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Last Updated: June 24, 2015
R for Statisitical Computing
Comments
Comments are typed with hashtags '#'
# This is a comment
cat("This is not a comment")
## This is not a comment
No block comments. So sad. =(
Data Types
Integers & Numerics
Examples: 1,2.0,1.1,pi
c(1,2.0,1.1,pi)
## [1] 1.000000 2.000000 1.100000 3.141593
Infcan also be used in calculations
1/Inf
## [1] 0
Complex Numbers
We can even use complex numbers.
complex(real = 1, imaginary = 2)
## [1] 1+2i
8+6i
## [1] 8+6i
Characters
Example: 'One', '1', 'pi'
c('One', '1', 'pi')
## [1] "One" "1" "pi"
Boolian (Logical) Values
Boolian values can take only two values: TRUE (T) or FALSE (F).
c(TRUE, FALSE, TRUE)
## [1] TRUE FALSE TRUE
Factors
A factor is a categorical variable that can take on only a finite set of values. i.e. Sex, Faculty in University
factor(c('Male','Female','Male','Male'))
## [1] Male Female Male Male ## Levels: Female Male
Everything is an object, including functions!
Vectors
Most common objects are called vectors.
Examples: vector of numbers
a1 <- c(1,2,3) a1
## [1] 1 2 3
a2 <- c('one','two','three')
a2
## [1] "one" "two" "three"
a3 <- c('1','2','3')
a3
## [1] "1" "2" "3"
You can also create a range of values using start:end
4:10
## [1] 4 5 6 7 8 9 10
4:-3
## [1] 4 3 2 1 0 -1 -2 -3
0.1:4
## [1] 0.1 1.1 2.1 3.1
Basic Numerical Operations: +, -, *, /, ^
Numerical operations are: +, -, *, /, ^
- These operate elementwise between vectors.
| Operator | Description |
|---|---|
| + | Addition |
| - | Subtraction |
| * | Multiplication |
| / | Division |
| ^ | Power |
c(1,2,3) * c(4,5,6)
## [1] 4 10 18
Note: They don't have to have the same length. If they don't then the vector will recycle though the shorter vector. The longer has to be a multiple of the shorter vector.
c(1,2,3) ^ c(1,2,3,4,5,6)
## [1] 1 4 27 1 32 729
Logical Operators
- Return a boolan value of
TRUEorFALSE
| Operator | Description |
|---|---|
| < | Less than |
| > | Greater than |
| <= | Less than or equal to |
| >= | Greater than or equal to |
| == | Equal to |
| != | Not equal to |
| | | Elementwise Or |
| Operator | Description |
|---|---|
| & | Elementwise And |
| || | Or |
| && | And |
c(TRUE, FALSE) | c(FALSE, FALSE)
## [1] TRUE FALSE
c(1,2,3) < c(2,1,4)
## [1] TRUE FALSE TRUE
Pro Tip: When interacting with number, boolians are converted to an integer: 0, or 1.
Type check
is.(typename)
Example: is.vector, is.integer, is.numeric, is.data.frame, is.matrix
- Not sure which type? Use
typeof()!
is.numeric(a1)
## [1] TRUE
is.vector(a1)
## [1] TRUE
is.data.frame(a1)
## [1] FALSE
Assignment Operator
Assignment can come in 3 forms:var_name <- evaluationvar_name = evaluationevaluation -> var_name
x <- 1 x
## [1] 1
Be careful: <- is not the same as < -
x < -1
## [1] FALSE
y = "string" y
## [1] "string"
"This isn't used much" -> z z
## [1] "This isn't used much"
Concatenating Vectors
They are different vectors! To concatenate two vectors, use c(vector.1, vector.2)
b12 <- c(a1,a2) b12
## [1] "1" "2" "3" "one" "two" "three"
b23 <- c(a2,a3) b23
## [1] "one" "two" "three" "1" "2" "3"
b13 <- c(a1,a3) b13
## [1] "1" "2" "3" "1" "2" "3"
b21 <- c(a2,a1) b21
## [1] "one" "two" "three" "1" "2" "3"
Notice that when combined with characters, numerics are changed into characters automatically. So b23 == b21.
b23 == b21
## [1] TRUE TRUE TRUE TRUE TRUE TRUE
b123 <- c(a1,a2,a3)
Dot Product
To use dot product of two vectors (instead of elementwise) use %*%
a1 %*% a1
## [,1] ## [1,] 14
c(1,4,5) %*% c(6,7,2)
## [,1] ## [1,] 44
Exercise
- What are the datatypes available in R?
