A brief Introduction to R
Subsections
R is a data plotting package and a programming language. In R, you issue
commands or combine them to make programs, in order to analyse your
data and turn it into exciting-looking, meaningful plots. R is
actually a free implementation of the S programming language.
1 Its origins are in the
statistics community but it is spreading into many other scientific
areas. R is both free, and cross-platform, so you can obtain and
install it on your Windows, Linux or MacOS X machine at home at no
cost.
R is an example of a type of product which one might call a
scientific data-analysis language.
Matlab and IDL are commercial examples of this kind of tool. Other
free examples include Octave, Yorick and Scilab. It is generally the
case that having learned to use one of these tools, learning to use
one of the others is just a matter of learning a new syntax, not of
learning a new way of thinking. This is the real reason for teaching
R: you may or may not use R for your project or for work later in your
career. But you are almost certain to use a
scientific
data-analysis language of one sort or another.
To start R, type ``
R'' at the prompt in a terminal
window. You should get a response like this:
halo.hcp>R
R version 2.4.1 (2006-12-18)
Copyright (C) 2006 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
Natural language support but running in an English locale
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
>
If you get that, you are ready to go -- the
> symbol is the R
prompt, waiting for you to type a command. If you get something else,
ask your instructor what is wrong. Let's assume now that R is working
properly and try out the demos. If you type
demo() at the R
prompt you will get a list of available demonstrations (you may need
to press
q to leave the list). Type
demo(graphics) to get
an idea of R's plotting capabilities.
The welcome message tells you how to access the on-line
documentation, which is quite detailed. It includes a longer
introduction than this one, and a formal language definition. Under
the heading
Packages is information on all of R's commands and
functions -- most of the functions we will be using are in package
base. Use of the on-line documentation is
very
important. You will be expected to be able to use it
effectively. It should be your first port of call when you have a
question about R, because it will nearly always have the answer. Often
help(something) doesn't tell you what you need to know, because
there is no R command called
something. R will then suggest that
you try
help.search("something") (you need the
""), which
will do a broader search and try to suggest the command that you
might be looking for.
Now that we have R working, let's make a plot with it. Let's suppose
that we have several points (each of which has a horizontal and a
vertical co-ordinate) and that we want to plot them on a graph. We'll
be traditional and call the horizontal co-ordinates
and the
vertical co-ordinates
. We can enter the data into R like
this
2.
> x <- c(1, 2, 4, 5, 6.7, 7, 8, 10 )
> y <- c(40, 30, 10, 20, 53, 20, 10, 5)
We now have two array variables called
and
, each containing
eight numbers. Note that the left-pointing arrow is traditionally used
for assignment in R, although recent versions permit the = used in
many other languages. The R command
c() is used to combine several
numbers into an array. You can print the contents of a variable by
typing its name:
> y
[1] 40 30 10 20 53 20 10 5
To make a plot of
against
, we just type this:
> plot(x,y)
and there it is. It is a bit plain, but we have visualised our
data. No-one else is going to know what it means unless we label the
axes, like this:
> plot(x,y,main="Should he resign?",xlab="Time / weeks",ylab="Popularity")
We suppose that the data is the popularity ratings of a politician as
determined by a polling organisation. Notice that there are two
different ways in which we have provided instructions to the `plot'
routine. The data,
x and
y, are provided as positional
parameters. The order they come in matters. Here, the first parameter
is the horizontal co-ordinates of our data, the second is the vertical
co-ordinates. Optional things like the labels are passed as keyword
parameters. An important R routine like
plot usually has many of
these. You can supply them in any order you like.
Now let's suppose that our politician's popularity is being measured
by two polling organisations. We put both sets of measurements
on the same plot by using
plot for the first set and
points for the
second. We can also use
lines to add lines joining the dots:
> y2<- c(44, 27, 14, 21, 50, 22, 11, 3)
> points(x,y2,col="red",pch=3)
> lines(x,y,col="blue")
> lines(x,y2,col="green",lty="dashed")
Note how we use the lty (line type) and col (colour) keywords to make
the second line different from the first.
This is getting to the stage where it might be tedious to re-type
everything to correct a mistake we made earlier. We can avoid this by
putting a list of R commands into a file to make a program. As an
example, use your favourite text editor
3 to create a file called dubya.R and put the
following lines in it:
# Program to plot fake poll results
x <- c(1, 2, 4, 5, 6.7, 7, 8, 10 ) ## time
y <- c(40, 30, 10, 20, 53, 20, 10, 5) ## first dataset
y2<- c(44, 27, 14, 21, 50, 22, 11, 3) ## second dataset
plot(x,y,main="Should he resign?",xlab="Time / weeks",ylab="Popularity")
points(x,y2,col="red",pch=3)
lines(x,y,col="blue")
lines(x,y2,col="green",lty="dashed")
legend(7,50,c("Gallup","Mori"),col=c("blue","green"),lty=c("solid","dashed"))
Note that the # character is used to indicate a comment - R ignores
everything on a line after the first #.
