EVOLUTION-MANAGER

Edit File: _add_newdocs.py

"""
This is only meant to add docs to objects defined in C-extension modules.
The purpose is to allow easier editing of the docstrings without
requiring a re-compile.

NOTE: Many of the methods of ndarray have corresponding functions.
      If you update these docstrings, please keep also the ones in
      core/fromnumeric.py, core/defmatrix.py up-to-date.

"""

from numpy.core import numerictypes as _numerictypes
from numpy.core import dtype
from numpy.core.function_base import add_newdoc

###############################################################################
#
# flatiter
#
# flatiter needs a toplevel description
#
###############################################################################

add_newdoc('numpy.core', 'flatiter',
    """
    Flat iterator object to iterate over arrays.

A `flatiter` iterator is returned by ``x.flat`` for any array `x`.
    It allows iterating over the array as if it were a 1-D array,
    either in a for-loop or by calling its `next` method.

Iteration is done in row-major, C-style order (the last
    index varying the fastest). The iterator can also be indexed using
    basic slicing or advanced indexing.

See Also
    --------
    ndarray.flat : Return a flat iterator over an array.
    ndarray.flatten : Returns a flattened copy of an array.

Notes
    -----
    A `flatiter` iterator can not be constructed directly from Python code
    by calling the `flatiter` constructor.

Examples
    --------
    >>> x = np.arange(6).reshape(2, 3)
    >>> fl = x.flat
    >>> type(fl)
    <class 'numpy.flatiter'>
    >>> for item in fl:
    ...     print(item)
    ...
    0
    1
    2
    3
    4
    5

>>> fl[2:4]
    array([2, 3])

""")

# flatiter attributes

add_newdoc('numpy.core', 'flatiter', ('base',
    """
    A reference to the array that is iterated over.

Examples
    --------
    >>> x = np.arange(5)
    >>> fl = x.flat
    >>> fl.base is x
    True

"""))

add_newdoc('numpy.core', 'flatiter', ('coords',
    """
    An N-dimensional tuple of current coordinates.

Examples
    --------
    >>> x = np.arange(6).reshape(2, 3)
    >>> fl = x.flat
    >>> fl.coords
    (0, 0)
    >>> next(fl)
    0
    >>> fl.coords
    (0, 1)

"""))

add_newdoc('numpy.core', 'flatiter', ('index',
    """
    Current flat index into the array.

Examples
    --------
    >>> x = np.arange(6).reshape(2, 3)
    >>> fl = x.flat
    >>> fl.index
    0
    >>> next(fl)
    0
    >>> fl.index
    1

"""))

# flatiter functions

add_newdoc('numpy.core', 'flatiter', ('__array__',
    """__array__(type=None) Get array from iterator

"""))

add_newdoc('numpy.core', 'flatiter', ('copy',
    """
    copy()

Get a copy of the iterator as a 1-D array.

Examples
    --------
    >>> x = np.arange(6).reshape(2, 3)
    >>> x
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> fl = x.flat
    >>> fl.copy()
    array([0, 1, 2, 3, 4, 5])

"""))

###############################################################################
#
# nditer
#
###############################################################################

add_newdoc('numpy.core', 'nditer',
    """
    nditer(op, flags=None, op_flags=None, op_dtypes=None, order='K', casting='safe', op_axes=None, itershape=None, buffersize=0)

Efficient multi-dimensional iterator object to iterate over arrays.
    To get started using this object, see the
    :ref:`introductory guide to array iteration <arrays.nditer>`.

Parameters
    ----------
    op : ndarray or sequence of array_like
        The array(s) to iterate over.

flags : sequence of str, optional
          Flags to control the behavior of the iterator.

* ``buffered`` enables buffering when required.
          * ``c_index`` causes a C-order index to be tracked.
          * ``f_index`` causes a Fortran-order index to be tracked.
          * ``multi_index`` causes a multi-index, or a tuple of indices
            with one per iteration dimension, to be tracked.
          * ``common_dtype`` causes all the operands to be converted to
            a common data type, with copying or buffering as necessary.
          * ``copy_if_overlap`` causes the iterator to determine if read
            operands have overlap with write operands, and make temporary
            copies as necessary to avoid overlap. False positives (needless
            copying) are possible in some cases.
          * ``delay_bufalloc`` delays allocation of the buffers until
            a reset() call is made. Allows ``allocate`` operands to
            be initialized before their values are copied into the buffers.
          * ``external_loop`` causes the ``values`` given to be
            one-dimensional arrays with multiple values instead of
            zero-dimensional arrays.
          * ``grow_inner`` allows the ``value`` array sizes to be made
            larger than the buffer size when both ``buffered`` and
            ``external_loop`` is used.
          * ``ranged`` allows the iterator to be restricted to a sub-range
            of the iterindex values.
          * ``refs_ok`` enables iteration of reference types, such as
            object arrays.
          * ``reduce_ok`` enables iteration of ``readwrite`` operands
            which are broadcasted, also known as reduction operands.
          * ``zerosize_ok`` allows `itersize` to be zero.
    op_flags : list of list of str, optional
          This is a list of flags for each operand. At minimum, one of
          ``readonly``, ``readwrite``, or ``writeonly`` must be specified.

* ``readonly`` indicates the operand will only be read from.
          * ``readwrite`` indicates the operand will be read from and written to.
          * ``writeonly`` indicates the operand will only be written to.
          * ``no_broadcast`` prevents the operand from being broadcasted.
          * ``contig`` forces the operand data to be contiguous.
          * ``aligned`` forces the operand data to be aligned.
          * ``nbo`` forces the operand data to be in native byte order.
          * ``copy`` allows a temporary read-only copy if required.
          * ``updateifcopy`` allows a temporary read-write copy if required.
          * ``allocate`` causes the array to be allocated if it is None
            in the ``op`` parameter.
          * ``no_subtype`` prevents an ``allocate`` operand from using a subtype.
          * ``arraymask`` indicates that this operand is the mask to use
            for selecting elements when writing to operands with the
            'writemasked' flag set. The iterator does not enforce this,
            but when writing from a buffer back to the array, it only
            copies those elements indicated by this mask.
          * ``writemasked`` indicates that only elements where the chosen
            ``arraymask`` operand is True will be written to.
          * ``overlap_assume_elementwise`` can be used to mark operands that are
            accessed only in the iterator order, to allow less conservative
            copying when ``copy_if_overlap`` is present.
    op_dtypes : dtype or tuple of dtype(s), optional
        The required data type(s) of the operands. If copying or buffering
        is enabled, the data will be converted to/from their original types.
    order : {'C', 'F', 'A', 'K'}, optional
        Controls the iteration order. 'C' means C order, 'F' means
        Fortran order, 'A' means 'F' order if all the arrays are Fortran
        contiguous, 'C' order otherwise, and 'K' means as close to the
        order the array elements appear in memory as possible. This also
        affects the element memory order of ``allocate`` operands, as they
        are allocated to be compatible with iteration order.
        Default is 'K'.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur when making a copy
        or buffering.  Setting this to 'unsafe' is not recommended,
        as it can adversely affect accumulations.

* 'no' means the data types should not be cast at all.
        * 'equiv' means only byte-order changes are allowed.
        * 'safe' means only casts which can preserve values are allowed.
        * 'same_kind' means only safe casts or casts within a kind,
          like float64 to float32, are allowed.
        * 'unsafe' means any data conversions may be done.
    op_axes : list of list of ints, optional
        If provided, is a list of ints or None for each operands.
        The list of axes for an operand is a mapping from the dimensions
        of the iterator to the dimensions of the operand. A value of
        -1 can be placed for entries, causing that dimension to be
        treated as `newaxis`.
    itershape : tuple of ints, optional
        The desired shape of the iterator. This allows ``allocate`` operands
        with a dimension mapped by op_axes not corresponding to a dimension
        of a different operand to get a value not equal to 1 for that
        dimension.
    buffersize : int, optional
        When buffering is enabled, controls the size of the temporary
        buffers. Set to 0 for the default value.

Attributes
    ----------
    dtypes : tuple of dtype(s)
        The data types of the values provided in `value`. This may be
        different from the operand data types if buffering is enabled.
        Valid only before the iterator is closed.
    finished : bool
        Whether the iteration over the operands is finished or not.
    has_delayed_bufalloc : bool
        If True, the iterator was created with the ``delay_bufalloc`` flag,
        and no reset() function was called on it yet.
    has_index : bool
        If True, the iterator was created with either the ``c_index`` or
        the ``f_index`` flag, and the property `index` can be used to
        retrieve it.
    has_multi_index : bool
        If True, the iterator was created with the ``multi_index`` flag,
        and the property `multi_index` can be used to retrieve it.
    index
        When the ``c_index`` or ``f_index`` flag was used, this property
        provides access to the index. Raises a ValueError if accessed
        and ``has_index`` is False.
    iterationneedsapi : bool
        Whether iteration requires access to the Python API, for example
        if one of the operands is an object array.
    iterindex : int
        An index which matches the order of iteration.
    itersize : int
        Size of the iterator.
    itviews
        Structured view(s) of `operands` in memory, matching the reordered
        and optimized iterator access pattern. Valid only before the iterator
        is closed.
    multi_index
        When the ``multi_index`` flag was used, this property
        provides access to the index. Raises a ValueError if accessed
        accessed and ``has_multi_index`` is False.
    ndim : int
        The dimensions of the iterator.
    nop : int
        The number of iterator operands.
    operands : tuple of operand(s)
        The array(s) to be iterated over. Valid only before the iterator is
        closed.
    shape : tuple of ints
        Shape tuple, the shape of the iterator.
    value
        Value of ``operands`` at current iteration. Normally, this is a
        tuple of array scalars, but if the flag ``external_loop`` is used,
        it is a tuple of one dimensional arrays.

Notes
    -----
    `nditer` supersedes `flatiter`.  The iterator implementation behind
    `nditer` is also exposed by the NumPy C API.

The Python exposure supplies two iteration interfaces, one which follows
    the Python iterator protocol, and another which mirrors the C-style
    do-while pattern.  The native Python approach is better in most cases, but
    if you need the coordinates or index of an iterator, use the C-style pattern.

Examples
    --------
    Here is how we might write an ``iter_add`` function, using the
    Python iterator protocol:

>>> def iter_add_py(x, y, out=None):
    ...     addop = np.add
    ...     it = np.nditer([x, y, out], [],
    ...                 [['readonly'], ['readonly'], ['writeonly','allocate']])
    ...     with it:
    ...         for (a, b, c) in it:
    ...             addop(a, b, out=c)
    ...     return it.operands[2]

Here is the same function, but following the C-style pattern:

>>> def iter_add(x, y, out=None):
    ...    addop = np.add
    ...    it = np.nditer([x, y, out], [],
    ...                [['readonly'], ['readonly'], ['writeonly','allocate']])
    ...    with it:
    ...        while not it.finished:
    ...            addop(it[0], it[1], out=it[2])
    ...            it.iternext()
    ...        return it.operands[2]

Here is an example outer product function:

>>> def outer_it(x, y, out=None):
    ...     mulop = np.multiply
    ...     it = np.nditer([x, y, out], ['external_loop'],
    ...             [['readonly'], ['readonly'], ['writeonly', 'allocate']],
    ...             op_axes=[list(range(x.ndim)) + [-1] * y.ndim,
    ...                      [-1] * x.ndim + list(range(y.ndim)),
    ...                      None])
    ...     with it:
    ...         for (a, b, c) in it:
    ...             mulop(a, b, out=c)
    ...         return it.operands[2]

>>> a = np.arange(2)+1
    >>> b = np.arange(3)+1
    >>> outer_it(a,b)
    array([[1, 2, 3],
           [2, 4, 6]])

Here is an example function which operates like a "lambda" ufunc:

