PDL::Impatient - PDL for the impatient (quick overview)

A brief summary of the main PDL features and how to use them.

Perl is an extremely good and versatile scripting language, well suited to beginners and allows rapid prototyping. However until recently it did not support data structures which allowed it to do fast number crunching.

However with the development of Perl v5, Perl acquired 'Objects'. To put it simply users can define their own special data types, and write custom routines to manipulate them either in low level languages (C and Fortran) or in Perl itself.

This has been fully exploited by the PerlDL developers. The 'PDL' module is a complete Object-Oriented extension to Perl (although you don't have to know what an object is to use it) which allows large N-dimensional data sets, such as large images, spectra, time series, etc to be stored efficiently and manipulated en masse. For example with the PDL module we can write the perl code CW$a=$b+$c, where CW$b and CW$c are large datasets (e.g. 2048x2048 images), and get the result in only a fraction of a second.

PDL variables (or 'piddles' as they have come to be known) support a wide range of fundamental data types - arrays can be bytes, short integers (signed or unsigned), long integers, floats or double precision floats. And because of the Object-Oriented nature of PDL new customised datatypes can be derived from them.

As well as the PDL modules, that can be used by normal perl programs, PerlDL comes with a command line perl shell, called 'perldl', which supports command line editing. In combination with the various PDL graphics modules this allows data to be easily played with and visualised.

PDL contains extensive documentation, available both within the perldl shell and from the command line, using the CWpdldoc program. For further information try either of:

 perldl> help help
 $ pdldoc

HTML copies of the documentation should also be available. To find their location, try the following:

 perldl> foreach ( map{"$_/PDL/HtmlDocs"}@INC ) { p "$_\n" if -d $_ }

The fundamental perl data structures are scalar variables, e.g. CW$x, which can hold numbers or strings, lists or arrays of scalars, e.g. CW@x, and associative arrays/hashes of scalars, e.g. CW%x.

perl v5 introduces to perl data structures and objects. A simple scalar variable CW$x now be a user-defined data type or full blown object (it actually holds a reference (a smart pointer) to this but that is not relevant for ordinary use of perlDL)

The fundamental idea behind perlDL is to allow CW$x to hold a whole 1D spectrum, or a 2D image, a 3D data cube, and so on up to large N-dimensional data sets. These can be manipulated all at once, e.g. CW$a = $b + 2 does a vector operation on each value in the spectrum/image/etc.

You may well ask: "Why not just store a spectrum as a simple perl CW@x style list with each pixel being a list item?" The two key answers to this are memory and speed. Because we know our spectrum consists of pure numbers we can compactly store them in a single block of memory corresponding to a C style numeric array. This takes up a LOT less memory than the equivalent perl list. It is then easy to pass this block of memory to a fast addition routine, or to any other C function which deals with arrays. As a result perlDL is very fast --- for example one can mulitiply a 2048*2048 image in exactly the same time as it would take in C or FORTRAN (0.1 sec on my SPARC). A further advantage of this is that for simple operations (e.g. CW$x += 2) one can manipulate the whole array without caring about its dimensionality.

I find when using perlDL it is most useful to think of standard perl CW@x variables as lists of generic things and PDL variables like CW$x as arrays which can be contained in lists or hashes. Quite often in my perlDL scripts I have CW@x contain a list of spectra, or a list of images (or even a mix!). Or perhaps one could have a hash (e.g. CW%x) of images... the only limit is memory!

perlDL variables support a range of data types - arrays can be bytes, short integers (signed or unsigned), long integers, floats or double precision floats.

PerlDL is loaded into your perl script using this command:

 use PDL;  # in perl scripts: use the standard perlDL modules

There are also a lot of extension modules, e.g. PDL::Graphics::TriD. Most of these (but not all as sometimes it is not appropriate) follow a standard convention. If you say:

 use PDL::Graphics::TriD;

You import everything in a standard list from the module. Sometimes you might want to import nothing (e.g. if you want to use OO syntax all the time and save the import tax). For these you say:

 use PDL::Graphics::TriD '';

And the blank quotes '' are regonised as meaning 'nothing'. You can also specify a list of functions to import in the normal Perl way.

There is also an interactive shell, CWperldl, see perldl.

