Using R Software
Introduction
Assignment of a variable:
x = 1
x <- 1
(X = 2)[1] 2x[1] 1X[1] 2Help:
?plotHelp on topic 'plot' was found in the following packages:
Package Library
graphics /usr/lib/R/library
base /usr/lib/R/library
Utilisation de la première correspondance ...Logic:
| Logic: | R |
|---|---|
| AND | & |
| OR | | |
| NO | ! |
| TRUE | T ou TRUE |
| FALSE | F ou FALSE |
| \(\neq\) | != |
| \(\geq\) | >= |
| \(=\) | == |
1+2==3[1] TRUE!((3>1) & (2>=2))[1] FALSEVector
Entering a vector:
1:10 [1] 1 2 3 4 5 6 7 8 9 10c(1,7,12,-1)[1] 1 7 12 -1seq(from=1, to=10, by=0.1) [1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
[16] 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
[31] 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4
[46] 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9
[61] 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4
[76] 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
[91] 10.0seq(0, 1, length=10) [1] 0.0000000 0.1111111 0.2222222 0.3333333 0.4444444 0.5555556 0.6666667
[8] 0.7777778 0.8888889 1.0000000rep(1:3, times=2)[1] 1 2 3 1 2 3rep(1:3, times=2, each=2) [1] 1 1 2 2 3 3 1 1 2 2 3 3rep(1:3, times=c(2,7,3)) [1] 1 1 2 2 2 2 2 2 2 3 3 3Numeric, character or boolean values :
(x=c(0,pi,-2.3,sqrt(7)))[1] 0.000000 3.141593 -2.300000 2.645751(x1=c(x,NA))[1] 0.000000 3.141593 -2.300000 2.645751 NA(y=c('Vietnam','France','Orleans'))[1] "Vietnam" "France" "Orleans"(z=c(T,F,F,TRUE,FALSE,1==2,2<3))[1] TRUE FALSE FALSE TRUE FALSE FALSE TRUEmode(x)[1] "numeric"mode(y)[1] "character"mode(z)[1] "logical"length(x)[1] 4length(y)[1] 3length(z)[1] 7is.numeric(x)[1] TRUEis.character(y) [1] TRUEis.logical(x>1)[1] TRUEis.vector(x)[1] TRUEis.matrix(x)[1] FALSEis.null(x)[1] FALSEis.na(x1)[1] FALSE FALSE FALSE FALSE TRUEUsual operations:
x + 2[1] 2.000000 5.141593 -0.300000 4.645751x>=1[1] FALSE TRUE FALSE TRUEx^2[1] 0.000000 9.869604 5.290000 7.000000sqrt(abs(x))[1] 0.000000 1.772454 1.516575 1.626577Name the components of a vector:
score=c(10,7,14,3)
lecture=c('Phy','Mat','Eco','Info')
names(score)=lecture
score Phy Mat Eco Info
10 7 14 3 names(score)=NULL
score=c(Phy=10,Mat=7,Eco=14,Info=3)
score Phy Mat Eco Info
10 7 14 3 Sort the components of a vector:
(x=c(pi,0,1,-3.2,(1+sqrt(5))/2))[1] 3.141593 0.000000 1.000000 -3.200000 1.618034sort(x)[1] -3.200000 0.000000 1.000000 1.618034 3.141593sort(x,decreasing = T)[1] 3.141593 1.618034 1.000000 0.000000 -3.200000sort(x,dec = T)[1] 3.141593 1.618034 1.000000 0.000000 -3.200000order(x)[1] 4 2 3 5 1x[order(x)][1] -3.200000 0.000000 1.000000 1.618034 3.141593Select components of a vector:
x[2][1] 0x[-2][1] 3.141593 1.000000 -3.200000 1.618034x[c(2,4)][1] 0.0 -3.2x[x>=1][1] 3.141593 1.000000 1.618034lecture[score>=10][1] "Phy" "Eco"Concatenation :
