R (and S, and S-Plus, another program based on S) is an interactive, interpretive, function language.

Transcription

1 R R (and S, and S-Plus, another program based on S) is an interactive, interpretive, function language. Available on Linux, Unix, Mac, and MS Windows systems. Documentation exists in several volumes, and in an on-line help system. On a windows device (such as X11 or MS Windows), the most common interface for R is the RGui, which has a pane called R Console in which R statements can be typed.

2 R Fundamentals Most statements are of the form variable <- function(...) or object or function(...) to make an assignment to display an object to execute a function Instead of <-, can use =, as in the text. (I use <- because I learned R (actually S) over 35 years ago, before = was acceptable in the language.) R is case sensitive.

3 R Fundamentals R objects: variables, vectors, lists, matrices, arrays, formulas, time series, factors (for statistical applictions), data frames (for statistical applictions), fits (for statistical applictions) R has an extensive set of functions, i.e. verbs. The specific meaning depends on the class of the object to which it is applied.

4 Objects are built by constructor functions such as c, data.frame, array, matrix, ts, etc. or by an analysis function such as lm, acf, etc. > A <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow=3) This object is a matrix and can participate in matrix multiplication and so on. Typing A results in A =

5 R Syntax, Functions All actions are functions. A function name is followed by a set of perentheses to enclose arguments. help() or help(plot), e.g. or?plot q() The syntax is somewhat similar to C++, except that there are no special delimiters for statements; statements continue as necessary to complete the function. Statements may be grouped by { and }. Blanks are significant only when it makes sense for them to be. The language is not strongly typed. Numbers are generally single precision floating point numbers.

6 Examples > x <- c(2, 5, 3) > x > z1 < *i > z2 <- complex(real=3, imaginary=4) > z <- scan(file="example.dat") > y <- scan() 1: : : : : > a <- 0:10 > b <- 0:10/10 > c <- seq(from=0, t=1, by=.1) > plot(y,type="1")

7 General Design R deals with functions. This dictates the syntax no statement delimiters (but does use { and }). Comments begin with #. No fixed naming conventions; the wise user, however, adopts mnemonic conventions. Use periods to represent components. Various ways of extracting components. $ component operator: object$member See objects with objects().

8 R Matrices A <- matrix(c(1, 3, 5, 2, 4, 6), nrow=3) x <- c(3, 4) z <- A[2, ] w <- A[2, 1:2] v <- c(1, 2, 1) b <- A%*%x; cc <- v%*%a D <- cbind(a, v) E <- solve(d) f <- solve(d, v) H <- D%*%A L <- D*D M <- D^2 objects() rm(...)

9 Other Operators and Functions <,<=, >, >=, ==,!= &,,! sin, cos,... abs, Arg, sqrt, Re, Im, Conj, round, trunc, floor, ceiling, sign, %%, exp, log, log10 t, crossprod, solve, sink("filename") sink() Plus lots of functions for statistical analyses.

10 Packages in R There are many packages that extend the functionality of R. Each package may contain several functions in a given area of application or of analysis. These must first be installed using files that you usually get from some online respository. Once you choose a mirror site from which to obtain the files, you choose the specific package from a drop-down list. Once a package is installed, it must be loaded in any R session in which you need a function from the package. A package can be loaded by using the drop-down menu under the Packages button, or else it can be loaded by means of the library function in R.

11 Programming Conditionals: if(x >= 3) { y <- 2 z <- 4 } else if (x <= 1) ## note how the command must be continued { y <- 1 } else y <- 5

12 Conditionals Conditionals resolve to a numeric value of 0 for false and 1 for true. They can be operated on. x <- 3 y <- 5*(x>2) + 4 Yields a value of 9 for y.

