c(100,200,300) + 5 # return a vector that contains c(105, 205, 305)[1] 105 205 3055 5. Intro to R vectors
5.1 What’s a vector? The is.vector() function.
A vector is a collection of several values. R streamlines processing of vector by working with all the values in a vector simultaneously. This is best explained with an example.
5.2 Example - using the c() function to create a vector
The c() function collects several values into a single “vector” of values. When you perform arithmetic with a vector each item in the vector is operated upon. In the following exmaple c(100,200,300) creates a single “vector” that includes the specified values. The number 5 is then added to each value in the vector. This produces a new vector that contains 105, 205 and 305.
The above demonstrates a simple example of “vector arithmetic”. Any arithmetic that is done with vectors operates on all values in the vector. We’ll explore this in more depth soon.
5.3 Many R functions can be used to create vectors.
c() is NOT the only function that can create a vector. R has many, many functions that create vectors.
5.3.1 Intro to seq() function
For example, the seq function can create a vector of values that follow some sequence or pattern. The following uses the seq function to create a sequences with the numbers 11,12,13,14,15.
seq(11, 15) [1] 11 12 13 14 15We can do vector arithmetic with the results. In the following example 100 gets added to each value in the vector 3,4,5,6 to result in 103,104,105,106
100 + seq(3, 6) [1] 103 104 105 1065.3.2 Intro to rep() function
The rep() function returns a vector that contains repetitions of the specified values. For example
rep("hello", 5) # repeat the word "hello" five times[1] "hello" "hello" "hello" "hello" "hello"rep(100,3) # repeat the number 100 three times[1] 100 100 1005.4 Nesting function calls
You can pass the return value of one function call into another function call.
rep(c(10,11,12), 4) # repeat 10,11,12 four times [1] 10 11 12 10 11 12 10 11 12 10 11 125.5 More vector arithmetic
Each of the above examples returns a single vector. We can do vector arithmetic with the results.
# repeat the number 100 three times then add 5 to each number
rep(100,3) + 5 [1] 105 105 105# add 1000 to each of the values in the vector produced by rep(seq(3,5), 4)
1000 + rep(seq(3,5), 4) [1] 1003 1004 1005 1003 1004 1005 1003 1004 1005 1003 1004 10055.5.1 The seq function
5.6 order of operations with vectors too
# vector arithmetic also respects the order of operations
# In the following example the multiplication is done before the addition
# to yield the value c(205, 405, 605)
5 + c(100, 200, 300) * 2 # do the multiplication first[1] 205 405 605# This works as follows
#
# original: 5 + c(100, 200, 300) * 2
#
# do the *: 5 + c(200, 400, 600)
#
# then do the +: c(205, 405, 605)
#
# result is displayed as: 205 405 6055.7 (parentheses) change the order of operations
# we can change the order of operations with parentheses
# This yields a different result.
(5 + c(100,200,300)) * 2 # pay close attention to the parenthesis!!![1] 210 410 610# This works follows
#
# original: (5 + c(100, 200, 300)) * 2
#
# do the +: c(105, 205, 305) * 2
#
# then do the *: c(210, 410, 610)
#
# result is displayed as: 210 410 6105.8 You may assign a vector to a variable
grades <- c(72,95,79,85)
grades # show the values[1] 72 95 79 85#---------------------------------------------------------------
# QUESTION:
#
# Modify the grades variable by adding 2 points to each grade
#---------------------------------------------------------------#---------------------------------------------------------------
# ANSWER
#---------------------------------------------------------------
grades = grades + 2 # you must assign the answer back to grades
grades[1] 74 97 81 87#---------------------------------------------------------------5.9 is.vector( SOME_VALUE )
R has several YRTODO - FIX THIS The is.vector function returns TRUE if its argument is a vector #### and FALSE otherwise.
As we said above, a vector is a “collection” of values. The simplest vector is just a single value. (it is technically a collection of just one value).
#-----------------------------------------------------------------------.
# The is.vector function returns TRUE if its argument is a vector ####
# and FALSE otherwise.
#-----------------------------------------------------------------------.
#-----------------------------------------------------------------------.
# The simplest vector is just a single value ... ####
# (it is technically a collection of just one value).
#-----------------------------------------------------------------------.