- What datatype would the vector
c(1,2,"three")be? - What is the vector
c(3,4,5,6)to the power of 4? - What elements of
c(3,4,5,6)greater than 4?
Answer
- What are the datatypes available in R?
- Numeric
- Integer
- Complex
- Character
- Boolian
- Factor
- What datatype would the vector
c(1,2,"three")be?
- Character
class(c(1,2,"three"))
## [1] "character"
- What is the vector
c(3,4,5,6)to the power of 4?
c(3,4,5,6) ^ 4
## [1] 81 256 625 1296
- What elements of
c(3,4,5,6)greater than 4?
c(3,4,5,6) > 4
## [1] FALSE FALSE TRUE TRUE
Lists
Different from vectors, they allow us to put multiple structures in a list.
- Useful when we need to store a list of objects with different datatypes
l12 <- list(a1,a2) l12
## [[1]] ## [1] 1 2 3 ## ## [[2]] ## [1] "one" "two" "three"
l23 <- list(a2,a3) l23
## [[1]] ## [1] "one" "two" "three" ## ## [[2]] ## [1] "1" "2" "3"
l13 <- list(a1,a3) l13
## [[1]] ## [1] 1 2 3 ## ## [[2]] ## [1] "1" "2" "3"
Notice they are stored in two 'different arrays'
as.vector, as.list can interchange list to vectors and vectors to list via as.vector and as.list
as.vector(l23)
## [[1]] ## [1] "one" "two" "three" ## ## [[2]] ## [1] "1" "2" "3"
as.list(a1)
## [[1]] ## [1] 1 ## ## [[2]] ## [1] 2 ## ## [[3]] ## [1] 3
Exercise
- Generate a vector of 1 to 10, a list of characters 2.1 to 2.5 separated by 0.1
- Add the list to the vector and return a vector
- Define 2 vectors, x1, x2, by using rnorm(7,mean = 13, sd = 5)
- Do the inner product of x1,x2
Answer
q1 = 1:10 #Question 1 q1c = as.list(as.character(seq(2.1,2.5,0.1))) q1 + as.numeric(q1c) # Question 2
## [1] 3.1 4.2 5.3 6.4 7.5 8.1 9.2 10.3 11.4 12.5
x1 = rnorm(7,mean = 13, sd = 5) #Question 3 x2 = rnorm(7,mean = 13, sd = 5) x1 %*% x2 #Question 4
## [,1] ## [1,] 695.1124
Matrix
- Each column needs to contain same type.
- Like a high level vector.
M1 <- matrix(c(1,2,3,4,5,6,7,8,9),nrow=3,ncol=3) M1
## [,1] [,2] [,3] ## [1,] 1 4 7 ## [2,] 2 5 8 ## [3,] 3 6 9
M2 <- matrix(9:1 ,3 ,3) M2
## [,1] [,2] [,3] ## [1,] 9 6 3 ## [2,] 8 5 2 ## [3,] 7 4 1
M3 <- matrix(c(a1,a2),2,3) M3
## [,1] [,2] [,3] ## [1,] "1" "3" "two" ## [2,] "2" "one" "three"
Data Frames
- Generalised matrix. Now we can store different data types in different columns! =)
- Like high level list
df1 <- data.frame(a1,a2,a3) df1
## a1 a2 a3 ## 1 1 one 1 ## 2 2 two 2 ## 3 3 three 3
Attributes
| Attribute | Description |
|---|---|
names |
Names of an object |
dimnames |
Names of the dimensions of an object |
dim |
Dimension of an object |
class |
Class of an object |
length |
Length of an object |
length(a1)
## [1] 3
names(a1) = c("a","b","c")
a1
## a b c ## 1 2 3
names(df1) = c("var_1","var_2","var_3")
df1
## var_1 var_2 var_3 ## 1 1 one 1 ## 2 2 two 2 ## 3 3 three 3
dim(M1)
## [1] 3 3
Data Manipulation
Indices, just like linear algebra, for vectors, specify thy entry, and matrix row first then column.
