Vektory a Matice

Numerické vektory

Generovanie vektorov

v1 <- c(4,7,10,13)
v2 <- 10:1                 
v3 <- seq(from = 15, to = 20, by = 0.50) 
v4 <- rep(4, times = 3)   
v5 <- runif(2)            
v6 <- rnorm(5)            
v1; v2; v3; v4; v5; v6

[1]  4  7 10 13
 [1] 10  9  8  7  6  5  4  3  2  1
 [1] 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0
[1] 4 4 4
[1] 0.1165475 0.3837036
[1]  0.5678121 -0.8632417  0.2897643 -0.1232291  0.8474662

Aritmetické operácie s vektormi

v <- c(20, 22, 24, 26)
v + 5           

[1] 25 27 29 31

v * 2            

[1] 40 44 48 52

(v + 4) / 2

[1] 12 13 14 15

exp(v)           

[1]    485165195   3584912846  26489122130 195729609429

sum(c(5,6,7),c(2,2,2))          

[1] 24

crossprod(c(5,6,7),c(2,2,2))   

     [,1]
[1,]   36

c(5,6,7)*c(2,2,2)               

[1] 10 12 14

Matematické operácie s 2 vektormi rovnakého rozmeru

length(c(6,7))

[1] 2

length(v5)            

[1] 2

c(6,7) + v5    

[1] 6.116548 7.383704

Indexovanie a výber niektorych prvkov vektora

x <- c(7, 81, 4, 3, 55, 0, 2, 23)
x[2]           

[1] 81

x[5:8]         

[1] 55  0  2 23

x[-8]          

[1]  7 81  4  3 55  0  2

x[x < 15]      

[1] 7 4 3 0 2

which(x > 30)  

[1] 2 5

Práca s chýbajúcimi hodnotami

y <- c(6, NA, 9, NA, 15)
is.na(y)

[1] FALSE  TRUE FALSE  TRUE FALSE

mean(y)                

[1] NA

mean(y, na.rm = TRUE)   

[1] 10

Základné štatistiky a usporiadanie prvkov vektora podľa veľkosti

z <- c(50, 5, 1, 81, 1)
mean(z)                 

[1] 27.6

sd(z)                 

[1] 36.32905

max(z)                  

[1] 81

summary(z)             

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    1.0     1.0     5.0    27.6    50.0    81.0 

sort(z)                 

[1]  1  1  5 50 81

sort(z, decreasing = TRUE)  

[1] 81 50  5  1  1

Malé cvičenie

Vytvorte vektor w s číslami 1..15 a vypočítajte sumu všetkých párnych čísel.

w <- 1:15
sum(w[w %% 2 == 0])

[1] 56

Triedenie vektora (vzostupne a zostupne)

v3 <- c(45, 12, 78, 34, 5)

sort(v3)                       # vzostupne

[1]  5 12 34 45 78

sort(v3, decreasing = TRUE)    # zostupne

[1] 78 45 34 12  5

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Matice

Vytvorenie matíc

m <- matrix(1:9, nrow = 3, ncol = 3)           
m_byrow <- matrix(1:9, nrow = 3, byrow = TRUE)  
m; m_byrow

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

Rozmery matice

dim(m)                  

[1] 3 3

m

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

Adresovanie prvkov matice

m[2, 3]      

[1] 8

m[ , 1]      

[1] 1 2 3

m[1, ]       

[1] 1 4 7

m[3:1, 2:1]  

     [,1] [,2]
[1,]    6    3
[2,]    5    2
[3,]    4    1

Maticové operácie

A <- matrix(c(5,10,11,2), nrow = 2)
B <- matrix(c(34,1,22,2), nrow = 2)

A + B       

     [,1] [,2]
[1,]   39   33
[2,]   11    4

A * B       

     [,1] [,2]
[1,]  170  242
[2,]   10    4

A %*% B      

     [,1] [,2]
[1,]  181  132
[2,]  342  224

t(A)         

     [,1] [,2]
[1,]    5   10
[2,]   11    2

det(A)       

[1] -100

solve(A)    

      [,1]  [,2]
[1,] -0.02  0.11
[2,]  0.10 -0.05

Zlučovanie vektorov do matíc

C <- cbind(1:4, 5:6)  
D <- rbind(2:3, 4:7)  
C; D

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

Vypočítanie zvolenej štatistiky po riadkoch (stĺpcoch) matice

M <- matrix(1:15, nrow = 5)
M

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

apply(M, 2, sum)   

[1] 15 40 65

apply(M, 1, mean)  

[1]  6  7  8  9 10

Malé cvičenie

Vytvorte maticu 6x6 s hodnotami po riadkoch 1..36, vypočítajte stĺpcové sumy a súčin matíc \(M^t M\).

M2 <- matrix(1:36, nrow = 6, byrow = TRUE)
colSums(M2)

[1]  96 102 108 114 120 126

t(M2) %*% M2

     [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2166 2262 2358 2454 2550 2646
[2,] 2262 2364 2466 2568 2670 2772
[3,] 2358 2466 2574 2682 2790 2898
[4,] 2454 2568 2682 2796 2910 3024
[5,] 2550 2670 2790 2910 3030 3150
[6,] 2646 2772 2898 3024 3150 3276

Premenovanie riadkov a stĺpcov

m <- matrix(1:9, nrow = 3, ncol = 3)
rownames(m) <- c("1.riadok","2.riadok","3.riadok")
colnames(m) <- c("1.stĺpec","2.stĺpec","3.stĺpec")
m

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