The number of dimensions in the array.

Returns an integer representing the :ref:`array-flags<array-flags>`.

Return the (builtin) typenumber for the elements of this array.

.. versionadded:: 2.0

Sets the memory location ``item`` of dtype ``descr`` to ``value``.

The function is equivalent to setting a single array element with a Python
assignment.  Returns 0 on success and -1 with an error set on failure.

.. note::
    If the ``descr`` has the :c:data:`NPY_NEEDS_INIT` flag set, the
    data must be valid or the memory zeroed.

Convert obj and place it in the ndarray, *arr*, at the place
pointed to by itemptr. Return -1 if an error occurs or 0 on
success.

.. note::
    In general, prefer the use of :c:func:`PyArray_Pack` when
    handling arbitrary Python objects.  Setitem is for example not able
    to handle arbitrary casts between different dtypes.

Enables the specified array flags. This function does no validation,
and assumes that you know what you're doing.

Clears the specified array flags. This function does no validation,
and assumes that you know what you're doing.

These two macros are similar and obtain the pointer to the
data-buffer for the array. The first macro can (and should be)
assigned to a particular pointer where the second is for generic
processing. If you have not guaranteed a contiguous and/or aligned
array then be sure you understand how to access the data in the
array to avoid memory and/or alignment problems.

Returns a pointer to the dimensions/shape of the array. The
number of elements matches the number of dimensions
of the array. Can return ``NULL`` for 0-dimensional arrays.

A synonym for :c:func:`PyArray_DIMS`, named to be consistent with the
`shape <numpy.ndarray.shape>` usage within Python.

Returns a pointer to the strides of the array. The
number of elements matches the number of dimensions
of the array.

Return the shape in the *n* :math:`^{\textrm{th}}` dimension.

Return the stride in the *n* :math:`^{\textrm{th}}` dimension.

Return the itemsize for the elements of this array.

Note that, in the old API that was deprecated in version 1.7, this function
had the return type ``int``.

Returns the total size (in number of elements) of the array.

Returns 0 if *obj* is not a sub-class of ndarray. Otherwise,
returns the total number of elements in the array. Safer version
of :c:func:`PyArray_SIZE` (*obj*).

Returns the total number of bytes consumed by the array.

This returns the base object of the array. In most cases, this
means the object which owns the memory the array is pointing at.

If you are constructing an array using the C API, and specifying
your own memory, you should use the function :c:func:`PyArray_SetBaseObject`
to set the base to an object which owns the memory.

If the :c:data:`NPY_ARRAY_WRITEBACKIFCOPY` flag is set, it has a different
meaning, namely base is the array into which the current array will
be copied upon copy resolution. This overloading of the base property
for two functions is likely to change in a future version of NumPy.

Returns a borrowed reference to the dtype property of the array.

A synonym for PyArray_DESCR, named to be consistent with the
'dtype' usage within Python.

Get a Python object of a builtin type from the ndarray, *arr*,
at the location pointed to by itemptr. Return ``NULL`` on failure.

`numpy.ndarray.item` is identical to PyArray_GETITEM.

The function pointed to by the :c:type:`PyCapsule`
:obj:`~numpy.class.__array_finalize__`.
The first argument is the newly created sub-type. The second argument
(if not NULL) is the "parent" array (if the array was created using
slicing or some other operation where a clearly-distinguishable parent
is present). This routine can do anything it wants to. It should
return a -1 on error and 0 otherwise.

These functions and macros provide easy access to elements of the
ndarray from C. These work for all arrays. You may need to take care
when accessing the data in the array, however, if it is not in machine
byte-order, misaligned, or not writeable. In other words, be sure to
respect the state of the flags unless you know what you are doing, or
have previously guaranteed an array that is writeable, aligned, and in
machine byte-order using :c:func:`PyArray_FromAny`. If you wish to handle all
types of arrays, the copyswap function for each type is useful for
handling misbehaved arrays. Some platforms (e.g. Solaris) do not like
misaligned data and will crash if you de-reference a misaligned
pointer. Other platforms (e.g. x86 Linux) will just work more slowly
with misaligned data.

.. c:function:: void* PyArray_GetPtr(PyArrayObject* aobj, npy_intp* ind)

    Return a pointer to the data of the ndarray, *aobj*, at the
    N-dimensional index given by the c-array, *ind*, (which must be
    at least *aobj* ->nd in size). You may want to typecast the
    returned pointer to the data type of the ndarray.

.. c:function:: void* PyArray_GETPTR1(PyArrayObject* obj, npy_intp i)

.. c:function:: void* PyArray_GETPTR2( \
        PyArrayObject* obj, npy_intp i, npy_intp j)

.. c:function:: void* PyArray_GETPTR3( \
        PyArrayObject* obj, npy_intp i, npy_intp j, npy_intp k)

.. c:function:: void* PyArray_GETPTR4( \
        PyArrayObject* obj, npy_intp i, npy_intp j, npy_intp k, npy_intp l)

    Quick, inline access to the element at the given coordinates in
    the ndarray, *obj*, which must have respectively 1, 2, 3, or 4
    dimensions (this is not checked). The corresponding *i*, *j*,
    *k*, and *l* coordinates can be any integer but will be
    interpreted as ``npy_intp``. You may want to typecast the
    returned pointer to the data type of the ndarray.


Creating arrays
---------------


From scratch

This function steals a reference to *descr*. The easiest way to get one
is using :c:func:`PyArray_DescrFromType`.

This is the main array creation function. Most new arrays are
created with this flexible function.

The returned object is an object of Python-type *subtype*, which
must be a subtype of :c:data:`PyArray_Type`.  The array has *nd*
dimensions, described by *dims*. The data-type descriptor of the
new array is *descr*.

If *subtype* is of an array subclass instead of the base
:c:data:`&PyArray_Type<PyArray_Type>`, then *obj* is the object to pass to
the :obj:`~numpy.class.__array_finalize__` method of the subclass.

If *data* is ``NULL``, then new unitinialized memory will be allocated and
*flags* can be non-zero to indicate a Fortran-style contiguous array. Use
:c:func:`PyArray_FILLWBYTE` to initialize the memory.

If *data* is not ``NULL``, then it is assumed to point to the memory
to be used for the array and the *flags* argument is used as the
new flags for the array (except the state of :c:data:`NPY_ARRAY_OWNDATA`,
:c:data:`NPY_ARRAY_WRITEBACKIFCOPY` flag of the new array will be reset).

In addition, if *data* is non-NULL, then *strides* can
also be provided. If *strides* is ``NULL``, then the array strides
are computed as C-style contiguous (default) or Fortran-style
contiguous (*flags* is nonzero for *data* = ``NULL`` or *flags* &
:c:data:`NPY_ARRAY_F_CONTIGUOUS` is nonzero non-NULL *data*). Any
provided *dims* and *strides* are copied into newly allocated
dimension and strides arrays for the new array object.

:c:func:`PyArray_CheckStrides` can help verify non- ``NULL`` stride
information.

If ``data`` is provided, it must stay alive for the life of the array. One
way to manage this is through :c:func:`PyArray_SetBaseObject`

This function steals a reference to *descr* if it is not NULL.
This array creation routine allows for the convenient creation of
a new array matching an existing array's shapes and memory layout,
possibly changing the layout and/or data type.

When *order* is :c:data:`NPY_ANYORDER`, the result order is
:c:data:`NPY_FORTRANORDER` if *prototype* is a fortran array,
:c:data:`NPY_CORDER` otherwise.  When *order* is
:c:data:`NPY_KEEPORDER`, the result order matches that of *prototype*, even
when the axes of *prototype* aren't in C or Fortran order.

If *descr* is NULL, the data type of *prototype* is used.

If *subok* is 1, the newly created array will use the sub-type of
*prototype* to create the new array, otherwise it will create a
base-class array.

This is similar to :c:func:`PyArray_NewFromDescr` (...) except you
specify the data-type descriptor with *type_num* and *itemsize*,
where *type_num* corresponds to a builtin (or user-defined)
type. If the type always has the same number of bytes, then
itemsize is ignored. Otherwise, itemsize specifies the particular
size of this array.

If data is passed to :c:func:`PyArray_NewFromDescr` or :c:func:`PyArray_New`,
this memory must not be deallocated until the new array is
deleted.  If this data came from another Python object, this can
be accomplished using :c:func:`Py_INCREF` on that object and setting the
base member of the new array to point to that object. If strides
are passed in they must be consistent with the dimensions, the
itemsize, and the data of the array.

Create a new uninitialized array of type, *typenum*, whose size in
each of *nd* dimensions is given by the integer array, *dims*.The memory
for the array is uninitialized (unless typenum is :c:data:`NPY_OBJECT`
in which case each element in the array is set to NULL). The
*typenum* argument allows specification of any of the builtin
data-types such as :c:data:`NPY_FLOAT` or :c:data:`NPY_LONG`. The
memory for the array can be set to zero if desired using
:c:func:`PyArray_FILLWBYTE` (return_object, 0).This function cannot be
used to create a flexible-type array (no itemsize given).

Create an array wrapper around *data* pointed to by the given
pointer. The array flags will have a default that the data area is
well-behaved and C-style contiguous. The shape of the array is
given by the *dims* c-array of length *nd*. The data-type of the
array is indicated by *typenum*. If data comes from another
reference-counted Python object, the reference count on this object
should be increased after the pointer is passed in, and the base member
of the returned ndarray should point to the Python object that owns
the data. This will ensure that the provided memory is not
freed while the returned array is in existence.

This function steals a reference to *descr*.

Create a new array with the provided data-type descriptor, *descr*,
of the shape determined by *nd* and *dims*.

Fill the array pointed to by *obj* ---which must be a (subclass
of) ndarray---with the contents of *val* (evaluated as a byte).
This macro calls memset, so obj must be contiguous.

Construct a new *nd* -dimensional array with shape given by *dims*
and data type given by *dtype*. If *fortran* is non-zero, then a
Fortran-order array is created, otherwise a C-order array is
created. Fill the memory with zeros (or the 0 object if *dtype*
corresponds to :c:type:`NPY_OBJECT` ).

Macro form of :c:func:`PyArray_Zeros` which takes a type-number instead
of a data-type object.

Construct a new *nd* -dimensional array with shape given by *dims*
and data type given by *dtype*. If *fortran* is non-zero, then a
Fortran-order array is created, otherwise a C-order array is
created. The array is uninitialized unless the data type
corresponds to :c:type:`NPY_OBJECT` in which case the array is
filled with :c:data:`Py_None`.

Macro form of :c:func:`PyArray_Empty` which takes a type-number,
*typenum*, instead of a data-type object.

Construct a new 1-dimensional array of data-type, *typenum*, that
ranges from *start* to *stop* (exclusive) in increments of *step*
. Equivalent to **arange** (*start*, *stop*, *step*, dtype).

Construct a new 1-dimensional array of data-type determined by
``descr``, that ranges from ``start`` to ``stop`` (exclusive) in
increments of ``step``. Equivalent to arange( ``start``,
``stop``, ``step``, ``typenum`` ).

This function **steals a reference** to ``obj`` and sets it as the
base property of ``arr``.

If you construct an array by passing in your own memory buffer as
a parameter, you need to set the array's `base` property to ensure
the lifetime of the memory buffer is appropriate.

The return value is 0 on success, -1 on failure.

If the object provided is an array, this function traverses the
chain of `base` pointers so that each array points to the owner
of the memory directly. Once the base is set, it may not be changed
to another value.

.. c:function:: PyObject* PyArray_FromAny( \
        PyObject* op, PyArray_Descr* dtype, int min_depth, int max_depth, \
        int requirements, PyObject* context)

    This is the main function used to obtain an array from any nested
    sequence, or object that exposes the array interface, *op*. The
    parameters allow specification of the required *dtype*, the
    minimum (*min_depth*) and maximum (*max_depth*) number of
    dimensions acceptable, and other *requirements* for the array. This
    function **steals a reference** to the dtype argument, which needs
    to be a :c:type:`PyArray_Descr` structure
    indicating the desired data-type (including required
    byteorder). The *dtype* argument may be ``NULL``, indicating that any
    data-type (and byteorder) is acceptable. Unless
    :c:data:`NPY_ARRAY_FORCECAST` is present in ``flags``,
    this call will generate an error if the data
    type cannot be safely obtained from the object. If you want to use
    ``NULL`` for the *dtype* and ensure the array is not swapped then
    use :c:func:`PyArray_CheckFromAny`. A value of 0 for either of the
    depth parameters causes the parameter to be ignored. Any of the
    following array flags can be added (*e.g.* using \|) to get the
    *requirements* argument. If your code can handle general (*e.g.*
    strided, byte-swapped, or unaligned arrays) then *requirements*
    may be 0. Also, if *op* is not already an array (or does not
    expose the array interface), then a new array will be created (and
    filled from *op* using the sequence protocol). The new array will
    have :c:data:`NPY_ARRAY_DEFAULT` as its flags member. The *context*
    argument is unused.

    :c:macro:`NPY_ARRAY_C_CONTIGUOUS`
        Make sure the returned array is C-style contiguous

    :c:macro:`NPY_ARRAY_F_CONTIGUOUS`
        Make sure the returned array is Fortran-style contiguous.

    :c:macro:`NPY_ARRAY_ALIGNED`
        Make sure the returned array is aligned on proper boundaries for its
        data type. An aligned array has the data pointer and every strides
        factor as a multiple of the alignment factor for the data-type-
        descriptor.

    :c:macro:`NPY_ARRAY_WRITEABLE`
        Make sure the returned array can be written to.

    :c:macro:`NPY_ARRAY_ENSURECOPY`
        Make sure a copy is made of *op*. If this flag is not
        present, data is not copied if it can be avoided.

    :c:macro:`NPY_ARRAY_ENSUREARRAY`
        Make sure the result is a base-class ndarray. By
        default, if *op* is an instance of a subclass of
        ndarray, an instance of that same subclass is returned. If
        this flag is set, an ndarray object will be returned instead.

    :c:macro:`NPY_ARRAY_FORCECAST`
        Force a cast to the output type even if it cannot be done
        safely.  Without this flag, a data cast will occur only if it
        can be done safely, otherwise an error is raised.

    :c:macro:`NPY_ARRAY_WRITEBACKIFCOPY`
        If *op* is already an array, but does not satisfy the
        requirements, then a copy is made (which will satisfy the
        requirements). If this flag is present and a copy (of an object
        that is already an array) must be made, then the corresponding
        :c:data:`NPY_ARRAY_WRITEBACKIFCOPY` flag is set in the returned
        copy and *op* is made to be read-only. You must be sure to call
        :c:func:`PyArray_ResolveWritebackIfCopy` to copy the contents
        back into *op* and the *op* array
        will be made writeable again. If *op* is not writeable to begin
        with, or if it is not already an array, then an error is raised.

    `Combinations of array flags`_ can also be added.

.. c:function:: PyObject* PyArray_CheckFromAny( \
        PyObject* op, PyArray_Descr* dtype, int min_depth, int max_depth, \
        int requirements, PyObject* context)

    Nearly identical to :c:func:`PyArray_FromAny` (...) except
    *requirements* can contain :c:data:`NPY_ARRAY_NOTSWAPPED` (over-riding the
    specification in *dtype*) and :c:data:`NPY_ARRAY_ELEMENTSTRIDES` which
    indicates that the array should be aligned in the sense that the
    strides are multiples of the element size.

.. c:function:: PyObject* PyArray_FromArray( \
        PyArrayObject* op, PyArray_Descr* newtype, int requirements)

    Special case of :c:func:`PyArray_FromAny` for when *op* is already an
    array but it needs to be of a specific *newtype* (including
    byte-order) or has certain *requirements*.

.. c:function:: PyObject* PyArray_FromStructInterface(PyObject* op)

    Returns an ndarray object from a Python object that exposes the
    :obj:`~object.__array_struct__` attribute and follows the array interface
    protocol. If the object does not contain this attribute then a
    borrowed reference to :c:data:`Py_NotImplemented` is returned.

.. c:function:: PyObject* PyArray_FromInterface(PyObject* op)

    Returns an ndarray object from a Python object that exposes the
    :obj:`~object.__array_interface__` attribute following the array interface
    protocol. If the object does not contain this attribute then a
    borrowed reference to :c:data:`Py_NotImplemented` is returned.

.. c:function:: PyObject* PyArray_FromArrayAttr( \
        PyObject* op, PyArray_Descr* dtype, PyObject* context)

    Return an ndarray object from a Python object that exposes the
    :obj:`~numpy.class.__array__` method. The third-party implementations of
    :obj:`~numpy.class.__array__` must take ``dtype`` and ``copy`` keyword
    arguments. ``context`` is unused.

.. c:function:: PyObject* PyArray_ContiguousFromAny( \
        PyObject* op, int typenum, int min_depth, int max_depth)

    This function returns a (C-style) contiguous and behaved function
    array from any nested sequence or array interface exporting
    object, *op*, of (non-flexible) type given by the enumerated
    *typenum*, of minimum depth *min_depth*, and of maximum depth
    *max_depth*. Equivalent to a call to :c:func:`PyArray_FromAny` with
    requirements set to :c:data:`NPY_ARRAY_DEFAULT` and the type_num member of the
    type argument set to *typenum*.

.. c:function:: PyObject* PyArray_ContiguousFromObject( \
        PyObject* op, int typenum, int min_depth, int max_depth)

    This function returns a well-behaved C-style contiguous array from any nested
    sequence or array-interface exporting object. The minimum number of dimensions
    the array can have is given by `min_depth` while the maximum is `max_depth`.
    This is equivalent to call :c:func:`PyArray_FromAny` with requirements
    :c:data:`NPY_ARRAY_DEFAULT` and :c:data:`NPY_ARRAY_ENSUREARRAY`.

.. c:function:: PyObject* PyArray_FromObject( \
        PyObject* op, int typenum, int min_depth, int max_depth)

    Return an aligned and in native-byteorder array from any nested
    sequence or array-interface exporting object, op, of a type given by
    the enumerated typenum. The minimum number of dimensions the array can
    have is given by min_depth while the maximum is max_depth. This is
    equivalent to a call to :c:func:`PyArray_FromAny` with requirements set to
    BEHAVED.

.. c:function:: PyObject* PyArray_EnsureArray(PyObject* op)

    This function **steals a reference** to ``op`` and makes sure that
    ``op`` is a base-class ndarray. It special cases array scalars,
    but otherwise calls :c:func:`PyArray_FromAny` ( ``op``, NULL, 0, 0,
    :c:data:`NPY_ARRAY_ENSUREARRAY`, NULL).

.. c:function:: PyObject* PyArray_FromString( \
        char* string, npy_intp slen, PyArray_Descr* dtype, npy_intp num, \
        char* sep)

    Construct a one-dimensional ndarray of a single type from a binary
    or (ASCII) text ``string`` of length ``slen``. The data-type of
    the array to-be-created is given by ``dtype``. If num is -1, then
    **copy** the entire string and return an appropriately sized
    array, otherwise, ``num`` is the number of items to **copy** from
    the string. If ``sep`` is NULL (or ""), then interpret the string
    as bytes of binary data, otherwise convert the sub-strings
    separated by ``sep`` to items of data-type ``dtype``. Some
    data-types may not be readable in text mode and an error will be
    raised if that occurs. All errors return NULL.

.. c:function:: PyObject* PyArray_FromFile( \
        FILE* fp, PyArray_Descr* dtype, npy_intp num, char* sep)

    Construct a one-dimensional ndarray of a single type from a binary
    or text file. The open file pointer is ``fp``, the data-type of
    the array to be created is given by ``dtype``. This must match
    the data in the file. If ``num`` is -1, then read until the end of
    the file and return an appropriately sized array, otherwise,
    ``num`` is the number of items to read. If ``sep`` is NULL (or
    ""), then read from the file in binary mode, otherwise read from
    the file in text mode with ``sep`` providing the item
    separator. Some array types cannot be read in text mode in which
    case an error is raised.