x0 = c(1,2)
y0 = c(3,4)
(z = c(x0,y0))[1] 1 2 3 4Matrix
Entering a matrix:
A = matrix(c(5,2,-1,3,-4,6), nrow=2, ncol=3)
B = matrix(c(5,2,-1,3,-4,6), nrow=2, ncol=3, byrow=T)Equality test:
1 == 2[1] FALSEx == 1[1] FALSE FALSE TRUE FALSE FALSEA == B [,1] [,2] [,3]
[1,] TRUE FALSE FALSE
[2,] FALSE FALSE TRUEany(A == B)[1] TRUEall(A == B)[1] FALSECoefficient in position (i, j):
A[2,3][1] 6Extracting a row/column:
A[2,][1] 2 3 6A[,1][1] 5 2Deleting a row/column (or several rows/columns):
A[-2,][1] 5 -1 -4A[,-1] [,1] [,2]
[1,] -1 -4
[2,] 3 6A[-2,-1][1] -1 -4A[-2,c(-1,-2)][1] -4Transpose a matrix :
t(A) [,1] [,2]
[1,] 5 2
[2,] -1 3
[3,] -4 6Usual operations:
A + B [,1] [,2] [,3]
[1,] 10 1 -5
[2,] 5 -1 12A * B [,1] [,2] [,3]
[1,] 25 -2 4
[2,] 6 -12 36A %*% t(B) [,1] [,2]
[1,] 27 -5
[2,] 10 30A + 3 [,1] [,2] [,3]
[1,] 8 2 -1
[2,] 5 6 93*A [,1] [,2] [,3]
[1,] 15 -3 -12
[2,] 6 9 18A^3 [,1] [,2] [,3]
[1,] 125 -1 -64
[2,] 8 27 2162^A [,1] [,2] [,3]
[1,] 32 0.5 0.0625
[2,] 4 8.0 64.0000Concatenation :
rbind(A, B) [,1] [,2] [,3]
[1,] 5 -1 -4
[2,] 2 3 6
[3,] 5 2 -1
[4,] 3 -4 6cbind(A, B) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 5 -1 -4 5 2 -1
[2,] 2 3 6 3 -4 6Special case of square matrices
Identity matrix of given format:
diag(4) [,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 0 1 0 0
[3,] 0 0 1 0
[4,] 0 0 0 1Diagonal matrix formed from given coefficients:
(C=diag(c(2,-1,5,0,8))) [,1] [,2] [,3] [,4] [,5]
[1,] 2 0 0 0 0
[2,] 0 -1 0 0 0
[3,] 0 0 5 0 0
[4,] 0 0 0 0 0
[5,] 0 0 0 0 8Determinant of a matrix
det(C)[1] 0Diagonal elements of a matrix:
diag(A)[1] 5 3Inverse :
A =matrix(c(6,12,3,5,10,5,3,8,2),3,3)
B =matrix(c(2,3,3,4,6,5,6,9,5),3,3)
solve(A) [,1] [,2] [,3]
[1,] 0.6666667 -0.1666667 -0.3333333
[2,] 0.0000000 -0.1000000 0.4000000
[3,] -1.0000000 0.5000000 0.0000000solve(A, B) [,1] [,2] [,3]
[1,] -0.1666667 -1.480297e-16 0.8333333
[2,] 0.9000000 1.400000e+00 1.1000000
[3,] -0.5000000 -1.000000e+00 -1.5000000solve(A) %*% B [,1] [,2] [,3]
[1,] -0.1666667 -5.551115e-17 0.8333333
[2,] 0.9000000 1.400000e+00 1.1000000
[3,] -0.5000000 -1.000000e+00 -1.5000000Random variable
Generate data
y = runif(1000)
y[1:30] [1] 0.835938710 0.428667026 0.407574144 0.006063845 0.977409488 0.262921007
[7] 0.537516835 0.885083936 0.266330516 0.108101886 0.342384226 0.899514456
[13] 0.142731028 0.448430820 0.460109022 0.808785409 0.747074644 0.452997989
[19] 0.106499520 0.566914315 0.126383577 0.109943035 0.279621152 0.126814258
[25] 0.328277479 0.507362241 0.860770951 0.174909196 0.687567855 0.182753417hist(y,freq=F)
y = runif(1000,2,3)
y[1:30] [1] 2.752475 2.607184 2.652447 2.064841 2.254607 2.348022 2.236251 2.834992
[9] 2.753475 2.672690 2.205300 2.807413 2.683947 2.251402 2.983518 2.011137
