Introduction to R - 2nd lesson (classes and data)
Nathalie Villa-Vialaneix - http://www.nathalievialaneix.eu
September 14-16th, 2015
Master TIDE, Université Paris 1
Class
a <- c(3, 4, 5); class(a)
[1] "numeric"
class is identical to mode for vectors. More complicated objects
have different classes, such as:
matrixandarraydata.framelist- …
Matrices and arrays
- class
matrix - definition, subsetting
- operations
- functions
- class
array
Matrix
matrix: two dimensional array with entries having the same mode
A <- matrix(0, ncol=3, nrow=2); A
[,1] [,2] [,3]
[1,] 0 0 0
[2,] 0 0 0
B <- matrix(1:10, ncol=5); B
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
Matrix definition and subsetting
C <- matrix(c("A", 1:9), ncol=5, byrow=TRUE); C
[,1] [,2] [,3] [,4] [,5]
[1,] "A" "1" "2" "3" "4"
[2,] "5" "6" "7" "8" "9"
C[2,3] <- 1; C
[,1] [,2] [,3] [,4] [,5]
[1,] "A" "1" "2" "3" "4"
[2,] "5" "6" "1" "8" "9"
Matrix block subsetting
B
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
B[1,]
[1] 1 3 5 7 9
B[,2:3]
[,1] [,2]
[1,] 3 5
[2,] 4 6
Elementwise operations
B[,1:2]+B[,3:4]
[,1] [,2]
[1,] 6 10
[2,] 8 12
B*B
[,1] [,2] [,3] [,4] [,5]
[1,] 1 9 25 49 81
[2,] 4 16 36 64 100
Matrix operations
B%*%t(B); tcrossprod(B,B) # faster
[,1] [,2]
[1,] 165 190
[2,] 190 220
[,1] [,2]
[1,] 165 190
[2,] 190 220
crossprod(B,B)
[,1] [,2] [,3] [,4] [,5]
[1,] 5 11 17 23 29
[2,] 11 25 39 53 67
[3,] 17 39 61 83 105
[4,] 23 53 83 113 143
[5,] 29 67 105 143 181
Matrix operations
crossprod(B,B)
[,1] [,2] [,3] [,4] [,5]
[1,] 5 11 17 23 29
[2,] 11 25 39 53 67
[3,] 17 39 61 83 105
[4,] 23 53 83 113 143
[5,] 29 67 105 143 181
outer(B[,1], B[,2])
[,1] [,2]
[1,] 3 4
[2,] 6 8
Matrix operations
D <- crossprod(B)
resEigen <- eigen(D)
resEigen$values
[1] 3.844798e+02 5.201834e-01 2.697369e-15 -4.583117e-15 -1.657516e-14
all.equal(resEigen$vectors%*%
diag(resEigen$values)%*%
t(resEigen$vectors),
D)
[1] TRUE
Matrix functions
ncol(B); nrow(B); dim(B)
[1] 5
[1] 2
[1] 2 5
mode(B); mode(C)
[1] "numeric"
[1] "character"
Matrix functions
rowSums(B); colSums(B)
[1] 25 30
[1] 3 7 11 15 19
colnames(B)
NULL
rownames(B) <- 1:nrow(B); rownames(B)
[1] "1" "2"
Functions on rows and columns
apply(B, 1, sum); apply(B, 2, sum)
1 2
25 30
[1] 3 7 11 15 19
apply(B, 2, as.character)
[,1] [,2] [,3] [,4] [,5]
[1,] "1" "3" "5" "7" "9"
[2,] "2" "4" "6" "8" "10"
Functions on rows and columns
sweep(B, 1, rep(2,nrow(B)), "+")
[,1] [,2] [,3] [,4] [,5]
1 3 5 7 9 11
2 4 6 8 10 12
sweep(B, 1, rowSums(B), "/")
[,1] [,2] [,3] [,4] [,5]
1 0.04000000 0.1200000 0.2 0.2800000 0.3600000
2 0.06666667 0.1333333 0.2 0.2666667 0.3333333
Arrays
array is similar to matrix but with more than 2 dimensions
E <- array(1:20, c(2,5,2)); E
, , 1
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
, , 2
[,1] [,2] [,3] [,4] [,5]
[1,] 11 13 15 17 19
[2,] 12 14 16 18 20
Exercise 1
vect <- 1:6
From vect, obtain in one command line each
[,1] [,2] [,3]
[1,] 1 1 1
[2,] 2 2 2
[3,] 3 3 3
[4,] 4 4 4
[5,] 5 5 5
[6,] 6 6 6
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 2 3 4 5 6
[2,] 1 2 3 4 5 6
[3,] 1 2 3 4 5 6
Exercise 2
data(Titanic)
cont <- t(apply(Titanic, c(1,4), sum)); cont
Class
Survived 1st 2nd 3rd Crew
No 122 167 528 673
Yes 203 118 178 212
Find the ratio of survivors in each class in one command line.
