Homework

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_dims^2.
Use the sample function to randomly reshuffle these values.
create a square matrix with these elements.
print out the matrix.
find a function in r to transpose the matrix.
print it out again and note how it has changed.
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.
look 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.
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.

n_dims <- sample(3:10,1)

vec <- c(1:(n_dims)^2)

sample(vec)

##  [1] 25 15 19 23  4  1 12 16 10 20 22 24  7 11 13  2 17  6  8  9  3 21 14  5 18

matr <- matrix(data = vec, nrow = n_dims)

print(matr)

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    6   11   16   21
## [2,]    2    7   12   17   22
## [3,]    3    8   13   18   23
## [4,]    4    9   14   19   24
## [5,]    5   10   15   20   25

matr <- t(matr)

print(matr)

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    2    3    4    5
## [2,]    6    7    8    9   10
## [3,]   11   12   13   14   15
## [4,]   16   17   18   19   20
## [5,]   21   22   23   24   25

sum(matr[1,])

## [1] 15

mean(matr[1,])

## [1] 3

sum(matr[n_dims,])

## [1] 115

mean(matr[n_dims,])

## [1] 23

eigen(matr)

## eigen() decomposition
## $values
## [1]  6.864208e+01+0.000000e+00i -3.642081e+00+0.000000e+00i
## [3] -2.153465e-15+2.015276e-15i -2.153465e-15-2.015276e-15i
## [5]  7.219523e-16+0.000000e+00i
## 
## $vectors
##               [,1]           [,2]                  [,3]                  [,4]
## [1,] -0.1079750+0i  0.67495283+0i  0.0381046+0.2345472i  0.0381046-0.2345472i
## [2,] -0.2527750+0i  0.36038970+0i  0.2645195-0.2955559i  0.2645195+0.2955559i
## [3,] -0.3975750+0i  0.04582657+0i -0.1224010-0.0257606i -0.1224010+0.0257606i
## [4,] -0.5423751+0i -0.26873656+0i -0.7011750+0.0000000i -0.7011750+0.0000000i
## [5,] -0.6871751+0i -0.58329969+0i  0.5209519+0.0867693i  0.5209519-0.0867693i
##                [,5]
## [1,] -0.11703805+0i
## [2,] -0.22725312+0i
## [3,]  0.82596595+0i
## [4,] -0.50202033+0i
## [5,]  0.02034555+0i

The $values are eigenvalues of the matrix which are the characteristic roots of the matrix, and they are scalar. The $vectors are the eigenvectors of the matrix, and are vectors so they are not scalar and have direction.

typeof(eigen(matr)$values)

## [1] "complex"

typeof(eigen(matr)$vectors)

## [1] "complex"

# these are complex numbers

2.

Create a list with the following named elements:

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.

Then, complete the following steps:

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?

mylist <- list(my_matrix=matrix(data = runif(16),nrow = 4), my_logical=(runif(100))<0.5, my_letters=sample(letters))
print(mylist)

## $my_matrix
##             [,1]       [,2]      [,3]       [,4]
## [1,] 0.725260447 0.57651754 0.7820777 0.56801887
## [2,] 0.009603657 0.01462046 0.6298037 0.02435276
## [3,] 0.133783261 0.80240908 0.8023232 0.04697961
## [4,] 0.634346471 0.54542652 0.4204182 0.65836008
## 
## $my_logical
##   [1]  TRUE FALSE  TRUE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE
##  [13]  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE  TRUE  TRUE FALSE  TRUE FALSE
##  [25]  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE
##  [37]  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE
##  [49]  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE FALSE  TRUE FALSE FALSE  TRUE
##  [61]  TRUE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE
##  [73]  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE  TRUE FALSE FALSE
##  [85]  TRUE FALSE  TRUE  TRUE FALSE FALSE  TRUE  TRUE FALSE FALSE  TRUE  TRUE
##  [97] FALSE FALSE FALSE FALSE
## 
## $my_letters
##  [1] "a" "j" "x" "v" "r" "c" "g" "b" "w" "n" "h" "z" "k" "l" "m" "p" "f" "s" "y"
## [20] "q" "o" "i" "e" "d" "u" "t"

newlist <- list(mylist$my_matrix[2,2], mylist$my_logical[2], mylist$my_letters[2])
print(newlist)

## [[1]]
## [1] 0.01462046
## 
## [[2]]
## [1] FALSE
## 
## [[3]]
## [1] "j"

typeof(newlist[[1]])

## [1] "double"

typeof(newlist[[2]])

## [1] "logical"

typeof(newlist[[3]])

## [1] "character"

myvec <- c(newlist[[1]],newlist[[2]],newlist[[3]])
typeof(myvec)

## [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
call the second variable my_letters and fill it with 26 capital letters in random order.
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.

myframe <- data.frame(my_unis=runif(26,min = 0,max = 10),my_letters=sample(LETTERS))
print(myframe)

##       my_unis my_letters
## 1  8.35157179          M
## 2  9.96715304          K
## 3  8.69563717          E
## 4  7.24752890          G
## 5  0.28279357          Y
## 6  3.59986997          P
## 7  0.29850483          L
## 8  0.87818203          U
## 9  7.93922206          D
## 10 9.63060810          T
## 11 8.90974517          X
## 12 0.05405679          Q
## 13 8.06707244          W
## 14 9.29516392          C
## 15 4.57337987          A
## 16 6.96246726          Z
## 17 8.65555684          N
## 18 9.15184251          J
## 19 7.28717337          R
## 20 7.07962466          S
## 21 2.11171730          F
## 22 9.36811574          V
## 23 2.28931822          I
## 24 2.57017151          H
## 25 8.85182761          O
## 26 5.08360072          B

myframe[sample(1:26,4),1]<-NA

which(is.na(myframe$my_unis))

## [1]  7 10 15 26

arrange(myframe,my_letters)

##       my_unis my_letters
## 1          NA          A
## 2          NA          B
## 3  9.29516392          C
## 4  7.93922206          D
## 5  8.69563717          E
## 6  2.11171730          F
## 7  7.24752890          G
## 8  2.57017151          H
## 9  2.28931822          I
## 10 9.15184251          J
## 11 9.96715304          K
## 12         NA          L
## 13 8.35157179          M
## 14 8.65555684          N
## 15 8.85182761          O
## 16 3.59986997          P
## 17 0.05405679          Q
## 18 7.28717337          R
## 19 7.07962466          S
## 20         NA          T
## 21 0.87818203          U
## 22 9.36811574          V
## 23 8.06707244          W
## 24 8.90974517          X
## 25 0.28279357          Y
## 26 6.96246726          Z

mean(myframe$my_unis,na.rm = TRUE)

## [1] 6.255264

Homework_05

Kelsey Soule

2024-02-14

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