Broadcasting rules

In any PDL expression, the active dims appropriate for each operator are used starting at the 0 dim and working forward through the dim list of each object. All additional dims after the active dims are "broadcast dims". The broadcast dims do not have to agree exactly: they are coerced to agree according to simple rules:

• Null PDLs match any dim list (see below).
• Dims with sizes other than 1 must all agree in size.
• Dims of size 1 are silently repeated as necessary except for "[phys]" PDLs.
• Missing dims are expanded appropriately.

A size-1 dim for "[phys]" PDLs causes an exception if the dim is used in another parameter and has a size greater than 1.

The "size 1" rule implements "generalized scalar" operation, by analogy to scalar multiplication. The "missing dims" rule acknowledges the ambiguity between a missing dim and a dim of size 1.

Null PDLs

PDLs on the left-hand side of assignment can have the special value "Null". A null PDL has no dim list and no set size; its shape is determined by the computed shape of the expression being assigned to it. Null PDLs contain no values and can only be assigned to. When assigned to (e.g. via the ".=" operator), they cease to be null PDLs.

To create a null PDL, use "PDL->null()".

Empty PDLs

PDLs can represent the empty set using "structured Empty" variables. An empty PDL is not a null PDL.

Any dim of a PDL can be set explicitly to size 0. If so, the PDL contains zero values (because the total number of values is the product of all the sizes in the PDL's shape or dimlist).

Scalar PDLs are zero-dimensional and have no entries in the dim list, so they cannot be empty. 1-D and higher PDLs can be empty. Empty PDLs are useful for set operations, and are most commonly encountered in the output from selection operators such as which and whichND. Not all empty PDLs have the same broadcasting properties -- e.g. a 2x0-PDL represents a collection of 2-vectors that happens to contain no elements, while a simple 0-PDL represents a collection of scalar values (that also happens to contain no elements).

Note that 0 dims are not adjustable via the broadcasting rules -- a dim with size 0 can only match a corresponding dim of size 0 or 1.

Broadcast rules and assignments

Versions of PDL through 2.4.10 have some irregularity with broadcasting and assignments. Currently the broadcasting engine performs a full expansion of both sides of the computed assignment operator ".=" (which assigns values to a pre-existing PDL). This leads to counter-intuitive behavior in some cases:

•

Empty PDLs and generalized scalars

Generalized scalars (PDLs with a dim of size 1) can match any size in the corresponding dim, including 0. Thus,

    $x = ones(2,0);
    $y = sequence(2,1);
    $c = $x * $y;
    print $c;
    

prints "Empty[2,0]".

This behavior is counterintuitive but desirable, and will be preserved in future versions of PDL.

barf

Standard error reporting routine for PDL.

"barf()" is the routine PDL modules should call to report errors. This is because "barf()" will report the error as coming from the correct line in the module user's script rather than in the PDL module.

For now, barf just calls Carp::confess()

Remember "barf()" is your friend. *Use* it!

At the perl level:

 barf("User has too low an IQ!");

In C or XS code:

 barf("You have made %d errors", count);

Note: this is one of the few functions ALWAYS exported by PDL::Core

pdl

PDL constructor - creates new ndarray from perl scalars/arrays, ndarrays, and strings

 $double_pdl = pdl(SCALAR|ARRAY REFERENCE|ARRAY|STRING);  # default type
 $type_pdl   = pdl(PDL::Type,SCALAR|ARRAY REFERENCE|ARRAY|STRING);

 $x = pdl [1..10];                    # 1D array of doubles
 $x = pdl ([1..10]);                  # 1D array
 $x = pdl (1,2,3,4);                  # Ditto
 $y = pdl [[1,2,3],[4,5,6]];          # 2D 3x2 array
 $y = pdl "[[1,2,3],[4,5,6]]";        # Ditto (slower)
 $y = pdl "[1 2 3; 4 5 6]";           # Ditto
 $y = pdl q[1 2 3; 4 5 6];            # Ditto, using the q quote operator
 $y = pdl "1 2 3; 4 5 6";             # Ditto, less obvious, but still works
 $y = pdl 42                          # 0-dimensional scalar
 $c = pdl $x;                         # Make a new copy
 $u = pdl ushort(), 42                # 0-dimensional ushort scalar
 $y = pdl(byte(),[[1,2,3],[4,5,6]]);  # 2D byte ndarray
 $n = pdl indx(), [1..5];             # 1D array of indx values
 $n = pdl indx, [1..5];               # ... can leave off parens
 $n = indx( [1..5] );                 # ... still the same!
 $n = pdl cdouble, 2, 3;              # native complex numbers, zero imaginary
 use Math::Complex qw(cplx);
 $n = pdl cdouble, 2, cplx(2, 1));    # explicit type
 $n = pdl 2, cplx(2, 1);              # default cdouble if Math::Complex obj
 $x = pdl([[1,2,3],[4,5,6]]);         # 2D
 $x = pdl([1,2,3],[4,5,6]);           # 2D

Note the last two are equivalent - a list is automatically converted to a list reference for syntactic convenience. i.e. you can omit the outer "[]"

You can mix and match arrays, array refs, and PDLs in your argument list, and "pdl" will sort them out. You get back a PDL whose last (slowest running) dim runs across the top level of the list you hand in, and whose first (fastest running) dim runs across the deepest level that you supply.

At the moment, you cannot mix and match those arguments with string arguments, though we can't imagine a situation in which you would really want to do that.

The string version of pdl also allows you to use the strings "bad", "inf", and "nan", and it will insert the values that you mean (and set the bad flag if you use "bad"). You can mix and match case, though you shouldn't. Here are some examples:

 $bad = pdl q[1 2 3 bad 5 6];  # Set fourth element to the bad value
 $bad = pdl q[1 2 3 BAD 5 6];  # ditto
 $bad = pdl q[1 2 inf bad 5];  # now third element is IEEE infinite value
 $bad = pdl q[nan 2 inf -inf]; # first value is IEEE nan value

The default constructor uses IEEE double-precision floating point numbers. You can use other types, but you will get a warning if you try to use "nan" with integer types (it will be replaced with the "bad" value) and you will get a fatal error if you try to use "inf".

Throwing a PDL into the mix has the same effect as throwing in a list ref:

  pdl(pdl(1,2),[3,4])

is the same as

  pdl([1,2],[3,4]).

All of the dimensions in the list are "padded-out" with undefval to meet the widest dim in the list, so (e.g.)