Here are some ways of creating a PDL variable:

 $a = pdl [1..10];             # 1D array
 $a = pdl (1,2,3,4);           # Ditto
 $b = pdl [[1,2,3],[4,5,6]];   # 2D 3x2 array
 $b = pdl 42                   # 0-dimensional scalar
 $c = pdl $a;                  # Make a new copy

 $d = byte [1..10];            # See "Type conversion"
 $e = zeroes(3,2,4);           # 3x2x4 zero-filled array

 $c = rfits $file;             # Read FITS file

 @x = ( pdl(4), zeroes(3,2,4), rfits($file) ); # Is a LIST of PDL variables!

The pdl() function is used to initialise a PDL variable from a scalar, list, list reference or another PDL variable.

In addition all PDL functions automatically convert normal perl scalars to PDL variables on-the-fly.

(also see Type Conversion and Input/Output sections below)

 $a = $b + 2; $a++; $a = $b / $c; # Etc.

 $c=sqrt($a); $d = log10($b+100); # Etc

 $e = $a>42; # Vector conditional

 $e = 42*($a>42) + $a*($a<=42); # Cap top

 $b = $a->log10 unless any ($a <= 0); # avoid floating point error

 $a = $a / ( max($a) - min($a) );

 $f = where($a, $a > 10); # where returns a piddle of elements for
                          # which the condition is true

 print $a; # $a in string context prints it in a N-dimensional format

(and other perl operators/functions)

When using piddles in conditional expressions (i.e. CWif, CWunless and CWwhile constructs) only piddles with exactly one element are allowed, e.g.

 $a = pdl (1,0,0,1);
 print "is set" if $a->index(2);

Note that the boolean operators return in general multielement piddles. Therefore, the following will raise an error

 print "is ok" if $a > 3;

since CW$a > 3 is a piddle with 4 elements. Rather use all or any to test if all or any of the elements fulfill the condition:

 print "some are > 3" if any $a>3;
 print "can't take logarithm" unless all $a>0;

There are also many predefined functions, which are described on other manpages. Check PDL::Index.

CW'x' is hijacked as the matrix multiplication operator. e.g. CW$c = $a x $b;

perlDL is row-major not column major so this is actually CWc(i,j) = sum_k a(k,j) b(i,k) - but when matrices are printed the results will look right. Just remember the indices are reversed. e.g.:

 $a = [                   $b = [
       [ 1  2  3  0]            [1 1]
       [ 1 -1  2  7]            [0 2]
       [ 1  0  0  1]            [0 2]
      ]                         [1 1]
                               ]

 gives $c = [
             [ 1 11]
             [ 8 10]
             [ 2  2]
            ]

Note: transpose() does what it says and is a convenient way to turn row vectors into column vectors. It is bound to the unary operator CW'~' for convenience.

 sub dotproduct {
     my ($a,$b) = @_;
     return sum($a*$b) ;
 }
 1;

If put in file dotproduct.pdl would be autoloaded if you are using PDL::AutoLoader (see below).

Of course, this function is already available as the inner function, see PDL::Primitive.

Default for pdl() is double. Conversions are:

 $a = float($b);
 $c = long($d);   # "long" is generally a 4 byte int
 $d = byte($a);

Also double(), short(), ushort().

These routines also automatically convert perl lists to allow the convenient shorthand:

 $a = byte [[1..10],[1..10]];  # Create 2D byte array
 $a = float [1..1000];         # Create 1D float array

etc.

Automatically expands array in N-dimensional format:

 print $a;

 $b = "Answer is = $a ";

PDL has very powerful multidimensional slicing and sectioning operators; see the PDL::Slices(3) man page for details; we'll describe the most imporant one here.

PDL shows its perl/C heritage in that arrays are zero-offset. Thus a 100x100 image has indices CW0..99,0..99. (The convention is that the center of pixel (0,0) is at coordinate (0.0,0.0). All PDL graphics functions conform to this definition and hide away the unit-offsetness of, for example, the PGPLOT FORTRAN library.

Following the usual convention coordinate (0,0) is displayed at the bottom left when displaying an image. It appears at the top left when using "CWprint $a" etc.

