R programming. 19 February, University of Trento - FBK 1 / 50

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1 R programming University of Trento - FBK 19 February, / 50

2 Hints on programming 1 Save all your commands in a SCRIPT FILE, they will be useful in future...no one knows... 2 Save your script file any time you can! You swet a lot writing those instructions; You don t want to loose them! 3 Try to give smart name to variables and functions (try to avoid pippo, pluto a, b etc...) 4 Use comments to define sections in your script and describe what the section does If you read the code after 2 month you won t be able to remember what it does, unless you try to read all the instructions...it s not worth spending time reading codes, use COMMENT instead 5 If using values in more than one instruction, try to avoid code repetitions and static values. BAD: sum(a[a>0]) GOOD: thr <- 0 sum(a[a>thr]) 2 / 50

3 Programming with R The if then else statement Check whether a condition is TRUE or FALSE Syntax: if (expr is TRUE){ do something } else { do something else} expr can be one logical expression as seen before A simple if statement: If the instruction is on one line and there is no else -> no need for curly brackets x <- 5 y <- 2 ## if (y!=0) xy <- x/y ## xy A more complex if statement: x <- 5 y <- 3 if (x > 5){ xy <- x - y ## expr = TRUE } else { xy <- x + y ## expr = FALSE } ## [1] 8 3 / 50

4 Testing condition using combination of epression (& ) a<-2 b<-3 d<-4 # Using & to test two conditions, both true if(a<b & b<d) x<-a+b+d x ## [1] 9 # Using & to test two conditions, one is false if(a>b & b<c) y<-a-b-d ## Error in b < c: comparison (3) is possible only for atomic and list types y ## Error in eval(expr, envir, enclos): object y not found # Using to test two conditions, both false if(a==b a>d) z<-a*b*d z ## [1] 24 # Using or to test two conditions, one true if(a<b a>d) z<-a*b*d z ## [1] 24 4 / 50

5 Looping The while() statement Syntax: while( expr ){ do something } An example x <- 0 ## set the counter to 0 while( x<5 ){ ## do the same operation until x is < 5 x <- x + 1 ## update x } x ## [1] 5 Pay attention to the condition x <- 0 y <- 0 ## while (x < 5){ ## y <- y + 1 ## } 5 / 50

6 Looping II The for() statement Syntax: for (i in start:stop ){ do something } An example y <- vector(mode="numeric") ## Allocating an empty vector of mode "numeric" for (i in 1:5){ y[i] <- i + 2 } Nested Loops mat <- matrix(nrow=2,ncol=4) for (i in 1:2){ for (j in 1:4){ mat[i,j] <- i + j } } mat ## [,1] [,2] [,3] [,4] ## [1,] ## [2,] / 50

7 Vectors I I Indexing Use the square brackets to access a slot in a vector [] a[2] ## Extract the second element ## [1] 89 R stats counting from 1 a[0] ## Does not exists! ## integer(0) We can pass multiple indexes using c() function a[2:3] ## [1] ## a[2,3] ## What happen here? What happen when I use a negative number as index b[-1] ## All but the first element ## [1] e[-c(1,4)] ## All but the first and the fourth elements ## Error in eval(expr, envir, enclos): object e not found NB: Do not use c as variable name 7 / 50

8 Subsetting using logical operators Using logic operator inside indexes Logical operator can be use to subset a vector Select only the element of the vector matching the TRUE condition x <- 5:15 y <- 10 x[x > y] ## [1] x[x==y] ## [1] 10 can be used also in matrices mymat <- matrix(3:9, ncol=3) ## Warning in matrix(3:9, ncol = 3): data length [7] is not a sub-multiple or multiple of the number of rows [3] mymat > 7 ## Get TRUE where mymat is bigger than 7 ## [,1] [,2] [,3] ## [1,] FALSE FALSE TRUE ## [2,] FALSE FALSE FALSE ## [3,] FALSE TRUE FALSE mymat[mymat>7] ## Get the actual values where mymat is bigger than 7 ## [1] / 50

9 Subsetting using logical operators II Getting indexes The which() function Syntax:which(expr) works only on vectors (matrix and data.frame) returns the indexes where the expr is TRUE expr can be any logical expression; combination of AND, OR are accepted mymat > 7 ## [,1] [,2] [,3] ## [1,] FALSE FALSE TRUE ## [2,] FALSE FALSE FALSE ## [3,] FALSE TRUE FALSE ## Get the indexes where mymat > 7 which(mymat>7) ## [1] 6 7 which(mymat>7, arr.ind=true) ## row col ## [1,] 3 2 ## [2,] / 50

