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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.

�)�division�absolute_import�print_function)�
add_newdocz
numpy.coreZflatitera�
    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)
    <type 'numpy.flatiter'>
    >>> for item in fl:
    ...     print(item)
    ...
    0
    1
    2
    3
    4
    5

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

    �base��
    A reference to the array that is iterated over.

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

    �coords��
    An N-dimensional tuple of current coordinates.

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

    �index��
    Current flat index into the array.

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

    �	__array__�2__array__(type=None) Get array from iterator

    �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])

    Znditera*
    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.
    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.
    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 iterator's dimension.
    nop : int
        The number of iterator operands.
    operands : tuple of operand(s)
        The array(s) to be iterated over.
    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 iterator's coordinates or index, 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']])
            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']])

            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=[range(x.ndim)+[-1]*y.ndim,
                             [-1]*x.ndim+range(y.ndim),
                             None])

            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])

    �
    copy()

    Get a copy of the iterator in its current state.

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

    �debug_print�h
    debug_print()

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

    �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.

    �iternext�8
    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.

    �remove_axis�w
    remove_axis(i)

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

    �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.

    �reset�@
    reset()

    Reset the iterator to its initial state.

    �	broadcasta�
    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]])

    �
    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
    >>> b.next(), b.next(), b.next()
    ((1, 4), (1, 5), (1, 6))
    >>> b.index
    3

    �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
    >>> row.next(), col.next()
    (1, 4)

    �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

    �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

    �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

    �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)

    �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

    �
    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
    >>> b.next(), b.next(), b.next()
    ((1, 4), (2, 4), (3, 4))
    >>> b.index
    3
    >>> b.reset()
    >>> b.index
    0

    znumpy.core.multiarray�arraya�

    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.  This argument can only be used to 'upcast' the array.  For
        downcasting, use the .astype(t) method.
    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, empty_like, zeros, zeros_like, ones, ones_like, full, full_like

    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]])

    �emptya�
    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
    dtype : data-type, optional
        Desired output data-type.
    order : {'C', 'F'}, optional
        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, zeros, ones

    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]])         #random

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

    Z
empty_likea�
    empty_like(a, dtype=None, order='K', subok=True)

    Return a new array with the same shape and type as a given array.

    Parameters
    ----------
    a : array_like
        The shape and data-type of `a` define these same attributes of the
        returned array.
    dtype : data-type, optional
        Overrides the data type of the result.

        .. versionadded:: 1.6.0
    order : {'C', 'F', 'A', or 'K'}, optional
        Overrides the memory layout of the result. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if ``a`` is Fortran contiguous,
        'C' otherwise. 'K' means match the layout of ``a`` as closely
        as possible.

        .. versionadded:: 1.6.0
    subok : bool, optional.
        If True, then the newly created array will use the sub-class
        type of 'a', otherwise it will be a base-class array. Defaults
        to True.

    Returns
    -------
    out : ndarray
        Array of uninitialized (arbitrary) data with the same
        shape and type as `a`.

    See Also
    --------
    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.
    empty : Return a new uninitialized array.
    ones : Return a new array setting values to one.
    zeros : Return a new array setting values to zero.

    Notes
    -----
    This function does *not* initialize the returned array; to do that use
    `zeros_like` or `ones_like` instead.  It may be marginally faster than
    the functions that do set the array values.

    Examples
    --------
    >>> a = ([1,2,3], [4,5,6])                         # a is array-like
    >>> np.empty_like(a)
    array([[-1073741821, -1073741821,           3],    #random
           [          0,           0, -1073741821]])
    >>> a = np.array([[1., 2., 3.],[4.,5.,6.]])
    >>> np.empty_like(a)
    array([[ -2.00000715e+000,   1.48219694e-323,  -2.00000572e+000],#random
           [  4.38791518e-305,  -2.00000715e+000,   4.17269252e-309]])

    Zscalara�
    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.

    �zerosa�
    zeros(shape, dtype=float, order='C')

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

    Parameters
    ----------
    shape : int or sequence 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
        Whether to store multidimensional data in C- or Fortran-contiguous
        (row- or column-wise) 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.
    ones_like : Return an array of ones with shape and type of input.
    empty_like : Return an empty array with shape and type of input.
    ones : Return a new array setting values to one.
    empty : Return a new uninitialized array.

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

    >>> np.zeros((5,), dtype=np.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')])

    Zset_typeDictzuset_typeDict(dict)

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

    �
fromstringa
    fromstring(string, dtype=float, count=-1, sep='')

    A new 1-D array initialized from raw binary or 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.
    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
        If not provided or, equivalently, the empty string, the data will
        be interpreted as binary data; otherwise, as ASCII text with
        decimal numbers.  Also in this latter case, this argument is
        interpreted as the string separating numbers in the data; extra
        whitespace between elements is also ignored.

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

    Zfromitera.
    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, np.float)
    array([  0.,   1.,   4.,   9.,  16.])

    �fromfilea!	
    fromfile(file, dtype=float, count=-1, sep='')

    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
        Open file object or filename.
    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.
    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.

    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 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', int), ('sec', int)]),
    ...                ('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', '<i4'), ('sec', '<i4')]), ('temp', '<f8')])

    Save the raw data to disk:

    >>> import os
    >>> fname = os.tmpnam()
    >>> x.tofile(fname)

    Read the raw data from disk:

    >>> np.fromfile(fname, dtype=dt)
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('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', '<i4'), ('sec', '<i4')]), ('temp', '<f8')])

    Z
frombuffera
    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)

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

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

    Zconcatenatea�	
    concatenate((a1, a2, ...), axis=0)

    Join a sequence of arrays along an existing axis.

    Parameters
    ----------
    a1, a2, ... : sequence of array_like
        The arrays must have the same shape, except in the dimension
        corresponding to `axis` (the first, by default).
    axis : int, optional
        The axis along which the arrays will be joined.  Default is 0.

    Returns
    -------
    res : ndarray
        The concatenated array.

    See Also
    --------
    ma.concatenate : Concatenate function that preserves input masks.
    array_split : Split an array into multiple sub-arrays of equal or
                  near-equal size.
    split : Split array into a list of multiple sub-arrays of equal size.
    hsplit : Split array into multiple sub-arrays horizontally (column wise)
    vsplit : Split array into multiple sub-arrays vertically (row wise)
    dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
    stack : Stack a sequence of arrays along a new axis.
    hstack : Stack arrays in sequence horizontally (column wise)
    vstack : Stack arrays in sequence vertically (row wise)
    dstack : Stack arrays in sequence depth wise (along third dimension)

    Notes
    -----
    When one or more of the arrays to be concatenated is a MaskedArray,
    this function will return a MaskedArray object instead of an ndarray,
    but the input masks are *not* preserved. In cases where a MaskedArray
    is expected as input, use the ma.concatenate function from the masked
    array module instead.

    Examples
    --------
    >>> a = np.array([[1, 2], [3, 4]])
    >>> b = np.array([[5, 6]])
    >>> np.concatenate((a, b), axis=0)
    array([[1, 2],
           [3, 4],
           [5, 6]])
    >>> np.concatenate((a, b.T), axis=1)
    array([[1, 2, 5],
           [3, 4, 6]])

    This function will not preserve masking of MaskedArray inputs.

    >>> a = np.ma.arange(3)
    >>> a[1] = np.ma.masked
    >>> b = np.arange(2, 5)
    >>> a
    masked_array(data = [0 -- 2],
                 mask = [False  True False],
           fill_value = 999999)
    >>> b
    array([2, 3, 4])
    >>> np.concatenate([a, b])
    masked_array(data = [0 1 2 2 3 4],
                 mask = False,
           fill_value = 999999)
    >>> np.ma.concatenate([a, b])
    masked_array(data = [0 -- 2 2 3 4],
                 mask = [False  True False False False False],
           fill_value = 999999)

    �inneraj
    inner(a, b)

    Inner product of two arrays.

    Ordinary inner product of vectors for 1-D arrays (without complex
    conjugation), in higher dimensions a sum product over the last axes.

    Parameters
    ----------
    a, b : array_like
        If `a` and `b` are nonscalar, their last dimensions must match.

    Returns
    -------
    out : ndarray
        `out.shape = a.shape[:-1] + b.shape[:-1]`

    Raises
    ------
    ValueError
        If the last dimension of `a` and `b` has different size.

    See Also
    --------
    tensordot : Sum products over arbitrary axes.
    dot : Generalised matrix product, using second last dimension of `b`.
    einsum : Einstein summation convention.

    Notes
    -----
    For vectors (1-D arrays) it computes the ordinary inner-product::

        np.inner(a, b) = sum(a[:]*b[:])

    More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`::

        np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))

    or explicitly::

        np.inner(a, b)[i0,...,ir-1,j0,...,js-1]
             = sum(a[i0,...,ir-1,:]*b[j0,...,js-1,:])

    In addition `a` or `b` may be scalars, in which case::

       np.inner(a,b) = a*b

    Examples
    --------
    Ordinary inner product for vectors:

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

    A multidimensional example:

    >>> a = np.arange(24).reshape((2,3,4))
    >>> b = np.arange(4)
    >>> np.inner(a, b)
    array([[ 14,  38,  62],
           [ 86, 110, 134]])

    An example where `b` is a scalar:

    >>> np.inner(np.eye(2), 7)
    array([[ 7.,  0.],
           [ 0.,  7.]])

    ZfastCopyAndTransposez_fastCopyAndTranspose(a)Z	correlatezcross_correlate(a,v, mode=0)ZarangeaT
    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 <http://docs.python.org/lib/built-in-funcs.html>`_ 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 ``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, `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
    --------
    linspace : Evenly spaced numbers with careful handling of endpoints.
    ogrid: Arrays of evenly spaced numbers in N-dimensions.
    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])

    Z_get_ndarray_c_versionzS_get_ndarray_c_version()

    Return the compile time NDARRAY_VERSION number.

    �_reconstructzY_reconstruct(subtype, shape, dtype)

    Construct an empty array. Used by Pickles.

    Zset_string_functionzx
    set_string_function(f, repr=1)

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

    Zset_numeric_opsaL
    set_numeric_ops(op1=func1, op2=func2, ...)

    Set numerical operators for array objects.

    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

    �wherea�
    where(condition, [x, y])

    Return elements, either from `x` or `y`, depending on `condition`.

    If only `condition` is given, return ``condition.nonzero()``.

    Parameters
    ----------
    condition : array_like, bool
        When True, yield `x`, otherwise yield `y`.
    x, y : array_like, optional
        Values from which to choose. `x`, `y` and `condition` need to be
        broadcastable to some shape.

    Returns
    -------
    out : ndarray or tuple of ndarrays
        If both `x` and `y` are specified, the output array contains
        elements of `x` where `condition` is True, and elements from
        `y` elsewhere.

        If only `condition` is given, return the tuple
        ``condition.nonzero()``, the indices where `condition` is True.

    See Also
    --------
    nonzero, choose

    Notes
    -----
    If `x` and `y` are given and input arrays are 1-D, `where` is
    equivalent to::

        [xv if c else yv for (c,xv,yv) in zip(condition,x,y)]

    Examples
    --------
    >>> np.where([[True, False], [True, True]],
    ...          [[1, 2], [3, 4]],
    ...          [[9, 8], [7, 6]])
    array([[1, 8],
           [3, 4]])

    >>> np.where([[0, 1], [1, 0]])
    (array([0, 1]), array([1, 0]))

    >>> x = np.arange(9.).reshape(3, 3)
    >>> np.where( x > 5 )
    (array([2, 2, 2]), array([0, 1, 2]))
    >>> x[np.where( x > 3.0 )]               # Note: result is 1D.
    array([ 4.,  5.,  6.,  7.,  8.])
    >>> np.where(x < 5, x, -1)               # Note: broadcasting.
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -1.],
           [-1., -1., -1.]])