13 Loops Suppose the vector x is given. n1 <- length(x)-1 y <- rep(1,n1) for (i in 1:n1) { if(x[i+1]<x[i]) y[i]<- -1 } or y <- rep(1,n1) i <- 1 while (i <= n1) { if(x[i+1]<x[i]) y[i]<- -1 i <- i+1 }

14 Vectorization Loops are inefficient in R. Try to implement as statements involving vectors. y <- ifelse(x[-1]<x[1:n1],-1,1) Now, let A be a matrix. Instead of y <- numeric(dim(a)[2]) for (i in 1:dim(A)[2]) { y[i] <- sum(a[,i]) } Use apply: y <- apply(a,2,sum)

15 R Functions for Graphics plot plot.factor pairs brush hist stem barplot persp faces stars matplot And others. The actual appearance of the graph depends on the class of the object. Arguments for functions may be required or optional. Most required ones are positional, many optional ones are keyword.

16 R Functions for Standard Distributions Some distributions: beta f gamma norm t unif

17 R Functions for Standard Distributions Functions d density p cumulative probability q quantile r random number generation Examples: rnorm(25, 100, 8) generates 25 N(100,64) numbers qf(.95, 5, 10) the.95 quantile of an F with 5 and 10 degrees of freedom.

18 The Object Orientation of R Most of the functions of R are overloaded and are data-driven. A new class can be defined by defining a constructor function that gives an identifier to the class: factor <- function(x, levels = sort(unique(x)), labels = as.character(levels)) { y <- match(x, levels) names(y) <- names(x) levels(y) <-labels class(y) <- "factor" y } The function factor will construct an object of class factor.

19 Saving Graphics Files There are several standard formats for storing graphics and pictures. The two I use are Encapsulated PostScript, for use in T E X JPEG, for use in HTML R can save graphics files in either of these formats. One way to do this is make the graph the active window, and then to choose Save as... on the File menu. It is annoying to have to point and click on menus. (Almost) everything I do in R is from a script (program) that I write prior to execution.

20 Graphics Devices The grdevices package has useful functions for specifying where a plot goes ; that is, the device on which it appears. By default, it goes to a pane in the RGui window. The function that opens a new pane, that is, a new device, in the RGui window is windows(). The panes are numbered sequentially; that is, each time windows() is invoked, a new device with a number one greater than the previous one (begining with 2) is created. A particular pane is made the active device by dev.cur(i), where i is the number of the device. A particular pane is closed by dev.off(i), where i is the number of the device.

21 Saving Graphics Files If the graphics device is the active pane in the RGui window, you can save it using the menus in the RGui. On windows devices, you can save the active pane by saveplot( ex0101,type="eps") This function creates a file with the extension eps. Another way of saving a graphics file is by printing directly to it. This is done by using various functions in the grdevices package that specify both the format and the name of the file, for example, pdf( ex0101.pdf ) or postscript( ex0101.eps ). Notice that these functions do not provide a extension on the file name. The file is only saved by using the dev.off() function.

22 Saving and Using Files in R Each time you reference an external file in an R session of course you can use the full path name, which is tiresome and requires multiple changes to a saved R script. R provides help in keeping your work organized into directories. One way is to set a working directory and then all external files come out of or go into that directory until you change it again. setwd( c:/work/china/gt/isye6740_course ) After this command, the command saveplot( ex0101,type="eps")ex0101 puts the file ex0101.eps in c:\work\china\gt\isye6740_course Notice the difference in / and \

23 Saving and Using Files in R If your R program interacts with external files in various directories, setting and resetting the directory is annoying. An alternative to setwd is to define one or more character strings and then use paste. datadir <- c:/work/china/gt/isye6740_course/data graphdir <- c:/work/china/gt/isye6740_course Then x <- read.table(filename=paste(datadir, rats.dat,sep=""))... saveplot(filename=paste(graphdir, ex0101,sep=""),type="eps")

24 Bringing Data into R There are several input functions in R. Which to use depends on the source and format of the data. scan readline read.csv read.table etc. url <- " x <- read.table(url)