To run the program, type
> source("dubya.R")
It is conventional for the filename to end in
.R; I suggest you
stick to this convention. The file also has to be in the directory
from where you started R (or you have to give a full pathname). If you
have never used R before, why not take this program, run it, and then
make some changes to it. Read up on the `plot' function in the manual
and find out how to do things like change the axis ranges, use
logarithmic axes, and so forth. One last thing to note about running R
programs is that just giving the name of a variable does not print its
value as it does at the prompt. Instead, you need to use the
print command.
You now know how to make a line plot of some data. In most cases you
will have far too much data to want to type it in. Typically the data
will be in a file and you will want R to read it in and then make a
plot of it. As an example, we will use some numbers generated by the
MODTRAN radiative transfer package. The instructions for one of the
M.Sc practicals show you how to run MODTRAN and how to remove the
header lines from the file. This leaves you with a file containing 14
columns of numbers, like this:
14000. 0.714 7.97E-31 1.56E-26 2.10E-07 4.12E-03 4.11E-08 1.18E-07 2.32E-03 2.94E-08 3.29E-07 6.44E-03 1.64E-05 0.3950
14100. 0.709 4.95E-31 9.84E-27 2.13E-07 4.24E-03 4.15E-08 1.18E-07 2.35E-03 2.90E-08 3.31E-07 6.59E-03 4.96E-05 0.3940
14200. 0.704 3.05E-31 6.15E-27 2.11E-07 4.25E-03 4.17E-08 1.15E-07 2.32E-03 2.81E-08 3.26E-07 6.58E-03 8.22E-05 0.3887
14300. 0.699 1.84E-31 3.77E-27 1.90E-07 3.90E-03 4.06E-08 1.03E-07 2.11E-03 2.56E-08 2.93E-07 6.00E-03 1.12E-04 0.3734
14400. 0.694 1.13E-31 2.35E-27 1.87E-07 3.88E-03 4.05E-08 9.90E-08 2.05E-03 2.46E-08 2.86E-07 5.93E-03 1.40E-04 0.3664
14500. 0.690 6.53E-32 1.37E-27 1.60E-07 3.36E-03 3.74E-08 8.57E-08 1.80E-03 2.17E-08 2.46E-07 5.17E-03 1.65E-04 0.3446
.
.
.
33800. 0.296 0.00E+00 0.00E+00 2.64E-10 3.01E-05 2.62E-10 2.91E-18 3.33E-13 1.99E-20 2.64E-10 3.01E-05 3.27E-03 0.0001
33900. 0.295 0.00E+00 0.00E+00 1.68E-10 1.93E-05 1.67E-10 1.52E-19 1.75E-14 1.05E-21 1.68E-10 1.93E-05 3.27E-03 0.0000
34000. 0.294 0.00E+00 0.00E+00 1.82E-10 2.10E-05 1.80E-10 1.83E-20 2.11E-15 1.26E-22 1.82E-10 2.10E-05 3.27E-03 0.0000
The columns are 201 rows long. Let us suppose that we want to plot the
12th column (which is total radiance) against the 2nd column (which
is wavelength). Here is a short R program which will do this.
## Read in rectangular table of data
moddat <-read.table("/home/hcp/wrk/rpms/modtran/pldat.dat")
## Result is a list, with each element of the list being a column from
## the table. The first column becomes moddat$V1, the second moddat$V2 etc.
## Plot col 2 against col 12
plot(moddat$V2,moddat$V12,xlab="Wavelength / microns",
ylab="Radiance in Watts/(cm2 Steradian Micron)",type="l")
It's great to have plots on the screen, but you will often need to get
them on paper to include in reports etc. R treats the screen as one
device and a postscript file (which you can print) as another. You can
save a graph you have on the screen as a postscript file like this:
> dev.copy2eps(file="foo.eps")
The resulting file
foo.eps can be printed, viewed on screen or
included in a report. If you want R to generate a postscript file
without displaying anything on the screen, you can do it by using
postscript() before your plotting commands and
dev.off()
after them. Here is a variant on the modtran plotting program which
does exactly this:
## Read in rectangular table of data
moddat <-read.table("/home/hcp/wrk/rpms/modtran/pldat.dat")
## Result is a list, with each element of the list being a column from
## the table. The first column becomes moddat$V1, the second moddat$V2 etc.
# Start a postscript plot
postscript(file="modtran.eps",onefile = FALSE,horizontal=FALSE,
width=6,height=5)
## Plot col 2 against col 12
plot(moddat$V2,moddat$V12,xlab="Wavelength / microns",
ylab="Radiance in Watts/(cm2 Steradian Micron)",type="l")
# Make sure the postscript file is closed
dev.off()
The
postscript command has a variety of options to control the
size of the plot, the sort of paper it is to be printed on, whether it
is to be included in another document etc.
