### Jürgen Kampf ### Stochastics III ### Introduction in Vectors and Data Frames ## THIS FILE SHOULD BE OPENED IN R USING THE MENU ITEM File - Open script. ## BY PRESING THE F5-BUTTON YOU CAN COPY LINES FROM THIS SCRIPT INTO THE ## CONSOLE. ### There are different ways to define a vector # Enumerating its elements c(0,1,3) # All numbers from 1 to 10 y=1:10 y # Several (here: 4) times the same number (here: 45) z=rep(45,4) z # One vector as the concatination of two (or more) vectors c(y,z) ### Elements and Subvectors # There are different ways to extract a subvector of a vector # We define a vector for the following examples A=c(15, 20,35, 0:8) A # Extracting only one element, e.g. the second A[2] # Extracting several elements: Give a vector with the position number in # []-brackets. E.g. to extract the 2nd to 4th argument, write A[2:4] # Give a Boolean vector (of same length as A) as argument in []-brackets. # Only those elements of A, for which the Boolean vector is TRUE will be # extracted. Example: Since A has length 12, the Boolean vector must have # length 12 as well. We define a vector S, which has TRUE on the 1st, 4th, # 7th and 10th place and FALSE on the other places. Thus the 1st, 4th, # 7th and 10th element of S are extracted. S=rep(c(TRUE, FALSE,FALSE), 4) S A[S] # This methods can not only be used to read the vector, but also to modify it. # Assigning to one element of the vector a new value. A[2]=5 A # Assigning to several arguments of a vector the same (new) value. A[6:9]=-1 A # Assigning to various elements of a vector various values (at one time). A[S]=c(60,63, 65, 66) A ### Vector Operation # When a function is applied to a vector, R returns a vector of the function # applied to all arguments. # So, if you want to have a vector consisting of all square roots from arguments # of A, a vector, in which every element of A is increasing by 1, or a Boolean # vector, which is TRUE exactly at those positions, where A is -1, then write: sqrt(A) A+1 A==-1 # You can also let R sort a vector or give a vector with the rank the elements # have within the whole sample. sort(A) rank(A) ### Data Frames ### Defining Data Frames # A data frame to a collection of several vectors of the same length. # Defining a data frame by hand x=data.frame(Year=2010:2013, Day.Temperature=c(21,19, 23,22), Night.Temperature=c(9,10,10,9)) x # Reading in data from a file y <- read.table("widerstand.txt", col.names = c("radius", "R")) ### Before you have to tell R, in which directory the data is, by clicking ### File - Change directory in the menu y ### Vectors and data # The second argument of the second vector x[2,2] # The second argument of all vectors x[2,] # The second vector x[,2] # The vector called "Day.Temperature" (another way of accessing the second # vector) x\$Day.Temperature ### Exercise # We want a vector of all year, in which the day temperature is larger than 20. # Solution see other script.