.. c:function:: PyObject* PyArray_FromBuffer( \
        PyObject* buf, PyArray_Descr* dtype, npy_intp count, npy_intp offset)

    Construct a one-dimensional ndarray of a single type from an
    object, ``buf``, that exports the (single-segment) buffer protocol
    (or has an attribute __buffer\__ that returns an object that
    exports the buffer protocol). A writeable buffer will be tried
    first followed by a read- only buffer. The :c:data:`NPY_ARRAY_WRITEABLE`
    flag of the returned array will reflect which one was
    successful. The data is assumed to start at ``offset`` bytes from
    the start of the memory location for the object. The type of the
    data in the buffer will be interpreted depending on the data- type
    descriptor, ``dtype.`` If ``count`` is negative then it will be
    determined from the size of the buffer and the requested itemsize,
    otherwise, ``count`` represents how many elements should be
    converted from the buffer.

.. c:function:: int PyArray_CopyInto(PyArrayObject* dest, PyArrayObject* src)

    Copy from the source array, ``src``, into the destination array,
    ``dest``, performing a data-type conversion if necessary. If an
    error occurs return -1 (otherwise 0). The shape of ``src`` must be
    broadcastable to the shape of ``dest``.
    NumPy checks for overlapping memory when copying two arrays.

.. c:function:: int PyArray_CopyObject(PyArrayObject* dest, PyObject* src)

    Assign an object ``src`` to a NumPy array ``dest`` according to
    array-coercion rules. This is basically identical to
    :c:func:`PyArray_FromAny`, but assigns directly to the output array.
    Returns 0 on success and -1 on failures.

.. c:function:: PyArrayObject* PyArray_GETCONTIGUOUS(PyObject* op)

    If ``op`` is already (C-style) contiguous and well-behaved then
    just return a reference, otherwise return a (contiguous and
    well-behaved) copy of the array. The parameter op must be a
    (sub-class of an) ndarray and no checking for that is done.

.. c:function:: PyObject* PyArray_FROM_O(PyObject* obj)

    Convert ``obj`` to an ndarray. The argument can be any nested
    sequence or object that exports the array interface. This is a
    macro form of :c:func:`PyArray_FromAny` using ``NULL``, 0, 0, 0 for the
    other arguments. Your code must be able to handle any data-type
    descriptor and any combination of data-flags to use this macro.

.. c:function:: PyObject* PyArray_FROM_OF(PyObject* obj, int requirements)

    Similar to :c:func:`PyArray_FROM_O` except it can take an argument
    of *requirements* indicating properties the resulting array must
    have. Available requirements that can be enforced are
    :c:data:`NPY_ARRAY_C_CONTIGUOUS`, :c:data:`NPY_ARRAY_F_CONTIGUOUS`,
    :c:data:`NPY_ARRAY_ALIGNED`, :c:data:`NPY_ARRAY_WRITEABLE`,
    :c:data:`NPY_ARRAY_NOTSWAPPED`, :c:data:`NPY_ARRAY_ENSURECOPY`,
    :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`, :c:data:`NPY_ARRAY_FORCECAST`, and
    :c:data:`NPY_ARRAY_ENSUREARRAY`. Standard combinations of flags can also
    be used:

.. c:function:: PyObject* PyArray_FROM_OT(PyObject* obj, int typenum)

    Similar to :c:func:`PyArray_FROM_O` except it can take an argument of
    *typenum* specifying the type-number the returned array.

.. c:function:: PyObject* PyArray_FROM_OTF( \
        PyObject* obj, int typenum, int requirements)

    Combination of :c:func:`PyArray_FROM_OF` and :c:func:`PyArray_FROM_OT`
    allowing both a *typenum* and a *flags* argument to be provided.

.. c:function:: PyObject* PyArray_FROMANY( \
        PyObject* obj, int typenum, int min, int max, int requirements)

    Similar to :c:func:`PyArray_FromAny` except the data-type is
    specified using a typenumber. :c:func:`PyArray_DescrFromType`
    (*typenum*) is passed directly to :c:func:`PyArray_FromAny`. This
    macro also adds :c:data:`NPY_ARRAY_DEFAULT` to requirements if
    :c:data:`NPY_ARRAY_ENSURECOPY` is passed in as requirements.

.. c:function:: PyObject *PyArray_CheckAxis( \
        PyObject* obj, int* axis, int requirements)

    Encapsulate the functionality of functions and methods that take
    the axis= keyword and work properly with None as the axis
    argument. The input array is ``obj``, while ``*axis`` is a
    converted integer (so that ``*axis == NPY_RAVEL_AXIS`` is the None value), and
    ``requirements`` gives the needed properties of ``obj``. The
    output is a converted version of the input so that requirements
    are met and if needed a flattening has occurred. On output
    negative values of ``*axis`` are converted and the new value is
    checked to ensure consistency with the shape of ``obj``.


Dealing with types
------------------


General check of Python Type

Evaluates true if *op* is a Python object whose type is a sub-type
of :c:data:`PyArray_Type`.

Evaluates true if *op* is a Python object with type
:c:data:`PyArray_Type`.

If ``op`` implements any part of the array interface, then ``out``
will contain a new reference to the newly created ndarray using
the interface or ``out`` will contain ``NULL`` if an error during
conversion occurs. Otherwise, out will contain a borrowed
reference to :c:data:`Py_NotImplemented` and no error condition is set.

If ``op`` implements any part of the array interface, then ``out``
will contain a new reference to the newly created ndarray using
the interface or ``out`` will contain ``NULL`` if an error during
conversion occurs. Otherwise, out will contain a borrowed
reference to Py_NotImplemented and no error condition is set.
This version allows setting of the dtype in the part of the array interface
that looks for the :obj:`~numpy.class.__array__` attribute. `context` is
unused.

Evaluates true if *op* is an instance of (a subclass of)
:c:data:`PyArray_Type` and has 0 dimensions.

Evaluates true if *op* is an instance of ``Py{cls}ArrType_Type``.

Evaluates true if *op* is either an array scalar (an instance of a
sub-type of :c:data:`PyGenericArrType_Type` ), or an instance of (a
sub-class of) :c:data:`PyArray_Type` whose dimensionality is 0.

Evaluates true if *op* is an instance of a builtin numeric type (int,
float, complex, long, bool)

Evaluates true if *op* is a builtin Python scalar object (int,
float, complex, bytes, str, long, bool).

Evaluates true if *op* is either a Python scalar object (see
:c:func:`PyArray_IsPythonScalar`) or an array scalar (an instance of a sub-
type of :c:data:`PyGenericArrType_Type` ).

Evaluates true if *op* is a Python scalar object (see
:c:func:`PyArray_IsPythonScalar`), an array scalar (an instance of a
sub-type of :c:data:`PyGenericArrType_Type`) or an instance of a sub-type of
:c:data:`PyArray_Type` whose dimensionality is 0.

Some of the descriptor attributes may not always be defined and should or
cannot not be accessed directly.

.. versionchanged:: 2.0
    Prior to NumPy 2.0 the ABI was different but unnecessary large for user
    DTypes.  These accessors were all added in 2.0 and can be backported
    (see :ref:`migration_c_descr`).

.. c:function:: npy_intp PyDataType_ELSIZE(PyArray_Descr *descr)

    The element size of the datatype (``itemsize`` in Python).

    .. note::
        If the ``descr`` is attached to an array ``PyArray_ITEMSIZE(arr)``
        can be used and is available on all NumPy versions.

.. c:function:: void PyDataType_SET_ELSIZE(PyArray_Descr *descr, npy_intp size)

    Allows setting of the itemsize, this is *only* relevant for string/bytes
    datatypes as it is the current pattern to define one with a new size.

.. c:function:: npy_intp PyDataType_ALIGNMENT(PyArray_Descr *descr)

    The alignment of the datatype.

.. c:function:: PyObject *PyDataType_METADATA(PyArray_Descr *descr)

    The Metadata attached to a dtype, either ``NULL`` or a dictionary.

.. c:function:: PyObject *PyDataType_NAMES(PyArray_Descr *descr)

    ``NULL`` or a tuple of structured field names attached to a dtype.

.. c:function:: PyObject *PyDataType_FIELDS(PyArray_Descr *descr)

    ``NULL``, ``None``, or a dict of structured dtype fields, this dict must
    not be mutated, NumPy may change the way fields are stored in the future.

    This is the same dict as returned by `np.dtype.fields`.

.. c:function:: NpyAuxData *PyDataType_C_METADATA(PyArray_Descr *descr)

    C-metadata object attached to a descriptor.  This accessor should not
    be needed usually.  The C-Metadata field does provide access to the
    datetime/timedelta time unit information.

.. c:function:: PyArray_ArrayDescr *PyDataType_SUBARRAY(PyArray_Descr *descr)

    Information about a subarray dtype equivalent to the Python `np.dtype.base`
    and `np.dtype.shape`.

    If this is non- ``NULL``, then this data-type descriptor is a
    C-style contiguous array of another data-type descriptor. In
    other-words, each element that this descriptor describes is
    actually an array of some other base descriptor. This is most
    useful as the data-type descriptor for a field in another
    data-type descriptor. The fields member should be ``NULL`` if this
    is non- ``NULL`` (the fields member of the base descriptor can be
    non- ``NULL`` however).

    .. c:type:: PyArray_ArrayDescr

        .. code-block:: c

            typedef struct {
                PyArray_Descr *base;
                PyObject *shape;
            } PyArray_ArrayDescr;

        .. c:member:: PyArray_Descr *base

            The data-type-descriptor object of the base-type.

        .. c:member:: PyObject *shape

            The shape (always C-style contiguous) of the sub-array as a Python
            tuple.


