numpy.i: a SWIG interface file for NumPy
========================================

Introduction
------------

The Simple Wrapper and Interface Generator (or `SWIG
<https://www.swig.org>`_) is a powerful tool for generating wrapper
code for interfacing to a wide variety of scripting languages.
`SWIG`_ can parse header files, and using only the code prototypes,
create an interface to the target language.  But `SWIG`_ is not
omnipotent.  For example, it cannot know from the prototype::

    double rms(double* seq, int n);

what exactly ``seq`` is.  Is it a single value to be altered in-place?
Is it an array, and if so what is its length?  Is it input-only?
Output-only?  Input-output?  `SWIG`_ cannot determine these details,
and does not attempt to do so.

If we designed ``rms``, we probably made it a routine that takes an
input-only array of length ``n`` of ``double`` values called ``seq``
and returns the root mean square.  The default behavior of `SWIG`_,
however, will be to create a wrapper function that compiles, but is
nearly impossible to use from the scripting language in the way the C
routine was intended.

For Python, the preferred way of handling contiguous (or technically,
*strided*) blocks of homogeneous data is with NumPy, which provides full
object-oriented access to multidimensial arrays of data.  Therefore, the most
logical Python interface for the ``rms`` function would be (including doc
string)::

    def rms(seq):
        """
        rms: return the root mean square of a sequence
        rms(numpy.ndarray) -> double
        rms(list) -> double
        rms(tuple) -> double
        """

where ``seq`` would be a NumPy array of ``double`` values, and its
length ``n`` would be extracted from ``seq`` internally before being
passed to the C routine.  Even better, since NumPy supports
construction of arrays from arbitrary Python sequences, ``seq``
itself could be a nearly arbitrary sequence (so long as each element
can be converted to a ``double``) and the wrapper code would
internally convert it to a NumPy array before extracting its data
and length.

`SWIG`_ allows these types of conversions to be defined via a
mechanism called *typemaps*.  This document provides information on
how to use ``numpy.i``, a `SWIG`_ interface file that defines a series
of typemaps intended to make the type of array-related conversions
described above relatively simple to implement.  For example, suppose
that the ``rms`` function prototype defined above was in a header file
named ``rms.h``.  To obtain the Python interface discussed above, your
`SWIG`_ interface file would need the following::

    %{
    #define SWIG_FILE_WITH_INIT
    #include "rms.h"
    %}

    %include "numpy.i"

    %init %{
    import_array();
    %}

    %apply (double* IN_ARRAY1, int DIM1) {(double* seq, int n)};
    %include "rms.h"

Typemaps are keyed off a list of one or more function arguments,
either by type or by type and name.  We will refer to such lists as
*signatures*.  One of the many typemaps defined by ``numpy.i`` is used
above and has the signature ``(double* IN_ARRAY1, int DIM1)``.  The
argument names are intended to suggest that the ``double*`` argument
is an input array of one dimension and that the ``int`` represents the
size of that dimension.  This is precisely the pattern in the ``rms``
prototype.

Most likely, no actual prototypes to be wrapped will have the argument
names ``IN_ARRAY1`` and ``DIM1``.  We use the `SWIG`_ ``%apply``
directive to apply the typemap for one-dimensional input arrays of
type ``double`` to the actual prototype used by ``rms``.  Using
``numpy.i`` effectively, therefore, requires knowing what typemaps are
available and what they do.

A `SWIG`_ interface file that includes the `SWIG`_ directives given
above will produce wrapper code that looks something like::

     1 PyObject *_wrap_rms(PyObject *args) {
     2   PyObject *resultobj = 0;
     3   double *arg1 = (double *) 0 ;
     4   int arg2 ;
     5   double result;
     6   PyArrayObject *array1 = NULL ;
     7   int is_new_object1 = 0 ;
     8   PyObject * obj0 = 0 ;
     9
    10   if (!PyArg_ParseTuple(args,(char *)"O:rms",&obj0)) SWIG_fail;
    11   {
    12     array1 = obj_to_array_contiguous_allow_conversion(
    13                  obj0, NPY_DOUBLE, &is_new_object1);
    14     npy_intp size[1] = {
    15       -1
    16     };
    17     if (!array1 || !require_dimensions(array1, 1) ||
    18         !require_size(array1, size, 1)) SWIG_fail;
    19     arg1 = (double*) array1->data;
    20     arg2 = (int) array1->dimensions[0];
    21   }
    22   result = (double)rms(arg1,arg2);
    23   resultobj = SWIG_From_double((double)(result));
    24   {
    25     if (is_new_object1 && array1) Py_DECREF(array1);
    26   }
    27   return resultobj;
    28 fail:
    29   {
    30     if (is_new_object1 && array1) Py_DECREF(array1);
    31   }
    32   return NULL;
    33 }

The typemaps from ``numpy.i`` are responsible for the following lines
of code: 12--20, 25 and 30.  Line 10 parses the input to the ``rms``
function.  From the format string ``"O:rms"``, we can see that the
argument list is expected to be a single Python object (specified
by the ``O`` before the colon) and whose pointer is stored in
``obj0``.  A number of functions, supplied by ``numpy.i``, are called
to make and check the (possible) conversion from a generic Python
object to a NumPy array.  These functions are explained in the
section `Helper Functions`_, but hopefully their names are
self-explanatory.  At line 12 we use ``obj0`` to construct a NumPy
array.  At line 17, we check the validity of the result: that it is
non-null and that it has a single dimension of arbitrary length.  Once
these states are verified, we extract the data buffer and length in
lines 19 and 20 so that we can call the underlying C function at line
22.  Line 25 performs memory management for the case where we have
created a new array that is no longer needed.