10 Exercises I 1 Given an integer number x check all its divisors. 2 Given an integer number x compute the sum of all its divisors. 3 A perfect number is a number whose sum of the divisors (apart from itself) is equal to the number itself. For example 6 is perfect because (the divisors) = 6. 1 Given an integer number check if it is perfect. 2 Given an integer number x find all perfect numbers i < x. 10 / 50

11 Functions I Define your own function We have seen many function such as: sum(mymat) ## [1] 49 mean(mymat) ## [1] Now you can define your custom function myfunction <- function(arg1, arg2){ do something with arg1 and arg2 return(results) } Define a function to convert Fahrenheit to Celsius FtoC <- function(f){ cels <- (F - 32) * (5/9) return(cels) } FtoC(212) ## [1] / 50

12 Functions II Define a function to make the power of a number/vector Use default argument mypow <- function(x, exponent=2){ res <- x^exponent return(res) } mypow(2) ## [1] 4 mypow(3,5) ## [1] 243 Variables defined inside a function will be valid only inside the function res ## Error in eval(expr, envir, enclos): object res not found Use debug() for debugging a function It will run line by line It allows to see the values of the variable inside the function Each time the function is defined the debug mode will be removed To exit the debug mode type c debug(mypow) 12 / 50

13 Functions II Function arguments can be call according to positions bt <- read.table("../lesson1/example1/bodytemperature.txt",true, " ") ## This will assign the f ## Gender Age HeartRate Temperature ## 1 M ## 2 M ## 3 M ## 4 F ## 5 F ## 6 M Function arguments can be call by name ## Call arguments by name (position does not count) bt <- read.table("../lesson1/example1/bodytemperature.txt",sep=" ", header=true) ## Gender Age HeartRate Temperature ## 1 M ## 2 M ## 3 M ## 4 F ## 5 F ## 6 M / 50

14 Data Exploration and summary statistic Develop high level understanding of the data Given a data.frame let s understand the data inside. What variables do we have? Do they have meaningful names? What are the variable types? (numeric, boolean, categorical) What is the distribution of the data? Are there any categorical variable? The aim is to reduce the amount of information and focus only on key aspect of the data 14 / 50

15 Working with data objects As an example let s work on the labdf dataset. bt <- read.table("bodytemperature.txt", header=true, sep=" ", as.is=true) head(bt) ## Let's look onlyt the firsts rows of the data.frame ## Gender Age HeartRate Temperature ## 1 M ## 2 M ## 3 M ## 4 F ## 5 F ## 6 M / 50

16 Working with data objects Get the structure and some useful statistic str(bt) ## See the structure of the data object ## 'data.frame': 100 obs. of 4 variables: ## $ Gender : chr "M" "M" "M" "F"... ## $ Age : int ## $ HeartRate : int ## $ Temperature: num summary(bt) ## Compute some statistic on each variable in the data.frame ## Gender Age HeartRate Temperature ## Length:100 Min. :21.0 Min. :61.0 Min. : 96.2 ## Class :character 1st Qu.:33.8 1st Qu.:69.0 1st Qu.: 97.7 ## Mode :character Median :37.0 Median :73.0 Median : 98.3 ## Mean :37.6 Mean :73.7 Mean : 98.3 ## 3rd Qu.:42.0 3rd Qu.:78.0 3rd Qu.: 98.9 ## Max. :50.0 Max. :87.0 Max. :101.3 names(bt) ## Get the variable names ## [1] "Gender" "Age" "HeartRate" "Temperature" 16 / 50

17 Working with data objects I Change the variable mode of the columns: Check the variable modes is.data.frame(bt) ## Check if the object is a data.frame ## [1] TRUE is.numeric(bt$age) ## Check if the mode of the column is numeric ## [1] TRUE is.character(bt$gender) ## Check if the mode of the variable Gender is character ## [1] TRUE Look at the variable Gender, it is categorical, but it s stored as character as.factor(bt$gender) ## Change variable mode Gender into factor (categorical) ## [1] M M M F F M F F F M M F F F F M F M F F F F F M F M M M M F F F M M M ## [36] F F M F F M M F M M M F F F F M F M M F F F M F F F M M F M M F M M M ## [71] F F M M M M F M F M M F F M F M M M F M F F M M F M F F F M ## Levels: F M 17 / 50

