LECTURE 3: DATA STRUCTURES IN R (contd)

STAT598z: Intro. to computing for statistics

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Vinayak Rao

Department of Statistics, Purdue University

SOME USEFUL R FUNCTIONS

seq(), seq_len(), min(), max(), length(), range(),
any(), all()

Comparison operators:

 <, <=, >, >=, ==, !=

Logical operators:

&& , ||, !, & , |, xor()

More on coercion:

is.logical(),is.integer(),is.double(),is.character()
as.logical(),as.integer(),as.double(),as.character()

Coercion often happens implicitly in function calls:

sum(rnorm(10) > 0)

Lists (generic vectors) in R

Elements of a list can be any R object (including other lists)

Lists are created using list() :

car <- list("Ford", "Mustang", 1999L, TRUE); length(car)

is.list(car)

Can have nested lists:

# car, house, cat and sofa are other lists
house <- "Apartment"; 
cat   <- list("Calico", "Flopsy", 3L); 
sofa  <- "Red" 
possessions <- list(car, house, cat, sofa, "3000USD")

Or lists containing functions:

mean_list <- list(mean, "Calculates mean of input");

Lists in R

Elements of a list can be anything (including other lists)

Lists are vectors (but not "atomic vectors")

See: is.vector(), is.list(), is.atomic()

car

What does concatenating lists do? E.g. c(car, house)

What does concatenating a list with a vector do?

What does unlist() do?

The str() function

Just as with vectors, can apply typeof() and class()

Another very useful function is str()

Provides a summary of the R object

str(car)

people <- c("Alice", "Bob", "Carol")
str(people)

Indexing elements of a list

Use brackets [] and double brackets [[]]

Brackets [] return a sublist of indexed elements

car[1]

typeof(car[1])

Double brackets [[]] return element of list

car[[1]]

typeof(car[[1]])

Vector in double brackets recursively indexes list

possessions[[1]][[1]]

possessions[[c(1,1)]]

Named lists

Can assign names to elements of a list

names(car) <- c("Manufacturer", "Make", "Year", "Gasoline")

car

Equivalently, on definition

car <- list("Manufacturer" = "Ford", "Make" = "Mustang", 
             "Year" = 1999, "Gasoline" = TRUE )

See also setNames()

Accessing elements using names

car[c("Manufacturer", "Make")]  # A two-element sublist

car[["Year"]]   # A length-one vector

car$Year   # Shorthand notation

car$year   # R is case-sensitive!

Names

The names() function can get/set names of elements of a list

names(car)   # Returns a character vector

names(car)[4] <- "Gasoline"; names(car)

Names need not be unique or complete

Can remove names using unname()

Can also assign names to atomic vectors

Object attributes

names() is an instance of an object attribute

These store useful information about the object

Get/set attributes using attributes()

attributes(car)

Get/set individual attributes using attr()

Object attributes

Other common attributes: class, dim and dimnames

Many have specific accessor functions e.g. class() or dim()

You can create your own

• Warning: careful about the effect of functions on attributes

Matrices and arrays

Are two- and higher-dimensional collections of objects

These have an appropriate dim attribute

my_mat <- 1:6  # vector  
my_mat

dim(my_mat) <- c(2,3) # 2 rows and 3 columns
print(my_mat)

Equivalently

my_mat <- matrix(0 , nrow = 2, ncol=3) # ncol is redundant
my_mat

Arrays work similarly

my_arr <- array(1 : 8, c(2,2,2)); print(my_arr)

Matrices and arrays

Useful functions include

• typeof(), class(), str()
• dim(), nrow(), ncol()
• is.matrix(), as.matrix(), ...
• dimnames(), rownames(), colnames()

dimnames(my_mat) <- list(c("r1", "r2"), c("c1", "c2", "c3"))
print(my_mat);my_mat['r1','c2']

A vector/list is NOT an 1-d matrix (no dim attribute)

is.matrix(1 : 6)

Use drop() to eliminate empty dimensions

my_mat <- array(1 : 6, c(2,3,1)) # dim(my_mat) is (2,3,1) 
print(my_mat)

my_mat <- drop(my_mat) # dim is now (2,3) 
print(my_mat)

Indexing matrices and arrays

print(my_mat); my_mat[2,3]   # Again, use square brackets

Excluding an index returns the entire dimension

my_mat[2,]

my_arr[1,,1] # slice along dim 2, with dims 1, 3 equal to 1

Usual ideas from indexing vectors still apply

print(my_mat[,c(2,3)])

Column-major order

We saw how to create a matrix from an array

my_mat <- (matrix(1 : 6, nrow = 3, ncol = 2)); print((my_mat)); print(t(my_mat))

In R matrices are stored in column-major order (like Fortran , and unlike C and Python )

print(my_mat[1,2])

Recycling

Column-major order explains recycling to fill larger matrices

ones <- matrix(1, nrow = 3, ncol = 3); print(ones)

my_seq <- matrix(c(1,2,3), nrow = 3, ncol = 3); print((my_seq))

print(t(t(my_seq) + c(.1,.2,.3)))