This code has a significant amount of error handling.  Note the
``SWIG_fail`` is a macro for ``goto fail``, referring to the label at
line 28.  If the user provides the wrong number of arguments, this
will be caught at line 10.  If construction of the NumPy array
fails or produces an array with the wrong number of dimensions, these
errors are caught at line 17.  And finally, if an error is detected,
memory is still managed correctly at line 30.

Note that if the C function signature was in a different order::

    double rms(int n, double* seq);

that `SWIG`_ would not match the typemap signature given above with
the argument list for ``rms``.  Fortunately, ``numpy.i`` has a set of
typemaps with the data pointer given last::

    %apply (int DIM1, double* IN_ARRAY1) {(int n, double* seq)};

This simply has the effect of switching the definitions of ``arg1``
and ``arg2`` in lines 3 and 4 of the generated code above, and their
assignments in lines 19 and 20.

Using numpy.i
-------------

The ``numpy.i`` file is currently located in the ``tools/swig``
sub-directory under the ``numpy`` installation directory.  Typically,
you will want to copy it to the directory where you are developing
your wrappers.

A simple module that only uses a single `SWIG`_ interface file should
include the following::

    %{
    #define SWIG_FILE_WITH_INIT
    %}
    %include "numpy.i"
    %init %{
    import_array();
    %}

Within a compiled Python module, ``import_array()`` should only get
called once.  This could be in a C/C++ file that you have written and
is linked to the module.  If this is the case, then none of your
interface files should ``#define SWIG_FILE_WITH_INIT`` or call
``import_array()``.  Or, this initialization call could be in a
wrapper file generated by `SWIG`_ from an interface file that has the
``%init`` block as above.  If this is the case, and you have more than
one `SWIG`_ interface file, then only one interface file should
``#define SWIG_FILE_WITH_INIT`` and call ``import_array()``.

Available typemaps
------------------

The typemap directives provided by ``numpy.i`` for arrays of different
data types, say ``double`` and ``int``, and dimensions of different
types, say ``int`` or ``long``, are identical to one another except
for the C and NumPy type specifications.  The typemaps are
therefore implemented (typically behind the scenes) via a macro::

    %numpy_typemaps(DATA_TYPE, DATA_TYPECODE, DIM_TYPE)

that can be invoked for appropriate ``(DATA_TYPE, DATA_TYPECODE,
DIM_TYPE)`` triplets.  For example::

    %numpy_typemaps(double, NPY_DOUBLE, int)
    %numpy_typemaps(int,    NPY_INT   , int)

The ``numpy.i`` interface file uses the ``%numpy_typemaps`` macro to
implement typemaps for the following C data types and ``int``
dimension types:

* ``signed char``
* ``unsigned char``
* ``short``
* ``unsigned short``
* ``int``
* ``unsigned int``
* ``long``
* ``unsigned long``
* ``long long``
* ``unsigned long long``
* ``float``
* ``double``

In the following descriptions, we reference a generic ``DATA_TYPE``, which
could be any of the C data types listed above, and ``DIM_TYPE`` which
should be one of the many types of integers.

The typemap signatures are largely differentiated on the name given to
the buffer pointer.  Names with ``FARRAY`` are for Fortran-ordered
arrays, and names with ``ARRAY`` are for C-ordered (or 1D arrays).

