BADVALUES(1p)

NAME
PDL::BadValues - Discussion of bad value support in PDL

DESCRIPTION

  What are bad values and why should I bother with them?
Sometimes it's useful to be able to specify a certain value is 'bad' or 'missing'; for example CCDs used in astronomy produce 2D images which are not perfect since certain areas contain invalid data due to imperfections in the detector. Whilst PDL's powerful index routines and all the complicated business with dataflow, slices, etc etc mean that these regions can be ignored in processing, it's awkward to do. It would be much easier to be able to say "$c = $x + $y" and leave all the hassle to the computer.

If you're not interested in this, then you may (rightly) be concerned with how this affects the speed of PDL, since the overhead of checking for a bad value at each operation can be large. Because of this, the code has been written to be as fast as possible - particularly when operating on ndarrays which do not contain bad values. In fact, you should notice essentially no speed difference when working with ndarrays which do not contain bad values.

You may also ask 'well, my computer supports IEEE NaN, so I already have this'. Well, yes and no - many routines, such as "y=sin(x)", will propagate NaN's without the user having to code differently, but routines such as "qsort", or finding the median of an array, need to be re-coded to handle bad values. For floating-point datatypes, "NaN" and "Inf" can be used to flag bad values, but by default special values are used (Default bad values). I do not have any benchmarks to see which option is faster.

As of PDL 2.040, you can have different bad values for separate ndarrays of the same type.

  A quick overview
 pdl> $x = sequence(4,3);
 pdl> p $x
 [
  [ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11]
 ]
 pdl> $x = $x->setbadif( $x % 3 == 2 )
 pdl> p $x
 [
  [  0   1 BAD   3]
  [  4 BAD   6   7]
  [BAD   9  10 BAD]
 ]
 pdl> $x *= 3
 pdl> p $x
 [
  [  0   3 BAD   9]
  [ 12 BAD  18  21]
  [BAD  27  30 BAD]
 ]
 pdl> p $x->sum
 120

"demo bad" and "demo bad2" within perldl or pdl2 gives a demonstration of some of the things possible with bad values. These are also available on PDL's web-site, at http://pdl.perl.org/demos/. See PDL::Bad for useful routines for working with bad values and t/bad.t to see them in action.

To find out if a routine supports bad values, use the "badinfo" command in perldl or pdl2 or the "-b" option to pdldoc. This facility is currently a 'proof of concept' (or, more realistically, a quick hack) so expect it to be rough around the edges.

Each ndarray contains a flag - accessible via "$pdl->badflag" - to say whether there's any bad data present:

•   If false/0, which means there's no bad data here, the code supplied by the "Code" option to "pp_def()" is executed.

•   If true/1, then this says there MAY be bad data in the ndarray, so use the code in the "BadCode" option (assuming that the "pp_def()" for this routine has been updated to have a BadCode key). You get all the advantages of threading, as with the "Code" option, but it will run slower since you are going to have to handle the presence of bad values.

If you create an ndarray, it will have its bad-value flag set to 0. To change this, use "$pdl->badflag($new_bad_status)", where $new_bad_status can be 0 or 1. When a routine creates an ndarray, its bad-value flag will depend on the input ndarrays: unless over-ridden (see the "CopyBadStatusCode" option to "pp_def"), the bad-value flag will be set true if any of the input ndarrays contain bad values. To check that an ndarray really contains bad data, use the "check_badflag" method.

NOTE: propagation of the badflag

If you change the badflag of an ndarray, this change is propagated to all the children of an ndarray, so

   pdl> $x = zeroes(20,30);
   pdl> $y = $x->slice('0:10,0:10');
   pdl> $c = $y->slice(',(2)');
   pdl> print ">>c: ", $c->badflag, "\n";
   >>c: 0
   pdl> $x->badflag(1);
   pdl> print ">>c: ", $c->badflag, "\n";
   >>c: 1

No change is made to the parents of an ndarray, so

   pdl> print ">>a: ", $x->badflag, "\n";
   >>a: 1
   pdl> $c->badflag(0);
   pdl> print ">>a: ", $x->badflag, "\n";
   >>a: 1

Thoughts:

•   the badflag can ONLY be cleared IF an ndarray has NO parents, and that this change will propagate to all the children of that ndarray. I am not so keen on this anymore (too awkward to code, for one).

•   "$x->badflag(1)" should propagate the badflag to BOTH parents and children.