25 Random Data Let s create a random dataset of 100 observations on 3 variables. Let s make a random sample from a N 3 (0,Σ) distribution where Σ = set.seed(555) sqrtsigma <- matrix(c(12, 0, 5, 0, 13, 0, 5, 0, 1), byrow=t, ncol=3) x <- matrix(rnorm(300), ncol=3) x <- x%*%sqrtsigma

26 Random Data Let s check our random dataset sqrtsigma%*%sqrtsigma [,1] [,2] [,3] [1,] [2,] [3,] round(cov(x)) [,1] [,2] [,3] [1,] [2,] [3,]

27 Saving and Using Graphics Then let s make a scatterplot graph of the first two variables (columns), save it, and then use it. setwd( c:/work/china/gt/isye6740_course ) set.seed(555) sqrtsigma <- matrix(c(12, 0, 5, 0, 13, 0, 5, 0, 1), byrow=t, ncol=3) x <- matrix(rnorm(300), ncol=3) x <- x%*%sqrtsigma plot(x[,1],x[,2]) saveplot( ex0101a,type="eps") saveplot( ex0101a,type="jpg")

28 Saving and Using Graphics Now in a T E X file in that directory, I use \begin{center} \includegraphics[width=5in,height=5in]{ex0101a.eps} \end{center} and in an HTML file in that directory, I use <img src="ex0101a.jpg" alt="x1 vs x2" width="800" height="800" border="0">

29 Saving and Using Graphics Example. In the LAT E X file that produces what you re seeing, the next 3 executable lines, which will be invisible, are the three lines on the previous slide. x[, 2] x[, 1]

30 More on Random Data and Graphics Let s generate a random dataset of 100 observations on 2 variables, where each observation is randomly from either a N 2 (0, Σ 1 ) distribution or a N 2 (0,Σ 2 ) distribution, with a fixed and independent probability of p 1 of being from the first distribution. Let Σ 1 = [ ] Σ 2 = So how do you get the square root matrix? [ ] Initialize S1, then svd.s1 <- svd(s1) sqrt.s1<-sqrt(svd.s1$d[1])*svd.s1$u[,1]%*%t(svd.s1$v[,1])+ sqrt(svd.s1$d[2])*svd.s1$u[,2]%*%t(svd.s1$v[,2])

31 To convert Z N 2 (0, I) to X N 2 (0, Σ 1 ), we can set but another way is X = ZΣ 1/2 1, X = ZT Σ1, where T Σ1 is the Cholesky factor of Σ 1. TS1 <- chol(s1)

32 The Random Data Now let s generate the random data from the two distributions and put them in a matrix with a third column of -1 and 1 to indicate the class. set.seed(5) n <- 500 X <- matrix(c(rnorm(2*n),rep(1,n)),nrow=n) S1 <- matrix(c(109, 45, 45, 34), byrow=t, ncol=2) TS1 <- chol(s1) S2 <- matrix(c( 53, -38, -38, 148), byrow=t, ncol=2) TS2 <- chol(s2) p1 <- 0.6 n1 <- rbinom(1,n,p1) X[1:n1,1:2] <- X[1:n1,1:2]%*%TS1 X[1:n1,3] <- rep(-1,n1) X[(n1+1):n,1:2] <- X[(n1+1):n,1:2]%*%TS2 rindex <- sample(n) X <- X[rindex,]

33 Now let s plot the data and make the color of the plotting character depend on the class of the observation. We ll use colors 2 (red) and 3 (green), with green for the group = -1. plot(x[,1],x[,2],xlim=c(min(x[,1],x[,2]),max(x[,1],x[,2])), ylim=c(min(x[,1],x[,2]),max(x[,1],x[,2])), xlab=expression(italic(x)[1]),ylab=expression(italic(x)[2]), col=(x[,3]<0)+2) legend("topright",legend=c("group 1","Group -1"),pch=c(1,1),col=c(2,3 saveplot( ex0102,type="eps")

34 This yields X Group 1 Group X 1

35 Packages in R A useful R package for statistical learning is class. This contains, among other functions, a function to do k-nearest neighbors.