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PDL::MATLAB - A guide for MATLAB users.

INTRODUCTION

If you are a MATLAB user, this page is for you. It explains the key differences between
MATLAB and PDL to help you get going as quickly as possible.

This document is not a tutorial. For that, go to PDL::QuickStart. This document
complements the Quick Start guide, as it highlights the key differences between MATLAB and
PDL.

Perl

The key difference between MATLAB and PDL is Perl.

Perl is a general purpose programming language with thousands of modules freely available
on the web. PDL is an extension of Perl. This gives PDL programs access to more features
than most numerical tools can dream of. At the same time, most syntax differences between
MATLAB and PDL are a result of its Perl foundation.

You do not have to learn much Perl to be effective with PDL. But if you wish to learn
Perl, there is excellent documentation available on-line (<http://perldoc.perl.org>) or
through the command "perldoc perl". There is also a beginner's portal
(<http://perl-begin.org>).

Perl's module repository is called CPAN (<http://www.cpan.org>) and it has a vast array of
modules. Run "perldoc cpan" for more information.

TERMINOLOGY: PIDDLE

MATLAB typically refers to vectors, matrices, and arrays. Perl already has arrays, and the
terms "vector" and "matrix" typically refer to one- and two-dimensional collections of
data. Having no good term to describe their object, PDL developers coined the term
"piddle" to give a name to their data type.

A piddle consists of a series of numbers organized as an N-dimensional data set. Piddles
provide efficient storage and fast computation of large N-dimensional matrices. They are
highly optimized for numerical work.

For more information, see "Piddles vs Perl Arrays" later in this document.

COMMAND WINDOW AND IDE

Unlike MATLAB, PDL does not come with a dedicated IDE. It does however come with an
interactive shell and you can use a Perl IDE to develop PDL programs.

PDL interactive shell
To start the interactive shell, open a terminal and run "perldl" or "pdl2". As in MATLAB,
the interactive shell is the best way to learn the language. To exit the shell, type
"exit", just like MATLAB.

Writing PDL programs
One popular IDE for Perl is called Padre (<http://padre.perlide.org>). It is cross
platform and easy to use.

Whenever you write a stand-alone PDL program (i.e. outside the "perldl" or "pdl2" shell)
you must start the program with "use PDL;". This command imports the PDL module into
Perl. Here is a sample PDL program:

use PDL; # Import main PDL module.
use PDL::NiceSlice; # Import additional PDL module.
use PDL::AutoLoader; # Import additional PDL module.

$b = pdl [2,3,4]; # Statements end in semicolon.
$A = pdl [ [1,2,3],[4,5,6] ]; # 2-dimensional matrix.

print $A x $b->transpose;

Save this file as "myprogram.pl" and run it with:

perl myprogram.pl

New: Flexible syntax
In current versions of PDL (version 2.4.7 or later) there is a flexible matrix syntax that
can look extremely similar to MATLAB:

1) Use a ';' to delimit rows:

$b = pdl q[ 2,3,4 ];
$A = pdl q[ 1,2,3 ; 4,5,6 ];

2) Use spaces to separate elements:

$b = pdl q[ 2 3 4 ];
$A = pdl q[ 1 2 3 ; 4 5 6 ];

Basically, as long as you put a "q" in front of the opening bracket, PDL should "do what
you mean". So you can write in a syntax that is more comfortable for you.

MODULES FOR MATLAB USERS

There are two modules that MATLAB users will want to use:

PDL::NiceSlice
Gives PDL a syntax for slices (sub-matrices) that is shorter and more familiar to
MATLAB users.

% MATLAB
b(1:5) --> Selects the first 5 elements from b.

# PDL without NiceSlice
$b->slice("0:4") --> Selects the first 5 elements from $b.

# PDL with NiceSlice
$b(0:4) --> Selects the first 5 elements from $b.

PDL::AutoLoader
Provides a MATLAB-style autoloader for PDL. If an unknown function "foo()" is called,
PDL looks for a file called "foo.pdl". If it finds one, it reads it.

BASIC FEATURES

This section explains how PDL's syntax differs from MATLAB. Most MATLAB users will want to
start here.

General "gotchas"
Indices
In PDL, indices start at '0' (like C and Java), not 1 (like MATLAB or FORTRAN). For
example, if $b is an array with 5 elements, the elements would be numbered from 0 to
4.

