PDL::QuickStartp - Online in the Cloud

PROGRAM:

NAME

PDL::QuickStart - Quick introduction to PDL features.

SYNOPSIS

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

DESCRIPTION

Introduction
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 "$a = $b + $c", where $b and $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.

Help
PDL contains extensive documentation, available both within the perldl or pdl2 shells and
from the command line, using the "pdldoc" program. For further information try either of:

pdl> help help
$ pdldoc

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

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

Perl Datatypes and how PDL extends them
The fundamental Perl data structures are scalar variables, e.g. $x, which can hold numbers
or strings, lists or arrays of scalars, e.g. @x, and associative arrays/hashes of scalars,
e.g. %x.

Perl v5 introduces to Perl data structures and objects. A simple scalar variable $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 $x to hold a whole 1D spectrum, or a 2D
image, a 3D data cube, and so on up to large N-dimensional data sets. These can be
manipulated all at once, e.g. "$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 @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 multiply 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. "$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 @x variables as
"lists" of generic "things" and PDL variables like $x as "arrays" which can be contained
in lists or hashes. Quite often in my perlDL scripts I have @x contain a list of spectra,
or a list of images (or even a mix!). Or perhaps one could have a hash (e.g. %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.

Usage
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 qw();

And the empty "qw()" quotes are recognised as meaning 'nothing'. You can also specify a
list of functions to import in the normal Perl way.

There is also an interactive shell, "perldl" or "pdl2", see perldl or pdl2 for details.

To create a new PDL variable
Here are some ways of creating a PDL variable:

$a = pdl [1..10]; # 1D array
$a = pdl (1,2,3,4); # Ditto
$a = pdl '[1 2 3 4]'; # Ditto
$b = pdl [[1,2,3],[4,5,6]]; # 2D 3x2 array
$b = pdl '[1 2 3; 4 5 6]'; # Ditto
$b = pdl q[1,2,3; 4,5,6]; # Ditto
$b = pdl <<NEWPDL # Ditto
[1 2 3]
[4 5 6]
NEWPDL
$c = pdl q[1 -2]; # 2-element piddle containing 1 and -2
$c = pdl q[1 - 2]; # 2-element piddle containing 1 and -2
$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(42), 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, another PDL variable, or a properly formatted string.

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)

Arithmetic (and boolean expressions)
$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. "if", "unless" and "while" 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 multi-element piddles. Therefore, the
following will raise an error

print "is ok" if $a > 3;

since "$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 man pages. Check
PDL::Index.

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

perlDL is row-major not column major so this is actually "c(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.

How to write a simple function
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.

Type Conversion
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(), indx().

NOTE: The indx() routine is a special integer type that
is the correct size for a PDL index value (dimension size,
index, or offest) which can be either a 32bit (long) or
64bit (longlong) quantity depending on whether the perl
is built with 32bit or 64bit support.

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.

Printing
Automatically expands array in N-dimensional format:

print $a;

$b = "Answer is = $a ";

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

PDL shows its Perl/C heritage in that arrays are zero-offset. Thus a 100x100 image has
indices "0..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
offsets 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 ""print $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, $a is a 3-dimensional variable, and $b gets a planar cutout that is defined by the
limits $x1, $x2, $y1, $y2, at the location $z1. The parenthesis around $z1 cause the
trivial index to be omitted -- otherwise $b would be three-dimensional with a third
dimension of order 1.

You can put PDL slices on either side of the element-wise assignment operator ".=", 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).

Input/Output
The "PDL::IO" modules implement several useful IO format functions. It would be too much
to give examples of each, but you can find a nice overview at PDL::IO. Here is a sample of
some of the supported IO formats in PDL.

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. Like FastRaw, only better.

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.

Graphics
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 provides 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::PLplot
PLplot provides a simple library for creating graphics with multiple output drivers,
including a direct-to-piddle driver.

This module provides both high-level and low-level functionality built on PLplot. The
low-level commands are pretty much direct bindings to PLplot's C interface. Read more
at PDL::Graphics::PLplot.

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.)

PDL::Graphics::TriD
See PDL::Graphics::TriD, 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.

Autoloading
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.

PDL shells
The Perl script "pdl2" (or "perldl") provides a simple command line interface to PDL. If
the latest Readlines/ReadKey modules have been installed "pdl2" detects this and enables
command line recall and editing. See the man page for details.

e.g.:

% perldl
perlDL shell v1.354
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, NiceSlice, MultiLines enabled
Reading PDL/default.perldlrc...
Found docs database /home/pdl/dev/lib/perl5/site_perl/PDL/pdldoc.db
Type 'help' for online help
Type 'demo' for online demos
Loaded PDL v2.4.9_003 (supports bad values)
pdl> $x = rfits 'm51.fits'
Reading IMAGE data...
BITPIX = 32 size = 147456 pixels
Reading 589824 bytes
BSCALE = && BZERO =

pdl> use PDL::Graphics::PGPLOT;
pdl> imag $x
Displaying 384 x 384 image from 40 to 761, using 84 colors (16-99)...

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

Miscellaneous shell features:

p The shell aliases "p" to be a convenient short form of "print", e.g.

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

Initialization
The files "~/.perldlrc" and "local.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 "#" character is treated as a shell escape. This character
is configurable by setting the Perl variable $PERLDL_ESCAPE. This could, for example,
be set in "~/.perldlrc".

Overload operators
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.]

Object-Orientation and perlDL
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

Memory usage and references
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 "malloc()" 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 $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 "$a+1" creates a
temporary copy of $a to hold the result, then $a is assigned a reference to that.
After this, the original $a is destroyed so there is no permanent memory waste. But on
a small machine, the growth in the memory footprint can be considerable. It is
obviously done this way so "$c=$a+1" works as expected.

Also if one says:

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

Then $b and $a end up being different, as one naively expects, because a new reference
is created and $a is assigned to it.

However if $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 "++,+=,--,-=", 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 "$b=$a" then $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. "log()", 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.
"convolve()") unexpected effects may occur! We try to indicate "inplace()"-safe
functions in the documentation.

3. Type conversions, such as"float()", may cause hidden copying.

Ensuring piddleness
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(...); ... }

"topdl()" 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.

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