    Find the indices of elements of `x` that are in `goodvalues`.

    >>> goodvalues = [3, 4, 7]
    >>> ix = np.isin(x, goodvalues)
    >>> ix
    array([[False, False, False],
           [ True,  True, False],
           [False,  True, False]], dtype=bool)
    >>> np.where(ix)
    (array([1, 1, 2]), array([0, 1, 1]))

    Zlexsorta�	
    lexsort(keys, axis=-1)

    Perform an indirect sort using a sequence of keys.

    Given multiple sorting keys, which can be interpreted as columns in a
    spreadsheet, lexsort returns an array of integer indices that describes
    the sort order by multiple columns. The last key in the sequence is used
    for the primary sort order, the second-to-last key for the secondary sort
    order, and so on. The keys argument must be a sequence of objects that
    can be converted to arrays of the same shape. If a 2D array is provided
    for the keys argument, it's rows are interpreted as the sorting keys and
    sorting is according to the last row, second last row etc.

    Parameters
    ----------
    keys : (k, N) array or tuple containing k (N,)-shaped sequences
        The `k` different "columns" to be sorted.  The last column (or row if
        `keys` is a 2D array) is the primary sort key.
    axis : int, optional
        Axis to be indirectly sorted.  By default, sort over the last axis.

    Returns
    -------
    indices : (N,) ndarray of ints
        Array of indices that sort the keys along the specified axis.

    See Also
    --------
    argsort : Indirect sort.
    ndarray.sort : In-place sort.
    sort : Return a sorted copy of an array.

    Examples
    --------
    Sort names: first by surname, then by name.

    >>> surnames =    ('Hertz',    'Galilei', 'Hertz')
    >>> first_names = ('Heinrich', 'Galileo', 'Gustav')
    >>> ind = np.lexsort((first_names, surnames))
    >>> ind
    array([1, 2, 0])

    >>> [surnames[i] + ", " + first_names[i] for i in ind]
    ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']

    Sort two columns of numbers:

    >>> a = [1,5,1,4,3,4,4] # First column
    >>> b = [9,4,0,4,0,2,1] # Second column
    >>> ind = np.lexsort((b,a)) # Sort by a, then by b
    >>> print(ind)
    [2 0 4 6 5 3 1]

    >>> [(a[i],b[i]) for i in ind]
    [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]

    Note that sorting is first according to the elements of ``a``.
    Secondary sorting is according to the elements of ``b``.

    A normal ``argsort`` would have yielded:

    >>> [(a[i],b[i]) for i in np.argsort(a)]
    [(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)]

    Structured arrays are sorted lexically by ``argsort``:

    >>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)],
    ...              dtype=np.dtype([('x', int), ('y', int)]))

    >>> np.argsort(x) # or np.argsort(x, order=('x', 'y'))
    array([2, 0, 4, 6, 5, 3, 1])

    Zcan_casta�

    can_cast(from, totype, casting = 'safe')

    Returns True if cast between data types can occur according to the
    casting rule.  If from is a scalar or array scalar, also returns
    True if the scalar value can be cast without overflow or truncation
    to an integer.

    Parameters
    ----------
    from : dtype, dtype specifier, scalar, or array
        Data type, scalar, or array to cast from.
    totype : dtype or dtype specifier
        Data type to cast to.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur.

          * '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.

    Returns
    -------
    out : bool
        True if cast can occur according to the casting rule.

    Notes
    -----
    Starting in NumPy 1.9, can_cast function now returns False in 'safe'
    casting mode for integer/float dtype and string dtype if the string dtype
    length is not long enough to store the max integer/float value converted
    to a string. Previously can_cast in 'safe' mode returned True for
    integer/float dtype and a string dtype of any length.

    See also
    --------
    dtype, result_type

    Examples
    --------
    Basic examples

    >>> np.can_cast(np.int32, np.int64)
    True
    >>> np.can_cast(np.float64, np.complex)
    True
    >>> np.can_cast(np.complex, np.float)
    False

    >>> np.can_cast('i8', 'f8')
    True
    >>> np.can_cast('i8', 'f4')
    False
    >>> np.can_cast('i4', 'S4')
    False

    Casting scalars

    >>> np.can_cast(100, 'i1')
    True
    >>> np.can_cast(150, 'i1')
    False
    >>> np.can_cast(150, 'u1')
    True

    >>> np.can_cast(3.5e100, np.float32)
    False
    >>> np.can_cast(1000.0, np.float32)
    True

    Array scalar checks the value, array does not

    >>> np.can_cast(np.array(1000.0), np.float32)
    True
    >>> np.can_cast(np.array([1000.0]), np.float32)
    False

    Using the casting rules

    >>> np.can_cast('i8', 'i8', 'no')
    True
    >>> np.can_cast('<i8', '>i8', 'no')
    False

    >>> np.can_cast('<i8', '>i8', 'equiv')
    True
    >>> np.can_cast('<i4', '>i8', 'equiv')
    False

    >>> np.can_cast('<i4', '>i8', 'safe')
    True
    >>> np.can_cast('<i8', '>i4', 'safe')
    False

    >>> np.can_cast('<i8', '>i4', 'same_kind')
    True
    >>> np.can_cast('<i8', '>u4', 'same_kind')
    False

    >>> np.can_cast('<i8', '>u4', 'unsafe')
    True

    Z
promote_typesa�
    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 and 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')

    Zmin_scalar_typea�
    min_scalar_type(a)

    For scalar ``a``, returns the data type with the smallest size
    and smallest scalar kind which can hold its value.  For non-scalar
    array ``a``, returns the vector's dtype unmodified.

    Floating point values are not demoted to integers,
    and complex values are not demoted to floats.

    Parameters
    ----------
    a : scalar or array_like
        The value whose minimal data type is to be found.

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

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

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

    Examples
    --------
    >>> np.min_scalar_type(10)
    dtype('uint8')

    >>> np.min_scalar_type(-260)
    dtype('int16')

    >>> np.min_scalar_type(3.1)
    dtype('float16')

    >>> np.min_scalar_type(1e50)
    dtype('float64')

    >>> np.min_scalar_type(np.arange(4,dtype='f8'))
    dtype('float64')

    Zresult_typea�
    result_type(*arrays_and_dtypes)

    Returns the type that results from applying the NumPy
    type promotion rules to the arguments.

    Type promotion in NumPy works similarly to the rules in languages
    like C++, with some slight differences.  When both scalars and
    arrays are used, the array's type takes precedence and the actual value
    of the scalar is taken into account.

    For example, calculating 3*a, where a is an array of 32-bit floats,
    intuitively should result in a 32-bit float output.  If the 3 is a
    32-bit integer, the NumPy rules indicate it can't convert losslessly
    into a 32-bit float, so a 64-bit float should be the result type.
    By examining the value of the constant, '3', we see that it fits in
    an 8-bit integer, which can be cast losslessly into the 32-bit float.

    Parameters
    ----------
    arrays_and_dtypes : list of arrays and dtypes
        The operands of some operation whose result type is needed.

    Returns
    -------
    out : dtype
        The result type.

    See also
    --------
    dtype, promote_types, min_scalar_type, can_cast

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

    The specific algorithm used is as follows.

    Categories are determined by first checking which of boolean,
    integer (int/uint), or floating point (float/complex) the maximum
    kind of all the arrays and the scalars are.

    If there are only scalars or the maximum category of the scalars
    is higher than the maximum category of the arrays,
    the data types are combined with :func:`promote_types`
    to produce the return value.

    Otherwise, `min_scalar_type` is called on each array, and
    the resulting data types are all combined with :func:`promote_types`
    to produce the return value.

    The set of int values is not a subset of the uint values for types
    with the same number of bits, something not reflected in
    :func:`min_scalar_type`, but handled as a special case in `result_type`.

    Examples
    --------
    >>> np.result_type(3, np.arange(7, dtype='i1'))
    dtype('int8')

    >>> np.result_type('i4', 'c8')
    dtype('complex128')

    >>> np.result_type(3.0, -2)
    dtype('float64')

    Z	newbuffera
    newbuffer(size)

    Return a new uninitialized buffer object.

    Parameters
    ----------
    size : int
        Size in bytes of returned buffer object.

    Returns
    -------
    newbuffer : buffer object
        Returned, uninitialized buffer object of `size` bytes.

    �	getbufferaa
    getbuffer(obj [,offset[, size]])

    Create a buffer object from the given object referencing a slice of
    length size starting at offset.

    Default is the entire buffer. A read-write buffer is attempted followed
    by a read-only buffer.

    Parameters
    ----------
    obj : object

    offset : int, optional

    size : int, optional

    Returns
    -------
    buffer_obj : buffer

    Examples
    --------
    >>> buf = np.getbuffer(np.ones(5), 1, 3)
    >>> len(buf)
    3
    >>> buf[0]
    '\x00'
    >>> buf
    <read-write buffer for 0x8af1e70, size 3, offset 1 at 0x8ba4ec0>

    �dota
    dot(a, b, out=None)

    Dot product of two arrays.

    For 2-D arrays it is equivalent to matrix multiplication, and for 1-D
    arrays to inner product of vectors (without complex conjugation). For
    N dimensions it is a sum product over the last axis of `a` and
    the second-to-last of `b`::

        dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

    Parameters
    ----------
    a : array_like
        First argument.
    b : array_like
        Second argument.
    out : ndarray, optional
        Output argument. This must have the exact kind that would be returned
        if it was not used. In particular, it must have the right type, must be
        C-contiguous, and its dtype must be the dtype that would be returned
        for `dot(a,b)`. This is a performance feature. Therefore, if these
        conditions are not met, an exception is raised, instead of attempting
        to be flexible.

    Returns
    -------
    output : ndarray
        Returns the dot product of `a` and `b`.  If `a` and `b` are both
        scalars or both 1-D arrays then a scalar is returned; otherwise
        an array is returned.
        If `out` is given, then it is returned.

    Raises
    ------
    ValueError
        If the last dimension of `a` is not the same size as
        the second-to-last dimension of `b`.

    See Also
    --------
    vdot : Complex-conjugating dot product.
    tensordot : Sum products over arbitrary axes.
    einsum : Einstein summation convention.
    matmul : '@' operator as method with out parameter.

    Examples
    --------
    >>> np.dot(3, 4)
    12

    Neither argument is complex-conjugated:

    >>> np.dot([2j, 3j], [2j, 3j])
    (-13+0j)

    For 2-D arrays it is the matrix product:

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

    >>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
    >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
    >>> np.dot(a, b)[2,3,2,1,2,2]
    499128
    >>> sum(a[2,3,2,:] * b[1,2,:,2])
    499128

    �matmulap
    matmul(a, b, out=None)

    Matrix product of two arrays.

    The behavior depends on the arguments in the following way.

    - If both arguments are 2-D they are multiplied like conventional
      matrices.
    - If either argument is N-D, N > 2, it is treated as a stack of
      matrices residing in the last two indexes and broadcast accordingly.
    - If the first argument is 1-D, it is promoted to a matrix by
      prepending a 1 to its dimensions. After matrix multiplication
      the prepended 1 is removed.
    - If the second argument is 1-D, it is promoted to a matrix by
      appending a 1 to its dimensions. After matrix multiplication
      the appended 1 is removed.

    Multiplication by a scalar is not allowed, use ``*`` instead. Note that
    multiplying a stack of matrices with a vector will result in a stack of
    vectors, but matmul will not recognize it as such.

    ``matmul`` differs from ``dot`` in two important ways.

    - Multiplication by scalars is not allowed.
    - Stacks of matrices are broadcast together as if the matrices
      were elements.

    .. warning::
       This function is preliminary and included in NumPy 1.10.0 for testing
       and documentation. Its semantics will not change, but the number and
       order of the optional arguments will.

