#!/usr/bin/env python

# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements.  See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership.  The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License.  You may obtain a copy of the License at
#
#   http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied.  See the License for the
# specific language governing permissions and limitations
# under the License.

# pylint: disable=too-many-lines, unused-argument
"""numpy ndarray and util functions."""

from __future__ import absolute_import
from __future__ import division

try:
    from __builtin__ import slice as py_slice
except ImportError:
    from builtins import slice as py_slice

from array import array as native_array
import ctypes
import warnings
import numpy as _np
from ..ndarray import NDArray, _DTYPE_NP_TO_MX, _GRAD_REQ_MAP
from ..ndarray import indexing_key_expand_implicit_axes, get_indexing_dispatch_code,\
                      get_oshape_of_gather_nd_op
from ..ndarray._internal import _set_np_ndarray_class
from . import _op as _mx_np_op
from ..base import check_call, _LIB, NDArrayHandle, c_array
from ..base import mx_real_t, c_array_buf, mx_uint, numeric_types, integer_types
from ..context import Context
from ..util import _sanity_check_params, set_module, wrap_np_unary_func, wrap_np_binary_func
from ..context import current_context
from ..ndarray import numpy as _mx_nd_np
from ..ndarray.numpy import _internal as _npi

__all__ = ['ndarray', 'empty', 'array', 'shape', 'zeros', 'ones', 'full', 'add', 'subtract', 'multiply', 'divide',
           'mod', 'remainder', 'power', 'arctan2', 'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'log10',
           'sqrt', 'cbrt', 'abs', 'absolute', 'exp', 'expm1', 'arcsin', 'arccos', 'arctan', 'sign', 'log',
           'degrees', 'log2', 'log1p', 'rint', 'radians', 'reciprocal', 'square', 'negative',
           'fix', 'ceil', 'floor', 'trunc', 'logical_not', 'arcsinh', 'arccosh', 'arctanh', 'append',
           'tensordot', 'histogram', 'eye', 'linspace', 'logspace', 'expand_dims', 'tile', 'arange',
           'split', 'vsplit', 'concatenate', 'stack', 'vstack', 'column_stack', 'dstack', 'mean', 'maximum', 'minimum',
           'swapaxes', 'clip', 'argmax', 'argmin', 'std', 'var', 'indices', 'copysign', 'ravel', 'hanning', 'hamming',
           'blackman', 'flip', 'around', 'arctan2', 'hypot', 'bitwise_xor', 'rad2deg', 'deg2rad', 'unique', 'lcm',
           'tril', 'identity', 'take', 'ldexp', 'vdot', 'inner', 'outer', 'equal', 'not_equal', 'greater', 'less',
           'greater_equal', 'less_equal', 'hsplit', 'rot90', 'einsum', 'true_divide', 'nonzero', 'shares_memory',
           'may_share_memory', 'diff']

# Return code for dispatching indexing function call
_NDARRAY_UNSUPPORTED_INDEXING = -1
_NDARRAY_BASIC_INDEXING = 0
_NDARRAY_ADVANCED_INDEXING = 1


# This function is copied from ndarray.py since pylint
# keeps giving false alarm error of undefined-all-variable
def _new_alloc_handle(shape, ctx, delay_alloc, dtype=mx_real_t):  # pylint: disable=redefined-outer-name
    """Return a new handle with specified shape and context.

    Empty handle is only used to hold results.

    Returns
    -------
    handle
        A new empty `ndarray` handle.
    """
    hdl = NDArrayHandle()
    check_call(_LIB.MXNDArrayCreateEx(
        c_array_buf(mx_uint, native_array('I', shape)),
        mx_uint(len(shape)),
        ctypes.c_int(ctx.device_typeid),
        ctypes.c_int(ctx.device_id),
        ctypes.c_int(int(delay_alloc)),
        ctypes.c_int(int(_DTYPE_NP_TO_MX[_np.dtype(dtype).type])),
        ctypes.byref(hdl)))
    return hdl


def _reshape_view(a, *shape):  # pylint: disable=redefined-outer-name
    """Returns a **view** of this array with a new shape without altering any data.

    Parameters
    ----------
    shape : tuple of int, or n ints
        The new shape should not change the array size, namely
        ``np.prod(new_shape)`` should be equal to ``np.prod(a.shape)``.
        Some dimensions of the shape can take special value -1, which
        infers the dimension of the output shape by using the remainder of the
        input dimensions keeping the size of the new array same as that of the input array.
        At most one dimension of shape can be -1.

    Returns
    -------
    ndarray
        An array with desired shape that shares data with this array.
    """
    if len(shape) == 1 and isinstance(shape[0], (list, tuple)):
        shape = shape[0]
    handle = NDArrayHandle()
    check_call(_LIB.MXNDArrayReshape64(a.handle,
                                       len(shape),
                                       c_array(ctypes.c_int64, shape),
                                       False,
                                       ctypes.byref(handle)))
    return ndarray(handle=handle, writable=a.writable)


# Have to use 0 as default value for stype since pylint does not allow
# importing _STORAGE_TYPE_DEFAULT from ndarray.py.
def _np_ndarray_cls(handle, writable=True, stype=0):
    if stype != 0:
        raise ValueError('_np_ndarray_cls currently only supports default storage '
                         'type, while received stype = {}'.format(stype))
    return ndarray(handle, writable=writable)


_set_np_ndarray_class(_np_ndarray_cls)

_NUMPY_ARRAY_FUNCTION_DICT = {}
_NUMPY_ARRAY_UFUNC_DICT = {}


@set_module('mxnet.numpy')  # pylint: disable=invalid-name
class ndarray(NDArray):
    """
    ndarray(handle, writable=True):

    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`. Currently, only c-contiguous arrays are supported.

    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 `mxnet.numpy` module and examine the
    methods and attributes of an array.

    Parameters
    ----------
    handle: int
        The ndarray handle in backend (C++).
    writable: bool
        Indicates whether inplace-assignment is allowed for the array.

    Attributes
    ----------
    T : ndarray
        Transpose of the array.
    dtype : dtype object
        Describes the format of the elements in the array.
    size : int
        Number of elements in the array.
    ndim : int
        The array's number of dimensions.
    shape : tuple of ints
        Shape of the array.