# View the help page by typing:
#
# ?is.vector
is.vector ( 3 )[1] TRUEis.vector( 99923141.32412431 )[1] TRUE# A variable that contains a vector is a vector ####
priceOfApple = 1.99
is.vector(priceOfApple) # TRUE[1] TRUE5.10 The c() function
# The c() function is used to combine multiple values into a single vector. ####
#
# You can think of the "c" as standing for the word "combine".
# "c" actually stands for the word "concatenate" which
# is a technical fancy shmancy word for "combine things together".
# The following is a vector with mutliple values.
# The c function combines (i.e. "concatenates") the multiple values into a
# single "vector"
c(100,200,300, 50, -2, 25)[1] 100 200 300 50 -2 25is.vector(c(100,200,300, 50, -2, 25)) # this works[1] TRUEis.vector(100,200,300, 50, -2, 25) # ERROR: use c() to tie together different valuesError in is.vector(100, 200, 300, 50, -2, 25): unused arguments (300, 50, -2, 25)someNumbers = c(100,200,300, 50, -2, 25) # combine (or concatenate) values into one vector
someNumbers[1] 100 200 300 50 -2 25is.vector(someNumbers) # TRUE[1] TRUE5.11 Other R functions return vectors
5.12 range() function
#-----------------------------------------------------.
# Other functions can also create vectors.
#-----------------------------------------------------.
#.............................................................................
# The range function returns a vector
#
# The range function returns the minimum and maximum values that are in a vector ####
#.............................................................................
range(someNumbers)[1] -2 300is.vector(range(someNumbers))[1] TRUE# You can also capture the result in a variable
lowestAndHighest = range(someNumbers)
lowestAndHighest # -2 300[1] -2 300is.vector(lowestAndHighest) # TRUE[1] TRUE5.13 seq() function
#.............................................................................
# The seq function returns a vector. In its simplest use,
# seq returns the sequence starting with the 1st argument, ending with the 2nd argument ####
#
# NOTE - we will come back to the seq function to learn about
# much more complex ways of using it.
#.............................................................................
# Example 1
seq(5,10) # 5 6 7 8 9 10[1] 5 6 7 8 9 10is.vector( seq(5, 10) ) # TRUE[1] TRUE# Example 2
seq(10,5) # 10 9 8 7 6 5[1] 10 9 8 7 6 5is.vector( seq(10,5) ) # TRUE[1] TRUE# Example 3
seq(0.5, 2.5) # 0.5 1.5 2.5[1] 0.5 1.5 2.5is.vector( seq(0.5, 2.5) ) # TRUE[1] TRUE# We can also capture the results in variables
example1 = seq(5,10)
example1 # 5 6 7 8 9 10[1] 5 6 7 8 9 10is.vector(example1) # TRUE[1] TRUEexample2 = seq(10,5)
example2 # 10 9 8 7 6 5 [1] 10 9 8 7 6 5is.vector(example2) # TRUE[1] TRUEexample3 = seq(.5, 2.5)
example3 # 0.5 1.5 2.5[1] 0.5 1.5 2.5is.vector(example3) # TRUE[1] TRUEseq(0.5, 3)[1] 0.5 1.5 2.55.14 rep() function
#.............................................................................
# The rep function returns a vector ####
#
# In its simplest use, the rep function returns a vector of it's first
# argument repeated the number of times specified by its 2nd argument.
#
# NOTE - we will come back to the rep function to learn about
# more complex ways of using it.
#.............................................................................
rep(100,3) # 100 100 100[1] 100 100 100rep( seq(1,3) , 2) # 1 2 3 1 2 3[1] 1 2 3 1 2 3# QUESTION
# Create a vector that has the numbers 1 3 1 3 1 3 etc. for a total
# of 20 numbers. Store the resulting vector into a variable named nums.
nums = rep( c(1,3) , 10) # ANSWER5.15 Use c() to combine vectors
#-------------------------------------------------------------------------------------.
# DO NOT WRITE INDIVIDUAL VALUES WITHOUT COMBINING THEM TOGETHER WITH A FUNCTION CALL!
#-------------------------------------------------------------------------------------.
100,200,300 # ERROR - individual values separated by commas are meaningless to R ####Error in parse(text = input): <text>:5:4: unexpected ','
4:
5: 100,
^# REMEMBER - if no other function call is being used, you can use the
# c function to combine individual values
c(100,200,300) # 100 200 300 (no error)[1] 100 200 300#-------------------------------------------------------------.