  $x = pdl([[1,2,3],[2]])

gives you the same answer as

  $x = pdl([[1,2,3],[2,undef,undef]]);

If your PDL module has bad values compiled into it (see PDL::Bad), you can pass BAD values into the constructor within pre-existing PDLs. The BAD values are automatically kept BAD and propagated correctly.

"pdl()" is a functional synonym for the 'new' constructor, e.g.:

 $x = new PDL [1..10];

In order to control how undefs are handled in converting from perl lists to PDLs, one can set the variable $PDL::undefval. For example:

 $foo = [[1,2,undef],[undef,3,4]];
 $PDL::undefval = -999;
 $f = pdl $foo;
 print $f
 [
  [   1    2 -999]
  [-999    3    4]
 ]

$PDL::undefval defaults to zero.

As a final note, if you include an Empty PDL in the list of objects to construct into a PDL, it is kept as a placeholder pane -- so if you feed in (say) 7 objects, you get a size of 7 in the 0th dim of the output PDL. The placeholder panes are completely padded out. But if you feed in only a single Empty PDL, you get back the Empty PDL (no padding).

empty

Returns an empty ndarray, with a single zero-length dimension. Only available as a function, not a method.

 $x = empty; # defaults to lowest type so it can always be promoted up
 $x = empty(float);

null

Returns a 'null' ndarray. It is an error to pass one of these as an input to a function.

 $x = null;

"null()" has a special meaning to PDL::PP. It is used to flag a special kind of empty ndarray, which can grow to appropriate dimensions to store a result (as opposed to storing a result in an existing ndarray).

 pdl> sumover sequence(10,10), $ans=null;p $ans
 [45 145 245 345 445 545 645 745 845 945]

nullcreate

Returns a 'null' ndarray.

 $x = PDL->nullcreate($arg)

This is an routine used by many of the broadcasting primitives (i.e. sumover, minimum, etc.) to generate a null ndarray for the function's output that will behave properly for derived (or subclassed) PDL objects.

For the above usage: If $arg is a PDL, or a derived PDL, then "$arg->null" is returned. If $arg is a scalar (i.e. a zero-dimensional PDL) then "PDL->null" is returned.

 PDL::Derived->nullcreate(10)
   returns PDL::Derived->null.
 PDL->nullcreate($pdlderived)
   returns $pdlderived->null.

nelem

Return the number of elements in an ndarray

 $n = nelem($ndarray); $n = $ndarray->nelem;

 $mean = sum($data)/nelem($data);

dims

Return ndarray dimensions as a perl list

 @dims = $ndarray->dims;  @dims = dims($ndarray);

 pdl> p @tmp = dims zeroes 10,3,22
 10 3 22

See also "shape" which returns an ndarray instead.

shape

Return ndarray dimensions as an ndarray

 $shape = $ndarray->shape;  $shape = shape($ndarray);

 pdl> p $shape = shape zeroes 10,3,22
 [10 3 22]

See also "dims" which returns a perl list.

ndims

Returns the number of dimensions in an ndarray. Alias for getndims.

getndims

Returns the number of dimensions in an ndarray

 $ndims = $ndarray->getndims;

 pdl> p zeroes(10,3,22)->getndims
 3

dim

Returns the size of the given dimension of an ndarray. Alias for getdim.

getdim

Returns the size of the given dimension.

 $dim0 = $ndarray->getdim(0);

 pdl> p zeroes(10,3,22)->getdim(1)
 3

Negative indices count from the end of the dims array. Indices beyond the end will return a size of 1. This reflects the idea that any pdl is equivalent to an infinitely dimensional array in which only a finite number of dimensions have a size different from one. For example, in that sense a 3D ndarray of shape [3,5,2] is equivalent to a [3,5,2,1,1,1,1,1,....] ndarray. Accordingly,

  print $x->getdim(10000);

will print 1 for most practically encountered ndarrays.

topdl

alternate ndarray constructor - ensures arg is an ndarray

 $x = topdl(SCALAR|ARRAY REFERENCE|ARRAY);

The difference between pdl() and "topdl()" is that the latter will just 'fall through' if the argument is already an ndarray. It will return a reference and NOT a new copy.

This is particularly useful if you are writing a function which is doing some fiddling with internals and assumes an ndarray argument (e.g. for method calls). Using "topdl()" will ensure nothing breaks if passed with '2'.

Note that "topdl()" is not exported by default (see example below for usage).

 use PDL::Core ':Internal'; # use the internal routines of
                            # the Core module
 $x = topdl 43;             # $x is ndarray with value '43'
 $y = topdl $ndarray;       # fall through
 $x = topdl (1,2,3,4);      # Convert 1D array

get_datatype

Internal: Return the numeric value identifying the ndarray datatype

 $x = $ndarray->get_datatype;

Mainly used for internal routines.

NOTE: get_datatype returns 'just a number' not any special type object, unlike "type".

howbig

Returns the sizeof an ndarray datatype in bytes.

Note that "howbig()" is not exported by default (see example below for usage).

 use PDL::Core ':Internal'; # use the internal routines of
                            # the Core module
 $size = howbig($ndarray->get_datatype);

Mainly used for internal routines.

NOTE: NOT a method! This is because get_datatype returns 'just a number' not any special object.

 pdl> p howbig(ushort([1..10])->get_datatype)
 2

get_dataref

Return the internal data for an ndarray, as a perl SCALAR ref.

Most ndarrays hold their internal data in a packed perl string, to take advantage of perl's memory management. This gives you direct access to the string, which is handy when you need to manipulate the binary data directly (e.g. for file I/O). If you modify the string, you'll need to call "upd_data" afterward, to make sure that the ndarray points to the new location of the underlying perl variable.

Calling "get_dataref" automatically physicalizes your ndarray (see "make_physical"). You definitely don't want to do anything to the SV to truncate or deallocate the string, unless you correspondingly call "reshape" to make the PDL match its new data dimension.

You definitely don't want to use get_dataref unless you know what you are doing (or are trying to find out): you can end up scrozzling memory if you shrink or eliminate the string representation of the variable. Here be dragons.

upd_data

Update the data pointer in an ndarray to match its perl SV.