    .. versionadded:: 1.10.0

    Parameters
    ----------
    a : array_like
        First argument.
    b : array_like
        Second argument.
    out : ndarray, optional
        Output argument. This must have the exact kind that would be returned
        if it was not used. In particular, it must have the right type, must be
        C-contiguous, and its dtype must be the dtype that would be returned
        for `dot(a,b)`. This is a performance feature. Therefore, if these
        conditions are not met, an exception is raised, instead of attempting
        to be flexible.

    Returns
    -------
    output : ndarray
        Returns the dot product of `a` and `b`.  If `a` and `b` are both
        1-D arrays then a scalar is returned; otherwise an array is
        returned.  If `out` is given, then it is returned.

    Raises
    ------
    ValueError
        If the last dimension of `a` is not the same size as
        the second-to-last dimension of `b`.

        If scalar value is passed.

    See Also
    --------
    vdot : Complex-conjugating dot product.
    tensordot : Sum products over arbitrary axes.
    einsum : Einstein summation convention.
    dot : alternative matrix product with different broadcasting rules.

    Notes
    -----
    The matmul function implements the semantics of the `@` operator introduced
    in Python 3.5 following PEP465.

    Examples
    --------
    For 2-D arrays it is the matrix product:

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

    For 2-D mixed with 1-D, the result is the usual.

    >>> a = [[1, 0], [0, 1]]
    >>> b = [1, 2]
    >>> np.matmul(a, b)
    array([1, 2])
    >>> np.matmul(b, a)
    array([1, 2])


    Broadcasting is conventional for stacks of arrays

    >>> a = np.arange(2*2*4).reshape((2,2,4))
    >>> b = np.arange(2*2*4).reshape((2,4,2))
    >>> np.matmul(a,b).shape
    (2, 2, 2)
    >>> np.matmul(a,b)[0,1,1]
    98
    >>> sum(a[0,1,:] * b[0,:,1])
    98

    Vector, vector returns the scalar inner product, but neither argument
    is complex-conjugated:

    >>> np.matmul([2j, 3j], [2j, 3j])
    (-13+0j)

    Scalar multiplication raises an error.

    >>> np.matmul([1,2], 3)
    Traceback (most recent call last):
    ...
    ValueError: Scalar operands are not allowed, use '*' instead

    Zc_einsuma
    c_einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe')

    Evaluates the Einstein summation convention on the operands.

    Using the Einstein summation convention, many common multi-dimensional
    array operations can be represented in a simple fashion.  This function
    provides a way to compute such summations. The best way to understand this
    function is to try the examples below, which show how many common NumPy
    functions can be implemented as calls to `einsum`.

    This is the core C function.

    Parameters
    ----------
    subscripts : str
        Specifies the subscripts for summation.
    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.

          * '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.

        Default is 'safe'.

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

    See Also
    --------
    einsum, dot, inner, outer, tensordot

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

    The subscripts string is a comma-separated list of subscript labels,
    where each label refers to a dimension of the corresponding operand.
    Repeated subscripts labels in one operand take the diagonal.  For example,
    ``np.einsum('ii', a)`` is equivalent to ``np.trace(a)``.

    Whenever a label is repeated, it is summed, so ``np.einsum('i,i', a, b)``
    is equivalent to ``np.inner(a,b)``.  If a label appears only once,
    it is not summed, so ``np.einsum('i', a)`` produces a view of ``a``
    with no changes.

    The order of labels in the output is by default alphabetical.  This
    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
    ``np.einsum('ji', a)`` takes its transpose.

    The output can be controlled by specifying output subscript labels
    as well.  This specifies the label order, and allows summing to
    be disallowed or forced when desired.  The call ``np.einsum('i->', a)``
    is like ``np.sum(a, axis=-1)``, and ``np.einsum('ii->i', a)``
    is like ``np.diag(a)``.  The difference is that `einsum` does not
    allow broadcasting by default.

    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, you 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.

    An alternative way to provide the subscripts and operands is as
    ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. 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 ``np.swapaxes(a, 0, 2)`` 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)

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

    >>> 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])

    >>> 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])

    >>> np.einsum('ji', c)
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.einsum(c, [1,0])
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> c.T
    array([[0, 3],
           [1, 4],
           [2, 5]])

    >>> np.einsum('..., ...', 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]])

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

    >>> 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]])

    >>> np.einsum('i...->...', a)
    array([50, 55, 60, 65, 70])
    >>> np.einsum(a, [0,Ellipsis], [Ellipsis])
    array([50, 55, 60, 65, 70])
    >>> np.sum(a, axis=0)
    array([50, 55, 60, 65, 70])

    >>> 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.]])

    >>> 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]])

    >>> # 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.]])

    Zvdota�
    vdot(a, b)

    Return the dot product of two vectors.

    The vdot(`a`, `b`) function handles complex numbers differently than
    dot(`a`, `b`).  If the first argument is complex the complex conjugate
    of the first argument is used for the calculation of the dot product.

    Note that `vdot` handles multidimensional arrays differently than `dot`:
    it does *not* perform a matrix product, but flattens input arguments
    to 1-D vectors first. Consequently, it should only be used for vectors.

    Parameters
    ----------
    a : array_like
        If `a` is complex the complex conjugate is taken before calculation
        of the dot product.
    b : array_like
        Second argument to the dot product.

    Returns
    -------
    output : ndarray
        Dot product of `a` and `b`.  Can be an int, float, or
        complex depending on the types of `a` and `b`.

    See Also
    --------
    dot : Return the dot product without using the complex conjugate of the
          first argument.

    Examples
    --------
    >>> a = np.array([1+2j,3+4j])
    >>> b = np.array([5+6j,7+8j])
    >>> np.vdot(a, b)
    (70-8j)
    >>> np.vdot(b, a)
    (70+8j)

    Note that higher-dimensional arrays are flattened!

    >>> a = np.array([[1, 4], [5, 6]])
    >>> b = np.array([[4, 1], [2, 2]])
    >>> np.vdot(a, b)
    30
    >>> np.vdot(b, a)
    30
    >>> 1*4 + 4*1 + 5*2 + 6*2
    30

    Zndarraya�
    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([[ -1.13698227e+002,   4.25087011e-303],
           [  2.88528414e-306,   3.27025015e-309]])         #random

    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])

    �__array_interface__�Array protocol: Python side.�__array_finalize__�None.�__array_priority__�Array priority.�__array_struct__�Array protocol: C-struct side.�_as_parameter_�rAllow the array to be interpreted as a ctypes object by returning the
    data-memory location as an integer

    �:
    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

    �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):

    * data: A pointer to the memory area of the array as a Python integer.
      This memory area may contain data that is not aligned, or not in correct
      byte-order. The memory area may not even be writeable. The array
      flags and data-type of this array should be respected when passing this
      attribute to arbitrary C-code to avoid trouble that can include Python
      crashing. User Beware! The value of this attribute is exactly the same
      as self._array_interface_['data'][0].

    * shape (c_intp*self.ndim): A ctypes array of length self.ndim where
      the basetype is the C-integer corresponding to dtype('p') on this
      platform. This base-type could be c_int, c_long, or c_longlong
      depending on the platform. The c_intp type is defined accordingly in
      numpy.ctypeslib. The ctypes array contains the shape of the underlying
      array.

    * strides (c_intp*self.ndim): A ctypes array of length self.ndim where
      the basetype is the same as for the shape attribute. This ctypes array
      contains the strides information from the underlying array. This strides
      information is important for showing how many bytes must be jumped to
      get to the next element in the array.

    * data_as(obj): Return the data pointer cast to a particular c-types object.
      For example, calling self._as_parameter_ is equivalent to
      self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a
      pointer to a ctypes array of floating-point data:
      self.data_as(ctypes.POINTER(ctypes.c_double)).

    * shape_as(obj): Return the shape tuple as an array of some other c-types
      type. For example: self.shape_as(ctypes.c_short).

    * strides_as(obj): Return the strides tuple as an array of some other
      c-types type. For example: self.strides_as(ctypes.c_longlong).

    Be careful using the ctypes attribute - especially on temporary
    arrays or arrays constructed on the fly. For example, calling
    ``(a+b).ctypes.data_as(ctypes.c_void_p)`` returns a pointer to memory
    that is invalid because the array created as (a+b) is deallocated
    before the next Python statement. You can avoid this problem using
    either ``c=a+b`` or ``ct=(a+b).ctypes``. In the latter case, ct will
    hold a reference to the array until ct is deleted or re-assigned.

    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
    array([[0, 1],
           [2, 3]])
    >>> x.ctypes.data
    30439712
    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long))
    <ctypes.LP_c_long object at 0x01F01300>
    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)).contents
    c_long(0)
    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_longlong)).contents
    c_longlong(4294967296L)
    >>> x.ctypes.shape
    <numpy.core._internal.c_long_Array_2 object at 0x01FFD580>
    >>> x.ctypes.shape_as(ctypes.c_long)
    <numpy.core._internal.c_long_Array_2 object at 0x01FCE620>
    >>> x.ctypes.strides
    <numpy.core._internal.c_long_Array_2 object at 0x01FCE620>
    >>> x.ctypes.strides_as(ctypes.c_longlong)
    <numpy.core._internal.c_longlong_Array_2 object at 0x01F01300>

    �data�?Python buffer object pointing to the start of the array's data.�dtype�R
    Data-type of the array's elements.

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

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

    See Also
    --------
    numpy.dtype

    Examples
    --------
    >>> x
    array([[0, 1],
           [2, 3]])
    >>> x.dtype
    dtype('int32')
    >>> type(x.dtype)
    <type 'numpy.dtype'>

    �imag��
    The imaginary part of the array.

    Examples
    --------
    >>> x = np.sqrt([1+0j, 0+1j])
    >>> x.imag
    array([ 0.        ,  0.70710678])
    >>> x.imag.dtype
    dtype('float64')

    �itemsize��
    Length of one array element in bytes.

    Examples
    --------
    >>> x = np.array([1,2,3], dtype=np.float64)
    >>> x.itemsize
    8
    >>> x = np.array([1,2,3], dtype=np.complex128)
    >>> x.itemsize
    16

    �flags�
    Information about the memory layout of the array.

    Attributes
    ----------
    C_CONTIGUOUS (C)
        The data is in a single, C-style contiguous segment.
    F_CONTIGUOUS (F)
        The data is in a single, Fortran-style contiguous segment.
    OWNDATA (O)
        The array owns the memory it uses or borrows it from another object.
    WRITEABLE (W)
        The data area can be written to.  Setting this to False locks
        the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
        from its base array at creation time, but a view of a writeable
        array may be subsequently locked while the base array remains writeable.
        (The opposite is not true, in that a view of a locked array may not
        be made writeable.  However, currently, locking a base object does not
        lock any views that already reference it, so under that circumstance it
        is possible to alter the contents of a locked array via a previously
        created writeable view onto it.)  Attempting to change a non-writeable
        array raises a RuntimeError exception.
    ALIGNED (A)
        The data and all elements are aligned appropriately for the hardware.
    UPDATEIFCOPY (U)
        This array is a copy of some other array. When this array is
        deallocated, the base array will be updated with the contents of
        this array.
    FNC
        F_CONTIGUOUS and not C_CONTIGUOUS.
    FORC
        F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
    BEHAVED (B)
        ALIGNED and WRITEABLE.
    CARRAY (CA)
        BEHAVED and C_CONTIGUOUS.
    FARRAY (FA)
        BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.

    Notes
    -----
    The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
    or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
    names are only supported in dictionary access.

    Only the UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be changed by
    the user, via direct assignment to the attribute or dictionary entry,
    or by calling `ndarray.setflags`.