[17] 2.554966 2.957088 2.597718 2.236718 2.733337 2.279272 2.448419 2.350797
[25] 2.221219 2.709922 2.348577 2.507301 2.180082 2.471986hist(y,freq=F)
z = rnorm(1000)
hist(z,freq=F)
z = rnorm(1000,10,2)
hist(z,freq=F)
?distributions Probability/Density Function
t=0:7
plot(t,dbinom(t,7,0.2),type='h')
t = seq(-7, 7, by=0.1)
f = dnorm(t)
plot(t,f,type='l')
Cumulative Distribution Function
t=0:7
plot(t,pbinom(t,7,0.2),type='s')
t = seq(-7, 7, by=0.1)
Fc = pnorm(t)
plot(t,Fc,type='l')
Quantile
qbinom(0.7,7,0.2)[1] 2t = seq(-7, 7, by=0.1)
Fc = pnorm(t)
plot(t,Fc,type='l')
q=qnorm(0.95)
segments(-7,0.95,q,0.95,col='orange')
segments(q,0,q,0.95,col='orange',lty=3)
f = dnorm(t)
plot(t,f,type='l')
value <- qnorm(0.95)
tq=max(which(t < value))
polygon(c(t[c(1, 1:tq, tq)]),
c(0,f[1:tq], 0),
col = 'orange')
legend("topright",
legend = c(0.95),
fill = 'orange') 
qnorm(0.95)[1] 1.644854Dataframe
x1=rnorm(100,2,10)
x2=rgeom(100,0.2)
x3=sample(0:9,100,replace = T)
Dataframe=data.frame(X=x1,Y=x2,Z=x3,row.names = NULL)
Dataframe$X [1] -8.79180921 4.13471722 10.36440021 1.14869767 14.66433955
[6] 3.08886560 9.48671653 7.05361537 -9.16318029 9.63624993
[11] 5.85390602 14.97642312 -12.59176181 11.80516142 31.25309838
[16] 0.98577879 -14.52082820 -8.27589227 6.90053945 6.48928780
[21] 24.51464902 11.70847706 10.80784501 -1.24622589 6.25858449
[26] 3.18786801 10.05446118 6.57528854 4.63030946 -6.13363762
[31] 7.76419265 10.74789321 -4.35830369 -9.90536586 18.38971537
[36] 4.24995241 3.13299987 -4.81719734 -0.36543800 -5.69964350
[41] -14.68430813 -22.24708705 -10.31430450 26.68027923 9.57073887
[46] 5.13069787 9.42859940 14.23796475 4.42070750 -1.25144451
[51] 14.79658001 -0.31301560 -2.91630942 -9.22491248 5.68602218
[56] 13.86216027 3.54142212 -1.80050111 6.87268531 1.65582584
[61] -5.19539324 10.78596350 6.28597619 -1.87146587 10.99575058
[66] 16.38924685 10.04237980 -0.06370955 -16.39620292 -1.38737191
[71] 0.74026802 2.14401918 -14.83989006 21.64705243 -5.24545651
[76] -9.82616070 -10.92668815 6.28421012 -17.97047621 -3.59247728
[81] 0.79022359 9.83097339 5.59893426 -9.22652104 2.07302804
[86] -6.30443179 18.21061418 9.71794961 -24.55376849 -3.90530043
[91] 20.39071365 5.50290413 11.24100411 8.66959041 14.39227432
[96] 3.98247038 -2.64719098 -9.11293864 -7.12800396 1.52292897Dataframe[10,] X Y Z
10 9.63625 9 0Data sets
From R
data()
data(trees)
?trees
attach(trees)
Height [1] 70 65 63 72 81 83 66 75 80 75 79 76 76 69 75 74 85 86 71 64 78 80 74 72 77
[26] 81 82 80 80 80 87Volume [1] 10.3 10.3 10.2 16.4 18.8 19.7 15.6 18.2 22.6 19.9 24.2 21.0 21.4 21.3 19.1
[16] 22.2 33.8 27.4 25.7 24.9 34.5 31.7 36.3 38.3 42.6 55.4 55.7 58.3 51.5 51.0
[31] 77.0Girth [1] 8.3 8.6 8.8 10.5 10.7 10.8 11.0 11.0 11.1 11.2 11.3 11.4 11.4 11.7 12.0