Input Arrays
~~~~~~~~~~~~

Input arrays are defined as arrays of data that are passed into a
routine but are not altered in-place or returned to the user.  The
Python input array is therefore allowed to be almost any Python
sequence (such as a list) that can be converted to the requested type
of array.  The input array signatures are

1D:

* ``(	DATA_TYPE IN_ARRAY1[ANY] )``
* ``(	DATA_TYPE* IN_ARRAY1, int DIM1 )``
* ``(	int DIM1, DATA_TYPE* IN_ARRAY1 )``

2D:

* ``(	DATA_TYPE IN_ARRAY2[ANY][ANY] )``
* ``(	DATA_TYPE* IN_ARRAY2, int DIM1, int DIM2 )``
* ``(	int DIM1, int DIM2, DATA_TYPE* IN_ARRAY2 )``
* ``(	DATA_TYPE* IN_FARRAY2, int DIM1, int DIM2 )``
* ``(	int DIM1, int DIM2, DATA_TYPE* IN_FARRAY2 )``

3D:

* ``(	DATA_TYPE IN_ARRAY3[ANY][ANY][ANY] )``
* ``(	DATA_TYPE* IN_ARRAY3, int DIM1, int DIM2, int DIM3 )``
* ``(	int DIM1, int DIM2, int DIM3, DATA_TYPE* IN_ARRAY3 )``
* ``(	DATA_TYPE* IN_FARRAY3, int DIM1, int DIM2, int DIM3 )``
* ``(	int DIM1, int DIM2, int DIM3, DATA_TYPE* IN_FARRAY3 )``

4D:

* ``(DATA_TYPE IN_ARRAY4[ANY][ANY][ANY][ANY])``
* ``(DATA_TYPE* IN_ARRAY4, DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, DIM_TYPE DIM4)``
* ``(DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, , DIM_TYPE DIM4, DATA_TYPE* IN_ARRAY4)``
* ``(DATA_TYPE* IN_FARRAY4, DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, DIM_TYPE DIM4)``
* ``(DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, DIM_TYPE DIM4, DATA_TYPE* IN_FARRAY4)``

The first signature listed, ``( DATA_TYPE IN_ARRAY[ANY] )`` is for
one-dimensional arrays with hard-coded dimensions.  Likewise,
``( DATA_TYPE IN_ARRAY2[ANY][ANY] )`` is for two-dimensional arrays
with hard-coded dimensions, and similarly for three-dimensional.

In-Place Arrays
~~~~~~~~~~~~~~~

In-place arrays are defined as arrays that are modified in-place.  The
input values may or may not be used, but the values at the time the
function returns are significant.  The provided Python argument
must therefore be a NumPy array of the required type.  The in-place
signatures are

1D:

* ``(	DATA_TYPE INPLACE_ARRAY1[ANY] )``
* ``(	DATA_TYPE* INPLACE_ARRAY1, int DIM1 )``
* ``(	int DIM1, DATA_TYPE* INPLACE_ARRAY1 )``

2D:

* ``(	DATA_TYPE INPLACE_ARRAY2[ANY][ANY] )``
* ``(	DATA_TYPE* INPLACE_ARRAY2, int DIM1, int DIM2 )``
* ``(	int DIM1, int DIM2, DATA_TYPE* INPLACE_ARRAY2 )``
* ``(	DATA_TYPE* INPLACE_FARRAY2, int DIM1, int DIM2 )``
* ``(	int DIM1, int DIM2, DATA_TYPE* INPLACE_FARRAY2 )``

3D:

* ``(	DATA_TYPE INPLACE_ARRAY3[ANY][ANY][ANY] )``
* ``(	DATA_TYPE* INPLACE_ARRAY3, int DIM1, int DIM2, int DIM3 )``
* ``(	int DIM1, int DIM2, int DIM3, DATA_TYPE* INPLACE_ARRAY3 )``
* ``(	DATA_TYPE* INPLACE_FARRAY3, int DIM1, int DIM2, int DIM3 )``
* ``(	int DIM1, int DIM2, int DIM3, DATA_TYPE* INPLACE_FARRAY3 )``

4D:

* ``(DATA_TYPE INPLACE_ARRAY4[ANY][ANY][ANY][ANY])``
* ``(DATA_TYPE* INPLACE_ARRAY4, DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, DIM_TYPE DIM4)``
* ``(DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, , DIM_TYPE DIM4, DATA_TYPE* INPLACE_ARRAY4)``
* ``(DATA_TYPE* INPLACE_FARRAY4, DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, DIM_TYPE DIM4)``
* ``(DIM_TYPE DIM1, DIM_TYPE DIM2, DIM_TYPE DIM3, DIM_TYPE DIM4, DATA_TYPE* INPLACE_FARRAY4)``

These typemaps now check to make sure that the ``INPLACE_ARRAY``
arguments use native byte ordering.  If not, an exception is raised.

There is also a "flat" in-place array for situations in which
you would like to modify or process each element, regardless of the
number of dimensions. One example is a "quantization" function that
quantizes each element of an array in-place, be it 1D, 2D or whatever.
This form checks for continuity but allows either C or Fortran ordering.

ND:

* ``(DATA_TYPE* INPLACE_ARRAY_FLAT, DIM_TYPE DIM_FLAT)``


Argout Arrays
~~~~~~~~~~~~~

Argout arrays are arrays that appear in the input arguments in C, but
are in fact output arrays.  This pattern occurs often when there is
more than one output variable and the single return argument is
therefore not sufficient.  In Python, the conventional way to return
multiple arguments is to pack them into a sequence (tuple, list, etc.)
and return the sequence.  This is what the argout typemaps do.  If a
wrapped function that uses these argout typemaps has more than one
return argument, they are packed into a tuple or list, depending on
the version of Python.  The Python user does not pass these
arrays in, they simply get returned.  For the case where a dimension
is specified, the python user must provide that dimension as an
argument.  The argout signatures are

1D:

* ``(	DATA_TYPE ARGOUT_ARRAY1[ANY] )``
* ``(	DATA_TYPE* ARGOUT_ARRAY1, int DIM1 )``
* ``(	int DIM1, DATA_TYPE* ARGOUT_ARRAY1 )``

2D:

* ``(	DATA_TYPE ARGOUT_ARRAY2[ANY][ANY] )``

3D:

* ``(	DATA_TYPE ARGOUT_ARRAY3[ANY][ANY][ANY] )``

4D:

* ``(	DATA_TYPE ARGOUT_ARRAY4[ANY][ANY][ANY][ANY] )``

These are typically used in situations where in C/C++, you would
allocate a(n) array(s) on the heap, and call the function to fill the
array(s) values.  In Python, the arrays are allocated for you and
returned as new array objects.

Note that we support ``DATA_TYPE*`` argout typemaps in 1D, but not 2D
or 3D.  This is because of a quirk with the `SWIG`_ typemap syntax and
cannot be avoided.  Note that for these types of 1D typemaps, the
Python function will take a single argument representing ``DIM1``.

Argout View Arrays
~~~~~~~~~~~~~~~~~~

Argoutview arrays are for when your C code provides you with a view of
its internal data and does not require any memory to be allocated by
the user.  This can be dangerous.  There is almost no way to guarantee
that the internal data from the C code will remain in existence for
the entire lifetime of the NumPy array that encapsulates it.  If
the user destroys the object that provides the view of the data before
destroying the NumPy array, then using that array may result in bad
memory references or segmentation faults.  Nevertheless, there are
situations, working with large data sets, where you simply have no
other choice.

The C code to be wrapped for argoutview arrays are characterized by
pointers: pointers to the dimensions and double pointers to the data,
so that these values can be passed back to the user.  The argoutview
typemap signatures are therefore

1D:

* ``( DATA_TYPE** ARGOUTVIEW_ARRAY1, DIM_TYPE* DIM1 )``
* ``( DIM_TYPE* DIM1, DATA_TYPE** ARGOUTVIEW_ARRAY1 )``

2D:

* ``( DATA_TYPE** ARGOUTVIEW_ARRAY2, DIM_TYPE* DIM1, DIM_TYPE* DIM2 )``
* ``( DIM_TYPE* DIM1, DIM_TYPE* DIM2, DATA_TYPE** ARGOUTVIEW_ARRAY2 )``
* ``( DATA_TYPE** ARGOUTVIEW_FARRAY2, DIM_TYPE* DIM1, DIM_TYPE* DIM2 )``
* ``( DIM_TYPE* DIM1, DIM_TYPE* DIM2, DATA_TYPE** ARGOUTVIEW_FARRAY2 )``

3D:

* ``( DATA_TYPE** ARGOUTVIEW_ARRAY3, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3)``
* ``( DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DATA_TYPE** ARGOUTVIEW_ARRAY3)``
* ``( DATA_TYPE** ARGOUTVIEW_FARRAY3, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3)``
* ``( DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DATA_TYPE** ARGOUTVIEW_FARRAY3)``

4D:

* ``(DATA_TYPE** ARGOUTVIEW_ARRAY4, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4, DATA_TYPE** ARGOUTVIEW_ARRAY4)``
* ``(DATA_TYPE** ARGOUTVIEW_FARRAY4, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4, DATA_TYPE** ARGOUTVIEW_FARRAY4)``

Note that arrays with hard-coded dimensions are not supported.  These
cannot follow the double pointer signatures of these typemaps.

Memory Managed Argout View Arrays
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A recent addition to ``numpy.i`` are typemaps that permit argout
arrays with views into memory that is managed.

1D:

* ``(DATA_TYPE** ARGOUTVIEWM_ARRAY1, DIM_TYPE* DIM1)``
* ``(DIM_TYPE* DIM1, DATA_TYPE** ARGOUTVIEWM_ARRAY1)``

2D:

* ``(DATA_TYPE** ARGOUTVIEWM_ARRAY2, DIM_TYPE* DIM1, DIM_TYPE* DIM2)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DATA_TYPE** ARGOUTVIEWM_ARRAY2)``
* ``(DATA_TYPE** ARGOUTVIEWM_FARRAY2, DIM_TYPE* DIM1, DIM_TYPE* DIM2)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DATA_TYPE** ARGOUTVIEWM_FARRAY2)``

3D:

* ``(DATA_TYPE** ARGOUTVIEWM_ARRAY3, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DATA_TYPE** ARGOUTVIEWM_ARRAY3)``
* ``(DATA_TYPE** ARGOUTVIEWM_FARRAY3, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DATA_TYPE** ARGOUTVIEWM_FARRAY3)``

4D:

* ``(DATA_TYPE** ARGOUTVIEWM_ARRAY4, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4, DATA_TYPE** ARGOUTVIEWM_ARRAY4)``
* ``(DATA_TYPE** ARGOUTVIEWM_FARRAY4, DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4)``
* ``(DIM_TYPE* DIM1, DIM_TYPE* DIM2, DIM_TYPE* DIM3, DIM_TYPE* DIM4, DATA_TYPE** ARGOUTVIEWM_FARRAY4)``