    The array flags cannot be set arbitrarily:

    - UPDATEIFCOPY can only be set ``False``.
    - ALIGNED can only be set ``True`` if the data is truly aligned.
    - WRITEABLE can only be set ``True`` if the array owns its own memory
      or the ultimate owner of the memory exposes a writeable buffer
      interface or is a string.

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

    Even for contiguous arrays a stride for a given dimension
    ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
    or the array has no elements.
    It does *not* generally hold that ``self.strides[-1] == self.itemsize``
    for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
    Fortran-style contiguous arrays is true.
    �flat��
    A 1-D iterator over the array.

    This is a `numpy.flatiter` instance, which acts similarly to, but is not
    a subclass of, Python's built-in iterator object.

    See Also
    --------
    flatten : Return a copy of the array collapsed into one dimension.

    flatiter

    Examples
    --------
    >>> x = np.arange(1, 7).reshape(2, 3)
    >>> x
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> x.flat[3]
    4
    >>> x.T
    array([[1, 4],
           [2, 5],
           [3, 6]])
    >>> x.T.flat[3]
    5
    >>> type(x.flat)
    <type 'numpy.flatiter'>

    An assignment example:

    >>> x.flat = 3; x
    array([[3, 3, 3],
           [3, 3, 3]])
    >>> x.flat[[1,4]] = 1; x
    array([[3, 1, 3],
           [3, 1, 3]])

    �nbytes�?
    Total bytes consumed by the elements of the array.

    Notes
    -----
    Does not include memory consumed by non-element attributes of the
    array object.

    Examples
    --------
    >>> x = np.zeros((3,5,2), dtype=np.complex128)
    >>> x.nbytes
    480
    >>> np.prod(x.shape) * x.itemsize
    480

    ��
    Number of array dimensions.

    Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> x.ndim
    1
    >>> y = np.zeros((2, 3, 4))
    >>> y.ndim
    3

    �real�
    The real part of the array.

    Examples
    --------
    >>> x = np.sqrt([1+0j, 0+1j])
    >>> x.real
    array([ 1.        ,  0.70710678])
    >>> x.real.dtype
    dtype('float64')

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

    �
    Tuple of array dimensions.

    Notes
    -----
    May be used to "reshape" the array, as long as this would not
    require a change in the total number of elements

    Examples
    --------
    >>> x = np.array([1, 2, 3, 4])
    >>> x.shape
    (4,)
    >>> y = np.zeros((2, 3, 4))
    >>> y.shape
    (2, 3, 4)
    >>> y.shape = (3, 8)
    >>> y
    array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
    >>> y.shape = (3, 6)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: total size of new array must be unchanged

    �
    Number of elements in the array.

    Equivalent to ``np.prod(a.shape)``, i.e., the product of the array's
    dimensions.

    Examples
    --------
    >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
    >>> x.size
    30
    >>> np.prod(x.shape)
    30

    �strides�
    Tuple of bytes to step in each dimension when traversing an array.

    The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
    is::

        offset = sum(np.array(i) * a.strides)

    A more detailed explanation of strides can be found in the
    "ndarray.rst" file in the NumPy reference guide.

    Notes
    -----
    Imagine an array of 32-bit integers (each 4 bytes)::

      x = np.array([[0, 1, 2, 3, 4],
                    [5, 6, 7, 8, 9]], dtype=np.int32)

    This array is stored in memory as 40 bytes, one after the other
    (known as a contiguous block of memory).  The strides of an array tell
    us how many bytes we have to skip in memory to move to the next position
    along a certain axis.  For example, we have to skip 4 bytes (1 value) to
    move to the next column, but 20 bytes (5 values) to get to the same
    position in the next row.  As such, the strides for the array `x` will be
    ``(20, 4)``.

    See Also
    --------
    numpy.lib.stride_tricks.as_strided

    Examples
    --------
    >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
    >>> y
    array([[[ 0,  1,  2,  3],
            [ 4,  5,  6,  7],
            [ 8,  9, 10, 11]],
           [[12, 13, 14, 15],
            [16, 17, 18, 19],
            [20, 21, 22, 23]]])
    >>> y.strides
    (48, 16, 4)
    >>> y[1,1,1]
    17
    >>> offset=sum(y.strides * np.array((1,1,1)))
    >>> offset/y.itemsize
    17

    >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
    >>> x.strides
    (32, 4, 224, 1344)
    >>> i = np.array([3,5,2,2])
    >>> offset = sum(i * x.strides)
    >>> x[3,5,2,2]
    813
    >>> offset / x.itemsize
    813

    �T�
    Same as self.transpose(), except that self is returned if
    self.ndim < 2.

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

    �� a.__array__(|dtype) -> reference if type unchanged, copy otherwise.

    Returns either a new reference to self if dtype is not given or a new array
    of provided data type if dtype is different from the current dtype of the
    array.

    �__array_prepare__�La.__array_prepare__(obj) -> Object of same type as ndarray object obj.

    �__array_wrap__�Ga.__array_wrap__(obj) -> Object of same type as ndarray object a.

    �__copy__�a.__copy__([order])

    Return a copy of the array.

    Parameters
    ----------
    order : {'C', 'F', 'A'}, optional
        If order is 'C' (False) then the result is contiguous (default).
        If order is 'Fortran' (True) then the result has fortran order.
        If order is 'Any' (None) then the result has fortran order
        only if the array already is in fortran order.

    �__deepcopy__�_a.__deepcopy__() -> Deep copy of array.

    Used if copy.deepcopy is called on an array.

    �
__reduce__�'a.__reduce__()

    For pickling.

    �__setstate__�fa.__setstate__(version, shape, dtype, isfortran, rawdata)

    For unpickling.

    Parameters
    ----------
    version : int
        optional pickle version. If omitted defaults to 0.
    shape : tuple
    dtype : data-type
    isFortran : bool
    rawdata : string or list
        a binary string with the data (or a list if 'a' is an object array)

    �all��
    a.all(axis=None, out=None, keepdims=False)

    Returns True if all elements evaluate to True.

    Refer to `numpy.all` for full documentation.

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

    �any��
    a.any(axis=None, out=None, keepdims=False)

    Returns True if any of the elements of `a` evaluate to True.

    Refer to `numpy.any` for full documentation.

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

    �argmax��
    a.argmax(axis=None, out=None)

    Return indices of the maximum values along the given axis.

    Refer to `numpy.argmax` for full documentation.

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

    �argmin��
    a.argmin(axis=None, out=None)

    Return indices of the minimum values along the given axis of `a`.

    Refer to `numpy.argmin` for detailed documentation.

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

    �argsort��
    a.argsort(axis=-1, kind='quicksort', order=None)

    Returns the indices that would sort this array.

    Refer to `numpy.argsort` for full documentation.

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

    �argpartition�!
    a.argpartition(kth, axis=-1, kind='introselect', order=None)

    Returns the indices that would partition this array.

    Refer to `numpy.argpartition` for full documentation.

    .. versionadded:: 1.8.0

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

    �astype��	
    a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)

    Copy of the array, cast to a specified type.

    Parameters
    ----------
    dtype : str or dtype
        Typecode or data-type to which the array is cast.
    order : {'C', 'F', 'A', 'K'}, optional
        Controls the memory layout order of the result.
        '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.
        Default is 'K'.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur. Defaults to 'unsafe'
        for backwards compatibility.

          * '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.
    subok : bool, optional
        If True, then sub-classes will be passed-through (default), otherwise
        the returned array will be forced to be a base-class array.
    copy : bool, optional
        By default, astype always returns a newly allocated array. If this
        is set to false, and the `dtype`, `order`, and `subok`
        requirements are satisfied, the input array is returned instead
        of a copy.

    Returns
    -------
    arr_t : ndarray
        Unless `copy` is False and the other conditions for returning the input
        array are satisfied (see description for `copy` input parameter), `arr_t`
        is a new array of the same shape as the input array, with dtype, order
        given by `dtype`, `order`.

    Notes
    -----
    Starting in NumPy 1.9, astype method now returns an error if the string
    dtype to cast to is not long enough in 'safe' casting mode to hold the max
    value of integer/float array that is being casted. Previously the casting
    was allowed even if the result was truncated.

    Raises
    ------
    ComplexWarning
        When casting from complex to float or int. To avoid this,
        one should use ``a.real.astype(t)``.

    Examples
    --------
    >>> x = np.array([1, 2, 2.5])
    >>> x
    array([ 1. ,  2. ,  2.5])

    >>> x.astype(int)
    array([1, 2, 2])

    �byteswap�]
    a.byteswap(inplace)

    Swap the bytes of the array elements

    Toggle between low-endian and big-endian data representation by
    returning a byteswapped array, optionally swapped in-place.

    Parameters
    ----------
    inplace : bool, optional
        If ``True``, swap bytes in-place, default is ``False``.

    Returns
    -------
    out : ndarray
        The byteswapped array. If `inplace` is ``True``, this is
        a view to self.

    Examples
    --------
    >>> A = np.array([1, 256, 8755], dtype=np.int16)
    >>> map(hex, A)
    ['0x1', '0x100', '0x2233']
    >>> A.byteswap(True)
    array([  256,     1, 13090], dtype=int16)
    >>> map(hex, A)
    ['0x100', '0x1', '0x3322']

    Arrays of strings are not swapped

    >>> A = np.array(['ceg', 'fac'])
    >>> A.byteswap()
    array(['ceg', 'fac'],
          dtype='|S3')

    �choose��
    a.choose(choices, out=None, mode='raise')

    Use an index array to construct a new array from a set of choices.

    Refer to `numpy.choose` for full documentation.

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

    �clip�
    a.clip(min=None, max=None, out=None)

    Return an array whose values are limited to ``[min, max]``.
    One of max or min must be given.

    Refer to `numpy.clip` for full documentation.

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

    �compress��
    a.compress(condition, axis=None, out=None)

    Return selected slices of this array along given axis.

    Refer to `numpy.compress` for full documentation.

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

    �conj��
    a.conj()

    Complex-conjugate all elements.

    Refer to `numpy.conjugate` for full documentation.

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

    �	conjugate��
    a.conjugate()

    Return the complex conjugate, element-wise.

    Refer to `numpy.conjugate` for full documentation.

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

    �E
    a.copy(order='C')

    Return a copy of the array.

    Parameters
    ----------
    order : {'C', 'F', 'A', 'K'}, optional
        Controls the memory layout of the copy. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
        'C' otherwise. 'K' means match the layout of `a` as closely
        as possible. (Note that this function and :func:numpy.copy are very
        similar, but have different default values for their order=
        arguments.)

    See also
    --------
    numpy.copy
    numpy.copyto

    Examples
    --------
    >>> x = np.array([[1,2,3],[4,5,6]], order='F')

    >>> y = x.copy()

    >>> x.fill(0)

    >>> x
    array([[0, 0, 0],
           [0, 0, 0]])

    >>> y
    array([[1, 2, 3],
           [4, 5, 6]])

    >>> y.flags['C_CONTIGUOUS']
    True

    �cumprod��
    a.cumprod(axis=None, dtype=None, out=None)

    Return the cumulative product of the elements along the given axis.

    Refer to `numpy.cumprod` for full documentation.

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

    �cumsum��
    a.cumsum(axis=None, dtype=None, out=None)

    Return the cumulative sum of the elements along the given axis.

    Refer to `numpy.cumsum` for full documentation.

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

    �diagonal�
    a.diagonal(offset=0, axis1=0, axis2=1)

    Return specified diagonals. In NumPy 1.9 the returned array is a
    read-only view instead of a copy as in previous NumPy versions.  In
    a future version the read-only restriction will be removed.

    Refer to :func:`numpy.diagonal` for full documentation.

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

    �
    a.dot(b, out=None)

    Dot product of two arrays.

    Refer to `numpy.dot` for full documentation.

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

    Examples
    --------
    >>> a = np.eye(2)
    >>> b = np.ones((2, 2)) * 2
    >>> a.dot(b)
    array([[ 2.,  2.],
           [ 2.,  2.]])