    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").
    """

    @staticmethod
    def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):  # pylint: disable=bad-staticmethod-argument
        """
        Dispatch official NumPy unary/binary operator calls on mxnet.numpy.ndarray
        to this function. The operators must comply with the ufunc definition in NumPy.
        The following code is adapted from CuPy.
        """
        if 'out' in kwargs:
            # need to unfold tuple argument in kwargs
            out = kwargs['out']
            if len(out) != 1:
                raise ValueError('The `out` parameter must have exactly one ndarray')
            kwargs['out'] = out[0]

        if method == '__call__':
            if ufunc.signature is not None:
                # we don't support generalised-ufuncs (gufuncs)
                return NotImplemented
            name = ufunc.__name__
            mx_ufunc = _NUMPY_ARRAY_UFUNC_DICT.get(name, None)
            if mx_ufunc is None:
                raise ValueError('mxnet.numpy operator `{}` has not been registered in '
                                 'the _NUMPY_ARRAY_UFUNC_LIST. Please make sure you are '
                                 'using NumPy >= 1.15.0 and the operator implementation '
                                 'is compatible with NumPy. Then add the operator name '
                                 'to the list.'
                                 .format(name))
            return mx_ufunc(*inputs, **kwargs)
        else:
            return NotImplemented

    @staticmethod
    def __array_function__(self, func, types, args, kwargs):  # pylint: disable=bad-staticmethod-argument
        """
        Dispatch official NumPy operators that comply with the array function protocol to
        this function.
        """
        mx_np_func = _NUMPY_ARRAY_FUNCTION_DICT.get(func, None)
        if mx_np_func is None:
            raise ValueError('mxnet.numpy operator `{}` has not been registered in '
                             'the _NUMPY_ARRAY_FUNCTION_LIST. Please make sure you are '
                             'using NumPy >= 1.17.0 and the operator '
                             'implementation is compatible with NumPy. Then add '
                             'the operator name to the list.'.format(func))
        # Note: this allows subclasses that don't override
        # __array_function__ to handle mxnet.numpy.ndarray objects
        if not all(issubclass(t, ndarray) for t in types):
            return NotImplemented
        return mx_np_func(*args, **kwargs)

    def _get_np_basic_indexing(self, key):
        """
        This function indexes ``self`` with a tuple of `slice` objects only.
        """
        key_nd = tuple(idx for idx in key if idx is not None)
        if len(key_nd) < self.ndim:
            raise RuntimeError(
                'too few indices after normalization: expected `ndim` ({}) '
                'but got {}. This is a bug, please report it!'
                ''.format(self.ndim, len(key_nd))
            )
        if len(key_nd) > self.ndim:
            raise IndexError(
                'too many indices ({}) for array with {} dimensions'
                ''.format(len(key_nd), self.ndim)
            )

        none_axes = [ax for ax in range(len(key)) if key[ax] is None]  # pylint: disable=invalid-name
        slc_key, int_axes = self._basic_indexing_key_int_to_slice(key_nd)
        new_axes = self._new_axes_after_basic_indexing(none_axes, key)

        # Check bounds for integer axes
        for ax in int_axes:  # pylint: disable=invalid-name
            if not -self.shape[ax] <= key_nd[ax] < self.shape[ax]:
                raise IndexError(
                    'index {} is out of bounds for axis {} with size {}'
                    ''.format(key_nd[ax], ax, self.shape[ax]))

        if self._basic_indexing_slice_is_contiguous(slc_key, self.shape):
            # Create a shared-memory view by using low-level flat slicing
            flat_begin, flat_end = self._basic_indexing_contiguous_flat_begin_end(
                slc_key, self.shape
            )
            handle = NDArrayHandle()
            flat_self = self.reshape_view(-1)
            check_call(
                _LIB.MXNDArraySlice(
                    flat_self.handle,
                    mx_uint(flat_begin),
                    mx_uint(flat_end),
                    ctypes.byref(handle),
                )
            )
            sliced_shape = self._basic_indexing_sliced_shape(slc_key, self.shape)
            sliced = self.__class__(handle=handle, writable=self.writable)
            if 0 in sliced_shape:
                sliced = sliced.reshape(sliced_shape)
            else:
                sliced = sliced.reshape_view(sliced_shape)

        else:
            begin, end, step = self._basic_indexing_key_to_begin_end_step(
                slc_key, self.shape, keep_none=True
            )
            sliced = _npi.slice(self, begin, end, step)

        # Reshape to final shape due to integer and `None` entries in `key`.
        final_shape = [sliced.shape[i] for i in range(sliced.ndim) if i not in int_axes]
        for ax in new_axes:  # pylint: disable=invalid-name
            final_shape.insert(ax, 1)

        if sliced.size == 0:
            return sliced.reshape(tuple(final_shape))
        else:
            return sliced.reshape_view(tuple(final_shape))

    def _get_np_advanced_indexing(self, key):
        idcs, new_axes = self._get_index_nd(key)
        if type(idcs) == NDArray:  # pylint: disable=unidiomatic-typecheck
            idcs = idcs.as_np_ndarray()
        else:
            idcs = _npi.stack(*[i if isinstance(i, self.__class__) else i.as_np_ndarray() for i in idcs])
        sliced = _npi.gather_nd(self, idcs)
        # Reshape due to `None` entries in `key`.
        if new_axes:
            final_shape = [sliced.shape[i] for i in range(sliced.ndim)]
            for ax in new_axes:  # pylint: disable=invalid-name
                final_shape.insert(ax, 1)
            return sliced.reshape(tuple(final_shape))
        else:
            return sliced

    def _set_np_advanced_indexing(self, key, value):
        """This function is called by __setitem__ when key is an advanced index."""
        idcs, new_axes = self._get_index_nd(key)
        if type(idcs) == NDArray:  # pylint: disable=unidiomatic-typecheck
            idcs = idcs.as_np_ndarray()
        else:
            idcs = _npi.stack(*[i if isinstance(i, self.__class__) else i.as_np_ndarray() for i in idcs])
        vshape = get_oshape_of_gather_nd_op(self.shape, idcs.shape)
        value_nd = self._prepare_value_nd(value, bcast_shape=vshape, squeeze_axes=new_axes)
        self._scatter_set_nd(value_nd, idcs)

    # pylint: disable=too-many-return-statements
    def __getitem__(self, key):
        """Return self[key].

        Returns a sliced view of this array if the elements fetched are contiguous in memory;
        otherwise, returns a newly created NDArray.
        This functions supports advanced indexing defined in the following reference with
        some restrictions. Boolean indexing is supported only for a single boolean ndarray
        as a key. Mixing boolean ndarray with other index types is not supported in ``advanced``
        indexing.

        For basic indexing, i.e., if ``key`` consists only of integers,
        ``slice``, ``Ellipsis`` (``...``) and ``None``, a mutable view is
        returned that shares memory with this array if the accessed portion is
        contiguous in memory.
        Otherwise, a newly created ``ndarray`` is returned.

        This functions supports advanced indexing as defined in `the NumPy
        advanced indexing documentation
        <https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html#advanced-indexing>`_.

        Parameters
        ----------
        key : int, slice, list, np.ndarray, mx.np.ndarray, or tuple of all previous types
            Indexing key.

        Examples
        --------
        The default is to give explicit indices for all axes:

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

        If fewer indices are given, they are automatically supplemented by an
        appropriate number of ``slice(None)`` ("``:``") to the right. For
        instance, a single integer indexes along the first axis:

        >>> x[0]
        array([0., 1., 2.])
        >>> x[1:]
        array([[3., 4., 5.]])

        To omit a range of axes that should be kept as-is, an `Ellipsis`
        ("``...``") can be used:

        >>> x = np.arange(16).reshape(2, 2, 2, 2)
        >>> x[0, ..., 1]
        array([[1., 3.],
               [5., 7.]])
        >>> x[0, :, :, 1]  # equivalent
        array([[1., 3.],
               [5., 7.]])