Output Arrays
~~~~~~~~~~~~~

The ``numpy.i`` interface file does not support typemaps for output
arrays, for several reasons.  First, C/C++ return arguments are
limited to a single value.  This prevents obtaining dimension
information in a general way.  Second, arrays with hard-coded lengths
are not permitted as return arguments.  In other words::

    double[3] newVector(double x, double y, double z);

is not legal C/C++ syntax.  Therefore, we cannot provide typemaps of
the form::

    %typemap(out) (TYPE[ANY]);

If you run into a situation where a function or method is returning a
pointer to an array, your best bet is to write your own version of the
function to be wrapped, either with ``%extend`` for the case of class
methods or ``%ignore`` and ``%rename`` for the case of functions.

Other Common Types: bool
~~~~~~~~~~~~~~~~~~~~~~~~

Note that C++ type ``bool`` is not supported in the list in the
`Available Typemaps`_ section.  NumPy bools are a single byte, while
the C++ ``bool`` is four bytes (at least on my system).  Therefore::

    %numpy_typemaps(bool, NPY_BOOL, int)

will result in typemaps that will produce code that reference
improper data lengths.  You can implement the following macro
expansion::

    %numpy_typemaps(bool, NPY_UINT, int)

to fix the data length problem, and `Input Arrays`_ will work fine,
but `In-Place Arrays`_ might fail type-checking.

Other Common Types: complex
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Typemap conversions for complex floating-point types is also not
supported automatically.  This is because Python and NumPy are
written in C, which does not have native complex types.  Both
Python and NumPy implement their own (essentially equivalent)
``struct`` definitions for complex variables::

    /* Python */
    typedef struct {double real; double imag;} Py_complex;

    /* NumPy */
    typedef struct {float  real, imag;} npy_cfloat;
    typedef struct {double real, imag;} npy_cdouble;

We could have implemented::

    %numpy_typemaps(Py_complex , NPY_CDOUBLE, int)
    %numpy_typemaps(npy_cfloat , NPY_CFLOAT , int)
    %numpy_typemaps(npy_cdouble, NPY_CDOUBLE, int)

which would have provided automatic type conversions for arrays of
type ``Py_complex``, ``npy_cfloat`` and ``npy_cdouble``.  However, it
seemed unlikely that there would be any independent (non-Python,
non-NumPy) application code that people would be using `SWIG`_ to
generate a Python interface to, that also used these definitions
for complex types.  More likely, these application codes will define
their own complex types, or in the case of C++, use ``std::complex``.
Assuming these data structures are compatible with Python and
NumPy complex types, ``%numpy_typemap`` expansions as above (with
the user's complex type substituted for the first argument) should
work.

NumPy array scalars and SWIG
----------------------------

`SWIG`_ has sophisticated type checking for numerical types.  For
example, if your C/C++ routine expects an integer as input, the code
generated by `SWIG`_ will check for both Python integers and
Python long integers, and raise an overflow error if the provided
Python integer is too big to cast down to a C integer.  With the
introduction of NumPy scalar arrays into your Python code, you
might conceivably extract an integer from a NumPy array and attempt
to pass this to a `SWIG`_-wrapped C/C++ function that expects an
``int``, but the `SWIG`_ type checking will not recognize the NumPy
array scalar as an integer.  (Often, this does in fact work -- it
depends on whether NumPy recognizes the integer type you are using
as inheriting from the Python integer type on the platform you are
using.  Sometimes, this means that code that works on a 32-bit machine
will fail on a 64-bit machine.)

If you get a Python error that looks like the following::

    TypeError: in method 'MyClass_MyMethod', argument 2 of type 'int'

and the argument you are passing is an integer extracted from a
NumPy array, then you have stumbled upon this problem.  The
solution is to modify the `SWIG`_ type conversion system to accept
NumPy array scalars in addition to the standard integer types.
Fortunately, this capability has been provided for you.  Simply copy
the file::

    pyfragments.swg

to the working build directory for you project, and this problem will
be fixed.  It is suggested that you do this anyway, as it only
increases the capabilities of your Python interface.

Why is There a Second File?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

The `SWIG`_ type checking and conversion system is a complicated
combination of C macros, `SWIG`_ macros, `SWIG`_ typemaps and `SWIG`_
fragments.  Fragments are a way to conditionally insert code into your
wrapper file if it is needed, and not insert it if not needed.  If
multiple typemaps require the same fragment, the fragment only gets
inserted into your wrapper code once.

There is a fragment for converting a Python integer to a C
``long``.  There is a different fragment that converts a Python
integer to a C ``int``, that calls the routine defined in the
``long`` fragment.  We can make the changes we want here by changing
the definition for the ``long`` fragment.  `SWIG`_ determines the
active definition for a fragment using a "first come, first served"
system.  That is, we need to define the fragment for ``long``
conversions prior to `SWIG`_ doing it internally.  `SWIG`_ allows us
to do this by putting our fragment definitions in the file
``pyfragments.swg``.  If we were to put the new fragment definitions
in ``numpy.i``, they would be ignored.