This is useful if you've been monkeying with the packed string representation of the PDL, which you probably shouldn't be doing anyway. (see "get_dataref".)

broadcastids

Returns the ndarray broadcast IDs as a perl list

Note that "broadcastids()" is not exported by default (see example below for usage).

 use PDL::Core ':Internal'; # use the internal routines of
                            # the Core module
 @ids = broadcastids $ndarray;

doflow

Turn on dataflow, forward only. This means any transformations (a.k.a. PDL operations) applied to this ndarray afterwards will have forward dataflow:

  $x = sequence 3;
  $x->doflow;
  $y = $x + 1;
  $x += 3;
  print "$y\n"; # [4 5 6]

As of 2.064, the core API does not automatically sever transformations that have forward dataflow into them:

  # following from the above
  $y->set(1, 9); # value now [4 9 6]
  $x += 11;
  print "$y\n"; # [15 16 17] - previously would have been [4 9 6]

If you want to sever such transformations, call "sever" on the child ndarray (above, $y).

 $x->doflow;  doflow($x);

flows

Whether or not an ndarray is indulging in dataflow

 something if $x->flows; $hmm = flows($x);

new

new ndarray constructor method

 $x = PDL->new(SCALAR|ARRAY|ARRAY REF|STRING);

 $x = PDL->new(42);             # new from a Perl scalar
 $x = new PDL 42;               # ditto
 $y = PDL->new(@list_of_vals);  # new from Perl list
 $y = new PDL @list_of_vals;    # ditto
 $z = PDL->new(\@list_of_vals); # new from Perl list reference
 $w = PDL->new("[1 2 3]");      # new from Perl string, using
                                # Matlab constructor syntax

Constructs ndarray from perl numbers and lists and strings with Matlab/Octave style constructor syntax.

The string input is fairly versatile though not performance optimized. The goal is to make it easy to copy and paste code from PDL output and to offer a familiar Matlab syntax for ndarray construction. As of May, 2010, it is a new feature, so feel free to report bugs or suggest new features. See documentation for pdl for more examples of usage.

copy

Make a physical copy of an ndarray

 $new = $old->copy;

Since "$new = $old" just makes a new reference, the "copy" method is provided to allow real independent copies to be made.

hdr_copy

Return an explicit copy of the header of a PDL.

hdr_copy is just a wrapper for the internal routine _hdr_copy, which takes the hash ref itself. That is the routine which is used to make copies of the header during normal operations if the hdrcpy() flag of a PDL is set.

General-purpose deep copies are expensive in perl, so some simple optimization happens:

If the header is a tied array or a blessed hash ref with an associated method called "copy", then that ->copy method is called. Otherwise, all elements of the hash are explicitly copied. References are recursively deep copied.

This routine seems to leak memory.

unwind

Return an ndarray which is the same as the argument except that all broadcastids have been removed.

 $y = $x->unwind;

make_physical

Make sure the data portion of an ndarray can be accessed from XS code.

 $x->make_physical;
 $x->call_my_xs_method;

Ensures that an ndarray gets its own allocated copy of data. This obviously implies that there are certain ndarrays which do not have their own data. These are so called virtual ndarrays that make use of the vaffine optimisation (see PDL::Indexing). They do not have their own copy of data but instead store only access information to some (or all) of another ndarray's data.

Note: this function should not be used unless absolutely necessary since otherwise memory requirements might be severely increased. Instead of writing your own XS code with the need to call "make_physical" you might want to consider using the PDL preprocessor (see PDL::PP) which can be used to transparently access virtual ndarrays without the need to physicalise them (though there are exceptions).

dummy

Insert a 'dummy dimension' of given length (defaults to 1)

No relation to the 'Dungeon Dimensions' in Discworld!

Negative positions specify relative to last dimension, i.e. "dummy(-1)" appends one dimension at end, "dummy(-2)" inserts a dummy dimension in front of the last dim, etc.

If you specify a dimension position larger than the existing dimension list of your PDL, the PDL gets automagically padded with extra dummy dimensions so that you get the dim you asked for, in the slot you asked for. This could cause you trouble if, for example, you ask for $x->dummy(5000,1) because $x will get 5,000 dimensions, each of rank 1.

Because padding at the beginning of the dimension list moves existing dimensions from slot to slot, it's considered unsafe, so automagic padding doesn't work for large negative indices -- only for large positive indices.

 $y = $x->dummy($position[,$dimsize]);

 pdl> p sequence(3)->dummy(0,3)
 [
  [0 0 0]
  [1 1 1]
  [2 2 2]
 ]
 pdl> p sequence(3)->dummy(3,2)
 [
  [
   [0 1 2]
  ]
  [
   [0 1 2]
  ]
 ]
 pdl> p sequence(3)->dummy(-3,2)
 Runtime error: PDL: For safety, <pos> < -(dims+1) forbidden in dummy.  min=-2, pos=-3

dup

Duplicates an ndarray along a dimension

 $x = sequence(3);
 $y = $x->dup(0, 2); # doubles along first dimension
 # $y now [0 1 2 0 1 2]

dupN

Duplicates an ndarray along several dimensions

 $x = sequence(3,2);
 $y = $x->dupN(2, 3); # doubles along first dimension, triples along second
 # [
 #  [0 1 2 0 1 2]
 #  [3 4 5 3 4 5]
 #  [0 1 2 0 1 2]
 #  [3 4 5 3 4 5]
 # ]

inflateN

Inflates an ndarray along several dimensions, useful for e.g. Kronecker products

cf "dupN"

 $x = sequence(3,2);
 $y = $x->inflateN(2, 2); # doubles along first two dimensions
 # [
 #  [0 0 1 1 2 2]
 #  [0 0 1 1 2 2]
 #  [3 3 4 4 5 5]
 #  [3 3 4 4 5 5]
 # ]

clump

"clumps" several dimensions into one large dimension

If called with one argument $n clumps the first $n dimensions into one. For example, if $x has dimensions "(5,3,4)" then after

 $y = $x->clump(2);   # Clump 2 first dimensions

the variable $y will have dimensions "(15,4)" and the element "$y->at(7,3)" refers to the element "$x->at(1,2,3)".

Use "clump(-1)" to flatten an ndarray. The method flat is provided as a convenient alias.

Clumping with a negative dimension in general leaves that many dimensions behind -- e.g. clump(-2) clumps all of the first few dimensions into a single one, leaving a 2-D ndarray.

