This document is a /brief/ introduction to =julia=. It is based on a /Brief Introduction to R/ (an abbreviated Chapter 2 of [[http:ipsur.org][IPSUR]]) which I usually distribute to students using R for the first time. One of the reasons for this document is that I wanted to get better acquainted with =julia= and make it easier for others to get better acquainted, too.
This document is a /brief/ introduction to =julia=. It is based on a
/Brief Introduction to R/ (an abbreviated Chapter 2 of [[http:ipsur.org][IPSUR]]) which I
usually distribute to students using R for the first time. One of the
reasons for this document is that I wanted to get better acquainted
with =julia= and make it easier for others to get better acquainted,
too.
* What you need to get started
* What you need to get started
This document assumes you have at least a passing familiarity with Org-mode and Emacs keybindings.
This document assumes you have at least a passing familiarity with
- Note: :: a lot of the code blocks below have the header argument =:eval no-export= which means that the code block can be evaluated interactively in this session by =C-c C-c= with point in the code block but will /not/ be evaluated during export. The reason is that those blocks have settings which conflict with my current setup but would be useful for others going through this document.
- *Note:* a lot of the code blocks below have the header argument
=:eval no-export= which means that the code block can be evaluated
interactively in this session by =C-c C-c= with point in the code
block but will /not/ be evaluated during export. The reason is that
those blocks have settings which conflict with my current setup but
would be useful for others going through this document.
** Julia
** Julia
- First install takes the longest, later updates not so bad.
- First install takes the longest, later updates not so bad.
...
@@ -41,13 +52,16 @@ Pkg.add("RDatasets")
...
@@ -41,13 +52,16 @@ Pkg.add("RDatasets")
*** Winston
*** Winston
The most stable and fully featured of the =julia= graphics packages at the time of this writing appears to be the =Winston= package, though the =Gadfly= package is available and looks promising.
The most stable and fully featured of the =julia= graphics packages at
the time of this writing appears to be the =Winston= package, though
the =Gadfly= package is available and looks promising.
#+BEGIN_SRC julia :eval never
#+BEGIN_SRC julia :eval never
Pkg.add("Winston")
Pkg.add("Winston")
#+END_SRC
#+END_SRC
The Winston package has lots of dependencies and many of them must be built from source (on Ubuntu).
The Winston package has lots of dependencies and many of them must be
built from source (on Ubuntu).
*** Gadfly
*** Gadfly
...
@@ -59,7 +73,9 @@ Pkg.add("Gadfly")
...
@@ -59,7 +73,9 @@ Pkg.add("Gadfly")
** Org-mode
** Org-mode
This document assumes that you have at least a passing familiarity with org-mode such that you likely have something like the following already in your =.emacs=:
This document assumes that you have at least a passing familiarity
with org-mode such that you likely have something like the following
already in your =.emacs=:
#+BEGIN_SRC emacs-lisp :eval never
#+BEGIN_SRC emacs-lisp :eval never
(require 'org)
(require 'org)
...
@@ -71,14 +87,19 @@ Another handy setting to have is
...
@@ -71,14 +87,19 @@ Another handy setting to have is
(setq org-confirm-babel-evaluate nil)
(setq org-confirm-babel-evaluate nil)
#+END_SRC
#+END_SRC
In order to run this org file you will need to load =ob-julia.el= at some point. One way is to edit the following code block and then =C-c C-c= with point inside the block:
In order to run this org file you will need to load =ob-julia.el= at
some point. One way is to edit the following code block and then =C-c
The first command loads the =ob-julia.el= file and the second initiates a =julia= session in a buffer called =*julia*=. An alternative method is to put the following in your =.emacs= (these should go below the =(require 'org)= line):
The first command loads the =ob-julia.el= file and the second
initiates a =julia= session in a buffer called =*julia*=. An
alternative method is to put the following in your =.emacs= (these
should go below the =(require 'org)= line):
#+BEGIN_SRC emacs-lisp :eval no-export
#+BEGIN_SRC emacs-lisp :eval no-export
(add-to-list 'load-path "/path/to/ob-julia.el")
(add-to-list 'load-path "/path/to/ob-julia.el")
...