As with most languages, R has several types of variables. I list
some of them here:
| type |
range |
to define |
to convert |
|
| numeric |
numbers |
x<-1.0 |
x<-as.numeric(y) |
|
| character |
text strings |
x<-"flarp" |
x<-as.character(z) |
|
| logical |
TRUE or FALSE |
x<-TRUE |
x<-as.logical(w) |
|
Variable names can have letters, numbers and the full
stop in them, but they can NOT have underscores
4. They are are case-sensitive: foo, Foo and FOO are
all different variables. Numeric variables can be integers or floating
point, but they are usually floating point and the distiction is less
important in R than in most other languages.
R is a dynamically typed language. That means that you don't have to
define your variables or say which variable is which type at the start
of your program. You can say
gak <-37.5 at any point in
your program and a numeric variable called gak will spring
into existance and take on the value 37.5 . If you had a variable of a
different type called gak at some earlier point in your program, it
will vanish when you create the numeric variable with the
same name.
In addition to single, scalar variables, R has vectors and arrays. A vector
is a numbered group of variables, all of the same type. We used
vectors in the first lecture to hold the data for line plots. You can
define a vector by using the function
c()
> a.vector <- c(3, 5, 6, 2.5, 100, 27.7)
You can refer to individual elements of the vector like this:
> a.vector[1]
[1] 3
> a.vector[3]
[1] 6
Note that the first element of the array is numbered 1 as in Fortran (not 0
as in `C', Java and python). Note also that you must use
[] for
indexing arrays. You can refer to a subset of the vector like this:
> a.vector[2:4]
[1] 5.0 6.0 2.5
R allows you to arrange your data into a 2-dimensional array (a
matrix) or indeed an array with any number of dimensions. An array in
R is a vector with a set of dimensions attached. We can make a copy of
our vector and convert it into an array, like this:
> a.matrix<-a.vector
> dim(a.matrix)<-c(2,3)
> a.matrix
[,1] [,2] [,3]
[1,] 3 6.0 100.0
[2,] 5 2.5 27.7
... and refer to parts of it like this:
> a.matrix[1,2]
[1] 6
> a.matrix[1,]
[1] 3 6 100
> a.matrix[,2]
[1] 6.0 2.5
> a.matrix[1,2:3]
[1] 6 100
Note how an omitted index is used to represent an entire column or row of
the array and how two integers and a colon are used to select part of
a row or column.
Finally, you can set up an array to use later like this:
> foo<-array(3,c(10,10,10))
will make foo a 10 by 10 by 10 element numeric array with all
elements initialised to 3.0. For 2-dimensional arrays you may find the
matrix command is more intuitive.
One of the most powerful features of R is that you can do mathematical
operations on entire vectors and arrays.
> x<-matrix(c(2,4,6,8),nrow=2)
> x+10
[,1] [,2]
[1,] 12 16
[2,] 14 18
> x*x
[,1] [,2]
[1,] 4 36
[2,] 16 64
> log10(x)
[,1] [,2]
[1,] 0.30103 0.7781513
[2,] 0.60206 0.9030900
Note how we can take
x and add either a scalar (which is added
to each element) or another array (which is added
element-by-element). The
* sign multiplies
element-by-element. To do a matrix multiplication, you need the
special operator
%*%:
> x %*% x
[,1] [,2]
[1,] 28 60
[2,] 40 88
R is a very convenient environment for working with matrices.
- A matrix is displayed the way round you expect
- The indices are the same way round as in mathematical texts
- There are built-in functions to find the inverses, determinants
and eigenvectors, to solve sets of simultaneous equations and so on
For some purposes, arrays are not flexible enough. One might want a
variable to contain elements of different types. If, for example, you
wanted to keep information about a person in one variable, you might
want to record his or her name (a string), age and height (numeric)
and whether they are a student or not (logical). You can set up such
variables, called lists, like this:
> elvis<-list(name="Elvis Aaron Presley",age=64,height=1.7,is.student=FALSE)
> fred<-list(name="Fred Smith",age=21,height=1.8,is.student=TRUE)
You can then access the different elements of the lists like this:
> elvis$name
[1] "Elvis Aaron Presley"
> fred$age
[1] 21
Lists can contain other lists and arrays as elements, too. You can
also refer to list elements by number:
> elvis[[1]]
[1] "Elvis Aaron Presley"
> elvis[[3]]
[1] 1.7
When we read data in with
read.table() the result is essentially a list.
