#Homewrok5
Nicolás Zapata
Assign to the variable n_dims a single random integer between 3 and 10.
n_dims <- sample(3:10, size=1)
print(n_dims)## [1] 9Create a vector of consecutive integers from 1 to n_dims2
my_vector <- seq(1:n_dims^2)Use the sample function to randomly reshuffle these values.
matrix1 <- matrix(sample(my_vector), nrow=n_dims)
# print out the matrix
print(matrix1) ## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 78 4 46 8 36 68 51 35 72
## [2,] 40 50 7 10 2 14 71 52 44
## [3,] 76 12 21 5 11 20 6 70 25
## [4,] 64 60 39 23 57 15 61 66 77
## [5,] 54 45 41 30 63 48 81 69 58
## [6,] 42 37 28 55 32 34 67 17 24
## [7,] 3 26 1 33 9 49 29 56 79
## [8,] 38 27 16 62 13 74 65 22 59
## [9,] 43 31 18 53 73 80 47 75 19Find a function in r to transpose the matrix
transposed_matrix1 <- t(matrix1)
print(transposed_matrix1)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 78 40 76 64 54 42 3 38 43
## [2,] 4 50 12 60 45 37 26 27 31
## [3,] 46 7 21 39 41 28 1 16 18
## [4,] 8 10 5 23 30 55 33 62 53
## [5,] 36 2 11 57 63 32 9 13 73
## [6,] 68 14 20 15 48 34 49 74 80
## [7,] 51 71 6 61 81 67 29 65 47
## [8,] 35 52 70 66 69 17 56 22 75
## [9,] 72 44 25 77 58 24 79 59 19Calculate the sum and the mean of the elements in the first row and then the last row.
# mean first row
firstrow_mean <- mean(matrix1[1,])
print(firstrow_mean) ## [1] 44.22222# sum first row
firstrow_sum <- sum(matrix1[1,])
print(firstrow_sum)## [1] 398# mean last row
lastrow_mean <- mean(matrix1[n_dims,])
print(lastrow_mean)## [1] 48.77778# sum last row
lastrow_sum <- sum(matrix1[n_dims,])
print(lastrow_sum)## [1] 439Read about the eigen() function and use it on your matrix
matrix_eigen <- eigen(matrix1)
print(matrix_eigen)## eigen() decomposition
## $values
## [1] 371.7380277+ 0.00000i 71.1977128+ 0.00000i -18.9569043+54.76163i
## [4] -18.9569043-54.76163i -33.4425473+32.25510i -33.4425473-32.25510i
## [7] 0.2367961+17.15548i 0.2367961-17.15548i 0.3895706+ 0.00000i
##
## $vectors
## [,1] [,2] [,3]
## [1,] 0.3506800+0i -0.596545683+0i -0.05884473-0.229956272i
## [2,] 0.2417436+0i 0.349817183+0i -0.50108748+0.000000000i
## [3,] 0.2191546+0i -0.591763068+0i -0.21616899+0.009436224i
## [4,] 0.4088426+0i -0.039941452+0i -0.20091008+0.183333698i
## [5,] 0.4277468+0i 0.056168998+0i -0.17531472+0.105079056i
## [6,] 0.2918612+0i 0.006997265+0i -0.04601784+0.336945052i
## [7,] 0.2600577+0i 0.391369526+0i 0.25835090-0.415410520i
## [8,] 0.3321607+0i 0.100958690+0i 0.19267888-0.088283166i
## [9,] 0.3966000+0i 0.058443627+0i 0.29686767+0.204908573i
## [,4] [,5] [,6]
## [1,] -0.05884473+0.229956272i -0.23276894+0.15891561i -0.23276894-0.15891561i
## [2,] -0.50108748+0.000000000i 0.36902796+0.22251688i 0.36902796-0.22251688i
## [3,] -0.21616899-0.009436224i 0.23472242-0.10200966i 0.23472242+0.10200966i
## [4,] -0.20091008-0.183333698i -0.08558977+0.02293721i -0.08558977-0.02293721i
## [5,] -0.17531472-0.105079056i 0.11010276+0.03040861i 0.11010276-0.03040861i
## [6,] -0.04601784-0.336945052i 0.32324073+0.07026102i 0.32324073-0.07026102i
## [7,] 0.25835090+0.415410520i -0.54766446+0.00000000i -0.54766446+0.00000000i
## [8,] 0.19267888+0.088283166i -0.07056112+0.10477936i -0.07056112-0.10477936i
## [9,] 0.29686767-0.204908573i 0.19003273-0.43248339i 0.19003273+0.43248339i
## [,7] [,8] [,9]
## [1,] 0.29232776-0.14786118i 0.29232776+0.14786118i 0.16643969+0i
## [2,] -0.30428333-0.01301204i -0.30428333+0.01301204i -0.58519547+0i
## [3,] -0.69884284+0.00000000i -0.69884284+0.00000000i -0.55488169+0i
## [4,] 0.07632344-0.17321553i 0.07632344+0.17321553i 0.19312256+0i
## [5,] 0.30085302+0.20969191i 0.30085302-0.20969191i 0.26060311+0i
## [6,] -0.21081844+0.09368379i -0.21081844-0.09368379i -0.33991183+0i
## [7,] 0.11197098+0.03669253i 0.11197098-0.03669253i 0.26775044+0i
## [8,] -0.13477234-0.08435733i -0.13477234+0.08435733i 0.04301394+0i
## [9,] 0.20929251+0.07101023i 0.20929251-0.07101023i 0.16631160+0iDig in with the typeof() function to figure out their type.