a1[2] # Second entry
## b ## 2
M1[1,2] #First row second column
## [1] 4
df1[2,3] # Second row third column
## [1] 2 ## Levels: 1 2 3
M1[1,] # First row
## [1] 1 4 7
M1[,3] # Third column
## [1] 7 8 9
You can also Boolian values to get a subset of values:
a1[a1 <= 2]
## a b ## 1 2
Accessing the elements of a list is slightly different. Use double [[]] notation:
l13[[1]]
## [1] 1 2 3
Assigning names to data.frame and matrices
rownames(M1) <- c('Ein','Zwei','Drei')
colnames(M1) <- c('Un','Deux','Trois')
M1
## Un Deux Trois ## Ein 1 4 7 ## Zwei 2 5 8 ## Drei 3 6 9
rownames(df1) <- c('Uno','Dos','Tres')
colnames(df1) <- c('yi','er','san')
df1
## yi er san ## Uno 1 one 1 ## Dos 2 two 2 ## Tres 3 three 3
Adding new rows or columns into matrix or data.frame
rbind(): Add new row to rbind, cbind
M1.rbind <- rbind(M1,M1) M1.rbind
## Un Deux Trois ## Ein 1 4 7 ## Zwei 2 5 8 ## Drei 3 6 9 ## Ein 1 4 7 ## Zwei 2 5 8 ## Drei 3 6 9
M2.rbind <- rbind(M1,M2) # Notice the names of columns and rows M2.rbind
## Un Deux Trois ## Ein 1 4 7 ## Zwei 2 5 8 ## Drei 3 6 9 ## 9 6 3 ## 8 5 2 ## 7 4 1
M1.cbind <- cbind(M1,M1) M1.cbind
## Un Deux Trois Un Deux Trois ## Ein 1 4 7 1 4 7 ## Zwei 2 5 8 2 5 8 ## Drei 3 6 9 3 6 9
Calling by Column Names
df1$yi
## [1] 1 2 3
df1$er
## [1] one two three ## Levels: one three two
df1$san
## [1] 1 2 3 ## Levels: 1 2 3
Reading csv/delim files
read.file_type(file = "Name.file_type", header = TRUE, sep = "")
Useful functions
attach(iris) head(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species ## 1 5.1 3.5 1.4 0.2 setosa ## 2 4.9 3.0 1.4 0.2 setosa ## 3 4.7 3.2 1.3 0.2 setosa ## 4 4.6 3.1 1.5 0.2 setosa ## 5 5.0 3.6 1.4 0.2 setosa ## 6 5.4 3.9 1.7 0.4 setosa
summary(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width ## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100 ## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300 ## Median :5.800 Median :3.000 Median :4.350 Median :1.300 ## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199 ## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800 ## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500 ## Species ## setosa :50 ## versicolor:50 ## virginica :50 ## ## ##
