Provided by: pdl_2.084-1_amd64 bug

NAME

       PDL::Core - fundamental PDL functionality and vectorization/broadcasting

DESCRIPTION

       Methods and functions for type conversions, PDL creation, type conversion, broadcasting
       etc.

SYNOPSIS

        use PDL::Core;             # Normal routines
        use PDL::Core ':Internal'; # Hairy routines

VECTORIZATION/BROADCASTING: METHOD AND NOMENCLATURE

       PDL provides vectorized operations via a built-in engine.  Vectorization in PDL is called
       "broadcasting" (formerly, up to 2.074, "threading").  The broadcasting engine implements
       simple rules for each operation.

       Each PDL object has a "shape" that is a generalized N-dimensional rectangle defined by a
       "dim list" of sizes in an arbitrary set of dimensions.  A PDL with shape 2x3 has 6
       elements and is said to be two-dimensional, or may be referred to as a 2x3-PDL.  The
       dimensions are indexed numerically starting at 0, so a 2x3-PDL has a dimension 0 (or "dim
       0") with size 2 and a 1 dimension (or "dim 1") with size 3.

       PDL generalizes *all* mathematical operations with the notion of "active dims": each
       operator has zero or more active dims that are used in carrying out the operation.  Simple
       scalar operations like scalar multiplication ('*') have 0 active dims.  More complicated
       operators can have more active dims.  For example, matrix multiplication ('x') has 2
       active dims.  Additional dims are automatically vectorized across -- e.g. multiplying a
       2x5-PDL with a 2x5-PDL requires 10 simple multiplication operations, and yields a 2x5-PDL
       result.

   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.

VARIABLES

       These are important variables of global scope and are placed in the PDL namespace.

       $PDL::debug

           When true, PDL debugging information is printed.

       $PDL::verbose

           When true, PDL functions provide chatty information.

       $PDL::use_commas

           Whether to insert commas when printing pdls

       $PDL::floatformat, $PDL::doubleformat, $PDL::indxformat

           The default print format for floats, doubles, and indx values, respectively.  The
           default default values are:

             $PDL::floatformat  = "%7g";
             $PDL::doubleformat = "%10.8g";
             $PDL::indxformat   = "%12d";

       $PDL::undefval

           The value to use instead of "undef" when creating pdls. If is "undef", 0 will be used.

       $PDL::toolongtoprint

           The maximal size pdls to print (defaults to 10000 elements)

FUNCTIONS

   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 = PDL->new([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
        $y = PDL->new(@list_of_vals);  # new from Perl list
        $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.

AUTHOR

       Copyright (C) Karl Glazebrook (kgb@aaoepp.aao.gov.au), Tuomas J. Lukka,
       (lukka@husc.harvard.edu) and Christian Soeller (c.soeller@auckland.ac.nz) 1997.  Modified,
       Craig DeForest (deforest@boulder.swri.edu) 2002.  All rights reserved. There is no
       warranty. You are allowed to redistribute this software / documentation under certain
       conditions. For details, see the file COPYING in the PDL distribution. If this file is
       separated from the PDL distribution, the copyright notice should be included in the file.