18 Working with data objects II Store the changes on the data.frame and check the data.frame bt$gender <- as.factor(bt$gender) ## Store the previous change str(bt) ## Look at the structure ## 'data.frame': 100 obs. of 4 variables: ## $ Gender : Factor w/ 2 levels "F","M": ## $ Age : int ## $ HeartRate : int ## $ Temperature: num summary(bt) ## Compute some statistic ## Gender Age HeartRate Temperature ## F:51 Min. :21.0 Min. :61.0 Min. : 96.2 ## M:49 1st Qu.:33.8 1st Qu.:69.0 1st Qu.: 97.7 ## Median :37.0 Median :73.0 Median : 98.3 ## Mean :37.6 Mean :73.7 Mean : 98.3 ## 3rd Qu.:42.0 3rd Qu.:78.0 3rd Qu.: 98.9 ## Max. :50.0 Max. :87.0 Max. : / 50

19 Exercise II 1 Define a function that converts km to miles and viceversa. 2 Define a function that check wheter a number is perfect (vd Exercise I). 3 Define a function that given a numeric matrix returns the log of the matrix where the matrix element is > 0 and NA otherwise. 4 Get the dataset SAheart_sub.data from the website and check the type for each column. Add a column of factor type with Alchoolic where the value of alchol consumption is > 13 and Non-Alcoholic otherwise. 19 / 50

20 Probability Distributions in R Probability functions: Every probability function in R has 4 functions denoted by the root (e.g. norm for normal distribution) and a prefix: p for probability, the cumulative distribution function (c.d.f.) F (x) = P(X <= x) q for quantile, the inverse of c.d.f. x = F 1 (p) d for density, the density function (p.d.f.) f (x) = 1 e x2 /2 2π r for random, the random variable having the specified distribution Example: For the normal distribution we have the functions: pnorm, qnorm, dnorm, rnorm 20 / 50

21 Probability distribution in R Available functions Distributions Functions Binomial pbinom qbinom dbinom rbinom Chi-Square pchisq qchisq dchisq rchisq Exponential pexp qexp dexp rexp Log Normal plnorm qlnorm dlnorm rlnorm Normal pnorm qnorm dnorm rnorm Poisson ppois qpois dpois rpois Student t pt qt dt rt Uniform punif qunif dunif runif Check the help (?<function>) for further information on the parameters and the usage of each function. 21 / 50

22 The Normal Distribution in R Cumulative Distribution Function pnorm: computes the Cumulative Distribution Function where X is normally distributed F (x) = P(X <= x) ## P(X<=2), X=N(0,1) pnorm(2) ## [1] ## P(X<=12), X=N(10,4) pnorm(12, mean=10, sd=2) ## [1] What is the P(X > 19) where X = N (17.4, )? pnorm Normal Cumulative x 22 / 50

23 The Normal Distribution in R The quantiles qnorm: computes the inverse of thd c.d.f. Given a number 0 p 1 it returns the p th quantile of the distribution. p = F (X) X = F 1 (p) ## X = F^-1(0.95), N(0,1) qnorm(0.95) Normal Density ## [1] ## X = F^-1(0.95), N(100,625) qnorm(0.95, mean=100, sd=25) ## [1] What is the 85-th quantile of X = N (72, 68)? pnorm p qnorm(p) x 23 / 50

24 The Normal Distribution in R The Density Function dnorm: computes the Probability Density Function (p.d.f.) of the normal distribution. f (x) = 1 e (x µ)2 2σ 2 2π ## F(0.5), X = N(0,1) dnorm(0.5) ## [1] ## F(-2.5), X = N(-1.5,2) dnorm(-2.5, mean=-1.5, sd=sqrt(2)) ## [1] dnorm Density Function x 24 / 50

25 The Normal Distribution in R The Random Function rnorm: simulates a random variates having a specified normal distribution. ## Extract 1000 samples X = N(0,1) x <- rnorm(1000) ## Extract 1000 samples X = N(100,225) x <- rnorm(1000, mean=100, sd=15) xx <- seq(min(x), max(x), length=100) hist(x, probability=true) lines(xx, dnorm(xx, mean=100, sd=15)) Density Histogram of x x 25 / 50