Displaying an object
MATLAB normally displays object contents automatically. In the PDL shells you display
objects explicitly with the "print" command or the shortcut "p":

MATLAB:

>> a = 12
a = 12
>> b = 23; % Suppress output.
>>

PDL Shell (perldl or pdl2):

pdl> $a = 12 # No output.
pdl> print $a # Print object.
12
pdl> p $a # "p" is a shorthand for "print" in the shell.
12
pdl>

Creating Piddles
Variables in PDL
Variables always start with the '$' sign.

MATLAB: value = 42
PerlDL: $value = 42

Basic syntax
Use the "pdl" constructor to create a new piddle.

MATLAB: v = [1,2,3,4]
PerlDL: $v = pdl [1,2,3,4]

MATLAB: A = [ 1,2,3 ; 3,4,5 ]
PerlDL: $A = pdl [ [1,2,3] , [3,4,5] ]

Simple matrices
MATLAB PDL
------ ------
Matrix of ones ones(5) ones 5,5
Matrix of zeros zeros(5) zeros 5,5
Random matrix rand(5) random 5,5
Linear vector 1:5 sequence 5

Notice that in PDL the parenthesis in a function call are often optional. It is
important to keep an eye out for possible ambiguities. For example:

pdl> p zeros 2, 2 + 2

Should this be interpreted as "zeros(2,2) + 2" or as "zeros 2, (2+2)"? Both are
valid statements:

pdl> p zeros(2,2) + 2
[
[2 2]
[2 2]
]
pdl> p zeros 2, (2+2)
[
[0 0]
[0 0]
[0 0]
[0 0]
]

Rather than trying to memorize Perl's order of precedence, it is best to use
parentheses to make your code unambiguous.

Linearly spaced sequences
MATLAB: >> linspace(2,10,5)
ans = 2 4 6 8 10

PerlDL: pdl> p zeroes(5)->xlinvals(2,10)
[2 4 6 8 10]

Explanation: Start with a 1-dimensional piddle of 5 elements and give it equally
spaced values from 2 to 10.

MATLAB has a single function call for this. On the other hand, PDL's method is more
flexible:

pdl> p zeros(5,5)->xlinvals(2,10)
[
[ 2 4 6 8 10]
[ 2 4 6 8 10]
[ 2 4 6 8 10]
[ 2 4 6 8 10]
[ 2 4 6 8 10]
]
pdl> p zeros(5,5)->ylinvals(2,10)
[
[ 2 2 2 2 2]
[ 4 4 4 4 4]
[ 6 6 6 6 6]
[ 8 8 8 8 8]
[10 10 10 10 10]
]
pdl> p zeros(3,3,3)->zlinvals(2,6)
[
[
[2 2 2]
[2 2 2]
[2 2 2]
]
[
[4 4 4]
[4 4 4]
[4 4 4]
]
[
[6 6 6]
[6 6 6]
[6 6 6]
]
]

Slicing and indices
Extracting a subset from a collection of data is known as slicing. PDL and MATLAB
have a similar syntax for slicing, but there are two important differences:

1) PDL indices start at 0, as in C and Java. MATLAB starts indices at 1.

2) In MATLAB you think "rows and columns". In PDL, think "x and y".

MATLAB PerlDL
------ ------
>> A pdl> p $A
A = [
1 2 3 [1 2 3]
4 5 6 [4 5 6]
7 8 9 [7 8 9]
]
-------------------------------------------------------
(row = 2, col = 1) (x = 0, y = 1)
>> A(2,1) pdl> p $A(0,1)
ans = [
4 [4]
]
-------------------------------------------------------
(row = 2 to 3, col = 1 to 2) (x = 0 to 1, y = 1 to 2)
>> A(2:3,1:2) pdl> p $A(0:1,1:2)
ans = [
4 5 [4 5]
7 8 [7 8]
]

Warning
When you write a stand-alone PDL program you have to include the PDL::NiceSlice
module. See the previous section "MODULES FOR MATLAB USERS" for more
information.

use PDL; # Import main PDL module.
use PDL::NiceSlice; # Nice syntax for slicing.
use PDL::AutoLoader; # MATLAB-like autoloader.

$A = random 4,4;
print $A(0,1);

Matrix Operations
Matrix multiplication
MATLAB: A * B
PerlDL: $A x $B

Element-wise multiplication
MATLAB: A .* B
PerlDL: $A * $B

Transpose
MATLAB: A'
PerlDL: $A->transpose

Functions that aggregate data
Some functions (like "sum", "max" and "min") aggregate data for an N-dimensional data set.
This is a place where MATLAB and PDL take a different approach:

In MATLAB, these functions all work along one dimension.
>> A = [ 1,5,4 ; 4,2,1 ]
A = 1 5 4
4 2 1
>> max(A)
ans = 4 5 4
>> max(A')
ans = 5 4

If you want the maximum for the entire data set, you can use the special A(:)
notation which basically turns the entire data set into a single 1-dimensional
vector.