Simple sectioning uses a syntax extension to perl, PDL::NiceSlice, that allows you to specify subranges via a null-method modifier to a PDL:

  $b = $a->($x1:$x2,$y1:$y2,($z1)); # Take subsection

Here, CW$a is a 3-dimensional variable, and CW$b gets a planar cutout that is defined by the limits CW$x1, CW$x2, CW$y1, CW$y2, at the location CW$z1. The parenthesis around CW$z1 cause the trivial index to be omitted otherwise CW$b would be three-dimensional with a third dimension of order 1.

You can put PDL slices on either side of the elementwise-assignment operator CW.=, like so:

  # Set part of $bigimage to values from $smallimage
  $bigimage->($xa:$xb,$ya:$yb) .= $smallimage;

Some other miscellany:

 $c  = nelem($a); # Number of pixels

 $val = at($object, $x,$y,$z...)    # Pixel value at position, as a perl scalar
 $val = $object->at($x,$y,$z...)    # equivalent (method syntax OK)

 $b = xvals($a); # Fill array with X-coord values (also yvals(), zvals(),
                 # axisvals($x,$axis) and rvals() for radial distance
                 # from centre).

The CWPDL::IO modules implement several useful IO format functions. It would be too much to give examples of each so you are referred to the individual manpages for details.

PDL::IO::Misc

Ascii, FITS and FIGARO/NDF IO routines.

PDL::IO::FastRaw

Using the raw data types of your machine, an unportable but blindingly fast IO format. Also supports memory mapping to conserve memory as well as get more speed.

PDL::IO::FlexRaw

General raw data formats.

PDL::IO::Browser

A Curses browser for arrays.

PDL::IO::Pnm

Portaple bitmap and pixmap support.

PDL::IO::Pic

Using the previous module and netpbm, makes it possible to easily write GIF, jpeg and whatever with simple commands.

The philosophy behind perlDL is to make it work with a variety of existing graphics libraries since no single package will satisfy all needs and all people and this allows one to work with packages one already knows and likes. Obviously there will be some overlaps in functionality and some lack of consistency and uniformity. However this allows PDL to keep up with a rapidly developing field - the latest PDL modules provide interfaces to OpenGL and VRML graphics!

PDL::Graphics::PGPLOT

PGPLOT provdes a simple library for line graphics and image display. There is an easy interface to this in the internal module PDL::Graphics::PGPLOT, which calls routines in the separately available PGPLOT top-level module.

PDL::Graphics::IIS

Many astronomers like to use SAOimage and Ximtool (or there derivations/clones). These are useful free widgets for inspection and visualisation of images. (They are not provided with perlDL but can easily be obtained from their official sites off the Net.) The PDL::Graphics::IIS package provides allows one to display images in these (IIS is the name of an ancient item of image display hardware whose protocols these tools conform to.)

Karma

The PDL::Graphics::Karma module provides an interface to the Karma visualisation suite. This is a set of GUI applications which are specially designed for visualising noisy 2D and 3D data sets.

PDL::Graphics::TriD

See PDL::Graphics::TriD (the name sucks...). this is a collection of 3D routines for OpenGL and (soon) VRML and other 3D formats which allow 3D point, line, and surface plots from PDL.

See PDL::AutoLoader. This allows one to autoload functions on demand, in a way perhaps familiar to users of MatLab.

One can also write PDL extensions as normal Perl modules.

The perl script CWperldl provides a simple command line - if the latest Readlines/ReadKey modules have beeen installed CWperldl detects this and enables command line recall and editing. See the manpage for details.

e.g.:

 jhereg% perldl
 perlDL shell v1.30
  PDL comes with ABSOLUTELY NO WARRANTY. For details, see the file
  'COPYING' in the PDL distribution. This is free software and you
  are welcome to redistribute it under certain conditions, see
  the same file for details.
 ReadLines enabled                                                               
 Reading PDL/default.perldlrc...
 Found docs database /home/kgb/soft/dev/lib/perl5/site_perl/PDL/pdldoc.db
 Type 'help' for online help
 Type 'demo' for online demos
 Loaded PDL v2.005                                                               
 perldl> $x = rfits 'm51.fits'
 BITPIX =  16  size = 65536 pixels
 Reading  131072 bytes
 BSCALE = 1.0000000000E0 &&  BZERO = 0.0000000000E0

 perldl> imag $x
 Loaded PGPLOT
 Displaying 256 x 256 image from 24 to 500 ...

You can also run it from the perl debugger (CWperl -MPDL -d -e 1) if you want.

