- •brief contents
- •contents
- •preface
- •acknowledgments
- •about this book
- •What’s new in the second edition
- •Who should read this book
- •Roadmap
- •Advice for data miners
- •Code examples
- •Code conventions
- •Author Online
- •About the author
- •about the cover illustration
- •1 Introduction to R
- •1.2 Obtaining and installing R
- •1.3 Working with R
- •1.3.1 Getting started
- •1.3.2 Getting help
- •1.3.3 The workspace
- •1.3.4 Input and output
- •1.4 Packages
- •1.4.1 What are packages?
- •1.4.2 Installing a package
- •1.4.3 Loading a package
- •1.4.4 Learning about a package
- •1.5 Batch processing
- •1.6 Using output as input: reusing results
- •1.7 Working with large datasets
- •1.8 Working through an example
- •1.9 Summary
- •2 Creating a dataset
- •2.1 Understanding datasets
- •2.2 Data structures
- •2.2.1 Vectors
- •2.2.2 Matrices
- •2.2.3 Arrays
- •2.2.4 Data frames
- •2.2.5 Factors
- •2.2.6 Lists
- •2.3 Data input
- •2.3.1 Entering data from the keyboard
- •2.3.2 Importing data from a delimited text file
- •2.3.3 Importing data from Excel
- •2.3.4 Importing data from XML
- •2.3.5 Importing data from the web
- •2.3.6 Importing data from SPSS
- •2.3.7 Importing data from SAS
- •2.3.8 Importing data from Stata
- •2.3.9 Importing data from NetCDF
- •2.3.10 Importing data from HDF5
- •2.3.11 Accessing database management systems (DBMSs)
- •2.3.12 Importing data via Stat/Transfer
- •2.4 Annotating datasets
- •2.4.1 Variable labels
- •2.4.2 Value labels
- •2.5 Useful functions for working with data objects
- •2.6 Summary
- •3 Getting started with graphs
- •3.1 Working with graphs
- •3.2 A simple example
- •3.3 Graphical parameters
- •3.3.1 Symbols and lines
- •3.3.2 Colors
- •3.3.3 Text characteristics
- •3.3.4 Graph and margin dimensions
- •3.4 Adding text, customized axes, and legends
- •3.4.1 Titles
- •3.4.2 Axes
- •3.4.3 Reference lines
- •3.4.4 Legend
- •3.4.5 Text annotations
- •3.4.6 Math annotations
- •3.5 Combining graphs
- •3.5.1 Creating a figure arrangement with fine control
- •3.6 Summary
- •4 Basic data management
- •4.1 A working example
- •4.2 Creating new variables
- •4.3 Recoding variables
- •4.4 Renaming variables
- •4.5 Missing values
- •4.5.1 Recoding values to missing
- •4.5.2 Excluding missing values from analyses
- •4.6 Date values
- •4.6.1 Converting dates to character variables
- •4.6.2 Going further
- •4.7 Type conversions
- •4.8 Sorting data
- •4.9 Merging datasets
- •4.9.1 Adding columns to a data frame
- •4.9.2 Adding rows to a data frame
- •4.10 Subsetting datasets
- •4.10.1 Selecting (keeping) variables
- •4.10.2 Excluding (dropping) variables
- •4.10.3 Selecting observations
- •4.10.4 The subset() function
- •4.10.5 Random samples
- •4.11 Using SQL statements to manipulate data frames
- •4.12 Summary
- •5 Advanced data management
- •5.2 Numerical and character functions
- •5.2.1 Mathematical functions
- •5.2.2 Statistical functions
- •5.2.3 Probability functions
- •5.2.4 Character functions
- •5.2.5 Other useful functions
- •5.2.6 Applying functions to matrices and data frames
- •5.3 A solution for the data-management challenge
- •5.4 Control flow
- •5.4.1 Repetition and looping
- •5.4.2 Conditional execution
- •5.5 User-written functions
- •5.6 Aggregation and reshaping
- •5.6.1 Transpose
- •5.6.2 Aggregating data
- •5.6.3 The reshape2 package
- •5.7 Summary
- •6 Basic graphs
- •6.1 Bar plots
- •6.1.1 Simple bar plots
- •6.1.2 Stacked and grouped bar plots
- •6.1.3 Mean bar plots
- •6.1.4 Tweaking bar plots
- •6.1.5 Spinograms
- •6.2 Pie charts
- •6.3 Histograms
- •6.4 Kernel density plots
- •6.5 Box plots
- •6.5.1 Using parallel box plots to compare groups
- •6.5.2 Violin plots
- •6.6 Dot plots
- •6.7 Summary
- •7 Basic statistics
- •7.1 Descriptive statistics
- •7.1.1 A menagerie of methods
- •7.1.2 Even more methods
- •7.1.3 Descriptive statistics by group
- •7.1.4 Additional methods by group
- •7.1.5 Visualizing results
- •7.2 Frequency and contingency tables
- •7.2.1 Generating frequency tables
- •7.2.2 Tests of independence
