Homework 5

1. Assign to the variable n_dims a single random integer between 3 and 10

n_dims <- runif(1, min = 3, max = 11)
print(n_dims)

## [1] 7.582827

Create a vector of consecutive integers from 1 to n_dims²

vec_con<-1:(n_dims^2)
print(vec_con)

##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## [51] 51 52 53 54 55 56 57

Use the sample function to randomly reshuffle these values.

vec_samp<-sample(vec_con)
print(vec_samp)

##  [1]  1 34 23 43 14 18 51 33 21 49 42 46 10  7  9 15 48 37 25 40 38 56 39 47 50
## [26] 20  3  6 45 29 30 36 32 35 12 27  8 55 22 44 28 19 41 53  2 13 16 11 57 31
## [51] 26 17  4 24 52 54  5

Create a square matrix with these elements.

m <- matrix(vec_samp, nrow = n_dims, ncol = n_dims)

## Warning in matrix(vec_samp, nrow = n_dims, ncol = n_dims): data length [57] is
## not a sub-multiple or multiple of the number of rows [7]

print(m)

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,]    1   33    9   56   45   27   41
## [2,]   34   21   15   39   29    8   53
## [3,]   23   49   48   47   30   55    2
## [4,]   43   42   37   50   36   22   13
## [5,]   14   46   25   20   32   44   16
## [6,]   18   10   40    3   35   28   11
## [7,]   51    7   38    6   12   19   57

Find a function in r to transpose the matrix.

transposed_matrix<-t(m)
print(transposed_matrix)

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,]    1   34   23   43   14   18   51
## [2,]   33   21   49   42   46   10    7
## [3,]    9   15   48   37   25   40   38
## [4,]   56   39   47   50   20    3    6
## [5,]   45   29   30   36   32   35   12
## [6,]   27    8   55   22   44   28   19
## [7,]   41   53    2   13   16   11   57

Calculate the sum and the mean of the elements in the first row and then the last row.

sum_first_row <- sum(transposed_matrix[1, ])
print(sum_first_row)

## [1] 184

mean_first_row <- mean(transposed_matrix[1, ])
print(mean_first_row)

## [1] 26.28571

sum_last_row <- sum(transposed_matrix[n_dims, ])
print(sum_last_row)

## [1] 193

mean_last_row <- mean(transposed_matrix[n_dims, ])
print(mean_last_row)

## [1] 27.57143

Read about the eigen() function and use it on your matrix

eigen_matrix <- eigen(transposed_matrix)
print(eigen_matrix$values)

## [1] 206.4520812+ 0.00000i -42.0415830+ 0.00000i  36.0707225+13.64676i
## [4]  36.0707225-13.64676i  22.9527086+ 0.00000i -22.3712528+ 0.00000i
## [7]  -0.1333988+ 0.00000i

print(eigen_matrix$vectors)

##               [,1]           [,2]                    [,3]
## [1,] -0.3378665+0i -0.70486405+0i  0.28858371+0.02192395i
## [2,] -0.3879549+0i  0.17661144+0i -0.34137898+0.14764595i
## [3,] -0.3904930+0i -0.35651104+0i -0.04922512-0.25889490i
## [4,] -0.4065137+0i  0.49583065+0i -0.11862771+0.20679474i
## [5,] -0.4012525+0i  0.11654236+0i -0.25963164+0.06931021i
## [6,] -0.3742594+0i  0.27821545+0i -0.21796296-0.23448749i
## [7,] -0.3413582+0i  0.08967138+0i  0.69058587+0.00000000i
##                         [,4]           [,5]           [,6]            [,7]
## [1,]  0.28858371-0.02192395i  0.35357642+0i -0.08886067+0i  0.383077242+0i
## [2,] -0.34137898-0.14764595i -0.47495397+0i  0.61052132+0i -0.717431031+0i
## [3,] -0.04922512+0.25889490i  0.03543112+0i -0.04010390+0i -0.270275284+0i
## [4,] -0.11862771-0.20679474i  0.13404280+0i -0.10803936+0i  0.349757772+0i
## [5,] -0.25963164-0.06931021i -0.45413088+0i -0.43990115+0i  0.002491901+0i
## [6,] -0.21796296+0.23448749i -0.30850569+0i  0.55064446+0i -0.147867198+0i
## [7,]  0.69058587+0.00000000i  0.57338380+0i -0.33070277+0i  0.348273451+0i

Dig in with the typeof() function to figure out their type.

typeof(eigen_matrix$values)

## [1] "complex"

typeof(eigen_matrix$vectors)

## [1] "complex"

2. Create a list with the following named elements:

A 4 x 4 matrix filled with random uniform values

my_matrix <- matrix(runif(16), nrow = 4, ncol = 4)
print(my_matrix)

##           [,1]       [,2]      [,3]      [,4]
## [1,] 0.2026923 0.14330438 0.8762692 0.4100841
## [2,] 0.7111212 0.23962942 0.7789147 0.8108702
## [3,] 0.1216919 0.05893438 0.7973088 0.6049333
## [4,] 0.2454885 0.64228826 0.4552745 0.6547239