Helper functions
----------------

The ``numpy.i`` file contains several macros and routines that it
uses internally to build its typemaps.  However, these functions may
be useful elsewhere in your interface file.  These macros and routines
are implemented as fragments, which are described briefly in the
previous section.  If you try to use one or more of the following
macros or functions, but your compiler complains that it does not
recognize the symbol, then you need to force these fragments to appear
in your code using::

    %fragment("NumPy_Fragments");

in your `SWIG`_ interface file.

Macros
~~~~~~

**is_array(a)**
  Evaluates as true if ``a`` is non-``NULL`` and can be cast to a
  ``PyArrayObject*``.

**array_type(a)**
  Evaluates to the integer data type code of ``a``, assuming ``a`` can
  be cast to a ``PyArrayObject*``.

**array_numdims(a)**
  Evaluates to the integer number of dimensions of ``a``, assuming
  ``a`` can be cast to a ``PyArrayObject*``.

**array_dimensions(a)**
  Evaluates to an array of type ``npy_intp`` and length
  ``array_numdims(a)``, giving the lengths of all of the dimensions
  of ``a``, assuming ``a`` can be cast to a ``PyArrayObject*``.

**array_size(a,i)**
  Evaluates to the ``i``-th dimension size of ``a``, assuming ``a``
  can be cast to a ``PyArrayObject*``.

**array_strides(a)**
  Evaluates to an array of type ``npy_intp`` and length
  ``array_numdims(a)``, giving the stridess of all of the dimensions
  of ``a``, assuming ``a`` can be cast to a ``PyArrayObject*``.  A
  stride is the distance in bytes between an element and its
  immediate neighbor along the same axis.

**array_stride(a,i)**
  Evaluates to the ``i``-th stride of ``a``, assuming ``a`` can be
  cast to a ``PyArrayObject*``.

**array_data(a)**
  Evaluates to a pointer of type ``void*`` that points to the data
  buffer of ``a``, assuming ``a`` can be cast to a ``PyArrayObject*``.

**array_descr(a)**
  Returns a borrowed reference to the dtype property
  (``PyArray_Descr*``) of ``a``, assuming ``a`` can be cast to a
  ``PyArrayObject*``.

**array_flags(a)**
  Returns an integer representing the flags of ``a``, assuming ``a``
  can be cast to a ``PyArrayObject*``.

**array_enableflags(a,f)**
  Sets the flag represented by ``f`` of ``a``, assuming ``a`` can be
  cast to a ``PyArrayObject*``.

**array_is_contiguous(a)**
  Evaluates as true if ``a`` is a contiguous array.  Equivalent to
  ``(PyArray_ISCONTIGUOUS(a))``.

**array_is_native(a)**
  Evaluates as true if the data buffer of ``a`` uses native byte
  order.  Equivalent to ``(PyArray_ISNOTSWAPPED(a))``.

**array_is_fortran(a)**
  Evaluates as true if ``a`` is FORTRAN ordered.

Routines
~~~~~~~~

**pytype_string()**
  Return type: ``const char*``

  Arguments:

  * ``PyObject* py_obj``, a general Python object.

  Return a string describing the type of ``py_obj``.


**typecode_string()**
  Return type: ``const char*``

  Arguments:

  * ``int typecode``, a NumPy integer typecode.

  Return a string describing the type corresponding to the NumPy
  ``typecode``.

**type_match()**
  Return type: ``int``

  Arguments:

  * ``int actual_type``, the NumPy typecode of a NumPy array.

  * ``int desired_type``, the desired NumPy typecode.

  Make sure that ``actual_type`` is compatible with
  ``desired_type``.  For example, this allows character and
  byte types, or int and long types, to match.  This is now
  equivalent to ``PyArray_EquivTypenums()``.


**obj_to_array_no_conversion()**
  Return type: ``PyArrayObject*``

  Arguments:

  * ``PyObject* input``, a general Python object.

  * ``int typecode``, the desired NumPy typecode.

  Cast ``input`` to a ``PyArrayObject*`` if legal, and ensure that
  it is of type ``typecode``.  If ``input`` cannot be cast, or the
  ``typecode`` is wrong, set a Python error and return ``NULL``.


**obj_to_array_allow_conversion()**
  Return type: ``PyArrayObject*``

  Arguments:

  * ``PyObject* input``, a general Python object.

  * ``int typecode``, the desired NumPy typecode of the resulting
    array.

  * ``int* is_new_object``, returns a value of 0 if no conversion
    performed, else 1.

  Convert ``input`` to a NumPy array with the given ``typecode``.
  On success, return a valid ``PyArrayObject*`` with the correct
  type.  On failure, the Python error string will be set and the
  routine returns ``NULL``.