@@ -88,14 +109,15 @@ The first command loads the =ob-julia.el= file and the second initiates a =julia
...
@@ -88,14 +109,15 @@ The first command loads the =ob-julia.el= file and the second initiates a =julia
(julia . t)))
(julia . t)))
#+END_SRC
#+END_SRC
The following lines (either here or in your =.emacs=) allow for inline image display in the Emacs buffer.
The following lines (either here or in your =.emacs=) allow for inline
If you'd like to do LaTeX export then put the following in your emacs.
If you'd like to do LaTeX export then put the following in your =.emacs=.
#+BEGIN_SRC emacs-lisp :eval never
#+BEGIN_SRC emacs-lisp :eval never
(require 'ox-latex)
(require 'ox-latex)
...
@@ -121,42 +143,41 @@ The place to get the latest version of ESS is [[http://stat.ethz.ch/ESS/index.ph
...
@@ -121,42 +143,41 @@ The place to get the latest version of ESS is [[http://stat.ethz.ch/ESS/index.ph
There are three basic methods for communicating with julia.
There are three basic methods for communicating with julia.
- An Interactive session (julia>). :: This is the most basic way to
- *An Interactive session (julia>).* This is the most basic way to
complete simple, one-line commands. Do =M-x julia RET= during an
complete simple, one-line commands. Do =M-x julia RET= during an
Emacs session and the Emacs/ESS =julia= mode will open in a buffer.
Emacs session and the Emacs/ESS =julia= mode will open in a buffer.
Type whatever command you like; =julia= will evaluate what is typed
Type whatever command you like; =julia= will evaluate what is typed
there and output the results in the buffer.
there and output the results in the buffer.
- Source files. :: For longer programs (called /scripts/) there is too
- *Source files.* For longer programs (called /scripts/) there is too
much code to write all at once in an interactive
much code to write all at once in an interactive session. Also,
session. Also, sometimes we only wish to modify a
sometimes we only wish to modify a small piece of the script and run
small piece of the script and run it again in
it again in =julia=.
=julia=.
The way to do this is to open a dedicated =julia= script buffer with
The way to do this is to open a dedicated =julia= script buffer with
the sequence =C-x C-f whatever.jl=, where
the sequence =C-x C-f whatever.jl=, where =whatever.jl= is a =julia=
=whatever.jl= is a =julia= script which you've named
script which you've named whatever. Write the code in the buffer,
whatever. Write the code in the buffer, then when
then when satisfied the user evaluates lines or regions according to
satisfied the user evaluates lines or regions
the following table. Then =julia= will evaluate the respective code
according to the following table. Then =julia= will
and give output in the interactive buffer.
evaluate the respective code and give output in the
interactive buffer.
| =C-RET= | Send region or current line and step to next line of code. |
| =C-RET= | Send region or current line and step to next line of code. |
| =M-C-x= | Send region or function or paragraph. |
| =M-C-x= | Send region or function or paragraph. |
| =C-c C-c= | Send region or function or paragraph and step to next line. |
| =C-c C-c= | Send region or function or paragraph and step to next line. |
- Script mode. ::
- *Script mode.* Hello there.
** =julia= is one fancy calculator
** =julia= is one fancy calculator
=julia= can do any arithmetic you can imagine. For example, in an interactive session type =2 + 3= and observe
=julia= can do any arithmetic you can imagine. For example, in an
interactive session type =2 + 3= and observe
#+BEGIN_SRC julia
#+BEGIN_SRC julia
2 + 3
2 + 3
#+END_SRC
#+END_SRC
The =julia>= means that =julia= is waiting on your next command. Entry numbers will be generated for each row, such as
The =julia>= means that =julia= is waiting on your next command. Entry
numbers will be generated for each row, such as
#+BEGIN_SRC julia
#+BEGIN_SRC julia
[3:50]
[3:50]
...