- •7.2.3 Measures of association
- •7.2.4 Visualizing results
- •7.3 Correlations
- •7.3.1 Types of correlations
- •7.3.2 Testing correlations for significance
- •7.3.3 Visualizing correlations
- •7.4 T-tests
- •7.4.3 When there are more than two groups
- •7.5 Nonparametric tests of group differences
- •7.5.1 Comparing two groups
- •7.5.2 Comparing more than two groups
- •7.6 Visualizing group differences
- •7.7 Summary
- •8 Regression
- •8.1 The many faces of regression
- •8.1.1 Scenarios for using OLS regression
- •8.1.2 What you need to know
- •8.2 OLS regression
- •8.2.1 Fitting regression models with lm()
- •8.2.2 Simple linear regression
- •8.2.3 Polynomial regression
- •8.2.4 Multiple linear regression
- •8.2.5 Multiple linear regression with interactions
- •8.3 Regression diagnostics
- •8.3.1 A typical approach
- •8.3.2 An enhanced approach
- •8.3.3 Global validation of linear model assumption
- •8.3.4 Multicollinearity
- •8.4 Unusual observations
- •8.4.1 Outliers
- •8.4.3 Influential observations
- •8.5 Corrective measures
- •8.5.1 Deleting observations
- •8.5.2 Transforming variables
- •8.5.3 Adding or deleting variables
- •8.5.4 Trying a different approach
- •8.6 Selecting the “best” regression model
- •8.6.1 Comparing models
- •8.6.2 Variable selection
- •8.7 Taking the analysis further
- •8.7.1 Cross-validation
- •8.7.2 Relative importance
- •8.8 Summary
- •9 Analysis of variance
- •9.1 A crash course on terminology
- •9.2 Fitting ANOVA models
- •9.2.1 The aov() function
- •9.2.2 The order of formula terms
- •9.3.1 Multiple comparisons
- •9.3.2 Assessing test assumptions
- •9.4 One-way ANCOVA
- •9.4.1 Assessing test assumptions
- •9.4.2 Visualizing the results
- •9.6 Repeated measures ANOVA
- •9.7 Multivariate analysis of variance (MANOVA)
- •9.7.1 Assessing test assumptions
- •9.7.2 Robust MANOVA
- •9.8 ANOVA as regression
- •9.9 Summary
- •10 Power analysis
- •10.1 A quick review of hypothesis testing
- •10.2 Implementing power analysis with the pwr package
- •10.2.1 t-tests
- •10.2.2 ANOVA
- •10.2.3 Correlations
- •10.2.4 Linear models
- •10.2.5 Tests of proportions
- •10.2.7 Choosing an appropriate effect size in novel situations
- •10.3 Creating power analysis plots
- •10.4 Other packages
- •10.5 Summary
- •11 Intermediate graphs
- •11.1 Scatter plots
- •11.1.3 3D scatter plots
- •11.1.4 Spinning 3D scatter plots
- •11.1.5 Bubble plots
- •11.2 Line charts
- •11.3 Corrgrams
- •11.4 Mosaic plots
- •11.5 Summary
- •12 Resampling statistics and bootstrapping
- •12.1 Permutation tests
- •12.2 Permutation tests with the coin package
- •12.2.2 Independence in contingency tables
- •12.2.3 Independence between numeric variables
- •12.2.5 Going further
- •12.3 Permutation tests with the lmPerm package
- •12.3.1 Simple and polynomial regression
- •12.3.2 Multiple regression
- •12.4 Additional comments on permutation tests
- •12.5 Bootstrapping
- •12.6 Bootstrapping with the boot package
- •12.6.1 Bootstrapping a single statistic
- •12.6.2 Bootstrapping several statistics
- •12.7 Summary
- •13 Generalized linear models
- •13.1 Generalized linear models and the glm() function
- •13.1.1 The glm() function
- •13.1.2 Supporting functions
- •13.1.3 Model fit and regression diagnostics
- •13.2 Logistic regression
- •13.2.1 Interpreting the model parameters
- •13.2.2 Assessing the impact of predictors on the probability of an outcome
- •13.2.3 Overdispersion
- •13.2.4 Extensions
- •13.3 Poisson regression
- •13.3.1 Interpreting the model parameters
- •13.3.2 Overdispersion
- •13.3.3 Extensions
- •13.4 Summary
- •14 Principal components and factor analysis
- •14.1 Principal components and factor analysis in R
- •14.2 Principal components
- •14.2.1 Selecting the number of components to extract
- •14.2.2 Extracting principal components
- •14.2.3 Rotating principal components
- •14.2.4 Obtaining principal components scores
- •14.3 Exploratory factor analysis
- •14.3.1 Deciding how many common factors to extract
- •14.3.2 Extracting common factors
- •14.3.3 Rotating factors
- •14.3.4 Factor scores