        New axes of length 1 can be created by inserting ``None``
        (`numpy.newaxis`) in the index:

        >>> x = np.arange(6).reshape(2, 3)
        >>> x[None, :, :]
        array([[[0., 1., 2.],
                [3., 4., 5.]]])
        >>> x[None, :, :].shape
        (1, 2, 3)

        If the indexed portion of the array is contiguous in memory, no data
        is copied. Instead, a shared-memory view of the original array is
        returned, and changes to that view affect the original array:

        >>> x = np.arange(8).reshape(2, 2, 2)
        >>> y = x[0]  # contiguous
        >>> y
        array([[0., 1.],
               [2., 3.]])
        >>> y[:] = -1
        >>> x
        array([[[-1., -1.],
                [-1., -1.]],
               [[ 4.,  5.],
                [ 6.,  7.]]])
        >>> x = np.arange(8).reshape(2, 2, 2)
        >>> y = x[1, :1, :]  # contiguous
        >>> y
        array([[4., 5.]])
        >>> y[:] = -1
        >>> x
        array([[[ 0.,  1.],
                [ 2.,  3.]],
               [[-1., -1.],
                [ 6.,  7.]]])
        >>> x = np.arange(0, 8).reshape(2, 2, 2)
        >>> y = x[:, :, 1]  # not contiguous
        >>> y
        array([[1., 3.],
               [5., 7.]])
        >>> y[:] = -1
        >>> x
        array([[[0., 1.],
                [2., 3.]],
               [[4., 5.],
                [6., 7.]]])

        If the indexing key contains `list`, `numpy.ndarray` or `NDArray`
        objects, advanced indexing is triggered, which always returns a
        copy:

        >>> x = np.arange(8).reshape(2, 2, 2)
        >>> x[[0, 1]]
        array([[[0., 1.],
                [2., 3.]],
               [[4., 5.],
                [6., 7.]]])
        >>> x[[0, 1], :]  # equivalent
        array([[[0., 1.],
                [2., 3.]],
               [[4., 5.],
                [6., 7.]]])
        >>> y = np.array([0, 1], dtype='int32')
        >>> x[1:, y]
        array([[[4., 5.],
                [6., 7.]]])
        >>> y = np.array([0, 1], dtype='int32')
        >>> x[1:, y]
        array([[[4., 5.],
                [6., 7.]]])

        Get negative elements in an ndarray through boolean array indexing
        >>> x = np.array([1., -1., -2., 3])
        >>> x[x < 0]
        array([-1., -2.])
        """
        # handling possible boolean indexing first
        ndim = self.ndim
        shape = self.shape  # pylint: disable=redefined-outer-name

        if isinstance(key, list):
            try:
                new_key = _np.array(key)
                if new_key.dtype == _np.bool_:
                    key = new_key
            except Exception as err:
                raise TypeError('{}'.format(str(err)))
        if isinstance(key, _np.ndarray) and key.dtype == _np.bool_:
            key = array(key, dtype='bool', ctx=self.ctx)
        if isinstance(key, ndarray) and key.dtype == _np.bool_:  # boolean indexing
            key_shape = key.shape
            key_ndim = len(key_shape)
            if ndim < key_ndim:
                raise IndexError('too many indices, whose ndim = {}, for array with ndim = {}'
                                 .format(key_ndim, ndim))
            for i in range(key_ndim):
                if key_shape[i] != shape[i]:
                    raise IndexError('boolean index did not match indexed array along dimension {};'
                                     ' dimension is {} but corresponding boolean dimension is {}'
                                     .format(i, shape[i], key_shape[i]))
            remaining_dims = shape[key_ndim:]
            data = _reshape_view(self, -1, *remaining_dims)
            key = _reshape_view(key, -1)
            return _reshape_view(_npi.boolean_mask(data, key), -1, *remaining_dims)

        if ndim == 0:
            if key != ():
                raise IndexError('scalar tensor can only accept `()` as index')
        # Handle simple cases for higher speed
        if isinstance(key, tuple) and len(key) == 0:
            return self
        if isinstance(key, tuple) and len(key) == ndim\
                and all(isinstance(idx, integer_types) for idx in key):
            out = self
            for idx in key:
                out = out[idx]
            return out
        if isinstance(key, integer_types):
            if key > shape[0] - 1:
                raise IndexError(
                    'index {} is out of bounds for axis 0 with size {}'.format(
                        key, shape[0]))
            return self._at(key)
        elif isinstance(key, py_slice):
            if key.step is None or key.step == 1:
                if key.start is not None or key.stop is not None:
                    return self._slice(key.start, key.stop)
                else:
                    return self
            elif key.step == 0:
                raise ValueError("slice step cannot be zero")

        key = indexing_key_expand_implicit_axes(key, self.shape)
        indexing_dispatch_code = get_indexing_dispatch_code(key)
        if indexing_dispatch_code == _NDARRAY_BASIC_INDEXING:
            return self._get_np_basic_indexing(key)
        elif indexing_dispatch_code == _NDARRAY_ADVANCED_INDEXING:
            return self._get_np_advanced_indexing(key)
        else:
            raise RuntimeError

    def __setitem__(self, key, value):
        """Sets ``self[key]`` to ``value``.

        This functions supports advanced indexing as defined in `the NumPy
        advanced indexing documentation
        <https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html#advanced-indexing>`_,
        with the restriction that boolean array indexing is not supported.

        Parameters
        ----------
        key : int, slice, list, np.ndarray, mx.np.ndarray, or tuple of all previous types
            The indexing key.
        value : scalar or array-like object that can be broadcast to the shape of self[key]
            The value to set.

        Examples
        --------
        >>> x = np.zeros((2, 3))
        >>> x[:] = 1
        >>> x
        array([[ 1.,  1.,  1.],
               [ 1.,  1.,  1.]])
        >>> x[:, 1:2] = 2
        >>> x
        array([[ 1.,  2.,  1.],
               [ 1.,  2.,  1.]])
        >>> x[1:2, 1:] = 3
        >>> x
        array([[ 1.,  2.,  1.],
               [ 1.,  3.,  3.]])
        >>> x[1:, 0:2] = np.zeros((1, 2))
        >>> x
        array([[ 1.,  2.,  1.],
               [ 0.,  0.,  3.]])
        >>> x[1, 2] = 4
        >>> x
        array([[ 1.,  2.,  1.],
               [ 0.,  0.,  4.]])
        >>> x[[0], [1, 2]] = 5
        >>> x
        array([[ 1.,  5.,  5.],
               [ 0.,  0.,  4.]])
        >>> x[::-1, 0:2:2] = [6]
        >>> x
        array([[ 6.,  5.,  5.],
               [ 6.,  0.,  4.]])
        """
        if isinstance(value, NDArray) and not isinstance(value, ndarray):
            raise TypeError('Cannot assign mx.nd.NDArray to mxnet.numpy.ndarray')