26 Exercise III 1 Compute the values for p = [0.01, 0.05, 0.1, 0.2, 0.25] given X = N ( 2, 8) 2 What is P(X = 1) when X = Bin(25, 0.005)? 3 What is P(13 X 22) where X = N (17.46, )? 26 / 50

27 Plotting in R High level plot functions Function Name plot(x,y) boxplot(x) hist(x) barplot(x) pairs(x) image(x,y,z) Plot Produced Plot vector x against vector y "Box and whiskers" plot Histogram of the frequencies of x Histogram of the value of x For a matrix or data.frame plots all bivariate pairs 3D plot using colors instead of lines 27 / 50

28 Simple visualization on numeric variables y Visualizing two vectors x <- 1:10 y <- 1:10 plot(x,y) x 28 / 50

29 Simple visualization on numeric variables Visualizing two vectors, adding axis labels and changin the line type plot(x,y, xlab="x values", ylab="y values", main="x vs Y", type="b") X vs Y Y values X values More graphical parameter can be seen looking at the help of par 29 / 50

30 y Additional parameter to graphical functions Low level plotting functions Adding point/line to an existing graph using points(x,y) and lines(x,y) Adding text to an existing plot using text(x,y,label= ") Adding a legend to a plot using legend(x,y,legend= ") plot(x,y) abline(0,1) points(2,3, pch=19) lines(x,y) text(4,6, label="slope=1") Slope= x 30 / 50

31 Barplot The function barplot() It plots the frequencies of the values of a variable It is useful for looking at categorical values It takes a vector or a matrix as input and use the values as frequencies barplot(1:10) / 50

32 Barplot The function barplot() Given a matrix as input (Death rates per 1000 population per year in Virginia) VADeaths ## Rural Male Rural Female Urban Male Urban Female ## ## ## ## ## barplot(vadeaths) Rural Male Rural Female Urban Male Urban Female 32 / 50

33 Visualization on Categorical variables Summarize the count for factors table(bt$gender) ## Collect the factors and count occurences for each factor ## ## F M ## Look at the summarization in a bar plot barplot(table(bt$gender), xlab="gender", ylab="frequency", main="summarize Gender variable") Summarize Gender variable Frequency F M Gender 33 / 50

34 Histograms The function hist() Normaly used to visualize numerical variables It is similar to a barplot but values are grouped into bins For each interval the bar height correspond to the frequency (count) of observation in that interval The heights sum to sample size 34 / 50

35 Look at the distribution of the data How the heart rate is distributed over our dataset? Histogram of the HeartRate variable using frequency on the Y axis hist(bt$heartrate, col="gray80") Histogram of bt$heartrate Frequency bt$heartrate 35 / 50

36 Look at the distribution of the data Density on the Y axis hist(bt$heartrate, col="gray80", freq=false) ## Use parameter freq to change behaviour Histogram of bt$heartrate Density bt$heartrate 36 / 50

37 Look at the distribution of the data Changing the intervals hist(bt$heartrate, col="gray80", breaks=50) ## Use parameter breaks to change intervals Histogram of bt$heartrate Frequency bt$heartrate 37 / 50

38 Look at the distribution of the data Adding information to the histogram, mean and median hist(bt$heartrate, col="gray80", main="histogram of Hear Rate") abline(v=mean(bt$heartrate), lwd=3) abline(v=median(bt$heartrate), lty=3, lwd=3) legend("right", legend=c("mean", "Median"), lty=c(1,3)) Histogram of Hear Rate Frequency Mean Median bt$heartrate 38 / 50

39 Boxplots The function boxplot() Visualize the 5-number summary, the range and the quartiles 39 / 50

40 Boxplots Look at the boxplot for the HearRate Variable boxplot(bt$heartrate, horizontal=true, col="grey80") / 50

41 Boxplots Look at the boxplot for the HeartRate Variable boxplot(bt$heartrate, horizontal=true, col="grey80") points(bt$heartrate, rep(1,length(bt$heartrat)), pch=19) ## See where the data are abline(h=1, lty=2) / 50

42 Using factors and formula objects Using a factor as categorical variable to condition the plot Conditioning a plot using the factor using the formula object: bt$heartrate ~ bt$gender The numeric values in bt$heartrate will be divided according to categories in bt$gender boxplot(bt$heartrate~bt$gender, horizontal=true, col="grey80") F M / 50

43 Pairs The pairs() function It plots all the possible pairwise comparison in a data.frame It allows a fast visual data exploration pairs(bt) ## Look at all possible comparison at once Gender Age HeartRate Temperature 43 / 50

