats the matrix as a vector—going down rows—and returns the indexed element of the vector.
where a is a matrix with at least four columns. The expression would return those rows of the first four columns for which the elements of the first column are bigger than three. Notice that the a[,1] consists of one column and contains all of the rows.
A matrix can also be subsetted using a matrix with two columns. The two-column matrix would contain row and column indices and would pick out individual cells in the matrix based on the indices in each row. For example, if b is a matrix with [ 1 2 ] in the first row and [ 2 3 ] in the second row, then a[b] would return the two elements a[1,2] and a[2,3].
Arrays
where a is a three-dimensional array with at least three levels in the first dimension and at least seven levels in the third dimension. The result of the subsetting would be all of the elements in the second dimension for which the index in the first dimension is one, two, or three and the indices in the third dimension are between two and seven inclusive.
Like matrices, arrays can be subsetted using a matrix that has the same number of columns as the number of dimensions of the array, the rows of which would consist of indices for individual cells of the array. Single square brackets with no comma and double square brackets work the same as with vectors and matrices.
Lists
would return the first five objects in blist and would also be a list.
would return the object in blist with name b1. Objects in a list can only be accessed one at a time.
If a list is created from objects that do not have names associated with the objects, names will be given to the objects when the list is created. The names can be changed at any time.
would return the element in the first row and second column of the data frame adframe.
Other Types
Other types of object can be subsetted, for example, factors and slots. Objects that are factors are vectors and can be subsetted like vectors. Slots are S4 objects and are subsetted using @. Slots should never be subsetted except in a method statement, which will be described in the chapter on functions. More information about subsetting both can be found by entering ??“Extract or Replace” at the R prompt or by using the R Studio Help tab.
Odds and Ends
Two main object systems—S3 and S4—are used in R. Slots are part of S4. S3 and S4 are discussed throughout the book and in the pdf at www.r-project.org/conferences/useR-2004/Keynotes/Leisch.pdf .
will do the replacement and leave the rest of the matrix intact.
In R Studio, the help pages are easy to access and have their own window. In R the ? and ?? operators open the help pages. For known function names, ?name (or help(name)) will return the help page for the function, where name is the name of the function. To search for functions related to some techniques or methods, the operator, ?? is used. Entering ??“keywords” (or help.search(“keywords”)), where keywords consists of keywords about the technique or method, may give a list of functions in packages related to the topic. Sometimes, the search comes up blank. Try again with different keywords.
The colon is used in four ways in R. Of interest here is just the use of a single colon to define a sequence and the double colon to refer to functions by package and name.
If a and b are two numbers, the expression a:b will give the sequence of integers between a rounded down to an integer and b rounded down to an integer. Note that the number a can be larger than the number b.
The functions that come with R are all part of some package. If a package is not loaded, a search using just the function name will return nothing. The full name of a function is package.name::function.name , where package.name is the name of the package and function name is the name of the function.
For more information on colons, enter ?“:” at the R prompt or : under the Help tab in R Studio.
The operator ~ is used in model formulas to separate the left and right sides of a model. For more information, type ?“~” at the R prompt or enter ~ under the Help tab in R Studio.
The symbol # is used for comments. When writing functions, anything found to the right of a # on a line of the code is ignored.
The operator %in% returns TRUE for the values in the object to the left of the operator that are in the object to the right of the operator and FALSE for those that are not. The length of the result is the length of the first object. If the first object has more than one dimension, it is converted to a vector to get the result.
The CRAN help pages for subsetting are found by entering ??“Extract or Replace” or by using the R Studio Help tab.