#
# More about the c function ####
#
#-------------------------------------------------------------.
#..............................................................................
# If you "nest" calls to "c", ie. if you combine one vector inside of another
# vector by using the c function, the result is a single vector
#..............................................................................
c(100, 200, c(30, 20, 10), 600) # same as c(100,200,300,400,500,600)[1] 100 200 30 20 10 600c(100, 200, 30, 20, 10, 600) # same thing[1] 100 200 30 20 10 600#..............................................................................
# You can use the c function to combine multiple vectors into a single vector.
#..............................................................................
x <- c(10,20,30)
y <- c(40, 50)
z <- c(x, y) # combine the values from x and y into z
z[1] 10 20 30 40 50z <- x, y # ERROR - use the c function to combine vectors into a single vectorError in parse(text = input): <text>:1:7: unexpected ','
1: z <- x,
^# QUESTION ####
# Find the sum of all the values that are in x and y, without using z
# ANSWER
sum(c(x,y)) # This works[1] 150sum(x,y) # This works too - sum allows multiple vectors to be summed[1] 150# QUESTION ####
#
# Find the average (i.e. mean) of all the values that are in x and y,
# without using z
# ANSWER
mean(c(x,y)) #This works[1] 30mean(x,y) # ERRORError in mean.default(x, y): 'trim' must be numeric of length one# QUESTION
# Why did we get an error in the last example?
# ANSWER
#
# From the documentation for sum and mean (i.e. ?sum and ?mean) we can
# see that the sum function allows multiple vectors that contain the numbers to be
# to be passed as separate arguments. However, the mean function requires
# all of the numbers to be averaged to be in a single vector that is passed
# to the argument named x. It's true that one might expect these functions
# to be more similar in how they are called. However, the designers of the
# language decided otherwise. The underlying reasons for the difference in
# the design of these functions is irrelevant - bottom line is you
# need to know how to call the functions. The place to learn this is
# in the documentation for the functions (i.e. ?sum and ?mean)
#
# Look at the documentation for sum and for mean (i.e. ?sum and ?mean).
# The "Usage" section shows the names of the arguments and their default values.
# The "Arguments" section explains what each argument is expected to contain.
# The "Value" section explains how the return value for the function is calculated.
#
# It takes some time and practice to be proficient at reading R's help pages.
# However, understanding how to read and interpret R's help pages
# is a critical skill that allows you to become familiar with R's built in
# functions.
#
# An "ellipsis" (i.e. three periods, ... ) in the help pages
# stands for the ability to type several values in place of the
# ellipsis. For example, the ... in the help page for sum, indicates
# the ability to type several different values to be summed. This is
# described in the ARGUMENTS section where it explains that ... stands
# for "numeric or complex or logical vectors".
# View the help page by typing:
#
# ?sum
# USAGE: sum(..., na.rm = FALSE)
# ARGUMENTS:
# ... numeric or complex or logical vectors
# na.rm (see the help page)
# However, for the mean function, there is a single argument named x that
# is expected to contain the values to be averaged. The ellipsis shown
# in the help page for mean is used for a more subtle reason. It shows where
# additional arguments, not listed on this help page, might be specified
# (this is an advanced concept that we'll return to later).
# View the help page by typing:
#
# ?mean
# USAGE: mean(x, trim = 0, na.rm = FALSE, ...)
# ARGUMENTS:
# x An R object. (i.e. a vector - these are the numbers)
# trim (see help page)
# na.rm (see help page)
# ... further arguments passed to or from other methods.
# You can use the c function to combine values from different functions.
# Make sure that you match parentheses correctly.
c( rep(100,3) , seq(-5,-7) ) # 100 100 100 -5 -6 -7[1] 100 100 100 -5 -6 -7# DON'T FORGET THE c( ... )
rep(100,3), seq(-5,-7) # ERRORError in parse(text = input): <text>:2:11: unexpected ','
1: # DON'T FORGET THE c( ... )
2: rep(100,3),
^5.16 — Practice —
#----------------------------------------------------.
# QUESTION
# What does the following code produce?
#
#
# range( c( rep(100,3) , seq(990,1005) , seq(-5,-7) ) )
#----------------------------------------------------.5.17 — Practice —
#----------------------------------------------------.