**make_contiguous()**
  Return type: ``PyArrayObject*``

  Arguments:

  * ``PyArrayObject* ary``, a NumPy array.

  * ``int* is_new_object``, returns a value of 0 if no conversion
    performed, else 1.

  * ``int min_dims``, minimum allowable dimensions.

  * ``int max_dims``, maximum allowable dimensions.

  Check to see if ``ary`` is contiguous.  If so, return the input
  pointer and flag it as not a new object.  If it is not contiguous,
  create a new ``PyArrayObject*`` using the original data, flag it
  as a new object and return the pointer.


**make_fortran()**
  Return type: ``PyArrayObject*``

  Arguments

  * ``PyArrayObject* ary``, a NumPy array.

  * ``int* is_new_object``, returns a value of 0 if no conversion
    performed, else 1.

  Check to see if ``ary`` is Fortran contiguous.  If so, return the
  input pointer and flag it as not a new object.  If it is not
  Fortran contiguous, create a new ``PyArrayObject*`` using the
  original data, flag it as a new object and return the pointer.


**obj_to_array_contiguous_allow_conversion()**
  Return type: ``PyArrayObject*``

  Arguments:

  * ``PyObject* input``, a general Python object.

  * ``int typecode``, the desired NumPy typecode of the resulting
    array.

  * ``int* is_new_object``, returns a value of 0 if no conversion
    performed, else 1.

  Convert ``input`` to a contiguous ``PyArrayObject*`` of the
  specified type.  If the input object is not a contiguous
  ``PyArrayObject*``, a new one will be created and the new object
  flag will be set.


**obj_to_array_fortran_allow_conversion()**
  Return type: ``PyArrayObject*``

  Arguments:

  * ``PyObject* input``, a general Python object.

  * ``int typecode``, the desired NumPy typecode of the resulting
    array.

  * ``int* is_new_object``, returns a value of 0 if no conversion
    performed, else 1.

  Convert ``input`` to a Fortran contiguous ``PyArrayObject*`` of
  the specified type.  If the input object is not a Fortran
  contiguous ``PyArrayObject*``, a new one will be created and the
  new object flag will be set.


**require_contiguous()**
  Return type: ``int``

  Arguments:

  * ``PyArrayObject* ary``, a NumPy array.

  Test whether ``ary`` is contiguous.  If so, return 1.  Otherwise,
  set a Python error and return 0.


**require_native()**
  Return type: ``int``

  Arguments:

  * ``PyArray_Object* ary``, a NumPy array.

  Require that ``ary`` is not byte-swapped.  If the array is not
  byte-swapped, return 1.  Otherwise, set a Python error and
  return 0.

**require_dimensions()**
  Return type: ``int``

  Arguments:

  * ``PyArrayObject* ary``, a NumPy array.

  * ``int exact_dimensions``, the desired number of dimensions.

  Require ``ary`` to have a specified number of dimensions.  If the
  array has the specified number of dimensions, return 1.
  Otherwise, set a Python error and return 0.


**require_dimensions_n()**
  Return type: ``int``

  Arguments:

  * ``PyArrayObject* ary``, a NumPy array.

  * ``int* exact_dimensions``, an array of integers representing
    acceptable numbers of dimensions.

  * ``int n``, the length of ``exact_dimensions``.

  Require ``ary`` to have one of a list of specified number of
  dimensions.  If the array has one of the specified number of
  dimensions, return 1.  Otherwise, set the Python error string
  and return 0.


**require_size()**
  Return type: ``int``

  Arguments:

  * ``PyArrayObject* ary``, a NumPy array.

  * ``npy_int* size``, an array representing the desired lengths of
    each dimension.

  * ``int n``, the length of ``size``.

  Require ``ary`` to have a specified shape.  If the array has the
  specified shape, return 1.  Otherwise, set the Python error
  string and return 0.


**require_fortran()**
  Return type: ``int``

  Arguments:

  * ``PyArrayObject* ary``, a NumPy array.

  Require the given ``PyArrayObject`` to be Fortran ordered.  If
  the ``PyArrayObject`` is already Fortran ordered, do nothing.
  Else, set the Fortran ordering flag and recompute the strides.


Beyond the provided typemaps
----------------------------

There are many C or C++ array/NumPy array situations not covered by
a simple ``%include "numpy.i"`` and subsequent ``%apply`` directives.

