Základné operácie v R

Numerické vektory

Generovanie vektorov

v1 <- c(1, 3, 7, 9)
v2 <- 1:6                 
v3 <- seq(from = 0, to = 4, by = 0.25)  
v4 <- rep(2, times = 6)    
v5 <- runif(7)             
v6 <- rnorm(4)            
v1; v2; v3; v4; v5

[1] 1 3 7 9
[1] 1 2 3 4 5 6
 [1] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00
[1] 2 2 2 2 2 2
[1] 0.39836832 0.08691421 0.69619160 0.23205830 0.02943422 0.42164100 0.06005022

Aritmetické operácie s vektormi

v <- c(5, 6, 7, 8)
v + 20           

[1] 25 26 27 28

v * 3           

[1] 15 18 21 24

(v + 3) / 2

[1] 4.0 4.5 5.0 5.5

exp(v)          

[1]  148.4132  403.4288 1096.6332 2980.9580

sum(c(4,5,6),c(2,2,2))         

[1] 21

crossprod(c(4,5,6),c(2,2,2))    

     [,1]
[1,]   30

c(4,5,6)*c(2,2,2)             

[1]  8 10 12

Matematické operácie s 2 vektormi rovnakého rozmeru

length(c(3,4,5,6,7,8,9))

[1] 7

length(v5)           

[1] 7

c(1,2,5,6,7,8,9) + v5   

[1] 1.398368 2.086914 5.696192 6.232058 7.029434 8.421641 9.060050

Indexovanie a výber niektorych prvkov vektora

x <- c(6, 10, 2, 17, 4, 1, 24)
x[2]          

[1] 10

x[4:6]        

[1] 17  4  1

x[-1]         

[1] 10  2 17  4  1 24

x[x > 10]      

[1] 17 24

which(x > 10)  

[1] 4 7

Práca s chýbajúcimi hodnotami

y <- c(2, NA, 7, NA, 9)
is.na(y)

[1] FALSE  TRUE FALSE  TRUE FALSE

mean(y)                 

[1] NA

mean(y, na.rm = TRUE)  

[1] 6

Základné štatistiky a usporiadanie prvkov vektora podľa veľkosti

z <- c(16, 6, 3, 5, 9)
mean(z)                

[1] 7.8

sd(z)                 

[1] 5.069517

max(z)                  

[1] 16

summary(z)              

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    3.0     5.0     6.0     7.8     9.0    16.0 

sort(z)                 

[1]  3  5  6  9 16

sort(z, decreasing = TRUE)  

[1] 16  9  6  5  3

Malé cvičenie

Vytvorte vektor w s číslami 1..20 a vypočítajte sumu všetkých párnych čísel.

w <- 1:20
sum(w[w %% 2 == 0])

[1] 110

body <- c(45, 60, 75, 90, 55, 80)
body[body > 70]

[1] 75 90 80

 
mean(body)

[1] 67.5

min(body)

[1] 45

max(body)

[1] 90

 
all(body > 40)

[1] TRUE

 
a <- c(1, 2, 3)
b <- c(4, 5, 6)
a + b

[1] 5 7 9

a * b

[1]  4 10 18

Matice

Vytvorenie matíc

m <- matrix(1:16, nrow = 4, ncol = 4)           
m_byrow <- matrix(1:16, nrow = 4, byrow = TRUE) 
m; m_byrow

     [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
[3,]    3    7   11   15
[4,]    4    8   12   16
     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    5    6    7    8
[3,]    9   10   11   12
[4,]   13   14   15   16

Rozmery matice

dim(m)                   

[1] 4 4

m

     [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
[3,]    3    7   11   15
[4,]    4    8   12   16

Adresovanie prvkov matice

m[3, 4]     

[1] 15

m[ , 4]      

[1] 13 14 15 16

m[2, ]       

[1]  2  6 10 14

m[3:4, 1:2]  

     [,1] [,2]
[1,]    3    7
[2,]    4    8

Maticové operácie

A <- matrix(c(3,5,7,9), nrow = 2)
B <- matrix(c(1,5,6,8), nrow = 2)
 
A + B        

     [,1] [,2]
[1,]    4   13
[2,]   10   17

A * B        

     [,1] [,2]
[1,]    3   42
[2,]   25   72

A %*% B      

     [,1] [,2]
[1,]   38   74
[2,]   50  102

t(A)        

     [,1] [,2]
[1,]    3    5
[2,]    7    9

det(A)       

[1] -8

solve(A)     

       [,1]   [,2]
[1,] -1.125  0.875
[2,]  0.625 -0.375

Zlučovanie vektorov do matíc

C <- cbind(1:2, 4:5)   
D <- rbind(1:2, 4:5)  
C; D

     [,1] [,2]
[1,]    1    4
[2,]    2    5
     [,1] [,2]
[1,]    1    2
[2,]    4    5

Vypočítanie zvolenej štatistiky po riadkoch (stĺpcoch) matice

M <- matrix(1:16, nrow = 4)
M

     [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
[3,]    3    7   11   15
[4,]    4    8   12   16

apply(M, 1, sum)  

[1] 28 32 36 40

apply(M, 2, mean)  

[1]  2.5  6.5 10.5 14.5

Malé cvičenie

Vytvorte maticu 5x5 s hodnotami po riadkoch 1..25, vypočítajte stĺpcové sumy a súčin matíc \(M^t M\).

M2 <- matrix(1:25, nrow = 5, byrow = TRUE)
colSums(M2)

[1] 55 60 65 70 75

t(M2) %*% M2

     [,1] [,2] [,3] [,4] [,5]
[1,]  855  910  965 1020 1075
[2,]  910  970 1030 1090 1150
[3,]  965 1030 1095 1160 1225
[4,] 1020 1090 1160 1230 1300
[5,] 1075 1150 1225 1300 1375

mat <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow = 3, ncol = 3, byrow = TRUE)
mat[2, 3]

[1] 6

mat[2, ]

[1] 4 5 6

mat[, 3]

[1] 3 6 9

mat[c(1, 3), c(2, 3)]

     [,1] [,2]
[1,]    2    3
[2,]    8    9

t(mat)

     [,1] [,2] [,3]
[1,]    1    4    7
[2,]    2    5    8
[3,]    3    6    9

A <- matrix(1:9, nrow = 3)
B <- matrix(9:1, nrow = 3)
A + B

     [,1] [,2] [,3]
[1,]   10   10   10
[2,]   10   10   10
[3,]   10   10   10

A * B

     [,1] [,2] [,3]
[1,]    9   24   21
[2,]   16   25   16
[3,]   21   24    9

A %*% B

     [,1] [,2] [,3]
[1,]   90   54   18
[2,]  114   69   24
[3,]  138   84   30

det(A)

[1] 0

diag(c(2, 4, 6))

     [,1] [,2] [,3]
[1,]    2    0    0
[2,]    0    4    0
[3,]    0    0    6

diag(3)

     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1

rowSums(A)

[1] 12 15 18

colSums(A)

[1]  6 15 24

rowMeans(A)

[1] 4 5 6

colMeans(A)

[1] 2 5 8

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