>>> def luf(lamdaexpr, *args, **kwargs):
    ...    '''luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)'''
    ...    nargs = len(args)
    ...    op = (kwargs.get('out',None),) + args
    ...    it = np.nditer(op, ['buffered','external_loop'],
    ...            [['writeonly','allocate','no_broadcast']] +
    ...                            [['readonly','nbo','aligned']]*nargs,
    ...            order=kwargs.get('order','K'),
    ...            casting=kwargs.get('casting','safe'),
    ...            buffersize=kwargs.get('buffersize',0))
    ...    while not it.finished:
    ...        it[0] = lamdaexpr(*it[1:])
    ...        it.iternext()
    ...        return it.operands[0]

>>> a = np.arange(5)
    >>> b = np.ones(5)
    >>> luf(lambda i,j:i*i + j/2, a, b)
    array([  0.5,   1.5,   4.5,   9.5,  16.5])

If operand flags `"writeonly"` or `"readwrite"` are used the
    operands may be views into the original data with the
    `WRITEBACKIFCOPY` flag. In this case `nditer` must be used as a
    context manager or the `nditer.close` method must be called before
    using the result. The temporary data will be written back to the
    original data when the `__exit__` function is called but not before:

>>> a = np.arange(6, dtype='i4')[::-2]
    >>> with np.nditer(a, [],
    ...        [['writeonly', 'updateifcopy']],
    ...        casting='unsafe',
    ...        op_dtypes=[np.dtype('f4')]) as i:
    ...    x = i.operands[0]
    ...    x[:] = [-1, -2, -3]
    ...    # a still unchanged here
    >>> a, x
    (array([-1, -2, -3], dtype=int32), array([-1., -2., -3.], dtype=float32))

It is important to note that once the iterator is exited, dangling
    references (like `x` in the example) may or may not share data with
    the original data `a`. If writeback semantics were active, i.e. if
    `x.base.flags.writebackifcopy` is `True`, then exiting the iterator
    will sever the connection between `x` and `a`, writing to `x` will
    no longer write to `a`. If writeback semantics are not active, then
    `x.data` will still point at some part of `a.data`, and writing to
    one will affect the other.

Context management and the `close` method appeared in version 1.15.0.

""")

# nditer methods

add_newdoc('numpy.core', 'nditer', ('copy',
    """
    copy()

Get a copy of the iterator in its current state.

Examples
    --------
    >>> x = np.arange(10)
    >>> y = x + 1
    >>> it = np.nditer([x, y])
    >>> next(it)
    (array(0), array(1))
    >>> it2 = it.copy()
    >>> next(it2)
    (array(1), array(2))

"""))

add_newdoc('numpy.core', 'nditer', ('operands',
    """
    operands[`Slice`]

The array(s) to be iterated over. Valid only before the iterator is closed.
    """))

add_newdoc('numpy.core', 'nditer', ('debug_print',
    """
    debug_print()

Print the current state of the `nditer` instance and debug info to stdout.

"""))

add_newdoc('numpy.core', 'nditer', ('enable_external_loop',
    """
    enable_external_loop()

When the "external_loop" was not used during construction, but
    is desired, this modifies the iterator to behave as if the flag
    was specified.

"""))

add_newdoc('numpy.core', 'nditer', ('iternext',
    """
    iternext()

Check whether iterations are left, and perform a single internal iteration
    without returning the result.  Used in the C-style pattern do-while
    pattern.  For an example, see `nditer`.

Returns
    -------
    iternext : bool
        Whether or not there are iterations left.

"""))

add_newdoc('numpy.core', 'nditer', ('remove_axis',
    """
    remove_axis(i)

Removes axis `i` from the iterator. Requires that the flag "multi_index"
    be enabled.

"""))

add_newdoc('numpy.core', 'nditer', ('remove_multi_index',
    """
    remove_multi_index()

When the "multi_index" flag was specified, this removes it, allowing
    the internal iteration structure to be optimized further.

"""))

add_newdoc('numpy.core', 'nditer', ('reset',
    """
    reset()

Reset the iterator to its initial state.

"""))

add_newdoc('numpy.core', 'nested_iters',
    """
    Create nditers for use in nested loops

Create a tuple of `nditer` objects which iterate in nested loops over
    different axes of the op argument. The first iterator is used in the
    outermost loop, the last in the innermost loop. Advancing one will change
    the subsequent iterators to point at its new element.

Parameters
    ----------
    op : ndarray or sequence of array_like
        The array(s) to iterate over.

axes : list of list of int
        Each item is used as an "op_axes" argument to an nditer

flags, op_flags, op_dtypes, order, casting, buffersize (optional)
        See `nditer` parameters of the same name

Returns
    -------
    iters : tuple of nditer
        An nditer for each item in `axes`, outermost first

See Also
    --------

:ref:`nditer-context-manager`

"""))

###############################################################################
#
# broadcast
#
###############################################################################

add_newdoc('numpy.core', 'broadcast',
    """
    Produce an object that mimics broadcasting.

Parameters
    ----------
    in1, in2, ... : array_like
        Input parameters.

Returns
    -------
    b : broadcast object
        Broadcast the input parameters against one another, and
        return an object that encapsulates the result.
        Amongst others, it has ``shape`` and ``nd`` properties, and
        may be used as an iterator.

See Also
    --------
    broadcast_arrays
    broadcast_to

Examples
    --------

Manually adding two vectors, using broadcasting:

>>> x = np.array([[1], [2], [3]])
    >>> y = np.array([4, 5, 6])
    >>> b = np.broadcast(x, y)

>>> out = np.empty(b.shape)
    >>> out.flat = [u+v for (u,v) in b]
    >>> out
    array([[5.,  6.,  7.],
           [6.,  7.,  8.],
           [7.,  8.,  9.]])

Compare against built-in broadcasting:

>>> x + y
    array([[5, 6, 7],
           [6, 7, 8],
           [7, 8, 9]])

""")

# attributes

add_newdoc('numpy.core', 'broadcast', ('index',
    """
    current index in broadcasted result

Examples
    --------
    >>> x = np.array([[1], [2], [3]])
    >>> y = np.array([4, 5, 6])
    >>> b = np.broadcast(x, y)
    >>> b.index
    0
    >>> next(b), next(b), next(b)
    ((1, 4), (1, 5), (1, 6))
    >>> b.index
    3

"""))

add_newdoc('numpy.core', 'broadcast', ('iters',
    """
    tuple of iterators along ``self``'s "components."

Returns a tuple of `numpy.flatiter` objects, one for each "component"
    of ``self``.

See Also
    --------
    numpy.flatiter

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> row, col = b.iters
    >>> next(row), next(col)
    (1, 4)

"""))

add_newdoc('numpy.core', 'broadcast', ('ndim',
    """
    Number of dimensions of broadcasted result. Alias for `nd`.

.. versionadded:: 1.12.0

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> b.ndim
    2

"""))

add_newdoc('numpy.core', 'broadcast', ('nd',
    """
    Number of dimensions of broadcasted result. For code intended for NumPy
    1.12.0 and later the more consistent `ndim` is preferred.

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> b.nd
    2

"""))

add_newdoc('numpy.core', 'broadcast', ('numiter',
    """
    Number of iterators possessed by the broadcasted result.

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> b.numiter
    2

"""))

add_newdoc('numpy.core', 'broadcast', ('shape',
    """
    Shape of broadcasted result.

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> b.shape
    (3, 3)

"""))

add_newdoc('numpy.core', 'broadcast', ('size',
    """
    Total size of broadcasted result.

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> b.size
    9

"""))

add_newdoc('numpy.core', 'broadcast', ('reset',
    """
    reset()

Reset the broadcasted result's iterator(s).

Parameters
    ----------
    None

Returns
    -------
    None

Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = np.array([[4], [5], [6]])
    >>> b = np.broadcast(x, y)
    >>> b.index
    0
    >>> next(b), next(b), next(b)
    ((1, 4), (2, 4), (3, 4))
    >>> b.index
    3
    >>> b.reset()
    >>> b.index
    0

"""))

###############################################################################
#
# numpy functions
#
###############################################################################

add_newdoc('numpy.core.multiarray', 'array',
    """
    array(object, dtype=None, *, copy=True, order='K', subok=False, ndmin=0)

Create an array.

Parameters
    ----------
    object : array_like
        An array, any object exposing the array interface, an object whose
        __array__ method returns an array, or any (nested) sequence.
    dtype : data-type, optional
        The desired data-type for the array.  If not given, then the type will
        be determined as the minimum type required to hold the objects in the
        sequence.
    copy : bool, optional
        If true (default), then the object is copied.  Otherwise, a copy will
        only be made if __array__ returns a copy, if obj is a nested sequence,
        or if a copy is needed to satisfy any of the other requirements
        (`dtype`, `order`, etc.).
    order : {'K', 'A', 'C', 'F'}, optional
        Specify the memory layout of the array. If object is not an array, the
        newly created array will be in C order (row major) unless 'F' is
        specified, in which case it will be in Fortran order (column major).
        If object is an array the following holds.

===== ========= ===================================================
        order  no copy                     copy=True
        ===== ========= ===================================================
        'K'   unchanged F & C order preserved, otherwise most similar order
        'A'   unchanged F order if input is F and not C, otherwise C order
        'C'   C order   C order
        'F'   F order   F order
        ===== ========= ===================================================

When ``copy=False`` and a copy is made for other reasons, the result is
        the same as if ``copy=True``, with some exceptions for `A`, see the
        Notes section. The default order is 'K'.
    subok : bool, optional
        If True, then sub-classes will be passed-through, otherwise
        the returned array will be forced to be a base-class array (default).
    ndmin : int, optional
        Specifies the minimum number of dimensions that the resulting
        array should have.  Ones will be pre-pended to the shape as
        needed to meet this requirement.

Returns
    -------
    out : ndarray
        An array object satisfying the specified requirements.

See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones_like : Return an array of ones with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full_like : Return a new array with shape of input filled with value.
    empty : Return a new uninitialized array.
    ones : Return a new array setting values to one.
    zeros : Return a new array setting values to zero.
    full : Return a new array of given shape filled with value.

Notes
    -----
    When order is 'A' and `object` is an array in neither 'C' nor 'F' order,
    and a copy is forced by a change in dtype, then the order of the result is
    not necessarily 'C' as expected. This is likely a bug.

Examples
    --------
    >>> np.array([1, 2, 3])
    array([1, 2, 3])

Upcasting:

>>> np.array([1, 2, 3.0])
    array([ 1.,  2.,  3.])

More than one dimension:

>>> np.array([[1, 2], [3, 4]])
    array([[1, 2],
           [3, 4]])

Minimum dimensions 2:

>>> np.array([1, 2, 3], ndmin=2)
    array([[1, 2, 3]])

Type provided:

>>> np.array([1, 2, 3], dtype=complex)
    array([ 1.+0.j,  2.+0.j,  3.+0.j])

Data-type consisting of more than one element:

>>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')])
    >>> x['a']
    array([1, 3])

Creating an array from sub-classes:

>>> np.array(np.mat('1 2; 3 4'))
    array([[1, 2],
           [3, 4]])

>>> np.array(np.mat('1 2; 3 4'), subok=True)
    matrix([[1, 2],
            [3, 4]])

""")

add_newdoc('numpy.core.multiarray', 'empty',
    """
    empty(shape, dtype=float, order='C')

Return a new array of given shape and type, without initializing entries.

Parameters
    ----------
    shape : int or tuple of int
        Shape of the empty array, e.g., ``(2, 3)`` or ``2``.
    dtype : data-type, optional
        Desired output data-type for the array, e.g, `numpy.int8`. Default is
        `numpy.float64`.
    order : {'C', 'F'}, optional, default: 'C'
        Whether to store multi-dimensional data in row-major
        (C-style) or column-major (Fortran-style) order in
        memory.

Returns
    -------
    out : ndarray
        Array of uninitialized (arbitrary) data of the given shape, dtype, and
        order.  Object arrays will be initialized to None.

See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones : Return a new array setting values to one.
    zeros : Return a new array setting values to zero.
    full : Return a new array of given shape filled with value.

Notes
    -----
    `empty`, unlike `zeros`, does not set the array values to zero,
    and may therefore be marginally faster.  On the other hand, it requires
    the user to manually set all the values in the array, and should be
    used with caution.