If "clump" is called with an index list with more than one element it is treated as a list of dimensions that should be clumped together into one. The resulting clumped dim is placed at the position of the lowest index in the list. This convention ensures that "clump" does the expected thing in the usual cases. The following example demonstrates typical usage:

  $x = sequence 2,3,3,3,5; # 5D ndarray
  $c = $x->clump(1..3);    # clump all the dims 1 to 3 into one
  print $c->info;          # resulting 3D ndarray has clumped dim at pos 1
 PDL: Double D [2,27,5]

broadcast_define

define functions that support broadcasting at the perl level

 broadcast_define 'tline(a(n);b(n))', over {
  line $_[0], $_[1]; # make line compliant with broadcasting
 };

"broadcast_define" provides some support for broadcasting (see PDL::Indexing) at the perl level. It allows you to do things for which you normally would have resorted to PDL::PP (see PDL::PP); however, it is most useful to wrap existing perl functions so that the new routine supports PDL broadcasting.

"broadcast_define" is used to define new broadcasting aware functions. Its first argument is a symbolic repesentation of the new function to be defined. The string is composed of the name of the new function followed by its signature (see PDL::Indexing and PDL::PP) in parentheses. The second argument is a subroutine that will be called with the slices of the actual runtime arguments as specified by its signature. Correct dimension sizes and minimal number of dimensions for all arguments will be checked (assuming the rules of PDL broadcasting, see PDL::Indexing).

The actual work is done by the "signature" class which parses the signature string, does runtime dimension checks and the routine "broadcastover" that generates the loop over all appropriate slices of pdl arguments and creates pdls as needed.

Similar to "pp_def" and its "OtherPars" option it is possible to define the new function so that it accepts normal perl args as well as ndarrays. You do this by using the "NOtherPars" parameter in the signature. The number of "NOtherPars" specified will be passed unaltered into the subroutine given as the second argument of "broadcast_define". Let's illustrate this with an example:

 PDL::broadcast_define 'triangles(inda();indb();indc()), NOtherPars => 2',
  PDL::over {
    ${$_[3]} .= $_[4].join(',',map {$_->at} @_[0..2]).",-1,\n";
  };

This defines a function "triangles" that takes 3 ndarrays as input plus 2 arguments which are passed into the routine unaltered. This routine is used to collect lists of indices into a perl scalar that is passed by reference. Each line is preceded by a prefix passed as $_[4]. Here is typical usage:

 $txt = '';
 triangles(pdl(1,2,3),pdl(1),pdl(0),\$txt," "x10);
 print $txt;

resulting in the following output

 1,1,0,-1,
 2,1,0,-1,
 3,1,0,-1,

which is used in PDL::Graphics::TriD::VRML to generate VRML output.

Currently, this is probably not much more than a POP (proof of principle) but is hoped to be useful enough for some real life work.

Check PDL::PP for the format of the signature. Currently, the "[t]" qualifier and all type qualifiers are ignored.

broadcast

Use explicit broadcasting over specified dimensions (see also PDL::Indexing)

 $y = $x->broadcast($dim,[$dim1,...])

 $x = zeroes 3,4,5;
 $y = $x->broadcast(2,0);

Same as "broadcast1", i.e. uses broadcast id 1.

broadcast1

Explicit broadcasting over specified dims using broadcast id 1.

 $xx = $x->broadcast1(3,1)

 Wibble

Convenience function interfacing to PDL::Slices::broadcastI.

broadcast2

Explicit broadcasting over specified dims using broadcast id 2.

 $xx = $x->broadcast2(3,1)

 Wibble

Convenience function interfacing to PDL::Slices::broadcastI.

broadcast3

Explicit broadcasting over specified dims using broadcast id 3.

 $xx = $x->broadcast3(3,1)

 Wibble

Convenience function interfacing to PDL::Slices::broadcastI.

sever

sever any links of this ndarray to parent ndarrays

In PDL it is possible for an ndarray to be just another view into another ndarray's data. In that case we call this ndarray a virtual ndarray and the original ndarray owning the data its parent. In other languages these alternate views sometimes run by names such as alias or smart reference.

Typical functions that return such ndarrays are "slice", "xchg", "index", etc. Sometimes, however, you would like to separate the virtual ndarray from its parent's data and just give it a life of its own (so that manipulation of its data doesn't change the parent). This is simply achieved by using "sever". For example,

   $x = $pdl->index(pdl(0,3,7))->sever;
   $x++;       # important: $pdl is not modified!

In many (but not all) circumstances it acts therefore similar to copy. However, in general performance is better with "sever" and secondly, "sever" doesn't lead to futile copying when used on ndarrays that already have their own data. On the other hand, if you really want to make sure to work on a copy of an ndarray use copy.

   $x = zeroes(20);
   $x->sever;   # NOOP since $x is already its own boss!

Again note: "sever" is not the same as copy! For example,

   $x = zeroes(1); # $x does not have a parent, i.e. it is not a slice etc
   $y = $x->sever; # $y is now pointing to the same ndarray as $x
   $y++;
   print $x;
 [1]

but

   $x = zeroes(1);
   $y = $x->copy; # $y is now pointing to a new ndarray
   $y++;
   print $x;
 [0]

info

Return formatted information about an ndarray.

 $x->info($format_string);

 print $x->info("Type: %T Dim: %-15D State: %S");

Returns a string with info about an ndarray. Takes an optional argument to specify the format of information a la sprintf. Format specifiers are in the form "%<width><letter>" where the width is optional and the letter is one of

T

Type

D

Formatted Dimensions

F

Dataflow status

S

Some internal flags (P=physical,V=Vaffine,C=changed,B=may contain bad data)

C

Class of this ndarray, i.e. "ref $pdl"

A

Address of the ndarray struct as a unique identifier

M

Calculated memory consumption of this ndarray's data area

approx

test for approximately equal values (relaxed "==")

  # ok if all corresponding values in
  # ndarrays are within 1e-8 of each other
  print "ok\n" if all approx $x, $y, 1e-8;

"approx" is a relaxed form of the "==" operator and often more appropriate for floating point types ("float" and "double").

Usage:

  $res = approx $x, $y [, $eps]

The optional parameter $eps is remembered across invocations and initially set to 1e-6, e.g.

  approx $x, $y;         # last $eps used (1e-6 initially)
  approx $x, $y, 1e-10;  # 1e-10
  approx $x, $y;         # also 1e-10

mslice

Alias to "slice" in PDL::Slices.

nslice_if_pdl

If $self is a PDL, then calls "slice" with all but the last argument, otherwise $self->($_[-1]) is called where $_[-1} is the original argument string found during PDL::NiceSlice filtering.