>> max(A(:))
ans = 5
>> A = ones(2,2,2,2)
>> max(A(:))
ans = 1

PDL offers two functions for each feature.
sum vs sumover
avg vs average
max vs maximum
min vs minimum

The long name works over a dimension, while the short name works over the entire
piddle.

pdl> p $A = pdl [ [1,5,4] , [4,2,1] ]
[
[1 5 4]
[4 2 1]
]
pdl> p $A->maximum
[5 4]
pdl> p $A->transpose->maximum
[4 5 4]
pdl> p $A->max
5
pdl> p ones(2,2,2)->max
1
pdl> p ones(2,2,2,2)->max
1

Note Notice that PDL aggregates horizontally while MATLAB aggregates vertically. In other
words:

MATLAB PerlDL
max(A) == $A->transpose->maximum
max(A') == $A->maximum

TIP: In MATLAB you think "rows and columns". In PDL, think "x and y".

Higher dimensional data sets
A related issue is how MATLAB and PDL understand data sets of higher dimension. MATLAB was
designed for 1D vectors and 2D matrices. Higher dimensional objects ("N-D arrays") were
added on top. In contrast, PDL was designed for N-dimensional piddles from the start. This
leads to a few surprises in MATLAB that don't occur in PDL:

MATLAB sees a vector as a 2D matrix.
MATLAB PerlDL
------ ------
>> vector = [1,2,3,4]; pdl> $vector = pdl [1,2,3,4]
>> size(vector) pdl> p $vector->dims
ans = 1 4 4

MATLAB sees "[1,2,3,4]" as a 2D matrix (1x4 matrix). PDL sees it as a 1D vector: A
single dimension of size 4.

But MATLAB ignores the last dimension of a 4x1x1 matrix.
MATLAB PerlDL
------ ------
>> A = ones(4,1,1); pdl> $A = ones 4,1,1
>> size(A) pdl> p $A->dims
ans = 4 1 4 1 1

And MATLAB treats a 4x1x1 matrix differently from a 1x1x4 matrix.
MATLAB PerlDL
------ ------
>> A = ones(1,1,4); pdl> $A = ones 1,1,4
>> size(A) pdl> p $A->dims
ans = 1 1 4 1 1 4

MATLAB has no direct syntax for N-D arrays.
pdl> $A = pdl [ [[1,2,3],[4,5,6]], [[2,3,4],[5,6,7]] ]
pdl> p $A->dims
3 2 2

Feature support.
In MATLAB, several features such as sparse matrix support are not available for N-D
arrays. In PDL, just about any feature supported by 1D and 2D piddles, is equally
supported by N-dimensional piddles. There is usually no distinction.

Loop Structures
Perl has many loop structures, but we will only show the one that is most familiar to
MATLAB users:

MATLAB PerlDL
------ ------
for i = 1:10 for $i (1..10) {
disp(i) print $i
endfor }

Note Never use for-loops for numerical work. Perl's for-loops are faster than MATLAB's,
but they both pale against a "vectorized" operation. PDL has many tools that
facilitate writing vectorized programs. These are beyond the scope of this guide. To
learn more, see: PDL::Indexing, PDL::Threading, and PDL::PP.

Likewise, never use 1..10 for numerical work, even outside a for-loop. 1..10 is a
Perl array. Perl arrays are designed for flexibility, not speed. Use piddles instead.
To learn more, see the next section.

Piddles vs Perl Arrays
It is important to note the difference between a Piddle and a Perl array. Perl has a
general-purpose array object that can hold any type of element:

@perl_array = 1..10;
@perl_array = ( 12, "Hello" );
@perl_array = ( 1, 2, 3, \@another_perl_array, sequence(5) );

Perl arrays allow you to create powerful data structures (see Data structures below), but
they are not designed for numerical work. For that, use piddles:

$pdl = pdl [ 1, 2, 3, 4 ];
$pdl = sequence 10_000_000;
$pdl = ones 600, 600;

For example:

$points = pdl 1..10_000_000 # 4.7 seconds
$points = sequence 10_000_000 # milliseconds

TIP: You can use underscores in numbers ("10_000_000" reads better than 10000000).