- •14.4 Other latent variable models
- •14.5 Summary
- •15 Time series
- •15.1 Creating a time-series object in R
- •15.2 Smoothing and seasonal decomposition
- •15.2.1 Smoothing with simple moving averages
- •15.2.2 Seasonal decomposition
- •15.3 Exponential forecasting models
- •15.3.1 Simple exponential smoothing
- •15.3.3 The ets() function and automated forecasting
- •15.4 ARIMA forecasting models
- •15.4.1 Prerequisite concepts
- •15.4.2 ARMA and ARIMA models
- •15.4.3 Automated ARIMA forecasting
- •15.5 Going further
- •15.6 Summary
- •16 Cluster analysis
- •16.1 Common steps in cluster analysis
- •16.2 Calculating distances
- •16.3 Hierarchical cluster analysis
- •16.4 Partitioning cluster analysis
- •16.4.2 Partitioning around medoids
- •16.5 Avoiding nonexistent clusters
- •16.6 Summary
- •17 Classification
- •17.1 Preparing the data
- •17.2 Logistic regression
- •17.3 Decision trees
- •17.3.1 Classical decision trees
- •17.3.2 Conditional inference trees
- •17.4 Random forests
- •17.5 Support vector machines
- •17.5.1 Tuning an SVM
- •17.6 Choosing a best predictive solution
- •17.7 Using the rattle package for data mining
- •17.8 Summary
- •18 Advanced methods for missing data
- •18.1 Steps in dealing with missing data
- •18.2 Identifying missing values
- •18.3 Exploring missing-values patterns
- •18.3.1 Tabulating missing values
- •18.3.2 Exploring missing data visually
- •18.3.3 Using correlations to explore missing values
- •18.4 Understanding the sources and impact of missing data
- •18.5 Rational approaches for dealing with incomplete data
- •18.6 Complete-case analysis (listwise deletion)
- •18.7 Multiple imputation
- •18.8 Other approaches to missing data
- •18.8.1 Pairwise deletion
- •18.8.2 Simple (nonstochastic) imputation
- •18.9 Summary
- •19 Advanced graphics with ggplot2
- •19.1 The four graphics systems in R
- •19.2 An introduction to the ggplot2 package
- •19.3 Specifying the plot type with geoms
- •19.4 Grouping
- •19.5 Faceting
- •19.6 Adding smoothed lines
- •19.7 Modifying the appearance of ggplot2 graphs
- •19.7.1 Axes
- •19.7.2 Legends
- •19.7.3 Scales
- •19.7.4 Themes
- •19.7.5 Multiple graphs per page
- •19.8 Saving graphs
- •19.9 Summary
- •20 Advanced programming
- •20.1 A review of the language
- •20.1.1 Data types
- •20.1.2 Control structures
- •20.1.3 Creating functions
- •20.2 Working with environments
- •20.3 Object-oriented programming
- •20.3.1 Generic functions
- •20.3.2 Limitations of the S3 model
- •20.4 Writing efficient code
- •20.5 Debugging
- •20.5.1 Common sources of errors
- •20.5.2 Debugging tools
- •20.5.3 Session options that support debugging
- •20.6 Going further
- •20.7 Summary
- •21 Creating a package
- •21.1 Nonparametric analysis and the npar package
- •21.1.1 Comparing groups with the npar package
- •21.2 Developing the package
- •21.2.1 Computing the statistics
- •21.2.2 Printing the results
- •21.2.3 Summarizing the results
- •21.2.4 Plotting the results
- •21.2.5 Adding sample data to the package
- •21.3 Creating the package documentation
- •21.4 Building the package
- •21.5 Going further
- •21.6 Summary
- •22 Creating dynamic reports
- •22.1 A template approach to reports
- •22.2 Creating dynamic reports with R and Markdown
- •22.3 Creating dynamic reports with R and LaTeX
- •22.4 Creating dynamic reports with R and Open Document
- •22.5 Creating dynamic reports with R and Microsoft Word
- •22.6 Summary
- •afterword Into the rabbit hole
- •appendix A Graphical user interfaces
- •appendix B Customizing the startup environment
- •appendix C Exporting data from R
- •Delimited text file
- •Excel spreadsheet
- •Statistical applications
- •appendix D Matrix algebra in R
- •appendix E Packages used in this book
- •appendix F Working with large datasets
- •F.1 Efficient programming
- •F.2 Storing data outside of RAM
- •F.3 Analytic packages for out-of-memory data
- •F.4 Comprehensive solutions for working with enormous datasets
- •appendix G Updating an R installation
- •G.1 Automated installation (Windows only)