print(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species ## 1 5.1 3.5 1.4 0.2 setosa ## 2 4.9 3.0 1.4 0.2 setosa ## 3 4.7 3.2 1.3 0.2 setosa ## 4 4.6 3.1 1.5 0.2 setosa ## 5 5.0 3.6 1.4 0.2 setosa ## 6 5.4 3.9 1.7 0.4 setosa ## 7 4.6 3.4 1.4 0.3 setosa ## 8 5.0 3.4 1.5 0.2 setosa ## 9 4.4 2.9 1.4 0.2 setosa ## 10 4.9 3.1 1.5 0.1 setosa ## 11 5.4 3.7 1.5 0.2 setosa ## 12 4.8 3.4 1.6 0.2 setosa ## 13 4.8 3.0 1.4 0.1 setosa ## 14 4.3 3.0 1.1 0.1 setosa ## 15 5.8 4.0 1.2 0.2 setosa ## 16 5.7 4.4 1.5 0.4 setosa ## 17 5.4 3.9 1.3 0.4 setosa ## 18 5.1 3.5 1.4 0.3 setosa ## 19 5.7 3.8 1.7 0.3 setosa ## 20 5.1 3.8 1.5 0.3 setosa ## 21 5.4 3.4 1.7 0.2 setosa ## 22 5.1 3.7 1.5 0.4 setosa ## 23 4.6 3.6 1.0 0.2 setosa ## 24 5.1 3.3 1.7 0.5 setosa ## 25 4.8 3.4 1.9 0.2 setosa ## 26 5.0 3.0 1.6 0.2 setosa ## 27 5.0 3.4 1.6 0.4 setosa ## 28 5.2 3.5 1.5 0.2 setosa ## 29 5.2 3.4 1.4 0.2 setosa ## 30 4.7 3.2 1.6 0.2 setosa ## 31 4.8 3.1 1.6 0.2 setosa ## 32 5.4 3.4 1.5 0.4 setosa ## 33 5.2 4.1 1.5 0.1 setosa ## 34 5.5 4.2 1.4 0.2 setosa ## 35 4.9 3.1 1.5 0.2 setosa ## 36 5.0 3.2 1.2 0.2 setosa ## 37 5.5 3.5 1.3 0.2 setosa ## 38 4.9 3.6 1.4 0.1 setosa ## 39 4.4 3.0 1.3 0.2 setosa ## 40 5.1 3.4 1.5 0.2 setosa ## 41 5.0 3.5 1.3 0.3 setosa ## 42 4.5 2.3 1.3 0.3 setosa ## 43 4.4 3.2 1.3 0.2 setosa ## 44 5.0 3.5 1.6 0.6 setosa ## 45 5.1 3.8 1.9 0.4 setosa ## 46 4.8 3.0 1.4 0.3 setosa ## 47 5.1 3.8 1.6 0.2 setosa ## 48 4.6 3.2 1.4 0.2 setosa ## 49 5.3 3.7 1.5 0.2 setosa ## 50 5.0 3.3 1.4 0.2 setosa ## 51 7.0 3.2 4.7 1.4 versicolor ## 52 6.4 3.2 4.5 1.5 versicolor ## 53 6.9 3.1 4.9 1.5 versicolor ## 54 5.5 2.3 4.0 1.3 versicolor ## 55 6.5 2.8 4.6 1.5 versicolor ## 56 5.7 2.8 4.5 1.3 versicolor ## 57 6.3 3.3 4.7 1.6 versicolor ## 58 4.9 2.4 3.3 1.0 versicolor ## 59 6.6 2.9 4.6 1.3 versicolor ## 60 5.2 2.7 3.9 1.4 versicolor ## 61 5.0 2.0 3.5 1.0 versicolor ## 62 5.9 3.0 4.2 1.5 versicolor ## 63 6.0 2.2 4.0 1.0 versicolor ## 64 6.1 2.9 4.7 1.4 versicolor ## 65 5.6 2.9 3.6 1.3 versicolor ## 66 6.7 3.1 4.4 1.4 versicolor ## 67 5.6 3.0 4.5 1.5 versicolor ## 68 5.8 2.7 4.1 1.0 versicolor ## 69 6.2 2.2 4.5 1.5 versicolor ## 70 5.6 2.5 3.9 1.1 versicolor ## 71 5.9 3.2 4.8 1.8 versicolor ## 72 6.1 2.8 4.0 1.3 versicolor ## 73 6.3 2.5 4.9 1.5 versicolor ## 74 6.1 2.8 4.7 1.2 versicolor ## 75 6.4 2.9 4.3 1.3 versicolor ## 76 6.6 3.0 4.4 1.4 versicolor ## 77 6.8 2.8 4.8 1.4 versicolor ## 78 6.7 3.0 5.0 1.7 versicolor ## 79 6.0 2.9 4.5 1.5 versicolor ## 80 5.7 2.6 3.5 1.0 versicolor ## 81 5.5 2.4 3.8 1.1 versicolor ## 82 5.5 2.4 3.7 1.0 versicolor ## 83 5.8 2.7 3.9 1.2 versicolor ## 84 6.0 2.7 5.1 1.6 versicolor ## 85 5.4 3.0 4.5 1.5 versicolor ## 86 6.0 3.4 4.5 1.6 versicolor ## 87 6.7 3.1 4.7 1.5 versicolor ## 88 6.3 2.3 4.4 1.3 versicolor ## 89 5.6 3.0 4.1 1.3 versicolor ## 90 5.5 2.5 4.0 1.3 versicolor ## 91 5.5 2.6 4.4 1.2 versicolor ## 92 6.1 3.0 4.6 1.4 versicolor ## 93 5.8 2.6 4.0 1.2 versicolor ## 94 5.0 2.3 3.3 1.0 versicolor ## 95 5.6 2.7 4.2 1.3 versicolor ## 96 5.7 3.0 4.2 1.2 versicolor ## 97 5.7 2.9 4.2 1.3 versicolor ## 98 6.2 2.9 4.3 1.3 versicolor ## 99 5.1 2.5 3.0 1.1 versicolor ## 100 5.7 2.8 4.1 1.3 versicolor ## 101 6.3 3.3 6.0 2.5 virginica ## 102 5.8 2.7 5.1 1.9 virginica ## 103 7.1 3.0 5.9 2.1 virginica ## 104 6.3 2.9 5.6 1.8 virginica ## 105 6.5 3.0 5.8 2.2 virginica ## 106 7.6 3.0 6.6 2.1 virginica ## 107 4.9 2.5 4.5 1.7 virginica ## 108 7.3 2.9 6.3 1.8 virginica ## 109 6.7 2.5 5.8 1.8 virginica ## 110 7.2 3.6 6.1 2.5 virginica ## 111 6.5 3.2 5.1 2.0 virginica ## 112 6.4 2.7 5.3 1.9 virginica ## 113 6.8 3.0 5.5 2.1 virginica ## 114 5.7 2.5 5.0 2.0 virginica ## 115 5.8 2.8 5.1 2.4 virginica ## 116 6.4 3.2 5.3 2.3 virginica ## 117 6.5 3.0 5.5 1.8 virginica ## 118 7.7 3.8 6.7 2.2 virginica ## 119 7.7 2.6 6.9 2.3 virginica ## 120 6.0 2.2 5.0 1.5 virginica ## 121 6.9 3.2 5.7 2.3 virginica ## 122 5.6 2.8 4.9 2.0 virginica ## 123 7.7 2.8 6.7 2.0 virginica ## 124 6.3 2.7 4.9 1.8 virginica ## 125 6.7 3.3 5.7 2.1 virginica ## 126 7.2 3.2 6.0 1.8 virginica ## 127 6.2 2.8 4.8 1.8 virginica ## 128 6.1 3.0 4.9 1.8 virginica ## 129 6.4 2.8 5.6 2.1 virginica ## 130 7.2 3.0 5.8 1.6 virginica ## 131 7.4 2.8 6.1 1.9 virginica ## 132 7.9 3.8 6.4 2.0 virginica ## 133 6.4 2.8 5.6 2.2 virginica ## 134 6.3 2.8 5.1 1.5 virginica ## 135 6.1 2.6 5.6 1.4 virginica ## 136 7.7 3.0 6.1 2.3 virginica ## 137 6.3 3.4 5.6 2.4 virginica ## 138 6.4 3.1 5.5 1.8 virginica ## 139 6.0 3.0 4.8 1.8 virginica ## 140 6.9 3.1 5.4 2.1 virginica ## 141 6.7 3.1 5.6 2.4 virginica ## 142 6.9 3.1 5.1 2.3 virginica ## 143 5.8 2.7 5.1 1.9 virginica ## 144 6.8 3.2 5.9 2.3 virginica ## 145 6.7 3.3 5.7 2.5 virginica ## 146 6.7 3.0 5.2 2.3 virginica ## 147 6.3 2.5 5.0 1.9 virginica ## 148 6.5 3.0 5.2 2.0 virginica ## 149 6.2 3.4 5.4 2.3 virginica ## 150 5.9 3.0 5.1 1.8 virginica
apply, sapply, lapply
- sapply, lapply takes in vectors/list
- sapply(lapply) returns a vector(list) of same length
WARNING: DO NOT USE ANY OF lapply OR sapply under normal circumstances
sapply(iris$Sepal.Width,floor)