typeof(matrix_eigen$values)## [1] "complex"typeof(matrix_eigen$vectors)## [1] "complex"Create a list with the following named elements:
# my_matrix, which is a 4 x 4 matrix filled with random uniform values
my_matrix <- matrix(data=runif(16), nrow=4)
print(my_matrix) ## [,1] [,2] [,3] [,4]
## [1,] 0.7449822 0.7315595 0.26298995 0.3767629
## [2,] 0.4400170 0.4839849 0.34148083 0.5623074
## [3,] 0.1150394 0.1710480 0.21024554 0.6799846
## [4,] 0.6756428 0.6758485 0.01631959 0.7453888# 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_logical <- (runif(100) > .8)
print(my_logical) ## [1] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [25] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE TRUE FALSE FALSE# my_letters, which is a 26-element vector of all the lower-case letters in random order.
my_letters <- sample(letters)
print(my_letters)## [1] "p" "r" "q" "g" "d" "x" "s" "m" "c" "z" "w" "a" "i" "e" "b" "f" "u" "h" "v"
## [20] "o" "l" "t" "k" "j" "n" "y"# create a new list, which has the element[2,2] from the matrix, the second element of the logical vector, and the second element of the letters vector
my_list1 <- list(my_matrix, my_logical, my_letters)
new_list <- list(my_matrix[2,2], my_logical [2], my_letters[2])
print(new_list)## [[1]]
## [1] 0.4839849
##
## [[2]]
## [1] FALSE
##
## [[3]]
## [1] "r"# use the typeof() function to confirm the underlying data types of each component in this list
typeof(new_list[[1]])## [1] "double"typeof(new_list[[2]])## [1] "logical"typeof(new_list[[3]])## [1] "character"# combine the underlying elements from the new list into a single atomic vector with the c() function
combined_elements_vector <- c(new_list[[1]], new_list[[2]], new_list[[3]])
print(combined_elements_vector)## [1] "0.483984902733937" "FALSE" "r"# what is the data type of this vector?
typeof(combined_elements_vector)## [1] "character"Create a data frame with the two variables (= columns) and 26 cases (= rows) below:
#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.
dataframe <- data.frame(my_unis = runif(26, min=0, max=10), my_letters = sample(LETTERS))
print(dataframe)## my_unis my_letters
## 1 9.6384166 S
## 2 0.0126048 P
## 3 7.0752621 R
## 4 6.3018760 E
## 5 7.7307804 A
## 6 8.9260688 B
## 7 5.1120408 W
## 8 7.4900107 N
## 9 9.2637980 H
## 10 0.9175352 T
## 11 4.9665549 D
## 12 1.9750126 V
## 13 9.9413290 Y
## 14 0.3682104 L
## 15 2.1756307 O
## 16 8.9093614 F
## 17 1.1893646 X
## 18 3.6903899 I
## 19 1.6237643 Z
## 20 1.6669152 K
## 21 9.7250471 Q
## 22 8.1039974 U
## 23 9.5332763 J
## 24 3.9991053 M
## 25 8.5224732 G
## 26 0.6452286 C# for the first variable, use a single line of code in R to select 4 random rows and replace the numerical values in those rows with NA.
dataframe[sample(1:26, size=4), 1] <- NA# for the first variable, write a single line of R code to identify which rows have the missing values
which(is.na(dataframe$my_unis))## [1] 12 13 17 21# re-order the entire data frame to arrange the second variable in alphabetical order
dataframe <- dataframe[order(dataframe$my_letters),]
print(dataframe)## my_unis my_letters
## 5 7.7307804 A
## 6 8.9260688 B
## 26 0.6452286 C
## 11 4.9665549 D
## 4 6.3018760 E
## 16 8.9093614 F
## 25 8.5224732 G
## 9 9.2637980 H
## 18 3.6903899 I
## 23 9.5332763 J
## 20 1.6669152 K
## 14 0.3682104 L
## 24 3.9991053 M
## 8 7.4900107 N
## 15 2.1756307 O
## 2 0.0126048 P
## 21 NA Q
## 3 7.0752621 R
## 1 9.6384166 S
## 10 0.9175352 T
## 22 8.1039974 U
## 12 NA V
## 7 5.1120408 W
## 17 NA X
## 13 NA Y
## 19 1.6237643 Z# calculate the column mean for the first variable
mean(dataframe$my_unis, na.rm=TRUE)## [1] 5.303332