        # handle basic and advanced indexing
        if self.ndim == 0:
            if not isinstance(key, tuple) or len(key) != 0:
                raise IndexError('scalar tensor can only accept `()` as index')
            if isinstance(value, numeric_types):
                self._full(value)
            elif isinstance(value, ndarray) and value.size == 1:
                if value.shape != self.shape:
                    value = value.reshape(self.shape)
                value.copyto(self)
            elif isinstance(value, (_np.ndarray, _np.generic)) and value.size == 1:
                if isinstance(value, _np.generic) or value.shape != self.shape:
                    value = value.reshape(self.shape)
                self._sync_copyfrom(value)
            else:
                raise ValueError('setting an array element with a sequence.')
        else:
            key = indexing_key_expand_implicit_axes(key, self.shape)
            slc_key = tuple(idx for idx in key if idx is not None)
            if len(slc_key) < self.ndim:
                raise RuntimeError(
                    'too few indices after normalization: expected `ndim` ({}) '
                    'but got {}. This is a bug, please report it!'
                    ''.format(self.ndim, len(slc_key))
                )
            if len(slc_key) > self.ndim and self.ndim != 0:
                raise IndexError(
                    'too many indices ({}) for array with {} dimensions'
                    ''.format(len(slc_key), self.ndim)
                )
            indexing_dispatch_code = get_indexing_dispatch_code(slc_key)
            if indexing_dispatch_code == _NDARRAY_BASIC_INDEXING:
                self._set_nd_basic_indexing(key, value)  # function is inheritated from NDArray class
            elif indexing_dispatch_code == _NDARRAY_ADVANCED_INDEXING:
                self._set_np_advanced_indexing(key, value)
            else:
                raise ValueError(
                    'Indexing NDArray with index {} of type {} is not supported'
                    ''.format(key, type(key))
                )

    def _prepare_value_nd(self, value, bcast_shape, squeeze_axes=None):
        """Return a broadcast `ndarray` with same context and dtype as ``self``.
        For setting item, The returned `ndarray` is squeezed according to squeeze_axes since the
        value_nd is assigned to not yet expanded space in original array.
        `value`: numeric types or array like.
        `bcast_shape`: a shape tuple.
        `squeeze_axes`: a sequence of axes to squeeze in the value array.
        Note: mxnet.numpy.ndarray not support NDArray as assigned value.
        """
        if isinstance(value, numeric_types):
            value_nd = full(bcast_shape, value, ctx=self.ctx, dtype=self.dtype)
        elif isinstance(value, self.__class__):
            value_nd = value.as_in_ctx(self.ctx)
            if value_nd.dtype != self.dtype:
                value_nd = value_nd.astype(self.dtype)
        else:
            try:
                value_nd = array(value, ctx=self.ctx, dtype=self.dtype)
            except:
                raise TypeError('mxnet.np.ndarray does not support assignment with non-array-like '
                                'object {} of type {}'.format(value, type(value)))

        # For advanced indexing setitem, if there is None in indices, we need to squeeze the
        # assigned value_nd since None is also ignored in slicing the original array.
        if squeeze_axes and value_nd.ndim > len(bcast_shape):
            squeeze_axes = tuple([ax for ax in squeeze_axes if ax < len(value_nd.shape)])
            value_nd = value_nd.squeeze(axis=tuple(squeeze_axes))

        # handle the cases like the following
        # a = np.zeros((3, 3)), b = np.ones((1, 1, 1, 1, 3)), a[0] = b
        # b cannot broadcast directly to a[0].shape unless its leading 1-size axes are trimmed
        if value_nd.ndim > len(bcast_shape):
            squeeze_axes = []
            for i in range(value_nd.ndim - len(bcast_shape)):
                if value_nd.shape[i] == 1:
                    squeeze_axes.append(i)
                else:
                    break
            if squeeze_axes:
                value_nd = value_nd.squeeze(squeeze_axes)

        if value_nd.shape != bcast_shape:
            if value_nd.size == 0:
                value_nd = value_nd.reshape(bcast_shape)
            else:
                value_nd = value_nd.broadcast_to(bcast_shape)
        return value_nd

    def __add__(self, other):
        """x.__add__(y) <=> x + y"""
        return add(self, other)

    def __iadd__(self, other):
        """x.__iadd__(y) <=> x += y"""
        if not self.writable:
            raise ValueError('trying to add to a readonly ndarray')
        return add(self, other, out=self)

    def __sub__(self, other):
        """x.__sub__(y) <=> x - y"""
        return subtract(self, other)

    def __isub__(self, other):
        """x.__isub__(y) <=> x -= y"""
        if not self.writable:
            raise ValueError('trying to subtract from a readonly ndarray')
        return subtract(self, other, out=self)

    def __rsub__(self, other):
        """x.__rsub__(y) <=> y - x"""
        return subtract(other, self)

    def __mul__(self, other):
        """x.__mul__(y) <=> x * y"""
        return multiply(self, other)

    def __neg__(self):
        return self.__mul__(-1.0)

    def __imul__(self, other):
        """x.__imul__(y) <=> x *= y"""
        if not self.writable:
            raise ValueError('trying to add to a readonly ndarray')
        return multiply(self, other, out=self)

    def __rmul__(self, other):
        """x.__rmul__(y) <=> y * x"""
        return self.__mul__(other)

    def __div__(self, other):
        """x.__div__(y) <=> x / y"""
        return divide(self, other)

    def __rdiv__(self, other):
        """x.__rdiv__(y) <=> y / x"""
        return divide(other, self)

    def __idiv__(self, other):
        """x.__idiv__(y) <=> x /= y"""
        return divide(self, other, out=self)

    def __truediv__(self, other):
        """x.__truediv__(y) <=> x / y"""
        return divide(self, other)

    def __rtruediv__(self, other):
        """x.__rtruediv__(y) <=> y / x"""
        return divide(other, self)

    def __itruediv__(self, other):
        """x.__itruediv__(y) <=> x /= y"""
        return divide(self, other, out=self)

    def __mod__(self, other):
        """x.__mod__(y) <=> x % y"""
        return mod(self, other)

    def __rmod__(self, other):
        """x.__rmod__(y) <=> y % x"""
        return mod(other, self)

    def __imod__(self, other):
        """x.__imod__(y) <=> x %= y"""
        return mod(self, other, out=self)

    def __pow__(self, other):
        """x.__pow__(y) <=> x ** y"""
        return power(self, other)

    def __rpow__(self, other):
        """x.__rpow__(y) <=> y ** x"""
        return power(other, self)

    def __eq__(self, other):
        """x.__eq__(y) <=> x == y"""
        return equal(self, other)

    def __hash__(self):
        raise NotImplementedError

    def __ne__(self, other):
        """x.__ne__(y) <=> x != y"""
        return not_equal(self, other)

    def __gt__(self, other):
        """x.__gt__(y) <=> x > y"""
        return greater(self, other)

    def __ge__(self, other):
        """x.__ge__(y) <=> x >= y"""
        return greater_equal(self, other)

    def __lt__(self, other):
        """x.__lt__(y) <=> x < y"""
        return less(self, other)

    def __le__(self, other):
        """x.__le__(y) <=> x <= y"""
        return less_equal(self, other)

    def __bool__(self):
        num_elements = self.size
        if num_elements == 0:
            warnings.simplefilter('default')
            warnings.warn('The truth value of an empty array is ambiguous. Returning False, but in'
                          ' future this will result in an error.', DeprecationWarning)
            return False
        elif num_elements == 1:
            return bool(self.item())
        else:
            raise ValueError("The truth value of an ndarray with multiple elements is ambiguous.")