[16] 12.9 12.9 13.3 13.7 13.8 14.0 14.2 14.5 16.0 16.3 17.3 17.5 17.9 18.0 18.0
[31] 20.6plot(Girth, Volume)
From a file
data=read.table(file='Students.txt',header=T)
data Transport Score Brotherhood Time
1 Public_Transport F 3 0.622526462
2 Car F 4 36.657511927
3 Public_Transport C 3 11.522504011
4 Public_Transport D 1 33.828593223
5 Bike D 0 9.060720704
6 Public_Transport F 4 4.857579940
7 Public_Transport A 5 11.671969750
8 Public_Transport C 2 18.826682988
9 Car D 4 1.900738537
10 Public_Transport A 4 12.803518513
11 Car D 1 2.836075382
12 Public_Transport D 2 20.945708765
13 Walk F 2 11.724335026
14 Motorbike C 2 21.810021646
15 Public_Transport C 5 34.394449328
16 Car C 2 41.642181424
17 Car B 4 2.348245194
18 Car D 2 16.857141836
19 Public_Transport B 3 5.928522913
20 Car C 3 28.115604846
21 Walk D 2 1.306014591
22 Public_Transport B 1 86.365817737
23 Public_Transport B 1 50.441392478
24 Bike B 2 30.058228249
25 Public_Transport B 3 24.271936752
26 Car C 1 4.105579573
27 Car D 3 47.241244459
28 Bike D 0 0.007837325
29 Car D 2 2.906950905
30 Bike C 1 11.342407078
31 Walk C 3 23.560583102
32 Public_Transport F 3 26.990008915
33 Public_Transport D 2 42.449839111
34 Bike C 3 7.878798416
35 Motorbike A 4 7.898013091
36 Car D 2 22.147315960
37 Public_Transport C 2 7.862954240
38 Car C 2 10.507826147
39 Car D 2 26.767066484
40 Car B 3 5.211386752
41 Car C 3 2.547239953
42 Bike C 4 10.893660760
43 Bike B 2 3.048932392
44 Public_Transport D 4 19.312018348
45 Public_Transport D 0 1.250998323
46 Car B 4 23.468056341
47 Car F 2 1.307201008
48 Public_Transport C 1 9.061298305
49 Car B 2 16.386605089
50 Public_Transport F 5 14.198586260
51 Public_Transport D 2 5.903930680
52 Car D 5 10.788057048
53 Car F 0 2.847771212
54 Public_Transport D 1 15.982389033
55 Public_Transport B 1 33.808323654
56 Public_Transport C 2 20.621755818
57 Car F 3 4.990251950
58 Public_Transport B 4 14.176132792
59 Public_Transport C 2 0.179795340
60 Car B 1 11.144025391
61 Car B 2 6.207213615
62 Car C 3 10.930397624
63 Public_Transport C 1 3.191945825
64 Car A 1 24.116514756
65 Walk C 1 9.085949403
66 Walk A 3 3.123102145
67 Car C 2 4.905990076
68 Car F 1 11.141701792
69 Car C 1 7.942769108
70 Public_Transport C 4 25.155511402
71 Walk D 2 6.966238022
72 Public_Transport B 0 12.714376537
73 Public_Transport A 4 10.094412043
74 Car D 0 0.492263361
75 Public_Transport B 2 3.412106307
76 Public_Transport B 3 0.868697702
77 Public_Transport C 4 5.920769674
78 Car C 1 5.628014676
79 Public_Transport D 4 3.345181326
80 Public_Transport D 4 16.678423936
81 Public_Transport B 1 3.234560808
82 Public_Transport F 3 20.669727642
83 Car C 1 5.861409699
84 Public_Transport C 2 7.774037436
85 Public_Transport D 2 4.237668986