A 100-element vector of TRUE or FALSE values

random_values <- runif(100)
my_logical <- random_values > 0.5
print(my_logical)

##   [1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE FALSE
##  [13] FALSE FALSE FALSE  TRUE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE
##  [25] FALSE  TRUE FALSE FALSE  TRUE  TRUE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
##  [37]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE
##  [49]  TRUE  TRUE  TRUE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE
##  [61]  TRUE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE  TRUE  TRUE
##  [73] FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE  TRUE  TRUE
##  [85] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE FALSE  TRUE FALSE
##  [97]  TRUE FALSE  TRUE FALSE

A 26-element vector of all the lower-case letters in random order.

my_letters <- sample(letters)
print(my_letters)

##  [1] "z" "m" "b" "x" "s" "q" "w" "k" "c" "r" "n" "u" "y" "v" "h" "i" "t" "l" "j"
## [20] "g" "d" "e" "a" "f" "o" "p"

The list

my_list <- list(my_matrix = my_matrix, my_logical = my_logical, my_letters = my_letters)

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_list2 <- list(my_matrix[2, 2], my_logical[2], my_letters[2])
print(my_list2)

## [[1]]
## [1] 0.2396294
## 
## [[2]]
## [1] FALSE
## 
## [[3]]
## [1] "m"

Use the typeof() function to confirm the underlying data types of each component in this list

sapply(my_list2, typeof)

## [1] "double"    "logical"   "character"

Combine the underlying elements from the new list into a single atomic vector with the c() function.

combined_vec <- c(my_list[[1]], my_list[[2]], my_list[[3]])

What is the data type of this vector?

typeof(combined_vec)

## [1] "character"

3.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

my_unis <- runif(26, min = 0, max = 10)

Call the second variable my_letters and fill it with 26 capital letters in random order.

my_letters <- sample(letters)

Create the data frame

my_data_frame <- data.frame(my_unis = my_unis, Letter = my_letters)
print(my_data_frame)

##     my_unis Letter
## 1  6.314202      h
## 2  3.900789      d
## 3  6.896278      q
## 4  6.894134      i
## 5  5.549006      u
## 6  4.296244      a
## 7  4.527201      t
## 8  3.064433      j
## 9  5.783539      n
## 10 9.103703      s
## 11 1.426041      w
## 12 4.150476      z
## 13 2.109258      e
## 14 4.287504      r
## 15 1.326900      f
## 16 4.600964      l
## 17 9.429571      b
## 18 7.619739      x
## 19 9.329098      o
## 20 4.706785      k
## 21 6.035881      g
## 22 4.849897      y
## 23 1.088063      p
## 24 2.477268      v
## 25 4.985145      c
## 26 3.728667      m

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

my_data_frame$my_unis[sample(1:26, 4)] <- NA

For the first variable, write a single line of R code to identify which rows have the missing values.

which(is.na(my_data_frame$my_unis))

## [1]  4  7 20 24

Re-order the entire data frame to arrange the second variable in alphabetical order

my_data_frame <- my_data_frame[order(my_data_frame$Letter), ]
print(my_data_frame)

##     my_unis Letter
## 6  4.296244      a
## 17 9.429571      b
## 25 4.985145      c
## 2  3.900789      d
## 13 2.109258      e
## 15 1.326900      f
## 21 6.035881      g
## 1  6.314202      h
## 4        NA      i
## 8  3.064433      j
## 20       NA      k
## 16 4.600964      l
## 26 3.728667      m
## 9  5.783539      n
## 19 9.329098      o
## 23 1.088063      p
## 3  6.896278      q
## 14 4.287504      r
## 10 9.103703      s
## 7        NA      t
## 5  5.549006      u
## 24       NA      v
## 11 1.426041      w
## 18 7.619739      x
## 22 4.849897      y
## 12 4.150476      z

Calculate the column mean for the first variable.

mean_my_unis <- mean(my_data_frame$my_unis, na.rm = TRUE)
print(mean_my_unis)

## [1] 4.994336

Homework 5

2025-02-12

1. Assign to the variable n_dims a single random integer between 3 and 10

Create a vector of consecutive integers from 1 to n_dims2

Use the sample function to randomly reshuffle these values.

Create a square matrix with these elements.

Find a function in r to transpose the matrix.

Calculate the sum and the mean of the elements in the first row and then the last row.

Read about the eigen() function and use it on your matrix

Dig in with the typeof() function to figure out their type.

2. Create a list with the following named elements:

A 4 x 4 matrix filled with random uniform values

A 100-element vector of TRUE or FALSE values

A 26-element vector of all the lower-case letters in random order.

The list

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.

Use the typeof() function to confirm the underlying data types of each component in this list

Combine the underlying elements from the new list into a single atomic vector with the c() function.

What is the data type of this vector?

3.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.

Create the data frame

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

For the first variable, write a single line of R code to identify which rows have the missing values.

Re-order the entire data frame to arrange the second variable in alphabetical order

Calculate the column mean for the first variable.

Create a vector of consecutive integers from 1 to n_dims²