    __nonzero__ = __bool__

    def __float__(self):
        num_elements = self.size
        if num_elements != 1:
            raise TypeError('only size-1 arrays can be converted to Python scalars')
        return float(self.item())

    def __int__(self):
        num_elements = self.size
        if num_elements != 1:
            raise TypeError('only size-1 arrays can be converted to Python scalars')
        return int(self.item())

    def __len__(self):
        """Number of elements along the first axis."""
        shape = self.shape  # pylint: disable=redefined-outer-name
        if len(shape) == 0:
            raise TypeError('len() of unsized object')
        return self.shape[0]

    def __reduce__(self):
        return ndarray, (None,), self.__getstate__()

    def item(self, *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.
        """
        # TODO(junwu): no need to call asnumpy() on the whole array.
        return self.asnumpy().item(*args)

    def nonzero(self):
        """Return the indices of the elements that are non-zero.

        Refer to `numpy.nonzero` for full documentation.

        See Also
        --------
        numpy.nonzero : equivalent function
        """
        return nonzero(self)

    @property
    # pylint: disable= invalid-name, undefined-variable
    def T(self):
        """Same as self.transpose(). This always returns a copy of self."""
        return self.transpose()
    # pylint: enable= invalid-name, undefined-variable

    def all(self, axis=None, out=None, keepdims=False):
        raise NotImplementedError

    def any(self, axis=None, out=None, keepdims=False):
        raise NotImplementedError

    def as_nd_ndarray(self):
        """Convert mxnet.numpy.ndarray to mxnet.ndarray.NDArray to use its fluent methods."""
        hdl = NDArrayHandle()
        check_call(_LIB.MXShallowCopyNDArray(self.handle, ctypes.byref(hdl)))
        return NDArray(handle=hdl, writable=self.writable)

    def as_np_ndarray(self):
        """A convenience function for creating a numpy ndarray from the current ndarray
        with zero copy. For this class, it just returns itself since it's already a
        numpy ndarray."""
        return self

    def __repr__(self):
        """
        Returns a string representation of the array. The dtype of the ndarray will not
        be appended to the string if it is `float32`. The context of the ndarray will
        be appended for devices other than CPU.

        Examples
        --------
        >>> from mxnet import np, npx
        >>> a = np.random.uniform(size=(2, 3))
        >>> a
        array([[0.5488135 , 0.5928446 , 0.71518934],
               [0.84426576, 0.60276335, 0.8579456 ]])
        >>> print(a)
        [[0.5488135  0.5928446  0.71518934]
         [0.84426576 0.60276335 0.8579456 ]]
        >>> a.dtype
        <class 'numpy.float32'>
        >>> b = a.astype(np.float64)
        >>> b
        array([[0.54881352, 0.59284461, 0.71518934],
               [0.84426576, 0.60276335, 0.85794562]], dtype=float64)
        >>> print(b)
        [[0.54881352 0.59284461 0.71518934]
         [0.84426576 0.60276335 0.85794562]]
        >>> b.dtype
        <class 'numpy.float64'>
        >>> c = a.copyto(npx.gpu(0))
        >>> c
        array([[0.5488135 , 0.5928446 , 0.71518934],
               [0.84426576, 0.60276335, 0.8579456 ]], ctx=gpu(0))
        >>> print(c)
        [[0.5488135  0.5928446  0.71518934]
         [0.84426576 0.60276335 0.8579456 ]] @gpu(0)
        >>> d = b.copyto(npx.gpu(0))
        >>> d
        array([[0.54881352, 0.59284461, 0.71518934],
               [0.84426576, 0.60276335, 0.85794562]], dtype=float64, ctx=gpu(0))
        >>> print(d)
        [[0.54881352 0.59284461 0.71518934]
         [0.84426576 0.60276335 0.85794562]] @gpu(0)
        """
        array_str = self.asnumpy().__repr__()
        dtype = self.dtype
        if 'dtype=' in array_str:
            if dtype == _np.float32:
                array_str = array_str[:array_str.rindex(',')] + ')'
        elif dtype not in (_np.float32, _np.bool_):
            array_str = array_str[:-1] + ', dtype={})'.format(dtype)

        context = self.context
        if context.device_type == 'cpu':
            return array_str
        return array_str[:-1] + ', ctx={})'.format(str(context))

    def __str__(self):
        """Returns a string representation of the array."""
        array_str = self.asnumpy().__str__()
        context = self.context
        if context.device_type == 'cpu' or self.ndim == 0:
            return array_str
        return '{array} @{ctx}'.format(array=array_str, ctx=context)

    def attach_grad(self, grad_req='write'):  # pylint: disable=arguments-differ
        """Attach a gradient buffer to this ndarray, so that `backward`
        can compute gradient with respect to it.

        Parameters
        ----------
        grad_req : {'write', 'add', 'null'}
            How gradient will be accumulated.
            - 'write': gradient will be overwritten on every backward.
            - 'add': gradient will be added to existing value on every backward.
            - 'null': do not compute gradient for this NDArray.
        """
        grad = _mx_np_op.zeros_like(self)  # pylint: disable=undefined-variable
        grad_req = _GRAD_REQ_MAP[grad_req]
        check_call(_LIB.MXAutogradMarkVariables(
            1, ctypes.pointer(self.handle),
            ctypes.pointer(mx_uint(grad_req)),
            ctypes.pointer(grad.handle)))

    @property
    def grad(self):
        """Returns gradient buffer attached to this ndarray."""
        hdl = NDArrayHandle()
        check_call(_LIB.MXNDArrayGetGrad(self.handle, ctypes.byref(hdl)))
        if hdl.value is None:
            return None
        return _np_ndarray_cls(hdl)

    def detach(self):
        """Returns a new ndarray, detached from the current graph."""
        hdl = NDArrayHandle()
        check_call(_LIB.MXNDArrayDetach(self.handle, ctypes.byref(hdl)))
        return _np_ndarray_cls(hdl)

    def astype(self, dtype, **kwargs):  # pylint: disable=arguments-differ,unused-argument
        """
        Copy of the array, cast to a specified type.

        Parameters
        ----------
        dtype : str or dtype
            Typecode or data-type to which the array is cast.
        copy : bool, optional
            Default `True`. By default, astype always returns a newly
            allocated ndarray on the same context. If this is set to
            `False`, and the dtype requested is the same as the ndarray's
            dtype, the ndarray 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`.
        """
        _sanity_check_params('astype', ['order', 'casting', 'subok'], kwargs)
        copy = kwargs.get('copy', True)
        if not copy and _np.dtype(dtype) == self.dtype:
            return self

        res = empty(self.shape, dtype=dtype, ctx=self.context)
        self.copyto(res)
        return res

    def copyto(self, other):
        """Copies the value of this array to another array.

        If ``other`` is a ``ndarray`` object, then ``other.shape`` and
        ``self.shape`` should be the same. This function copies the value from
        ``self`` to ``other``.

        If ``other`` is a context, a new ``np.ndarray`` will be first created on
        the target context, and the value of ``self`` is copied.

        Parameters
        ----------
        other : ndarray or Context
            The destination array or context.

        Returns
        -------
        out: ndarray
            The copied array. If ``other`` is an ``ndarray``, then the return value
            and ``other`` will point to the same ``ndarray``.