86 Car B 2 15.835740114
87 Bike A 2 22.383022838
88 Bike C 4 64.356934684
89 Public_Transport C 2 58.376442213
90 Public_Transport D 3 8.445475412
91 Car D 5 29.818047602
92 Car C 2 12.984430205
93 Car B 1 19.110928737
94 Car B 0 72.178583905
95 Public_Transport C 3 7.568940726
96 Walk D 0 24.049530272
97 Public_Transport C 2 12.698371948
98 Car F 3 8.964170181
99 Motorbike D 2 17.777711578
100 Bike F 3 8.675561884head(data) Transport Score Brotherhood Time
1 Public_Transport F 3 0.6225265
2 Car F 4 36.6575119
3 Public_Transport C 3 11.5225040
4 Public_Transport D 1 33.8285932
5 Bike D 0 9.0607207
6 Public_Transport F 4 4.8575799attach(data)
detach(data)From a saved R workspace
rm(list=ls())
load("Students.RData")
data Transport Score Brotherhood Time
1 Public_Transport F 3 0.622526462
2 Car F 4 36.657511927
3 Public_Transport C 3 11.522504011
4 Public_Transport D 1 33.828593223
5 Bike D 0 9.060720704
6 Public_Transport F 4 4.857579940
7 Public_Transport A 5 11.671969750
8 Public_Transport C 2 18.826682988
9 Car D 4 1.900738537
10 Public_Transport A 4 12.803518513
11 Car D 1 2.836075382
12 Public_Transport D 2 20.945708765
13 Walk F 2 11.724335026
14 Motorbike C 2 21.810021646
15 Public_Transport C 5 34.394449328
16 Car C 2 41.642181424
17 Car B 4 2.348245194
18 Car D 2 16.857141836
19 Public_Transport B 3 5.928522913
20 Car C 3 28.115604846
21 Walk D 2 1.306014591
22 Public_Transport B 1 86.365817737
23 Public_Transport B 1 50.441392478
24 Bike B 2 30.058228249
25 Public_Transport B 3 24.271936752
26 Car C 1 4.105579573
27 Car D 3 47.241244459
28 Bike D 0 0.007837325
29 Car D 2 2.906950905
30 Bike C 1 11.342407078
31 Walk C 3 23.560583102
32 Public_Transport F 3 26.990008915
33 Public_Transport D 2 42.449839111
34 Bike C 3 7.878798416
35 Motorbike A 4 7.898013091
36 Car D 2 22.147315960
37 Public_Transport C 2 7.862954240
38 Car C 2 10.507826147
39 Car D 2 26.767066484
40 Car B 3 5.211386752
41 Car C 3 2.547239953
42 Bike C 4 10.893660760
43 Bike B 2 3.048932392
44 Public_Transport D 4 19.312018348
45 Public_Transport D 0 1.250998323
46 Car B 4 23.468056341
47 Car F 2 1.307201008
48 Public_Transport C 1 9.061298305
49 Car B 2 16.386605089
50 Public_Transport F 5 14.198586260
51 Public_Transport D 2 5.903930680
52 Car D 5 10.788057048
53 Car F 0 2.847771212
54 Public_Transport D 1 15.982389033
55 Public_Transport B 1 33.808323654
56 Public_Transport C 2 20.621755818
57 Car F 3 4.990251950
58 Public_Transport B 4 14.176132792
59 Public_Transport C 2 0.179795340
60 Car B 1 11.144025391
61 Car B 2 6.207213615
62 Car C 3 10.930397624
63 Public_Transport C 1 3.191945825
64 Car A 1 24.116514756
65 Walk C 1 9.085949403
66 Walk A 3 3.123102145
67 Car C 2 4.905990076
68 Car F 1 11.141701792