DEVELOPER'S NOTE: this routine is found in Core.pm.PL but would be better placed in Slices/slices.pd. It is likely to be moved there and/or changed to "slice_if_pdl" for PDL 3.0.

 $w = $x->nslice_if_pdl(...,'(args)');

inplace

Flag an ndarray so that the next operation is done 'in place'

 somefunc($x->inplace); somefunc(inplace $x);

In most cases one likes to use the syntax "$y = f($x)", however in many case the operation "f()" can be done correctly 'in place', i.e. without making a new copy of the data for output. To make it easy to use this, we write "f()" in such a way that it operates in-place, and use "inplace" to hint that a new copy should be disabled. This also makes for clear syntax.

Obviously this will not work for all functions, and if in doubt see the function's documentation. However one can assume this is true for all elemental functions (i.e. those which just operate array element by array element like "log10").

 pdl> $x = xvals zeroes 10;
 pdl> log10(inplace $x)
 pdl> p $x
 [-inf 0    0.30103 0.47712125 0.60205999    0.69897 0.77815125 0.84509804 0.90308999 0.95424251]

is_inplace

Test the in-place flag on an ndarray

  $out = ($in->is_inplace) ? $in : zeroes($in);
  $in->set_inplace(0)

Provides access to the "inplace" hint flag, within the perl milieu. That way functions you write can be inplace aware... If given an argument the inplace flag will be set or unset depending on the value at the same time. Can be used for shortcut tests that delete the inplace flag while testing:

  $out = ($in->is_inplace(0)) ? $in : zeroes($in); # test & unset!

set_inplace

Set the in-place flag on an ndarray

  $out = ($in->is_inplace) ? $in : zeroes($in);
  $in->set_inplace(0);

Provides access to the "inplace" hint flag, within the perl milieu. Useful mainly for turning it OFF, as "inplace" turns it ON more conveniently.

new_or_inplace

    $w = new_or_inplace(shift());
    $w = new_or_inplace(shift(),$preferred_type);

Return back either the argument pdl or a copy of it depending on whether it be flagged in-place or no. Handy for building inplace-aware functions.

If you specify a preferred type (must be one of the usual PDL type strings, a list ref containing several of them, or a comma-separated string containing several of them), then the copy is coerced into the first preferred type listed if it is not already one of the preferred types.

Note that if the inplace flag is set, no coercion happens even if you specify a preferred type.

new_from_specification

Internal method: create ndarray by specification

This is the argument processing method called by "zeroes" and some other functions which constructs ndarrays from argument lists of the form:

 [type], $nx, $ny, $nz,...

For $nx, $ny, etc. 0 and 1D ndarrays are allowed. Giving those has the same effect as if saying "$arg->list", e.g.

   1, pdl(5,2), 4

is equivalent to

   1, 5, 2, 4

Note, however, that in all functions using "new_from_specification" calling "func $ndarray" will probably not do what you want. So to play safe use (e.g. with zeroes)

  $pdl = zeroes $dimpdl->list;

Calling

  $pdl = zeroes $dimpdl;

will rather be equivalent to

  $pdl = zeroes $dimpdl->dims;

However,

  $pdl = zeroes ushort, $dimpdl;

will again do what you intended since it is interpreted as if you had said

  $pdl = zeroes ushort, $dimpdl->list;

This is unfortunate and confusing but no good solution seems obvious that would not break existing scripts.

isnull

Test whether an ndarray is null

 croak("Input ndarray mustn't be null!")
     if $input_ndarray->isnull;

This function returns 1 if the ndarray is null, zero if it is not. The purpose of null ndarrays is to "tell" any PDL::PP methods to allocate new memory for an output ndarray, but only when that PDL::PP method is called in full-arg form. Of course, there's no reason you couldn't commandeer the special value for your own purposes, for which this test function would prove most helpful. But in general, you shouldn't need to test for an ndarray's nullness.

See "Null PDLs" for more information.

isempty

Test whether an ndarray is empty

 print "The ndarray has zero dimension\n" if $pdl->isempty;

This function returns 1 if the ndarray has zero elements. This is useful in particular when using the indexing function which. In the case of no match to a specified criterion, the returned ndarray has zero dimension.

 pdl> $w=sequence(10)
 pdl> $i=which($w < -1)
 pdl> print "I found no matches!\n" if ($i->isempty);
 I found no matches!

Note that having zero elements is rather different from the concept of being a null ndarray, see the PDL::FAQ and PDL::Indexing manpages for discussions of this.

zeroes

construct a zero filled ndarray from dimension list or template ndarray. If called with no arguments, returns a zero-dimension ndarray (a scalar).

Various forms of usage,

(i) by specification or (ii) by template ndarray:

 # usage type (i):
 $w = zeroes([type], $nx, $ny, $nz,...);
 $w = PDL->zeroes([type], $nx, $ny, $nz,...);
 $w = $pdl->zeroes([type], $nx, $ny, $nz,...); # all info about $pdl ignored
 # usage type (ii):
 $w = zeroes $y;
 $w = $y->zeroes
 zeroes inplace $w;     # Equivalent to   $w .= 0;
 $w->inplace->zeroes;   #  ""

 pdl> $z = zeroes 4,3
 pdl> p $z
 [
  [0 0 0 0]
  [0 0 0 0]
  [0 0 0 0]
 ]
 pdl> $z = zeroes ushort, 3,2 # Create ushort array
 [ushort() etc. with no arg returns a PDL::Types token]

See also "new_from_specification" for details on using ndarrays in the dimensions list.

zeros

construct a zero filled ndarray (see zeroes for usage)

ones

construct a one filled ndarray. If called with no arguments, returns a zero-dimension ndarray (a scalar).

 $w = ones([type], $nx, $ny, $nz,...);
 etc. (see 'zeroes')

 see zeroes() and add one

See also "new_from_specification" for details on using ndarrays in the dimensions list.

nan

construct a "NaN" filled ndarray. If called with no arguments, returns a zero-dimension ndarray (a scalar).

 $w = nan([type], $nx, $ny, $nz,...);
 etc. (see 'zeroes')

 see zeroes() and add NaN

See also "new_from_specification" for details on using ndarrays in the dimensions list.

inf

construct an "Inf" filled ndarray. If called with no arguments, returns a zero-dimension ndarray (a scalar).