    This array method can be conveniently chained:

    >>> a.dot(b).dot(b)
    array([[ 8.,  8.],
           [ 8.,  8.]])

    �dump��a.dump(file)

    Dump a pickle of the array to the specified file.
    The array can be read back with pickle.load or numpy.load.

    Parameters
    ----------
    file : str
        A string naming the dump file.

    �dumps��
    a.dumps()

    Returns the pickle of the array as a string.
    pickle.loads or numpy.loads will convert the string back to an array.

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

    �fill�\
    a.fill(value)

    Fill the array with a scalar value.

    Parameters
    ----------
    value : scalar
        All elements of `a` will be assigned this value.

    Examples
    --------
    >>> a = np.array([1, 2])
    >>> a.fill(0)
    >>> a
    array([0, 0])
    >>> a = np.empty(2)
    >>> a.fill(1)
    >>> a
    array([ 1.,  1.])

    �flatten�
    a.flatten(order='C')

    Return a copy of the array collapsed into one dimension.

    Parameters
    ----------
    order : {'C', 'F', 'A', 'K'}, optional
        'C' means to flatten in row-major (C-style) order.
        'F' means to flatten in column-major (Fortran-
        style) order. 'A' means to flatten in column-major
        order if `a` is Fortran *contiguous* in memory,
        row-major order otherwise. 'K' means to flatten
        `a` in the order the elements occur in memory.
        The default is 'C'.

    Returns
    -------
    y : ndarray
        A copy of the input array, flattened to one dimension.

    See Also
    --------
    ravel : Return a flattened array.
    flat : A 1-D flat iterator over the array.

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

    �getfield�
    a.getfield(dtype, offset=0)

    Returns a field of the given array as a certain type.

    A field is a view of the array data with a given data-type. The values in
    the view are determined by the given type and the offset into the current
    array in bytes. The offset needs to be such that the view dtype fits in the
    array dtype; for example an array of dtype complex128 has 16-byte elements.
    If taking a view with a 32-bit integer (4 bytes), the offset needs to be
    between 0 and 12 bytes.

    Parameters
    ----------
    dtype : str or dtype
        The data type of the view. The dtype size of the view can not be larger
        than that of the array itself.
    offset : int
        Number of bytes to skip before beginning the element view.

    Examples
    --------
    >>> x = np.diag([1.+1.j]*2)
    >>> x[1, 1] = 2 + 4.j
    >>> x
    array([[ 1.+1.j,  0.+0.j],
           [ 0.+0.j,  2.+4.j]])
    >>> x.getfield(np.float64)
    array([[ 1.,  0.],
           [ 0.,  2.]])

    By choosing an offset of 8 bytes we can select the complex part of the
    array for our view:

    >>> x.getfield(np.float64, offset=8)
    array([[ 1.,  0.],
       [ 0.,  4.]])

    �item�
    a.item(*args)

    Copy an element of an array to a standard Python scalar and return it.

    Parameters
    ----------
    \*args : Arguments (variable number and type)

        * none: in this case, the method only works for arrays
          with one element (`a.size == 1`), which element is
          copied into a standard Python scalar object and returned.

        * int_type: this argument is interpreted as a flat index into
          the array, specifying which element to copy and return.

        * tuple of int_types: functions as does a single int_type argument,
          except that the argument is interpreted as an nd-index into the
          array.

    Returns
    -------
    z : Standard Python scalar object
        A copy of the specified element of the array as a suitable
        Python scalar

    Notes
    -----
    When the data type of `a` is longdouble or clongdouble, item() returns
    a scalar array object because there is no available Python scalar that
    would not lose information. Void arrays return a buffer object for item(),
    unless fields are defined, in which case a tuple is returned.

    `item` is very similar to a[args], except, instead of an array scalar,
    a standard Python scalar is returned. This can be useful for speeding up
    access to elements of the array and doing arithmetic on elements of the
    array using Python's optimized math.

    Examples
    --------
    >>> x = np.random.randint(9, size=(3, 3))
    >>> x
    array([[3, 1, 7],
           [2, 8, 3],
           [8, 5, 3]])
    >>> x.item(3)
    2
    >>> x.item(7)
    5
    >>> x.item((0, 1))
    1
    >>> x.item((2, 2))
    3

    �itemset�
    a.itemset(*args)

    Insert scalar into an array (scalar is cast to array's dtype, if possible)

    There must be at least 1 argument, and define the last argument
    as *item*.  Then, ``a.itemset(*args)`` is equivalent to but faster
    than ``a[args] = item``.  The item should be a scalar value and `args`
    must select a single item in the array `a`.

    Parameters
    ----------
    \*args : Arguments
        If one argument: a scalar, only used in case `a` is of size 1.
        If two arguments: the last argument is the value to be set
        and must be a scalar, the first argument specifies a single array
        element location. It is either an int or a tuple.

    Notes
    -----
    Compared to indexing syntax, `itemset` provides some speed increase
    for placing a scalar into a particular location in an `ndarray`,
    if you must do this.  However, generally this is discouraged:
    among other problems, it complicates the appearance of the code.
    Also, when using `itemset` (and `item`) inside a loop, be sure
    to assign the methods to a local variable to avoid the attribute
    look-up at each loop iteration.

    Examples
    --------
    >>> x = np.random.randint(9, size=(3, 3))
    >>> x
    array([[3, 1, 7],
           [2, 8, 3],
           [8, 5, 3]])
    >>> x.itemset(4, 0)
    >>> x.itemset((2, 2), 9)
    >>> x
    array([[3, 1, 7],
           [2, 0, 3],
           [8, 5, 9]])

    �max��
    a.max(axis=None, out=None)

    Return the maximum along a given axis.

    Refer to `numpy.amax` for full documentation.

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

    �mean��
    a.mean(axis=None, dtype=None, out=None, keepdims=False)

    Returns the average of the array elements along given axis.

    Refer to `numpy.mean` for full documentation.

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

    �min��
    a.min(axis=None, out=None, keepdims=False)

    Return the minimum along a given axis.

    Refer to `numpy.amin` for full documentation.

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

    Z
shares_memorya�
    shares_memory(a, b, max_work=None)

    Determine if two arrays share memory

    Parameters
    ----------
    a, b : ndarray
        Input arrays
    max_work : int, optional
        Effort to spend on solving the overlap problem (maximum number
        of candidate solutions to consider). The following special
        values are recognized:

        max_work=MAY_SHARE_EXACT  (default)
            The problem is solved exactly. In this case, the function returns
            True only if there is an element shared between the arrays.
        max_work=MAY_SHARE_BOUNDS
            Only the memory bounds of a and b are checked.

    Raises
    ------
    numpy.TooHardError
        Exceeded max_work.

    Returns
    -------
    out : bool

    See Also
    --------
    may_share_memory

    Examples
    --------
    >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
    False

    Zmay_share_memorya1
    may_share_memory(a, b, max_work=None)

    Determine if two arrays might share memory

    A return of True does not necessarily mean that the two arrays
    share any element.  It just means that they *might*.

    Only the memory bounds of a and b are checked by default.

    Parameters
    ----------
    a, b : ndarray
        Input arrays
    max_work : int, optional
        Effort to spend on solving the overlap problem.  See
        `shares_memory` for details.  Default for ``may_share_memory``
        is to do a bounds check.

    Returns
    -------
    out : bool

    See Also
    --------
    shares_memory

    Examples
    --------
    >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
    False
    >>> x = np.zeros([3, 4])
    >>> np.may_share_memory(x[:,0], x[:,1])
    True

    �newbyteorder�O
    arr.newbyteorder(new_order='S')

    Return the array with the same data viewed with a different byte order.

    Equivalent to::

        arr.view(arr.dtype.newbytorder(new_order))

    Changes are also made in all fields and sub-arrays of the array data
    type.



    Parameters
    ----------
    new_order : string, optional
        Byte order to force; a value from the byte order specifications
        below. `new_order` codes can be any of:

        * 'S' - swap dtype from current to opposite endian
        * {'<', 'L'} - little endian
        * {'>', 'B'} - big endian
        * {'=', 'N'} - native order
        * {'|', 'I'} - ignore (no change to byte order)

        The default value ('S') results in swapping the current
        byte order. The code does a case-insensitive check on the first
        letter of `new_order` for the alternatives above.  For example,
        any of 'B' or 'b' or 'biggish' are valid to specify big-endian.


    Returns
    -------
    new_arr : array
        New array object with the dtype reflecting given change to the
        byte order.

    �nonzero��
    a.nonzero()

    Return the indices of the elements that are non-zero.

    Refer to `numpy.nonzero` for full documentation.

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

    �prod��
    a.prod(axis=None, dtype=None, out=None, keepdims=False)

    Return the product of the array elements over the given axis

    Refer to `numpy.prod` for full documentation.

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

    �ptp��
    a.ptp(axis=None, out=None)

    Peak to peak (maximum - minimum) value along a given axis.

    Refer to `numpy.ptp` for full documentation.

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

    �put��
    a.put(indices, values, mode='raise')

    Set ``a.flat[n] = values[n]`` for all `n` in indices.

    Refer to `numpy.put` for full documentation.

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

    Zcopytoa�
    copyto(dst, src, casting='same_kind', where=None)

    Copies values from one array to another, broadcasting as necessary.

    Raises a TypeError if the `casting` rule is violated, and if
    `where` is provided, it selects which elements to copy.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    dst : ndarray
        The array into which values are copied.
    src : array_like
        The array from which values are copied.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur when copying.

          * '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.
    where : array_like of bool, optional
        A boolean array which is broadcasted to match the dimensions
        of `dst`, and selects elements to copy from `src` to `dst`
        wherever it contains the value True.

    Zputmaska�
    putmask(a, mask, values)

    Changes elements of an array based on conditional and input values.

    Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``.

    If `values` is not the same size as `a` and `mask` then it will repeat.
    This gives behavior different from ``a[mask] = values``.

    Parameters
    ----------
    a : array_like
        Target array.
    mask : array_like
        Boolean mask array. It has to be the same shape as `a`.
    values : array_like
        Values to put into `a` where `mask` is True. If `values` is smaller
        than `a` it will be repeated.

    See Also
    --------
    place, put, take, copyto

    Examples
    --------
    >>> x = np.arange(6).reshape(2, 3)
    >>> np.putmask(x, x>2, x**2)
    >>> x
    array([[ 0,  1,  2],
           [ 9, 16, 25]])

    If `values` is smaller than `a` it is repeated:

    >>> x = np.arange(5)
    >>> np.putmask(x, x>1, [-33, -44])
    >>> x
    array([  0,   1, -33, -44, -33])

    �ravel��
    a.ravel([order])

    Return a flattened array.

    Refer to `numpy.ravel` for full documentation.

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

    ndarray.flat : a flat iterator on the array.

    �repeat��
    a.repeat(repeats, axis=None)

    Repeat elements of an array.

    Refer to `numpy.repeat` for full documentation.

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

    �reshape��
    a.reshape(shape, order='C')

    Returns an array containing the same data with a new shape.

    Refer to `numpy.reshape` for full documentation.

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

    �resize�:	
    a.resize(new_shape, refcheck=True)

    Change shape and size of array in-place.

    Parameters
    ----------
    new_shape : tuple of ints, or `n` ints
        Shape of resized array.
    refcheck : bool, optional
        If False, reference count will not be checked. Default is True.

    Returns
    -------
    None

    Raises
    ------
    ValueError
        If `a` does not own its own data or references or views to it exist,
        and the data memory must be changed.
        PyPy only: will always raise if the data memory must be changed, since
        there is no reliable way to determine if references or views to it
        exist.

    SystemError
        If the `order` keyword argument is specified. This behaviour is a
        bug in NumPy.