You will notice that when you type
q() to leave R, it asks you
whether you want to
Save workspace image? [y/n/c]: . If you say
y then R will create a files called .RData and .Rhistory, which
contain all of your variables, and a history of the commands you
typed. These will be loaded next time you start R. You can safely
delete either one, or both, if you do not want them.
And that's it for the first session. You can now make most of the 2-D
graphs that you will need. In the next session we'll look at some more
sophisticated programming techniques.
- File /home/hcp/wrk/rpms/week1data.txt contains three columns of
data. The columns are labelled. Read the data in and make a graph of
voltage and and pressure as a function of time. Use red squares for
voltage and blue triangles for pressure, and provide a legend. Make
the title of the graph include your name.
- Take the fast discrete Fourier transforms (FFT) of the voltage
and pressure from the above question and plot both real and imaginary
parts against frequency. Note that the spacing between points in
frequency space is
where 
is the difference
between the first and last time in the above question. Use red lines
for the FFT of voltage and blue lines for the FFT of pressure. Use
solid lines for the real parts and dashed lines for the imaginary
parts.
- Find the solution to this set of simultaneous equations
- Find the eigenvalues and eigenvectors of this matrix:
Your answers to these problems should be handed in for assessment.
Please hand in the code you wrote, together with graphical output (for
Q1 and Q2) and your answers (for the other questions). Remember:
The on-line help is your friend.
Subsections
This lecture covers the nuts and bolts of R programming. There won't
be much graphics but we will look at many things which will help you
to make good use of R. This is the bit of the course where I assume
that you can program in a computer language already. If you don't
like the way I present the material, type
help.start() at the R
prompt and hit the link ``An introduction to R''.
R has most of the constructs that you would expect for arranging
loops, conditions and the like.
This is used when you want to do something if a condition is true and
something else otherwise. The statement looks like this:
if ( condition ) statement 1 else statement 2
This will execute statement 1 if the condition is true and statement 2
if the condition is false. (Note that in these descriptions of what a
statement does I use
typewriter font to show what you actually
type and
italics to indicate where you have to put in your own
stuff.)
Here is an example if an `if' statement:
if (x < 3) print("x less than 3") else print ("x not less than 3")
Notice how the logical operators you need to set up the condition look
like the ones in C (and many other languages). Here is a table of
relational and boolean operators which you can use in the condition of
an if statement.
| Purpose |
R |
C |
FORTRAN |
| Relational Operators |
|
|
|
| Equal to |
== |
== |
.EQ. |
| Not equal to |
!= |
!= |
.NE. |
| Less than or equal to |
 = |
= |
.LE. |
| Less than |
|
|
.LT. |
| Greater than or equal to |
 = |
= |
.GE. |
| Greater than |
|
|
.GT. |
| Boolean Operators |
|
|
|
| And |
&& |
&& |
.AND. |
| Not |
! |
! |
.NOT. |
| Or |
|| |
|| |
.OR. |
If you want statement 1 and / or statement 2 to consist of more than
one statement, then the if construct looks like this:
if (condition) {
statement 1a
statement 1b
statement 1c
} else {
statement 2a
statement 2b
statement 2c
}
The group of statements between a
{ and a
} are
treated as one statement by the
if and
else.
If you have a statement or statements that you want to repeat a number
of times, you can use the
for statement to do so. The
for statement loops over all elements in a list or vector:
for (variable in sequence) statement.1
Try these examples at the R prompt.
> for (i in 1:3) print(i)
> fnord <- list("Cheese",TRUE,27.5)
> for (i in fnord) print(i)
Note the colon (
:) operator generates a sequence of
integers. You can use this in places other than the for loop or array
indexing, too. Also note that
statement.1 can be a group of
statements inside braces, just as with
if and
else.
If you need a loop for which you don't know in advance how many
iterations there will be, you can use the `while' statement. It works
like this:
while(condition) statement
Again, if you are using this in a program you can replace
statement with a group of statements in braces. You can construct
condition in the same way as for an if statement.
R has two statements
break and
next: these
discontinue normal execution in the middle of a
while or
for loop. The
next statement causes the next pass through the
loop to begin at once, while
break causes a jump to the
statement immediately after the end of the loop.
We found out in the first lecture that R allows you to do many
operations on whole arrays. Suppose, for example, you wanted to make
an array whose elements were the squares of the elements in another
array. You could use a for loop, like this:
n<-length(x)
xsquared <- array(0,n)
for ( i in 1:n) xsquared[i]<-x[i]*x[i]
This is how you would
have to go about it in C or Fortran 77.