Examples
    --------
    >>> np.empty([2, 2])
    array([[ -9.74499359e+001,   6.69583040e-309],
           [  2.13182611e-314,   3.06959433e-309]])         #uninitialized

>>> np.empty([2, 2], dtype=int)
    array([[-1073741821, -1067949133],
           [  496041986,    19249760]])                     #uninitialized

""")

add_newdoc('numpy.core.multiarray', 'scalar',
    """
    scalar(dtype, obj)

Return a new scalar array of the given type initialized with obj.

This function is meant mainly for pickle support. `dtype` must be a
    valid data-type descriptor. If `dtype` corresponds to an object
    descriptor, then `obj` can be any object, otherwise `obj` must be a
    string. If `obj` is not given, it will be interpreted as None for object
    type and as zeros for all other types.

""")

add_newdoc('numpy.core.multiarray', 'zeros',
    """
    zeros(shape, dtype=float, order='C')

Return a new array of given shape and type, filled with zeros.

Parameters
    ----------
    shape : int or tuple of ints
        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
    dtype : data-type, optional
        The desired data-type for the array, e.g., `numpy.int8`.  Default is
        `numpy.float64`.
    order : {'C', 'F'}, optional, default: 'C'
        Whether to store multi-dimensional data in row-major
        (C-style) or column-major (Fortran-style) order in
        memory.

Returns
    -------
    out : ndarray
        Array of zeros with the given shape, dtype, and order.

See Also
    --------
    zeros_like : Return an array of zeros with shape and type of input.
    empty : Return a new uninitialized array.
    ones : Return a new array setting values to one.
    full : Return a new array of given shape filled with value.

Examples
    --------
    >>> np.zeros(5)
    array([ 0.,  0.,  0.,  0.,  0.])

>>> np.zeros((5,), dtype=int)
    array([0, 0, 0, 0, 0])

>>> np.zeros((2, 1))
    array([[ 0.],
           [ 0.]])

>>> s = (2,2)
    >>> np.zeros(s)
    array([[ 0.,  0.],
           [ 0.,  0.]])

>>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype
    array([(0, 0), (0, 0)],
          dtype=[('x', '<i4'), ('y', '<i4')])

""")

add_newdoc('numpy.core.multiarray', 'set_typeDict',
    """set_typeDict(dict)

Set the internal dictionary that can look up an array type using a
    registered code.

""")

add_newdoc('numpy.core.multiarray', 'fromstring',
    """
    fromstring(string, dtype=float, count=-1, sep='')

A new 1-D array initialized from text data in a string.

Parameters
    ----------
    string : str
        A string containing the data.
    dtype : data-type, optional
        The data type of the array; default: float.  For binary input data,
        the data must be in exactly this format. Most builtin numeric types are
        supported and extension types may be supported.

.. versionadded:: 1.18.0
            Complex dtypes.

count : int, optional
        Read this number of `dtype` elements from the data.  If this is
        negative (the default), the count will be determined from the
        length of the data.
    sep : str, optional
        The string separating numbers in the data; extra whitespace between
        elements is also ignored.

.. deprecated:: 1.14
            Passing ``sep=''``, the default, is deprecated since it will
            trigger the deprecated binary mode of this function. This mode
            interprets `string` as binary bytes, rather than ASCII text with
            decimal numbers, an operation which is better spelt
            ``frombuffer(string, dtype, count)``. If `string` contains unicode
            text, the binary mode of `fromstring` will first encode it into
            bytes using either utf-8 (python 3) or the default encoding
            (python 2), neither of which produce sane results.

Returns
    -------
    arr : ndarray
        The constructed array.

Raises
    ------
    ValueError
        If the string is not the correct size to satisfy the requested
        `dtype` and `count`.

See Also
    --------
    frombuffer, fromfile, fromiter

Examples
    --------
    >>> np.fromstring('1 2', dtype=int, sep=' ')
    array([1, 2])
    >>> np.fromstring('1, 2', dtype=int, sep=',')
    array([1, 2])

""")

add_newdoc('numpy.core.multiarray', 'compare_chararrays',
    """
    compare_chararrays(a, b, cmp_op, rstrip)

Performs element-wise comparison of two string arrays using the
    comparison operator specified by `cmp_op`.

Parameters
    ----------
    a, b : array_like
        Arrays to be compared.
    cmp_op : {"<", "<=", "==", ">=", ">", "!="}
        Type of comparison.
    rstrip : Boolean
        If True, the spaces at the end of Strings are removed before the comparison.

Returns
    -------
    out : ndarray
        The output array of type Boolean with the same shape as a and b.

Raises
    ------
    ValueError
        If `cmp_op` is not valid.
    TypeError
        If at least one of `a` or `b` is a non-string array

Examples
    --------
    >>> a = np.array(["a", "b", "cde"])
    >>> b = np.array(["a", "a", "dec"])
    >>> np.compare_chararrays(a, b, ">", True)
    array([False,  True, False])

""")

add_newdoc('numpy.core.multiarray', 'fromiter',
    """
    fromiter(iterable, dtype, count=-1)

Create a new 1-dimensional array from an iterable object.

Parameters
    ----------
    iterable : iterable object
        An iterable object providing data for the array.
    dtype : data-type
        The data-type of the returned array.
    count : int, optional
        The number of items to read from *iterable*.  The default is -1,
        which means all data is read.

Returns
    -------
    out : ndarray
        The output array.

Notes
    -----
    Specify `count` to improve performance.  It allows ``fromiter`` to
    pre-allocate the output array, instead of resizing it on demand.

Examples
    --------
    >>> iterable = (x*x for x in range(5))
    >>> np.fromiter(iterable, float)
    array([  0.,   1.,   4.,   9.,  16.])

""")

add_newdoc('numpy.core.multiarray', 'fromfile',
    """
    fromfile(file, dtype=float, count=-1, sep='', offset=0)

Construct an array from data in a text or binary file.

A highly efficient way of reading binary data with a known data-type,
    as well as parsing simply formatted text files.  Data written using the
    `tofile` method can be read using this function.

Parameters
    ----------
    file : file or str or Path
        Open file object or filename.

.. versionchanged:: 1.17.0
            `pathlib.Path` objects are now accepted.

dtype : data-type
        Data type of the returned array.
        For binary files, it is used to determine the size and byte-order
        of the items in the file.
        Most builtin numeric types are supported and extension types may be supported.

.. versionadded:: 1.18.0
            Complex dtypes.

count : int
        Number of items to read. ``-1`` means all items (i.e., the complete
        file).
    sep : str
        Separator between items if file is a text file.
        Empty ("") separator means the file should be treated as binary.
        Spaces (" ") in the separator match zero or more whitespace characters.
        A separator consisting only of spaces must match at least one
        whitespace.
    offset : int
        The offset (in bytes) from the file's current position. Defaults to 0.
        Only permitted for binary files.

.. versionadded:: 1.17.0

See also
    --------
    load, save
    ndarray.tofile
    loadtxt : More flexible way of loading data from a text file.

Notes
    -----
    Do not rely on the combination of `tofile` and `fromfile` for
    data storage, as the binary files generated are not platform
    independent.  In particular, no byte-order or data-type information is
    saved.  Data can be stored in the platform independent ``.npy`` format
    using `save` and `load` instead.

Examples
    --------
    Construct an ndarray:

>>> dt = np.dtype([('time', [('min', np.int64), ('sec', np.int64)]),
    ...                ('temp', float)])
    >>> x = np.zeros((1,), dtype=dt)
    >>> x['time']['min'] = 10; x['temp'] = 98.25
    >>> x
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])

Save the raw data to disk:

>>> import tempfile
    >>> fname = tempfile.mkstemp()[1]
    >>> x.tofile(fname)

Read the raw data from disk:

>>> np.fromfile(fname, dtype=dt)
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])

The recommended way to store and load data:

>>> np.save(fname, x)
    >>> np.load(fname + '.npy')
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])

""")

add_newdoc('numpy.core.multiarray', 'frombuffer',
    """
    frombuffer(buffer, dtype=float, count=-1, offset=0)

Interpret a buffer as a 1-dimensional array.

Parameters
    ----------
    buffer : buffer_like
        An object that exposes the buffer interface.
    dtype : data-type, optional
        Data-type of the returned array; default: float.
    count : int, optional
        Number of items to read. ``-1`` means all data in the buffer.
    offset : int, optional
        Start reading the buffer from this offset (in bytes); default: 0.

Notes
    -----
    If the buffer has data that is not in machine byte-order, this should
    be specified as part of the data-type, e.g.::

>>> dt = np.dtype(int)
      >>> dt = dt.newbyteorder('>')
      >>> np.frombuffer(buf, dtype=dt) # doctest: +SKIP

The data of the resulting array will not be byteswapped, but will be
    interpreted correctly.

Examples
    --------
    >>> s = b'hello world'
    >>> np.frombuffer(s, dtype='S1', count=5, offset=6)
    array([b'w', b'o', b'r', b'l', b'd'], dtype='|S1')

>>> np.frombuffer(b'\\x01\\x02', dtype=np.uint8)
    array([1, 2], dtype=uint8)
    >>> np.frombuffer(b'\\x01\\x02\\x03\\x04\\x05', dtype=np.uint8, count=3)
    array([1, 2, 3], dtype=uint8)

""")

add_newdoc('numpy.core', 'fastCopyAndTranspose',
    """_fastCopyAndTranspose(a)""")

add_newdoc('numpy.core.multiarray', 'correlate',
    """cross_correlate(a,v, mode=0)""")

add_newdoc('numpy.core.multiarray', 'arange',
    """
    arange([start,] stop[, step,], dtype=None)

Return evenly spaced values within a given interval.

Values are generated within the half-open interval ``[start, stop)``
    (in other words, the interval including `start` but excluding `stop`).
    For integer arguments the function is equivalent to the Python built-in
    `range` function, but returns an ndarray rather than a list.

When using a non-integer step, such as 0.1, the results will often not
    be consistent.  It is better to use `numpy.linspace` for these cases.

Parameters
    ----------
    start : number, optional
        Start of interval.  The interval includes this value.  The default
        start value is 0.
    stop : number
        End of interval.  The interval does not include this value, except
        in some cases where `step` is not an integer and floating point
        round-off affects the length of `out`.
    step : number, optional
        Spacing between values.  For any output `out`, this is the distance
        between two adjacent values, ``out[i+1] - out[i]``.  The default
        step size is 1.  If `step` is specified as a position argument,
        `start` must also be given.
    dtype : dtype
        The type of the output array.  If `dtype` is not given, infer the data
        type from the other input arguments.

Returns
    -------
    arange : ndarray
        Array of evenly spaced values.

For floating point arguments, the length of the result is
        ``ceil((stop - start)/step)``.  Because of floating point overflow,
        this rule may result in the last element of `out` being greater
        than `stop`.

See Also
    --------
    numpy.linspace : Evenly spaced numbers with careful handling of endpoints.
    numpy.ogrid: Arrays of evenly spaced numbers in N-dimensions.
    numpy.mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions.

Examples
    --------
    >>> np.arange(3)
    array([0, 1, 2])
    >>> np.arange(3.0)
    array([ 0.,  1.,  2.])
    >>> np.arange(3,7)
    array([3, 4, 5, 6])
    >>> np.arange(3,7,2)
    array([3, 5])

""")

add_newdoc('numpy.core.multiarray', '_get_ndarray_c_version',
    """_get_ndarray_c_version()

Return the compile time NPY_VERSION (formerly called NDARRAY_VERSION) number.

""")

add_newdoc('numpy.core.multiarray', '_reconstruct',
    """_reconstruct(subtype, shape, dtype)

Construct an empty array. Used by Pickles.

""")

add_newdoc('numpy.core.multiarray', 'set_string_function',
    """
    set_string_function(f, repr=1)

Internal method to set a function to be used when pretty printing arrays.

""")

add_newdoc('numpy.core.multiarray', 'set_numeric_ops',
    """
    set_numeric_ops(op1=func1, op2=func2, ...)

