PSTAT 10 Homework 1 Solutions

Problem 2: More ecosystem exploration

In R 4.2.0 it is now possible to pipe into a placeholder using the |> operator.

Problem 3: State areas

1. Find the mean area of all states.

mean(state.area)

## [1] 72367.98

2. Find the median area of all states.

median(state.area)

## [1] 56222

3. Find the name and the area of the smallest state.

smallest <- which.min(state.area)
c(state.area[smallest], state.name[smallest])

## [1] "1214"         "Rhode Island"

4. Find the name and the area of the largest state.

largest <- which.max(state.area)
c(state.area[largest], state.name[largest])

## [1] "589757" "Alaska"

Problem 4: Dot product

dot_product <- function(x, y) {
  if (is.numeric(x) && is.numeric(y)) {
    return(sum(x * y))
  }
  print("Both arguments must be numeric!")
}
dot_product(1:3, c(0, 1, 5))

## [1] 17

dot_product(2, 4)

## [1] 8

dot_product(c(1, 1), c("dog", "cat"))

## [1] "Both arguments must be numeric!"

Problem 5: Frobenius norm

frobenius_norm <- function(mx) {
  if (!is.numeric(mx)) {
    print("Argument must be numeric!")
  } else if (!is.matrix(mx)) {
    print("Argument must be a matrix!")
  } else {
    sqrt(sum(mx^2))
  }
}
frobenius_norm(matrix(1:4, nrow = 2, ncol = 2))

## [1] 5.477226

frobenius_norm(c(3,5,7,10,15,21))

## [1] "Argument must be a matrix!"

frobenius_norm(matrix(c(3,5,7,10,15,21), nrow = 2, ncol = 3))

## [1] 29.1376

frobenius_norm(matrix(c(3,"fish",7,10,15,21), nrow = 2, ncol = 3))

## [1] "Argument must be numeric!"

Problem 6: Compare Count

compare_count <- function(x, y, comp = ">") {
  if(!is.numeric(x) || !is.numeric(y)) {
    print("Both vectors must be numeric!")
    return()
  }
  
  if (length(x) != length(y)){
    print("Both vectors must have the same length!")
    return()
  }
  
  if (!(comp %in% c('>', '<', '='))) {
    print("Unrecognized compare operator!")
    return()
  }
  
  if (comp == '>') {
    return(sum(x > y))
  }
  
  if (comp == '<') {
    return(sum(x < y))
  }
  
  if (comp == '=') {
    return(sum(x == y))
  }
}
compare_count(rep(1, 5), rep(2, 5))

## [1] 0

compare_count(rep(1, 5), rep(2, 5), ">")

## [1] 0

compare_count(c(1, 2, 1, 2, 1), rep(2, 5), "<")

## [1] 3

compare_count(c(1, 2, 1, 2, 1), rep(2, 5), "=")

## [1] 2

compare_count(c(1, 2, 1, 2, 1), rep(2, 5), ">=")

## [1] "Unrecognized compare operator!"

## NULL

compare_count(c(1, 2, 1, 2, 1), rep(2, 6), "=")

## [1] "Both vectors must have the same length!"

## NULL

compare_count(c(1, 2, 1, 2, "owl"), rep(2, 6))

## [1] "Both vectors must be numeric!"

## NULL