# QUESTION
# Write R code that takes the average of the first
# 200 even numbers.
#----------------------------------------------------.5.18 non-vectors (later in the course).
#----------------------------------------------------------------------------.
# Things that aren't vectors (e.g. dataframes, factors, matrices, etc) ####
#----------------------------------------------------------------------------.
# A vector is the simplest arrangement of values in R.
# R allows for more complex arrangements of data, which we will learn about
# later in the course, such as factors, matrices, dataframes, etc.
# These more complex arrangements of data are created from vectors but are
# technically not vectors themselves. One example of such an arrangement
# of data is a data.frame.
# We will cover dataframes later in the course.
# For now, I just want to demonstrate that R has structures that are NOT vectors.
# A dataframe is made up of vectors, but it itself is NOT a vector.
example = data.frame(students = c("joe", "sue", "bob"),
test1 = c(71,85,90),
test2 = c(83, 92, 95), stringsAsFactors = FALSE)
example students test1 test2
1 joe 71 83
2 sue 85 92
3 bob 90 95is.vector(example) # FALSE[1] FALSEis.data.frame(example) # TRUE[1] TRUE5.19 length( SOME_VECTOR )
#-----------------------------------------------------------------------.
#
# length(vector) returns the number of values in the vector ####
#
#-----------------------------------------------------------------------.
# Set the value of grades
grades <- c(72,95,79,85)
# the length function returns the number of values in a vector
length(grades) #4[1] 4length(c(25, 10)) #2[1] 2length(c(100,200,300)) #3[1] 3# A single value is a vector - but it doesn't need to be surrounded with c()
length(c(100)) # the length of a vector that contains a single item is 1[1] 1length(100) # ... same thing ... don't use the c - it's not necessary[1] 1c(100) # this is the same as just 100, the "c" is not necessary if you have just one value.[1] 100100 # same thing - don't use the c for a single value[1] 100grades # show all grades[1] 72 95 79 85grades + 5 # show what the values would be if we added 5 to each grade[1] 77 100 84 90grades # however, grades did NOT actually change[1] 72 95 79 85# If you want to change the value of grades, you need to
# use the = sign or the <- or the ->. For example:
grades # show grades[1] 72 95 79 85grades <- grades + 10 # add 10 to each grade and update grades with the new values
grades # grades now has the new values[1] 82 105 89 95prices = c(1.99, 2.99, 3.99)
doublePrices = 2 * prices
doublePrices[1] 3.98 5.98 7.985.20 Counting arguments
#############################################################.
#
# Arguments (AKA "parameters") to a function. ####
#
# It is important to know how many arguments are being passed
# to a function. The arguments to a function appear in the (parentheses)
# next to the function name and are separated from each other with commas.
#
#########################################################################.
# Remember that the round function takes TWO arguments
#
# x is the values to round
#
# digits is the position to round to
round(100.729, 1) # 100.7[1] 100.7round(100.729, 2) # 100.73[1] 100.73round (100.729) # 101[1] 101# The first argument is allowed to be a vector with multiple values
round ( c(100.729, 200.618) , 1) # 100.7 200.6[1] 100.7 200.6grades = c(82, 105, 89, 95)
sum(grades) # one argument - add up all grades (not very useful for grading ...)[1] 371sum(c(82,105,89,95)) # also one argument - same exact thing, sum is given 1 vector[1] 371sum(82,105,89,95) # four arguments - same result, HOWEVER sum is given 4 different vectors - same answer[1] 371# The sum function will sum all of the values in all
# of its arguments. The following all produce the same
# result (i.e. 306) but in different ways.
sum( c(100,200) , c(1,2,3)) # 2 arguments[1] 306sum( c(100,200,1,2,3) ) # 1 argument[1] 306sum( 100,200,1,2,3 ) # 5 arguments[1] 3065.21 To get an average use the mean function