Set numerical operators for array objects.

.. deprecated:: 1.16

For the general case, use :c:func:`PyUFunc_ReplaceLoopBySignature`.
        For ndarray subclasses, define the ``__array_ufunc__`` method and
        override the relevant ufunc.

Parameters
    ----------
    op1, op2, ... : callable
        Each ``op = func`` pair describes an operator to be replaced.
        For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace
        addition by modulus 5 addition.

Returns
    -------
    saved_ops : list of callables
        A list of all operators, stored before making replacements.

Notes
    -----
    .. WARNING::
       Use with care!  Incorrect usage may lead to memory errors.

A function replacing an operator cannot make use of that operator.
    For example, when replacing add, you may not use ``+``.  Instead,
    directly call ufuncs.

Examples
    --------
    >>> def add_mod5(x, y):
    ...     return np.add(x, y) % 5
    ...
    >>> old_funcs = np.set_numeric_ops(add=add_mod5)

>>> x = np.arange(12).reshape((3, 4))
    >>> x + x
    array([[0, 2, 4, 1],
           [3, 0, 2, 4],
           [1, 3, 0, 2]])

>>> ignore = np.set_numeric_ops(**old_funcs) # restore operators

""")

add_newdoc('numpy.core.multiarray', 'promote_types',
    """
    promote_types(type1, type2)

Returns the data type with the smallest size and smallest scalar
    kind to which both ``type1`` and ``type2`` may be safely cast.
    The returned data type is always in native byte order.

This function is symmetric, but rarely associative.

Parameters
    ----------
    type1 : dtype or dtype specifier
        First data type.
    type2 : dtype or dtype specifier
        Second data type.

Returns
    -------
    out : dtype
        The promoted data type.

Notes
    -----
    .. versionadded:: 1.6.0

Starting in NumPy 1.9, promote_types function now returns a valid string
    length when given an integer or float dtype as one argument and a string
    dtype as another argument. Previously it always returned the input string
    dtype, even if it wasn't long enough to store the max integer/float value
    converted to a string.

See Also
    --------
    result_type, dtype, can_cast

Examples
    --------
    >>> np.promote_types('f4', 'f8')
    dtype('float64')

>>> np.promote_types('i8', 'f4')
    dtype('float64')

>>> np.promote_types('>i8', '<c8')
    dtype('complex128')

>>> np.promote_types('i4', 'S8')
    dtype('S11')

An example of a non-associative case:

>>> p = np.promote_types
    >>> p('S', p('i1', 'u1'))
    dtype('S6')
    >>> p(p('S', 'i1'), 'u1')
    dtype('S4')

""")

add_newdoc('numpy.core.multiarray', 'c_einsum',
    """
    c_einsum(subscripts, *operands, out=None, dtype=None, order='K',
           casting='safe')

*This documentation shadows that of the native python implementation of the `einsum` function,
    except all references and examples related to the `optimize` argument (v 0.12.0) have been removed.*

Evaluates the Einstein summation convention on the operands.

Using the Einstein summation convention, many common multi-dimensional,
    linear algebraic array operations can be represented in a simple fashion.
    In *implicit* mode `einsum` computes these values.

In *explicit* mode, `einsum` provides further flexibility to compute
    other array operations that might not be considered classical Einstein
    summation operations, by disabling, or forcing summation over specified
    subscript labels.

See the notes and examples for clarification.

Parameters
    ----------
    subscripts : str
        Specifies the subscripts for summation as comma separated list of
        subscript labels. An implicit (classical Einstein summation)
        calculation is performed unless the explicit indicator '->' is
        included as well as subscript labels of the precise output form.
    operands : list of array_like
        These are the arrays for the operation.
    out : ndarray, optional
        If provided, the calculation is done into this array.
    dtype : {data-type, None}, optional
        If provided, forces the calculation to use the data type specified.
        Note that you may have to also give a more liberal `casting`
        parameter to allow the conversions. Default is None.
    order : {'C', 'F', 'A', 'K'}, optional
        Controls the memory layout of the output. 'C' means it should
        be C contiguous. 'F' means it should be Fortran contiguous,
        'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
        'K' means it should be as close to the layout as the inputs as
        is possible, including arbitrarily permuted axes.
        Default is 'K'.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur.  Setting this to
        'unsafe' is not recommended, as it can adversely affect accumulations.

Default is 'safe'.
    optimize : {False, True, 'greedy', 'optimal'}, optional
        Controls if intermediate optimization should occur. No optimization
        will occur if False and True will default to the 'greedy' algorithm.
        Also accepts an explicit contraction list from the ``np.einsum_path``
        function. See ``np.einsum_path`` for more details. Defaults to False.

Returns
    -------
    output : ndarray
        The calculation based on the Einstein summation convention.

See Also
    --------
    einsum_path, dot, inner, outer, tensordot, linalg.multi_dot

Notes
    -----
    .. versionadded:: 1.6.0

The Einstein summation convention can be used to compute
    many multi-dimensional, linear algebraic array operations. `einsum`
    provides a succinct way of representing these.

A non-exhaustive list of these operations,
    which can be computed by `einsum`, is shown below along with examples:

* Trace of an array, :py:func:`numpy.trace`.
    * Return a diagonal, :py:func:`numpy.diag`.
    * Array axis summations, :py:func:`numpy.sum`.
    * Transpositions and permutations, :py:func:`numpy.transpose`.
    * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`.
    * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`.
    * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`.
    * Tensor contractions, :py:func:`numpy.tensordot`.
    * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`.

The subscripts string is a comma-separated list of subscript labels,
    where each label refers to a dimension of the corresponding operand.
    Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
    is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
    appears only once, it is not summed, so ``np.einsum('i', a)`` produces a
    view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)``
    describes traditional matrix multiplication and is equivalent to
    :py:func:`np.matmul(a,b) <numpy.matmul>`. Repeated subscript labels in one
    operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent
    to :py:func:`np.trace(a) <numpy.trace>`.

In *implicit mode*, the chosen subscripts are important
    since the axes of the output are reordered alphabetically.  This
    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
    ``np.einsum('ji', a)`` takes its transpose. Additionally,
    ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
    ``np.einsum('ij,jh', a, b)`` returns the transpose of the
    multiplication since subscript 'h' precedes subscript 'i'.

In *explicit mode* the output can be directly controlled by
    specifying output subscript labels.  This requires the
    identifier '->' as well as the list of output subscript labels.
    This feature increases the flexibility of the function since
    summing can be disabled or forced when required. The call
    ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) <numpy.sum>`,
    and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) <numpy.diag>`.
    The difference is that `einsum` does not allow broadcasting by default.
    Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
    order of the output subscript labels and therefore returns matrix
    multiplication, unlike the example above in implicit mode.

To enable and control broadcasting, use an ellipsis.  Default
    NumPy-style broadcasting is done by adding an ellipsis
    to the left of each term, like ``np.einsum('...ii->...i', a)``.
    To take the trace along the first and last axes,
    you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
    product with the left-most indices instead of rightmost, one can do
    ``np.einsum('ij...,jk...->ik...', a, b)``.

When there is only one operand, no axes are summed, and no output
    parameter is provided, a view into the operand is returned instead
    of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
    produces a view (changed in version 1.10.0).

`einsum` also provides an alternative way to provide the subscripts
    and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
    If the output shape is not provided in this format `einsum` will be
    calculated in implicit mode, otherwise it will be performed explicitly.
    The examples below have corresponding `einsum` calls with the two
    parameter methods.

.. versionadded:: 1.10.0

Views returned from einsum are now writeable whenever the input array
    is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
    have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
    and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
    of a 2D array.

Examples
    --------
    >>> a = np.arange(25).reshape(5,5)
    >>> b = np.arange(5)
    >>> c = np.arange(6).reshape(2,3)

Trace of a matrix:

>>> np.einsum('ii', a)
    60
    >>> np.einsum(a, [0,0])
    60
    >>> np.trace(a)
    60

Extract the diagonal (requires explicit form):

>>> np.einsum('ii->i', a)
    array([ 0,  6, 12, 18, 24])
    >>> np.einsum(a, [0,0], [0])
    array([ 0,  6, 12, 18, 24])
    >>> np.diag(a)
    array([ 0,  6, 12, 18, 24])

Sum over an axis (requires explicit form):

>>> np.einsum('ij->i', a)
    array([ 10,  35,  60,  85, 110])
    >>> np.einsum(a, [0,1], [0])
    array([ 10,  35,  60,  85, 110])
    >>> np.sum(a, axis=1)
    array([ 10,  35,  60,  85, 110])

For higher dimensional arrays summing a single axis can be done with ellipsis:

>>> np.einsum('...j->...', a)
    array([ 10,  35,  60,  85, 110])
    >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
    array([ 10,  35,  60,  85, 110])

Compute a matrix transpose, or reorder any number of axes:

>>> np.einsum('ji', c)
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.einsum('ij->ji', c)
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.einsum(c, [1,0])
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.transpose(c)
    array([[0, 3],
           [1, 4],
           [2, 5]])

Vector inner products:

>>> np.einsum('i,i', b, b)
    30
    >>> np.einsum(b, [0], b, [0])
    30
    >>> np.inner(b,b)
    30

Matrix vector multiplication:

>>> np.einsum('ij,j', a, b)
    array([ 30,  80, 130, 180, 230])
    >>> np.einsum(a, [0,1], b, [1])
    array([ 30,  80, 130, 180, 230])
    >>> np.dot(a, b)
    array([ 30,  80, 130, 180, 230])
    >>> np.einsum('...j,j', a, b)
    array([ 30,  80, 130, 180, 230])

Broadcasting and scalar multiplication:

>>> np.einsum('..., ...', 3, c)
    array([[ 0,  3,  6],
           [ 9, 12, 15]])
    >>> np.einsum(',ij', 3, c)
    array([[ 0,  3,  6],
           [ 9, 12, 15]])
    >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
    array([[ 0,  3,  6],
           [ 9, 12, 15]])
    >>> np.multiply(3, c)
    array([[ 0,  3,  6],
           [ 9, 12, 15]])

Vector outer product:

>>> np.einsum('i,j', np.arange(2)+1, b)
    array([[0, 1, 2, 3, 4],
           [0, 2, 4, 6, 8]])
    >>> np.einsum(np.arange(2)+1, [0], b, [1])
    array([[0, 1, 2, 3, 4],
           [0, 2, 4, 6, 8]])
    >>> np.outer(np.arange(2)+1, b)
    array([[0, 1, 2, 3, 4],
           [0, 2, 4, 6, 8]])

Tensor contraction:

>>> a = np.arange(60.).reshape(3,4,5)
    >>> b = np.arange(24.).reshape(4,3,2)
    >>> np.einsum('ijk,jil->kl', a, b)
    array([[ 4400.,  4730.],
           [ 4532.,  4874.],
           [ 4664.,  5018.],
           [ 4796.,  5162.],
           [ 4928.,  5306.]])
    >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
    array([[ 4400.,  4730.],
           [ 4532.,  4874.],
           [ 4664.,  5018.],
           [ 4796.,  5162.],
           [ 4928.,  5306.]])
    >>> np.tensordot(a,b, axes=([1,0],[0,1]))
    array([[ 4400.,  4730.],
           [ 4532.,  4874.],
           [ 4664.,  5018.],
           [ 4796.,  5162.],
           [ 4928.,  5306.]])

Writeable returned arrays (since version 1.10.0):

>>> a = np.zeros((3, 3))
    >>> np.einsum('ii->i', a)[:] = 1
    >>> a
    array([[ 1.,  0.,  0.],
           [ 0.,  1.,  0.],
           [ 0.,  0.,  1.]])