        Examples
        --------
        >>> x = np.ones((2, 3))
        >>> y = np.zeros((2, 3), ctx=npx.gpu(0))
        >>> z = x.copyto(y)
        >>> z is y
        True
        >>> y
        array([[ 1.,  1.,  1.],
               [ 1.,  1.,  1.]])
        """
        if isinstance(other, ndarray):
            if other.handle is self.handle:
                warnings.warn('You are attempting to copy an array to itself', RuntimeWarning)
                return False
            return _npi.copyto(self, out=other)
        elif isinstance(other, Context):
            hret = ndarray(_new_alloc_handle(self.shape, other, True, self.dtype))
            return _npi.copyto(self, out=hret)
        else:
            raise TypeError('copyto does not support type ' + str(type(other)))

    def asscalar(self):
        raise AttributeError('mxnet.numpy.ndarray object has no attribute asscalar')

    def argmax(self, axis=None, out=None):  # pylint: disable=arguments-differ
        """Return indices of the maximum values along the given axis.
        Refer to `mxnet.numpy.argmax` for full documentation."""
        return argmax(self, axis, out)

    def as_in_context(self, context):
        """This function has been deprecated. Please refer to ``ndarray.as_in_ctx``."""
        warnings.warn('ndarray.context has been renamed to ndarray.ctx', DeprecationWarning)
        return self.as_nd_ndarray().as_in_context(context).as_np_ndarray()

    def as_in_ctx(self, ctx):
        """Returns an array on the target device with the same value as this array.

        If the target context is the same as ``self.context``, then ``self`` is
        returned.  Otherwise, a copy is made.

        Parameters
        ----------
        context : Context
            The target context.

        Returns
        -------
        ndarray
            The target array.
        """
        if self.ctx == ctx:
            return self
        return self.copyto(ctx)

    @property
    def ctx(self):
        """Device context of the array.

        Examples
        --------
        >>> x = np.array([1, 2, 3, 4])
        >>> x.ctx
        cpu(0)
        >>> type(x.ctx)
        <class 'mxnet.context.Context'>
        >>> y = np.zeros((2, 3), npx.gpu(0))
        >>> y.ctx
        gpu(0)
        """
        dev_typeid = ctypes.c_int()
        dev_id = ctypes.c_int()
        check_call(_LIB.MXNDArrayGetContext(
            self.handle, ctypes.byref(dev_typeid), ctypes.byref(dev_id)))
        return Context(Context.devtype2str[dev_typeid.value], dev_id.value)

    @property
    def context(self):
        """This function has been deprecated. Please refer to ``ndarray.ctx``."""
        warnings.warn('ndarray.context has been renamed to ndarray.ctx', DeprecationWarning)
        return self.as_nd_ndarray().context

    def copy(self, order='C'):  # pylint: disable=arguments-differ
        """Return a coyp of the array, keeping the same context.

        Parameters
        ----------
        order : str
            The memory layout of the copy. Currently, only c-contiguous memory
            layout is supported.

        Examples
        --------
        >>> x = np.ones((2, 3))
        >>> y = x.copy()
        >>> y
        array([[ 1.,  1.,  1.],
               [ 1.,  1.,  1.]])
        """
        if order != 'C':
            raise NotImplementedError('ndarray.copy only supports order=\'C\', while '
                                      'received {}'.format(str(order)))
        return self.copyto(self.ctx)

    def dot(self, b, out=None):
        """Dot product of two arrays.
        Refer to ``numpy.dot`` for full documentation."""
        return _mx_np_op.dot(self, b, out=out)

    def reshape(self, *args, **kwargs):  # pylint: disable=arguments-differ
        """Returns a copy of the array with a new shape.

        Notes
        -----
        Unlike the free function `numpy.reshape`, this method on `ndarray` allows
        the elements of the shape parameter to be passed in as separate arguments.
        For example, ``a.reshape(10, 11)`` is equivalent to
        ``a.reshape((10, 11))``.
        """
        order = 'C'
        if len(kwargs) > 1:
            raise TypeError('function takes at most 1 keyword argument')
        if len(kwargs) == 1:
            if 'order' not in kwargs:
                raise TypeError('{} is an invalid keyword argument for this function'
                                .format(kwargs.keys()[0]))
            order = kwargs.pop('order', 'C')
            if order != 'C':
                raise NotImplementedError('only supports C-order,'
                                          ' while received {}'.format(order))
        if len(args) == 0:
            raise TypeError('reshape() takes exactly 1 argument (0 given)')
        if len(args) == 1 and isinstance(args[0], tuple):
            return _mx_np_op.reshape(self, newshape=args[0], order=order)
        else:
            return _mx_np_op.reshape(self, newshape=args, order=order)

    def reshape_like(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`reshape_like`.

        The arguments are the same as for :py:func:`reshape_like`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute reshape_like')

    def reshape_view(self, *shape, **kwargs):  # pylint: disable=redefined-outer-name
        """Returns a **view** of this array with a new shape without altering any data.
        Inheritated from NDArray.reshape.
        """
        return super(ndarray, self).reshape(*shape, **kwargs)

    def zeros_like(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`zeros_like`.

        The arguments are the same as for :py:func:`zeros_like`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute zeros_like')

    def ones_like(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`ones_like`.

        The arguments are the same as for :py:func:`ones_like`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute ones_like')

    def broadcast_axes(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`broadcast_axes`.

        The arguments are the same as for :py:func:`broadcast_axes`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute broadcast_like')

    def repeat(self, repeats, axis=None):  # pylint: disable=arguments-differ
        """Repeat elements of an array."""
        return _mx_np_op.repeat(self, repeats=repeats, axis=axis)

    def pad(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`pad`.

        The arguments are the same as for :py:func:`pad`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute pad')

    def swapaxes(self, axis1, axis2):  # pylint: disable=arguments-differ
        """Return a copy of the array with axis1 and axis2 interchanged.
        Refer to `mxnet.numpy.swapaxes` for full documentation.
        """
        return swapaxes(self, axis1, axis2)

    def split(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`split`.

        The arguments are the same as for :py:func:`split`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute split')

    def split_v2(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`split_v2`.

        The arguments are the same as for :py:func:`split_v2`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute split_v2')

    def slice(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`slice`.

        The arguments are the same as for :py:func:`slice`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute slice')

    def slice_axis(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`slice_axis`.

        The arguments are the same as for :py:func:`slice_axis`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute slice_axis')

    def slice_like(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`slice_like`.

        The arguments are the same as for :py:func:`slice_like`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute slice_like')

    def slice_assign_scalar(self, value, begin, end, step):
        """
        Assign the scalar to a cropped subset of this ndarray. Value will broadcast to the shape of the cropped shape
        and will be cast to the same dtype of the ndarray.

        Parameters
        ----------
        value: numeric value
            Value and this ndarray should be of the same data type.
            The shape of rhs should be the same as the cropped shape of this ndarray.
        begin: tuple of begin indices
        end: tuple of end indices
        step: tuple of step lenghths

        Returns
        -------
        This ndarray.

        Examples
        --------
        >>> x = np.ones((2, 2, 2))
        >>> y = x.slice_assign_scalar(0, (0, 0, None), (1, 1, None), (None, None, None))
        >>> y
        array([[[0., 0.],
                [1., 1.]],

               [[1., 1.],
                [1., 1.]]])
        >>> x
        array([[[0., 0.],
                [1., 1.]],

               [[1., 1.],
                [1., 1.]]])
        """
        return _npi.slice_assign_scalar(self, value, begin=begin, end=end, step=step, out=self)

    def slice_assign(self, rhs, begin, end, step):
        """
        Assign the rhs to a cropped subset of this ndarray in place.
        Returns the view of this ndarray.