    See Also
    --------
    resize : Return a new array with the specified shape.

    Notes
    -----
    This reallocates space for the data area if necessary.

    Only contiguous arrays (data elements consecutive in memory) can be
    resized.

    The purpose of the reference count check is to make sure you
    do not use this array as a buffer for another Python object and then
    reallocate the memory. However, reference counts can increase in
    other ways so if you are sure that you have not shared the memory
    for this array with another Python object, then you may safely set
    `refcheck` to False.

    Examples
    --------
    Shrinking an array: array is flattened (in the order that the data are
    stored in memory), resized, and reshaped:

    >>> a = np.array([[0, 1], [2, 3]], order='C')
    >>> a.resize((2, 1))
    >>> a
    array([[0],
           [1]])

    >>> a = np.array([[0, 1], [2, 3]], order='F')
    >>> a.resize((2, 1))
    >>> a
    array([[0],
           [2]])

    Enlarging an array: as above, but missing entries are filled with zeros:

    >>> b = np.array([[0, 1], [2, 3]])
    >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
    >>> b
    array([[0, 1, 2],
           [3, 0, 0]])

    Referencing an array prevents resizing...

    >>> c = a
    >>> a.resize((1, 1))
    Traceback (most recent call last):
    ...
    ValueError: cannot resize an array that has been referenced ...

    Unless `refcheck` is False:

    >>> a.resize((1, 1), refcheck=False)
    >>> a
    array([[0]])
    >>> c
    array([[0]])

    �round��
    a.round(decimals=0, out=None)

    Return `a` with each element rounded to the given number of decimals.

    Refer to `numpy.around` for full documentation.

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

    �searchsorted�
    a.searchsorted(v, side='left', sorter=None)

    Find indices where elements of v should be inserted in a to maintain order.

    For full documentation, see `numpy.searchsorted`

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

    �setfield�
    a.setfield(val, dtype, offset=0)

    Put a value into a specified place in a field defined by a data-type.

    Place `val` into `a`'s field defined by `dtype` and beginning `offset`
    bytes into the field.

    Parameters
    ----------
    val : object
        Value to be placed in field.
    dtype : dtype object
        Data-type of the field in which to place `val`.
    offset : int, optional
        The number of bytes into the field at which to place `val`.

    Returns
    -------
    None

    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]])
    >>> x
    array([[  1.00000000e+000,   1.48219694e-323,   1.48219694e-323],
           [  1.48219694e-323,   1.00000000e+000,   1.48219694e-323],
           [  1.48219694e-323,   1.48219694e-323,   1.00000000e+000]])
    >>> x.setfield(np.eye(3), np.int32)
    >>> x
    array([[ 1.,  0.,  0.],
           [ 0.,  1.,  0.],
           [ 0.,  0.,  1.]])

    �setflags�		
    a.setflags(write=None, align=None, uic=None)

    Set array flags WRITEABLE, ALIGNED, 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 UPDATEIFCOPY flag 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 6 Boolean flags
    in use, only three of which can be changed by the user:
    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) this array is a copy of some other array (referenced
    by .base). When this array is deallocated, the base array will be
    updated with the contents of this array.

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

    Examples
    --------
    >>> 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
      UPDATEIFCOPY : False
    >>> y.setflags(write=0, align=0)
    >>> y.flags
      C_CONTIGUOUS : True
      F_CONTIGUOUS : False
      OWNDATA : True
      WRITEABLE : False
      ALIGNED : False
      UPDATEIFCOPY : False
    >>> y.setflags(uic=1)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: cannot set UPDATEIFCOPY flag to True

    �sort�	
    a.sort(axis=-1, kind='quicksort', order=None)

    Sort an array, in-place.

    Parameters
    ----------
    axis : int, optional
        Axis along which to sort. Default is -1, which means sort along the
        last axis.
    kind : {'quicksort', 'mergesort', 'heapsort'}, optional
        Sorting algorithm. Default is 'quicksort'.
    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.
    argsort : Indirect sort.
    lexsort : Indirect stable sort on multiple keys.
    searchsorted : Find elements in sorted array.
    partition: Partial sort.

    Notes
    -----
    See ``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([('c', 1), ('a', 2)],
          dtype=[('x', '|S1'), ('y', '<i4')])

    �	partition�
    a.partition(kth, axis=-1, kind='introselect', order=None)

    Rearranges the elements in the array in such a way that 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 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 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))
    array([1, 2, 3, 4])
    �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

    �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

    �sum��
    a.sum(axis=None, dtype=None, out=None, keepdims=False)

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

    Refer to `numpy.sum` for full documentation.

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

    �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

    �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

    �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
        An open file object, or a string containing a filename.
    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.

    �tolist�y
    a.tolist()

    Return the array as a (possibly nested) list.

    Return a copy of the array data as a (nested) Python list.
    Data items are converted to the nearest compatible Python type.

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

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

    Notes
    -----
    The array may be recreated, ``a = np.array(a.tolist())``.

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

    a�
    a.{name}(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.

    {deprecated}

    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]])
    >>> x.tobytes()
    b'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00'
    >>> x.tobytes('C') == x.tobytes()
    True
    >>> x.tobytes('F')
    b'\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'

    �tostring�nameZ
deprecatedzbThis function is a compatibility alias for tobytes. Despite its name it returns bytes not strings.�tobytesz.. versionadded:: 1.9.0�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

    �	transpose�
    a.transpose(*axes)

    Returns a view of the array with axes transposed.

    For a 1-D array, this has no effect. (To change between column and
    row vectors, first cast the 1-D array into a matrix object.)
    For a 2-D array, this is the usual 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.

    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]])

    �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

    �view��
    a.view(dtype=None, type=None)

    New view of array with the same data.

    Parameters
    ----------
    dtype : data-type or ndarray sub-class, optional
        Data-type descriptor of the returned view, e.g., float32 or int16. The
        default, None, 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, the
        default None 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.matrixlib.defmatrix.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
    >>> print(x)
    [(1, 20) (3, 4)]

    Using a view to convert an array to a recarray:

    >>> z = x.view(np.recarray)
    >>> z.a
    array([1], 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):
      File "<stdin>", line 1, in <module>
    ValueError: new type not compatible with array.
    >>> z = y.copy()
    >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
    array([[(1, 2)],
           [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')])
    znumpy.core.umathZ
frompyfunca5
    frompyfunc(func, nin, nout)

    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`.

    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([012, 036, 0144], dtype=object)
    >>> np.array((oct(10), oct(30), oct(100))) # for comparison
    array(['012', '036', '0144'],
          dtype='|S4')

    Z	geterrobja�
    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
    [10000, 0, 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()
    [20000, 2, <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'

    Z	seterrobja 
    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].

        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
    --------
    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
    [10000, 0, 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

    Zdigitizea�

    digitize(x, bins, right=False)

    Return the indices of the bins to which each value in input array belongs.

    Each index ``i`` returned is such that ``bins[i-1] <= x < bins[i]`` if
    `bins` is monotonically increasing, or ``bins[i-1] > x >= bins[i]`` if
    `bins` is monotonically decreasing. If values in `x` are beyond the
    bounds of `bins`, 0 or ``len(bins)`` is returned as appropriate. If right
    is True, then the right bin is closed so that the index ``i`` is such
    that ``bins[i-1] < x <= bins[i]`` or ``bins[i-1] >= x > bins[i]`` if `bins`
    is monotonically increasing or decreasing, respectively.

    Parameters
    ----------
    x : array_like
        Input array to be binned. Prior to NumPy 1.10.0, this array had to
        be 1-dimensional, but can now have any shape.
    bins : array_like
        Array of bins. It has to be 1-dimensional and monotonic.
    right : bool, optional
        Indicating whether the intervals include the right or the left bin
        edge. Default behavior is (right==False) indicating that the interval
        does not include the right edge. The left bin end is open in this
        case, i.e., bins[i-1] <= x < bins[i] is the default behavior for
        monotonically increasing bins.

    Returns
    -------
    out : ndarray of ints
        Output array of indices, of same shape as `x`.

    Raises
    ------
    ValueError
        If `bins` is not monotonic.
    TypeError
        If the type of the input is complex.

    See Also
    --------
    bincount, histogram, unique, searchsorted

    Notes
    -----
    If values in `x` are such that they fall outside the bin range,
    attempting to index `bins` with the indices that `digitize` returns
    will result in an IndexError.

    .. versionadded:: 1.10.0

    `np.digitize` is  implemented in terms of `np.searchsorted`. This means
    that a binary search is used to bin the values, which scales much better
    for larger number of bins than the previous linear search. It also removes
    the requirement for the input array to be 1-dimensional.

    Examples
    --------
    >>> x = np.array([0.2, 6.4, 3.0, 1.6])
    >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])
    >>> inds = np.digitize(x, bins)
    >>> inds
    array([1, 4, 3, 2])
    >>> for n in range(x.size):
    ...   print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]])
    ...
    0.0 <= 0.2 < 1.0
    4.0 <= 6.4 < 10.0
    2.5 <= 3.0 < 4.0
    1.0 <= 1.6 < 2.5

    >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.])
    >>> bins = np.array([0, 5, 10, 15, 20])
    >>> np.digitize(x,bins,right=True)
    array([1, 2, 3, 4, 4])
    >>> np.digitize(x,bins,right=False)
    array([1, 3, 3, 4, 5])
    Zbincounta�
    bincount(x, weights=None, minlength=0)

    Count number of occurrences of each value in array of non-negative ints.

    The number of bins (of size 1) is one larger than the largest value in
    `x`. If `minlength` is specified, there will be at least this number
    of bins in the output array (though it will be longer if necessary,
    depending on the contents of `x`).
    Each bin gives the number of occurrences of its index value in `x`.
    If `weights` is specified the input array is weighted by it, i.e. if a
    value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead
    of ``out[n] += 1``.

    Parameters
    ----------
    x : array_like, 1 dimension, nonnegative ints
        Input array.
    weights : array_like, optional
        Weights, array of the same shape as `x`.
    minlength : int, optional
        A minimum number of bins for the output array.

        .. versionadded:: 1.6.0

    Returns
    -------
    out : ndarray of ints
        The result of binning the input array.
        The length of `out` is equal to ``np.amax(x)+1``.

    Raises
    ------
    ValueError
        If the input is not 1-dimensional, or contains elements with negative
        values, or if `minlength` is negative.
    TypeError
        If the type of the input is float or complex.

    See Also
    --------
    histogram, digitize, unique

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

    >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])
    >>> np.bincount(x).size == np.amax(x)+1
    True

    The input array needs to be of integer dtype, otherwise a
    TypeError is raised:

    >>> np.bincount(np.arange(5, dtype=np.float))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: array cannot be safely cast to required type

    A possible use of ``bincount`` is to perform sums over
    variable-size chunks of an array, using the ``weights`` keyword.

    >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights
    >>> x = np.array([0, 1, 1, 2, 2, 2])
    >>> np.bincount(x,  weights=w)
    array([ 0.3,  0.7,  1.1])

    Zravel_multi_indexa�
    ravel_multi_index(multi_index, dims, mode='raise', order='C')

    Converts a tuple of index arrays into an array of flat
    indices, applying boundary modes to the multi-index.

    Parameters
    ----------
    multi_index : tuple of array_like
        A tuple of integer arrays, one array for each dimension.
    dims : tuple of ints
        The shape of array into which the indices from ``multi_index`` apply.
    mode : {'raise', 'wrap', 'clip'}, optional
        Specifies how out-of-bounds indices are handled.  Can specify
        either one mode or a tuple of modes, one mode per index.

        * 'raise' -- raise an error (default)
        * 'wrap' -- wrap around
        * 'clip' -- clip to the range

        In 'clip' mode, a negative index which would normally
        wrap will clip to 0 instead.
    order : {'C', 'F'}, optional
        Determines whether the multi-index should be viewed as
        indexing in row-major (C-style) or column-major
        (Fortran-style) order.