Example of ellipsis use:

>>> a = np.arange(6).reshape((3,2))
    >>> b = np.arange(12).reshape((4,3))
    >>> np.einsum('ki,jk->ij', a, b)
    array([[10, 28, 46, 64],
           [13, 40, 67, 94]])
    >>> np.einsum('ki,...k->i...', a, b)
    array([[10, 28, 46, 64],
           [13, 40, 67, 94]])
    >>> np.einsum('k...,jk', a, b)
    array([[10, 28, 46, 64],
           [13, 40, 67, 94]])

""")

##############################################################################
#
# Documentation for ndarray attributes and methods
#
##############################################################################

##############################################################################
#
# ndarray object
#
##############################################################################

add_newdoc('numpy.core.multiarray', 'ndarray',
    """
    ndarray(shape, dtype=float, buffer=None, offset=0,
            strides=None, order=None)

An array object represents a multidimensional, homogeneous array
    of fixed-size items.  An associated data-type object describes the
    format of each element in the array (its byte-order, how many bytes it
    occupies in memory, whether it is an integer, a floating point number,
    or something else, etc.)

Arrays should be constructed using `array`, `zeros` or `empty` (refer
    to the See Also section below).  The parameters given here refer to
    a low-level method (`ndarray(...)`) for instantiating an array.

For more information, refer to the `numpy` module and examine the
    methods and attributes of an array.

Parameters
    ----------
    (for the __new__ method; see Notes below)

shape : tuple of ints
        Shape of created array.
    dtype : data-type, optional
        Any object that can be interpreted as a numpy data type.
    buffer : object exposing buffer interface, optional
        Used to fill the array with data.
    offset : int, optional
        Offset of array data in buffer.
    strides : tuple of ints, optional
        Strides of data in memory.
    order : {'C', 'F'}, optional
        Row-major (C-style) or column-major (Fortran-style) order.

Attributes
    ----------
    T : ndarray
        Transpose of the array.
    data : buffer
        The array's elements, in memory.
    dtype : dtype object
        Describes the format of the elements in the array.
    flags : dict
        Dictionary containing information related to memory use, e.g.,
        'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    flat : numpy.flatiter object
        Flattened version of the array as an iterator.  The iterator
        allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for
        assignment examples; TODO).
    imag : ndarray
        Imaginary part of the array.
    real : ndarray
        Real part of the array.
    size : int
        Number of elements in the array.
    itemsize : int
        The memory use of each array element in bytes.
    nbytes : int
        The total number of bytes required to store the array data,
        i.e., ``itemsize * size``.
    ndim : int
        The array's number of dimensions.
    shape : tuple of ints
        Shape of the array.
    strides : tuple of ints
        The step-size required to move from one element to the next in
        memory. For example, a contiguous ``(3, 4)`` array of type
        ``int16`` in C-order has strides ``(8, 2)``.  This implies that
        to move from element to element in memory requires jumps of 2 bytes.
        To move from row-to-row, one needs to jump 8 bytes at a time
        (``2 * 4``).
    ctypes : ctypes object
        Class containing properties of the array needed for interaction
        with ctypes.
    base : ndarray
        If the array is a view into another array, that array is its `base`
        (unless that array is also a view).  The `base` array is where the
        array data is actually stored.

See Also
    --------
    array : Construct an array.
    zeros : Create an array, each element of which is zero.
    empty : Create an array, but leave its allocated memory unchanged (i.e.,
            it contains "garbage").
    dtype : Create a data-type.

Notes
    -----
    There are two modes of creating an array using ``__new__``:

1. If `buffer` is None, then only `shape`, `dtype`, and `order`
       are used.
    2. If `buffer` is an object exposing the buffer interface, then
       all keywords are interpreted.

No ``__init__`` method is needed because the array is fully initialized
    after the ``__new__`` method.

Examples
    --------
    These examples illustrate the low-level `ndarray` constructor.  Refer
    to the `See Also` section above for easier ways of constructing an
    ndarray.

First mode, `buffer` is None:

>>> np.ndarray(shape=(2,2), dtype=float, order='F')
    array([[0.0e+000, 0.0e+000], # random
           [     nan, 2.5e-323]])

Second mode:

>>> np.ndarray((2,), buffer=np.array([1,2,3]),
    ...            offset=np.int_().itemsize,
    ...            dtype=int) # offset = 1*itemsize, i.e. skip first element
    array([2, 3])

""")

##############################################################################
#
# ndarray attributes
#
##############################################################################

add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_interface__',
    """Array protocol: Python side."""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_finalize__',
    """None."""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_priority__',
    """Array priority."""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_struct__',
    """Array protocol: C-struct side."""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('base',
    """
    Base object if memory is from some other object.

Examples
    --------
    The base of an array that owns its memory is None:

>>> x = np.array([1,2,3,4])
    >>> x.base is None
    True

Slicing creates a view, whose memory is shared with x:

>>> y = x[2:]
    >>> y.base is x
    True

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('ctypes',
    """
    An object to simplify the interaction of the array with the ctypes
    module.

This attribute creates an object that makes it easier to use arrays
    when calling shared libraries with the ctypes module. The returned
    object has, among others, data, shape, and strides attributes (see
    Notes below) which themselves return ctypes objects that can be used
    as arguments to a shared library.

Parameters
    ----------
    None

Returns
    -------
    c : Python object
        Possessing attributes data, shape, strides, etc.

See Also
    --------
    numpy.ctypeslib

Notes
    -----
    Below are the public attributes of this object which were documented
    in "Guide to NumPy" (we have omitted undocumented public attributes,
    as well as documented private attributes):

.. autoattribute:: numpy.core._internal._ctypes.data
        :noindex:

.. autoattribute:: numpy.core._internal._ctypes.shape
        :noindex:

.. autoattribute:: numpy.core._internal._ctypes.strides
        :noindex:

.. automethod:: numpy.core._internal._ctypes.data_as
        :noindex:

.. automethod:: numpy.core._internal._ctypes.shape_as
        :noindex:

.. automethod:: numpy.core._internal._ctypes.strides_as
        :noindex:

If the ctypes module is not available, then the ctypes attribute
    of array objects still returns something useful, but ctypes objects
    are not returned and errors may be raised instead. In particular,
    the object will still have the ``as_parameter`` attribute which will
    return an integer equal to the data attribute.

Examples
    --------
    >>> import ctypes
    >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
    >>> x
    array([[0, 1],
           [2, 3]], dtype=int32)
    >>> x.ctypes.data
    31962608 # may vary
    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
    <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
    c_uint(0)
    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
    c_ulong(4294967296)
    >>> x.ctypes.shape
    <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
    >>> x.ctypes.strides
    <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('data',
    """Python buffer object pointing to the start of the array's data."""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('dtype',
    """
    Data-type of the array's elements.

Parameters
    ----------
    None

Returns
    -------
    d : numpy dtype object

See Also
    --------
    getfield

Examples
    --------
    >>> x = np.eye(3)
    >>> x.getfield(np.float64)
    array([[1.,  0.,  0.],
           [0.,  1.,  0.],
           [0.,  0.,  1.]])
    >>> x.setfield(3, np.int32)
    >>> x.getfield(np.int32)
    array([[3, 3, 3],
           [3, 3, 3],
           [3, 3, 3]], dtype=int32)
    >>> x
    array([[1.0e+000, 1.5e-323, 1.5e-323],
           [1.5e-323, 1.0e+000, 1.5e-323],
           [1.5e-323, 1.5e-323, 1.0e+000]])
    >>> x.setfield(np.eye(3), np.int32)
    >>> x
    array([[1.,  0.,  0.],
           [0.,  1.,  0.],
           [0.,  0.,  1.]])

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('setflags',
    """
    a.setflags(write=None, align=None, uic=None)

Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY),
    respectively.

These Boolean-valued flags affect how numpy interprets the memory
    area used by `a` (see Notes below). The ALIGNED flag can only
    be set to True if the data is actually aligned according to the type.
    The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set
    to True. The flag WRITEABLE can only be set to True if the array owns its
    own memory, or the ultimate owner of the memory exposes a writeable buffer
    interface, or is a string. (The exception for string is made so that
    unpickling can be done without copying memory.)

Parameters
    ----------
    write : bool, optional
        Describes whether or not `a` can be written to.
    align : bool, optional
        Describes whether or not `a` is aligned properly for its type.
    uic : bool, optional
        Describes whether or not `a` is a copy of another "base" array.

Notes
    -----
    Array flags provide information about how the memory area used
    for the array is to be interpreted. There are 7 Boolean flags
    in use, only four of which can be changed by the user:
    WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED.

WRITEABLE (W) the data area can be written to;

ALIGNED (A) the data and strides are aligned appropriately for the hardware
    (as determined by the compiler);

UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY;

WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
    by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
    called, the base array will be updated with the contents of this array.

All flags can be accessed using the single (upper case) letter as well
    as the full name.

Examples
    --------
    >>> y = np.array([[3, 1, 7],
    ...               [2, 0, 0],
    ...               [8, 5, 9]])
    >>> y
    array([[3, 1, 7],
           [2, 0, 0],
           [8, 5, 9]])
    >>> y.flags
      C_CONTIGUOUS : True
      F_CONTIGUOUS : False
      OWNDATA : True
      WRITEABLE : True
      ALIGNED : True
      WRITEBACKIFCOPY : False
      UPDATEIFCOPY : False
    >>> y.setflags(write=0, align=0)
    >>> y.flags
      C_CONTIGUOUS : True
      F_CONTIGUOUS : False
      OWNDATA : True
      WRITEABLE : False
      ALIGNED : False
      WRITEBACKIFCOPY : False
      UPDATEIFCOPY : False
    >>> y.setflags(uic=1)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: cannot set WRITEBACKIFCOPY flag to True

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('sort',
    """
    a.sort(axis=-1, kind=None, order=None)

Sort an array in-place. Refer to `numpy.sort` for full documentation.

Parameters
    ----------
    axis : int, optional
        Axis along which to sort. Default is -1, which means sort along the
        last axis.
    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
        and 'mergesort' use timsort under the covers and, in general, the
        actual implementation will vary with datatype. The 'mergesort' option
        is retained for backwards compatibility.

.. versionchanged:: 1.15.0.
           The 'stable' option was added.

order : str or list of str, optional
        When `a` is an array with fields defined, this argument specifies
        which fields to compare first, second, etc.  A single field can
        be specified as a string, and not all fields need be specified,
        but unspecified fields will still be used, in the order in which
        they come up in the dtype, to break ties.

See Also
    --------
    numpy.sort : Return a sorted copy of an array.
    numpy.argsort : Indirect sort.
    numpy.lexsort : Indirect stable sort on multiple keys.
    numpy.searchsorted : Find elements in sorted array.
    numpy.partition: Partial sort.

Notes
    -----
    See `numpy.sort` for notes on the different sorting algorithms.

Examples
    --------
    >>> a = np.array([[1,4], [3,1]])
    >>> a.sort(axis=1)
    >>> a
    array([[1, 4],
           [1, 3]])
    >>> a.sort(axis=0)
    >>> a
    array([[1, 3],
           [1, 4]])

Use the `order` keyword to specify a field to use when sorting a
    structured array:

>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
    >>> a.sort(order='y')
    >>> a
    array([(b'c', 1), (b'a', 2)],
          dtype=[('x', 'S1'), ('y', '<i8')])

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('partition',
    """
    a.partition(kth, axis=-1, kind='introselect', order=None)

Rearranges the elements in the array in such a way that the value of the
    element in kth position is in the position it would be in a sorted array.
    All elements smaller than the kth element are moved before this element and
    all equal or greater are moved behind it. The ordering of the elements in
    the two partitions is undefined.

.. versionadded:: 1.8.0

Parameters
    ----------
    kth : int or sequence of ints
        Element index to partition by. The kth element value will be in its
        final sorted position and all smaller elements will be moved before it
        and all equal or greater elements behind it.
        The order of all elements in the partitions is undefined.
        If provided with a sequence of kth it will partition all elements
        indexed by kth of them into their sorted position at once.
    axis : int, optional
        Axis along which to sort. Default is -1, which means sort along the
        last axis.
    kind : {'introselect'}, optional
        Selection algorithm. Default is 'introselect'.
    order : str or list of str, optional
        When `a` is an array with fields defined, this argument specifies
        which fields to compare first, second, etc. A single field can
        be specified as a string, and not all fields need to be specified,
        but unspecified fields will still be used, in the order in which
        they come up in the dtype, to break ties.