Data-type checking
~~~~~~~~~~~~~~~~~~

For the typenum macros, the argument is an integer representing an
enumerated array data type. For the array type checking macros the
argument must be a :c:expr:`PyObject *` that can be directly interpreted as a
:c:expr:`PyArrayObject *`.

.. c:function:: int PyTypeNum_ISUNSIGNED(int num)

.. c:function:: int PyDataType_ISUNSIGNED(PyArray_Descr *descr)

.. c:function:: int PyArray_ISUNSIGNED(PyArrayObject *obj)

    Type represents an unsigned integer.

.. c:function:: int PyTypeNum_ISSIGNED(int num)

.. c:function:: int PyDataType_ISSIGNED(PyArray_Descr *descr)

.. c:function:: int PyArray_ISSIGNED(PyArrayObject *obj)

    Type represents a signed integer.

.. c:function:: int PyTypeNum_ISINTEGER(int num)

.. c:function:: int PyDataType_ISINTEGER(PyArray_Descr* descr)

.. c:function:: int PyArray_ISINTEGER(PyArrayObject *obj)

    Type represents any integer.

.. c:function:: int PyTypeNum_ISFLOAT(int num)

.. c:function:: int PyDataType_ISFLOAT(PyArray_Descr* descr)

.. c:function:: int PyArray_ISFLOAT(PyArrayObject *obj)

    Type represents any floating point number.

.. c:function:: int PyTypeNum_ISCOMPLEX(int num)

.. c:function:: int PyDataType_ISCOMPLEX(PyArray_Descr* descr)

.. c:function:: int PyArray_ISCOMPLEX(PyArrayObject *obj)

    Type represents any complex floating point number.

.. c:function:: int PyTypeNum_ISNUMBER(int num)

.. c:function:: int PyDataType_ISNUMBER(PyArray_Descr* descr)

.. c:function:: int PyArray_ISNUMBER(PyArrayObject *obj)

    Type represents any integer, floating point, or complex floating point
    number.

.. c:function:: int PyTypeNum_ISSTRING(int num)

.. c:function:: int PyDataType_ISSTRING(PyArray_Descr* descr)

.. c:function:: int PyArray_ISSTRING(PyArrayObject *obj)

    Type represents a string data type.

.. c:function:: int PyTypeNum_ISFLEXIBLE(int num)

.. c:function:: int PyDataType_ISFLEXIBLE(PyArray_Descr* descr)

.. c:function:: int PyArray_ISFLEXIBLE(PyArrayObject *obj)

    Type represents one of the flexible array types ( :c:data:`NPY_STRING`,
    :c:data:`NPY_UNICODE`, or :c:data:`NPY_VOID` ).

.. c:function:: int PyDataType_ISUNSIZED(PyArray_Descr* descr)

    Type has no size information attached, and can be resized. Should only be
    called on flexible dtypes. Types that are attached to an array will always
    be sized, hence the array form of this macro not existing.

    For structured datatypes with no fields this function now returns False.

.. c:function:: int PyTypeNum_ISUSERDEF(int num)

.. c:function:: int PyDataType_ISUSERDEF(PyArray_Descr* descr)

.. c:function:: int PyArray_ISUSERDEF(PyArrayObject *obj)

    Type represents a user-defined type.

.. c:function:: int PyTypeNum_ISEXTENDED(int num)

.. c:function:: int PyDataType_ISEXTENDED(PyArray_Descr* descr)

.. c:function:: int PyArray_ISEXTENDED(PyArrayObject *obj)

    Type is either flexible or user-defined.

.. c:function:: int PyTypeNum_ISOBJECT(int num)

.. c:function:: int PyDataType_ISOBJECT(PyArray_Descr* descr)

.. c:function:: int PyArray_ISOBJECT(PyArrayObject *obj)

    Type represents object data type.

.. c:function:: int PyTypeNum_ISBOOL(int num)

.. c:function:: int PyDataType_ISBOOL(PyArray_Descr* descr)

.. c:function:: int PyArray_ISBOOL(PyArrayObject *obj)

    Type represents Boolean data type.

.. c:function:: int PyDataType_HASFIELDS(PyArray_Descr* descr)

.. c:function:: int PyArray_HASFIELDS(PyArrayObject *obj)

    Type has fields associated with it.

.. c:function:: int PyArray_ISNOTSWAPPED(PyArrayObject *m)

    Evaluates true if the data area of the ndarray *m* is in machine
    byte-order according to the array's data-type descriptor.

.. c:function:: int PyArray_ISBYTESWAPPED(PyArrayObject *m)

    Evaluates true if the data area of the ndarray *m* is **not** in
    machine byte-order according to the array's data-type descriptor.

.. c:function:: npy_bool PyArray_EquivTypes( \
        PyArray_Descr* type1, PyArray_Descr* type2)

    Return :c:data:`NPY_TRUE` if *type1* and *type2* actually represent
    equivalent types for this platform (the fortran member of each
    type is ignored). For example, on 32-bit platforms,
    :c:data:`NPY_LONG` and :c:data:`NPY_INT` are equivalent. Otherwise
    return :c:data:`NPY_FALSE`.

.. c:function:: npy_bool PyArray_EquivArrTypes( \
        PyArrayObject* a1, PyArrayObject * a2)

    Return :c:data:`NPY_TRUE` if *a1* and *a2* are arrays with equivalent
    types for this platform.

.. c:function:: npy_bool PyArray_EquivTypenums(int typenum1, int typenum2)

    Special case of :c:func:`PyArray_EquivTypes` (...) that does not accept
    flexible data types but may be easier to call.

.. c:function:: int PyArray_EquivByteorders(int b1, int b2)

    True if byteorder characters *b1* and *b2* ( :c:data:`NPY_LITTLE`,
    :c:data:`NPY_BIG`, :c:data:`NPY_NATIVE`, :c:data:`NPY_IGNORE` ) are
    either equal or equivalent as to their specification of a native
    byte order. Thus, on a little-endian machine :c:data:`NPY_LITTLE`
    and :c:data:`NPY_NATIVE` are equivalent where they are not
    equivalent on a big-endian machine.


Converting data types

Mainly for backwards compatibility to the Numeric C-API and for
simple casts to non-flexible types. Return a new array object with
the elements of *arr* cast to the data-type *typenum* which must
be one of the enumerated types and not a flexible type.

Return a new array of the *type* specified, casting the elements
of *arr* as appropriate. The fortran argument specifies the
ordering of the output array.

As of 1.6, this function simply calls :c:func:`PyArray_CopyInto`,
which handles the casting.

Cast the elements of the array *in* into the array *out*. The
output array should be writeable, have an integer-multiple of the
number of elements in the input array (more than one copy can be
placed in out), and have a data type that is one of the builtin
types.  Returns 0 on success and -1 if an error occurs.

Returns non-zero if an array of data type *fromtype* can be cast
to an array of data type *totype* without losing information. An
exception is that 64-bit integers are allowed to be cast to 64-bit
floating point values even though this can lose precision on large
integers so as not to proliferate the use of long doubles without
explicit requests. Flexible array types are not checked according
to their lengths with this function.

:c:func:`PyArray_CanCastTypeTo` supersedes this function in
NumPy 1.6 and later.

Equivalent to PyArray_CanCastTypeTo(fromtype, totype, NPY_SAFE_CASTING).

Returns non-zero if an array of data type *fromtype* (which can
include flexible types) can be cast safely to an array of data
type *totype* (which can include flexible types) according to
the casting rule *casting*. For simple types with :c:data:`NPY_SAFE_CASTING`,
this is basically a wrapper around :c:func:`PyArray_CanCastSafely`, but
for flexible types such as strings or unicode, it produces results
taking into account their sizes. Integer and float types can only be cast
to a string or unicode type using :c:data:`NPY_SAFE_CASTING` if the string
or unicode type is big enough to hold the max value of the integer/float
type being cast from.

Returns non-zero if *arr* can be cast to *totype* according
to the casting rule given in *casting*.  If *arr* is an array
scalar, its value is taken into account, and non-zero is also
returned when the value will not overflow or be truncated to
an integer when converting to a smaller type.

.. note::
    With the adoption of NEP 50 in NumPy 2, this function is not used
    internally.  It is currently provided for backwards compatibility,
    but expected to be eventually deprecated.

If *arr* is an array, returns its data type descriptor, but if
*arr* is an array scalar (has 0 dimensions), it finds the data type
of smallest size to which the value may be converted
without overflow or truncation to an integer.

This function will not demote complex to float or anything to
boolean, but will demote a signed integer to an unsigned integer
when the scalar value is positive.

Finds the data type of smallest size and kind to which *type1* and
*type2* may be safely converted. This function is symmetric and
associative. A string or unicode result will be the proper size for
storing the max value of the input types converted to a string or unicode.

This applies type promotion to all the input arrays and dtype
objects, using the NumPy rules for combining scalars and arrays, to
determine the output type for an operation with the given set of
operands. This is the same result type that ufuncs produce.

See the documentation of :func:`numpy.result_type` for more
detail about the type promotion algorithm.

This function is superseded by :c:func:`PyArray_ResultType`.

This function is useful for determining a common type that two or
more arrays can be converted to. It only works for non-flexible
array types as no itemsize information is passed. The *mintype*
argument represents the minimum type acceptable, and *op*
represents the object that will be converted to an array. The
return value is the enumerated typenumber that represents the
data-type that *op* should have.

The functionality this provides is largely superseded by iterator
:c:type:`NpyIter` introduced in 1.6, with flag
:c:data:`NPY_ITER_COMMON_DTYPE` or with the same dtype parameter for
all operands.

Convert a sequence of Python objects contained in *op* to an array
of ndarrays each having the same data type. The type is selected
in the same way as :c:func:`PyArray_ResultType`. The length of the sequence is
returned in *n*, and an *n* -length array of :c:type:`PyArrayObject`
pointers is the return value (or ``NULL`` if an error occurs).
The returned array must be freed by the caller of this routine
(using :c:func:`PyDataMem_FREE` ) and all the array objects in it
``DECREF`` 'd or a memory-leak will occur. The example template-code
below shows a typical usage:

.. code-block:: c

    mps = PyArray_ConvertToCommonType(obj, &n);
    if (mps==NULL) return NULL;
    {code}
    <before return>
    for (i=0; i<n; i++) Py_DECREF(mps[i]);
    PyDataMem_FREE(mps);
    {return}

A pointer to newly created memory of size *arr* ->itemsize that
holds the representation of 0 for that type. The returned pointer,
*ret*, **must be freed** using :c:func:`PyDataMem_FREE` (ret) when it is
not needed anymore.

A pointer to newly created memory of size *arr* ->itemsize that
holds the representation of 1 for that type. The returned pointer,
*ret*, **must be freed** using :c:func:`PyDataMem_FREE` (ret) when it
is not needed anymore.

Returns :c:data:`NPY_TRUE` if *typenum* represents a valid type-number
(builtin or user-defined or character code). Otherwise, this
function returns :c:data:`NPY_FALSE`.

.. c:function:: void PyArray_InitArrFuncs(PyArray_ArrFuncs* f)

    Initialize all function pointers and members to ``NULL``.

.. c:function:: int PyArray_RegisterDataType(PyArray_DescrProto* dtype)

    .. note::
        As of NumPy 2.0 this API is considered legacy, the new DType API
        is more powerful and provides additional flexibility.
        The API may eventually be deprecated but support is continued for
        the time being.

        **Compiling for NumPy 1.x and 2.x**

        NumPy 2.x requires passing in a ``PyArray_DescrProto`` typed struct
        rather than a ``PyArray_Descr``.  This is necessary to allow changes.
        To allow code to run and compile on both 1.x and 2.x you need to
        change the type of your struct to ``PyArray_DescrProto`` and add::

            /* Allow compiling on NumPy 1.x */
            #if NPY_ABI_VERSION < 0x02000000
            #define PyArray_DescrProto PyArray_Descr
            #endif

        for 1.x compatibility.  Further, the struct will *not* be the actual
        descriptor anymore, only it's type number will be updated.
        After successful registration, you must thus fetch the actual
        dtype with::

            int type_num = PyArray_RegisterDataType(&my_descr_proto);
            if (type_num < 0) {
                /* error */
            }
            PyArray_Descr *my_descr = PyArray_DescrFromType(type_num);

        With these two changes, the code should compile and work on both 1.x
        and 2.x or later.

        In the unlikely case that you are heap allocating the dtype struct you
        should free it again on NumPy 2, since a copy is made.
        The struct is not a valid Python object, so do not use ``Py_DECREF``
        on it.

    Register a data-type as a new user-defined data type for
    arrays. The type must have most of its entries filled in. This is
    not always checked and errors can produce segfaults. In
    particular, the typeobj member of the ``dtype`` structure must be
    filled with a Python type that has a fixed-size element-size that
    corresponds to the elsize member of *dtype*. Also the ``f``
    member must have the required functions: nonzero, copyswap,
    copyswapn, getitem, setitem, and cast (some of the cast functions
    may be ``NULL`` if no support is desired). To avoid confusion, you
    should choose a unique character typecode but this is not enforced
    and not relied on internally.

    A user-defined type number is returned that uniquely identifies
    the type. A pointer to the new structure can then be obtained from
    :c:func:`PyArray_DescrFromType` using the returned type number. A -1 is
    returned if an error occurs.  If this *dtype* has already been
    registered (checked only by the address of the pointer), then
    return the previously-assigned type-number.

    The number of user DTypes known to numpy is stored in
    ``NPY_NUMUSERTYPES``, a static global variable that is public in the
    C API.  Accessing this symbol is inherently *not* thread-safe. If
    for some reason you need to use this API in a multithreaded context,
    you will need to add your own locking, NumPy does not ensure new
    data types can be added in a thread-safe manner.

.. c:function:: int PyArray_RegisterCastFunc( \
        PyArray_Descr* descr, int totype, PyArray_VectorUnaryFunc* castfunc)

    Register a low-level casting function, *castfunc*, to convert
    from the data-type, *descr*, to the given data-type number,
    *totype*. Any old casting function is over-written. A ``0`` is
    returned on success or a ``-1`` on failure.

    .. c:type:: PyArray_VectorUnaryFunc

        The function pointer type for low-level casting functions.

.. c:function:: int PyArray_RegisterCanCast( \
        PyArray_Descr* descr, int totype, NPY_SCALARKIND scalar)

    Register the data-type number, *totype*, as castable from
    data-type object, *descr*, of the given *scalar* kind. Use
    *scalar* = :c:data:`NPY_NOSCALAR` to register that an array of data-type
    *descr* can be cast safely to a data-type whose type_number is
    *totype*. The return value is 0 on success or -1 on failure.


Special functions for NPY_OBJECT

When working with arrays or buffers filled with objects NumPy tries to
ensure such buffers are filled with ``None`` before any data may be read.
However, code paths may existed where an array is only initialized to
``NULL``.
NumPy itself accepts ``NULL`` as an alias for ``None``, but may ``assert``
non-``NULL`` when compiled in debug mode.

Because NumPy is not yet consistent about initialization with None,
users **must** expect a value of ``NULL`` when working with buffers created
by NumPy.  Users **should** also ensure to pass fully initialized buffers
to NumPy, since NumPy may make this a strong requirement in the future.

There is currently an intention to ensure that NumPy always initializes
object arrays before they may be read.  Any failure to do so will be
regarded as a bug.
In the future, users may be able to rely on non-NULL values when reading
from any array, although exceptions for writing to freshly created arrays
may remain (e.g. for output arrays in ufunc code).  As of NumPy 1.23
known code paths exists where proper filling is not done.

Used for an array, *op*, that contains any Python objects. It
increments the reference count of every object in the array
according to the data-type of *op*. A -1 is returned if an error
occurs, otherwise 0 is returned.

A function to INCREF all the objects at the location *ptr*
according to the data-type *dtype*. If *ptr* is the start of a
structured type with an object at any offset, then this will (recursively)
increment the reference count of all object-like items in the
structured type.

Used for an array, *op*, that contains any Python objects. It
decrements the reference count of every object in the array
according to the data-type of *op*. Normal return value is 0. A
-1 is returned if an error occurs.

A function to XDECREF all the object-like items at the location
*ptr* as recorded in the data-type, *dtype*. This works
recursively so that if ``dtype`` itself has fields with data-types
that contain object-like items, all the object-like fields will be
XDECREF ``'d``.

Precondition: ``arr`` is a copy of ``base`` (though possibly with different
strides, ordering, etc.) Sets the :c:data:`NPY_ARRAY_WRITEBACKIFCOPY` flag
and ``arr->base``, and set ``base`` to READONLY. Call
:c:func:`PyArray_ResolveWritebackIfCopy` before calling
:c:func:`Py_DECREF` in order to copy any changes back to ``base`` and
reset the READONLY flag.

Returns 0 for success, -1 for failure.

An ndarray can have a data segment that is not a simple contiguous
chunk of well-behaved memory you can manipulate. It may not be aligned
with word boundaries (very important on some platforms). It might have
its data in a different byte-order than the machine recognizes. It
might not be writeable. It might be in Fortran-contiguous order. The
array flags are used to indicate what can be said about data
associated with an array.

.. c:macro:: NPY_ARRAY_C_CONTIGUOUS

    The data area is in C-style contiguous order (last index varies the
    fastest).

.. c:macro:: NPY_ARRAY_F_CONTIGUOUS

    The data area is in Fortran-style contiguous order (first index varies
    the fastest).

.. note::

    Arrays can be both C-style and Fortran-style contiguous simultaneously.
    This is clear for 1-dimensional arrays, but can also be true for higher
    dimensional arrays.

    Even for contiguous arrays a stride for a given dimension
    ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
    or the array has no elements.
    It does *not* generally hold that ``self.strides[-1] == self.itemsize``
    for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
    Fortran-style contiguous arrays is true. The correct way to access the
    ``itemsize`` of an array from the C API is ``PyArray_ITEMSIZE(arr)``.

    .. seealso:: :ref:`Internal memory layout of an ndarray <arrays.ndarray>`

.. c:macro:: NPY_ARRAY_OWNDATA

    The data area is owned by this array. Should never be set manually, instead
    create a ``PyObject`` wrapping the data and set the array's base to that
    object. For an example, see the test in ``test_mem_policy``.

.. c:macro:: NPY_ARRAY_ALIGNED

    The data area and all array elements are aligned appropriately.

.. c:macro:: NPY_ARRAY_WRITEABLE

    The data area can be written to.

    Notice that the above 3 flags are defined so that a new, well-
    behaved array has these flags defined as true.

.. c:macro:: NPY_ARRAY_WRITEBACKIFCOPY

    The data area represents a (well-behaved) copy whose information
    should be transferred back to the original when
    :c:func:`PyArray_ResolveWritebackIfCopy` is called.

    This is a special flag that is set if this array represents a copy
    made because a user required certain flags in
    :c:func:`PyArray_FromAny` and a copy had to be made of some other
    array (and the user asked for this flag to be set in such a
    situation). The base attribute then points to the "misbehaved"
    array (which is set read_only). :c:func:`PyArray_ResolveWritebackIfCopy`
    will copy its contents back to the "misbehaved"
    array (casting if necessary) and will reset the "misbehaved" array
    to :c:data:`NPY_ARRAY_WRITEABLE`. If the "misbehaved" array was not
    :c:data:`NPY_ARRAY_WRITEABLE` to begin with then :c:func:`PyArray_FromAny`
    would have returned an error because :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`
    would not have been possible.

:c:func:`PyArray_UpdateFlags` (obj, flags) will update the ``obj->flags``
for ``flags`` which can be any of :c:data:`NPY_ARRAY_C_CONTIGUOUS`,
:c:data:`NPY_ARRAY_F_CONTIGUOUS`, :c:data:`NPY_ARRAY_ALIGNED`, or
:c:data:`NPY_ARRAY_WRITEABLE`.


Combinations of array flags

:c:data:`NPY_ARRAY_ALIGNED` \| :c:data:`NPY_ARRAY_WRITEABLE`

:c:data:`NPY_ARRAY_C_CONTIGUOUS` \| :c:data:`NPY_ARRAY_BEHAVED`

:c:data:`NPY_ARRAY_C_CONTIGUOUS` \| :c:data:`NPY_ARRAY_ALIGNED`

:c:data:`NPY_ARRAY_F_CONTIGUOUS` \| :c:data:`NPY_ARRAY_BEHAVED`

:c:data:`NPY_ARRAY_F_CONTIGUOUS` \| :c:data:`NPY_ARRAY_ALIGNED`

:c:data:`NPY_ARRAY_CARRAY`

:c:data:`NPY_ARRAY_C_CONTIGUOUS` \| :c:data:`NPY_ARRAY_ALIGNED`

:c:data:`NPY_ARRAY_F_CONTIGUOUS` \| :c:data:`NPY_ARRAY_ALIGNED`

:c:data:`NPY_ARRAY_C_CONTIGUOUS` \| :c:data:`NPY_ARRAY_WRITEABLE` \|
:c:data:`NPY_ARRAY_ALIGNED`

:c:data:`NPY_ARRAY_F_CONTIGUOUS` \| :c:data:`NPY_ARRAY_WRITEABLE` \|
:c:data:`NPY_ARRAY_ALIGNED`

:c:data:`NPY_ARRAY_C_CONTIGUOUS` \| :c:data:`NPY_ARRAY_WRITEABLE` \|
:c:data:`NPY_ARRAY_ALIGNED` \| :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`

:c:data:`NPY_ARRAY_F_CONTIGUOUS` \| :c:data:`NPY_ARRAY_WRITEABLE` \|
:c:data:`NPY_ARRAY_ALIGNED` \| :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`

:c:data:`NPY_ARRAY_C_CONTIGUOUS` \| :c:data:`NPY_ARRAY_F_CONTIGUOUS` \| :c:data:`NPY_ARRAY_ALIGNED`

These constants are used in :c:func:`PyArray_FromAny` (and its macro forms) to
specify desired properties of the new array.

.. c:macro:: NPY_ARRAY_FORCECAST

    Cast to the desired type, even if it can't be done without losing
    information.

.. c:macro:: NPY_ARRAY_ENSURECOPY

    Make sure the resulting array is a copy of the original.

.. c:macro:: NPY_ARRAY_ENSUREARRAY

    Make sure the resulting object is an actual ndarray, and not a sub-class.

These constants are used in :c:func:`PyArray_CheckFromAny` (and its macro forms)
to specify desired properties of the new array.

.. c:macro:: NPY_ARRAY_NOTSWAPPED

    Make sure the returned array has a data-type descriptor that is in
    machine byte-order, over-riding any specification in the *dtype*
    argument. Normally, the byte-order requirement is determined by
    the *dtype* argument. If this flag is set and the dtype argument
    does not indicate a machine byte-order descriptor (or is NULL and
    the object is already an array with a data-type descriptor that is
    not in machine byte- order), then a new data-type descriptor is
    created and used with its byte-order field set to native.

.. c:macro:: NPY_ARRAY_BEHAVED_NS

    :c:data:`NPY_ARRAY_ALIGNED` \| :c:data:`NPY_ARRAY_WRITEABLE` \|
    :c:data:`NPY_ARRAY_NOTSWAPPED`

.. c:macro:: NPY_ARRAY_ELEMENTSTRIDES

    Make sure the returned array has strides that are multiples of the
    element size.


Flag checking
~~~~~~~~~~~~~

For all of these macros *arr* must be an instance of a (subclass of)
:c:data:`PyArray_Type`.

.. c:function:: int PyArray_CHKFLAGS(const PyArrayObject *arr, int flags)

    The first parameter, arr, must be an ndarray or subclass. The
    parameter, *flags*, should be an integer consisting of bitwise
    combinations of the possible flags an array can have:
    :c:data:`NPY_ARRAY_C_CONTIGUOUS`, :c:data:`NPY_ARRAY_F_CONTIGUOUS`,
    :c:data:`NPY_ARRAY_OWNDATA`, :c:data:`NPY_ARRAY_ALIGNED`,
    :c:data:`NPY_ARRAY_WRITEABLE`, :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`.

.. c:function:: int PyArray_IS_C_CONTIGUOUS(const PyArrayObject *arr)

    Evaluates true if *arr* is C-style contiguous.

.. c:function:: int PyArray_IS_F_CONTIGUOUS(const PyArrayObject *arr)

    Evaluates true if *arr* is Fortran-style contiguous.

.. c:function:: int PyArray_ISFORTRAN(const PyArrayObject *arr)

    Evaluates true if *arr* is Fortran-style contiguous and *not*
    C-style contiguous. :c:func:`PyArray_IS_F_CONTIGUOUS`
    is the correct way to test for Fortran-style contiguity.

.. c:function:: int PyArray_ISWRITEABLE(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* can be written to

.. c:function:: int PyArray_ISALIGNED(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is properly aligned on
    the machine.

.. c:function:: int PyArray_ISBEHAVED(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is aligned and writeable
    and in machine byte-order according to its descriptor.

.. c:function:: int PyArray_ISBEHAVED_RO(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is aligned and in machine
    byte-order.

.. c:function:: int PyArray_ISCARRAY(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is C-style contiguous,
    and :c:func:`PyArray_ISBEHAVED` (*arr*) is true.

.. c:function:: int PyArray_ISFARRAY(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is Fortran-style
    contiguous and :c:func:`PyArray_ISBEHAVED` (*arr*) is true.

.. c:function:: int PyArray_ISCARRAY_RO(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is C-style contiguous,
    aligned, and in machine byte-order.

.. c:function:: int PyArray_ISFARRAY_RO(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* is Fortran-style
    contiguous, aligned, and in machine byte-order **.**

.. c:function:: int PyArray_ISONESEGMENT(const PyArrayObject *arr)

    Evaluates true if the data area of *arr* consists of a single
    (C-style or Fortran-style) contiguous segment.

.. c:function:: void PyArray_UpdateFlags(PyArrayObject* arr, int flagmask)

    The :c:data:`NPY_ARRAY_C_CONTIGUOUS`, :c:data:`NPY_ARRAY_ALIGNED`, and
    :c:data:`NPY_ARRAY_F_CONTIGUOUS` array flags can be "calculated" from the
    array object itself. This routine updates one or more of these
    flags of *arr* as specified in *flagmask* by performing the
    required calculation.


.. warning::

    It is important to keep the flags updated (using
    :c:func:`PyArray_UpdateFlags` can help) whenever a manipulation with an
    array is performed that might cause them to change. Later
    calculations in NumPy that rely on the state of these flags do not
    repeat the calculation to update them.

.. c:function:: int PyArray_FailUnlessWriteable(PyArrayObject *obj, const char *name)

    This function does nothing and returns 0 if *obj* is writeable.
    It raises an exception and returns -1 if *obj* is not writeable.
    It may also do other house-keeping, such as issuing warnings on
    arrays which are transitioning to become views. Always call this
    function at some point before writing to an array.

    *name* is a name for the array, used to give better error messages.
    It can be something like "assignment destination", "output array",
    or even just "array".

ArrayMethod API
---------------

ArrayMethod loops are intended as a generic mechanism for writing loops
over arrays, including ufunc loops and casts. The public API is defined in the
``numpy/dtype_api.h`` header. See :ref:`arraymethod-structs` for
documentation on the C structs exposed in the ArrayMethod API.