    Returns
    -------
    raveled_indices : ndarray
        An array of indices into the flattened version of an array
        of dimensions ``dims``.

    See Also
    --------
    unravel_index

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

    Examples
    --------
    >>> arr = np.array([[3,6,6],[4,5,1]])
    >>> np.ravel_multi_index(arr, (7,6))
    array([22, 41, 37])
    >>> np.ravel_multi_index(arr, (7,6), order='F')
    array([31, 41, 13])
    >>> np.ravel_multi_index(arr, (4,6), mode='clip')
    array([22, 23, 19])
    >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
    array([12, 13, 13])

    >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))
    1621
    Z
unravel_indexa�
    unravel_index(indices, dims, order='C')

    Converts a flat index or array of flat indices into a tuple
    of coordinate arrays.

    Parameters
    ----------
    indices : array_like
        An integer array whose elements are indices into the flattened
        version of an array of dimensions ``dims``. Before version 1.6.0,
        this function accepted just one index value.
    dims : tuple of ints
        The shape of the array to use for unraveling ``indices``.
    order : {'C', 'F'}, optional
        Determines whether the indices should be viewed as indexing in
        row-major (C-style) or column-major (Fortran-style) order.

        .. versionadded:: 1.6.0

    Returns
    -------
    unraveled_coords : tuple of ndarray
        Each array in the tuple has the same shape as the ``indices``
        array.

    See Also
    --------
    ravel_multi_index

    Examples
    --------
    >>> np.unravel_index([22, 41, 37], (7,6))
    (array([3, 6, 6]), array([4, 5, 1]))
    >>> np.unravel_index([31, 41, 13], (7,6), order='F')
    (array([3, 6, 6]), array([4, 5, 1]))

    >>> np.unravel_index(1621, (6,7,8,9))
    (3, 1, 4, 1)

    Z
add_docstringz�
    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
    Z_add_newdoc_ufuncaI
    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.
    Zpackbitsa
    packbits(myarray, axis=None)

    Packs the elements of a binary-valued array into bits in a uint8 array.

    The result is padded to full bytes by inserting zero bits at the end.

    Parameters
    ----------
    myarray : array_like
        An array of integers or booleans whose elements should be packed to
        bits.
    axis : int, optional
        The dimension over which bit-packing is done.
        ``None`` implies packing the flattened array.

    Returns
    -------
    packed : ndarray
        Array of type uint8 whose elements represent bits corresponding to the
        logical (0 or nonzero) value of the input elements. The shape of
        `packed` has the same number of dimensions as the input (unless `axis`
        is None, in which case the output is 1-D).

    See Also
    --------
    unpackbits: Unpacks elements of a uint8 array into a binary-valued output
                array.

    Examples
    --------
    >>> a = np.array([[[1,0,1],
    ...                [0,1,0]],
    ...               [[1,1,0],
    ...                [0,0,1]]])
    >>> b = np.packbits(a, axis=-1)
    >>> b
    array([[[160],[64]],[[192],[32]]], dtype=uint8)

    Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000,
    and 32 = 0010 0000.

    Z
unpackbitsaG
    unpackbits(myarray, axis=None)

    Unpacks elements of a uint8 array into a binary-valued output array.

    Each element of `myarray` represents a bit-field that should be unpacked
    into a binary-valued output array. The shape of the output array is either
    1-D (if `axis` is None) or the same shape as the input array with unpacking
    done along the axis specified.

    Parameters
    ----------
    myarray : ndarray, uint8 type
       Input array.
    axis : int, optional
       Unpacks along this axis.

    Returns
    -------
    unpacked : ndarray, uint8 type
       The elements are binary-valued (0 or 1).

    See Also
    --------
    packbits : Packs the elements of a binary-valued array into bits in a uint8
               array.

    Examples
    --------
    >>> a = np.array([[2], [7], [23]], dtype=np.uint8)
    >>> a
    array([[ 2],
           [ 7],
           [23]], dtype=uint8)
    >>> b = np.unpackbits(a, axis=1)
    >>> b
    array([[0, 0, 0, 0, 0, 0, 1, 0],
           [0, 0, 0, 0, 0, 1, 1, 1],
           [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)

    Zufunca�
    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 outputs to be allocated by the ufunc.
    where : array_like, optional
        Values of True indicate to calculate the ufunc at that position, values
        of False indicate to leave the value in the output alone.
    **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, `r` will be equal to `out`. If the function has more than one
        output, then the result will be a tuple of arrays.

    �identity�D
    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
    �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
    �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
    �nout�e
    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

    �ntypes�u
    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

    �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']

    �reduce�Q
    reduce(a, axis=0, dtype=None, out=None, keepdims=False)

    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
        :ref:`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

    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]])

    �
accumulate�c	
    accumulate(array, axis=0, dtype=None, out=None, keepdims=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
        :ref:`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
        Has no effect. Deprecated, and will be removed in future.

    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.]])

    �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
        :ref:`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.]])

    �outer�
    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

    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]]]])

    �at�E
    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])
    >>> print(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)
    >>> print(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)
    >>> print(a)
    array([2, 4, 3, 4])

    a�	
    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.

    See also
    --------
    result_type

    Examples
    --------
    Using array-scalar type:

    >>> np.dtype(np.int16)
    dtype('int16')

    Structured type, one field name 'f1', containing int16:

    >>> np.dtype([('f1', np.int16)])
    dtype([('f1', '<i2')])

    Structured type, one field named 'f1', in itself containing a structured
    type with one field:

    >>> np.dtype([('f1', [('f1', np.int16)])])
    dtype([('f1', [('f1', '<i2')])])

    Structured type, two fields: the first field contains an unsigned int, the
    second an int32:

    >>> np.dtype([('f1', np.uint), ('f2', np.int32)])
    dtype([('f1', '<u4'), ('f2', '<i4')])

    Using array-protocol type strings:

    >>> np.dtype([('a','f8'),('b','S10')])
    dtype([('a', '<f8'), ('b', '|S10')])

    Using comma-separated field formats.  The shape is (2,3):

    >>> np.dtype("i4, (2,3)f8")
    dtype([('f0', '<i4'), ('f1', '<f8', (2, 3))])

    Using tuples.  ``int`` is a fixed type, 3 the field's shape.  ``void``
    is a flexible type, here of size 10:

    >>> np.dtype([('hello',(np.int,3)),('world',np.void,10)])
    dtype([('hello', '<i4', 3), ('world', '|V10')])

    Subdivide ``int16`` into 2 ``int8``'s, called x and y.  0 and 1 are
    the offsets in bytes:

    >>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)}))
    dtype(('<i2', [('x', '|i1'), ('y', '|i1')]))

    Using dictionaries.  Two fields named 'gender' and 'age':

    >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]})
    dtype([('gender', '|S1'), ('age', '|u1')])

    Offsets in bytes, here 0 and 25:

    >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)})
    dtype([('surname', '|S25'), ('age', '|u1')])

    �	alignment��
    The required alignment (bytes) of this data-type according to the compiler.

    More information is available in the C-API section of the manual.

    �	byteorder��
    A character indicating the byte-order of this data-type object.

    One of:

    ===  ==============
    '='  native
    '<'  little-endian
    '>'  big-endian
    '|'  not applicable
    ===  ==============

    All built-in data-type objects have byteorder either '=' or '|'.

    Examples
    --------

    >>> dt = np.dtype('i2')
    >>> dt.byteorder
    '='
    >>> # endian is not relevant for 8 bit numbers
    >>> np.dtype('i1').byteorder
    '|'
    >>> # or ASCII strings
    >>> np.dtype('S2').byteorder
    '|'
    >>> # Even if specific code is given, and it is native
    >>> # '=' is the byteorder
    >>> import sys
    >>> sys_is_le = sys.byteorder == 'little'
    >>> native_code = sys_is_le and '<' or '>'
    >>> swapped_code = sys_is_le and '>' or '<'
    >>> dt = np.dtype(native_code + 'i2')
    >>> dt.byteorder
    '='
    >>> # Swapped code shows up as itself
    >>> dt = np.dtype(swapped_code + 'i2')
    >>> dt.byteorder == swapped_code
    True

    �char�DA unique character code for each of the 21 different built-in types.�descr�,
    PEP3118 interface description of the data-type.

    The format is that required by the 'descr' key in the
    PEP3118 `__array_interface__` attribute.

    Warning: This attribute exists specifically for PEP3118 compliance, and
    is not a datatype description compatible with `np.dtype`.
    �fields�X
    Dictionary of named fields defined for this data type, or ``None``.

    The dictionary is indexed by keys that are the names of the fields.
    Each entry in the dictionary is a tuple fully describing the field::

      (dtype, offset[, title])

    If present, the optional title can be any object (if it is a string
    or unicode then it will also be a key in the fields dictionary,
    otherwise it's meta-data). Notice also that the first two elements
    of the tuple can be passed directly as arguments to the ``ndarray.getfield``
    and ``ndarray.setfield`` methods.

    See Also
    --------
    ndarray.getfield, ndarray.setfield

    Examples
    --------
    >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
    >>> print(dt.fields)
    {'grades': (dtype(('float64',(2,))), 16), 'name': (dtype('|S16'), 0)}

    �x
    Bit-flags describing how this data type is to be interpreted.

    Bit-masks are in `numpy.core.multiarray` as the constants
    `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`,
    `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation
    of these flags is in C-API documentation; they are largely useful
    for user-defined data-types.

    �	hasobject�
    Boolean indicating whether this dtype contains any reference-counted
    objects in any fields or sub-dtypes.

    Recall that what is actually in the ndarray memory representing
    the Python object is the memory address of that object (a pointer).
    Special handling may be required, and this attribute is useful for
    distinguishing data types that may contain arbitrary Python objects
    and data-types that won't.

    �	isbuiltin�1
    Integer indicating how this dtype relates to the built-in dtypes.

    Read-only.

    =  ========================================================================
    0  if this is a structured array type, with fields
    1  if this is a dtype compiled into numpy (such as ints, floats etc)
    2  if the dtype is for a user-defined numpy type
       A user-defined type uses the numpy C-API machinery to extend
       numpy to handle a new array type. See
       :ref:`user.user-defined-data-types` in the NumPy manual.
    =  ========================================================================

    Examples
    --------
    >>> dt = np.dtype('i2')
    >>> dt.isbuiltin
    1
    >>> dt = np.dtype('f8')
    >>> dt.isbuiltin
    1
    >>> dt = np.dtype([('field1', 'f8')])
    >>> dt.isbuiltin
    0

    �isnative�a
    Boolean indicating whether the byte order of this dtype is native
    to the platform.

    �isalignedstruct��
    Boolean indicating whether the dtype is a struct which maintains
    field alignment. This flag is sticky, so when combining multiple
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    are also aligned.
    ��
    The element size of this data-type object.

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    �kind�e
    A character code (one of 'biufcmMOSUV') identifying the general kind of data.

    =  ======================
    b  boolean
    i  signed integer
    u  unsigned integer
    f  floating-point
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    m  timedelta
    M  datetime
    O  object
    S  (byte-)string
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    V  void
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    �t
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        below.  The default value ('S') results in swapping the current
        byte order.  `new_order` codes can be any of:

        * 'S' - swap dtype from current to opposite endian
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        * {'>', 'B'} - big endian
        * {'=', 'N'} - native order
        * {'|', 'I'} - ignore (no change to byte order)

        The code does a case-insensitive check on the first letter of
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        or 'B' or 'b' or 'brian' are valid to specify big-endian.

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    new_dtype : dtype
        New dtype object with the given change to the byte order.

    Notes
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    Changes are also made in all fields and sub-arrays of the data type.