In R, however, you can do this:
xsquared <- x*x
This will clearly make your code shorter and clearer but it will also
make it
much faster. This is true for matrix multiplication, too.
Our examples so far have been too short to break up into
sub-programs. However, any sizeable R project will be easier to deal
with if each specific task is put into its own sub-program or
function5, which your main program can call.
Here is an example of a function. This calculates
. For
this can be calculated directly using R's built-in function
sin(), but for values near 0, we would be calculating
, or
something very close to it, so we use the power series:
Note the use of
if,
for and
break.
sinc <- function(x){
if (abs(x) > 1) {
## x not near 0: calculate in the obvious way.
s <- sin(x)/x
}else{
## x too close to 0 for sin(x) / x to work. Use power series instead.
s <- 1
term <- 1
for( j in seq(3,100,by=2) ){
term <- term*(-x*x)/(j*(j-1))
s <- s+term
if(abs(term) < 1.e-10) break
}
}
## Value returned is value of last expression: s in this case
s
}
To use this, put the text into a file and
source it. Nothing
appears to happen, but your function has been added to the large set
already available to you, so you can now type:
> sinc(0.01)
then the value of
will be printed out.
To summarise, we have learned about R's programming features and
that we should use array operations instead of loops where that is
possible. In the next lecture we will learn how to display
two-dimensional data sets and how to make use of colour in R.
Please indent your code tidily: it makes it much easier for me to
understand what it does. And please put the
} at the end of a
block on a line by itelf.
- Write a program to calculate all the prime numbers between 3 and
500. You can use any algorithm you like. You will need to know that
the operator
%% is used to give the remainder from an integer
division. Ensure that the program is all in one file, so that you
can type
source("myprimesprogram.R")
to make it do the
calculations. If 
is the 
-th prime number, make a plot of
as a function of .
- Write a function which takes a vector x as its only
argument and returns a list containing the mean and standard deviation
of the values in x. Your function should do all the calculation
itself, using loops and standard arithmetic operators. It should not
use any of R's built-in functions. (As an exception, you can use length(x) to get the number of elements in x.) I have made a
file containing 1000 random numbers, which you can read into R like
this:
x<-scan("/home/hcp/wrk/rpms/randomdata1.txt")
Use your
function to calculate the mean and standard deviation of these
numbers. Compare your results with those returned by R's built-in
functions mean and sd. (Do remember to hand in the results
as well as your program.) For those of you not doing Inverse Theory,
for a list of 
numbers 
, the mean 
is given by
and the variance by
The standard deviation is
the square root of the variance.
Subsections
In this lecture we will learn how to display data that are a function
of two variables. An example would be the height of the ground above
sea level as a function of distance East and distance North. We'll
also look at a few of R's more esoteric graphics features. There are
no figures in these notes - if you want to see what the plots look
like, start R up and run the examples. We will construct an example
data set using this short program:
## Set up vectors of x and y values
x <- seq(-2,2,by=0.05)
y <- seq(-2,2,by=0.1)
## Define a function of x and y
myfn <- function(x,y){exp(-(x^2 +y^2)) + 0.6*exp( -((x+1.8)^2 + y^2)) }
## use outer() to apply that function to all our x and y values
z <- outer(x,y,myfn)
If you type this program into a file called setup2d.R ( or, if
you are looking at the HTML version of these notes with a web browser, cut
and paste it) and then type:
> source("setup2d.R")
you will be left with two vectors called x and y and a 2-d array
called z. You can imagine that x is distance East, y is distance North
and z is height above sea level. We will investigate several ways of
displaying these data.
Perhaps the most immediate way of displaying a data set like our
example is as a surface plot. Type
> persp(x,y,z,theta=-40,phi=30)
You can get more informative axis labels like this:
> persp(x,y,z,theta=-40,phi=30,xlab="East",ylab="North",zlab="Height",ticktype="detailed")
Like many R functions, persp has lots of keywords to enable you
to tweak the plot to look how you want it to look. Note particularly
the theta and phi keywords, which let you look at the plot from different
angles. Try these examples:
> persp(x,y,z,theta=40,phi=60)
> persp(x,y,z,theta=10,phi=10)
An alternative to the wire frame is a shaded surface, which you can
get with the
shade keyword:
> persp(x,y,z,theta=-70,phi=50,shade=0.7)
If you don't want the grid lines, you can remove them:
> persp(x,y,z,theta=-70,phi=50,shade=0.7,border=NA)
It is less visually striking, but sometimes more useful, to display
2-d data as a contour plot. For a basic contour plot, do:
> contour(x,y,z)
It's a start, but we might not like the contour levels chosen. We can
specify them by hand:
> contour(x,y,z,lev=seq(0,1,by=0.05))
Note that
seq(0,1,by=0.05) returns a vector with the elements set
to
. You can use any vector as long
as the values increase monotonically.