This shouldn't be hard to implement (although an initial attempt failed!). Does it make sense though? There's also the issue of what happens if you change the badvalue of an ndarray - should these propagate to children/parents (yes) or whether you should only be able to change the badvalue at the 'top' level - i.e. those ndarrays which do not have parents.

The "orig_badvalue()" method returns the compile-time value for a given datatype. It works on ndarrays, PDL::Type objects, and numbers - eg

  $pdl->orig_badvalue(), byte->orig_badvalue(), and orig_badvalue(4).

It also has a horrible name...

To get the current bad value, use the "badvalue()" method - it has the same syntax as "orig_badvalue()".

To change the current bad value, supply the new number to badvalue - eg

  $pdl->badvalue(2.3), byte->badvalue(2), badvalue(5,-3e34).

Note: the value is silently converted to the correct C type, and returned - i.e. "byte->badvalue(-26)" returns 230 on my Linux machine.

Note that changes to the bad value are NOT propagated to previously-created ndarrays - they will still have the bad value set, but suddenly the elements that were bad will become 'good', but containing the old bad value. See discussion below. It's not a problem for floating-point types which use NaN, since you can not change their badvalue.

  Bad values and boolean operators
For those boolean operators in PDL::Ops, evaluation on a bad value returns the bad value. Whilst this means that

 $mask = $img > $thresh;

correctly propagates bad values, it will cause problems for checks such as

 do_something() if any( $img > $thresh );

which need to be re-written as something like

 do_something() if any( setbadtoval( ($img > $thresh), 0 ) );

When using one of the 'projection' functions in PDL::Ufunc - such as orover - bad values are skipped over (see the documentation of these functions for the current (poor) handling of the case when all elements are bad).

  A bad value for each ndarray, and related issues
There is one default bad value for each datatype, but you can have a separate bad value for each ndarray as of PDL 2.040.

IMPLEMENTATION DETAILS
PDL code just needs to access the %PDL::Config array (e.g. Basic/Bad/bad.pd) to find out whether bad-value support is required.

A new flag has been added to the state of an ndarray - "PDL_BADVAL". If unset, then the ndarray does not contain bad values, and so all the support code can be ignored. If set, it does not guarantee that bad values are present, just that they should be checked for. Thanks to Christian, "badflag()" - which sets/clears this flag (see Basic/Bad/bad.pd) - will update ALL the children/grandchildren/etc of an ndarray if its state changes (see "badflag" in Basic/Bad/bad.pd and "propagate_badflag" in Basic/Core/Core.xs.PL). It's not clear what to do with parents: I can see the reason for propagating a 'set badflag' request to parents, but I think a child should NOT be able to clear the badflag of a parent. There's also the issue of what happens when you change the bad value for an ndarray.

The "pdl_trans" structure has been extended to include an integer value, "bvalflag", which acts as a switch to tell the code whether to handle bad values or not. This value is set if any of the input ndarrays have their "PDL_BADVAL" flag set (although this code can be replaced by setting "FindBadStateCode" in pp_def). The logic of the check is going to get a tad more complicated if I allow routines to fall back to using the "Code" section for floating-point types.

The default bad values are now stored in a structure within the Core PDL structure - "PDL.bvals" (eg Basic/Core/pdlcore.h.PL); see also "typedef badvals" in Basic/Core/pdl.h.PL and the BOOT code of Basic/Core/Core.xs.PL where the values are initialised to (hopefully) sensible values. See PDL/Bad/bad.pd for read/write routines to the values.

  Why not make a PDL subclass?
The support for bad values could have been done as a PDL sub-class. The advantage of this approach would be that you only load in the code to handle bad values if you actually want to use them. The downside is that the code then gets separated: any bug fixes/improvements have to be done to the code in two different files. With the present approach the code is in the same "pp_def" function (although there is still the problem that both "Code" and "BadCode" sections need updating).

  Default bad values
The default/original bad values are set to (taken from the Starlink distribution):

  #include <limits.h>

  PDL_Byte    ==  UCHAR_MAX
  PDL_Short   ==   SHRT_MIN
  PDL_Ushort  ==  USHRT_MAX
  PDL_Long    ==    INT_MIN
  PDL_Float   ==   -FLT_MAX
  PDL_Double  ==   -DBL_MAX

  How do I change a routine to handle bad values?
Examples can be found in most of the *.pd files in Basic/ (and hopefully many more places soon!). Some of the logic might appear a bit unclear - that's probably because it is! Comments appreciated.

All routines should automatically propagate the bad status flag to output ndarrays, unless you declare otherwise.