44 Normal plot Let s look at the variable HearRate vs Temperature See the use of in the plot command ## plot(bt$heartrate, bt$temperature) plot(bt$heartrate~bt$temperature, main="heart Rate vs Temperature") Heart Rate vs Temperature bt$temperature bt$heartrate 44 / 50

45 Multiple plots on the same windows Put more information together on the same plot par(mfrow=c(2,1)) ## Note mfrow defining 2 rows and 1 column for allowing 2 plots hist(bt$heartrate, col="grey80", main="heartrate histogram") abline(v=mean(bt$heartrate), lwd=3) abline(v=median(bt$heartrate), lty=3, lwd=3) legend("right", legend=c("mean", "Median"), lty=c(1,3)) boxplot(bt$heartrate~bt$gender, horizontal=true, col=c( "pink", "blue")) title("boxplot for different gender") points(bt$heartrate[bt$gender=="f"], rep(1,length(bt$heartrate[bt$gender=="f"])), pch=19) points(bt$heartrate[bt$gender=="m"], rep(2,length(bt$heartrate[bt$gender=="m"])), pch=19) HeartRate histogram Frequency Mean Median bt$heartrate Boxplot for different gender F M / 50

46 Exporting graphs It is possible to export graph in different formats Png, Jpg, Pdf, Eps, Tiff Look at the help for the functions pdf,png pdf("myfirstgraph.pdf") ## Start the png device par(mfrow=c(2,1)) hist(bt$heartrate, col="grey80", main="heartrate histogram") boxplot(bt$heartrate, horizontal=true, col="grey80", main="boxplot") dev.off() ## switch off the device nif / 50

47 Look probability distribution in plot How an extraction from a N distribution looks like? Extract enough samples from a N (0, 1) Use Histogram to look at the data x <- seq(-3,3,by=0.1) ## Create a vector of x values y <- dnorm(x) ## Compute the normal density function over the vector x plot(x,y,type="l") ## Plot it y x 47 / 50

48 Data in R R comes with a lot of dataset included Look at all the available data sets with: data() ## See all the availabel datasets data(package =.packages(all.available = TRUE)) ## See all the available dataset in all the pav ## Warning in data(package =.packages(all.available = TRUE)): datasets have been moved from package base to package datasets ## Warning in data(package =.packages(all.available = TRUE)): datasets have been moved from package stats to package datasets Get the VADeaths dataset from the datasets package data(vadeaths, package="datasets") ## Load the dataset ## ls() ## Look if the dataseta has been loaded ##?VADeaths ## Look at the documentation 48 / 50

49 Exercise I 1 Define a function that transform Celsius to Fahrenheit Given the function defined before think on using an argument to compute the inverse (Fahreneit to Celsius) 2 Define a function that given a number it computes the Fibonacci series What can happen if a float number or a negative number is given? 3 Define a function that given a number it checks if it is a prime number 4 Two integer number are friends if the quotient between the number itself and the sum of the divisors are equal. For example the sum of divisors of 6 is =12. The sum of divisors of 28 is = 56. Then 12 /6 = 56 / 28 = 2, thus 6 and 28 are friends. Define a function that given 2 number as input checks if the numbers are friends. 5 Fix the number of samples to 1000 and extract at least 8 N (m, 1) where m [ 3, 3]. With the same number of samples extract at least 8 N (0, s) where s [0.1, 2]. Plot the results in a same window with 3 different plot, one for N (m, 1), one for N (0, s) and one for N (m, 1) and N (0, s) together. Decide the color code for each line suggestion: search for R color charts in google and the function colors() in R Plot the different distribution on the sample plot 49 / 50

50 Exercise II 6 Extract form a normal distribution an increasing number of samples ( ) and look at the differences in the distribution between sample sizes 7 The dataset Pima.tr collects samples from the US National Institute of Diabetes and Difestive and Kidney Disease. It includes 200 women of Pima Indian heritage living near Phoenix, Arizona. Get the dataset from the MASS package or download it from the website. Describe the dataset, how many variables, which type of variable, how many samples... What do the variable mean? Get the frquencies of the women affected by diabetes. Explore the dataset using histograms, barplot and plots. For each plot you do describe what you see and why did you do that plot. Using categorical variable type to see if there is any difference in age distribution, bmi, and glu variables 50 / 50