- •G.2 Manual installation (Windows and Mac OS X)
- •G.3 Updating an R installation (Linux)
- •references
- •index
- •Symbols
- •Numerics
- •23.1 The lattice package
- •23.2 Conditioning variables
- •23.3 Panel functions
- •23.4 Grouping variables
- •23.5 Graphic parameters
- •23.6 Customizing plot strips
- •23.7 Page arrangement
- •23.8 Going further
Debugging |
483 |
The four efficiency measures described in this section can help with everyday coding problems. But they only go so far in helping you to process really large datasets (for example, datasets in the terabyte range). When you’re working with big datasets, methods like those described in appendix G are required.
Locating bottlenecks
“Why is my code taking so long?” R provides tools for profiling programs in order to identify the most time-consuming functions. Place the code to be profiled between Rprof() and Rprof(NULL). Then execute summaryRprof() to get a summary of the time spent executing each function. See ?Rprof and ?summaryRprof for details.
Efficiency is little comfort when a program won’t execute or gives nonsensical results. Methods for uncovering programming errors are considered next.
20.5 Debugging
Debugging is the process of finding and reducing the number of errors or defects in a program. It would be wonderful if programs worked the first time. It would also be wonderful if unicorns lived in my neighborhood. In all but the simplest programs, errors occur. Determining the cause of these errors and fixing them is a time-consuming process. In this section, we’ll look at common sources of error and tools that can help to uncover errors.
20.5.1Common sources of errors
The following are some common reasons functions fail in R:
■An object name is misspelled, or the object doesn’t exist.
■There is a misspecification of the parameters in a function call.
■The contents of an object aren’t what the user expects. In particular, errors are often caused by passing objects that are NULL or contain NaN or NA values to a function that can’t handle them.
The third reason is more common than you may think. It results from R’s terse approach to errors and warnings.
Consider the following example. For the mtcars dataset in the base installation, you want to provide the variable am (transmission type) with a more informative title and labels. Next, you want to compare the gas mileage of cars with automatic transmissions to those with manual transmissions:
> mtcars$Transmission <- factor(mtcars$a, levels=c(1,2),
labels=c("Automatic", "Manual")) > aov(mpg ~ Transmission, data=mtcars)
Error in `contrasts<-`(`*tmp*`, value = contr.funs[1 + isOF[nn]]) : contrasts can be applied only to factors with 2 or more levels
484 |
CHAPTER 20 Advanced programming |
Yikes! (Embarrassing, but this is actually what I said.) What happened?
You didn’t get an “Object xxx not found” error, so you probably didn’t misspell a function, data frame, or variable name. Let’s look at the data that was passed to the aov() function:
> head(mtcars[c("mpg", |
"Transmission")]) |
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mpg |
Transmission |
Mazda RX4 |
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21.0 |
Automatic |
Mazda RX4 Wag |
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21.0 |
Automatic |
Datsun 710 |
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22.8 |
Automatic |
Hornet 4 Drive |
21.4 |
<NA> |
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Hornet Sportabout |
18.7 |
<NA> |
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Valiant |
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18.1 |
<NA> |
> table(mtcars$Transmission) |
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Automatic |
Manual |
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13 |
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0 |
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There are no cars with a manual transmission. Looking back at the original dataset, the variable am is coded 0=automatic, 1=manual (not 1=automatic, 2=manual).