.. _arraymethod-typedefs:

Slots and Typedefs
~~~~~~~~~~~~~~~~~~

These are used to identify which kind of function an ArrayMethod slot
implements. See :ref:`arraymethod-typedefs` below for documentation on
the functions that must be implemented for each slot.

.. c:macro:: NPY_METH_resolve_descriptors

.. c:type:: NPY_CASTING (PyArrayMethod_ResolveDescriptors)( \
                struct PyArrayMethodObject_tag *method, \
                PyArray_DTypeMeta *const *dtypes, \
                PyArray_Descr *const *given_descrs, \
                PyArray_Descr **loop_descrs, \
                npy_intp *view_offset)

   The function used to set the descriptors for an operation based on
   the descriptors of the operands. For example, a ufunc operation with
   two input operands and one output operand that is called without
   ``out`` being set in the python API, ``resolve_descriptors`` will be
   passed the descriptors for the two operands and determine the correct
   descriptor to use for the output based on the output DType set for
   the ArrayMethod. If ``out`` is set, then the output descriptor would
   be passed in as well and should not be overridden.

   The *method* is a pointer to the underlying cast or ufunc loop. In
   the future we may expose this struct publicly but for now this is an
   opaque pointer and the method cannot be inspected. The *dtypes* is an
   ``nargs`` length array of ``PyArray_DTypeMeta`` pointers,
   *given_descrs* is an ``nargs`` length array of input descriptor
   instances (output descriptors may be NULL if no output was provided
   by the user), and *loop_descrs* is an ``nargs`` length array of
   descriptors that must be filled in by the resolve descriptors
   implementation.  *view_offset* is currently only interesting for
   casts and can normally be ignored.  When a cast does not require any
   operation, this can be signalled by setting ``view_offset`` to 0.  On
   error, you must return ``(NPY_CASTING)-1`` with an error set.

.. c:macro:: NPY_METH_strided_loop
.. c:macro:: NPY_METH_contiguous_loop
.. c:macro:: NPY_METH_unaligned_strided_loop
.. c:macro:: NPY_METH_unaligned_contiguous_loop

   One dimensional strided loops implementing the behavior (either a
   ufunc or cast).  In most cases, ``NPY_METH_strided_loop`` is the
   generic and only version that needs to be implemented.
   ``NPY_METH_contiguous_loop`` can be implemented additionally as a
   more light-weight/faster version and it is used when all inputs and
   outputs are contiguous.

   To deal with possibly unaligned data, NumPy needs to be able to copy
   unaligned to aligned data.  When implementing a new DType, the "cast"
   or copy for it needs to implement
   ``NPY_METH_unaligned_strided_loop``.  Unlike the normal versions,
   this loop must not assume that the data can be accessed in an aligned
   fashion.  These loops must copy each value before accessing or
   storing::

       type_in in_value;
       type_out out_value
       memcpy(&value, in_data, sizeof(type_in));
       out_value = in_value;
       memcpy(out_data, &out_value, sizeof(type_out)

   while a normal loop can just use::

       *(type_out *)out_data = *(type_in)in_data;

   The unaligned loops are currently only used in casts and will never
   be picked in ufuncs (ufuncs create a temporary copy to ensure aligned
   inputs).  These slot IDs are ignored when ``NPY_METH_get_loop`` is
   defined, where instead whichever loop returned by the ``get_loop``
   function is used.

.. c:macro:: NPY_METH_contiguous_indexed_loop

   A specialized inner-loop option to speed up common ``ufunc.at`` computations.

.. c:type:: int (PyArrayMethod_StridedLoop)(PyArrayMethod_Context *context, \
        char *const *data, const npy_intp *dimensions, const npy_intp *strides, \
        NpyAuxData *auxdata)

   An implementation of an ArrayMethod loop. All of the loop slot IDs
   listed above must provide a ``PyArrayMethod_StridedLoop``
   implementation. The *context* is a struct containing context for the
   loop operation - in particular the input descriptors. The *data* are
   an array of pointers to the beginning of the input and output array
   buffers. The *dimensions* are the loop dimensions for the
   operation. The *strides* are an ``nargs`` length array of strides for
   each input. The *auxdata* is an optional set of auxiliary data that
   can be passed in to the loop - helpful to turn on and off optional
   behavior or reduce boilerplate by allowing similar ufuncs to share
   loop implementations or to allocate space that is persistent over
   multiple strided loop calls.

.. c:macro:: NPY_METH_get_loop

   Allows more fine-grained control over loop selection. Accepts an
   implementation of PyArrayMethod_GetLoop, which in turn returns a
   strided loop implementation. If ``NPY_METH_get_loop`` is defined,
   the other loop slot IDs are ignored, if specified.

.. c:type:: int (PyArrayMethod_GetLoop)( \
	    PyArrayMethod_Context *context, int aligned, int move_references, \
        const npy_intp *strides, PyArrayMethod_StridedLoop **out_loop, \
        NpyAuxData **out_transferdata, NPY_ARRAYMETHOD_FLAGS *flags);

   Sets the loop to use for an operation at runtime. The *context* is the
   runtime context for the operation. *aligned* indicates whether the data
   access for the loop is aligned (1) or unaligned (0). *move_references*
   indicates whether embedded references in the data should be copied. *strides*
   are the strides for the input array, *out_loop* is a pointer that must be
   filled in with a pointer to the loop implementation. *out_transferdata* can
   be optionally filled in to allow passing in extra user-defined context to an
   operation. *flags* must be filled in with ArrayMethod flags relevant for the
   operation.  This is for example necessary to indicate if the inner loop
   requires the Python GIL to be held.

.. c:macro:: NPY_METH_get_reduction_initial

.. c:type:: int (PyArrayMethod_GetReductionInitial)( \
        PyArrayMethod_Context *context, npy_bool reduction_is_empty, \
        char *initial)

   Query an ArrayMethod for the initial value for use in reduction. The
   *context* is the ArrayMethod context, mainly to access the input
   descriptors. *reduction_is_empty* indicates whether the reduction is
   empty. When it is, the value returned may differ.  In this case it is a
   "default" value that may differ from the "identity" value normally used.
   For example:

   - ``0.0`` is the default for ``sum([])``.  But ``-0.0`` is the correct
     identity otherwise as it preserves the sign for ``sum([-0.0])``.
   - We use no identity for object, but return the default of ``0`` and
     ``1`` for the empty ``sum([], dtype=np.object_)`` and
     ``prod([], dtype=np.object_)``.
     This allows ``np.sum(np.array(["a", "b"], dtype=np.object_))`` to work.
   - ``-inf`` or ``INT_MIN`` for ``max`` is an identity, but at least
     ``INT_MIN`` not a good *default* when there are no items.

   *initial* is a pointer to the data for the initial value, which should be
   filled in. Returns -1, 0, or 1 indicating error, no initial value, and the
   initial value being successfully filled. Errors must not be given when no
   initial value is correct, since NumPy may call this even when it is not
   strictly necessary to do so.

Flags
~~~~~

.. c:enum:: NPY_ARRAYMETHOD_FLAGS

   These flags allow switching on and off custom runtime behavior for
   ArrayMethod loops.  For example, if a ufunc cannot possibly trigger floating
   point errors, then the ``NPY_METH_NO_FLOATINGPOINT_ERRORS`` flag should be
   set on the ufunc when it is registered.

   .. c:enumerator:: NPY_METH_REQUIRES_PYAPI

      Indicates the method must hold the GIL. If this flag is not set, the GIL
      is released before the loop is called.

   .. c:enumerator:: NPY_METH_NO_FLOATINGPOINT_ERRORS

      Indicates the method cannot generate floating errors, so checking for
      floating errors after the loop completes can be skipped.

   .. c:enumerator:: NPY_METH_SUPPORTS_UNALIGNED

      Indicates the method supports unaligned access.

   .. c:enumerator:: NPY_METH_IS_REORDERABLE

      Indicates that the result of applying the loop repeatedly (for example, in
      a reduction operation) does not depend on the order of application.

   .. c:enumerator:: NPY_METH_RUNTIME_FLAGS

      The flags that can be changed at runtime.

Typedefs
~~~~~~~~

Typedefs for functions that users of the ArrayMethod API can implement are
described below.

.. c:type:: int (PyArrayMethod_TraverseLoop)( \
        void *traverse_context, const PyArray_Descr *descr, char *data, \
        npy_intp size, npy_intp stride, NpyAuxData *auxdata)

   A traverse loop working on a single array. This is similar to the general
   strided-loop function. This is designed for loops that need to visit every
   element of a single array.

   Currently this is used for array clearing, via the ``NPY_DT_get_clear_loop``
   DType API hook, and zero-filling, via the ``NPY_DT_get_fill_zero_loop``
   DType API hook.  These are most useful for handling arrays storing embedded
   references to python objects or heap-allocated data.

   The *descr* is the descriptor for the array, *data* is a pointer to the array
   buffer, *size* is the 1D size of the array buffer, *stride* is the stride,
   and *auxdata* is optional extra data for the loop.

   The *traverse_context* is passed in because we may need to pass in
   Interpreter state or similar in the future, but we don't want to pass in a
   full context (with pointers to dtypes, method, caller which all make no sense
   for a traverse function). We assume for now that this context can be just
   passed through in the future (for structured dtypes).

.. c:type:: int (PyArrayMethod_GetTraverseLoop)( \
                void *traverse_context, const PyArray_Descr *descr, \
                int aligned, npy_intp fixed_stride, \
                PyArrayMethod_TraverseLoop **out_loop, NpyAuxData **out_auxdata, \
                NPY_ARRAYMETHOD_FLAGS *flags)

   Simplified get_loop function specific to dtype traversal

   It should set the flags needed for the traversal loop and set *out_loop* to the
   loop function, which must be a valid ``PyArrayMethod_TraverseLoop``
   pointer. Currently this is used for zero-filling and clearing arrays storing
   embedded references.

API Functions and Typedefs

.. c:struct:: PyUFunc_LoopSlot

    .. c:member:: const char *name

        The name of the ufunc to add the loop to, in the form like that of
        entry points, ``(module ':')? (object '.')* name``, with ``numpy``
        the default module. Examples: ``sin``, ``strings.str_len``,
        ``numpy.strings:str_len``.

    .. c:member:: PyArrayMethod_Spec *spec

        The ArrayMethod spec to use to create the loop.

.. versionadded:: 2.4

Add multiple loops to ufuncs from ArrayMethod specs. This also
handles the registration of methods for the ufunc-like functions
``sort`` and ``argsort``. See :ref:`array-methods-sorting` for details.

The ``slots`` argument must be a  NULL-terminated array of
`PyUFunc_LoopSlot` (see above), which give the name of the
ufunc and spec needed to create the loop.

Checks for a floating point error after performing a floating point
operation in a manner that takes into account the error signaling configured
via `numpy.errstate`. Takes the name of the operation to use in the error
message and an integer flag that is one of ``NPY_FPE_DIVIDEBYZERO``,
``NPY_FPE_OVERFLOW``, ``NPY_FPE_UNDERFLOW``, ``NPY_FPE_INVALID`` to indicate
which error to check for.

Returns -1 on failure (an error was raised) and 0 on success.

Allows creating of a fairly lightweight wrapper around an existing
ufunc loop.  The idea is mainly for units, as this is currently
slightly limited in that it enforces that you cannot use a loop from
another ufunc.

The function to convert the given descriptors (passed in to
``resolve_descriptors``) and translates them for the wrapped loop.
The new descriptors MUST be viewable with the old ones, `NULL` must be
supported (for output arguments) and should normally be forwarded.

The output of of this function will be used to construct
views of the arguments as if they were the translated dtypes and
does not use a cast. This means this mechanism is mostly useful for
DTypes that "wrap" another DType implementation. For example, a unit
DType could use this to wrap an existing floating point DType
without needing to re-implement low-level ufunc logic. In the unit
example, ``resolve_descriptors`` would handle computing the output
unit from the input unit.

PyArray_DTypeMeta *orig_dtypes[3] = {
    &WrappedDoubleDType, &WrappedDoubleDType, &WrappedDoubleDType};
PyArray_DTypeMeta *wrapped_dtypes[3] = {
     &PyArray_Float64DType, &PyArray_Float64DType, &PyArray_Float64DType}

PyObject *mod = PyImport_ImportModule("numpy");
if (mod == NULL) {
    return -1;
}
PyObject *multiply = PyObject_GetAttrString(mod, "multiply");
Py_DECREF(mod);

if (multiply == NULL) {
    return -1;
}

int res = PyUFunc_AddWrappingLoop(
    multiply, orig_dtypes, wrapped_dtypes, &translate_given_descrs
    &translate_loop_descrs);

Py_DECREF(multiply);

static int
translate_given_descrs(int nin, int nout,
                       PyArray_DTypeMeta *NPY_UNUSED(wrapped_dtypes[]),
                       PyArray_Descr *given_descrs[],
                       PyArray_Descr *new_descrs[])
{
    for (int i = 0; i < nin + nout; i++) {
        if (given_descrs[i] == NULL) {
            new_descrs[i] = NULL;
        }
        else {
            new_descrs[i] = PyArray_DescrFromType(NPY_DOUBLE);
        }
    }
    return 0;
}

static int
translate_loop_descrs(int nin, int NPY_UNUSED(nout),
                      PyArray_DTypeMeta *NPY_UNUSED(new_dtypes[]),
                      PyArray_Descr *given_descrs[],
                      PyArray_Descr *original_descrs[],
                      PyArray_Descr *loop_descrs[])
{
    // more complicated parametric DTypes may need to
    // to do additional checking, but we know the wrapped
    // DTypes *have* to be float64 for this example.
    loop_descrs[0] = PyArray_DescrFromType(NPY_FLOAT64);
    Py_INCREF(loop_descrs[0]);
    loop_descrs[1] = PyArray_DescrFromType(NPY_FLOAT64);
    Py_INCREF(loop_descrs[1]);
    loop_descrs[2] = PyArray_DescrFromType(NPY_FLOAT64);
    Py_INCREF(loop_descrs[2]);
}

Sorting and argsorting methods for dtypes can be registered using the
ArrayMethod API. This is done by adding an ArrayMethod spec with the name
``"sort"`` or ``"argsort"`` respectively.  The spec must have ``nin=1``
and ``nout=1`` for both sort and argsort. Sorting is inplace, hence we
enforce that ``data[0] == data[1]``. Argsorting returns a new array of
indices, so the output must be of ``NPY_INTP`` type.

The ``context`` passed to the loop contains the ``parameters`` field which
for these operations is a ``PyArrayMethod_SortParameters *`` struct. This
struct contains a ``flags`` field which is a bitwise OR of ``NPY_SORTKIND``
values indicating the kind of sort to perform (that is, whether it is a
stable and/or descending sort). If the strided loop depends on the flags,
a good way to deal with this is to define :c:macro:`NPY_METH_get_loop`,
and not set any of the other loop slots.

.. c:struct:: PyArrayMethod_SortParameters

    .. c:member:: NPY_SORTKIND flags

        The flags passed to the sort operation. This is a bitwise OR of
        ``NPY_SORTKIND`` values indicating the kind of sort to perform.

These specs can be registered using :c:func:`PyUFunc_AddLoopsFromSpecs`
along with other ufunc loops.

API for calling array methods
-----------------------------

Conversion
~~~~~~~~~~

.. c:function:: PyObject* PyArray_GetField( \
        PyArrayObject* self, PyArray_Descr* dtype, int offset)

    Equivalent to :meth:`ndarray.getfield<numpy.ndarray.getfield>`
    (*self*, *dtype*, *offset*). This function `steals a reference
    <https://docs.python.org/3/c-api/intro.html?reference-count-details>`_
    to :c:func:`PyArray_Descr` and returns a new array of the given `dtype` using
    the data in the current array at a specified `offset` in bytes. The
    `offset` plus the itemsize of the new array type must be less than
    ``self->descr->elsize`` or an error is raised. The same shape and strides
    as the original array are used. Therefore, this function has the
    effect of returning a field from a structured array. But, it can also
    be used to select specific bytes or groups of bytes from any array
    type.

.. c:function:: int PyArray_SetField( \
        PyArrayObject* self, PyArray_Descr* dtype, int offset, PyObject* val)

    Equivalent to :meth:`ndarray.setfield<numpy.ndarray.setfield>` (*self*, *val*, *dtype*, *offset*
    ). Set the field starting at *offset* in bytes and of the given
    *dtype* to *val*. The *offset* plus *dtype* ->elsize must be less
    than *self* ->descr->elsize or an error is raised. Otherwise, the
    *val* argument is converted to an array and copied into the field
    pointed to. If necessary, the elements of *val* are repeated to
    fill the destination array, But, the number of elements in the
    destination must be an integer multiple of the number of elements
    in *val*.

.. c:function:: PyObject* PyArray_Byteswap(PyArrayObject* self, npy_bool inplace)

    Equivalent to :meth:`ndarray.byteswap<numpy.ndarray.byteswap>` (*self*, *inplace*). Return an array
    whose data area is byteswapped. If *inplace* is non-zero, then do
    the byteswap inplace and return a reference to self. Otherwise,
    create a byteswapped copy and leave self unchanged.

.. c:function:: PyObject* PyArray_NewCopy(PyArrayObject* old, NPY_ORDER order)

    Equivalent to :meth:`ndarray.copy<numpy.ndarray.copy>` (*self*, *fortran*). Make a copy of the
    *old* array. The returned array is always aligned and writeable
    with data interpreted the same as the old array. If *order* is
    :c:data:`NPY_CORDER`, then a C-style contiguous array is returned. If
    *order* is :c:data:`NPY_FORTRANORDER`, then a Fortran-style contiguous
    array is returned. If *order is* :c:data:`NPY_ANYORDER`, then the array
    returned is Fortran-style contiguous only if the old one is;
    otherwise, it is C-style contiguous.

.. c:function:: PyObject* PyArray_ToList(PyArrayObject* self)

    Equivalent to :meth:`ndarray.tolist<numpy.ndarray.tolist>` (*self*). Return a nested Python list
    from *self*.

.. c:function:: PyObject* PyArray_ToString(PyArrayObject* self, NPY_ORDER order)

    Equivalent to :meth:`ndarray.tobytes<numpy.ndarray.tobytes>` (*self*, *order*). Return the bytes
    of this array in a Python string.

.. c:function:: PyObject* PyArray_ToFile( \
        PyArrayObject* self, FILE* fp, char* sep, char* format)

    Write the contents of *self* to the file pointer *fp* in C-style
    contiguous fashion. Write the data as binary bytes if *sep* is the
    string ""or ``NULL``. Otherwise, write the contents of *self* as
    text using the *sep* string as the item separator. Each item will
    be printed to the file.  If the *format* string is not ``NULL`` or
    "", then it is a Python print statement format string showing how
    the items are to be written.

.. c:function:: int PyArray_Dump(PyObject* self, PyObject* file, int protocol)

    Pickle the object in *self* to the given *file* (either a string
    or a Python file object). If *file* is a Python string it is
    considered to be the name of a file which is then opened in binary
    mode. The given *protocol* is used (if *protocol* is negative, or
    the highest available is used). This is a simple wrapper around
    cPickle.dump(*self*, *file*, *protocol*).

.. c:function:: PyObject* PyArray_Dumps(PyObject* self, int protocol)

    Pickle the object in *self* to a Python string and return it. Use
    the Pickle *protocol* provided (or the highest available if
    *protocol* is negative).

.. c:function:: int PyArray_FillWithScalar(PyArrayObject* arr, PyObject* obj)

    Fill the array, *arr*, with the given scalar object, *obj*. The
    object is first converted to the data type of *arr*, and then
    copied into every location. A -1 is returned if an error occurs,
    otherwise 0 is returned.

.. c:function:: PyObject* PyArray_View( \
        PyArrayObject* self, PyArray_Descr* dtype, PyTypeObject *ptype)

    Equivalent to :meth:`ndarray.view<numpy.ndarray.view>` (*self*, *dtype*). Return a new
    view of the array *self* as possibly a different data-type, *dtype*,
    and different array subclass *ptype*.

    If *dtype* is ``NULL``, then the returned array will have the same
    data type as *self*. The new data-type must be consistent with the
    size of *self*. Either the itemsizes must be identical, or *self* must
    be single-segment and the total number of bytes must be the same.
    In the latter case the dimensions of the returned array will be
    altered in the last (or first for Fortran-style contiguous arrays)
    dimension. The data area of the returned array and self is exactly
    the same.