Plain contours are not very striking - it looks more eye-catching if we
fill the spaces between the contours with colours, like this:
> filled.contour(x,y,z)
That makes the general form of the data clearer as you can see
immediately where the highs and lows are. Those colours are a bit
nasty, though. There are better choices available:
> filled.contour(x,y,z,color.palette=terrain.colors)
If you want to see your array without it being contoured, try this:
image(x,y,z)
The
image function doesn't provide a scale bar. But you can
overlay some contours:
> contour(x,y,z,add=TRUE)
We have already seen that colours in R can be specified by name, and
also that some functions make use of some of R's built-in colour
schemes. Individual colours can also be specified by giving the
brightness of red, green and blue on a scale from 0 to 255. These are
given as a # symbol and a string of 6 hexadecimal digits, so that
#ff0000 is red,
#00ff00 is green,
#ffff00 is
yellow,
#0000ff is blue and so on. You can convert these rgb
strings into numbers with
col2rgb and generate them with
rgb. Try these examples:
> col2rgb("orange")
> col2rgb("#ffff00")
> rgb(1,0.5,0)
If you don't like R's built-in colorscales, you can use
colorRampPalette to make your own:
> filled.contour(x,y,z,color.palette=colorRampPalette(c("black","green","white")))
R does not have a built-in capacity to put data on a map of the
world. Like many of R's non-core features, mapping is provided by
external packages
6 To
use this, start R and type
> library(maps)
> library(mapproj)
Nothing will appear to happen
7 Try out these examples:
> map()
> map(proj="mercator",xlim=c(-178,178),ylim=c(-70,70)
> map(proj="aitoff",xlim=c(-178,178))
> map.grid()
> map(proj="orthographic",orientation=c(55,0,0))
> map.grid()
To get rid of the white space around the map, you may want to do
> par(mai=c(0,0,0,0))
before making the plots: this sets all the margins to 0 inches. To add
data to your map, you need to convert its latitude and longitude to
the projected map co-ordinates:
longs<-c(0, -3.1, 2.4, -3, -77)
lats<-c(51.5, 55.9, 48.8, 17, 38.8)
labs<-c("London","Edinburgh","Paris","Timbuktu","Washington")
points(mapproject(longs,lats),col="red",pch=19)
text(mapproject(longs,lats),labs,col="red",adj=-0.1)
Note that
mapproject converts your lat and long to the correct x and y
co-ordinates for the last map you drew. Also, don't forget that the
on-line documentation works for add-on packages like those used for
mapping, so you can find out more by typing
> help(map)
To most computer systems a grayscale image is just a 2-D data set such
as we looked at earlier. The differences between images and other data
sets are simply that:
- Images are (usually) bigger, perhaps several hundred data points
in each direction.
- Images are (usually) of type byte. This means that each pixel
can have only 256 values. Remote-sensed images may have more bits per
pixel than this, though.
...and that's all. You can display and process greyscale images just like
any other 2-dimensional array. You will find that contour or surface plots of
an image of any size are not very useful and take a very long time to draw. In
this section we look at ways of reading, displaying and processing images in
R. As with maps, R's image-handling capabilities are provided by
add-on packages, so you need to type
> library(pixmap)
> library(imageio)
The pixmap package provides a way to read in the portable pixmap image
format, while the imageio package adds on the ability to read many
other image formats
8.
An image can be read in like this
9:
> im<-read.image("/home/hcp/wrk/rpms/light-g.png",fformat="png")
Here, im is not a simple 2-D array, but is a more complex object,
containing information about the image, whether it is greyscale or
colour, what size it is, and so forth. This means that you can
display the image like this:
plot(im)
...but if you want to get the data out and process them, you need
to do this:
imdat<-getChannels(im)
The array imdat is now a perfectly ordinary 2-d array: you can try
drawing a contour plot of it if you like. You will notice that if you
try to plot it using
image or
contour that the axes are
reversed. This is a consequence of the order in which the data are
traditionally arranged in image files. You may also notice that the
data lie in the range between 0 and 1: the pixmap package always
scales images so that 0 means dark and 1 means bright.
We can do some mathematical
operations on the image, plot the result and write the result to a
file, like this:
> d<-dim(imdat)
> newdat<-1-imdat + imdat[,d[2]:1]
> newim<-pixmapGrey(newdat)
> plot(newim)
> write.image(newim,file="newim.png",fformat="png")
What is the result? Was it what you expected? Note that when you
convert your data to a pixmap object with
pixmapGrey the data
are automatically scaled to the range
. Also note that R's
image plotting is rather slow for large images. In many cases it is
more convenient to write the image out with
write.image and view
it with a separate image viewing program such as
gthumb, or the GNOME
image viewer
eog.