## [1] 3 3 3 3 3 3 3 3 2 3 3 3 3 3 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 3 ## [36] 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 2 2 2 3 2 2 2 2 3 2 2 2 3 3 2 2 2 ## [71] 3 2 2 2 2 3 2 3 2 2 2 2 2 2 3 3 3 2 3 2 2 3 2 2 2 3 2 2 2 2 3 2 3 2 3 ## [106] 3 2 2 2 3 3 2 3 2 2 3 3 3 2 2 3 2 2 2 3 3 2 3 2 3 2 3 2 2 2 3 3 3 3 3 ## [141] 3 3 2 3 3 3 2 3 3 3
lapply(iris$Sepal.width,floor)
## list()
floor(iris$Sepal.Width)
## [1] 3 3 3 3 3 3 3 3 2 3 3 3 3 3 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 3 ## [36] 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 2 2 2 3 2 2 2 2 3 2 2 2 3 3 2 2 2 ## [71] 3 2 2 2 2 3 2 3 2 2 2 2 2 2 3 3 3 2 3 2 2 3 2 2 2 3 2 2 2 2 3 2 3 2 3 ## [106] 3 2 2 2 3 3 2 3 2 2 3 3 3 2 2 3 2 2 2 3 3 2 3 2 3 2 3 2 2 2 3 3 3 3 3 ## [141] 3 3 2 3 3 3 2 3 3 3
Notice that this returns same thing as sapply, so there is no reason to use sapply under most of the cases.
applyis a function to apply a function to a matrix by row or column or both
apply(M2,1,min)# Minimum for each row
## [1] 3 2 1
apply(M2,2,min)# Minimum for each column
## [1] 7 4 1
apply(M2,c(1,2),min)# Minimum of all entries, same as min(M2)
## [,1] [,2] [,3] ## [1,] 9 6 3 ## [2,] 8 5 2 ## [3,] 7 4 1
User define functions
Can predefine default value for argument(s) - Can take in vectors instead of scalars
random.walk <- function(n=1000,p=0.5, start = 0,min = 0, max = 1){
rand <- runif(n = n, min = min, max = max)/(max - min);
steps <- sign(2*(rand - p));
out <- start + cumsum(steps);
return(out)
}
plot(random.walk(),type = "l")
Exercise
Use the iris dataset in R and build a matrix call iris.matrix with the followings:
1. Columns and rows of iris corresponds to columns and rows of iris.matrix
2. Change the Species column of iris.matrix into the following indicator variables
- 1 - setosa, 2 - versicolor, 3 - virginica
3. Get the mean of every column except for Species column
4. Take away respective mean from each column except for the Species column
5. Produce the summary of the new matrix
Futher Notes
browser()is useful to help debugging, talk about this later?function_nameis useful to look up what a function does
Interesting reads:
ggplot2: Plot package based around "the grammer of graphics" data.table: Package showcasing a faster version of data.frame
Next Steps:
R Programming Reference: http://rpubs.com/uwaterloodatateam/r-programming-reference
Learn more R using swirl: http://swirlstats.com/students.html
Contribute useful code snippets: https://github.com/uWaterlooDataTeam/r-programming-tutorial