Miscellaneous shell features:

p

The shell aliases CWp to be a convenient short form of CWprint, e.g.

   perldl> p ones 5,3
   [
    [1 1 1 1 1]
    [1 1 1 1 1]
    [1 1 1 1 1]
   ]

Initialization

The files CW~/.perldlrc and CWlocal.perldlrc (in the current directory) are sourced if found. This allows the user to have global and local PDL code for startup.

Help

Type 'help'! One can search the PDL documentation, and look up documentation on any function.

Escape

Any line starting with the CW# character is treated as a shell escape. This character is configurable by setting the perl variable CW$PERLDL_ESCAPE. This could, for example, be set in CW~/.perldlrc.

The following builtin perl operators and functions have been overloaded to work on PDL variables:

 + - * / > < >= <= << >> & | ^ == != <=> ** % ! ~
 sin log abs atan2 sqrt cos exp

[All the unary functions (sin etc.) may be used with inplace() - see Memory below.]

PDL operations are available as functions and methods. Thus one can derive new types of object, to represent custom data classes.

By using overloading one can make mathematical operators do whatever you please, and PDL has some built-in tricks which allow existing PDL functions to work unchanged, even if the underlying data representation is vastly changed! See PDL::Objects

Messing around with really huge data arrays may require some care. perlDL provides many facilities to let you perform operations on big arrays without generating extra copies though this does require a bit more thought and care from the programmer.

NOTE: On some most systems it is better to configure perl (during the build options) to use the system CWmalloc() function rather than perl's built-in one. This is because perl's one is optimised for speed rather than consumption of virtual memory - this can result in a factor of two improvement in the amount of memory storage you can use. The Perl malloc in 5.004 and later does have a number of compile-time options you can use to tune the behaviour.

Simple arithmetic

If CW$a is a big image (e.g. occupying 10MB) then the command

 $a = $a + 1;

eats up another 10MB of memory. This is because the expression CW$a+1 creates a temporary copy of CW$a to hold the result, then CW$a is assigned a reference to that. After this, the original CW$a is destroyed so there is no permanent memory waste. But on a small machine, the growth in the memory footprint can be considerable. It is obviously done this way so CW$c=$a+1 works as expected. Also if one says:

 $b = $a;     # $b and $a now point to same data
 $a = $a + 1;

Then CW$b and CW$a end up being different, as one naively expects, because a new reference is created and CW$a is assigned to it. However if CW$a was a huge memory hog (e.g. a 3D volume) creating a copy of it may not be a good thing. One can avoid this memory overhead in the above example by saying:

 $a++;

The operations CW++,+=,--,-=, etc. all call a special in-place version of the arithmetic subroutine. This means no more memory is needed - the downside of this is that if CW$b=$a then CW$b is also incremented. To force a copy explicitly:

 $b = pdl $a; # Real copy

or, alternatively, perhaps better style:

 $b = $a->copy;

Functions

Most functions, e.g. CWlog(), return a result which is a transformation of their argument. This makes for good programming practice. However many operations can be done in-place and this may be required when large arrays are in use and memory is at a premium. For these circumstances the operator inplace() is provided which prevents the extra copy and allows the argument to be modified. e.g.:

 $x = log($array);          # $array unaffected
 log( inplace($bigarray) ); # $bigarray changed in situ

WARNINGS:

1

The usual caveats about duplicate references apply.

2

Obviously when used with some functions which can not be applied in situ (e.g. CWconvolve()) unexpected effects may occur! We try to indicate CWinplace()-safe functions in the documentation.

3

Type conversions, such asCWfloat(), may cause hidden copying.

If you have written a simple function and you don't want it to blow up in your face if you pass it a simple number rather than a PDL variable. Simply call the function topdl() first to make it safe. e.g.:

 sub myfiddle { my $pdl = topdl(shift); $pdl->fiddle_foo(...); ... }

CWtopdl() does NOT perform a copy if a pdl variable is passed - it just falls through - which is obviously the desired behaviour. The routine is not of course necessary in normal user defined functions which do not care about internals.

Copyright (C) Karl Glazebrook (kgb@aaoepp.aao.gov.au), Tuomas J. Lukka, (lukka@husc.harvard.edu) and Christian Soeller (c.soeller@auckland.ac.nz) 1997. Commercial reproduction of this documentation in a different format is forbidden.