 $w = inf([type], $nx, $ny, $nz,...);
 etc. (see 'zeroes')

 see zeroes() and add Inf

See also "new_from_specification" for details on using ndarrays in the dimensions list.

i

construct an ndarray filled with a native complex value equal to the imaginary number "i", the square root of -1. If called with no arguments, returns a zero-dimension ndarray (a scalar).

 $w = i([type], $nx, $ny, $nz,...);
 etc. (see 'zeroes')

 see zeroes() and add "i"

See also "new_from_specification" for details on using ndarrays in the dimensions list.

reshape

Change the shape (i.e. dimensions) of an ndarray, preserving contents.

 $x->reshape(NEWDIMS); reshape($x, NEWDIMS);

The data elements are preserved, obviously they will wrap differently and get truncated if the new array is shorter. If the new array is longer it will be zero-padded.

***Potential incompatibility with earlier versions of PDL**** If the list of "NEWDIMS" is empty "reshape" will just drop all dimensions of size 1 (preserving the number of elements):

  $w = sequence(3,4,5);
  $y = $w(1,3);
  $y->reshape();
  print $y->info;
 PDL: Double D [5]

Dimensions of size 1 will also be dropped if "reshape" is invoked with the argument -1:

  $y = $w->reshape(-1);

As opposed to "reshape" without arguments, "reshape(-1)" preserves dataflow:

  $w = ones(2,1,2);
  $y = $w(0)->reshape(-1);
  $y++;
  print $w;
 [
  [
   [2 1]
  ]
  [
   [2 1]
  ]
 ]

Important: ndarrays are changed inplace!

Note: If $x is connected to any other PDL (e.g. if it is a slice) then the connection is first severed.

 pdl> $x = sequence(10)
 pdl> reshape $x,3,4; p $x
 [
  [0 1 2]
  [3 4 5]
  [6 7 8]
  [9 0 0]
 ]
 pdl> reshape $x,5; p $x
 [0 1 2 3 4]

squeeze

eliminate all singleton dimensions (dims of size 1)

 $y = $w(0,0)->squeeze;

Alias for "reshape(-1)". Removes all singleton dimensions and preserves dataflow. A more concise interface is provided by PDL::NiceSlice via modifiers:

 use PDL::NiceSlice;
 $y = $w(0,0;-); # same as $w(0,0)->squeeze

flat

flatten an ndarray (alias for "$pdl->clump(-1)")

  $srt = $pdl->flat->qsort;

Useful method to make a 1D ndarray from an arbitrarily sized input ndarray. Data flows back and forth as usual with slicing routines. Falls through if argument already <= 1D.

convert

Generic datatype conversion function

 $y = convert($x, $newtype);

$newtype is a type number or PDL::Type object, for convenience they are returned by "long()" etc when called without arguments.

 $y = convert $x, long;
 $y = convert $x, ushort;

Datatype_conversions

sbyte|byte|short|ushort|long|ulong|indx|longlong|ulonglong|float|double|ldouble|cfloat|cdouble|cldouble (shorthands to convert datatypes)

 $y = double $x; $y = ushort [1..10];
 # all of the above listed shorthands behave similarly

When called with an ndarray argument, they convert to the specific datatype.

When called with a numeric, list, listref, or string argument they construct a new ndarray. This is a convenience to avoid having to be long-winded and say "$x = long(pdl(42))"

Thus one can say:

 $w = float(1,2,3,4);           # 1D
 $w = float q[1 2 3; 4 5 6];    # 2D
 $w = float([1,2,3],[4,5,6]);   # 2D
 $w = float([[1,2,3],[4,5,6]]); # 2D

Note the last three give identical results, and the last two are exactly equivalent - a list is automatically converted to a list reference for syntactic convenience. i.e. you can omit the outer "[]"

When called with no arguments, these functions return a special type token. This allows syntactical sugar like:

 $x = ones byte, 1000,1000;

This example creates a large ndarray directly as byte datatype in order to save memory.

In order to control how undefs are handled in converting from perl lists to PDLs, one can set the variable $PDL::undefval; see the function pdl() for more details.

 pdl> p $x=sqrt float [1..10]
 [1 1.41421 1.73205 2 2.23607 2.44949 2.64575 2.82843 3 3.16228]
 pdl> p byte $x
 [1 1 1 2 2 2 2 2 3 3]

byte

Convert to byte datatype

short

Convert to short datatype

ushort

Convert to ushort datatype

long

Convert to long datatype

indx

Convert to indx datatype

longlong

Convert to longlong datatype

float

Convert to float datatype

double

Convert to double datatype

cfloat

Convert to complex float datatype

cdouble

Convert to complex double datatype

type

return the type of an ndarray as a blessed type object

A convenience function for use with the ndarray constructors, e.g.

 $y = PDL->zeroes($x->type,$x->dims,3);
 die "must be float" unless $x->type == float;

See also the discussion of the "PDL::Type" class in PDL::Types. Note that the "PDL::Type" objects have overloaded comparison and stringify operators so that you can compare and print types:

 $x = $x->float if $x->type < float;
 $t = $x->type; print "Type is $t\n";

list

Convert ndarray to perl list

 @tmp = list $x;

Obviously this is grossly inefficient for the large datasets PDL is designed to handle. This was provided as a get out while PDL matured. It should now be mostly superseded by superior constructs, such as PP/broadcasting. However it is still occasionally useful and is provided for backwards compatibility.

 for (list $x) {
   # Do something on each value...
 }

list converts any bad values into the string 'BAD'.

unpdl

Convert ndarray to nested Perl array references

 $arrayref = unpdl $x;

This function returns a reference to a Perl list-of-lists structure equivalent to the input ndarray (within the limitation that while values of elements should be preserved, the detailed datatypes will not as perl itself basically has "number" data rather than byte, short, int... E.g., "sum($x - pdl( $x->unpdl ))" should equal 0.

Obviously this is grossly inefficient in memory and processing for the large datasets PDL is designed to handle. Sometimes, however, you really want to move your data back to Perl, and with proper dimensionality, unlike "list".

If you want to round-trip data including the use of "PDL::undefval", "unpdl" does not support this. However, it is suggested you would generate an index-set with "$pdl->whereND($pdl == $PDL::undefval)", then loop over the Perl data, setting those locations to "undef".

 use JSON;
 my $json = encode_json unpdl $pdl;

unpdl converts any bad values into the string 'BAD'.

listindices

Convert ndarray indices to perl list

 @tmp = listindices $x;

@tmp now contains the values "0..nelem($x)".