Shape Manipulation
~~~~~~~~~~~~~~~~~~

.. c:function:: PyObject* PyArray_Newshape( \
        PyArrayObject* self, PyArray_Dims* newshape, NPY_ORDER order)

    Result will be a new array (pointing to the same memory location
    as *self* if possible), but having a shape given by *newshape*.
    If the new shape is not compatible with the strides of *self*,
    then a copy of the array with the new specified shape will be
    returned.

.. c:function:: PyObject* PyArray_Reshape(PyArrayObject* self, PyObject* shape)

    Equivalent to :meth:`ndarray.reshape<numpy.ndarray.reshape>` (*self*, *shape*) where *shape* is a
    sequence. Converts *shape* to a :c:type:`PyArray_Dims` structure and
    calls :c:func:`PyArray_Newshape` internally.
    For back-ward compatibility -- Not recommended

.. c:function:: PyObject* PyArray_Squeeze(PyArrayObject* self)

    Equivalent to :meth:`ndarray.squeeze<numpy.ndarray.squeeze>` (*self*). Return a new view of *self*
    with all of the dimensions of length 1 removed from the shape.

.. warning::

    matrix objects are always 2-dimensional. Therefore,
    :c:func:`PyArray_Squeeze` has no effect on arrays of matrix sub-class.

.. c:function:: PyObject* PyArray_SwapAxes(PyArrayObject* self, int a1, int a2)

    Equivalent to :meth:`ndarray.swapaxes<numpy.ndarray.swapaxes>` (*self*, *a1*, *a2*). The returned
    array is a new view of the data in *self* with the given axes,
    *a1* and *a2*, swapped.

.. c:function:: PyObject* PyArray_Resize( \
        PyArrayObject* self, PyArray_Dims* newshape, int refcheck, \
        NPY_ORDER fortran)

    Equivalent to :meth:`ndarray.resize<numpy.ndarray.resize>` (*self*, *newshape*, *refcheck*).
    This function only works on single-segment arrays. It changes the shape of
    *self* inplace and will reallocate the memory for *self* if *newshape* has
    a different total number of elements then the old shape. If reallocation is
    necessary, then *self* must own its data, have *self* - ``>base==NULL``,
    have *self* - ``>weakrefs==NULL``, and (unless refcheck is 0) not be
    referenced by any other array.  The fortran argument can be
    :c:data:`NPY_ANYORDER`, :c:data:`NPY_CORDER`, or
    :c:data:`NPY_FORTRANORDER`.  It currently has no effect. Eventually it
    could be used to determine how the resize operation should view the data
    when constructing a differently-dimensioned array.  Returns None on success
    and NULL on error.

.. c:function:: PyObject* PyArray_Transpose( \
        PyArrayObject* self, PyArray_Dims* permute)

    Equivalent to :meth:`ndarray.transpose<numpy.ndarray.transpose>` (*self*, *permute*). Permute the
    axes of the ndarray object *self* according to the data structure
    *permute* and return the result. If *permute* is ``NULL``, then
    the resulting array has its axes reversed. For example if *self*
    has shape :math:`10\times20\times30`, and *permute* ``.ptr`` is
    (0,2,1) the shape of the result is :math:`10\times30\times20.` If
    *permute* is ``NULL``, the shape of the result is
    :math:`30\times20\times10.`

.. c:function:: PyObject* PyArray_Flatten(PyArrayObject* self, NPY_ORDER order)

    Equivalent to :meth:`ndarray.flatten<numpy.ndarray.flatten>` (*self*, *order*). Return a 1-d copy
    of the array. If *order* is :c:data:`NPY_FORTRANORDER` the elements are
    scanned out in Fortran order (first-dimension varies the
    fastest). If *order* is :c:data:`NPY_CORDER`, the elements of ``self``
    are scanned in C-order (last dimension varies the fastest). If
    *order* :c:data:`NPY_ANYORDER`, then the result of
    :c:func:`PyArray_ISFORTRAN` (*self*) is used to determine which order
    to flatten.

.. c:function:: PyObject* PyArray_Ravel(PyArrayObject* self, NPY_ORDER order)

    Equivalent to *self*.ravel(*order*). Same basic functionality
    as :c:func:`PyArray_Flatten` (*self*, *order*) except if *order* is 0
    and *self* is C-style contiguous, the shape is altered but no copy
    is performed.


Item selection and manipulation

Equivalent to :meth:`ndarray.take<numpy.ndarray.take>` (*self*, *indices*, *axis*, *ret*,
*clipmode*) except *axis* =None in Python is obtained by setting
*axis* = :c:data:`NPY_MAXDIMS` in C. Extract the items from self
indicated by the integer-valued *indices* along the given *axis.*
The clipmode argument can be :c:data:`NPY_RAISE`, :c:data:`NPY_WRAP`, or
:c:data:`NPY_CLIP` to indicate what to do with out-of-bound indices. The
*ret* argument can specify an output array rather than having one
created internally.

Equivalent to *self*.put(*values*, *indices*, *clipmode*
). Put *values* into *self* at the corresponding (flattened)
*indices*. If *values* is too small it will be repeated as
necessary.

Place the *values* in *self* wherever corresponding positions
(using a flattened context) in *mask* are true. The *mask* and
*self* arrays must have the same total number of elements. If
*values* is too small, it will be repeated as necessary.

Equivalent to :meth:`ndarray.repeat<numpy.ndarray.repeat>` (*self*, *op*, *axis*). Copy the
elements of *self*, *op* times along the given *axis*. Either
*op* is a scalar integer or a sequence of length *self*
->dimensions[ *axis* ] indicating how many times to repeat each
item along the axis.

Equivalent to :meth:`ndarray.choose<numpy.ndarray.choose>` (*self*, *op*, *ret*, *clipmode*).
Create a new array by selecting elements from the sequence of
arrays in *op* based on the integer values in *self*. The arrays
must all be broadcastable to the same shape and the entries in
*self* should be between 0 and len(*op*). The output is placed
in *ret* unless it is ``NULL`` in which case a new output is
created. The *clipmode* argument determines behavior for when
entries in *self* are not between 0 and len(*op*).

.. c:macro:: NPY_RAISE

    raise a ValueError;

.. c:macro:: NPY_WRAP

    wrap values < 0 by adding len(*op*) and values >=len(*op*)
    by subtracting len(*op*) until they are in range;

.. c:macro:: NPY_CLIP

    all values are clipped to the region [0, len(*op*) ).

Return an array with the items of ``self`` sorted along ``axis``. The array
is sorted using an algorithm whose properties are specified by the value of
``kind``, an integer/enum specifying the requirements of the sorting
algorithm used. If ``self* ->descr`` is a data-type with fields defined,
then ``self->descr->names`` is used to determine the sort order. A comparison
where the first field is equal will use the second field and so on. To
alter the sort order of a structured array, create a new data-type with a
different order of names and construct a view of the array with that new
data-type.

This is the C level function called by the ndarray method
:meth:`ndarray.sort<numpy.ndarray.sort>`, though with a different meaning
of ``kind`` -- see ``NPY_SORTKIND`` below.

Return an array of indices such that selection of these indices along the
given ``axis`` would return a sorted version of ``self``.  The array is
sorted using an algorithm whose properties are specified by ``kind``, an
integer/enum specifying the requirements of the sorting algorithm used. If
``self->descr`` is a data-type with fields defined, then
``self->descr->names`` is used to determine the sort order. A comparison
where the first field is equal will use the second field and so on. To
alter the sort order of a structured array, create a new data-type with a
different order of names and construct a view of the array with that new
data-type.

This is the C level function called by the ndarray method
:meth:`ndarray.argsort<numpy.ndarray.argsort>`, though with a different
meaning of ``kind`` -- see ``NPY_SORTKIND`` below.

Given a sequence of arrays (*sort_keys*) of the same shape,
return an array of indices (similar to :c:func:`PyArray_ArgSort` (...))
that would sort the arrays lexicographically. A lexicographic sort
specifies that when two keys are found to be equal, the order is
based on comparison of subsequent keys. A merge sort (which leaves
equal entries unmoved) is required to be defined for the
types. The sort is accomplished by sorting the indices first using
the first *sort_key* and then using the second *sort_key* and so
forth. This is equivalent to the lexsort(*sort_keys*, *axis*)
Python command. Because of the way the merge-sort works, be sure
to understand the order the *sort_keys* must be in (reversed from
the order you would use when comparing two elements).

If these arrays are all collected in a structured array, then
:c:func:`PyArray_Sort` (...) can also be used to sort the array
directly.

Equivalent to :meth:`ndarray.searchsorted<numpy.ndarray.searchsorted>` (*self*, *values*, *side*,
*perm*). Assuming *self* is a 1-d array in ascending order, then the
output is an array of indices the same shape as *values* such that, if
the elements in *values* were inserted before the indices, the order of
*self* would be preserved. No checking is done on whether or not self is
in ascending order.

The *side* argument indicates whether the index returned should be that of
the first suitable location (if :c:data:`NPY_SEARCHLEFT`) or of the last
(if :c:data:`NPY_SEARCHRIGHT`).

The *sorter* argument, if not ``NULL``, must be a 1D array of integer
indices the same length as *self*, that sorts it into ascending order.
This is typically the result of a call to :c:func:`PyArray_ArgSort` (...)
Binary search is used to find the required insertion points.

Equivalent to :meth:`ndarray.partition<numpy.ndarray.partition>` (*self*, *ktharray*, *axis*,
*kind*). Partitions the array so that the values of the element indexed by
*ktharray* are in the positions they would be if the array is fully sorted
and places all elements smaller than the kth before and all elements equal
or greater after the kth element. The ordering of all elements within the
partitions is undefined.
If *self*->descr is a data-type with fields defined, then
self->descr->names is used to determine the sort order. A comparison where
the first field is equal will use the second field and so on. To alter the
sort order of a structured array, create a new data-type with a different
order of names and construct a view of the array with that new data-type.
Returns zero on success and -1 on failure.

Equivalent to :meth:`ndarray.argpartition<numpy.ndarray.argpartition>` (*self*, *ktharray*, *axis*,
*kind*). Return an array of indices such that selection of these indices
along the given ``axis`` would return a partitioned version of *self*.

Equivalent to :meth:`ndarray.diagonal<numpy.ndarray.diagonal>` (*self*, *offset*, *axis1*, *axis2*
). Return the *offset* diagonals of the 2-d arrays defined by
*axis1* and *axis2*.

Counts the number of non-zero elements in the array object *self*.

Equivalent to :meth:`ndarray.nonzero<numpy.ndarray.nonzero>` (*self*). Returns a tuple of index
arrays that select elements of *self* that are nonzero. If (nd=
:c:func:`PyArray_NDIM` ( ``self`` ))==1, then a single index array is
returned. The index arrays have data type :c:data:`NPY_INTP`. If a
tuple is returned (nd :math:`\neq` 1), then its length is nd.

Equivalent to :meth:`ndarray.compress<numpy.ndarray.compress>` (*self*, *condition*, *axis*
). Return the elements along *axis* corresponding to elements of
*condition* that are true.

.. tip::

    Pass in :c:data:`NPY_RAVEL_AXIS` for axis in order to achieve the same
    effect that is obtained by passing in ``axis=None`` in Python
    (treating the array as a 1-d array).


.. note::

    The out argument specifies where to place the result. If out is
    NULL, then the output array is created, otherwise the output is
    placed in out which must be the correct size and type. A new
    reference to the output array is always returned even when out
    is not NULL. The caller of the routine has the responsibility
    to ``Py_DECREF`` out if not NULL or a memory-leak will occur.


.. c:function:: PyObject* PyArray_ArgMax( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Equivalent to :meth:`ndarray.argmax<numpy.ndarray.argmax>` (*self*, *axis*). Return the index of
    the largest element of *self* along *axis*.

.. c:function:: PyObject* PyArray_ArgMin( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Equivalent to :meth:`ndarray.argmin<numpy.ndarray.argmin>` (*self*, *axis*). Return the index of
    the smallest element of *self* along *axis*.

.. c:function:: PyObject* PyArray_Max( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Equivalent to :meth:`ndarray.max<numpy.ndarray.max>` (*self*, *axis*). Returns the largest
    element of *self* along the given *axis*. When the result is a single
    element, returns a numpy scalar instead of an ndarray.

.. c:function:: PyObject* PyArray_Min( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Equivalent to :meth:`ndarray.min<numpy.ndarray.min>` (*self*, *axis*). Return the smallest
    element of *self* along the given *axis*. When the result is a single
    element, returns a numpy scalar instead of an ndarray.


.. c:function:: PyObject* PyArray_Ptp( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Return the difference between the largest element of *self* along *axis* and the
    smallest element of *self* along *axis*. When the result is a single
    element, returns a numpy scalar instead of an ndarray.




.. note::

    The rtype argument specifies the data-type the reduction should
    take place over. This is important if the data-type of the array
    is not "large" enough to handle the output. By default, all
    integer data-types are made at least as large as :c:data:`NPY_LONG`
    for the "add" and "multiply" ufuncs (which form the basis for
    mean, sum, cumsum, prod, and cumprod functions).

.. c:function:: PyObject* PyArray_Mean( \
        PyArrayObject* self, int axis, int rtype, PyArrayObject* out)

    Equivalent to :meth:`ndarray.mean<numpy.ndarray.mean>` (*self*, *axis*, *rtype*). Returns the
    mean of the elements along the given *axis*, using the enumerated
    type *rtype* as the data type to sum in. Default sum behavior is
    obtained using :c:data:`NPY_NOTYPE` for *rtype*.

.. c:function:: PyObject* PyArray_Trace( \
        PyArrayObject* self, int offset, int axis1, int axis2, int rtype, \
        PyArrayObject* out)

    Equivalent to :meth:`ndarray.trace<numpy.ndarray.trace>` (*self*, *offset*, *axis1*, *axis2*,
    *rtype*). Return the sum (using *rtype* as the data type of
    summation) over the *offset* diagonal elements of the 2-d arrays
    defined by *axis1* and *axis2* variables. A positive offset
    chooses diagonals above the main diagonal. A negative offset
    selects diagonals below the main diagonal.

.. c:function:: PyObject* PyArray_Clip( \
        PyArrayObject* self, PyObject* min, PyObject* max)

    Equivalent to :meth:`ndarray.clip<numpy.ndarray.clip>` (*self*, *min*, *max*). Clip an array,
    *self*, so that values larger than *max* are fixed to *max* and
    values less than *min* are fixed to *min*.

.. c:function:: PyObject* PyArray_Conjugate(PyArrayObject* self, PyArrayObject* out)

    Equivalent to :meth:`ndarray.conjugate<numpy.ndarray.conjugate>` (*self*).
    Return the complex conjugate of *self*. If *self* is not of
    complex data type, then return *self* with a reference.

    :param self: Input array.
    :param out:  Output array. If provided, the result is placed into this array.

    :return: The complex conjugate of *self*.



.. c:function:: PyObject* PyArray_Round( \
        PyArrayObject* self, int decimals, PyArrayObject* out)

    Equivalent to :meth:`ndarray.round<numpy.ndarray.round>` (*self*, *decimals*, *out*). Returns
    the array with elements rounded to the nearest decimal place. The
    decimal place is defined as the :math:`10^{-\textrm{decimals}}`
    digit so that negative *decimals* cause rounding to the nearest 10's, 100's, etc. If out is ``NULL``, then the output array is created, otherwise the output is placed in *out* which must be the correct size and type.

.. c:function:: PyObject* PyArray_Std( \
        PyArrayObject* self, int axis, int rtype, PyArrayObject* out)

    Equivalent to :meth:`ndarray.std<numpy.ndarray.std>` (*self*, *axis*, *rtype*). Return the
    standard deviation using data along *axis* converted to data type
    *rtype*.

.. c:function:: PyObject* PyArray_Sum( \
        PyArrayObject* self, int axis, int rtype, PyArrayObject* out)

    Equivalent to :meth:`ndarray.sum<numpy.ndarray.sum>` (*self*, *axis*, *rtype*). Return 1-d
    vector sums of elements in *self* along *axis*. Perform the sum
    after converting data to data type *rtype*.

.. c:function:: PyObject* PyArray_CumSum( \
        PyArrayObject* self, int axis, int rtype, PyArrayObject* out)

    Equivalent to :meth:`ndarray.cumsum<numpy.ndarray.cumsum>` (*self*, *axis*, *rtype*). Return
    cumulative 1-d sums of elements in *self* along *axis*. Perform
    the sum after converting data to data type *rtype*.

.. c:function:: PyObject* PyArray_Prod( \
        PyArrayObject* self, int axis, int rtype, PyArrayObject* out)

    Equivalent to :meth:`ndarray.prod<numpy.ndarray.prod>` (*self*, *axis*, *rtype*). Return 1-d
    products of elements in *self* along *axis*. Perform the product
    after converting data to data type *rtype*.

.. c:function:: PyObject* PyArray_CumProd( \
        PyArrayObject* self, int axis, int rtype, PyArrayObject* out)

    Equivalent to :meth:`ndarray.cumprod<numpy.ndarray.cumprod>` (*self*, *axis*, *rtype*). Return
    1-d cumulative products of elements in ``self`` along ``axis``.
    Perform the product after converting data to data type ``rtype``.

.. c:function:: PyObject* PyArray_All( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Equivalent to :meth:`ndarray.all<numpy.ndarray.all>` (*self*, *axis*). Return an array with
    True elements for every 1-d sub-array of ``self`` defined by
    ``axis`` in which all the elements are True.

.. c:function:: PyObject* PyArray_Any( \
        PyArrayObject* self, int axis, PyArrayObject* out)

    Equivalent to :meth:`ndarray.any<numpy.ndarray.any>` (*self*, *axis*). Return an array with
    True elements for every 1-d sub-array of *self* defined by *axis*
    in which any of the elements are True.

Functions
---------


Array Functions

Sometimes it is useful to access a multidimensional array as a
C-style multi-dimensional array so that algorithms can be
implemented using C's a[i][j][k] syntax. This routine returns a
pointer, *ptr*, that simulates this kind of C-style array, for
1-, 2-, and 3-d ndarrays.

:param op:

    The address to any Python object. This Python object will be replaced
    with an equivalent well-behaved, C-style contiguous, ndarray of the
    given data type specified by the last two arguments. Be sure that
    stealing a reference in this way to the input object is justified.

:param ptr:

    The address to a (ctype* for 1-d, ctype** for 2-d or ctype*** for 3-d)
    variable where ctype is the equivalent C-type for the data type. On
    return, *ptr* will be addressable as a 1-d, 2-d, or 3-d array.

:param dims:

    An output array that contains the shape of the array object. This
    array gives boundaries on any looping that will take place.

:param nd:

    The dimensionality of the array (1, 2, or 3).

:param typedescr:

    A :c:type:`PyArray_Descr` structure indicating the desired data-type
    (including required byteorder). The call will steal a reference to
    the parameter.

The simulation of a C-style array is not complete for 2-d and 3-d
arrays. For example, the simulated arrays of pointers cannot be passed
to subroutines expecting specific, statically-defined 2-d and 3-d
arrays. To pass to functions requiring those kind of inputs, you must
statically define the required array and copy data.

Must be called with the same objects and memory locations returned
from :c:func:`PyArray_AsCArray` (...). This function cleans up memory
that otherwise would get leaked.

Join the sequence of objects in *obj* together along *axis* into a
single array. If the dimensions or types are not compatible an
error is raised.

Compute a product-sum over the last dimensions of *obj1* and
*obj2*. Neither array is conjugated.

Compute a product-sum over the last dimension of *obj1* and the
second-to-last dimension of *obj2*. For 2-d arrays this is a
matrix-product. Neither array is conjugated.

Same as PyArray_MatrixProduct, but store the result in *out*.  The
output array must have the correct shape, type, and be
C-contiguous, or an exception is raised.

Applies the Einstein summation convention to the array operands
provided, returning a new array or placing the result in *out*.
The string in *subscripts* is a comma separated list of index
letters. The number of operands is in *nop*, and *op_in* is an
array containing those operands. The data type of the output can
be forced with *dtype*, the output order can be forced with *order*
(:c:data:`NPY_KEEPORDER` is recommended), and when *dtype* is specified,
*casting* indicates how permissive the data conversion should be.

See the :func:`~numpy.einsum` function for more details.

Compute the 1-d correlation of the 1-d arrays *op1* and *op2*
. The correlation is computed at each output point by multiplying
*op1* by a shifted version of *op2* and summing the result. As a
result of the shift, needed values outside of the defined range of
*op1* and *op2* are interpreted as zero. The mode determines how
many shifts to return: 0 - return only shifts that did not need to
assume zero- values; 1 - return an object that is the same size as
*op1*, 2 - return all possible shifts (any overlap at all is
accepted).

.. rubric:: Notes

This does not compute the usual correlation: if op2 is larger than op1, the
arguments are swapped, and the conjugate is never taken for complex arrays.
See PyArray_Correlate2 for the usual signal processing correlation.

Updated version of PyArray_Correlate, which uses the usual definition of
correlation for 1d arrays. The correlation is computed at each output point
by multiplying *op1* by a shifted version of *op2* and summing the result.
As a result of the shift, needed values outside of the defined range of
*op1* and *op2* are interpreted as zero. The mode determines how many
shifts to return: 0 - return only shifts that did not need to assume zero-
values; 1 - return an object that is the same size as *op1*, 2 - return all
possible shifts (any overlap at all is accepted).

.. rubric:: Notes

Compute z as follows::

  z[k] = sum_n op1[n] * conj(op2[n+k])

If both ``x`` and ``y`` are ``NULL``, then return
:c:func:`PyArray_Nonzero` (*condition*). Otherwise, both *x* and *y*
must be given and the object returned is shaped like *condition*
and has elements of *x* and *y* where *condition* is respectively
True or False.

.. c:function:: npy_bool PyArray_CheckStrides( \
        int elsize, int nd, npy_intp numbytes, npy_intp const* dims, \
        npy_intp const* newstrides)

    Determine if *newstrides* is a strides array consistent with the
    memory of an *nd* -dimensional array with shape ``dims`` and
    element-size, *elsize*. The *newstrides* array is checked to see
    if jumping by the provided number of bytes in each direction will
    ever mean jumping more than *numbytes* which is the assumed size
    of the available memory segment. If *numbytes* is 0, then an
    equivalent *numbytes* is computed assuming *nd*, *dims*, and
    *elsize* refer to a single-segment array. Return :c:data:`NPY_TRUE` if
    *newstrides* is acceptable, otherwise return :c:data:`NPY_FALSE`.

.. c:function:: npy_intp PyArray_MultiplyList(npy_intp const* seq, int n)

.. c:function:: int PyArray_MultiplyIntList(int const* seq, int n)

    Both of these routines multiply an *n* -length array, *seq*, of
    integers and return the result. No overflow checking is performed.

.. c:function:: int PyArray_CompareLists(npy_intp const* l1, npy_intp const* l2, int n)

    Given two *n* -length arrays of integers, *l1*, and *l2*, return
    1 if the lists are identical; otherwise, return 0.


Auxiliary data with object semantics
------------------------------------

.. c:type:: NpyAuxData

When working with more complex dtypes which are composed of other dtypes,
such as the struct dtype, creating inner loops that manipulate the dtypes
requires carrying along additional data. NumPy supports this idea
through a struct :c:type:`NpyAuxData`, mandating a few conventions so that
it is possible to do this.

Defining an :c:type:`NpyAuxData` is similar to defining a class in C++,
but the object semantics have to be tracked manually since the API is in C.
Here's an example for a function which doubles up an element using
an element copier function as a primitive.

.. code-block:: c

    typedef struct {
        NpyAuxData base;
        ElementCopier_Func *func;
        NpyAuxData *funcdata;
    } eldoubler_aux_data;

    void free_element_doubler_aux_data(NpyAuxData *data)
    {
        eldoubler_aux_data *d = (eldoubler_aux_data *)data;
        /* Free the memory owned by this auxdata */
        NPY_AUXDATA_FREE(d->funcdata);
        PyArray_free(d);
    }

    NpyAuxData *clone_element_doubler_aux_data(NpyAuxData *data)
    {
        eldoubler_aux_data *ret = PyArray_malloc(sizeof(eldoubler_aux_data));
        if (ret == NULL) {