Some additional image-processing tools are provided in the rimage
package. Rather annoyingly, this uses its own sort of image object, (
an
imagematrix) which is slightly different from the one used by
pixmap and imageio. An
imagematrix object can be regarded as an
ordinary matrix for many purposes. Like pixmap, rimage scales its data
to lie between 0 and 1. Try these examples: they demonstrate several
of the functions provided by the rimage package.
> library(rimage)
> flarp<-sobel(imdat)
> plot(normalize(flarp))
> flarp<-laplacian(imdat)
> plot(normalize(flarp))
> flarp<-clipping(imdat,low=0.45,high=0.55)
> plot(pixmapGrey(normalize(flarp)))
> flarp<-equalize(imdat)
> plot(normalize(flarp))
> flarp<-fftImg(imdat)
> plot(normalize(flarp))
Note in particular the function
fftimg() which calculates the
Fourier transform of the image.
A colour image is really three images, a red one, a green one and a
blue one. If you want to do image processing things to a colour image,
smoothing for example, then you have to apply your algorithm to the
three colours separately. In R, you can read a colour image like this:
> imc<-read.image("/home/hcp/wrk/rpms/light.tif")
As before, imc is a special pixmap object: you need to use
getChannels
to extract the data from it. What you get, for an image of size
is an array of dimensions
. Try this
example, which swaps around the red, green and blue planes of the image.
imcdat<-getChannels(imc)
newdat<-array(0,dim(imcdat))
newdat[,,1]<-imcdat[,,2]
newdat[,,2]<-imcdat[,,3]
newdat[,,3]<-imcdat[,,1]
newim<-pixmapRGB(newdat)
plot(newim)
Subsections
There is only so much that can be fitted into the assessed part of the
course. In an attempt to make these notes a more useful reference, I
am collecting here various things which have proved useful in the past
to me or to others.
To get encapsulated postscript output for including in a MicroSoft
Word, OpenOffice Writer or L
AT
EX document:
postscript(file="myplot.eps",width=6,height=5,paper="special",onefile=FALSE,
family="Times",horizontal=FALSE,pointsize=14)
myplot() ## Replace this with all your plotting commands
dev.off()
You can tinker with the width, height and pointsize arguments to get
the plot to look right. The
family="Times" bit will make the
axis labels come out in a serif font, which will probably match the
one in the body of your document. The
paper="special" bit is
necessary to prevent R worrying about whether your width and height
values are too big for your paper.
If you have an application that can import PDF figures, you might want
to generate these with R. (The only such application that I have used
is
pdflatex.) The procedure is almost identical to that for postscript
files:
pdf(file="myplot.pdf",width=6,height=5,paper="special",onefile=FALSE,
family="Times",horizontal=FALSE,pointsize=14)
myplot() ## Replace this with all your plotting commands
dev.off()
If you want to be able to annotate your figure by hand after you have
made it, you need to be able to import it into a vector drawing
program. An old-fashioned (but widely available) program of this type
is
xfig. You can get R to produce figures in xfig's native
format like this:
xfig(file="myplot.fig",width=6,height=5,onefile=TRUE,
family="Times",horizontal=FALSE,pointsize=14)
myplot() ## Replace this with all your plotting commands
dev.off()
Xfig can export your figure in a variety of formats that R cannot
generate, such as enhanced metafile (
.emf) and scalable vector
graphics
10 (
.svg). If you really need such a format and do not want to annotate
your figure, you can use the
fig2dev command to convert xfig
output without having to start xfig:
bash$ fig2dev -L emf myplot.fig myplot.emf
bash$ fig2dev -L svg myplot.fig myplot.svg
If you want your figure as a bitmapped image, R can do this for
you. Typically you would do this to include the plot in a web page or
a presentation slide.
png(file="myplot.png",width=600,height=500,pointsize=14)
myplot()## Replace this with all your plotting commands
dev.off()
jpeg(file="myplot.jpg",width=600,height=500,pointsize=14,quality=95)
myplot()## Replace this with all your plotting commands
dev.off()
For most sorts of R plot, png is a more suitable choice than
jpeg. Note that the size is given in pixels. If you find that you need
to stretch or shrink the image once you get it into another
application, you will probably want to re-run your R program with
different width and height settings, to re-generate the image at the
right size.
R can put plain text on a plot in a number of ways. You can use the
xlab,
ylab, and
main keywords to
plot, and you
can also use the
text function to put text in an arbitrary
position. If you want mathematical formulae in any of these places,
you can use the
expression function instead of a text string.