Conditionals
Perl has many conditionals, but we will only show the one that is most familiar to MATLAB
users:

MATLAB PerlDL
------ ------
if value > MAX if ($value > $MAX) {
disp("Too large") print "Too large\n";
elseif value < MIN } elsif ($value < $MIN) {
disp("Too small") print "Too small\n";
else } else {
disp("Perfect!") print "Perfect!\n";
end }

Note Here is a "gotcha":

MATLAB: elseif
PerlDL: elsif

If your conditional gives a syntax error, check that you wrote your "elsif"'s
correctly.

TIMTOWDI (There Is More Than One Way To Do It)
One of the most interesting differences between PDL and other tools is the expressiveness
of the Perl language. TIMTOWDI, or "There Is More Than One Way To Do It", is Perl's motto.

Perl was written by a linguist, and one of its defining properties is that statements can
be formulated in different ways to give the language a more natural feel. For example, you
are unlikely to say to a friend:

"While I am not finished, I will keep working."

Human language is more flexible than that. Instead, you are more likely to say:

"I will keep working until I am finished."

Owing to its linguistic roots, Perl is the only programming language with this sort of
flexibility. For example, Perl has traditional while-loops and if-statements:

while ( ! finished() ) {
keep_working();
}

if ( ! wife_angry() ) {
kiss_wife();
}

But it also offers the alternative until and unless statements:

until ( finished() ) {
keep_working();
}

unless ( wife_angry() ) {
kiss_wife();
}

And Perl allows you to write loops and conditionals in "postfix" form:

keep_working() until finished();

kiss_wife() unless wife_angry();

In this way, Perl often allows you to write more natural, easy to understand code than is
possible in more restrictive programming languages.

Functions
PDL's syntax for declaring functions differs significantly from MATLAB's.

MATLAB PerlDL
------ ------
function retval = foo(x,y) sub foo {
retval = x.**2 + x.*y my ($x, $y) = @_;
endfunction return $x**2 + $x*$y;
}

Don't be intimidated by all the new syntax. Here is a quick run through a function
declaration in PDL:

1) "sub" stands for "subroutine".

2) "my" declares variables to be local to the function.

3) "@_" is a special Perl array that holds all the function parameters. This might seem
like a strange way to do functions, but it allows you to make functions that take a
variable number of parameters. For example, the following function takes any number of
parameters and adds them together:

sub mysum {
my ($i, $total) = (0, 0);
for $i (@_) {
$total += $i;
}
return $total;
}

4) You can assign values to several variables at once using the syntax:

($a, $b, $c) = (1, 2, 3);

So, in the previous examples:

# This declares two local variables and initializes them to 0.
my ($i, $total) = (0, 0);

# This takes the first two elements of @_ and puts them in $x and $y.
my ($x, $y) = @_;

5) The "return" statement gives the return value of the function, if any.

ADDITIONAL FEATURES

ASCII File IO
To read data files containing whitespace separated columns of numbers (as would be read
using the MATLAB load command) one uses the PDL rcols in PDL::IO::Misc. For a general
review of the IO functionality available in PDL, see the documentation for PDL::IO, e.g.,
"help PDL::IO" in the pdl2 shell or " pdldoc PDL::IO " from the shell command line.

Data structures
To create complex data structures, MATLAB uses "cell arrays" and "structure arrays".
Perl's arrays and hashes offer similar functionality but are more powerful and flexible.
This section is only a quick overview of what Perl has to offer. To learn more about this,
please go to <http://perldoc.perl.org/perldata.html> or run the command "perldoc
perldata".

Arrays
Perl arrays are similar to MATLAB's cell arrays, but more flexible. For example, in
MATLAB, a cell array is still fundamentally a matrix. It is made of rows, and rows
must have the same length.

MATLAB
------
array = {1, 12, 'hello'; rand(3, 2), ones(3), 'junk'}
=> OK
array = {1, 12, 'hello'; rand(3, 2), ones(3) }
=> ERROR

A Perl array is a general purpose, sequential data structure. It can contain any data
type.

PerlDL
------
@array = ( [1, 12, 'hello'] , [ random(3,2), ones(3,3), 'junk' ] )
=> OK
@array = ( [1, 12, 'hello'] , [ random(3,2), ones(3,3) ] )
=> OK
@array = ( 5 , {'name' => 'Mike'} , [1, 12, 'hello'] )
=> OK

Notice that Perl array's start with the "@" prefix instead of the "$" used by
piddles.