            return NULL;
        }

        /* Raw copy of all data */
        memcpy(ret, data, sizeof(eldoubler_aux_data));

        /* Fix up the owned auxdata so we have our own copy */
        ret->funcdata = NPY_AUXDATA_CLONE(ret->funcdata);
        if (ret->funcdata == NULL) {
            PyArray_free(ret);
            return NULL;
        }

        return (NpyAuxData *)ret;
    }

    NpyAuxData *create_element_doubler_aux_data(
                                ElementCopier_Func *func,
                                NpyAuxData *funcdata)
    {
        eldoubler_aux_data *ret = PyArray_malloc(sizeof(eldoubler_aux_data));
        if (ret == NULL) {
            PyErr_NoMemory();
            return NULL;
        }
        memset(&ret, 0, sizeof(eldoubler_aux_data));
        ret->base->free = &free_element_doubler_aux_data;
        ret->base->clone = &clone_element_doubler_aux_data;
        ret->func = func;
        ret->funcdata = funcdata;

        return (NpyAuxData *)ret;
    }

.. c:type:: NpyAuxData_FreeFunc

    The function pointer type for NpyAuxData free functions.

.. c:type:: NpyAuxData_CloneFunc

    The function pointer type for NpyAuxData clone functions. These
    functions should never set the Python exception on error, because
    they may be called from a multi-threaded context.

.. c:function:: void NPY_AUXDATA_FREE(NpyAuxData *auxdata)

    A macro which calls the auxdata's free function appropriately,
    does nothing if auxdata is NULL.

.. c:function:: NpyAuxData *NPY_AUXDATA_CLONE(NpyAuxData *auxdata)

    A macro which calls the auxdata's clone function appropriately,
    returning a deep copy of the auxiliary data.

Array iterators
---------------

As of NumPy 1.6.0, these array iterators are superseded by
the new array iterator, :c:type:`NpyIter`.

An array iterator is a simple way to access the elements of an
N-dimensional array quickly and efficiently, as seen in :ref:`the
example <iteration-example>` which provides more description
of this useful approach to looping over an array from C.

.. c:function:: PyObject* PyArray_IterNew(PyObject* arr)

    Return an array iterator object from the array, *arr*. This is
    equivalent to *arr*. **flat**. The array iterator object makes
    it easy to loop over an N-dimensional non-contiguous array in
    C-style contiguous fashion.

.. c:function:: PyObject* PyArray_IterAllButAxis(PyObject* arr, int* axis)

    Return an array iterator that will iterate over all axes but the
    one provided in *\*axis*. The returned iterator cannot be used
    with :c:func:`PyArray_ITER_GOTO1D`. This iterator could be used to
    write something similar to what ufuncs do wherein the loop over
    the largest axis is done by a separate sub-routine. If *\*axis* is
    negative then *\*axis* will be set to the axis having the smallest
    stride and that axis will be used.

.. c:function:: PyObject *PyArray_BroadcastToShape( \
        PyObject* arr, npy_intp const *dimensions, int nd)

    Return an array iterator that is broadcast to iterate as an array
    of the shape provided by *dimensions* and *nd*.

.. c:function:: int PyArrayIter_Check(PyObject* op)

    Evaluates true if *op* is an array iterator (or instance of a
    subclass of the array iterator type).

.. c:function:: void PyArray_ITER_RESET(PyObject* iterator)

    Reset an *iterator* to the beginning of the array.

.. c:function:: void PyArray_ITER_NEXT(PyObject* iterator)

    Increment the index and the dataptr members of the *iterator* to
    point to the next element of the array. If the array is not
    (C-style) contiguous, also increment the N-dimensional coordinates
    array.

.. c:function:: void *PyArray_ITER_DATA(PyObject* iterator)

    A pointer to the current element of the array.

.. c:function:: void PyArray_ITER_GOTO( \
        PyObject* iterator, npy_intp* destination)

    Set the *iterator* index, dataptr, and coordinates members to the
    location in the array indicated by the N-dimensional c-array,
    *destination*, which must have size at least *iterator*
    ->nd_m1+1.

.. c:function:: void PyArray_ITER_GOTO1D(PyObject* iterator, npy_intp index)

    Set the *iterator* index and dataptr to the location in the array
    indicated by the integer *index* which points to an element in the
    C-styled flattened array.

.. c:function:: int PyArray_ITER_NOTDONE(PyObject* iterator)

    Evaluates TRUE as long as the iterator has not looped through all of
    the elements, otherwise it evaluates FALSE.


Broadcasting (multi-iterators)
------------------------------

.. c:function:: PyObject* PyArray_MultiIterNew(int num, ...)

    A simplified interface to broadcasting. This function takes the
    number of arrays to broadcast and then *num* extra ( :c:type:`PyObject *<PyObject>`
    ) arguments. These arguments are converted to arrays and iterators
    are created. :c:func:`PyArray_Broadcast` is then called on the resulting
    multi-iterator object. The resulting, broadcasted mult-iterator
    object is then returned. A broadcasted operation can then be
    performed using a single loop and using :c:func:`PyArray_MultiIter_NEXT`
    (..)

.. c:function:: void PyArray_MultiIter_RESET(PyObject* multi)

    Reset all the iterators to the beginning in a multi-iterator
    object, *multi*.

.. c:function:: void PyArray_MultiIter_NEXT(PyObject* multi)

    Advance each iterator in a multi-iterator object, *multi*, to its
    next (broadcasted) element.

.. c:function:: void *PyArray_MultiIter_DATA(PyObject* multi, int i)

    Return the data-pointer of the *i* :math:`^{\textrm{th}}` iterator
    in a multi-iterator object.

.. c:function:: void PyArray_MultiIter_NEXTi(PyObject* multi, int i)

    Advance the pointer of only the *i* :math:`^{\textrm{th}}` iterator.

.. c:function:: void PyArray_MultiIter_GOTO( \
        PyObject* multi, npy_intp* destination)

    Advance each iterator in a multi-iterator object, *multi*, to the
    given :math:`N` -dimensional *destination* where :math:`N` is the
    number of dimensions in the broadcasted array.

.. c:function:: void PyArray_MultiIter_GOTO1D(PyObject* multi, npy_intp index)

    Advance each iterator in a multi-iterator object, *multi*, to the
    corresponding location of the *index* into the flattened
    broadcasted array.

.. c:function:: int PyArray_MultiIter_NOTDONE(PyObject* multi)

    Evaluates TRUE as long as the multi-iterator has not looped
    through all of the elements (of the broadcasted result), otherwise
    it evaluates FALSE.

.. c:function:: npy_intp PyArray_MultiIter_SIZE(PyArrayMultiIterObject* multi)

    .. versionadded:: 1.26.0

    Returns the total broadcasted size of a multi-iterator object.

.. c:function:: int PyArray_MultiIter_NDIM(PyArrayMultiIterObject* multi)

    .. versionadded:: 1.26.0

    Returns the number of dimensions in the broadcasted result of
    a multi-iterator object.

.. c:function:: npy_intp PyArray_MultiIter_INDEX(PyArrayMultiIterObject* multi)

    .. versionadded:: 1.26.0

    Returns the current (1-d) index into the broadcasted result
    of a multi-iterator object.

.. c:function:: int PyArray_MultiIter_NUMITER(PyArrayMultiIterObject* multi)

    .. versionadded:: 1.26.0

    Returns the number of iterators that are represented by a
    multi-iterator object.

.. c:function:: void** PyArray_MultiIter_ITERS(PyArrayMultiIterObject* multi)

    .. versionadded:: 1.26.0

    Returns an array of iterator objects that holds the iterators for the
    arrays to be broadcast together. On return, the iterators are adjusted
    for broadcasting.

.. c:function:: npy_intp* PyArray_MultiIter_DIMS(PyArrayMultiIterObject* multi)

    .. versionadded:: 1.26.0

    Returns a pointer to the dimensions/shape of the broadcasted result of a
    multi-iterator object.

.. c:function:: int PyArray_Broadcast(PyArrayMultiIterObject* mit)

    This function encapsulates the broadcasting rules. The *mit*
    container should already contain iterators for all the arrays that
    need to be broadcast. On return, these iterators will be adjusted
    so that iteration over each simultaneously will accomplish the
    broadcasting. A negative number is returned if an error occurs.

.. c:function:: int PyArray_RemoveSmallest(PyArrayMultiIterObject* mit)

    This function takes a multi-iterator object that has been
    previously "broadcasted," finds the dimension with the smallest
    "sum of strides" in the broadcasted result and adapts all the
    iterators so as not to iterate over that dimension (by effectively
    making them of length-1 in that dimension). The corresponding
    dimension is returned unless *mit* ->nd is 0, then -1 is
    returned. This function is useful for constructing ufunc-like
    routines that broadcast their inputs correctly and then call a
    strided 1-d version of the routine as the inner-loop.  This 1-d
    version is usually optimized for speed and for this reason the
    loop should be performed over the axis that won't require large
    stride jumps.

Neighborhood iterator
---------------------

Neighborhood iterators are subclasses of the iterator object, and can be used
to iter over a neighborhood of a point. For example, you may want to iterate
over every voxel of a 3d image, and for every such voxel, iterate over an
hypercube. Neighborhood iterator automatically handle boundaries, thus making
this kind of code much easier to write than manual boundaries handling, at the
cost of a slight overhead.

.. c:function:: PyObject* PyArray_NeighborhoodIterNew( \
        PyArrayIterObject* iter, npy_intp bounds, int mode, \
        PyArrayObject* fill_value)

    This function creates a new neighborhood iterator from an existing
    iterator.  The neighborhood will be computed relatively to the position
    currently pointed by *iter*, the bounds define the shape of the
    neighborhood iterator, and the mode argument the boundaries handling mode.

    The *bounds* argument is expected to be a (2 * iter->ao->nd) arrays, such
    as the range bound[2*i]->bounds[2*i+1] defines the range where to walk for
    dimension i (both bounds are included in the walked coordinates). The
    bounds should be ordered for each dimension (bounds[2*i] <= bounds[2*i+1]).

    The mode should be one of:

    .. c:macro:: NPY_NEIGHBORHOOD_ITER_ZERO_PADDING

            Zero padding. Outside bounds values will be 0.

    .. c:macro:: NPY_NEIGHBORHOOD_ITER_ONE_PADDING

            One padding, Outside bounds values will be 1.

    .. c:macro:: NPY_NEIGHBORHOOD_ITER_CONSTANT_PADDING

            Constant padding. Outside bounds values will be the
            same as the first item in fill_value.

    .. c:macro:: NPY_NEIGHBORHOOD_ITER_MIRROR_PADDING

            Mirror padding. Outside bounds values will be as if the
            array items were mirrored. For example, for the array [1, 2, 3, 4],
            x[-2] will be 2, x[-2] will be 1, x[4] will be 4, x[5] will be 1,
            etc...

    .. c:macro:: NPY_NEIGHBORHOOD_ITER_CIRCULAR_PADDING

            Circular padding. Outside bounds values will be as if the array
            was repeated. For example, for the array [1, 2, 3, 4], x[-2] will
            be 3, x[-2] will be 4, x[4] will be 1, x[5] will be 2, etc...

    If the mode is constant filling (:c:macro:`NPY_NEIGHBORHOOD_ITER_CONSTANT_PADDING`),
    fill_value should point to an array object which holds the filling value
    (the first item will be the filling value if the array contains more than
    one item). For other cases, fill_value may be NULL.

    - The iterator holds a reference to iter
    - Return NULL on failure (in which case the reference count of iter is not
      changed)
    - iter itself can be a Neighborhood iterator: this can be useful for .e.g
      automatic boundaries handling
    - the object returned by this function should be safe to use as a normal
      iterator
    - If the position of iter is changed, any subsequent call to
      PyArrayNeighborhoodIter_Next is undefined behavior, and
      PyArrayNeighborhoodIter_Reset must be called.
    - If the position of iter is not the beginning of the data and the
      underlying data for iter is contiguous, the iterator will point to the
      start of the data instead of position pointed by iter.
      To avoid this situation, iter should be moved to the required position
      only after the creation of iterator, and PyArrayNeighborhoodIter_Reset
      must be called.

    .. code-block:: c

       PyArrayIterObject *iter;
       PyArrayNeighborhoodIterObject *neigh_iter;
       iter = PyArray_IterNew(x);

       /*For a 3x3 kernel */
       bounds = {-1, 1, -1, 1};
       neigh_iter = (PyArrayNeighborhoodIterObject*)PyArray_NeighborhoodIterNew(
            iter, bounds, NPY_NEIGHBORHOOD_ITER_ZERO_PADDING, NULL);

       for(i = 0; i < iter->size; ++i) {
            for (j = 0; j < neigh_iter->size; ++j) {
                    /* Walk around the item currently pointed by iter->dataptr */
                    PyArrayNeighborhoodIter_Next(neigh_iter);
            }

            /* Move to the next point of iter */
            PyArrayIter_Next(iter);
            PyArrayNeighborhoodIter_Reset(neigh_iter);
       }

.. c:function:: int PyArrayNeighborhoodIter_Reset( \
        PyArrayNeighborhoodIterObject* iter)

    Reset the iterator position to the first point of the neighborhood. This
    should be called whenever the iter argument given at
    PyArray_NeighborhoodIterObject is changed (see example)

.. c:function:: int PyArrayNeighborhoodIter_Next( \
        PyArrayNeighborhoodIterObject* iter)

    After this call, iter->dataptr points to the next point of the
    neighborhood. Calling this function after every point of the
    neighborhood has been visited is undefined.


Array scalars
-------------

.. c:function:: PyObject* PyArray_Return(PyArrayObject* arr)

    This function steals a reference to *arr*.

    This function checks to see if *arr* is a 0-dimensional array and,
    if so, returns the appropriate array scalar. It should be used
    whenever 0-dimensional arrays could be returned to Python.

.. c:function:: PyObject* PyArray_Scalar( \
        void* data, PyArray_Descr* dtype, PyObject* base)

    Return an array scalar object of the given *dtype* by **copying**
    from memory pointed to by *data*.  *base* is expected to be the
    array object that is the owner of the data.  *base* is required
    if `dtype` is a ``void`` scalar, or if the ``NPY_USE_GETITEM``
    flag is set and it is known that the ``getitem`` method uses
    the ``arr`` argument without checking if it is ``NULL``.  Otherwise
    `base` may be ``NULL``.

    If the data is not in native byte order (as indicated by
    ``dtype->byteorder``) then this function will byteswap the data,
    because array scalars are always in correct machine-byte order.

.. c:function:: PyObject* PyArray_ToScalar(void* data, PyArrayObject* arr)

    Return an array scalar object of the type and itemsize indicated
    by the array object *arr* copied from the memory pointed to by
    *data* and swapping if the data in *arr* is not in machine
    byte-order.

.. c:function:: PyObject* PyArray_FromScalar( \
        PyObject* scalar, PyArray_Descr* outcode)

    Return a 0-dimensional array of type determined by *outcode* from
    *scalar* which should be an array-scalar object. If *outcode* is
    NULL, then the type is determined from *scalar*.

.. c:function:: void PyArray_ScalarAsCtype(PyObject* scalar, void* ctypeptr)

    Return in *ctypeptr* a pointer to the actual value in an array
    scalar. There is no error checking so *scalar* must be an
    array-scalar object, and ctypeptr must have enough space to hold
    the correct type. For flexible-sized types, a pointer to the data
    is copied into the memory of *ctypeptr*, for all other types, the
    actual data is copied into the address pointed to by *ctypeptr*.

.. c:function:: int PyArray_CastScalarToCtype( \
        PyObject* scalar, void* ctypeptr, PyArray_Descr* outcode)

    Return the data (cast to the data type indicated by *outcode*)
    from the array-scalar, *scalar*, into the memory pointed to by
    *ctypeptr* (which must be large enough to handle the incoming
    memory).

    Returns -1 on failure, and 0 on success.

.. c:function:: PyObject* PyArray_TypeObjectFromType(int type)

    Returns a scalar type-object from a type-number, *type*
    . Equivalent to :c:func:`PyArray_DescrFromType` (*type*)->typeobj
    except for reference counting and error-checking. Returns a new
    reference to the typeobject on success or ``NULL`` on failure.

.. c:function:: NPY_SCALARKIND PyArray_ScalarKind( \
        int typenum, PyArrayObject** arr)

    Legacy way to query special promotion for scalar values.  This is not
    used in NumPy itself anymore and is expected to be deprecated eventually.

    New DTypes can define promotion rules specific to Python scalars.

.. c:function:: int PyArray_CanCoerceScalar( \
        char thistype, char neededtype, NPY_SCALARKIND scalar)

    Legacy way to query special promotion for scalar values.  This is not
    used in NumPy itself anymore and is expected to be deprecated eventually.

    Use ``PyArray_ResultType`` for similar purposes.


Data-type descriptors
---------------------



.. warning::

    Data-type objects must be reference counted so be aware of the
    action on the data-type reference of different C-API calls. The
    standard rule is that when a data-type object is returned it is a
    new reference.  Functions that take :c:expr:`PyArray_Descr *` objects and
    return arrays steal references to the data-type their inputs
    unless otherwise noted. Therefore, you must own a reference to any
    data-type object used as input to such a function.

.. c:function:: int PyArray_DescrCheck(PyObject* obj)

    Evaluates as true if *obj* is a data-type object ( :c:expr:`PyArray_Descr *` ).

.. c:function:: PyArray_Descr* PyArray_DescrNew(PyArray_Descr* obj)

    Return a new data-type object copied from *obj* (the fields
    reference is just updated so that the new object points to the
    same fields dictionary if any).

.. c:function:: PyArray_Descr* PyArray_DescrNewFromType(int typenum)

    Create a new data-type object from the built-in (or
    user-registered) data-type indicated by *typenum*. All builtin
    types should not have any of their fields changed. This creates a
    new copy of the :c:type:`PyArray_Descr` structure so that you can fill
    it in as appropriate. This function is especially needed for
    flexible data-types which need to have a new elsize member in
    order to be meaningful in array construction.

.. c:function:: PyArray_Descr* PyArray_DescrNewByteorder( \
        PyArray_Descr* obj, char newendian)

    Create a new data-type object with the byteorder set according to
    *newendian*. All referenced data-type objects (in subdescr and
    fields members of the data-type object) are also changed
    (recursively).

    The value of *newendian* is one of these macros:
..
    dedent the enumeration of flags to avoid missing references sphinx warnings

.. c:macro:: NPY_IGNORE
             NPY_SWAP
             NPY_NATIVE
             NPY_LITTLE
             NPY_BIG

    If a byteorder of :c:data:`NPY_IGNORE` is encountered it
    is left alone. If newendian is :c:data:`NPY_SWAP`, then all byte-orders
    are swapped. Other valid newendian values are :c:data:`NPY_NATIVE`,
    :c:data:`NPY_LITTLE`, and :c:data:`NPY_BIG` which all cause
    the returned data-typed descriptor (and all it's
    referenced data-type descriptors) to have the corresponding byte-
    order.

.. c:function:: PyArray_Descr* PyArray_DescrFromObject( \
        PyObject* op, PyArray_Descr* mintype)

    Determine an appropriate data-type object from the object *op*
    (which should be a "nested" sequence object) and the minimum
    data-type descriptor mintype (which can be ``NULL`` ). Similar in
    behavior to array(*op*).dtype. Don't confuse this function with
    :c:func:`PyArray_DescrConverter`. This function essentially looks at
    all the objects in the (nested) sequence and determines the
    data-type from the elements it finds.

.. c:function:: PyArray_Descr* PyArray_DescrFromScalar(PyObject* scalar)

    Return a data-type object from an array-scalar object. No checking
    is done to be sure that *scalar* is an array scalar. If no
    suitable data-type can be determined, then a data-type of
    :c:data:`NPY_OBJECT` is returned by default.

.. c:function:: PyArray_Descr* PyArray_DescrFromType(int typenum)

    Returns a data-type object corresponding to *typenum*. The
    *typenum* can be one of the enumerated types, a character code for
    one of the enumerated types, or a user-defined type. If you want to use a
    flexible size array, then you need to ``flexible typenum`` and set the
    results ``elsize`` parameter to the desired size. The typenum is one of the
    :c:data:`NPY_TYPES`.

.. c:function:: int PyArray_DescrConverter(PyObject* obj, PyArray_Descr** dtype)

    Convert any compatible Python object, *obj*, to a data-type object
    in *dtype*. A large number of Python objects can be converted to
    data-type objects. See :ref:`arrays.dtypes` for a complete
    description. This version of the converter converts None objects
    to a :c:data:`NPY_DEFAULT_TYPE` data-type object. This function can
    be used with the "O&" character code in :c:func:`PyArg_ParseTuple`
    processing.

.. c:function:: int PyArray_DescrConverter2( \
        PyObject* obj, PyArray_Descr** dtype)

    Convert any compatible Python object, *obj*, to a data-type
    object in *dtype*. This version of the converter converts None
    objects so that the returned data-type is ``NULL``. This function
    can also be used with the "O&" character in PyArg_ParseTuple
    processing.

.. c:function:: int PyArray_DescrAlignConverter( \
        PyObject* obj, PyArray_Descr** dtype)

    Like :c:func:`PyArray_DescrConverter` except it aligns C-struct-like
    objects on word-boundaries as the compiler would.

.. c:function:: int PyArray_DescrAlignConverter2( \
        PyObject* obj, PyArray_Descr** dtype)

    Like :c:func:`PyArray_DescrConverter2` except it aligns C-struct-like
    objects on word-boundaries as the compiler would.

Data Type Promotion and Inspection
----------------------------------

.. c:function:: PyArray_DTypeMeta *PyArray_CommonDType( \
            const PyArray_DTypeMeta *dtype1, const PyArray_DTypeMeta *dtype2)

   This function defines the common DType operator. Note that the common DType
   will not be ``object`` (unless one of the DTypes is ``object``). Similar to
   `numpy.result_type`, but works on the classes and not instances.

.. c:function:: PyArray_DTypeMeta *PyArray_PromoteDTypeSequence( \
                    npy_intp length, PyArray_DTypeMeta **dtypes_in)

   Promotes a list of DTypes with each other in a way that should guarantee
   stable results even when changing the order.  This function is smarter and
   can often return successful and unambiguous results when
   ``common_dtype(common_dtype(dt1, dt2), dt3)`` would depend on the operation
   order or fail.  Nevertheless, DTypes should aim to ensure that their
   common-dtype implementation is associative and commutative!  (Mainly,
   unsigned and signed integers are not.)

   For guaranteed consistent results DTypes must implement common-Dtype
   "transitively".  If A promotes B and B promotes C, than A must generally
   also promote C; where "promotes" means implements the promotion.  (There
   are some exceptions for abstract DTypes)

   In general this approach always works as long as the most generic dtype
   is either strictly larger, or compatible with all other dtypes.
   For example promoting ``float16`` with any other float, integer, or unsigned
   integer again gives a floating point number.

.. c:function:: PyArray_Descr *PyArray_GetDefaultDescr(const PyArray_DTypeMeta *DType)

   Given a DType class, returns the default instance (descriptor).  This checks
   for a ``singleton`` first and only calls the ``default_descr`` function if
   necessary.

.. _dtype-api:

Custom Data Types
-----------------

.. versionadded:: 2.0

These functions allow defining custom flexible data types outside of NumPy.  See
:ref:`NEP 42 <NEP42>` for more details about the rationale and design of the new
DType system. See the `numpy-user-dtypes repository
<https://github.com/numpy/numpy-user-dtypes>`_ for a number of example DTypes.
Also see :ref:`dtypemeta` for documentation on ``PyArray_DTypeMeta`` and
``PyArrayDTypeMeta_Spec``.

.. c:function:: int PyArrayInitDTypeMeta_FromSpec( \
                PyArray_DTypeMeta *Dtype, PyArrayDTypeMeta_Spec *spec)

 Initialize a new DType.  It must currently be a static Python C type that is
 declared as :c:type:`PyArray_DTypeMeta` and not :c:type:`PyTypeObject`.
 Further, it must subclass `np.dtype` and set its type to
 :c:type:`PyArrayDTypeMeta_Type` (before calling :c:func:`PyType_Ready()`),
 which has additional fields compared to a normal :c:type:`PyTypeObject`. See
 the examples in the ``numpy-user-dtypes`` repository for usage with both
 parametric and non-parametric data types.

.. _dtype-flags:

Flags
~~~~~