See Also
    --------
    numpy.partition : Return a parititioned copy of an array.
    argpartition : Indirect partition.
    sort : Full sort.

Notes
    -----
    See ``np.partition`` for notes on the different algorithms.

Examples
    --------
    >>> a = np.array([3, 4, 2, 1])
    >>> a.partition(3)
    >>> a
    array([2, 1, 3, 4])

>>> a.partition((1, 3))
    >>> a
    array([1, 2, 3, 4])
    """))

add_newdoc('numpy.core.multiarray', 'ndarray', ('squeeze',
    """
    a.squeeze(axis=None)

Remove single-dimensional entries from the shape of `a`.

Refer to `numpy.squeeze` for full documentation.

See Also
    --------
    numpy.squeeze : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('std',
    """
    a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False)

Returns the standard deviation of the array elements along given axis.

Refer to `numpy.std` for full documentation.

See Also
    --------
    numpy.std : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('sum',
    """
    a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)

Return the sum of the array elements over the given axis.

Refer to `numpy.sum` for full documentation.

See Also
    --------
    numpy.sum : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('swapaxes',
    """
    a.swapaxes(axis1, axis2)

Return a view of the array with `axis1` and `axis2` interchanged.

Refer to `numpy.swapaxes` for full documentation.

See Also
    --------
    numpy.swapaxes : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('take',
    """
    a.take(indices, axis=None, out=None, mode='raise')

Return an array formed from the elements of `a` at the given indices.

Refer to `numpy.take` for full documentation.

See Also
    --------
    numpy.take : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('tofile',
    """
    a.tofile(fid, sep="", format="%s")

Write array to a file as text or binary (default).

Data is always written in 'C' order, independent of the order of `a`.
    The data produced by this method can be recovered using the function
    fromfile().

Parameters
    ----------
    fid : file or str or Path
        An open file object, or a string containing a filename.

.. versionchanged:: 1.17.0
            `pathlib.Path` objects are now accepted.

sep : str
        Separator between array items for text output.
        If "" (empty), a binary file is written, equivalent to
        ``file.write(a.tobytes())``.
    format : str
        Format string for text file output.
        Each entry in the array is formatted to text by first converting
        it to the closest Python type, and then using "format" % item.

Notes
    -----
    This is a convenience function for quick storage of array data.
    Information on endianness and precision is lost, so this method is not a
    good choice for files intended to archive data or transport data between
    machines with different endianness. Some of these problems can be overcome
    by outputting the data as text files, at the expense of speed and file
    size.

When fid is a file object, array contents are directly written to the
    file, bypassing the file object's ``write`` method. As a result, tofile
    cannot be used with files objects supporting compression (e.g., GzipFile)
    or file-like objects that do not support ``fileno()`` (e.g., BytesIO).

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('tolist',
    """
    a.tolist()

Return the array as an ``a.ndim``-levels deep nested list of Python scalars.

Return a copy of the array data as a (nested) Python list.
    Data items are converted to the nearest compatible builtin Python type, via
    the `~numpy.ndarray.item` function.

If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will
    not be a list at all, but a simple Python scalar.

Parameters
    ----------
    none

Returns
    -------
    y : object, or list of object, or list of list of object, or ...
        The possibly nested list of array elements.

Notes
    -----
    The array may be recreated via ``a = np.array(a.tolist())``, although this
    may sometimes lose precision.

Examples
    --------
    For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,
    except that ``tolist`` changes numpy scalars to Python scalars:

>>> a = np.uint32([1, 2])
    >>> a_list = list(a)
    >>> a_list
    [1, 2]
    >>> type(a_list[0])
    <class 'numpy.uint32'>
    >>> a_tolist = a.tolist()
    >>> a_tolist
    [1, 2]
    >>> type(a_tolist[0])
    <class 'int'>

Additionally, for a 2D array, ``tolist`` applies recursively:

>>> a = np.array([[1, 2], [3, 4]])
    >>> list(a)
    [array([1, 2]), array([3, 4])]
    >>> a.tolist()
    [[1, 2], [3, 4]]

The base case for this recursion is a 0D array:

>>> a = np.array(1)
    >>> list(a)
    Traceback (most recent call last):
      ...
    TypeError: iteration over a 0-d array
    >>> a.tolist()
    1
    """))

add_newdoc('numpy.core.multiarray', 'ndarray', ('tobytes', """
    a.tobytes(order='C')

Construct Python bytes containing the raw data bytes in the array.

Constructs Python bytes showing a copy of the raw contents of
    data memory. The bytes object can be produced in either 'C' or 'Fortran',
    or 'Any' order (the default is 'C'-order). 'Any' order means C-order
    unless the F_CONTIGUOUS flag in the array is set, in which case it
    means 'Fortran' order.

.. versionadded:: 1.9.0

Parameters
    ----------
    order : {'C', 'F', None}, optional
        Order of the data for multidimensional arrays:
        C, Fortran, or the same as for the original array.

Returns
    -------
    s : bytes
        Python bytes exhibiting a copy of `a`'s raw data.

Examples
    --------
    >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
    >>> x.tobytes()
    b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'
    >>> x.tobytes('C') == x.tobytes()
    True
    >>> x.tobytes('F')
    b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('tostring', r"""
    a.tostring(order='C')

A compatibility alias for `tobytes`, with exactly the same behavior.

Despite its name, it returns `bytes` not `str`\ s.

.. deprecated:: 1.19.0
    """))

add_newdoc('numpy.core.multiarray', 'ndarray', ('trace',
    """
    a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)

Return the sum along diagonals of the array.

Refer to `numpy.trace` for full documentation.

See Also
    --------
    numpy.trace : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('transpose',
    """
    a.transpose(*axes)

Returns a view of the array with axes transposed.

For a 1-D array this has no effect, as a transposed vector is simply the
    same vector. To convert a 1-D array into a 2D column vector, an additional
    dimension must be added. `np.atleast2d(a).T` achieves this, as does
    `a[:, np.newaxis]`.
    For a 2-D array, this is a standard matrix transpose.
    For an n-D array, if axes are given, their order indicates how the
    axes are permuted (see Examples). If axes are not provided and
    ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then
    ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``.

Parameters
    ----------
    axes : None, tuple of ints, or `n` ints

* None or no argument: reverses the order of the axes.

* tuple of ints: `i` in the `j`-th place in the tuple means `a`'s
       `i`-th axis becomes `a.transpose()`'s `j`-th axis.

* `n` ints: same as an n-tuple of the same ints (this form is
       intended simply as a "convenience" alternative to the tuple form)

Returns
    -------
    out : ndarray
        View of `a`, with axes suitably permuted.

See Also
    --------
    ndarray.T : Array property returning the array transposed.
    ndarray.reshape : Give a new shape to an array without changing its data.

Examples
    --------
    >>> a = np.array([[1, 2], [3, 4]])
    >>> a
    array([[1, 2],
           [3, 4]])
    >>> a.transpose()
    array([[1, 3],
           [2, 4]])
    >>> a.transpose((1, 0))
    array([[1, 3],
           [2, 4]])
    >>> a.transpose(1, 0)
    array([[1, 3],
           [2, 4]])

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('var',
    """
    a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False)

Returns the variance of the array elements, along given axis.

Refer to `numpy.var` for full documentation.

See Also
    --------
    numpy.var : equivalent function

"""))

add_newdoc('numpy.core.multiarray', 'ndarray', ('view',
    """
    a.view([dtype][, type])

New view of array with the same data.

.. note::
        Passing None for ``dtype`` is different from omitting the parameter,
        since the former invokes ``dtype(None)`` which is an alias for
        ``dtype('float_')``.

Parameters
    ----------
    dtype : data-type or ndarray sub-class, optional
        Data-type descriptor of the returned view, e.g., float32 or int16.
        Omitting it results in the view having the same data-type as `a`.
        This argument can also be specified as an ndarray sub-class, which
        then specifies the type of the returned object (this is equivalent to
        setting the ``type`` parameter).
    type : Python type, optional
        Type of the returned view, e.g., ndarray or matrix.  Again, omission
        of the parameter results in type preservation.

Notes
    -----
    ``a.view()`` is used two different ways:

``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
    of the array's memory with a different data-type.  This can cause a
    reinterpretation of the bytes of memory.

``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
    returns an instance of `ndarray_subclass` that looks at the same array
    (same shape, dtype, etc.)  This does not cause a reinterpretation of the
    memory.

For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
    bytes per entry than the previous dtype (for example, converting a
    regular array to a structured array), then the behavior of the view
    cannot be predicted just from the superficial appearance of ``a`` (shown
    by ``print(a)``). It also depends on exactly how ``a`` is stored in
    memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus
    defined as a slice or transpose, etc., the view may give different
    results.

Examples
    --------
    >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])

Viewing array data using a different type and dtype:

>>> y = x.view(dtype=np.int16, type=np.matrix)
    >>> y
    matrix([[513]], dtype=int16)
    >>> print(type(y))
    <class 'numpy.matrix'>

Creating a view on a structured array so it can be used in calculations

>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
    >>> xv = x.view(dtype=np.int8).reshape(-1,2)
    >>> xv
    array([[1, 2],
           [3, 4]], dtype=int8)
    >>> xv.mean(0)
    array([2.,  3.])

Making changes to the view changes the underlying array

>>> xv[0,1] = 20
    >>> x
    array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])

Using a view to convert an array to a recarray:

>>> z = x.view(np.recarray)
    >>> z.a
    array([1, 3], dtype=int8)

Views share data:

>>> x[0] = (9, 10)
    >>> z[0]
    (9, 10)

Views that change the dtype size (bytes per entry) should normally be
    avoided on arrays defined by slices, transposes, fortran-ordering, etc.:

>>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16)
    >>> y = x[:, 0:2]
    >>> y
    array([[1, 2],
           [4, 5]], dtype=int16)
    >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
    Traceback (most recent call last):
        ...
    ValueError: To change to a dtype of a different size, the array must be C-contiguous
    >>> z = y.copy()
    >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
    array([[(1, 2)],
           [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')])
    """))

##############################################################################
#
# umath functions
#
##############################################################################

add_newdoc('numpy.core.umath', 'frompyfunc',
    """
    frompyfunc(func, nin, nout, *[, identity])

Takes an arbitrary Python function and returns a NumPy ufunc.

Can be used, for example, to add broadcasting to a built-in Python
    function (see Examples section).

Parameters
    ----------
    func : Python function object
        An arbitrary Python function.
    nin : int
        The number of input arguments.
    nout : int
        The number of objects returned by `func`.
    identity : object, optional
        The value to use for the `~numpy.ufunc.identity` attribute of the resulting
        object. If specified, this is equivalent to setting the underlying
        C ``identity`` field to ``PyUFunc_IdentityValue``.
        If omitted, the identity is set to ``PyUFunc_None``. Note that this is
        _not_ equivalent to setting the identity to ``None``, which implies the
        operation is reorderable.

Returns
    -------
    out : ufunc
        Returns a NumPy universal function (``ufunc``) object.

See Also
    --------
    vectorize : Evaluates pyfunc over input arrays using broadcasting rules of numpy.

Notes
    -----
    The returned ufunc always returns PyObject arrays.

Examples
    --------
    Use frompyfunc to add broadcasting to the Python function ``oct``:

>>> oct_array = np.frompyfunc(oct, 1, 1)
    >>> oct_array(np.array((10, 30, 100)))
    array(['0o12', '0o36', '0o144'], dtype=object)
    >>> np.array((oct(10), oct(30), oct(100))) # for comparison
    array(['0o12', '0o36', '0o144'], dtype='<U5')

""")

add_newdoc('numpy.core.umath', 'geterrobj',
    """
    geterrobj()

Return the current object that defines floating-point error handling.

The error object contains all information that defines the error handling
    behavior in NumPy. `geterrobj` is used internally by the other
    functions that get and set error handling behavior (`geterr`, `seterr`,
    `geterrcall`, `seterrcall`).