69 Car C 1 7.942769108
70 Public_Transport C 4 25.155511402
71 Walk D 2 6.966238022
72 Public_Transport B 0 12.714376537
73 Public_Transport A 4 10.094412043
74 Car D 0 0.492263361
75 Public_Transport B 2 3.412106307
76 Public_Transport B 3 0.868697702
77 Public_Transport C 4 5.920769674
78 Car C 1 5.628014676
79 Public_Transport D 4 3.345181326
80 Public_Transport D 4 16.678423936
81 Public_Transport B 1 3.234560808
82 Public_Transport F 3 20.669727642
83 Car C 1 5.861409699
84 Public_Transport C 2 7.774037436
85 Public_Transport D 2 4.237668986
86 Car B 2 15.835740114
87 Bike A 2 22.383022838
88 Bike C 4 64.356934684
89 Public_Transport C 2 58.376442213
90 Public_Transport D 3 8.445475412
91 Car D 5 29.818047602
92 Car C 2 12.984430205
93 Car B 1 19.110928737
94 Car B 0 72.178583905
95 Public_Transport C 3 7.568940726
96 Walk D 0 24.049530272
97 Public_Transport C 2 12.698371948
98 Car F 3 8.964170181
99 Motorbike D 2 17.777711578
100 Bike F 3 8.675561884head(data) Transport Score Brotherhood Time
1 Public_Transport F 3 0.6225265
2 Car F 4 36.6575119
3 Public_Transport C 3 11.5225040
4 Public_Transport D 1 33.8285932
5 Bike D 0 9.0607207
6 Public_Transport F 4 4.8575799attach(data)
detach(data)
save(data,file="Students.RData")
save.image("Students.RData")Write functions
square=function(x)
{
res=x^2
return(res)
}
square(2)[1] 4square.root=function(x)
{
if (x>=0)
{
res=x^{1/2}
return(res)
}
else
{
print(paste(x,'is a negative number'))
}
}
square.root(2)[1] 1.414214square.root(-1)[1] "-1 is a negative number"Syracuse=function(x,n)
{
x_seq=x
for (j in 1:n)
{
if (x%%2==0)
{
x=x/2
}
else
{
x=3*x+1
}
x_seq=c(x_seq,x)
}
return(list(n,x_seq))
}
Syracuse(17,100)[[1]]
[1] 100
[[2]]
[1] 17 52 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1
[26] 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4
[51] 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2
[76] 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1
[101] 4Syracuse_rec=function(x,n)
{
m=length(x)
res=x
if (n>0)
{
if (x[m]%%2==0)
{
res=Syracuse_rec(c(x,x[m]/2),n-1)
}
else
{
res=Syracuse_rec(c(x,3*x[m]+1),n-1)
}
}
return(res)
}
Syracuse_rec(17,100) [1] 17 52 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1
[26] 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4
[51] 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2
[76] 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1
[101] 4Fibonacci_game=function(x,y)
{
num=rep(NA,10)
num[1:2]=c(x,y)
for (j in 3:10)
{
num[j]=sum(num[j-(1:2)])
}
ratio=num[10]/num[9]
total=sum(num)
estim=num[7]*11
return(list('num'=num,'ratio'=ratio, 'total'=total,'estim'=estim ))
}
Fibonacci_game(7,3)$num
[1] 7 3 10 13 23 36 59 95 154 249
$ratio
[1] 1.616883
$total
[1] 649
$estim
[1] 649