Provided by: pdl_2.080-3_amd64 
NAME
PDL::Dataflow -- description of the dataflow implementation and philosophy
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]
DESCRIPTION
As of 2.079, this is now a description of the current implementation, together with some
design thoughts from its original author, Tuomas Lukka.
Two-directional dataflow (which implements "->slice()" etc.) is fully functional, as
shown in the SYNOPSIS. One-way is implemented, but with restrictions.
TWO-WAY
Just about any function which returns some subset of the values in some ndarray will make
a binding. $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")->sever;
The "sever" destroys the "slice" transform, thereby turning off all dataflow between the
two ndarrays.
Type conversions
This works, thanks to a two-way flowing transform that implements type-conversions,
particularly for supplied outputs of the "wrong" type for the given transform:
pdl> $a_bad = pdl double, '[1 BAD 3]';
pdl> $b_float = zeroes float, 3;
pdl> $a_bad->assgn($b_float); # could be written as $b_float .= $a_bad
pdl> p $b_float->badflag;
1
pdl> p $b_float;
[1 BAD 3]
ONE-WAY
You need to explicitly turn on one-way dataflow on an ndarray to activate it for non-
flowing operations, so
pdl> $x = pdl 2,3,4;
pdl> $x->doflow;
pdl> $y = $x * 2;
pdl> print $y;
[4 6 8]
pdl> $x->set(0,5);
pdl> print $y;
[10 6 8]
It is not possible to turn on backwards dataflow (such as is used by "slice"-type
operations), because there is no general way for PDL (or maths, in fact) to know how to
reverse most operations - consider "$z = $x * $y", then adding one to $z.
Consider the following code:
$u = sequence(3,3); $u->doflow;
$v = ones(3,3); $v->doflow;
$w = $u + $v; $w->doflow; # must turn on for each
$y = $w + 1; $y->doflow;
$x = $w->diagonal(0,1);
$x += 50;
$z = $w + 2;
What do $y and $z contain now?
pdl> p $y
[
[52 3 4]
[ 5 56 7]
[ 8 9 60]
]
pdl> p $z
[
[53 4 5]
[ 6 57 8]
[ 9 10 61]
]
What about when $u is changed and a recalculation is triggered? A problem arises, in that
PDL currently (as of 2.079) disallows (see pdlapi.c), for normal transforms, output
ndarrays with flow, or output ndarrays with any parent with dataflow. So "$u++" throws an
exception. But it is currently possible to use "set", which is a sort of micro-transform
that calls (in the C API) "PDL.set" to mutate the data, then "PDL.changed" to trigger flow
updates:
pdl> $u->set(1,1,90)
pdl> p $y
[
[ 2 3 4]
[ 5 92 7]
[ 8 9 10]
]
You'll notice that while the setting of "1,1" (the middle) of $u updated $y, the changes
to $y that resulted from adding 50 to the diagonal (via $x, and two-way flow) got lost.
This is one-way flow.
LAZY EVALUATION
In one-way flow context like the above, with:
pdl> $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
pdl> 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:
pdl> $x = pdl 2,3,4; $x->doflow;
pdl> $y = pdl 5,6,7; $y->doflow;
pdl> $c = $x + $y;
pdl> $x->setdims([4]);
pdl> $y->setdims([4]);
pdl> 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.
FAMILIES
This is one of the more intricate concepts of dataflow. In order to make dataflow work
like you'd expect, a rather strange concept must be introduced: families. Let us make a
diagram of the one-way flow example - it uses a hypergraph because the transforms (with
"+") are connectors between ndarrays (with "*"):
u* *v
\ /
+(plus)
|
1* *w
\ /|\
\ / | \
(plus)+ | +(diagonal)
| | |
y* | *x
|
| *1
|/
+(plus)
|
z*
This is what PDL actually has in memory after the first three lines. When $x is changed,
$w changes due to "diagonal" being a two-way operation.
If you want flow from $w, you opt in using "$w->doflow" (as shown in this scenario). If
you didn't, then don't enable it. If you have it but want to stop it, call
"$ndarray->sever". That will destroy the ndarray's "trans_parent" (here, a node marked
with "+"), and as you can visually tell, will stop changes flowing thereafter. If you want
to leave the flow operating, but get a copy of the ndarray at that point, use
"$ndarray->copy" - it will have the same data at that moment, but have no flow
relationships.
EVENTS
There is the start of a mechanism to bind events onto changed data, intended to allow this
to work:
pdl> $x = pdl 2,3,4
pdl> $y = $x + 1;
pdl> $c = $y * 2;
pdl> $c->bind( sub { print "A now: $x, C now: $c\n" } )
pdl> PDL::dowhenidle();
A now: [2,3,4], C now: [6 8 10]
pdl> $x->set(0,1);
pdl> $x->set(1,1);
pdl> PDL::dowhenidle();
A now: [1,1,4], C now: [4 4 10]
This hooks into PDL's "magic" which resembles Perl's, but does not currently operate.
There would be many kinds of uses for this feature: self-updating charts, for instance. It
is not yet fully clear whether it would be most useful to queue up changes (useful for
doing asynchronously, e.g. when idle), or to activate things immediately.
In the 2022 era of both GPUs and multiple cores, it is a pity that Perl's dominant model
remains single-threaded on CPU, but PDL can use multi-cores for CPU processing (albeit
controlled in a single-threaded style) - see PDL::ParallelCPU. It is planned that PDL will
gain the ability to use GPUs, and there might be a way to hook that up albeit probably
with an event loop to "subscribe" to GPU events.
TRANSFORMATIONS
PDL implements nearly everything (except for XS oddities like "set") using transforms
which connect ndarrays. This includes data transformations like addition, "slicing" to
access/operate on subsets, and data-type conversions (which have two-way dataflow, see
"Type conversions").
This does not currently include a resizing transformation, and "setdims" mutates its
input. This is intended to change.
AUTHOR
Copyright(C) 1997 Tuomas J. Lukka (lukka@fas.harvard.edu). Same terms as the rest of PDL.