Returns
    -------
    errobj : list
        The error object, a list containing three elements:
        [internal numpy buffer size, error mask, error callback function].

The error mask is a single integer that holds the treatment information
        on all four floating point errors. The information for each error type
        is contained in three bits of the integer. If we print it in base 8, we
        can see what treatment is set for "invalid", "under", "over", and
        "divide" (in that order). The printed string can be interpreted with

* 0 : 'ignore'
        * 1 : 'warn'
        * 2 : 'raise'
        * 3 : 'call'
        * 4 : 'print'
        * 5 : 'log'

See Also
    --------
    seterrobj, seterr, geterr, seterrcall, geterrcall
    getbufsize, setbufsize

Notes
    -----
    For complete documentation of the types of floating-point exceptions and
    treatment options, see `seterr`.

Examples
    --------
    >>> np.geterrobj()  # first get the defaults
    [8192, 521, None]

>>> def err_handler(type, flag):
    ...     print("Floating point error (%s), with flag %s" % (type, flag))
    ...
    >>> old_bufsize = np.setbufsize(20000)
    >>> old_err = np.seterr(divide='raise')
    >>> old_handler = np.seterrcall(err_handler)
    >>> np.geterrobj()
    [8192, 521, <function err_handler at 0x91dcaac>]

>>> old_err = np.seterr(all='ignore')
    >>> np.base_repr(np.geterrobj()[1], 8)
    '0'
    >>> old_err = np.seterr(divide='warn', over='log', under='call',
    ...                     invalid='print')
    >>> np.base_repr(np.geterrobj()[1], 8)
    '4351'

""")

add_newdoc('numpy.core.umath', 'seterrobj',
    """
    seterrobj(errobj)

Set the object that defines floating-point error handling.

The error object contains all information that defines the error handling
    behavior in NumPy. `seterrobj` is used internally by the other
    functions that set error handling behavior (`seterr`, `seterrcall`).

Parameters
    ----------
    errobj : list
        The error object, a list containing three elements:
        [internal numpy buffer size, error mask, error callback function].

* 0 : 'ignore'
        * 1 : 'warn'
        * 2 : 'raise'
        * 3 : 'call'
        * 4 : 'print'
        * 5 : 'log'

See Also
    --------
    geterrobj, seterr, geterr, seterrcall, geterrcall
    getbufsize, setbufsize

Notes
    -----
    For complete documentation of the types of floating-point exceptions and
    treatment options, see `seterr`.

Examples
    --------
    >>> old_errobj = np.geterrobj()  # first get the defaults
    >>> old_errobj
    [8192, 521, None]

>>> def err_handler(type, flag):
    ...     print("Floating point error (%s), with flag %s" % (type, flag))
    ...
    >>> new_errobj = [20000, 12, err_handler]
    >>> np.seterrobj(new_errobj)
    >>> np.base_repr(12, 8)  # int for divide=4 ('print') and over=1 ('warn')
    '14'
    >>> np.geterr()
    {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'}
    >>> np.geterrcall() is err_handler
    True

""")

##############################################################################
#
# compiled_base functions
#
##############################################################################

add_newdoc('numpy.core.multiarray', 'add_docstring',
    """
    add_docstring(obj, docstring)

Add a docstring to a built-in obj if possible.
    If the obj already has a docstring raise a RuntimeError
    If this routine does not know how to add a docstring to the object
    raise a TypeError
    """)

add_newdoc('numpy.core.umath', '_add_newdoc_ufunc',
    """
    add_ufunc_docstring(ufunc, new_docstring)

Replace the docstring for a ufunc with new_docstring.
    This method will only work if the current docstring for
    the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.)

Parameters
    ----------
    ufunc : numpy.ufunc
        A ufunc whose current doc is NULL.
    new_docstring : string
        The new docstring for the ufunc.

Notes
    -----
    This method allocates memory for new_docstring on
    the heap. Technically this creates a mempory leak, since this
    memory will not be reclaimed until the end of the program
    even if the ufunc itself is removed. However this will only
    be a problem if the user is repeatedly creating ufuncs with
    no documentation, adding documentation via add_newdoc_ufunc,
    and then throwing away the ufunc.
    """)

add_newdoc('numpy.core.multiarray', '_set_madvise_hugepage',
    """
    _set_madvise_hugepage(enabled: bool) -> bool

Set  or unset use of ``madvise (2)`` MADV_HUGEPAGE support when
    allocating the array data. Returns the previously set value.
    See `global_state` for more information.
    """)

add_newdoc('numpy.core._multiarray_tests', 'format_float_OSprintf_g',
    """
    format_float_OSprintf_g(val, precision)

Print a floating point scalar using the system's printf function,
    equivalent to:

printf("%.*g", precision, val);

for half/float/double, or replacing 'g' by 'Lg' for longdouble. This
    method is designed to help cross-validate the format_float_* methods.

Parameters
    ----------
    val : python float or numpy floating scalar
        Value to format.

precision : non-negative integer, optional
        Precision given to printf.

Returns
    -------
    rep : string
        The string representation of the floating point value

See Also
    --------
    format_float_scientific
    format_float_positional
    """)

##############################################################################
#
# Documentation for ufunc attributes and methods
#
##############################################################################

##############################################################################
#
# ufunc object
#
##############################################################################

add_newdoc('numpy.core', 'ufunc',
    """
    Functions that operate element by element on whole arrays.

To see the documentation for a specific ufunc, use `info`.  For
    example, ``np.info(np.sin)``.  Because ufuncs are written in C
    (for speed) and linked into Python with NumPy's ufunc facility,
    Python's help() function finds this page whenever help() is called
    on a ufunc.

A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`.

Calling ufuncs:
    ===============

op(*x[, out], where=True, **kwargs)
    Apply `op` to the arguments `*x` elementwise, broadcasting the arguments.

The broadcasting rules are:

* Dimensions of length 1 may be prepended to either array.
    * Arrays may be repeated along dimensions of length 1.

Parameters
    ----------
    *x : array_like
        Input arrays.
    out : ndarray, None, or tuple of ndarray and None, optional
        Alternate array object(s) in which to put the result; if provided, it
        must have a shape that the inputs broadcast to. A tuple of arrays
        (possible only as a keyword argument) must have length equal to the
        number of outputs; use None for uninitialized outputs to be
        allocated by the ufunc.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.

Returns
    -------
    r : ndarray or tuple of ndarray
        `r` will have the shape that the arrays in `x` broadcast to; if `out` is
        provided, it will be returned. If not, `r` will be allocated and
        may contain uninitialized values. If the function has more than one
        output, then the result will be a tuple of arrays.

""")

##############################################################################
#
# ufunc attributes
#
##############################################################################

add_newdoc('numpy.core', 'ufunc', ('identity',
    """
    The identity value.

Data attribute containing the identity element for the ufunc, if it has one.
    If it does not, the attribute value is None.

Examples
    --------
    >>> np.add.identity
    0
    >>> np.multiply.identity
    1
    >>> np.power.identity
    1
    >>> print(np.exp.identity)
    None
    """))

add_newdoc('numpy.core', 'ufunc', ('nargs',
    """
    The number of arguments.

Data attribute containing the number of arguments the ufunc takes, including
    optional ones.

Notes
    -----
    Typically this value will be one more than what you might expect because all
    ufuncs take  the optional "out" argument.

Examples
    --------
    >>> np.add.nargs
    3
    >>> np.multiply.nargs
    3
    >>> np.power.nargs
    3
    >>> np.exp.nargs
    2
    """))

add_newdoc('numpy.core', 'ufunc', ('nin',
    """
    The number of inputs.

Data attribute containing the number of arguments the ufunc treats as input.

Examples
    --------
    >>> np.add.nin
    2
    >>> np.multiply.nin
    2
    >>> np.power.nin
    2
    >>> np.exp.nin
    1
    """))

add_newdoc('numpy.core', 'ufunc', ('nout',
    """
    The number of outputs.

Data attribute containing the number of arguments the ufunc treats as output.

Notes
    -----
    Since all ufuncs can take output arguments, this will always be (at least) 1.

Examples
    --------
    >>> np.add.nout
    1
    >>> np.multiply.nout
    1
    >>> np.power.nout
    1
    >>> np.exp.nout
    1

"""))

add_newdoc('numpy.core', 'ufunc', ('ntypes',
    """
    The number of types.

The number of numerical NumPy types - of which there are 18 total - on which
    the ufunc can operate.

See Also
    --------
    numpy.ufunc.types

Examples
    --------
    >>> np.add.ntypes
    18
    >>> np.multiply.ntypes
    18
    >>> np.power.ntypes
    17
    >>> np.exp.ntypes
    7
    >>> np.remainder.ntypes
    14

"""))

add_newdoc('numpy.core', 'ufunc', ('types',
    """
    Returns a list with types grouped input->output.

Data attribute listing the data-type "Domain-Range" groupings the ufunc can
    deliver. The data-types are given using the character codes.

See Also
    --------
    numpy.ufunc.ntypes

Examples
    --------
    >>> np.add.types
    ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',
    'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',
    'GG->G', 'OO->O']

>>> np.multiply.types
    ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',
    'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',
    'GG->G', 'OO->O']

>>> np.power.types
    ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',
    'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G',
    'OO->O']

>>> np.exp.types
    ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O']

>>> np.remainder.types
    ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',
    'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O']

"""))

add_newdoc('numpy.core', 'ufunc', ('signature',
    """
    Definition of the core elements a generalized ufunc operates on.

The signature determines how the dimensions of each input/output array
    are split into core and loop dimensions:

1. Each dimension in the signature is matched to a dimension of the
       corresponding passed-in array, starting from the end of the shape tuple.
    2. Core dimensions assigned to the same label in the signature must have
       exactly matching sizes, no broadcasting is performed.
    3. The core dimensions are removed from all inputs and the remaining
       dimensions are broadcast together, defining the loop dimensions.

Notes
    -----
    Generalized ufuncs are used internally in many linalg functions, and in
    the testing suite; the examples below are taken from these.
    For ufuncs that operate on scalars, the signature is None, which is
    equivalent to '()' for every argument.

Examples
    --------
    >>> np.core.umath_tests.matrix_multiply.signature
    '(m,n),(n,p)->(m,p)'
    >>> np.linalg._umath_linalg.det.signature
    '(m,m)->()'
    >>> np.add.signature is None
    True  # equivalent to '(),()->()'
    """))

##############################################################################
#
# ufunc methods
#
##############################################################################

add_newdoc('numpy.core', 'ufunc', ('reduce',
    """
    reduce(a, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)

Reduces `a`'s dimension by one, by applying ufunc along one axis.

Let :math:`a.shape = (N_0, ..., N_i, ..., N_{M-1})`.  Then
    :math:`ufunc.reduce(a, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` =
    the result of iterating `j` over :math:`range(N_i)`, cumulatively applying
    ufunc to each :math:`a[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`.
    For a one-dimensional array, reduce produces results equivalent to:
    ::

r = op.identity # op = ufunc
     for i in range(len(A)):
       r = op(r, A[i])
     return r

For example, add.reduce() is equivalent to sum().

Parameters
    ----------
    a : array_like
        The array to act on.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a reduction is performed.
        The default (`axis` = 0) is perform a reduction over the first
        dimension of the input array. `axis` may be negative, in
        which case it counts from the last to the first axis.

.. versionadded:: 1.7.0

If this is None, a reduction is performed over all the axes.
        If this is a tuple of ints, a reduction is performed on multiple
        axes, instead of a single axis or all the axes as before.

For operations which are either not commutative or not associative,
        doing a reduction over multiple axes is not well-defined. The
        ufuncs do not currently raise an exception in this case, but will
        likely do so in the future.
    dtype : data-type code, optional
        The type used to represent the intermediate results. Defaults
        to the data-type of the output array if this is provided, or
        the data-type of the input array if no output array is provided.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If not provided or None,
        a freshly-allocated array is returned. For consistency with
        ``ufunc.__call__``, if given as a keyword, this may be wrapped in a
        1-element tuple.