Flags that can be set on the ``PyArrayDTypeMeta_Spec`` to initialize the DType.

.. c:macro:: NPY_DT_ABSTRACT

   Indicates the DType is an abstract "base" DType in a DType hierarchy and
   should not be directly instantiated.

.. c:macro:: NPY_DT_PARAMETRIC

   Indicates the DType is parametric and does not have a unique singleton
   instance.

.. c:macro:: NPY_DT_NUMERIC

   Indicates the DType represents a numerical value.


.. _dtype-slots:

Slot IDs and API Function Typedefs

The following constant IDs are defined for retrieving dtype-specific values:

**Basic constants** (available for all numeric types):

   The zero value for the dtype.

   The one value for the dtype.

   The minimum finite value representable by the dtype. For floating-point types,
   this is the most negative finite value (e.g., ``-FLT_MAX``).

   The maximum finite value representable by the dtype.

   Positive infinity (only for floating-point types).

   Negative infinity (only for floating-point types).

   Not-a-Number (only for floating-point types).

   The radix (base) of the floating-point representation. This is 2 for all
   floating-point types.

   Machine epsilon: the difference between 1.0 and the next representable value
   greater than 1.0. Corresponds to C macros like ``FLT_EPSILON``, ``DBL_EPSILON``.

   .. note::
       For long double in IBM double-double format (PowerPC), this is defined as
       ``0x1p-105L`` (2^-105) based on the ~106 bits of mantissa precision.

   The difference between 1.0 and the next representable value less than 1.0.
   Typically ``eps / radix`` for binary floating-point types.

   The smallest positive normalized floating-point number. Corresponds to C
   macros like ``FLT_MIN``, ``DBL_MIN``. This is the smallest value with a
   leading 1 bit in the mantissa.

   The smallest positive subnormal (denormalized) floating-point number.
   Corresponds to C macros like ``FLT_TRUE_MIN``, ``DBL_TRUE_MIN``. This is
   the smallest representable positive value, with leading 0 bits in the mantissa.

   Number of mantissa bits (excluding the implicit leading bit). For example,
   IEEE 754 binary64 (double) has 52 explicit mantissa bits, so this returns 52.
   Corresponds to ``MANT_DIG - 1`` from C standard macros.

   Minimum exponent value. This is the minimum negative integer such that the
   radix raised to the power of one less than that integer is a normalized
   floating-point number. Corresponds to ``MIN_EXP - 1`` from C standard macros
   (e.g., ``FLT_MIN_EXP - 1``).

   Maximum exponent value. This is the maximum positive integer such that the
   radix raised to the power of one less than that integer is a representable
   finite floating-point number. Corresponds to ``MAX_EXP`` from C standard
   macros (e.g., ``FLT_MAX_EXP``).

   The number of decimal digits of precision. Corresponds to ``DIG`` from C
   standard macros (e.g., ``FLT_DIG``, ``DBL_DIG``).

These macros and static inline functions are provided to allow more
understandable and idiomatic code when working with ``PyArray_DTypeMeta``
instances.

.. c:macro:: NPY_DTYPE(descr)

   Returns a ``PyArray_DTypeMeta *`` pointer to the DType of a given
   descriptor instance.

.. c:function:: static inline PyArray_DTypeMeta \
                *NPY_DT_NewRef(PyArray_DTypeMeta *o)

   Returns a ``PyArray_DTypeMeta *`` pointer to a new reference to a
   DType.

Conversion utilities
--------------------

For use with :c:func:`PyArg_ParseTuple`

Be sure to understand what steps you should take to manage the
memory when using these conversion functions. These functions can
require freeing memory, and/or altering the reference counts of
specific objects based on your use.

Convert any Python object to a :c:type:`PyArrayObject`. If
:c:func:`PyArray_Check` (*obj*) is TRUE then its reference count is
incremented and a reference placed in *address*. If *obj* is not
an array, then convert it to an array using :c:func:`PyArray_FromAny`
. No matter what is returned, you must DECREF the object returned
by this routine in *address* when you are done with it.

This is a default converter for output arrays given to
functions. If *obj* is :c:data:`Py_None` or ``NULL``, then *\*address*
will be ``NULL`` but the call will succeed. If :c:func:`PyArray_Check` (
*obj*) is TRUE then it is returned in *\*address* without
incrementing its reference count.

Convert any Python sequence, *obj*, smaller than :c:data:`NPY_MAXDIMS`
to a C-array of :c:type:`npy_intp`. The Python object could also be a
single number. The *seq* variable is a pointer to a structure with
members ptr and len. On successful return, *seq* ->ptr contains a
pointer to memory that must be freed, by calling :c:func:`PyDimMem_FREE`,
to avoid a memory leak. The restriction on memory size allows this
converter to be conveniently used for sequences intended to be
interpreted as array shapes.

Convert any Python object, *obj*, with a (single-segment) buffer
interface to a variable with members that detail the object's use
of its chunk of memory. The *buf* variable is a pointer to a
structure with base, ptr, len, and flags members. The
:c:type:`PyArray_Chunk` structure is binary compatible with the
Python's buffer object (through its len member on 32-bit platforms
and its ptr member on 64-bit platforms). On return, the base member
is set to *obj* (or its base if *obj* is already a buffer object
pointing to another object). If you need to hold on to the memory
be sure to INCREF the base member. The chunk of memory is pointed
to by *buf* ->ptr member and has length *buf* ->len. The flags
member of *buf* is :c:data:`NPY_ARRAY_ALIGNED` with the
:c:data:`NPY_ARRAY_WRITEABLE` flag set if *obj* has a writeable
buffer interface.

Convert a Python object, *obj*, representing an axis argument to
the proper value for passing to the functions that take an integer
axis. Specifically, if *obj* is None, *axis* is set to
:c:data:`NPY_RAVEL_AXIS` which is interpreted correctly by the C-API
functions that take axis arguments.

Convert any Python object, *obj*, to :c:data:`NPY_TRUE` or
:c:data:`NPY_FALSE`, and place the result in *value*.

Convert Python strings into the corresponding byte-order
character:
'>', '<', 's', '=', or '\|'.

Convert Python strings into one of :c:data:`NPY_QUICKSORT` (starts
with 'q' or 'Q'), :c:data:`NPY_HEAPSORT` (starts with 'h' or 'H'),
:c:data:`NPY_MERGESORT` (starts with 'm' or 'M') or :c:data:`NPY_STABLESORT`
(starts with 't' or 'T'). :c:data:`NPY_MERGESORT` and :c:data:`NPY_STABLESORT`
are aliased to each other for backwards compatibility and may refer to one
of several stable sorting algorithms depending on the data type.

Convert Python strings into one of :c:data:`NPY_SEARCHLEFT` (starts with 'l'
or 'L'), or :c:data:`NPY_SEARCHRIGHT` (starts with 'r' or 'R').

Convert the Python strings 'clip', 'wrap', and 'raise' into the
:c:type:`NPY_CLIPMODE` enumeration :c:data:`NPY_CLIP`, :c:data:`NPY_WRAP`,
and :c:data:`NPY_RAISE`.

.. c:function:: int PyArray_PyIntAsInt(PyObject* op)

    Convert all kinds of Python objects (including arrays and array
    scalars) to a standard integer. On error, -1 is returned and an
    exception set. You may find useful the macro:

    .. code-block:: c

        #define error_converting(x) (((x) == -1) && PyErr_Occurred())

.. c:function:: npy_intp PyArray_PyIntAsIntp(PyObject* op)

    Convert all kinds of Python objects (including arrays and array
    scalars) to a (platform-pointer-sized) integer. On error, -1 is
    returned and an exception set.

.. c:function:: int PyArray_IntpFromSequence( \
        PyObject* seq, npy_intp* vals, int maxvals)

    Convert any Python sequence (or single Python number) passed in as
    *seq* to (up to) *maxvals* pointer-sized integers and place them
    in the *vals* array. The sequence can be smaller then *maxvals* as
    the number of converted objects is returned.

.. _including-the-c-api:

Including and importing the C API
---------------------------------

To use the NumPy C-API you typically need to include the
``numpy/ndarrayobject.h`` header and ``numpy/ufuncobject.h`` for some ufunc
related functionality (``arrayobject.h`` is an alias for ``ndarrayobject.h``).

These two headers export most relevant functionality.  In general any project
which uses the NumPy API must import NumPy using one of the functions
``PyArray_ImportNumPyAPI()`` or ``import_array()``.
In some places, functionality which requires ``import_array()`` is not
needed, because you only need type definitions.  In this case, it is
sufficient to include ``numpy/ndarratypes.h``.

For the typical Python project, multiple C or C++ files will be compiled into
a single shared object (the Python C-module) and ``PyArray_ImportNumPyAPI()``
should be called inside it's module initialization.

When you have a single C-file, this will consist of:

.. code-block:: c

    #include "numpy/ndarrayobject.h"

    PyMODINIT_FUNC PyInit_my_module(void)
    {
        if (PyArray_ImportNumPyAPI() < 0) {
            return NULL;
        }
        /* Other initialization code. */
    }

However, most projects will have additional C files which are all
linked together into a single Python module.
In this case, the helper C files typically do not have a canonical place
where ``PyArray_ImportNumPyAPI`` should be called (although it is OK and
fast to call it often).

To solve this, NumPy provides the following pattern that the main
file is modified to define ``PY_ARRAY_UNIQUE_SYMBOL`` before the include:

.. code-block:: c

    /* Main module file */
    #define PY_ARRAY_UNIQUE_SYMBOL MyModule
    #include "numpy/ndarrayobject.h"

    PyMODINIT_FUNC PyInit_my_module(void)
    {
        if (PyArray_ImportNumPyAPI() < 0) {
            return NULL;
        }
        /* Other initialization code. */
    }

while the other files use:

.. code-block:: C

    /* Second file without any import */
    #define NO_IMPORT_ARRAY
    #define PY_ARRAY_UNIQUE_SYMBOL MyModule
    #include "numpy/ndarrayobject.h"

You can of course add the defines to a local header used throughout.
You just have to make sure that the main file does _not_ define
``NO_IMPORT_ARRAY``.

For ``numpy/ufuncobject.h`` the same logic applies, but the unique symbol
mechanism is ``#define PY_UFUNC_UNIQUE_SYMBOL`` (both can match).

Additionally, you will probably wish to add a
``#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION``
to avoid warnings about possible use of old API.

.. note::
    If you are experiencing access violations make sure that the NumPy API
    was properly imported and the symbol ``PyArray_API`` is not ``NULL``.
    When in a debugger, this symbols actual name will be
    ``PY_ARRAY_UNIQUE_SYMBOL``+``PyArray_API``, so for example
    ``MyModulePyArray_API`` in the above.
    (E.g. even a ``printf("%p\n", PyArray_API);`` just before the crash.)


Mechanism details and dynamic linking

Ensures that the NumPy C-API is imported and usable.  It returns ``0``
on success and ``-1`` with an error set if NumPy couldn't be imported.
While preferable to call it once at module initialization, this function
is very light-weight if called multiple times.

.. versionadded:: 2.0
    This function is backported in the ``npy_2_compat.h`` header.

This function must be called in the initialization section of a
module that will make use of the C-API. It imports the module
where the function-pointer table is stored and points the correct
variable to it.
This macro includes a ``return NULL;`` on error, so that
``PyArray_ImportNumPyAPI()`` is preferable for custom error checking.
You may also see use of ``_import_array()`` (a function, not
a macro, but you may want to raise a better error if it fails) and
the variations ``import_array1(ret)`` which customizes the return value.

.. versionadded:: 2.1

An additional symbol which can be used to share e.g. visibility beyond
shared object boundaries.
By default, NumPy adds the C visibility hidden attribute (if available):
``void __attribute__((visibility("hidden"))) **PyArray_API;``.
You can change this by defining ``NPY_API_SYMBOL_ATTRIBUTE``, which will
make this:
``void NPY_API_SYMBOL_ATTRIBUTE **PyArray_API;`` (with additional
name mangling via the unique symbol).