@@ -188,7 +209,10 @@ The =julia>= means that =julia= is waiting on your next command. Entry numbers w
...
@@ -188,7 +209,10 @@ The =julia>= means that =julia= is waiting on your next command. Entry numbers w
50
50
#+end_example
#+end_example
Notice that =julia= doesn't show the whole list of numbers, it elides them with vertical ellipses \(\vdots\). Note also the =[3:50]= notation, which generates all integers in sequence from 3 to 50. One can also do things like
Notice that =julia= doesn't show the whole list of numbers, it elides
them with vertical ellipses \(\vdots\). Note also the =[3:50]=
notation, which generates all integers in sequence from 3 to 50. One
can also do things like
#+BEGIN_SRC julia :eval no-export
#+BEGIN_SRC julia :eval no-export
2 * 3 * 4 * 5 # multiply
2 * 3 * 4 * 5 # multiply
...
@@ -204,20 +228,36 @@ sqrt(-2)
...
@@ -204,20 +228,36 @@ sqrt(-2)
: ERROR: DomainError()
: ERROR: DomainError()
: in sqrt at math.jl:111
: in sqrt at math.jl:111
Notice that a =DomainError()= was produced; we are not allowed to take square roots of negative numbers. Also notice the number sign =#=, which is used for comments. Everything typed on the same line after the =#= will be ignored by julia. There is no =julia= continuation prompt. If you press =RET= before a statement is complete then empty lines keep piling up until you finish the command.
Notice that a =DomainError()= was produced; we are not allowed to take
square roots of negative numbers. Also notice the number sign =#=,
which is used for comments. Everything typed on the same line after
the =#= will be ignored by julia. There is no =julia= continuation
prompt. If you press =RET= before a statement is complete then empty
lines keep piling up until you finish the command.
Some other fuctions that will be of use are =abs()= for absolute value, =log()= for the natural logarithm, =exp()= for the exponential function, and =factorial()= for... uh... factorials.
Some other fuctions that will be of use are =abs()= for absolute
value, =log()= for the natural logarithm, =exp()= for the exponential
function, and =factorial()= for... uh... factorials.
Assignment is useful for storing values to be used later. Notice the semicolon at the end of the first statement. Without the semicolon, =julia= would print the result of the assigment (namely, =5=).
Assignment is useful for storing values to be used later. Notice the
semicolon at the end of the first statement. Without the semicolon,
=julia= would print the result of the assigment (namely, =5=).
#+BEGIN_SRC julia
#+BEGIN_SRC julia
y = 5; # stores the value 5 in y
y = 5; # stores the value 5 in y
3 + y
3 + y
#+END_SRC
#+END_SRC
There aren't other assignment operators (like =<-= in R). For variable names you can use letters. (possibly followed by) numbers, and/or underscore "_" characters. You cannot use mathematical operators, you cannot use dots, and numbers can't go in front of numbers (those are interpreted by =julia= as coefficients). Examples: =x=, =x1=, =y32=, =z_var=.
There aren't other assignment operators (like =<-= in R). For
variable names you can use letters. (possibly followed by) numbers,
and/or underscore "_" characters. You cannot use mathematical
operators, you cannot use dots, and numbers can't go in front of
numbers (those are interpreted by =julia= as coefficients). Examples:
=x=, =x1=, =y32=, =z_var=.
If you would like to enter the data 74,31,95,61,76,34,23,54,96 into julia, you may create a data array with double brackets (the analogue of the =c()= function in R).
If you would like to enter the data 74,31,95,61,76,34,23,54,96 into
julia, you may create a data array with double brackets (the analogue
The array =fred= has 9 entries. We can access individual components with bracket =[ ]= notation:
The array =fred= has 9 entries. We can access individual components
with bracket =[ ]= notation:
#+BEGIN_SRC julia
#+BEGIN_SRC julia
fred[3]
fred[3]
...