Obviously this is grossly inefficient for the large datasets PDL is designed to handle. This was provided as a get out while PDL matured. It should now be mostly superseded by superior constructs, such as PP/broadcasting. However it is still occasionally useful and is provied for backwards compatibility.

 for $i (listindices $x) {
   # Do something on each value...
 }

set

Set a single value inside an ndarray

 set $ndarray, @position, $value

@position is a coordinate list, of size equal to the number of dimensions in the ndarray. Occasionally useful, mainly provided for backwards compatibility as superseded by use of slice and assignment operator ".=".

 pdl> $x = sequence 3,4
 pdl> set $x, 2,1,99
 pdl> p $x
 [
  [ 0  1  2]
  [ 3  4 99]
  [ 6  7  8]
  [ 9 10 11]
 ]

at

Returns a single value inside an ndarray as perl scalar. If the ndarray is a native complex value (cdouble, cfloat), it will be a PDL::Complex::Overloads object.

 $z = at($ndarray, @position); $z=$ndarray->at(@position);

@position is a coordinate list, of size equal to the number of dimensions in the ndarray. Occasionally useful in a general context, quite useful too inside PDL internals.

 pdl> $x = sequence 3,4
 pdl> p $x->at(1,2)
 7

at converts any bad values into the string 'BAD'.

sclr

return a single value from an ndarray as a scalar, ignoring whether it is bad.

  $val = $x(10)->sclr;
  $val = sclr inner($x,$y);

The "sclr" method is useful to turn a single-element ndarray into a normal Perl scalar. Its main advantage over using "at" for this purpose is the fact that you do not need to worry if the ndarray is 0D, 1D or higher dimensional. Using "at" you have to supply the correct number of zeroes, e.g.

  $x = sequence(10);
  $y = $x->slice('4');
  print $y->sclr; # no problem
  print $y->at(); # error: needs at least one zero

"sclr" is generally used when a Perl scalar is required instead of a one-element ndarray. As of 2.064, if the input is a multielement ndarray it will throw an exception.

cat

concatenate ndarrays to N+1 dimensional ndarray

Takes a list of N ndarrays of same shape as argument, returns a single ndarray of dimension N+1.

 pdl> $x = cat ones(3,3),zeroes(3,3),rvals(3,3); p $x
 [
  [
   [1 1 1]
   [1 1 1]
   [1 1 1]
  ]
  [
   [0 0 0]
   [0 0 0]
   [0 0 0]
  ]
  [
   [1 1 1]
   [1 0 1]
   [1 1 1]
  ]
 ]

The output ndarray is set bad if any input ndarrays have their bad flag set.

Similar functions include append, which appends only two ndarrays along their first dimension, and glue, which can append more than two ndarrays along an arbitrary dimension.

Also consider the generic constructor "pdl", which can handle ndarrays of different sizes (with zero-padding), and will return a ndarray of type 'double' by default, but may be considerably faster (up to 10x) than cat.

dog

Opposite of 'cat' :). Split N dim ndarray to list of N-1 dim ndarrays

Takes a single N-dimensional ndarray and splits it into a list of N-1 dimensional ndarrays. The breakup is done along the last dimension. Note the dataflowed connection is still preserved by default, e.g.:

 pdl> $p = ones 3,3,3
 pdl> ($x,$y,$c) = dog $p
 pdl> $y++; p $p
 [
  [
   [1 1 1]
   [1 1 1]
   [1 1 1]
  ]
  [
   [2 2 2]
   [2 2 2]
   [2 2 2]
  ]
  [
   [1 1 1]
   [1 1 1]
   [1 1 1]
  ]
 ]

 Break => 1   Break dataflow connection (new copy)

The output ndarrays are set bad if the original ndarray has its bad flag set.

gethdr

Retrieve header information from an ndarray

 $pdl=rfits('file.fits');
 $h=$pdl->gethdr;
 print "Number of pixels in the X-direction=$$h{NAXIS1}\n";

The "gethdr" function retrieves whatever header information is contained within an ndarray. The header can be set with "sethdr" and is always a hash reference or undef.

"gethdr" returns undef if the ndarray has not yet had a header defined; compare with "hdr" and "fhdr", which are guaranteed to return a defined value.

Note that gethdr() works by reference: you can modify the header in-place once it has been retrieved:

  $x  = rfits($filename);
  $xh = $x->gethdr();
  $xh->{FILENAME} = $filename;

It is also important to realise that in most cases the header is not automatically copied when you copy the ndarray. See "hdrcpy" to enable automatic header copying.

Here's another example: a wrapper around rcols that allows your ndarray to remember the file it was read from and the columns could be easily written (here assuming that no regexp is needed, extensions are left as an exercise for the reader)

 sub ext_rcols {
    my ($file, @columns)=@_;
    my $header={};
    $$header{File}=$file;
    $$header{Columns}=\@columns;
    @ndarrays=rcols $file, @columns;
    foreach (@ndarrays) { $_->sethdr($header); }
    return @ndarrays;
 }

hdr

Retrieve or set header information from an ndarray

 $pdl->hdr->{CDELT1} = 1;

The "hdr" function allows convenient access to the header of a ndarray. Unlike "gethdr" it is guaranteed to return a defined value, so you can use it in a hash dereference as in the example. If the header does not yet exist, it gets autogenerated as an empty hash.

Note that this is usually -- but not always -- What You Want. If you want to use a tied Astro::FITS::Header hash, for example, you should either construct it yourself and use "sethdr" to put it into the ndarray, or use "fhdr" instead. (Note that you should be able to write out the FITS file successfully regardless of whether your PDL has a tied FITS header object or a vanilla hash).

fhdr

Retrieve or set FITS header information from an ndarray

 $pdl->fhdr->{CDELT1} = 1;

The "fhdr" function allows convenient access to the header of a ndarray. Unlike "gethdr" it is guaranteed to return a defined value, so you can use it in a hash dereference as in the example. If the header does not yet exist, it gets autogenerated as a tied Astro::FITS::Header hash.

Astro::FITS::Header tied hashes are better at matching the behavior of FITS headers than are regular hashes. In particular, the hash keys are CAsE INsEnSItiVE, unlike normal hash keys. See Astro::FITS::Header for details.