        Parameters
        ----------
        rhs: ndarray.
            rhs and this NDArray should be of the same data type, and on the same device.
            The shape of rhs should be the same as the cropped shape of this ndarray.
        begin: tuple of begin indices
        end: tuple of end indices
        step: tuple of step lenghths

        Returns
        -------
        out : ndarray
            This ndarray.

        Examples
        --------
        >>> x = np.ones((2, 2, 2))
        >>> assigned = np.zeros((1, 1, 2))
        >>> y = x.slice_assign(assigned, (0, 0, None), (1, 1, None), (None, None, None))
        >>> y
        array([[[0., 0.],
                [1., 1.]],

               [[1., 1.],
                [1., 1.]]])
        >>> x
        array([[[0., 0.],
                [1., 1.]],

               [[1., 1.],
                [1., 1.]]])
        """
        return _npi.slice_assign(self, rhs, begin=begin, end=end, step=step, out=self)

    def take(self, indices, axis=None, mode='raise'):  # pylint: disable=arguments-differ, redefined-outer-name
        """Convenience fluent method for :py:func:`take`.

        The arguments are the same as for :py:func:`take`, with
        this array as data.
        """
        return take(self, indices, axis, mode=mode)

    def one_hot(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`one_hot`.

        The arguments are the same as for :py:func:`one_hot`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute one_hot')

    def pick(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`pick`.

        The arguments are the same as for :py:func:`pick`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute pick')

    def sort(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`sort`.

        The arguments are the same as for :py:func:`sort`, with
        this array as data.
        """
        raise NotImplementedError

    def topk(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`topk`.

        The arguments are the same as for :py:func:`topk`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute topk')

    def argsort(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`argsort`.

        The arguments are the same as for :py:func:`argsort`, with
        this array as data.
        """
        raise NotImplementedError

    def argmax_channel(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`argmax_channel`.

        The arguments are the same as for :py:func:`argmax_channel`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute argmax_channel')

    def argmin(self, axis=None, out=None):  # pylint: disable=arguments-differ
        """Return indices of the minium values along the given axis.
        Refer to `mxnet.numpy.argmin` for full documentation."""
        return argmin(self, axis, out)

    def clip(self, min=None, max=None, out=None):  # pylint: disable=arguments-differ
        """Return an array whose values are limited to [min, max].
        One of max or min must be given.
        """
        return clip(self, min, max, out=out)

    def abs(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`abs`.

        The arguments are the same as for :py:func:`abs`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute abs')

    def sign(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`sign`.

        The arguments are the same as for :py:func:`sign`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute sign')

    def flatten(self, order='C'):  # pylint: disable=arguments-differ
        """Return a copy of the array collapsed into one dimension."""
        return self.reshape(-1, order=order)

    def shape_array(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`shape_array`.

        The arguments are the same as for :py:func:`shape_array`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute shape_array')

    def size_array(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`size_array`.

        The arguments are the same as for :py:func:`size_array`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute size_array')

    def expand_dims(self, *args, **kwargs):  # pylint: disable=arguments-differ,unused-argument
        """Convenience fluent method for :py:func:`expand_dims`.

        The arguments are the same as for :py:func:`expand_dims`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute expand_dims')

    def tile(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`tile`.

        The arguments are the same as for :py:func:`tile`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute tile')

    def transpose(self, *axes):  # pylint: disable=arguments-differ
        """Permute the dimensions of an array."""
        if len(axes) == 0:
            axes = None
        elif len(axes) == 1:
            if isinstance(axes[0], (tuple, list)):
                axes = axes[0]
            elif axes[0] is None:
                axes = None
        return _mx_np_op.transpose(self, axes=axes)

    def flip(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`flip`.

        The arguments are the same as for :py:func:`flip`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute flip')

    def depth_to_space(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`depth_to_space`.

        The arguments are the same as for :py:func:`depth_to_space`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute depth_to_space')

    def space_to_depth(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`space_to_depth`.

        The arguments are the same as for :py:func:`space_to_depth`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute space_to_depth')

    def diag(self, k=0, **kwargs):
        """Convenience fluent method for :py:func:`diag`.

        The arguments are the same as for :py:func:`diag`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute diag')

    def sum(self, axis=None, dtype=None, out=None, keepdims=False):  # pylint: disable=arguments-differ
        """Return the sum of the array elements over the given axis."""
        return _mx_np_op.sum(self, axis=axis, dtype=dtype, out=out, keepdims=keepdims)

    def nansum(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`nansum`.

        The arguments are the same as for :py:func:`nansum`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute nansum')

    def prod(self, axis=None, dtype=None, out=None, keepdims=False):  # pylint: disable=arguments-differ
        """Return the product of the array elements over the given axis."""
        return _mx_np_op.prod(self, axis=axis, dtype=dtype, keepdims=keepdims, out=out)

    def nanprod(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`nanprod`.

        The arguments are the same as for :py:func:`nanprod`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute nanprod')

    def mean(self, axis=None, dtype=None, out=None, keepdims=False):  # pylint: disable=arguments-differ
        """Returns the average of the array elements along given axis."""
        return mean(self, axis=axis, dtype=dtype, out=out, keepdims=keepdims)

    # pylint: disable=too-many-arguments, arguments-differ
    def std(self, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
        """Returns the standard deviation of the array elements along given axis."""
        return std(self, axis=axis, dtype=dtype, ddof=ddof, keepdims=keepdims, out=out)

    def var(self, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
        """Returns the variance of the array elements, along given axis."""
        return var(self, axis=axis, dtype=dtype, out=out, ddof=ddof, keepdims=keepdims)
    # pylint: enable=too-many-arguments, arguments-differ

    def cumsum(self, axis=None, dtype=None, out=None):
        """Return the cumulative sum of the elements along the given axis."""
        return _mx_np_op.cumsum(self, axis=axis, dtype=dtype, out=out)

    def tolist(self):
        return self.asnumpy().tolist()

    def max(self, axis=None, out=None, keepdims=False):  # pylint: disable=arguments-differ
        """Return the maximum along a given axis."""
        return _mx_np_op.max(self, axis=axis, keepdims=keepdims, out=out)

    def min(self, axis=None, out=None, keepdims=False):  # pylint: disable=arguments-differ
        """Convenience fluent method for :py:func:`min`.

        The arguments are the same as for :py:func:`min`, with
        this array as data.
        """
        return _mx_np_op.min(self, axis=axis, keepdims=keepdims, out=out)

    def norm(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`norm`.

        The arguments are the same as for :py:func:`norm`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute norm')

    def round(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`round`.

        The arguments are the same as for :py:func:`round`, with
        this array as data.
        """
        raise NotImplementedError

    def rint(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`rint`.

        The arguments are the same as for :py:func:`rint`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute rint')

    def fix(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`fix`.

        The arguments are the same as for :py:func:`fix`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute fix')

    def floor(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`floor`.

        The arguments are the same as for :py:func:`floor`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute floor')

    def ceil(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`ceil`.

        The arguments are the same as for :py:func:`ceil`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute ceil')

    def trunc(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`trunc`.

        The arguments are the same as for :py:func:`trunc`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute trunc')

    def sin(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`sin`.