For example, instead of
"x squared" you can use
expression(x^2) and get
. To get the online docs for this
feature, type
help(plotmath) and for a demo of the
possibilities try
demo(plotmath) One thing which may not be
obvious is how to mix text and mathematics. The answer seems to be
expression(paste("The area,",x^2,",is too large"))
Suppose you have two sets of values which are both
functions of the same variable, but have different units and wildly
different values. Maybe you measured Ozone (in parts per million) and
Temperature (in K) at the same point in the atmosphere at 12:00 every
day for a year. How can you get the two sets of data onto the same
graph, with a different axis for each? The hidden magic is to use
par(new=TRUE) to prevent the second plot erasing the first one,
and to do the axes for the second plot by hand. Here is a complete example:
### Generate the data to plot
tm<-seq(0,4*pi,by=pi/20) ## The times
x1<-cos(tm) ## the first data set
x2<-117*exp(-0.1*tm)*sin(tm) + 33 ## the second data set
### ... and plot them
plot(tm,x1,type="l",frame.plot=FALSE) ### the first dataset
par(new=TRUE) ### The magic to stop the second plot erasing the first
plot(tm,x2,type="l",frame.plot=FALSE,axes=FALSE,col="red") ## the second
axis(side=4,col="red") ### The axis for the second dataset
Often, one has a set of points in which each point has cartesian
co-ordinates
and a value
to be plotted. Perhaps the
simplest way to display the data is to put a point at each
position whose colour represents the
value. Here is a full example
that generates a dataset, plots it, and adds a colour bar:
## Generate a test set of data
npts <- 1000
x <- runif(npts,min=0,max=10)
y <- runif(npts,min=0,max=10)
z <- sin(x)*cos(y) + rnorm(npts,mean=0,sd=0.01)
## Choose the z-values at which the colour will change
levs <- pretty(z,n=20)
## Work out which colour level each point is at
nl <- length(levs)
icols <- as.integer(1 + (nl-1) * (z-levs[1])/(levs[nl]-levs[1]))
mypalette <- rainbow(nl-1)
palette(mypalette)
## Divide up the plot so we can have a colour bar
m <- matrix(c(1,2),nrow=1,ncol=2)
layout(m,widths=c(1,0.25))
## Plot the data
plot(x,y,pch=19,col=icols)
## Make the colour bar
plot(c(0,1),c(0,1),type="n",xlim = c(0, 1), ylim = range(levs), xaxt = "n",
yaxs = "i",xlab="",ylab="",axes={axis(2)})
rect(0, levs[-nl], 1, levs[-1], col = mypalette)
R runs well on all modern flavours of Unix, where it is essentially
identical to R on Linux. It also runs on MacOSX and Windows. I can't
offer much information about the MacOSX port as I don't have a
Mac.
11 On the other hand, I have access to plenty of
University managed-desktop machines on which R is installed. Most of
the experience on which these notes are based was gained on the
managed desktop, although I do have R installed on a Windows XP
machine at home. Most aspects of R are the same on Windows as on other
platforms. In this section I not a few of the important differences.
On Linux, most users run R in a terminal window (although there is at
least one GUI in development.) On Windows, R is usually started from
the start menu, presenting the user with a GUI. The GUI takes up the
whole screen by default. An R command line and any graphics windows
that you start live inside this big R window. If you don't like this
MDI interface, you can switch to an SDI one where the R windows live
directly on your desktop. The button to do this is under
Edit --> GUI Preferences.
One of the initially puzzling things about R on Windows is that the
working folder used when R starts up may not be your home
directory. Instead, it may turn out to be the system directory into
which R was installed and for which you probably do not have write
permission. You can find out what the current working directory is by
typing
getwd() and set it to be a directory of your choice by
doing
setwd("my/working/folder"). For example, you can set
the working directory to be your home directory like this:
setwd{"M:/"}. Note that you will want to use forward slashes
to separate folders, even though this is Windows.
One of the menu items under
Help is the R FAQ for Windows. This
covers many of the obscure issues to do with using R on Windows -- it
should be the first thing you turn to if you have any Windows-specific
R problems.
![\begin{displaymath}\left[ \begin{array}{ccc} 2 & 1 & 0 1 & 3 & 1 0 & 1 & 2
\end{array} \right] \end{displaymath}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tTs_Iw_bZDpNfvwRWXPC4-wHpUuTvf2uRY-EP7YRXrxUdy_RidYUebWYb_YTKfI0PhuwSaCnOHjb_llbXxxNSJObAlUmAOVwAqTEz606aG6Bgr1HXr=s0-d)
. How many maxima and minima does the function have
in this range?
S and 30