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    >>> sys_is_le = sys.byteorder == 'little'
    >>> native_code = sys_is_le and '<' or '>'
    >>> swapped_code = sys_is_le and '>' or '<'
    >>> native_dt = np.dtype(native_code+'i2')
    >>> swapped_dt = np.dtype(swapped_code+'i2')
    >>> native_dt.newbyteorder('S') == swapped_dt
    True
    >>> native_dt.newbyteorder() == swapped_dt
    True
    >>> native_dt == swapped_dt.newbyteorder('S')
    True
    >>> native_dt == swapped_dt.newbyteorder('=')
    True
    >>> native_dt == swapped_dt.newbyteorder('N')
    True
    >>> native_dt == native_dt.newbyteorder('|')
    True
    >>> np.dtype('<i2') == native_dt.newbyteorder('<')
    True
    >>> np.dtype('<i2') == native_dt.newbyteorder('L')
    True
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    Zbusdaycalendara�	
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    valid days, plus an optional "holiday" dates that always will be invalid.

    Once a busdaycalendar object is created, the weekmask and holidays
    cannot be modified.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
        weekdays, optionally separated by white space. Valid abbreviations
        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates, no matter which
        weekday they fall upon.  Holiday dates may be specified in any
        order, and NaT (not-a-time) dates are ignored.  This list is
        saved in a normalized form that is suited for fast calculations
        of valid days.

    Returns
    -------
    out : busdaycalendar
        A business day calendar object containing the specified
        weekmask and holidays values.

    See Also
    --------
    is_busday : Returns a boolean array indicating valid days.
    busday_offset : Applies an offset counted in valid days.
    busday_count : Counts how many valid days are in a half-open date range.

    Attributes
    ----------
    Note: once a busdaycalendar object is created, you cannot modify the
    weekmask or holidays.  The attributes return copies of internal data.
    weekmask : (copy) seven-element array of bool
    holidays : (copy) sorted array of datetime64[D]

    Examples
    --------
    >>> # Some important days in July
    ... bdd = np.busdaycalendar(
    ...             holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
    >>> # Default is Monday to Friday weekdays
    ... bdd.weekmask
    array([ True,  True,  True,  True,  True, False, False], dtype='bool')
    >>> # Any holidays already on the weekend are removed
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    array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]')
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    is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None)

    Calculates which of the given dates are valid days, and which are not.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    dates : array_like of datetime64[D]
        The array of dates to process.
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
        weekdays, optionally separated by white space. Valid abbreviations
        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates.  They may be
        specified in any order, and NaT (not-a-time) dates are ignored.
        This list is saved in a normalized form that is suited for
        fast calculations of valid days.
    busdaycal : busdaycalendar, optional
        A `busdaycalendar` object which specifies the valid days. If this
        parameter is provided, neither weekmask nor holidays may be
        provided.
    out : array of bool, optional
        If provided, this array is filled with the result.

    Returns
    -------
    out : array of bool
        An array with the same shape as ``dates``, containing True for
        each valid day, and False for each invalid day.

    See Also
    --------
    busdaycalendar: An object that specifies a custom set of valid days.
    busday_offset : Applies an offset counted in valid days.
    busday_count : Counts how many valid days are in a half-open date range.

    Examples
    --------
    >>> # The weekdays are Friday, Saturday, and Monday
    ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'],
    ...                 holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
    array([False, False,  True], dtype='bool')
    Z
busday_offseta)
    busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None)

    First adjusts the date to fall on a valid day according to
    the ``roll`` rule, then applies offsets to the given dates
    counted in valid days.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    dates : array_like of datetime64[D]
        The array of dates to process.
    offsets : array_like of int
        The array of offsets, which is broadcast with ``dates``.
    roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional
        How to treat dates that do not fall on a valid day. The default
        is 'raise'.

          * 'raise' means to raise an exception for an invalid day.
          * 'nat' means to return a NaT (not-a-time) for an invalid day.
          * 'forward' and 'following' mean to take the first valid day
            later in time.
          * 'backward' and 'preceding' mean to take the first valid day
            earlier in time.
          * 'modifiedfollowing' means to take the first valid day
            later in time unless it is across a Month boundary, in which
            case to take the first valid day earlier in time.
          * 'modifiedpreceding' means to take the first valid day
            earlier in time unless it is across a Month boundary, in which
            case to take the first valid day later in time.
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
        weekdays, optionally separated by white space. Valid abbreviations
        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates.  They may be
        specified in any order, and NaT (not-a-time) dates are ignored.
        This list is saved in a normalized form that is suited for
        fast calculations of valid days.
    busdaycal : busdaycalendar, optional
        A `busdaycalendar` object which specifies the valid days. If this
        parameter is provided, neither weekmask nor holidays may be
        provided.
    out : array of datetime64[D], optional
        If provided, this array is filled with the result.

    Returns
    -------
    out : array of datetime64[D]
        An array with a shape from broadcasting ``dates`` and ``offsets``
        together, containing the dates with offsets applied.

    See Also
    --------
    busdaycalendar: An object that specifies a custom set of valid days.
    is_busday : Returns a boolean array indicating valid days.
    busday_count : Counts how many valid days are in a half-open date range.

    Examples
    --------
    >>> # First business day in October 2011 (not accounting for holidays)
    ... np.busday_offset('2011-10', 0, roll='forward')
    numpy.datetime64('2011-10-03','D')
    >>> # Last business day in February 2012 (not accounting for holidays)
    ... np.busday_offset('2012-03', -1, roll='forward')
    numpy.datetime64('2012-02-29','D')
    >>> # Third Wednesday in January 2011
    ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed')
    numpy.datetime64('2011-01-19','D')
    >>> # 2012 Mother's Day in Canada and the U.S.
    ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun')
    numpy.datetime64('2012-05-13','D')

    >>> # First business day on or after a date
    ... np.busday_offset('2011-03-20', 0, roll='forward')
    numpy.datetime64('2011-03-21','D')
    >>> np.busday_offset('2011-03-22', 0, roll='forward')
    numpy.datetime64('2011-03-22','D')
    >>> # First business day after a date
    ... np.busday_offset('2011-03-20', 1, roll='backward')
    numpy.datetime64('2011-03-21','D')
    >>> np.busday_offset('2011-03-22', 1, roll='backward')
    numpy.datetime64('2011-03-23','D')
    Zbusday_counta�	
    busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None)

    Counts the number of valid days between `begindates` and
    `enddates`, not including the day of `enddates`.

    If ``enddates`` specifies a date value that is earlier than the
    corresponding ``begindates`` date value, the count will be negative.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    begindates : array_like of datetime64[D]
        The array of the first dates for counting.
    enddates : array_like of datetime64[D]
        The array of the end dates for counting, which are excluded
        from the count themselves.
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
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        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates.  They may be
        specified in any order, and NaT (not-a-time) dates are ignored.
        This list is saved in a normalized form that is suited for
        fast calculations of valid days.
    busdaycal : busdaycalendar, optional
        A `busdaycalendar` object which specifies the valid days. If this
        parameter is provided, neither weekmask nor holidays may be
        provided.
    out : array of int, optional
        If provided, this array is filled with the result.

    Returns
    -------
    out : array of int
        An array with a shape from broadcasting ``begindates`` and ``enddates``
        together, containing the number of valid days between
        the begin and end dates.

    See Also
    --------
    busdaycalendar: An object that specifies a custom set of valid days.
    is_busday : Returns a boolean array indicating valid days.
    busday_offset : Applies an offset counted in valid days.

    Examples
    --------
    >>> # Number of weekdays in January 2011
    ... np.busday_count('2011-01', '2011-02')
    21
    >>> # Number of weekdays in 2011
    ...  np.busday_count('2011', '2012')
    260
    >>> # Number of Saturdays in 2011
    ... np.busday_count('2011', '2012', weekmask='Sat')
    53
    Znormalize_axis_indexaz
    normalize_axis_index(axis, ndim, msg_prefix=None)

    Normalizes an axis index, `axis`, such that is a valid positive index into
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    appropriate message if this is not possible.

    Used internally by all axis-checking logic.

    .. versionadded:: 1.13.0

    Parameters
    ----------
    axis : int
        The un-normalized index of the axis. Can be negative
    ndim : int
        The number of dimensions of the array that `axis` should be normalized
        against
    msg_prefix : str
        A prefix to put before the message, typically the name of the argument

    Returns
    -------
    normalized_axis : int
        The normalized axis index, such that `0 <= normalized_axis < ndim`

    Raises
    ------
    AxisError
        If the axis index is invalid, when `-ndim <= axis < ndim` is false.

    Examples
    --------
    >>> normalize_axis_index(0, ndim=3)
    0
    >>> normalize_axis_index(1, ndim=3)
    1
    >>> normalize_axis_index(-1, ndim=3)
    2

    >>> normalize_axis_index(3, ndim=3)
    Traceback (most recent call last):
    ...
    AxisError: axis 3 is out of bounds for array of dimension 3
    >>> normalize_axis_index(-4, ndim=3, msg_prefix='axes_arg')
    Traceback (most recent call last):
    ...
    AxisError: axes_arg: axis -4 is out of bounds for array of dimension 3
    znumpy.lib.index_tricksZmgridag
    `nd_grid` instance which returns a dense multi-dimensional "meshgrid".

    An instance of `numpy.lib.index_tricks.nd_grid` which returns an dense
    (or fleshed out) mesh-grid when indexed, so that each returned argument
    has the same shape.  The dimensions and number of the output arrays are
    equal to the number of indexing dimensions.  If the step length is not a
    complex number, then the stop is not inclusive.

    However, if the step length is a **complex number** (e.g. 5j), then
    the integer part of its magnitude is interpreted as specifying the
    number of points to create between the start and stop values, where
    the stop value **is inclusive**.

    Returns
    ----------
    mesh-grid `ndarrays` all of the same dimensions

    See Also
    --------
    numpy.lib.index_tricks.nd_grid : class of `ogrid` and `mgrid` objects
    ogrid : like mgrid but returns open (not fleshed out) mesh grids
    r_ : array concatenator

    Examples
    --------
    >>> np.mgrid[0:5,0:5]
    array([[[0, 0, 0, 0, 0],
            [1, 1, 1, 1, 1],
            [2, 2, 2, 2, 2],
            [3, 3, 3, 3, 3],
            [4, 4, 4, 4, 4]],
           [[0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4]]])
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    array([-1. , -0.5,  0. ,  0.5,  1. ])

    Zogrida�
    `nd_grid` instance which returns an open multi-dimensional "meshgrid".

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    of each returned array is greater than 1.  The dimension and number of the
    output arrays are equal to the number of indexing dimensions.  If the step
    length is not a complex number, then the stop is not inclusive.

    However, if the step length is a **complex number** (e.g. 5j), then
    the integer part of its magnitude is interpreted as specifying the
    number of points to create between the start and stop values, where
    the stop value **is inclusive**.

    Returns
    ----------
    mesh-grid `ndarrays` with only one dimension :math:`\neq 1`

    See Also
    --------
    np.lib.index_tricks.nd_grid : class of `ogrid` and `mgrid` objects
    mgrid : like `ogrid` but returns dense (or fleshed out) mesh grids
    r_ : array concatenator

    Examples
    --------
    >>> from numpy import ogrid
    >>> ogrid[-1:1:5j]
    array([-1. , -0.5,  0. ,  0.5,  1. ])
    >>> ogrid[0:5,0:5]
    [array([[0],
            [1],
            [2],
            [3],
            [4]]), array([[0, 1, 2, 3, 4]])]

    znumpy.core.numerictypesZgenericai
    Base class for numpy scalar types.

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    * {'|', 'I'} - ignore (no change to byte order)

    Parameters
    ----------
    new_order : str, optional
        Byte order to force; a value from the byte order specifications
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