The factor() function happily did what you asked without warnings or errors. It set all cars with manual transmissions to automatic and all cars with automatic transmissions to missing. With only one group available, the analysis of variance failed. Confirming that each input to a function contains the expected data can save you hours of frustrating detective work.
20.5.2Debugging tools
Although examining object names, function parameters, and function inputs will uncover many sources of error, sometimes you have to delve into the inner workings of functions and functions that call functions. In these cases, the internal debugger that comes with R can be useful. Some helpful debugging functions are listed table 20.1.
Table 20.1 Built-in debugging functions
Function |
Action |
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debug() |
Marks a function for debugging. |
undebug() |
Unmarks a function for debugging. |
browser() |
Allows single-stepping through the execution of a function. While you’re debugging, |
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typing n or pressing <RET> (the Enter key) executes the current statement and |
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moves on to the next. Typing c continues execution to the end of the function without |
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single-stepping. Typing where displays the call stack, and Q halts execution and |
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jumps to the top level immediately. Other R commands like ls(), print(), and |
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assignment statements can also be submitted at the debugger prompt. |
trace() |
Modifies a function to allow debug code to be temporarily inserted. |
untrace() |
Cancels tracing and removes the temporary code. |
traceback() |
Prints the sequence of function calls that led to the last uncaught error. |
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Debugging |
485 |
The debug() function marks a function for debugging. When the function is executed, the browser() function is called and allows you to step through the function’s execution one line at a time. The undebug() function turns this off, allowing the function to execute normally. You can temporarily insert debugging code into a function with the trace() function. This is particularly useful when you’re debugging base functions and CRAN-contributed functions that can’t be edited directly.
If a function calls other functions, it can be hard to determine where an error has occurred. In this case, executing the traceback() function immediately after an error will list the sequence of function calls that led to the error. The last call is the one that produced the error.
Let’s look at an example. The mad() function calculates the median absolute deviation for a numeric vector. You’ll use debug() to explore how this function works. The debugging session is displayed in the following listing.
Listing 20.4 A sample debugging session
> args(mad)
function (x, center = median(x), constant = 1.4826, na.rm = FALSE, low = FALSE, high = FALSE)
Views the formal b arguments
NULL |
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> debug(mad) |
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Sets the function |
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> mad(1:10) |
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c to debug |
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debugging in: mad(x) |
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debug: { |
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if (na.rm) |
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x <- x[!is.na(x)] |
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n <- length(x) |
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constant * if ((low || high) && n%%2 == 0) { |
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if (low && high) |
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stop("'low' and 'high' cannot be both TRUE") |
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n2 <- n%/%2 + as.integer(high) |
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sort(abs(x - center), partial = n2)[n2] |
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} |
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else median(abs(x - center)) |
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d Lists objects |
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} |
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Browse[2]> ls() |
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[1] "center" |
"constant" "high" |
"low" |
"na.rm" |
"x" |
Browse[2]> |
center |
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[1] 5.5 |
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Browse[2]> |
constant |
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[1] 1.4826 |
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Browse[2]> |
na.rm |
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[1] FALSE |
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Browse[2]> |
x |
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[1] |
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8 |
9 |
10 |
Browse[2]> n |
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Single-steps |
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debug: if (na.rm) x <- x[!is.na(x)] |
e through the code |
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Browse[2]> n |
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debug: n <- length(x) Browse[2]> n
debug: constant * if ((low || high) && n%%2 == 0) {
486 CHAPTER 20 Advanced programming
if (low && high)
stop("'low' and 'high' cannot be both TRUE") n2 <- n%/%2 + as.integer(high)
sort(abs(x - center), partial = n2)[n2]
} else median(abs(x - center)) |
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Browse[2]> |
print(n) |
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[1] 10 |
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Browse[2]> |
where |
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where 1: mad(x) |
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Browse[2]> |
c |
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Resumes continuous |
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exiting from: mad(x) |
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f execution |
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[1] 3.7065 |
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> undebug(mad) |
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First, the arg() function is used to display the argument names and default values for the mad() function b. The debug flag is then set using debug(mad) c. Now, whenever mad() is called, the browser() function is executed, allowing you to step through the function a line at a time.