.. versionchanged:: 1.13.0
           Tuples are allowed for keyword argument.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

.. versionadded:: 1.7.0
    initial : scalar, optional
        The value with which to start the reduction.
        If the ufunc has no identity or the dtype is object, this defaults
        to None - otherwise it defaults to ufunc.identity.
        If ``None`` is given, the first element of the reduction is used,
        and an error is thrown if the reduction is empty.

.. versionadded:: 1.15.0

where : array_like of bool, optional
        A boolean array which is broadcasted to match the dimensions
        of `a`, and selects elements to include in the reduction. Note
        that for ufuncs like ``minimum`` that do not have an identity
        defined, one has to pass in also ``initial``.

.. versionadded:: 1.17.0

Returns
    -------
    r : ndarray
        The reduced array. If `out` was supplied, `r` is a reference to it.

Examples
    --------
    >>> np.multiply.reduce([2,3,5])
    30

A multi-dimensional array example:

>>> X = np.arange(8).reshape((2,2,2))
    >>> X
    array([[[0, 1],
            [2, 3]],
           [[4, 5],
            [6, 7]]])
    >>> np.add.reduce(X, 0)
    array([[ 4,  6],
           [ 8, 10]])
    >>> np.add.reduce(X) # confirm: default axis value is 0
    array([[ 4,  6],
           [ 8, 10]])
    >>> np.add.reduce(X, 1)
    array([[ 2,  4],
           [10, 12]])
    >>> np.add.reduce(X, 2)
    array([[ 1,  5],
           [ 9, 13]])

You can use the ``initial`` keyword argument to initialize the reduction
    with a different value, and ``where`` to select specific elements to include:

>>> np.add.reduce([10], initial=5)
    15
    >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)
    array([14., 14.])
    >>> a = np.array([10., np.nan, 10])
    >>> np.add.reduce(a, where=~np.isnan(a))
    20.0

Allows reductions of empty arrays where they would normally fail, i.e.
    for ufuncs without an identity.

>>> np.minimum.reduce([], initial=np.inf)
    inf
    >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])
    array([ 1., 10.])
    >>> np.minimum.reduce([])
    Traceback (most recent call last):
        ...
    ValueError: zero-size array to reduction operation minimum which has no identity
    """))

add_newdoc('numpy.core', 'ufunc', ('accumulate',
    """
    accumulate(array, axis=0, dtype=None, out=None)

Accumulate the result of applying the operator to all elements.

For a one-dimensional array, accumulate produces results equivalent to::

r = np.empty(len(A))
      t = op.identity        # op = the ufunc being applied to A's  elements
      for i in range(len(A)):
          t = op(t, A[i])
          r[i] = t
      return r

For example, add.accumulate() is equivalent to np.cumsum().

For a multi-dimensional array, accumulate is applied along only one
    axis (axis zero by default; see Examples below) so repeated use is
    necessary if one wants to accumulate over multiple axes.

Parameters
    ----------
    array : array_like
        The array to act on.
    axis : int, optional
        The axis along which to apply the accumulation; default is zero.
    dtype : data-type code, optional
        The data-type used to represent the intermediate results. Defaults
        to the data-type of the output array if such is provided, or the
        the data-type of the input array if no output array is provided.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If not provided or None,
        a freshly-allocated array is returned. For consistency with
        ``ufunc.__call__``, if given as a keyword, this may be wrapped in a
        1-element tuple.

.. versionchanged:: 1.13.0
           Tuples are allowed for keyword argument.

Returns
    -------
    r : ndarray
        The accumulated values. If `out` was supplied, `r` is a reference to
        `out`.

Examples
    --------
    1-D array examples:

>>> np.add.accumulate([2, 3, 5])
    array([ 2,  5, 10])
    >>> np.multiply.accumulate([2, 3, 5])
    array([ 2,  6, 30])

2-D array examples:

>>> I = np.eye(2)
    >>> I
    array([[1.,  0.],
           [0.,  1.]])

Accumulate along axis 0 (rows), down columns:

>>> np.add.accumulate(I, 0)
    array([[1.,  0.],
           [1.,  1.]])
    >>> np.add.accumulate(I) # no axis specified = axis zero
    array([[1.,  0.],
           [1.,  1.]])

Accumulate along axis 1 (columns), through rows:

>>> np.add.accumulate(I, 1)
    array([[1.,  1.],
           [0.,  1.]])

"""))

add_newdoc('numpy.core', 'ufunc', ('reduceat',
    """
    reduceat(a, indices, axis=0, dtype=None, out=None)

Performs a (local) reduce with specified slices over a single axis.

For i in ``range(len(indices))``, `reduceat` computes
    ``ufunc.reduce(a[indices[i]:indices[i+1]])``, which becomes the i-th
    generalized "row" parallel to `axis` in the final result (i.e., in a
    2-D array, for example, if `axis = 0`, it becomes the i-th row, but if
    `axis = 1`, it becomes the i-th column).  There are three exceptions to this:

* when ``i = len(indices) - 1`` (so for the last index),
      ``indices[i+1] = a.shape[axis]``.
    * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is
      simply ``a[indices[i]]``.
    * if ``indices[i] >= len(a)`` or ``indices[i] < 0``, an error is raised.

The shape of the output depends on the size of `indices`, and may be
    larger than `a` (this happens if ``len(indices) > a.shape[axis]``).

Parameters
    ----------
    a : array_like
        The array to act on.
    indices : array_like
        Paired indices, comma separated (not colon), specifying slices to
        reduce.
    axis : int, optional
        The axis along which to apply the reduceat.
    dtype : data-type code, optional
        The type used to represent the intermediate results. Defaults
        to the data type of the output array if this is provided, or
        the data type of the input array if no output array is provided.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If not provided or None,
        a freshly-allocated array is returned. For consistency with
        ``ufunc.__call__``, if given as a keyword, this may be wrapped in a
        1-element tuple.

.. versionchanged:: 1.13.0
           Tuples are allowed for keyword argument.

Returns
    -------
    r : ndarray
        The reduced values. If `out` was supplied, `r` is a reference to
        `out`.

Notes
    -----
    A descriptive example:

If `a` is 1-D, the function `ufunc.accumulate(a)` is the same as
    ``ufunc.reduceat(a, indices)[::2]`` where `indices` is
    ``range(len(array) - 1)`` with a zero placed
    in every other element:
    ``indices = zeros(2 * len(a) - 1)``, ``indices[1::2] = range(1, len(a))``.

Don't be fooled by this attribute's name: `reduceat(a)` is not
    necessarily smaller than `a`.

Examples
    --------
    To take the running sum of four successive values:

>>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2]
    array([ 6, 10, 14, 18])

A 2-D example:

>>> x = np.linspace(0, 15, 16).reshape(4,4)
    >>> x
    array([[ 0.,   1.,   2.,   3.],
           [ 4.,   5.,   6.,   7.],
           [ 8.,   9.,  10.,  11.],
           [12.,  13.,  14.,  15.]])

# reduce such that the result has the following five rows:
     # [row1 + row2 + row3]
     # [row4]
     # [row2]
     # [row3]
     # [row1 + row2 + row3 + row4]

>>> np.add.reduceat(x, [0, 3, 1, 2, 0])
    array([[12.,  15.,  18.,  21.],
           [12.,  13.,  14.,  15.],
           [ 4.,   5.,   6.,   7.],
           [ 8.,   9.,  10.,  11.],
           [24.,  28.,  32.,  36.]])

# reduce such that result has the following two columns:
     # [col1 * col2 * col3, col4]

>>> np.multiply.reduceat(x, [0, 3], 1)
    array([[   0.,     3.],
           [ 120.,     7.],
           [ 720.,    11.],
           [2184.,    15.]])

"""))

add_newdoc('numpy.core', 'ufunc', ('outer',
    r"""
    outer(A, B, **kwargs)

Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`.

Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of
    ``op.outer(A, B)`` is an array of dimension M + N such that:

.. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =
       op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])

For `A` and `B` one-dimensional, this is equivalent to::

r = empty(len(A),len(B))
      for i in range(len(A)):
          for j in range(len(B)):
              r[i,j] = op(A[i], B[j]) # op = ufunc in question

Parameters
    ----------
    A : array_like
        First array
    B : array_like
        Second array
    kwargs : any
        Arguments to pass on to the ufunc. Typically `dtype` or `out`.

Returns
    -------
    r : ndarray
        Output array

See Also
    --------
    numpy.outer : A less powerful version of ``np.multiply.outer``
                  that `ravel`\ s all inputs to 1D. This exists
                  primarily for compatibility with old code.

tensordot : ``np.tensordot(a, b, axes=((), ()))`` and
                ``np.multiply.outer(a, b)`` behave same for all
                dimensions of a and b.

Examples
    --------
    >>> np.multiply.outer([1, 2, 3], [4, 5, 6])
    array([[ 4,  5,  6],
           [ 8, 10, 12],
           [12, 15, 18]])

A multi-dimensional example:

>>> A = np.array([[1, 2, 3], [4, 5, 6]])
    >>> A.shape
    (2, 3)
    >>> B = np.array([[1, 2, 3, 4]])
    >>> B.shape
    (1, 4)
    >>> C = np.multiply.outer(A, B)
    >>> C.shape; C
    (2, 3, 1, 4)
    array([[[[ 1,  2,  3,  4]],
            [[ 2,  4,  6,  8]],
            [[ 3,  6,  9, 12]]],
           [[[ 4,  8, 12, 16]],
            [[ 5, 10, 15, 20]],
            [[ 6, 12, 18, 24]]]])

"""))

add_newdoc('numpy.core', 'ufunc', ('at',
    """
    at(a, indices, b=None)

Performs unbuffered in place operation on operand 'a' for elements
    specified by 'indices'. For addition ufunc, this method is equivalent to
    ``a[indices] += b``, except that results are accumulated for elements that
    are indexed more than once. For example, ``a[[0,0]] += 1`` will only
    increment the first element once because of buffering, whereas
    ``add.at(a, [0,0], 1)`` will increment the first element twice.

.. versionadded:: 1.8.0

Parameters
    ----------
    a : array_like
        The array to perform in place operation on.
    indices : array_like or tuple
        Array like index object or slice object for indexing into first
        operand. If first operand has multiple dimensions, indices can be a
        tuple of array like index objects or slice objects.
    b : array_like
        Second operand for ufuncs requiring two operands. Operand must be
        broadcastable over first operand after indexing or slicing.

Examples
    --------
    Set items 0 and 1 to their negative values:

>>> a = np.array([1, 2, 3, 4])
    >>> np.negative.at(a, [0, 1])
    >>> a
    array([-1, -2,  3,  4])

Increment items 0 and 1, and increment item 2 twice:

>>> a = np.array([1, 2, 3, 4])
    >>> np.add.at(a, [0, 1, 2, 2], 1)
    >>> a
    array([2, 3, 5, 4])

Add items 0 and 1 in first array to second array,
    and store results in first array:

>>> a = np.array([1, 2, 3, 4])
    >>> b = np.array([1, 2])
    >>> np.add.at(a, [0, 1], b)
    >>> a
    array([2, 4, 3, 4])

"""))

##############################################################################
#
# Documentation for dtype attributes and methods
#
##############################################################################

##############################################################################
#
# dtype object
#
##############################################################################

add_newdoc('numpy.core.multiarray', 'dtype',
    """
    dtype(obj, align=False, copy=False)

Create a data type object.

A numpy array is homogeneous, and contains elements described by a
    dtype object. A dtype object can be constructed from different
    combinations of fundamental numeric types.

Parameters
    ----------
    obj
        Object to be converted to a data type object.
    align : bool, optional
        Add padding to the fields to match what a C compiler would output
        for a similar C-struct. Can be ``True`` only if `obj` is a dictionary
        or a comma-separated string. If a struct dtype is being created,
        this also sets a sticky alignment flag ``isalignedstruct``.
    copy : bool, optional
        Make a new copy of the data-type object. If ``False``, the result
        may just be a reference to a built-in data-type object.