To Lecture Notes

CSC 433 -- 5/1/17

D2L Quiz

• Take the D2L Quiz in groups of 2 or 3.

R Review Exercises

1. How do you run an R script?
   Ans: After invoking the R GUI, you can run R scripts from the R Console or from the R Editor with Control-R. You can also run R scripts through RStudio or from a Command Prompt Window:
   

   Rscript test.R
   

   Before using the Rscript command, set the environment path to use the Rscript executable.
    
2. List the R builtin functions that we discussed last week. Ans:
   

   c  scan  mode  print  cat  
   

3. What is the difference between the print and cat functions?
   Ans: print can only print a single object and it knows how to format the object. cat can print multiple objects, but does not know about formatting.  Most nonatomic objects, for example lists and data frames, cannot be printed with cat.
    
4. What are the R operators for
    
   
   1. integer division
       
   2. remainder from integer division (mod)
       
   3. exponentiation
       
   4. sequence
       
   5. help
   
   Ans: a. %/%        b. %%        c. ** or ^        d. :        e. ?
    
5. What are some R special values? See the MaxDouble Example.
   Ans: NA (missing value or not available), Inf (Infinity or numeric value out of range), NaN (Not a number), NULL (Undefined value)
    
6. What is an R vector? How do you create one?
   Ans: You can create an R vector by combining values or vectors with the c (combine) function:
   

   > u = c(2, 4, 6)
   > v = c(3, 7, 9)
   > w = c(u, v, 11)
   > w
   [1]  2  4  6  3  7  9 11
   

   You can also create a vector with the scan function, which allows values to be entered at the keyboard:
   

   > w = scan( )
   1: 2 4 6 3 7
   6: 9 11
   10:
   Read 10 items.
   > w
   [1]  2  4  6  3  7  9 11
   

   The scan function also reads values for a vector from an input file:
   

   w = scan("values.txt")
   

7. What is the mode of an R object? What are some common modes?
   Ans: The mode of an object is its datatype. Common atomic modes, listed from most restrictive to least restrictive, are logical, numeric, complex, character. An example a nonatomic mode is list. The integer atomic mode is also available, although it is usually not needed. Append an L suffix to designate a long (32 bit integer):
   

   w = c(32L, 17L, -345L)
   

8. How do you
    
   
   1. change the mode of an object?
      Ans: You can use a function like as.numeric or as.character. You can also change the mode directly:
      

      mode(v) <- "character"
      

   2. change the length of a vector?
      Ans: You can append an item to the array to make it longer:
      

      v = c(v, 376)
      

      or you can change the length directly:
      

      length(v) <- 10
      

   
   
9. What is the result of this statement?
   

   1:5 + 1:7
   

   Ans: The values of the shorter vector are padded with recycled values to make it the same length as the longer vector:
   

   [1] 2  4  6  8 10  7  9
   

   This warning message is given if the length of the longer item is not a multiple of the length of the shorter item:
   

   Warning message:
   In 1:5 + 1:7 :
     longer object length is not a multiple of shorter object length
   

10. What is the result of this statement?
    

    M = matrix(c(4, 2, 7, 5), 4, 2)
    M
    

    Ans: It produces this matrix. The values in the vector are cycled to fill out the six matrix entries in column major order.
    

          [,1] [,2]
    [1,]    4    4
    [2,]    2    2
    [3,]    7    7
    [4,]    5    5
    

    Because the matrix function argument byrow=TRUE is not supplied, the matrix values are filled in by columns. This is probably because S (the predecessor of R) was written Fortran, which is a column major language. Newer languages like C++, Java, and C# are all row major languages.
     
11. How do the R while and for loops work?
    Ans: A while loop repeats as long as its condition is TRUE.  If the condition is a vector, the while loop repeats as long as the first component of its vector is TRUE. For example:
    

    n = 1
    while(n < 100) {
       cat(n, " ")
       n = n * 2
    }
    cat("\n")
    

    A for loop repeats the loop body for each item in a vector or list. For example:
    

    for (n in c(4, 2, 6, 5)) {
       cat(n ^ 2, " ")
    }
    

    Note: a for loop can often be written more simply by using R's vector capabilities:
    

    print c(4, 2, 6, 5)^2
    

Matrices

• Example: SAS script to multiply two matrices (same matrices as in the SAS Example IML). The R Command Window prompt is > .
  