If a routine explicitly deals with bad values, you must provide this option to pp_def:

   HandleBad => 1

This ensures that the correct variables are initialised for the $ISBAD etc macros. It is also used by the automatic document-creation routines to provide default information on the bad value support of a routine without the user having to type it themselves (this is in its early stages).

To flag a routine as NOT handling bad values, use

   HandleBad => 0

This should cause the routine to print a warning if it's sent any ndarrays with the bad flag set. Primitive's "intover" has had this set - since it would be awkward to convert - but I've not tried it out to see if it works.

If you want to handle bad values but not set the state of all the output ndarrays, or if it's only one input ndarray that's important, then look at the PP rules "NewXSFindBadStatus" and "NewXSCopyBadStatus" and the corresponding "pp_def" options:

FindBadStatusCode
    By default, "FindBadStatusCode" creates code which sets "$PRIV(bvalflag)" depending on the state of the bad flag of the input ndarrays: see "findbadstatus" in Basic/Gen/PP.pm. User-defined code should also store the value of "bvalflag" in the "$BADFLAGCACHE()" variable.

CopyBadStatusCode
    The default code here is a bit simpler than for "FindBadStatusCode": the bad flag of the output ndarrays are set if "$BADFLAGCACHE()" is true after the code has been evaluated. Sometimes "CopyBadStatusCode" is set to an empty string, with the responsibility of setting the badflag of the output ndarray left to the "BadCode" section (e.g. the "xxxover" routines in Basic/Primitive/primitive.pd).

    Prior to PDL 2.4.3 we used "$PRIV(bvalflag)" instead of "$BADFLAGCACHE()". This is dangerous since the "$PRIV()" structure is not guaranteed to be valid at this point in the code.

If you have a routine that you want to be able to use as in-place, look at the routines in bad.pd (or ops.pd) which use the "in-place" option to see how the bad flag is propagated to children using the "xxxBadStatusCode" options. I decided not to automate this as rules would be a little complex, since not every in-place op will need to propagate the badflag (eg unary functions).

If the option

   HandleBad => 1

is given, then many things happen. For integer types, the readdata code automatically creates a variable called "(pdl name)_badval", which contains the bad value for that ndarray (see "get_xsdatapdecl()" in Basic/Gen/PP/PdlParObjs.pm). However, do not hard code this name into your code! Instead use macros (thanks to Tuomas for the suggestion):

  '$ISBAD(a(n=>1))'  expands to '$a(n=>1) == a_badval'
  '$ISGOOD(a())'                '$a()     != a_badval'
  '$SETBAD(bob())'              '$bob()    = bob_badval'

well, the "$a(...)" is expanded as well. Also, you can use a "$" before the pdl name, if you so wish, but it begins to look like line noise - eg "$ISGOOD($a())".

If you cache an ndarray value in a variable -- eg "index" in slices.pd -- the following routines are useful:

   '$ISBADVAR(c_var,pdl)'       'c_var == pdl_badval'
   '$ISGOODVAR(c_var,pdl)'      'c_var != pdl_badval'
   '$SETBADVAR(c_var,pdl)'      'c_var  = pdl_badval'

The following have been introduced, They may need playing around with to improve their use.

  '$PPISBAD(CHILD,[i])          'CHILD_physdatap[i] == CHILD_badval'
  '$PPISGOOD(CHILD,[i])         'CHILD_physdatap[i] != CHILD_badval'
  '$PPSETBAD(CHILD,[i])         'CHILD_physdatap[i]  = CHILD_badval'

You can use "NaN" as the bad value for any floating-point type, including complex.

This all means that you can change

   Code => '$a() = $b() + $c();'

to

   BadCode => 'if ( $ISBAD(b()) || $ISBAD(c()) ) {
                 $SETBAD(a());
               } else {
                 $a() = $b() + $c();
               }'

leaving Code as it is. PP::PDLCode will then create a loop something like

   if ( __trans->bvalflag ) {
        threadloop over BadCode
   } else {
        threadloop over Code
   }

(it's probably easier to just look at the .xs file to see what goes on).

  Going beyond the Code section
Similar to "BadCode", there's "BadBackCode", and "BadRedoDimsCode".

Handling "EquivCPOffsCode" is a bit different: under the assumption that the only access to data is via the "$EQUIVCPOFFS(i,j)" macro, then we can automatically create the 'bad' version of it; see the "[EquivCPOffsCode]" and "[Code]" rules in PDL::PP.

