PDL::MATLAB (1)

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NAME

PDL::MATLAB - A guide for MATLAB users.

INTRODUCTION

If you are a user, this page is for you. It explains the key differences between and 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

and

Perl

The key difference between and is Perl.

Perl is a general purpose programming language with thousands of modules freely available on the web.

is an extension of Perl. This gives programs access to more features than most numerical tools can dream of. At the same time, most syntax differences between and are a result of its Perl foundation.

You do not have to learn much Perl to be effective with

. But if you wish to learn Perl, there is excellent documentation available on-line (<perldoc.perl.org>) or through the command "perldoc perl". There is also a beginner's portal (<perl-begin.org>).

Perl's module repository is called

(<www.cpan.org>) and it has a vast array of modules. Run "perldoc cpan" for more information.

TERMINOLOGY: PIDDLE

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

PDL

interactive shell

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

Writing

PDL

programs

One popular for Perl is called Padre (<padre.perlide.org>). It is cross platform and easy to use.

Whenever you write a stand-alone

program (i.e. outside the "perldl" or "pdl2" shell) you must start the program with "use PDL;". This command imports the module into Perl. Here is a sample 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 (version 2.4.7 or later) there is a flexible matrix syntax that can look extremely similar to

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,

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 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 's syntax differs from Most 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 and 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 and understand data sets of higher dimension. was designed for 1D vectors and 2D matrices. Higher dimensional objects (``N-D arrays'') were added on top. In contrast, was designed for N-dimensional piddles from the start. This leads to a few surprises in that don't occur in

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 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

: 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 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 and other tools is the expressiveness of the Perl language. 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

's syntax for declaring functions differs significantly from '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

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 load command) one uses the rcols in PDL::IO::Misc. For a general review of the functionality available in see the documentation for , 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, 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 <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 <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 <perldoc.perl.org/perldata.html> or run the command "perldoc perldata".

Performance

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 (<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

has full-featured plotting abilities. Unlike 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. 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, has access to all the major toolkits for creating a cross platform graphical user interface. One popular option is wxPerl (<wxperl.sourceforge.net>). These are the Perl bindings for wxWidgets, a powerful 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

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 and Perl do not have a direct equivalent to 's Simulink. If this feature is important to you, then take a look at Scilab:

<www.scilab.org>

Scilab is another numerical analysis software. Like

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

COPYRIGHT

Copyright 2010 Daniel Carrera (dcarrera@gmail.com). You can distribute and/or modify this document under the same terms as the current Perl license.

See: 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.