  > A <- matrix(c(3, 0, 2, 1, 1, 5), 2, 3, byrow=TRUE)
  > A
       [,1] [,2] [,3]
  [1,]    3    0    2
  [2,]    1    1    5
  ># Alternative way to create a matrix:
  > B <- matrix(c(scan( ), 2, 3, byrow=TRUE)
  1: 2 1 -3 0 -2 4
  7:
  Read 6 items
  > B
       [,1] [,2] [,3]
  [1,]    2    1   -3
  [2,]    0   -2    4
  > A + B
       [,1] [,2] [,3]
  [1,]    5    1   -1
  [2,]    1   -1    9
  > C <- matrix(c(2, -1, 0, 1, 7, 3), 
                3, 2, byrow=TRUE)
  > C
       [,1] [,2]
  [1,]    2   -1
  [2,]    0    1
  [3,]    7    3
  > D = A %*% B
  > D
       [,1] [,2]
  [1,]   20    3
  [2,]   37   15
  > 
  

• Reading a matrix from a file: Matrix Example.
   
• R can also represent higher dimensional arrays. This example creates a 3x3x3 array: Array Example.
   
• The SAS Interactive Matrix Language, invoked using proc iml, provides an extensive library for manipulating data matrices.
   
• See the IML Example.

Topics in Introduction to R

• Attributes   Attributes Example
   
• Subsetting   Kids1 Example
   
• Lists

Some R Builtin Functions

• Look at these categories of R builtin functions:
   
  
  Stats   Math Utility   Trig, Exponential, and Log
  

User Defined Functions

Project 5

• See the Project 5b Description.

Practice Problems

1. Write a function that computes the monthly loan payment m, given the principal p, the length of the loan in years y, and the interest rate in percent i. Here is the formula:
    
   

   m =	p(i/1200)(1 + i/1200)12y (1 + i/1200)12y - 1

   Ans:

   monthlyPayment <- function(p, y, i) {
      return((p * (i/1200) * (1 + i/1200)^(12*y)) / 
        ((1 + i/1200)^(12*y) - 1))
   }
   
   monthlyPayment(100000, 15, 6)
   

   What would be the monthly payment for a loan with principal $100,000, interest rate 6%, and term of loan 15 years?
   Ans: 843.8568
    
2. Write an R function that accepts a numeric parameter less than 1 million and returns that number written in words. The simplest is to write a recursive function. Use these vectors in your function:
   

   ones <- c('one', 'two', 'three', 'four', 'five', 'six',
      'seven', 'eight', 'nine', 'ten', 'eleven', 'twelve',
      'thirteen', 'fourteen', 'fifteen', 'sixteen',
      'seventeen', 'eighteen', 'nineteen')
   tens <- c('ten', 'twenty', 'thirty', 'forty', 'fifty',
      'sixty', 'seventy', 'eighty', 'ninety')
   

   Ans:

   numToWords <- function(n) {
      if (n < 1) return("zero")
      else if (n < 20) 
         return(ones[n])
      else if (n < 99) 
         return(paste(tens[n %/% 10], ones[n %% 10]))
      else if (n < 999) 
         return(paste(numToWords(n %/% 100), "hundred",
            numToWords(n %% 100)))
      else if (n < 999999) 
         return(paste(numToWords(n %/% 1000), "thousand",
            numToWords(n %% 1000)))
   }
   

R Library Datasets

• A number of datasets install with R, for example, the cars dataset is used in the Cars1 and Cars2 Examples.
   
• The objects in the datasets library are loaded automatically when R loads. To use an object, for example cars, enter the name of the object interactively:
  

  > cars
   speed dist
  1 4 2
  2 4 10
  3 7 4
  ...
  

• To display the cars object from a script, use
  

  print(cars)
  

• For a complete list of the objects in the datasets library, type
  

  > library(help=datasets)
  

R Graphics