Working with matrices, lists, and data frames
n_dims a single random integer
between 3 and 10. Create a vector of consecutive integers from 1 to
n_dims^2n_dims <- runif(n=1, min=3, max=10)
my_vec <- seq(from=1, to=n_dims^2)
head(my_vec)## [1] 1 2 3 4 5 6Use the sample function to randomly reshuffle these values.
new_vec <- sample(x=my_vec)
print(new_vec)## [1] 35 71 65 49 20 63 47 7 18 88 83 73 22 80 55 34 8 85 37 6 11 82 59 70 75
## [26] 2 84 67 15 4 42 50 10 87 54 40 69 5 36 26 12 14 16 25 13 68 77 38 33 52
## [51] 62 46 1 61 79 74 51 76 41 48 43 3 64 23 31 44 58 53 89 30 81 72 60 56 9
## [76] 86 27 39 29 78 28 21 19 24 57 66 45 32 17Create a square matrix with these elements.
m <- matrix(data=new_vec, nrow=n_dims, ncol=n_dims)## Warning in matrix(data = new_vec, nrow = n_dims, ncol = n_dims): data length
## [89] is not a sub-multiple or multiple of the number of rows [9]Print out the matrix.
print(m)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 35 88 37 67 69 68 79 23 60
## [2,] 71 83 6 15 5 77 74 31 56
## [3,] 65 73 11 4 36 38 51 44 9
## [4,] 49 22 82 42 26 33 76 58 86
## [5,] 20 80 59 50 12 52 41 53 27
## [6,] 63 55 70 10 14 62 48 89 39
## [7,] 47 34 75 87 16 46 43 30 29
## [8,] 7 8 2 54 25 1 3 81 78
## [9,] 18 85 84 40 13 61 64 72 28Find a function in r to transpose the matrix. Print it out again and note how it has changed.
tm <- t(m)
print(tm)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 35 71 65 49 20 63 47 7 18
## [2,] 88 83 73 22 80 55 34 8 85
## [3,] 37 6 11 82 59 70 75 2 84
## [4,] 67 15 4 42 50 10 87 54 40
## [5,] 69 5 36 26 12 14 16 25 13
## [6,] 68 77 38 33 52 62 46 1 61
## [7,] 79 74 51 76 41 48 43 3 64
## [8,] 23 31 44 58 53 89 30 81 72
## [9,] 60 56 9 86 27 39 29 78 28Calculate the sum and the mean of the elements in the first row and then the last row.
sum(tm[1,])## [1] 375mean(tm[1,])## [1] 41.66667sum(tm[n_dims,])## [1] 412mean(tm[n_dims,])## [1] 45.77778Read about the eigen() function and use it on your
matrix
eigen(tm)## eigen() decomposition
## $values
## [1] 410.968762+ 0.00000i 78.638010+ 0.00000i -29.374061+56.10170i
## [4] -29.374061-56.10170i -42.236126+16.28036i -42.236126-16.28036i
## [7] 44.160076+ 0.00000i 3.226763+28.19350i 3.226763-28.19350i
##
## $vectors
## [,1] [,2] [,3]
## [1,] -0.3083029+0i -0.331518117+0i -0.095184759-0.394406740i
## [2,] -0.4085802+0i -0.222988768+0i -0.099050261-0.006346444i
## [3,] -0.3227800+0i 0.113563988+0i 0.612216669+0.000000000i
## [4,] -0.2897126+0i 0.264464565+0i -0.173168599+0.304224321i
## [5,] -0.1686343+0i 0.009174565+0i -0.388142243-0.009026475i
## [6,] -0.3473150+0i -0.383465189+0i 0.057626640+0.066986131i
## [7,] -0.3783007+0i -0.152615169+0i 0.152772449-0.036532821i
## [8,] -0.3819648+0i 0.634544372+0i 0.108707705-0.239735173i
## [9,] -0.3343911+0i 0.429494806+0i 0.009398433+0.274929692i
## [,4] [,5] [,6]
## [1,] -0.095184759+0.394406740i 0.36096188-0.19511562i 0.36096188+0.19511562i
## [2,] -0.099050261+0.006346444i -0.25253554+0.14211319i -0.25253554-0.14211319i
## [3,] 0.612216669+0.000000000i 0.14072626+0.03056449i 0.14072626-0.03056449i
## [4,] -0.173168599-0.304224321i -0.35677177+0.31040641i -0.35677177-0.31040641i
## [5,] -0.388142243+0.009026475i -0.52838925+0.00000000i -0.52838925+0.00000000i
## [6,] 0.057626640-0.066986131i -0.01126115+0.05340200i -0.01126115-0.05340200i
## [7,] 0.152772449+0.036532821i 0.10678814-0.14560636i 0.10678814+0.14560636i
## [8,] 0.108707705+0.239735173i 0.10154324-0.06881902i 0.10154324+0.06881902i
## [9,] 0.009398433-0.274929692i 0.39495995-0.13217635i 0.39495995+0.13217635i
## [,7] [,8] [,9]
## [1,] -0.25231262+0i -0.058467900+0.25089411i -0.058467900-0.25089411i
## [2,] -0.31075002+0i -0.077136271-0.36692498i -0.077136271+0.36692498i
## [3,] 0.39025147+0i 0.115718719+0.14092596i 0.115718719-0.14092596i
## [4,] 0.47495975+0i 0.188473853-0.07468343i 0.188473853+0.07468343i
## [5,] 0.15261269+0i 0.673079258+0.00000000i 0.673079258+0.00000000i
## [6,] -0.62646779+0i -0.216456507+0.20283402i -0.216456507-0.20283402i
## [7,] 0.08053782+0i -0.235355155+0.03556831i -0.235355155-0.03556831i
## [8,] 0.11292842+0i 0.002161857-0.02502693i 0.002161857+0.02502693i
## [9,] 0.16400642+0i -0.293021886-0.18579020i -0.293021886+0.18579020iLook carefully at the elements of values and vectors in the output.