A Common Example
~~~~~~~~~~~~~~~~

Consider a reasonable prototype for a dot product function::

    double dot(int len, double* vec1, double* vec2);

The Python interface that we want is::

    def dot(vec1, vec2):
        """
        dot(PyObject,PyObject) -> double
        """

The problem here is that there is one dimension argument and two array
arguments, and our typemaps are set up for dimensions that apply to a
single array (in fact, `SWIG`_ does not provide a mechanism for
associating ``len`` with ``vec2`` that takes two Python input
arguments).  The recommended solution is the following::

    %apply (int DIM1, double* IN_ARRAY1) {(int len1, double* vec1),
                                          (int len2, double* vec2)}
    %rename (dot) my_dot;
    %exception my_dot {
        $action
	if (PyErr_Occurred()) SWIG_fail;
    }
    %inline %{
    double my_dot(int len1, double* vec1, int len2, double* vec2) {
        if (len1 != len2) {
	    PyErr_Format(PyExc_ValueError,
                         "Arrays of lengths (%d,%d) given",
                         len1, len2);
	    return 0.0;
        }
        return dot(len1, vec1, vec2);
    }
    %}

If the header file that contains the prototype for ``double dot()``
also contains other prototypes that you want to wrap, so that you need
to ``%include`` this header file, then you will also need a ``%ignore
dot;`` directive, placed after the ``%rename`` and before the
``%include`` directives.  Or, if the function in question is a class
method, you will want to use ``%extend`` rather than ``%inline`` in
addition to ``%ignore``.

**A note on error handling:** Note that ``my_dot`` returns a
``double`` but that it can also raise a Python error.  The
resulting wrapper function will return a Python float
representation of 0.0 when the vector lengths do not match.  Since
this is not ``NULL``, the Python interpreter will not know to check
for an error.  For this reason, we add the ``%exception`` directive
above for ``my_dot`` to get the behavior we want (note that
``$action`` is a macro that gets expanded to a valid call to
``my_dot``).  In general, you will probably want to write a `SWIG`_
macro to perform this task.

Other Situations
~~~~~~~~~~~~~~~~

There are other wrapping situations in which ``numpy.i`` may be
helpful when you encounter them.

* In some situations, it is possible that you could use the
  ``%numpy_typemaps`` macro to implement typemaps for your own
  types.  See the `Other Common Types: bool`_ or `Other Common
  Types: complex`_ sections for examples.  Another situation is if
  your dimensions are of a type other than ``int`` (say ``long`` for
  example)::

      %numpy_typemaps(double, NPY_DOUBLE, long)

* You can use the code in ``numpy.i`` to write your own typemaps.
  For example, if you had a five-dimensional array as a function
  argument, you could cut-and-paste the appropriate four-dimensional
  typemaps into your interface file.  The modifications for the
  fourth dimension would be trivial.

* Sometimes, the best approach is to use the ``%extend`` directive
  to define new methods for your classes (or overload existing ones)
  that take a ``PyObject*`` (that either is or can be converted to a
  ``PyArrayObject*``) instead of a pointer to a buffer.  In this
  case, the helper routines in ``numpy.i`` can be very useful.

* Writing typemaps can be a bit nonintuitive.  If you have specific
  questions about writing `SWIG`_ typemaps for NumPy, the
  developers of ``numpy.i`` do monitor the
  `Numpy-discussion <mailto:Numpy-discussion@python.org>`_ and
  `Swig-user <mailto:Swig-user@lists.sourceforge.net>`_ mail lists.

A Final Note
~~~~~~~~~~~~

When you use the ``%apply`` directive, as is usually necessary to use
``numpy.i``, it will remain in effect until you tell `SWIG`_ that it
shouldn't be.  If the arguments to the functions or methods that you
are wrapping have common names, such as ``length`` or ``vector``,
these typemaps may get applied in situations you do not expect or
want.  Therefore, it is always a good idea to add a ``%clear``
directive after you are done with a specific typemap::

    %apply (double* IN_ARRAY1, int DIM1) {(double* vector, int length)}
    %include "my_header.h"
    %clear (double* vector, int length);

In general, you should target these typemap signatures specifically
where you want them, and then clear them after you are done.

Summary
-------

Out of the box, ``numpy.i`` provides typemaps that support conversion
between NumPy arrays and C arrays:

* That can be one of 12 different scalar types: ``signed char``,
  ``unsigned char``, ``short``, ``unsigned short``, ``int``,
  ``unsigned int``, ``long``, ``unsigned long``, ``long long``,
  ``unsigned long long``, ``float`` and ``double``.

* That support 74 different argument signatures for each data type,
  including:

  + One-dimensional, two-dimensional, three-dimensional and
    four-dimensional arrays.

  + Input-only, in-place, argout, argoutview, and memory managed
    argoutview behavior.

  + Hard-coded dimensions, data-buffer-then-dimensions
    specification, and dimensions-then-data-buffer specification.

  + Both C-ordering ("last dimension fastest") or Fortran-ordering
    ("first dimension fastest") support for 2D, 3D and 4D arrays.

The ``numpy.i`` interface file also provides additional tools for
wrapper developers, including:

* A `SWIG`_ macro (``%numpy_typemaps``) with three arguments for
  implementing the 74 argument signatures for the user's choice of
  (1) C data type, (2) NumPy data type (assuming they match), and
  (3) dimension type.

* Fourteen C macros and fifteen C functions that can be used to
  write specialized typemaps, extensions, or inlined functions that
  handle cases not covered by the provided typemaps.  Note that the
  macros and functions are coded specifically to work with the NumPy
  C/API regardless of NumPy version number, both before and after
  the deprecation of some aspects of the API after version 1.6.