To learn about Perl arrays, please go to <http://perldoc.perl.org/perldata.html> or
run the command "perldoc perldata".

Hashes
Perl hashes are similar to MATLAB's structure arrays:

MATLAB
------
>> drink = struct('type', 'coke', 'size', 'large', 'myarray', {1,2,3})
>> drink.type = 'sprite'
>> drink.price = 12 % Add new field to structure array.

PerlDL
------
pdl> %drink = ( type => 'coke' , size => 'large', mypiddle => ones(3,3,3) )
pdl> $drink{type} = 'sprite'
pdl> $drink{price} = 12 # Add new field to hash.

Notice that Perl hashes start with the "%" prefix instead of the "@" for arrays and
"$" used by piddles.

To learn about Perl hashes, please go to <http://perldoc.perl.org/perldata.html> or
run the command "perldoc perldata".

Performance
PDL has powerful performance features, some of which are not normally available in
numerical computation tools. The following pages will guide you through these features:

PDL::Indexing
Level: Beginner

This beginner tutorial covers the standard "vectorization" feature that you already
know from MATLAB. Use this page to learn how to avoid for-loops to make your program
more efficient.

PDL::Threading
Level: Intermediate

PDL's "vectorization" feature goes beyond what most numerical software can do. In
this tutorial you'll learn how to "thread" over higher dimensions, allowing you to
vectorize your program further than is possible in MATLAB.

Benchmarks
Level: Intermediate

Perl comes with an easy to use benchmarks module to help you find how long it takes
to execute different parts of your code. It is a great tool to help you focus your
optimization efforts. You can read about it online
(<http://perldoc.perl.org/Benchmark.html>) or through the command "perldoc
Benchmark".

PDL::PP
Level: Advanced

PDL's Pre-Processor is one of PDL's most powerful features. You write a function
definition in special markup and the pre-processor generates real C code which can be
compiled. With PDL:PP you get the full speed of native C code without having to deal
with the full complexity of the C language.

Plotting
PDL has full-featured plotting abilities. Unlike MATLAB, PDL relies more on third-party
libraries (pgplot and PLplot) for its 2D plotting features. Its 3D plotting and graphics
uses OpenGL for performance and portability. PDL has three main plotting modules:

PDL::Graphics::PGPLOT
Best for: Plotting 2D functions and data sets.

This is an interface to the venerable PGPLOT library. PGPLOT has been widely used in
the academic and scientific communities for many years. In part because of its age,
PGPLOT has some limitations compared to newer packages such as PLplot (e.g. no RGB
graphics). But it has many features that still make it popular in the scientific
community.

PDL::Graphics::PLplot
Best for: Plotting 2D functions as well as 2D and 3D data sets.

This is an interface to the PLplot plotting library. PLplot is a modern, open source
library for making scientific plots. It supports plots of both 2D and 3D data sets.
PLplot is best supported for unix/linux/macosx platforms. It has an active developers
community and support for win32 platforms is improving.

PDL::Graphics::TriD
Best for: Plotting 3D functions.

The native PDL 3D graphics library using OpenGL as a backend for 3D plots and data
visualization. With OpenGL, it is easy to manipulate the resulting 3D objects with
the mouse in real time.

Writing GUIs
Through Perl, PDL has access to all the major toolkits for creating a cross platform
graphical user interface. One popular option is wxPerl (<http://wxperl.sourceforge.net>).
These are the Perl bindings for wxWidgets, a powerful GUI toolkit for writing cross-
platform applications.

wxWidgets is designed to make your application look and feel like a native application in
every platform. For example, the Perl IDE Padre is written with wxPerl.

Simulink
Simulink is a graphical dynamical system modeler and simulator. It can be purchased
separately as an add-on to MATLAB. PDL and Perl do not have a direct equivalent to
MATLAB's Simulink. If this feature is important to you, then take a look at Scilab:

<http://www.scilab.org>

Scilab is another numerical analysis software. Like PDL, it is free and open source. It
doesn't have PDL's unique features, but it is very similar to MATLAB. Scilab comes with
Xcos (previously Scicos), a graphical system modeler and simulator similar to Simulink.

COPYRIGHT

Copyright 2010 Daniel Carrera ([email protected]). You can distribute and/or modify this
document under the same terms as the current Perl license.

See: http://dev.perl.org/licenses/

Acknowledgements
I'd like to thank David Mertens, Chris Marshall and Sigrid Carrera for their immense
help reviewing earlier drafts of this guide. Without their hours of work, this
document would not be remotely as useful to MATLAB users as it is today.

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