@@ -259,9 +300,16 @@ fred[[1, 3, 5, 8]]
...
@@ -259,9 +300,16 @@ fred[[1, 3, 5, 8]]
54
54
#+end_example
#+end_example
Notice we needed double brackets for the third example. If you would like to empty the array =fred=, you can do it by typing =fred = []=.
Notice we needed double brackets for the third example. If you would
like to empty the array =fred=, you can do it by typing =fred = []=.
Data arrays in =julia= have type. There are all sorts of integer types (=Int8=, =uInt8=, =Int32=, ...), strings (=ASCIIString=), logical (=Bool=), unicode characters (=Char=), then there are floating-point types (=Float16=, =Float32=), even complex numbers like =1 + 2im= and even rational numbers like =3//4=, not to mention =Inf=, =-Inf=, and =NaN= (which stands for /not a number/). If you ever want to know what it is you're dealing with you can find out with the =typeof= function.
Data arrays in =julia= have type. There are all sorts of integer types
Notice the ~>=~ symbol which stands for "greater than or equal to". Many functions in =julia= are vectorized. Once we have stored a data vector then we can evaluate functions on it.
Notice the ~>=~ symbol which stands for "greater than or equal to".
Many functions in =julia= are vectorized. Once we have stored a data
vector then we can evaluate functions on it.
#+BEGIN_SRC julia
#+BEGIN_SRC julia
sum(fred)
sum(fred)
...
@@ -303,9 +353,11 @@ mean(fred) # sample mean, should be same answer
...
@@ -303,9 +353,11 @@ mean(fred) # sample mean, should be same answer
: 60.44444444444444
: 60.44444444444444
: 60.44444444444444
: 60.44444444444444
Other popular functions for vectors are =min()=, =max()=, =sort()=, and =cumsum()=.
Other popular functions for vectors are =min()=, =max()=, =sort()=,
and =cumsum()=.
Arithmetic in =julia= is usually done element-wise, and the operands must be of conformable dimensions.
Arithmetic in =julia= is usually done element-wise, and the operands
must be of conformable dimensions.
#+BEGIN_SRC julia
#+BEGIN_SRC julia
fred2 = [4, 5, 3, 6, 4, 6, 7, 3, 1];
fred2 = [4, 5, 3, 6, 4, 6, 7, 3, 1];
...
@@ -349,11 +401,19 @@ fred - mean(fred)
...
@@ -349,11 +401,19 @@ fred - mean(fred)
35.5556
35.5556
#+end_example
#+end_example
The operations =+= and =-= are performed element-wise. Notice in the last vector that =mean(fred)= was subtracted from each entry in turn. This is also known as data recycling. Other popular vectorizing functions are =sin()=, =cos()=, =exp()=, =log()=, and =sqrt()=.
The operations =+= and =-= are performed element-wise. Notice in the
last vector that =mean(fred)= was subtracted from each entry in
turn. This is also known as data recycling. Other popular vectorizing
functions are =sin()=, =cos()=, =exp()=, =log()=, and =sqrt()=.
** Getting Help
** Getting Help
When you are using =julia= it will not take long before you find yourself needing help. The help resources for =julia= are not as extensive as those for some other languages (such as R). =julia= is new and many of the help topics haven't been written yet. Nevertheless sometimes a person is lucky and you can get help on a function when it's available with the =help()= function.
When you are using =julia= it will not take long before you find
yourself needing help. The help resources for =julia= are not as
extensive as those for some other languages (such as R). =julia= is
new and many of the help topics haven't been written yet.
Nevertheless sometimes a person is lucky and you can get help on a
function when it's available with the =help()= function.
#+BEGIN_SRC julia
#+BEGIN_SRC julia
help("factorial")
help("factorial")
...