# IMPORTANT: the mean function works a little differently than the sum function.
#
# The mean function requires that all values being averaged are passed as a single vector. ####
grades # show all the grades[1] 82 105 89 95grades = c(82, 105, 89, 95)
mean(grades) # get the average[1] 92.75mean( c(82,105,89,95) ) # same thing - there is ONE vector, ie a vector, c(72,95,79,85)[1] 92.75mean(82,105,89,95) # I didn't use the c() function here - there are 4 vectors!!![1] 82# To summarize:
# sum and mean are not consistent in the way they handle multiple arguments
sum(1,2,3) # works as expected[1] 6mean(1,2,3) # does not work as most people would expect - answer is 1[1] 1# View the help page by typing:
#
# ?mean
# Examine the documentation for mean to see why. The Usage section of the
# documentation includes the following: mean(x, trim = 0, na.rm = FALSE, ...)
# The "x" corresponds to a single vector that contains
# the values to be averaged. If you pass the values without
# the c() function, then the 2nd value listed is actually
# passed to the "trim" argument of mean. If you want to know
# what the "trim" argument is used for, see the help
# page for "mean". If you don't specify any value for "trim"
# then "mean" will work as you expect.
# "x"
#
# View the help page by typing:
#
# ?mean # see the documentation for mean
# Arguments passed to mean:
#
# x - a vector that contains the values to be averaged
#
# trim - a fraction (0 to 0.5) of observations to be ignored (i.e. trimmed) from the beginning and end of the vector
#
# na.rm - WE WILL DISCUSS THIS LATER ...
# Return the average of the numbers in the vector.
#
# Return value is 400 , i.e. (100+200+300+500+900) / 5
mean(c(100,200,300,500,900)) [1] 400# the code above does the same as the next line
sum(c(100,200,300,500,900)) / 5[1] 400# DO NOT DO THE FOLLOWING !!!!
# The mean function is being passed a SINGLE value and
# does nothing meaningful in this case.
mean(sum(100,200,300,500,900) / 5) # basically same as: sum(100,200,300,500,900) / 5[1] 400# This is because by the time, the mean function
# starts working the value: sum(100,200,300,500,900) / 5
# has already been calculated as 400.
# It would be just as ridiculous as running the following code
# which just returns the number 400 - the mean function does
# nothing meaningful in this case.
mean ( 400 ) # This is the same as 400 / 1 [1] 4005.21.1 trim argument to mean
# the "trim" argument to mean ####
#
# trim (ie. remove) 0.2 (ie. 1/5) of the values (ie. 1 value)
# from the beginning and end of the vector
#
# Return value is 333.333, ie. mean(c(200,300,500))
mean(c(100,200,300,500,900), 0.2) [1] 333.3333mean(c(200,300,500)) # same result[1] 333.3333grades = c(5, 82, 85, 89, 105)
mean(grades) # mean ( c(5,82,85,89,105))[1] 73.2mean(grades, trim = 0.2) # mean(c(82,85,89))[1] 85.33333grades[1] 5 82 85 89 105# trim (ie. remove) 0.4 (ie. 2/5) of the values (i.e. 2 values)
# from the beginning and end of the vector
#
# Return value is 300, i.e. mean(300)
mean(c(100,200,300,500,900), 0.4) # trim 0.4 = 2/5 of the values from the beginning and end[1] 300mean(c(500,200,300,900,100), 0.4) # trim 0.4 = 2/5 of the values from the beginning and end[1] 300# In the following the result is 100
# This is because the arguments are assigned in the following order
#
# x, ie. the values to be averaged = first argument = 100
# trim = second argument = 200
# na.rm = 3rd argument = 300
# ... = all other arguments = c(500,900)
#
# Other than the x=100, the other arguments are really meaningless so
# the result is the average of 100, which is 100.
mean(100,200,300,500,900)[1] 100# PROBLEM:
#
# REMEMBER that mean requires that all values being averaged are in a SINGLE vector
# Therefore to take the average of the values in x and in y the following WILL NOT WORK:
mean(x, y) # will not work - will just show the mean of the values in xError in mean.default(x, y): 'trim' must be numeric of length one# SOLUTION:
#
# Remember that you can combine multiple vectors into a single vector with
# the c function.
x <- c(10,20,30)
y <- c(40, 50)
mean(c(x,y)) # combine x and y into a single vector and take the mean of that vector[1] 30#--------------------------------------------------------.
# QUESTION : ####
#
# Grades for class1 and class2 are as shown below.
#
# class1grades <- c(80,90,100)
# class2grades <- c(85, 88)
#
# (a) get the two averages, one for each class
# (b) get the average for all the students in both classes
#--------------------------------------------------------.