What kind of numbers are these? Dig in with the typeof()
function to figure out their type.
typeof(eigen(tm)$values)## [1] "complex"typeof(eigen(tm)$vectors)## [1] "complex"These are complex numbers.
If have set your code up properly, you should be able to re-run it and create a matrix of different size because n_dims will change.
my_matrix, which is a 4 x 4 matrix filled with
random uniform values
my_logical which is a 100-element vector of TRUE or
FALSE values. Do this efficiently by setting up a vector of random
values and then applying an inequality to it.
my_letters, which is a 26-element vector of all the
lower-case letters in random order.
my_matrix <- matrix(data=runif(16), nrow=4, ncol=4)
my_logical <- runif(100)<0.5
my_letters <- sample(letters)
my_list <- list(my_matrix, my_logical, my_letters)Then, complete the following steps:
new_list <- list(my_matrix[2,2], my_logical[2], my_letters[2])typeof() function to confirm the underlying
data types of each component in this listtypeof(new_list[[1]])## [1] "double"typeof(new_list[[2]])## [1] "logical"typeof(new_list[[3]])## [1] "character"c() function. What is the data type
of this vector?atomic_vector <- c(new_list[[1]], new_list[[2]], new_list[[3]])
print(atomic_vector)## [1] "0.994857588084415" "FALSE" "a"typeof(atomic_vector)## [1] "character"Call the first variable my_unis and fill it with 26 random uniform values from 0 to 10
Call the second variable my_letters and fill it with 26 capital letters in random order.
my_unis <- runif(n=26, min=0, max=10)
my_letters <- sample(LETTERS)
data_frame <- data.frame(my_unis, my_letters)
print(data_frame)## my_unis my_letters
## 1 7.8547594 K
## 2 0.9796932 W
## 3 5.3713267 U
## 4 5.6226966 E
## 5 8.8405213 L
## 6 6.8492564 P
## 7 3.2006808 H
## 8 8.6874164 X
## 9 3.5056613 V
## 10 4.9680235 M
## 11 8.9918071 D
## 12 5.2723138 C
## 13 1.2043848 N
## 14 6.3615537 Y
## 15 8.2470004 J
## 16 3.0854342 B
## 17 7.7935806 S
## 18 0.7072426 O
## 19 3.8622090 I
## 20 6.1442755 Q
## 21 7.0761349 F
## 22 2.6729233 R
## 23 6.5265862 G
## 24 2.1404349 Z
## 25 8.8508021 T
## 26 6.7541962 Adata_frame[ ,1] <- my_unis
print(data_frame)## my_unis my_letters
## 1 7.8547594 K
## 2 0.9796932 W
## 3 5.3713267 U
## 4 5.6226966 E
## 5 8.8405213 L
## 6 6.8492564 P
## 7 3.2006808 H
## 8 8.6874164 X
## 9 3.5056613 V
## 10 4.9680235 M
## 11 8.9918071 D
## 12 5.2723138 C
## 13 1.2043848 N
## 14 6.3615537 Y
## 15 8.2470004 J
## 16 3.0854342 B
## 17 7.7935806 S
## 18 0.7072426 O
## 19 3.8622090 I
## 20 6.1442755 Q
## 21 7.0761349 F
## 22 2.6729233 R
## 23 6.5265862 G
## 24 2.1404349 Z
## 25 8.8508021 T
## 26 6.7541962 Adata_frame[sample(x=1:26, size=4, replace=TRUE),1] <- NA
print(data_frame)## my_unis my_letters
## 1 7.8547594 K
## 2 0.9796932 W
## 3 5.3713267 U
## 4 5.6226966 E
## 5 8.8405213 L
## 6 6.8492564 P
## 7 3.2006808 H
## 8 8.6874164 X
## 9 3.5056613 V
## 10 4.9680235 M
## 11 8.9918071 D
## 12 5.2723138 C
## 13 NA N
## 14 6.3615537 Y
## 15 8.2470004 J
## 16 3.0854342 B
## 17 NA S
## 18 0.7072426 O
## 19 3.8622090 I
## 20 NA Q
## 21 7.0761349 F
## 22 2.6729233 R
## 23 6.5265862 G
## 24 2.1404349 Z
## 25 8.8508021 T
## 26 NA Awhich(!complete.cases(data_frame))## [1] 13 17 20 26data_frame <- data_frame[order(data_frame$my_letters),]
print(data_frame)## my_unis my_letters
## 26 NA A
## 16 3.0854342 B
## 12 5.2723138 C
## 11 8.9918071 D
## 4 5.6226966 E
## 21 7.0761349 F
## 23 6.5265862 G
## 7 3.2006808 H
## 19 3.8622090 I
## 15 8.2470004 J
## 1 7.8547594 K
## 5 8.8405213 L
## 10 4.9680235 M
## 13 NA N
## 18 0.7072426 O
## 6 6.8492564 P
## 20 NA Q
## 22 2.6729233 R
## 17 NA S
## 25 8.8508021 T
## 3 5.3713267 U
## 9 3.5056613 V
## 2 0.9796932 W
## 8 8.6874164 X
## 14 6.3615537 Y
## 24 2.1404349 Zmean(data_frame$my_unis, na.rm=TRUE)## [1] 5.439749