=head1 NAME

PDL::Dataflow -- description of the dataflow philosophy

=head1 SYNOPSIS

	pdl> $x = zeroes(10);
	pdl> $y = $x->slice("2:4:2");
	pdl> $y ++;
	pdl> print $x;
	[0 0 1 0 1 0 0 0 0 0]


=head1 WARNING

Dataflow is very experimental. Many features of it are disabled
for 2.0, particularly families for one-directional
dataflow. If you wish to use one-directional dataflow for
something, please contact the author first and we'll work out
how to make it functional again.

Two-directional dataflow (which implements ->slice() etc.)
is fully functional, however. Just about any function which
returns some subset of the values in some ndarray will make a binding
so that

	$x = some ndarray
	$y = $x->slice("some parts");
	$y->set(3,3,10);

also changes the corresponding element in $x. $y has become effectively
a window to some sub-elements of $x. You can also define your own routines
that do different types of subsets. If you don't want $y to be a window
to $x, you must do

	$y = $x->slice("some parts")->copy;

The copying turns off all dataflow between the two ndarrays.

The difficulties with one-directional
dataflow are related to sequences like

	$y = $x + 1;
	$y ++;

where there are several possible outcomes and the semantics get a little
murky.

=head1 DESCRIPTION

Dataflow is new to PDL2.0. The basic philosophy
behind dataflow is that

	> $x = pdl 2,3,4;
	> $y = $x * 2;
	> print $y
	[2 3 4]
	> $x->set(0,5);
	> print $y;
	[10 3 4]

should work. It doesn't. It was considered that doing this
might be too confusing for novices and occasional users of the language.
Therefore, you need to explicitly turn on dataflow, so

	> $x = pdl 2,3,4;
	> $x->doflow();
	> $y = $x * 2;
	...

produces the unexpected result. The rest of this documents
explains various features and details of the dataflow implementation.

=head1 Lazy evaluation

When you calculate something like the above

	> $x = pdl 2,3,4;
	> $x->doflow();
	> $y = $x * 2;

nothing will have been calculated at this point. Even the memory for
the contents of $y has not been allocated. Only the command

	> print $y

will actually cause $y to be calculated. This is important to bear
in mind when doing performance measurements and benchmarks as well
as when tracking errors.

There is an explanation for this behaviour: it may save cycles
but more importantly, imagine the following:

	> $x = pdl 2,3,4;
	> $y = pdl 5,6,7;
	> $c = $x + $y;
	...
	> $x->resize(4);
	> $y->resize(4);
	> print $c;

Now, if $c were evaluated between the two resizes, an error condition
of incompatible sizes would occur.

What happens in the current version is that resizing $x raises
a flag in $c: "PDL_PARENTDIMSCHANGED" and $y just raises the same flag
again. When $c is next evaluated, the flags are checked and it is found
that a recalculation is needed.

Of course, lazy evaluation can sometimes make debugging more painful
because errors may occur somewhere where you'd not expect them.
A better stack trace for errors is in the works for PDL, probably
so that you can toggle a switch $PDL::traceevals and get a good trace
of where the error actually was.

=head1 Families

This is one of the more intricate concepts of one-directional dataflow.
Consider the following code ($x and $y are pdls that have dataflow enabled):

	$w = $u + $v;
	$y = $w + 1;
	$x = $w->diagonal();
	$x++;
	$z = $w + 1;

What should $y and $z contain now? What about when $u is changed
and a recalculation is triggered.

In order to make dataflow work like you'd expect, a rather strange
concept must be introduced: families. Let us make a diagram:

	u   v
	 \ /
	  w
	 /|
	/ |
       y  x

This is what PDL actually has in memory after the first three lines.
When $x is changed, we want $w to change but we don't want $y to change
because it already is on the graph. It may not be clear now why you don't
want it to change but if there were 40 lines of code between the 2nd
and 4th lines, you would. So we need to make a copy of $w and $x:

	u   v
	 \ /
	  w' . . . w
	 /|        |\
	/ |        | \
       y  x' . . . x  z

Notice that we primed the original w and x, because they do not correspond
to the objects in $w and $x any more. Also, notice the dotted lines
between the two objects: when $u is changed and this diagram is re-evaluated,
$w really does get the value of w' with the diagonal incremented.

To generalize on the above, whenever an ndarray is mutated i.e.
when its actual *value* is forcibly changed (not just the reference):

	$x = $x + 1

would produce a completely different result ($w and $x would not be bound
any more whereas

	$x .= $x + 1

would yield the same as $x++), a "family" consisting of all other ndarrays
joined to the mutated ndarray by a two-way transformation is created
and all those are copied.

All slices or transformations that simply select a subset of the original
pdl are two-way. Matrix inverse should be. No arithmetic
operators are.

=head1 Sources

What you were told in the previous section is not quite true:
the behaviour described is not *always* what you want. Sometimes you
would probably like to have a data "source":

	$x = pdl 2,3,4; $y = pdl 5,6,7;
	$c = $x + $y;
	line($c);

Now, if you know that $x is going to change and that you want
its children to change with it, you can declare it into a data source
(XXX unimplemented in current version):

	$x->datasource(1);

After this, $x++ or $x .= something will not create a new family
but will alter $x and cut its relation with its previous parents.
All its children will follow its current value.

So if $c in the previous section had been declared as a source,
$e and $f would remain equal.

=head1 Binding

A dataflow mechanism would not be very useful without the ability
to bind events onto changed data. Therefore, we provide such a mechanism:

	> $x = pdl 2,3,4
	> $y = $x + 1;
	> $c = $y * 2;
	> $c->bind( sub { print "A now: $x, C now: $c\n" } )
	> PDL::dowhenidle();
	A now: [2,3,4], C now: [6 8 10]
	> $x->set(0,1);
	> $x->set(1,1);
	> PDL::dowhenidle();
	A now: [1,1,4], C now: [4 4 10]

Notice how the callbacks only get called during PDL::dowhenidle.
An easy way to interface this to Perl event loop mechanisms
(such as Tk) is being planned.

There are many kinds of uses for this feature: self-updating graphs,
for instance.

Blah blah blah XXX more explanation

=head1 Limitations

Dataflow as such is a fairly limited addition on top of Perl.
To get a more refined addition, the internals of Perl need to be
hacked a little. A true implementation would enable flow of everything,
including

=over 12

=item data

=item data size

=item datatype

=item operations

=back

At the moment we only have the first two (hey, 50% in a couple of months
is not bad ;) but even this is useful by itself. However, especially
the last one is desirable since it would add the possibility
of flowing closures from place to place and would make many things
more flexible.

To get the rest working, the internals of dataflow probably need to
be changed to be a more general framework.

Additionally, it would be nice to be able to flow data in time,
lucid-like (so you could easily define all kinds of signal processing
things).

=head1 AUTHOR

Copyright(C) 1997 Tuomas J. Lukka (lukka@fas.harvard.edu).
Redistribution in the same form is allowed provided that the copyright
notice stays intact but reprinting requires
a permission from the author.