If you do not have Astro::FITS::Header installed, you get back a normal hash instead of a tied object.

sethdr

Set header information of an ndarray

 $pdl = zeroes(100,100);
 $h = {NAXIS=>2, NAXIS1=>100, NAXIS=>100, COMMENT=>"Sample FITS-style header"};
 # add a FILENAME field to the header
 $$h{FILENAME} = 'file.fits';
 $pdl->sethdr( $h );

The "sethdr" function sets the header information for an ndarray. You must feed in a hash ref or undef, and the header field of the PDL is set to be a new ref to the same hash (or undefined).

The hash ref requirement is a speed bump put in place since the normal use of headers is to store fits header information and the like. Of course, if you want you can hang whatever ugly old data structure you want off of the header, but that makes life more complex.

Remember that the hash is not copied -- the header is made into a ref that points to the same underlying data. To get a real copy without making any assumptions about the underlying data structure, you can use one of the following:

  use PDL::IO::Dumper;
  $pdl->sethdr( deep_copy($h) );

(which is slow but general), or

  $pdl->sethdr( PDL::_hdr_copy($h) )

(which uses the built-in sleazy deep copier), or (if you know that all the elements happen to be scalars):

  { my %a = %$h;
    $pdl->sethdr(\%a);
  }

which is considerably faster but just copies the top level.

The "sethdr" function must be given a hash reference or undef. For further information on the header, see "gethdr", "hdr", "fhdr" and "hdrcpy".

hdrcpy

switch on/off/examine automatic header copying

 print "hdrs will be copied" if $x->hdrcpy;
 $x->hdrcpy(1);       # switch on automatic header copying
 $y = $x->sumover;    # and $y will inherit $x's hdr
 $x->hdrcpy(0);       # and now make $x non-infectious again

"hdrcpy" without an argument just returns the current setting of the flag. See also "hcpy" which returns its PDL argument (and so is useful in method-call pipelines).

Normally, the optional header of an ndarray is not copied automatically in pdl operations. Switching on the hdrcpy flag using the "hdrcpy" method will enable automatic hdr copying. Note that an actual deep copy gets made, which is rather processor-inefficient -- so avoid using header copying in tight loops!

Most PDLs have the "hdrcpy" flag cleared by default; however, some routines (notably rfits) set it by default where that makes more sense.

The "hdrcpy" flag is viral: if you set it for a PDL, then derived PDLs will get copies of the header and will also have their "hdrcpy" flags set. For example:

  $x = xvals(50,50);
  $x->hdrcpy(1);
  $x->hdr->{FOO} = "bar";
  $y = $x++;
  $c = $y++;
  print $y->hdr->{FOO}, " - ", $c->hdr->{FOO}, "\n";
  $y->hdr->{FOO} = "baz";
  print $x->hdr->{FOO}, " - ", $y->hdr->{FOO}, " - ", $c->hdr->{FOO}, "\n";

will print:

  bar - bar
  bar - baz - bar

Performing an operation in which more than one PDL has its hdrcpy flag causes the resulting PDL to take the header of the first PDL:

  ($x,$y) = sequence(5,2)->dog;
  $x->hdrcpy(1); $y->hdrcpy(1);
  $x->hdr->{foo} = 'a';
  $y->hdr->{foo} = 'b';
  print (($x+$y)->hdr->{foo} , ($y+$x)->hdr->{foo});

will print:

  a b

hcpy

Switch on/off automatic header copying, with PDL pass-through

  $x = rfits('foo.fits')->hcpy(0);
  $x = rfits('foo.fits')->hcpy(1);

"hcpy" sets or clears the hdrcpy flag of a PDL, and returns the PDL itself. That makes it convenient for inline use in expressions.

online_cpus

Returns the number of available processors cores. Used to set the number of threads with "set_autopthread_targ" if $ENV{PDL_AUTOPTHREAD_TARG} is not set.

set_autopthread_targ

Set the target number of processor threads (pthreads) for multi-threaded processing.

 set_autopthread_targ($num_pthreads);

$num_pthreads is the target number of pthreads the auto-pthread process will try to achieve.

See PDL::ParallelCPU for an overview of the auto-pthread process.

  # Example turning on auto-pthreading for a target of 2 pthreads and for functions involving
  #   PDLs with greater than 1M elements
  set_autopthread_targ(2);
  set_autopthread_size(1);
  # Execute a pdl function, processing will split into two pthreads
  $x = minimum($y);
  # Get the actual number of pthreads that were run.
  $actual_pthread = get_autopthread_actual();

get_autopthread_targ

Get the current target number of processor threads (pthreads) for multi-threaded processing.

 $num_pthreads = get_autopthread_targ();

$num_pthreads is the target number of pthreads the auto-pthread process will try to achieve.

See PDL::ParallelCPU for an overview of the auto-pthread process.

get_autopthread_actual

Get the actual number of pthreads executed for the last pdl processing function.

 $autopthread_actual = get_autopthread_actual();

$autopthread_actual is the actual number of pthreads executed for the last pdl processing function.

See PDL::ParallelCPU for an overview of the auto-pthread process.

get_autopthread_dim

Get the actual dimension on which pthreads were used for the last pdl processing function.

 $autopthread_dim = get_autopthread_dim();

$autopthread_dim is the actual dimension on which pthreads were used for the last pdl processing function.

See PDL::ParallelCPU for an overview of the auto-pthread process.

set_autopthread_size

Set the minimum size (in M-elements or 2^20 elements) of the largest PDL involved in a function where auto-pthreading will be performed. For small PDLs, it probably isn't worth starting multiple pthreads, so this function is used to define a minimum threshold where auto-pthreading won't be attempted.

 set_autopthread_size($size);

$size is the mimumum size, in M-elements or 2^20 elements (approx 1e6 elements) for the largest PDL involved in a function.

See PDL::ParallelCPU for an overview of the auto-pthread process.

  # Example turning on auto-pthreading for a target of 2 pthreads and for functions involving
  #   PDLs with greater than 1M elements
  set_autopthread_targ(2);
  set_autopthread_size(1);
  # Execute a pdl function, processing will split into two pthreads as long as
  #  one of the pdl-threaded dimensions is at least 2.
  $x = minimum($y);
  # Get the actual number of pthreads that were run.
  $actual_pthread = get_autopthread_actual();

get_autopthread_size

Get the current autopthread_size setting.

 $autopthread_size = get_autopthread_size();

$autopthread_size is the mimumum size limit for auto_pthreading to occur, in M-elements or 2^20 elements (approx 1e6 elements) for the largest PDL involved in a function

See PDL::ParallelCPU for an overview of the auto-pthread process.