  Macro access to the bad flag of an ndarray
Macros have been provided to provide access to the bad-flag status of a pdl:

  '$PDLSTATEISBAD(a)'    -> '($PDL(a)->state & PDL_BADVAL) > 0'
  '$PDLSTATEISGOOD(a)'      '($PDL(a)->state & PDL_BADVAL) == 0'

  '$PDLSTATESETBAD(a)'      '$PDL(a)->state |= PDL_BADVAL'
  '$PDLSTATESETGOOD(a)'     '$PDL(a)->state &= ~PDL_BADVAL'

For use in "xxxxBadStatusCode" (+ other stuff that goes into the INIT: section) there are:

  '$SETPDLSTATEBAD(a)'       -> 'a->state |= PDL_BADVAL'
  '$SETPDLSTATEGOOD(a)'      -> 'a->state &= ~PDL_BADVAL'

  '$ISPDLSTATEBAD(a)'        -> '((a->state & PDL_BADVAL) > 0)'
  '$ISPDLSTATEGOOD(a)'       -> '((a->state & PDL_BADVAL) == 0)'

In PDL 2.4.3 the "$BADFLAGCACHE()" macro was introduced for use in "FindBadStatusCode" and "CopyBadStatusCode".

WHAT ABOUT DOCUMENTATION?
One of the strengths of PDL is its on-line documentation. The aim is to use this system to provide information on how/if a routine supports bad values: in many cases "pp_def()" contains all the information anyway, so the function-writer doesn't need to do anything at all! For the cases when this is not sufficient, there's the "BadDoc" option. For code written at the Perl level - i.e. in a .pm file - use the "=for bad" pod directive.

This information will be available via man/pod2man/html documentation. It's also accessible from the "perldl" or "pdl2" shells - using the "badinfo" command - and the "pdldoc" shell command - using the "-b" option.

CURRENT ISSUES
There are a number of areas that need work, user input, or both! They are mentioned elsewhere in this document, but this is just to make sure they don't get lost.

  Trapping invalid mathematical operations
Should we add exceptions to the functions in "PDL::Ops" to set the output bad for out-of-range input values?

 pdl> p log10(pdl(10,100,-1))

I would like the above to produce "[1 2 BAD]", but this would slow down operations on all ndarrays. We could check for "NaN"/"Inf" values after the operation, but I doubt that would be any faster.

  Dataflow of the badflag
Currently changes to the bad flag are propagated to the children of an ndarray, but perhaps they should also be passed on to the parents as well. With the advent of per-ndarray bad values we need to consider how to handle changes to the value used to represent bad items too.

EVERYTHING ELSE
The build process has been affected. The following files are now created during the build:

  Basic/Core/pdlcore.h      pdlcore.h.PL
             pdlcore.c      pdlcore.c.PL
             pdlapi.c       pdlapi.c.PL
             Core.xs        Core.xs.PL
             Core.pm        Core.pm.PL

Several new files have been added:

  Basic/Pod/BadValues.pod (i.e. this file)

  t/bad.t

  Basic/Bad/
  Basic/Bad/Makefile.PL
            bad.pd

etc

TODO/SUGGESTIONS

•   what to do about "$y = pdl(-2); $x = log10($y)" - $x should be set bad, but it currently isn't.

•   Allow the operations in PDL::Ops to skip the check for bad values when using NaN as a bad value and processing a floating-point ndarray. Needs a fair bit of work to PDL::PP::PDLCode.

•   "$pdl->badflag()" now updates all the children of this ndarray as well. However, not sure what to do with parents, since:

      $y = $x->slice();
      $y->badflag(0)

    doesn't mean that $x shouldn't have its badvalue cleared. however, after

      $y->badflag(1)

    it's sensible to assume that the parents now get flagged as containing bad values.

    PERHAPS you can only clear the bad value flag if you are NOT a child of another ndarray, whereas if you set the flag then all children AND parents should be set as well?

    Similarly, if you change the bad value in an ndarray, should this be propagated to parent & children? Or should you only be able to do this on the 'top-level' ndarray? Nasty...

•   some of the names aren't appealing - I'm thinking of "orig_badvalue()" in Basic/Bad/bad.pd in particular. Any suggestions appreciated.

AUTHOR
Copyright (C) Doug Burke (djburke@cpan.org), 2000, 2006.

The per-ndarray bad value support is by Heiko Klein (2006).

Commercial reproduction of this documentation in a different format is forbidden.