Adding an empty ``#define NPY_API_SYMBOL_ATTRIBUTE`` will have the same
behavior as NumPy 1.x.

.. note::
    Windows never had shared visibility although you can use this macro
    to achieve it.  We generally discourage sharing beyond shared boundary
    lines since importing the array API includes NumPy version checks.

Defining ``NO_IMPORT_ARRAY`` before the ``ndarrayobject.h`` include
indicates that the NumPy C API import is handled in a different file
and the include mechanism will not be added here.
You must have one file without ``NO_IMPORT_ARRAY`` defined.

.. code-block:: c

    #define PY_ARRAY_UNIQUE_SYMBOL cool_ARRAY_API
    #include <numpy/arrayobject.h>

On the other hand, coolhelper.c would contain at the top:

.. code-block:: c

    #define NO_IMPORT_ARRAY
    #define PY_ARRAY_UNIQUE_SYMBOL cool_ARRAY_API
    #include <numpy/arrayobject.h>

You can also put the common two last lines into an extension-local
header file as long as you make sure that NO_IMPORT_ARRAY is
#defined before #including that file.

Internally, these #defines work as follows:

* If neither is defined, the C-API is declared to be
  ``static void**``, so it is only visible within the
  compilation unit that #includes numpy/arrayobject.h.
* If :c:macro:`PY_ARRAY_UNIQUE_SYMBOL` is #defined, but
  :c:macro:`NO_IMPORT_ARRAY` is not, the C-API is declared to
  be ``void**``, so that it will also be visible to other
  compilation units.
* If :c:macro:`NO_IMPORT_ARRAY` is #defined, regardless of
  whether :c:macro:`PY_ARRAY_UNIQUE_SYMBOL` is, the C-API is
  declared to be ``extern void**``, so it is expected to
  be defined in another compilation unit.
* Whenever :c:macro:`PY_ARRAY_UNIQUE_SYMBOL` is #defined, it
  also changes the name of the variable holding the C-API, which
  defaults to ``PyArray_API``, to whatever the macro is
  #defined to.

Because python extensions are not used in the same way as usual libraries on
most platforms, some errors cannot be automatically detected at build time or
even runtime. For example, if you build an extension using a function available
only for numpy >= 1.3.0, and you import the extension later with numpy 1.2, you
will not get an import error (but almost certainly a segmentation fault when
calling the function). That's why several functions are provided to check for
numpy versions. The macros :c:data:`NPY_VERSION`  and
:c:data:`NPY_FEATURE_VERSION` corresponds to the numpy version used to build the
extension, whereas the versions returned by the functions
:c:func:`PyArray_GetNDArrayCVersion` and :c:func:`PyArray_GetNDArrayCFeatureVersion`
corresponds to the runtime numpy's version.

The rules for ABI and API compatibilities can be summarized as follows:

* Whenever :c:data:`NPY_VERSION` != ``PyArray_GetNDArrayCVersion()``, the
  extension has to be recompiled (ABI incompatibility).
* :c:data:`NPY_VERSION` == ``PyArray_GetNDArrayCVersion()`` and
  :c:data:`NPY_FEATURE_VERSION` <= ``PyArray_GetNDArrayCFeatureVersion()`` means
  backward compatible changes.

ABI incompatibility is automatically detected in every numpy's version. API
incompatibility detection was added in numpy 1.4.0. If you want to supported
many different numpy versions with one extension binary, you have to build your
extension with the lowest :c:data:`NPY_FEATURE_VERSION` as possible.

.. c:macro:: NPY_VERSION

    The current version of the ndarray object (check to see if this
    variable is defined to guarantee the ``numpy/arrayobject.h`` header is
    being used).

.. c:macro:: NPY_FEATURE_VERSION

    The current version of the C-API.

.. c:function:: unsigned int PyArray_GetNDArrayCVersion(void)

    This just returns the value :c:data:`NPY_VERSION`. :c:data:`NPY_VERSION`
    changes whenever a backward incompatible change at the ABI level. Because
    it is in the C-API, however, comparing the output of this function from the
    value defined in the current header gives a way to test if the C-API has
    changed thus requiring a re-compilation of extension modules that use the
    C-API. This is automatically checked in the function :c:func:`import_array`.

.. c:function:: unsigned int PyArray_GetNDArrayCFeatureVersion(void)

    This just returns the value :c:data:`NPY_FEATURE_VERSION`.
    :c:data:`NPY_FEATURE_VERSION` changes whenever the API changes (e.g. a
    function is added). A changed value does not always require a recompile.


Memory management
~~~~~~~~~~~~~~~~~

.. c:function:: char* PyDataMem_NEW(size_t nbytes)

.. c:function:: void PyDataMem_FREE(char* ptr)

.. c:function:: char* PyDataMem_RENEW(void * ptr, size_t newbytes)

    Functions to allocate, free, and reallocate memory. These are used
    internally to manage array data memory unless overridden.

.. c:function:: npy_intp*  PyDimMem_NEW(int nd)

.. c:function:: void PyDimMem_FREE(char* ptr)

.. c:function:: npy_intp* PyDimMem_RENEW(void* ptr, size_t newnd)

    Macros to allocate, free, and reallocate dimension and strides memory.

.. c:function:: void* PyArray_malloc(size_t nbytes)

.. c:function:: void PyArray_free(void* ptr)

.. c:function:: void* PyArray_realloc(npy_intp* ptr, size_t nbytes)

    These macros use different memory allocators, depending on the
    constant :c:data:`NPY_USE_PYMEM`. The system malloc is used when
    :c:data:`NPY_USE_PYMEM` is 0, if :c:data:`NPY_USE_PYMEM` is 1, then
    the Python memory allocator is used.

    .. c:macro:: NPY_USE_PYMEM

.. c:function:: int PyArray_ResolveWritebackIfCopy(PyArrayObject* obj)

    If ``obj->flags`` has :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`, this function
    clears the flags, `DECREF` s
    `obj->base` and makes it writeable, and sets ``obj->base`` to NULL. It then
    copies ``obj->data`` to `obj->base->data`, and returns the error state of
    the copy operation. This is the opposite of
    :c:func:`PyArray_SetWritebackIfCopyBase`. Usually this is called once
    you are finished with ``obj``, just before ``Py_DECREF(obj)``. It may be called
    multiple times, or with ``NULL`` input. See also
    :c:func:`PyArray_DiscardWritebackIfCopy`.

    Returns 0 if nothing was done, -1 on error, and 1 if action was taken.

.. _array.ndarray.capi.threading:

Threading support
~~~~~~~~~~~~~~~~~

These macros are only meaningful if :c:data:`NPY_ALLOW_THREADS`
evaluates True during compilation of the extension module. Otherwise,
these macros are equivalent to whitespace. Python uses a single Global
Interpreter Lock (GIL) for each Python process so that only a single
thread may execute at a time (even on multi-cpu machines). When
calling out to a compiled function that may take time to compute (and
does not have side-effects for other threads like updated global
variables), the GIL should be released so that other Python threads
can run while the time-consuming calculations are performed. This can
be accomplished using two groups of macros. Typically, if one macro in
a group is used in a code block, all of them must be used in the same
code block. :c:data:`NPY_ALLOW_THREADS` is true (defined as ``1``) unless the
build option ``-Ddisable-threading`` is set to ``true`` - in which case
:c:data:`NPY_ALLOW_THREADS` is false (``0``).

.. c:macro:: NPY_ALLOW_THREADS

Group 1
^^^^^^^

This group is used to call code that may take some time but does not
use any Python C-API calls. Thus, the GIL should be released during
its calculation.

.. c:macro:: NPY_BEGIN_ALLOW_THREADS

    Equivalent to :c:macro:`Py_BEGIN_ALLOW_THREADS` except it uses
    :c:data:`NPY_ALLOW_THREADS` to determine if the macro if
    replaced with white-space or not.

.. c:macro:: NPY_END_ALLOW_THREADS

    Equivalent to :c:macro:`Py_END_ALLOW_THREADS` except it uses
    :c:data:`NPY_ALLOW_THREADS` to determine if the macro if
    replaced with white-space or not.

.. c:macro:: NPY_BEGIN_THREADS_DEF

    Place in the variable declaration area. This macro sets up the
    variable needed for storing the Python state.

.. c:macro:: NPY_BEGIN_THREADS

    Place right before code that does not need the Python
    interpreter (no Python C-API calls). This macro saves the
    Python state and releases the GIL.

.. c:macro:: NPY_END_THREADS

    Place right after code that does not need the Python
    interpreter. This macro acquires the GIL and restores the
    Python state from the saved variable.

.. c:function:: void NPY_BEGIN_THREADS_DESCR(PyArray_Descr *dtype)

    Useful to release the GIL only if *dtype* does not contain
    arbitrary Python objects which may need the Python interpreter
    during execution of the loop.

.. c:function:: void NPY_END_THREADS_DESCR(PyArray_Descr *dtype)

    Useful to regain the GIL in situations where it was released
    using the BEGIN form of this macro.

.. c:function:: void NPY_BEGIN_THREADS_THRESHOLDED(int loop_size)

    Useful to release the GIL only if *loop_size* exceeds a
    minimum threshold, currently set to 500. Should be matched
    with a :c:macro:`NPY_END_THREADS` to regain the GIL.

Group 2
^^^^^^^

This group is used to re-acquire the Python GIL after it has been
released. For example, suppose the GIL has been released (using the
previous calls), and then some path in the code (perhaps in a
different subroutine) requires use of the Python C-API, then these
macros are useful to acquire the GIL. These macros accomplish
essentially a reverse of the previous three (acquire the LOCK saving
what state it had) and then re-release it with the saved state.

.. c:macro:: NPY_ALLOW_C_API_DEF

    Place in the variable declaration area to set up the necessary
    variable.

.. c:macro:: NPY_ALLOW_C_API

    Place before code that needs to call the Python C-API (when it is
    known that the GIL has already been released).

.. c:macro:: NPY_DISABLE_C_API

    Place after code that needs to call the Python C-API (to re-release
    the GIL).

.. tip::

    Never use semicolons after the threading support macros.


Priority
~~~~~~~~

.. c:macro:: NPY_PRIORITY

    Default priority for arrays.

.. c:macro:: NPY_SUBTYPE_PRIORITY

    Default subtype priority.

.. c:macro:: NPY_SCALAR_PRIORITY

    Default scalar priority (very small)

.. c:function:: double PyArray_GetPriority(PyObject* obj, double def)

    Return the :obj:`~numpy.class.__array_priority__` attribute (converted to a
    double) of *obj* or *def* if no attribute of that name
    exists. Fast returns that avoid the attribute lookup are provided
    for objects of type :c:data:`PyArray_Type`.


Default buffers
~~~~~~~~~~~~~~~

.. c:macro:: NPY_BUFSIZE

    Default size of the user-settable internal buffers.

.. c:macro:: NPY_MIN_BUFSIZE

    Smallest size of user-settable internal buffers.

.. c:macro:: NPY_MAX_BUFSIZE

    Largest size allowed for the user-settable buffers.


Other constants
~~~~~~~~~~~~~~~

.. c:macro:: NPY_NUM_FLOATTYPE

    The number of floating-point types

.. c:macro:: NPY_MAXDIMS

    The maximum number of dimensions that may be used by NumPy.
    This is set to 64 and was 32 before NumPy 2.

    .. note::
        We encourage you to avoid ``NPY_MAXDIMS``.  A future version of NumPy
        may wish to remove any dimension limitation (and thus the constant).
        The limitation was created so that NumPy can use stack allocations
        internally for scratch space.

        If your algorithm has a reasonable maximum number of dimension you
        could check and use that locally.

.. c:macro:: NPY_MAXARGS

    The maximum number of array arguments that can be used in some
    functions.  This used to be 32 before NumPy 2 and is now 64.
    To continue to allow using it as a check whether a number of arguments
    is compatible ufuncs, this macro is now runtime dependent.

    .. note::
        We discourage any use of ``NPY_MAXARGS`` that isn't explicitly tied
        to checking for known NumPy limitations.

.. c:macro:: NPY_FALSE

    Defined as 0 for use with Bool.

.. c:macro:: NPY_TRUE

    Defined as 1 for use with Bool.

.. c:macro:: NPY_FAIL

    The return value of failed converter functions which are called using
    the "O&" syntax in :c:func:`PyArg_ParseTuple`-like functions.

.. c:macro:: NPY_SUCCEED

    The return value of successful converter functions which are called
    using the "O&" syntax in :c:func:`PyArg_ParseTuple`-like functions.

.. c:macro:: NPY_RAVEL_AXIS

    Some NumPy functions (mainly the C-entrypoints for Python functions)
    have an ``axis`` argument.  This macro may be passed for ``axis=None``.

    .. note::
        This macro is NumPy version dependent at runtime. The value is now
        the minimum integer. However, on NumPy 1.x ``NPY_MAXDIMS`` was used
        (at the time set to 32).


Miscellaneous Macros
~~~~~~~~~~~~~~~~~~~~

.. c:function:: int PyArray_SAMESHAPE(PyArrayObject *a1, PyArrayObject *a2)

    Evaluates as True if arrays *a1* and *a2* have the same shape.

.. c:macro:: PyArray_MAX(a,b)

    Returns the maximum of *a* and *b*. If (*a*) or (*b*) are
    expressions they are evaluated twice.

.. c:macro:: PyArray_MIN(a,b)

    Returns the minimum of *a* and *b*. If (*a*) or (*b*) are
    expressions they are evaluated twice.

.. c:function:: void PyArray_DiscardWritebackIfCopy(PyArrayObject* obj)

    If ``obj->flags`` has :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`, this function
    clears the flags, `DECREF` s
    `obj->base` and makes it writeable, and sets ``obj->base`` to NULL. In
    contrast to :c:func:`PyArray_ResolveWritebackIfCopy` it makes no attempt
    to copy the data from `obj->base`. This undoes
    :c:func:`PyArray_SetWritebackIfCopyBase`. Usually this is called after an
    error when you are finished with ``obj``, just before ``Py_DECREF(obj)``.
    It may be called multiple times, or with ``NULL`` input.


Enumerated Types
~~~~~~~~~~~~~~~~

.. c:enum:: NPY_SORTKIND

    A special variable-type which can take on different values to indicate
    the sorting algorithm being used. These algorithm types have not been
    treated strictly for some time, but rather treated as stable/not stable.
    In NumPy 2.4 they are replaced by requirements (see below), but done in a
    backwards compatible way. These values will continue to work, except that
    that NPY_HEAPSORT will do the same thing as NPY_QUICKSORT.

    .. c:enumerator:: NPY_QUICKSORT

    .. c:enumerator:: NPY_HEAPSORT

    .. c:enumerator:: NPY_MERGESORT

    .. c:enumerator:: NPY_STABLESORT

        Used as an alias of :c:data:`NPY_MERGESORT` and vice versa.

    .. c:enumerator:: NPY_NSORTS

        Defined to be the number of sorts. It is fixed at three by the need for
        backwards compatibility, and consequently :c:data:`NPY_MERGESORT` and
        :c:data:`NPY_STABLESORT` are aliased to each other and may refer to one
        of several stable sorting algorithms depending on the data type.

    In NumPy 2.4 the algorithm names are replaced by requirements. You can still use
    the old values, a recompile is not needed, but they are reinterpreted such that

    * NPY_QUICKSORT and NPY_HEAPSORT -> NPY_SORT_DEFAULT
    * NPY_MERGESORT and NPY_STABLE -> NPY_SORT_STABLE

    .. c:enumerator:: NPY_SORT_DEFAULT

        The default sort for the type. For the NumPy builtin types it may be
        stable or not, but will be ascending and sort NaN types to the end. It
        is usually chosen for speed and/or low memory.

    .. c:enumerator:: NPY_SORT_STABLE

        (Requirement) Specifies that the sort must be stable.

    .. c:enumerator:: NPY_SORT_DESCENDING

        (Requirement) Specifies that the sort must be in descending order.
        This functionality is not yet implemented for any of the NumPy types
        and cannot yet be set from the Python interface.

.. c:enum:: NPY_SCALARKIND

    A special variable type indicating the number of "kinds" of
    scalars distinguished in determining scalar-coercion rules. This
    variable can take on the values:

    .. c:enumerator:: NPY_NOSCALAR

    .. c:enumerator:: NPY_BOOL_SCALAR

    .. c:enumerator:: NPY_INTPOS_SCALAR

    .. c:enumerator:: NPY_INTNEG_SCALAR

    .. c:enumerator:: NPY_FLOAT_SCALAR

    .. c:enumerator:: NPY_COMPLEX_SCALAR

    .. c:enumerator:: NPY_OBJECT_SCALAR

    .. c:enumerator:: NPY_NSCALARKINDS

       Defined to be the number of scalar kinds
       (not including :c:data:`NPY_NOSCALAR`).

.. c:enum:: NPY_ORDER

    An enumeration type indicating the element order that an array should be
    interpreted in. When a brand new array is created, generally
    only **NPY_CORDER** and **NPY_FORTRANORDER** are used, whereas
    when one or more inputs are provided, the order can be based on them.

    .. c:enumerator:: NPY_ANYORDER

        Fortran order if all the inputs are Fortran, C otherwise.

    .. c:enumerator:: NPY_CORDER

        C order.

    .. c:enumerator:: NPY_FORTRANORDER

        Fortran order.

    .. c:enumerator:: NPY_KEEPORDER

        An order as close to the order of the inputs as possible, even
        if the input is in neither C nor Fortran order.

.. c:enum:: NPY_CLIPMODE

    A variable type indicating the kind of clipping that should be
    applied in certain functions.

    .. c:enumerator:: NPY_RAISE

        The default for most operations, raises an exception if an index
        is out of bounds.

    .. c:enumerator:: NPY_CLIP

        Clips an index to the valid range if it is out of bounds.

    .. c:enumerator:: NPY_WRAP

        Wraps an index to the valid range if it is out of bounds.

.. c:enum:: NPY_SEARCHSIDE

    A variable type indicating whether the index returned should be that of
    the first suitable location (if :c:data:`NPY_SEARCHLEFT`) or of the last
    (if :c:data:`NPY_SEARCHRIGHT`).

    .. c:enumerator:: NPY_SEARCHLEFT

    .. c:enumerator:: NPY_SEARCHRIGHT

.. c:enum:: NPY_SELECTKIND

    A variable type indicating the selection algorithm being used.

    .. c:enumerator:: NPY_INTROSELECT

.. c:enum:: NPY_CASTING

    An enumeration type indicating how permissive data conversions should
    be. This is used by the iterator added in NumPy 1.6, and is intended
    to be used more broadly in a future version.

    .. c:enumerator:: NPY_NO_CASTING

        Only allow identical types.

    .. c:enumerator:: NPY_EQUIV_CASTING

       Allow identical and casts involving byte swapping.

    .. c:enumerator:: NPY_SAFE_CASTING

       Only allow casts which will not cause values to be rounded,
       truncated, or otherwise changed.

    .. c:enumerator:: NPY_SAME_KIND_CASTING

       Allow any safe casts, and casts between types of the same kind.
       For example, float64 -> float32 is permitted with this rule.

    .. c:enumerator:: NPY_UNSAFE_CASTING

       Allow any cast, no matter what kind of data loss may occur.

.. c:macro:: NPY_SAME_VALUE_CASTING

       Error if any values change during a cast. Currently
       supported only in ``ndarray.astype(... casting='same_value')``

       .. versionadded:: 2.4

.. index::
   pair: ndarray; C-API