Data frames
- class
data.frame - definition
- subsetting
- operators and vectors
- basic statistics
Definition
data.frame objects are 2 dimensional arrays with different modes in the
different columns. They are well suited to store several observations (rows) of
various variables (columns).
df <- data.frame(nom=c("Nathalie",
"Madalina",
"Nicolas"),
age=c(38,34,31))
df
nom age
1 Nathalie 38
2 Madalina 34
3 Nicolas 31
Data frames and class
Unlike matrices, the columns might not have the same class
class(df); sapply(df, class)
[1] "data.frame"
nom age
"factor" "numeric"
Subsetting
Columns can be extracted by number or name
names(df)
[1] "nom" "age"
df[,2]; df$age
[1] 38 34 31
[1] 38 34 31
Subsetting
df[1,]
nom age
1 Nathalie 38
df[df$age>32,]; subset(df, age>32, c("nom"))
nom age
1 Nathalie 38
2 Madalina 34
nom
1 Nathalie
2 Madalina
Exploring a data frame
data(iris);
dim(iris); names(iris); sapply(iris,class)
[1] 150 5
[1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
[5] "Species"
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
"numeric" "numeric" "numeric" "numeric" "factor"
Exploring a data frame
summary(iris[,3:5])
Petal.Length Petal.Width Species
Min. :1.000 Min. :0.100 setosa :50
1st Qu.:1.600 1st Qu.:0.300 versicolor:50
Median :4.350 Median :1.300 virginica :50
Mean :3.758 Mean :1.199
3rd Qu.:5.100 3rd Qu.:1.800
Max. :6.900 Max. :2.500
Basic numeric statistics
min(iris$Sepal.Width); max(iris$Sepal.Width)
[1] 2
[1] 4.4
mean(iris$Sepal.Width)
[1] 3.057333
median(iris$Sepal.Width)
[1] 3
Basic numeric statistics
range(iris$Sepal.Width)
[1] 2.0 4.4
sd(iris$Sepal.Width); var(iris$Sepal.Width)
[1] 0.4358663
[1] 0.1899794
quantile(iris$Sepal.Width, c(0,0.25,0.5,0.75,1))
0% 25% 50% 75% 100%
2.0 2.8 3.0 3.3 4.4
Contingency tables
table(iris$Species)
setosa versicolor virginica
50 50 50
iris$Large <- factor(iris$Sepal.Width>3)
table(iris$Species,iris$Large)
FALSE TRUE
setosa 8 42
versicolor 42 8
virginica 33 17
Operations on rows and columns
apply(iris[,1:4], 2, mean)
Sepal.Length Sepal.Width Petal.Length Petal.Width
5.843333 3.057333 3.758000 1.199333
s.iris <- sweep(iris[,1:4], 2,
apply(iris[,1:4],2,mean),
"-")
head(s.iris[,1:2], 3)
Sepal.Length Sepal.Width
1 -0.7433333 0.44266667
2 -0.9433333 -0.05733333
3 -1.1433333 0.14266667
Operations on rows and columns
apply(s.iris, 2, mean)
Sepal.Length Sepal.Width Petal.Length Petal.Width
-3.666902e-16 9.169893e-17 -3.158931e-17 -3.359437e-17
s2.iris <- scale(iris[,1:2])
apply(s2.iris,2,mean); apply(s2.iris,2,sd)
Sepal.Length Sepal.Width
-4.484318e-16 2.034094e-16
Sepal.Length Sepal.Width
1 1
Conditional statistics
by(iris$Sepal.Length, iris$Species, mean)
iris$Species: setosa
[1] 5.006
--------------------------------------------------------
iris$Species: versicolor
[1] 5.936
--------------------------------------------------------
iris$Species: virginica
[1] 6.588
Conditional statistics
tapply(iris$Sepal.Length, iris$Species, sd)
setosa versicolor virginica
0.3524897 0.5161711 0.6358796
head(tapply(iris$Sepal.Length, iris$Species,
quantile, probs=c(0.25,0.75)), 2)
$setosa
25% 75%
4.8 5.2
$versicolor
25% 75%
5.6 6.3
Exercise 3
data(airquality)
What is the dimension of the data?
What are the variables included in the data? What are their types?
How can you obtain a summary of the data?
What is the number of days having a temperature larger than 80°F? What is the average Ozone rate and Wind speed for these days?
What is the average Ozone rate for each month?
Lists
- class
list - definition
- subsetting
- operators and vectors
- basic statistics
Lists
list is a collection of heterogeneous objects:
a.list <- list("name"="a list", "matrix"=B,
"dataframe"=df); a.list
$name
[1] "a list"
$matrix
[,1] [,2] [,3] [,4] [,5]
1 1 3 5 7 9
2 2 4 6 8 10
$dataframe
nom age
1 Nathalie 38
2 Madalina 34
3 Nicolas 31
Basic operations
class(a.list)
[1] "list"
length(a.list)
[1] 3
names(a.list)
[1] "name" "matrix" "dataframe"
Basic operations
lapply(a.list, class)
$name
[1] "character"
$matrix
[1] "matrix"
$dataframe
[1] "data.frame"
Basic operations
lapply(a.list, length)
$name
[1] 1
$matrix
[1] 10
$dataframe
[1] 2