When mad() is called, the session goes into browser() mode. The code for the function is listed but not executed. Additionally, the prompt changes to Browse[n]>, where n indicates the browser level. The number increments with each recursive call.
In browser() mode, other R commands can be executed. For example, ls() lists the objects in existence at a given point during the function’s execution d. Typing an object’s name displays its contents. If an object is named n, c, or Q, you must use print(n), print(c), or print(Q) to view its contents. You can change the values of objects by typing assignment statements.
You step through the function and execute the statements one at a time by entering the letter n or pressing the Return or Enter key e. The where statement indicates where you are in the stack of function calls being executed. With a single function, this isn’t very interesting; but if you have functions that call other functions, it can be helpful.
Typing c moves out of single-step mode and executes the remainder of the current function f. Typing Q exits the function and returns you to the R prompt.
The debug() function is useful when you have loops and want to see how values are changing. You can also embed the browser() function directly in code in order to help locate a problem. Let’s say that you have a variable X that should never be negative. Adding the code
if (X < 0) browser()
allows you to explore the current state of the function when the problem occurs. You can take out the extra code when the function is sufficiently debugged. (I originally wrote “fully debugged,” but this almost never happens, so I changed it to “sufficiently debugged” to reflect a programmer’s reality.)
20.5.3Session options that support debugging
When you have functions that call functions, two session options can help in the debugging process. Normally, when R encounters an error, it prints an error message
Debugging |
487 |
and exits the function. Setting options(error=traceback) prints the call stack (the sequence of function calls that led to the error) as soon as an error occurs. This can help you to determine which function generated the error.
Setting options(error=recover) also prints the call stack when an error occurs. In addition, it prompts you to select one of the functions on the list and then invokes browser() in the corresponding environment. Typing c returns you to the list, and typing 0 quits back to the R prompt.
Using this recover() mode lets you explore the contents of any object in any function chosen from the sequence of functions called. By selectively viewing the contents of objects, you can frequently determine the origin of the problem. To return to R’s default state, set options(error=NULL). A toy example is given next.
Listing 20.5 Sample debugging session with recover()
f <- function(x, y){ |
Creates functions |
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z <- |
x + y |
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g(z) |
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}
g <- function(x){
z <- round(x) h(z)
}
h <- function(x){ set.seed(1234) z <- rnorm(x) print(z)
}
>options(error=recover)
>f(2,3)
[1] -1.207 |
0.277 |
1.084 -2.346 0.429 |
> f(2, -3) |
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Error in rnorm(x) |
: invalid arguments |
Enter a frame number, or 0 to exit
1:f(2, -3)
2:#3: g(z)
3:#3: h(z)
4:#3: rnorm(x)
Selection: |
4 |
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Examines rnorm() |
Called from: rnorm(x) |
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Browse[1]> |
ls() |
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[1] "mean" |
"n" |
"sd" |
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Browse[1]> |
mean |
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[1] 0 |
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Browse[1]> |
print(n) |
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[1] -1 |
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Browse[1]> |
c |
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Enters values
that cause an error
Enter a frame number, or 0 to exit
488 |
CHAPTER 20 Advanced programming |
1:f(2, -3)
2:#3: g(z)
3:#3: h(z)
4:#3: rnorm(x)
Selection: 3 |
Examines h(z) |
Called from: h(z) |
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Browse[1]> ls() |
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[1] "x" |
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Browse[1]> x |
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[1] -1 |
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Browse[1]> c |
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Enter a frame number, or 0 to exit
1:f(2, -3)
2:#3: g(z)
3:#3: h(z)
4:#3: rnorm(x)
Selection: 2 |
Examines g(z) |
Called from: g(z) |
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Browse[1]> ls() |
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[1] "x" "z" |
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Browse[1]> x |
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[1] -1 |
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Browse[1]> z |
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[1] -1 |
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Browse[1]> c |
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Enter a frame number, or 0 to exit
1:f(2, -3)
2:#3: g(z)
3:#3: h(z)
4:#3: rnorm(x)
Selection: 1 |
Examines f(2, -3) |
Called from: f(2, -3) |
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Browse[1]> ls() |
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[1] "x" "y" "z" |
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Browse[1]> x |
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[1] 2 |
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Browse[1]> y |
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[1] -3 |
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Browse[1]> z |
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[1] -1 |
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Browse[1]> print(f) |
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function(x, y){ |
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z <- x + y |
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g(z) |
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} |
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Browse[1]> c |
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Enter a frame number, or 0 to exit