CSC121 - R Console
Monday February 26th
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> # Different ways to create vectors
> # Repeating values: we can make a vector by repeating values a set number of times
> # We use the function rep()
> rep(5, 10)
 [1] 5 5 5 5 5 5 5 5 5 5
> # This repeats the value 5 ten times
> rep(c(8, 1, 2), 5)
 [1] 8 1 2 8 1 2 8 1 2 8 1 2 8 1 2
> rep(c("hi", "csc121"), 3)
[1] "hi"     "csc121" "hi"     "csc121" "hi"     "csc121"
> # Instead of saying how many times to repeat, you can instead say what the final length should be
> rep(c(8, 1, 2), length=10)
 [1] 8 1 2 8 1 2 8 1 2 8
> # this will continue repeating the values until the desired length is reached
> # Another option is to say how many times each element should be repeated immediately
> rep(c(8, 1, 2), each=3)
[1] 8 8 8 1 1 1 2 2 2
> # This repeats each element in the vector 3 times
> 
> # Sequence vectors
> # We've seen that you can create a vector consisting of a sequence of consecutive integers
> 1:20
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
> # If we make the starting number larger than the ending number, we get a sequence that decreases
> 20:1
 [1] 20 19 18 17 16 15 14 13 12 11 10  9  8  7  6  5  4  3  2  1
> 
> # All of these sequences increment by 1
> # The seq() function allows us to create a sequence of numbers that increment by an amount other than 1
> seq(1, 2, by=0.1)
 [1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
> # this creates a sequence from 1 to 2, but increments by 0.1
> 
> seq(1, 30, by=5)
[1]  1  6 11 16 21 26
> # It will start at the starting number, but it will not go above the ending number
> 
> # We can also specify the desired length of the sequence instead of an ending number:
> seq(1.1, by=0.01, length=13)
 [1] 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22
> # this starts at 1.1 and increments by 0.01 until we get to a vector of length 13
> 
> # You can combine normal a:b seuqnces, rep(), seq(), to create different combinations of vectors
> c(1:5, 5:1)
 [1] 1 2 3 4 5 5 4 3 2 1
> rep(1:5, 3)
 [1] 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
> c(seq(1, 2, by=0.2), rep(2, 5))
 [1] 1.0 1.2 1.4 1.6 1.8 2.0 2.0 2.0 2.0 2.0 2.0
> seq(1:5, by=0.01)
Error in seq.default(1:5, by = 0.01) : 'from' must be of length 1
> 
> 
> # MATRICES
> 
> # A matrix is a data structure that has m rows and n columns
> # They are made using the matrix() function
> # Let's try putting in one value
> matrix(4)
     [,1]
[1,]    4
> # A default matrix has one row and one column
> # To make a multi-row/column matrix, we specify the data, the number of rows, and the number of columns
> matrix(3, nrow=2, ncol=2)
     [,1] [,2]
[1,]    3    3
[2,]    3    3
> # The data repeats until the matrix is filled
> # If we have a set of more than one value as the data, it will fill them in column by column
> matrix(1:6, nrow=2, ncol=3)
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
> # You can choose to fill the data in by rows if you want by specificying the 'byrow' argument
> matrix(1:6, nrow=2, ncol=3, byrow=TRUE)
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6
> 
> # Matrix operations
> A <- matrix(1:4, nrow=2, ncol=2)
> A
     [,1] [,2]
[1,]    1    3
[2,]    2    4
> # Matrix addition
> A + A
     [,1] [,2]
[1,]    2    6
[2,]    4    8
> # The operations we've seen before work on matrices element-by-element
> -A
     [,1] [,2]
[1,]   -1   -3
[2,]   -2   -4
> A^2
     [,1] [,2]
[1,]    1    9
[2,]    4   16
> 
> # There are 'matrix operations' which come to us from linear algebra
> # For example, matrix multiplication
> B <- matrix(c(4, 0, 3, 1), nrow=2, ncol=2)
> # We can perform matrix multiplication using the %*%
> A %*% B
     [,1] [,2]
[1,]    4    6
[2,]    8   10
> A * B
     [,1] [,2]
[1,]    4    9
[2,]    0    4
> # First one multiplies using matrix multiplication (review your linear algrebra)
> # second one multiplies element-by-element
> 
> # You can think of matrices simply as another way to organize values of any type
> matrix(c(TRUE, FALSE), nrow=2, ncol=2)
      [,1]  [,2]
[1,]  TRUE  TRUE
[2,] FALSE FALSE
> matrix(c("hi", 4), nrow=2, ncol=2)
     [,1] [,2]
[1,] "hi" "hi"
[2,] "4"  "4" 
> matrix(list("hi", 4), nrow=2, ncol=2)
     [,1] [,2]
[1,] "hi" "hi"
[2,] 4    4   
> # You can have multiple types in a matrix, just make sure you put them in a list when creating the matrix - vectors will convert everything to one type
> # R will warn you if the data you're using isn't a multiple of the row number
> matrix(1:4, nrow=3, ncol=6)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    4    3    2    1    4
[2,]    2    1    4    3    2    1
[3,]    3    2    1    4    3    2
Warning message:
In matrix(1:4, nrow = 3, ncol = 6) :
  data length [4] is not a sub-multiple or multiple of the number of rows [3]
> 
> # Indexing matrix elements
> # To get an element of a matrix, you must specify the row and column
> X <- matrix(1:6, nrow=2, ncol=3)
> X
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
> # You will need two indexes/subscripts. First the row, then the column
> X[1, 3]
[1] 5
> X[2, 1]
[1] 2
> # You can index an entire row or column of a matrix
> X[1,]
[1] 1 3 5
> # ^ we got the first row
> # Get the second column:
> X[,2]
[1] 3 4
> X[1,] + X[,2]
[1] 4 7 8
Warning message:
In X[1, ] + X[, 2] :
  longer object length is not a multiple of shorter object length
> X[1,] + X[2,]
[1]  3  7 11
> # Can find the number of rows and columns
> nrow(X)
[1] 2
> ncol(X)
[1] 3
> # Length tells you the number of elements:
> length(X)
[1] 6
>