@@ -368,15 +428,25 @@ help("factorial")
...
@@ -368,15 +428,25 @@ help("factorial")
:
:
: Compute "factorial(n)/factorial(k)"
: Compute "factorial(n)/factorial(k)"
In addition to this, you can type =help()= which gives an extended list of help topics. For instance, I find myself doing =help("Statistics")= a lot.
In addition to this, you can type =help()= which gives an extended
list of help topics. For instance, I find myself doing
=help("Statistics")= a lot.
Note also =example()=. This initiates the running of examples, if available, of the use of the function specified by the argument.
Note also =example()=. This initiates the running of examples, if
available, of the use of the function specified by the argument.
* Other tips
* Other tips
It is unnecessary to retype commands repeatedly, since Emacs/ESS remembers what you have entered at the =julia>= prompt. To navigate through previous commands put point at the lowest command line and push either =M-p= or =M-n=.
It is unnecessary to retype commands repeatedly, since Emacs/ESS
remembers what you have entered at the =julia>= prompt. To navigate
through previous commands put point at the lowest command line and
push either =M-p= or =M-n=.
To find out what all variables are in the current work environment, use the commands =ls()= or =objects()=. These list all available objects in the workspace. If you wish to remove one or more variables, use =remove(var1, var2)=, and to remove all of them use =rm(list=ls())=.
To find out what all variables are in the current work environment,
use the commands =ls()= or =objects()=. These list all available
objects in the workspace. If you wish to remove one or more variables,
use =remove(var1, var2)=, and to remove all of them use
=rm(list=ls())=.
** Other resources
** Other resources
...
@@ -407,7 +477,12 @@ file(p, "example1.png")
...
@@ -407,7 +477,12 @@ file(p, "example1.png")
* Fitting (generalized) linear models
* Fitting (generalized) linear models
Douglas Bates (of [[http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4419-0317-4][Mixed Effects Models in S and S-PLUS]] fame) has been putting together a =julia= package called GLM which already supports fitting generalized linear models to datasets. This, together with the RDatasets package means there is already a bunch of stuff to keep a person busy. Below is a modified example from the Multiple Regression chapter of IPSUR, translated to =julia= speak.
Douglas Bates (of [[http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4419-0317-4][Mixed Effects Models in S and S-PLUS]] fame) has been
putting together a =julia= package called GLM which already supports
fitting generalized linear models to datasets. This, together with
the RDatasets package means there is already a bunch of stuff to keep
a person busy. Below is a modified example from the Multiple
Regression chapter of IPSUR, translated to =julia= speak.
First, we load the packages we'll need.
First, we load the packages we'll need.
...
@@ -415,20 +490,24 @@ First, we load the packages we'll need.
...
@@ -415,20 +490,24 @@ First, we load the packages we'll need.
using RDatasets, DataFrames, Distributions, GLM
using RDatasets, DataFrames, Distributions, GLM
#+END_SRC
#+END_SRC
Next we load the =trees= data frame from the RDatasets package and fit a linear model to the data.
Next we load the =trees= data frame from the RDatasets package and fit
a linear model to the data.
#+BEGIN_SRC julia :exports code
#+BEGIN_SRC julia :exports code
trees = data("datasets", "trees");
trees = data("datasets", "trees");
treeslm = lm(:(Girth ~ Height + Volume), trees)
treeslm = lm(:(Girth ~ Height + Volume), trees)
#+END_SRC
#+END_SRC
The extended output above should look similar to something we might see in an R session. We can extract the model coefficients with the =coef= function:
The extended output above should look similar to something we might
see in an R session. We can extract the model coefficients with the
=coef= function:
#+BEGIN_SRC julia :exports code
#+BEGIN_SRC julia :exports code
coef(treeslm)
coef(treeslm)
#+END_SRC
#+END_SRC
and we can look at a summary table similar to something like =summary(treeslm)= in R
and we can finish by looking at a summary table similar to something