        The arguments are the same as for :py:func:`sin`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute sin')

    def cos(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`cos`.

        The arguments are the same as for :py:func:`cos`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute cos')

    def tan(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`tan`.

        The arguments are the same as for :py:func:`tan`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute tan')

    def arcsin(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`arcsin`.

        The arguments are the same as for :py:func:`arcsin`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute arcsin')

    def arccos(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`arccos`.

        The arguments are the same as for :py:func:`arccos`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute arccos')

    def arctan(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`arctan`.

        The arguments are the same as for :py:func:`arctan`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute arctan')

    def degrees(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`degrees`.

        The arguments are the same as for :py:func:`degrees`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute degrees')

    def radians(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`radians`.

        The arguments are the same as for :py:func:`radians`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute radians')

    def sinh(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`sinh`.

        The arguments are the same as for :py:func:`sinh`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute sinh')

    def cosh(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`cosh`.

        The arguments are the same as for :py:func:`cosh`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute cosh')

    def tanh(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`tanh`.

        The arguments are the same as for :py:func:`tanh`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute tanh')

    def arcsinh(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`arcsinh`.

        The arguments are the same as for :py:func:`arcsinh`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute arcsinh')

    def arccosh(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`arccosh`.

        The arguments are the same as for :py:func:`arccosh`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute arccosh')

    def arctanh(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`arctanh`.

        The arguments are the same as for :py:func:`arctanh`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute arctanh')

    def exp(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`exp`.

        The arguments are the same as for :py:func:`exp`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute exp')

    def expm1(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`expm1`.

        The arguments are the same as for :py:func:`expm1`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute expm1')

    def log(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`log`.

        The arguments are the same as for :py:func:`log`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute log')

    def log10(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`log10`.

        The arguments are the same as for :py:func:`log10`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute log10')

    def log2(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`log2`.

        The arguments are the same as for :py:func:`log2`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute log2')

    def log1p(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`log1p`.

        The arguments are the same as for :py:func:`log1p`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute log1p')

    def sqrt(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`sqrt`.

        The arguments are the same as for :py:func:`sqrt`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute sqrt')

    def rsqrt(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`rsqrt`.

        The arguments are the same as for :py:func:`rsqrt`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute rsqrt')

    def cbrt(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`cbrt`.

        The arguments are the same as for :py:func:`cbrt`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute cqrt')

    def rcbrt(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`rcbrt`.

        The arguments are the same as for :py:func:`rcbrt`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute rcqrt')

    def square(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`square`.

        The arguments are the same as for :py:func:`square`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute square')

    def reciprocal(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`reciprocal`.

        The arguments are the same as for :py:func:`reciprocal`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute reciprocal')

    def relu(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`relu`.

        The arguments are the same as for :py:func:`relu`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute relu')

    def sigmoid(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`sigmoid`.

        The arguments are the same as for :py:func:`sigmoid`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute sigmoid')

    def softmax(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`softmax`.

        The arguments are the same as for :py:func:`softmax`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute softmax')

    def log_softmax(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`log_softmax`.

        The arguments are the same as for :py:func:`log_softmax`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute log_softmax')

    def softmin(self, *args, **kwargs):
        """Convenience fluent method for :py:func:`softmin`.

        The arguments are the same as for :py:func:`softmin`, with
        this array as data.
        """
        raise AttributeError('mxnet.numpy.ndarray object has no attribute softmin')

    def squeeze(self, axis=None):  # pylint: disable=arguments-differ
        """Remove single-dimensional entries from the shape of a."""
        return _mx_np_op.squeeze(self, axis=axis)

    def broadcast_to(self, shape):  # pylint: disable=redefined-outer-name
        return _mx_np_op.broadcast_to(self, shape)

    def broadcast_like(self, other):
        raise AttributeError('mxnet.numpy.ndarray object has no attribute broadcast_like')

    def _full(self, value):
        """
        Currently for internal use only. Implemented for __setitem__.
        Assign to self an array of self's same shape and type, filled with value.
        """
        return _mx_nd_np.full(self.shape, value, ctx=self.context, dtype=self.dtype, out=self)

    # pylint: disable=redefined-outer-name
    def _scatter_set_nd(self, value_nd, indices):
        """
        This is added as an ndarray class method in order to support polymorphism in NDArray and numpy.ndarray indexing
        """
        return _npi.scatter_set_nd(
            lhs=self, rhs=value_nd, indices=indices, shape=self.shape, out=self
        )
    # pylint: enable=redefined-outer-name

    @property
    def shape(self):
        return super(ndarray, self).shape

    @property
    def ndim(self):
        """Number of array dimensions."""
        return len(self.shape)

    @property
    def size(self):
        """Number of elements in the array."""
        return super(ndarray, self).size

    @property
    def dtype(self):
        """Data-type of the array's elements.

        Returns
        -------
        numpy.dtype
            This NDArray's data type.

        Examples
        --------
        >>> x = np.zeros((2,3))
        >>> x.dtype
        dtype('float32')
        >>> y = np.zeros((2,3), dtype='int32')
        >>> y.dtype
        dtype('int32')
        """
        return _np.dtype(super(ndarray, self).dtype)

    def tostype(self, stype):
        raise AttributeError('mxnet.numpy.ndarray object has no attribute tostype')


@set_module('mxnet.numpy')
def empty(shape, dtype=_np.float32, order='C', ctx=None):  # pylint: disable=redefined-outer-name
    """Return a new array of given shape and type, without initializing entries.

    Parameters
    ----------
    shape : int or tuple of int Shape of the empty array, e.g., ``(2, 3)`` or ``2``.
    dtype : data-type, optional
        Desired output data-type for the array, e.g, `numpy.int8`. Default is
        `numpy.float32`. Note that this behavior is different from NumPy's `empty`
        function where `float64` is the default value, because `float32` is
        considered as the default data type in deep learning.
    order : {'C'}, optional, default: 'C'
        How to store multi-dimensional data in memory, currently only row-major
        (C-style) is supported.
    ctx : device context, optional
        Device context on which the memory is allocated. Default is
        `mxnet.context.current_context()`.

    Returns
    -------
    out : ndarray
        Array of uninitialized (arbitrary) data of the given shape, dtype, and order.

    Examples
    --------
    >>> np.empty([2, 2])
    array([[ 0.000000e+00, -2.524355e-29],
           [          nan, -8.592023e+09]])  # uninitialized

    >>> np.empty([2, 2], dtype=int)
    array([[8751743591039004782, 3196766424264760104],
           [7583328881310196768,     562950123910254]], dtype=int64)  # uninitialized
    """
    if order != 'C':
        raise NotImplementedError('`empty` only supports order equal to `C`, while received {}'
                                  .format(str(order)))
    if ctx is None:
        ctx = current_context()
    if dtype is None:
        dtype = _np.float32
    if isinstance(shape, int):
        shape = (shape,)
    return ndarray(handle=_new_alloc_handle(shape, ctx, False, dtype))


@set_module('mxnet.numpy')
def array(object, dtype=None, ctx=None):
    """
    Create an array.

    Parameters
    ----------
    object : array_like or `numpy.ndarray` or `mxnet.numpy.ndarray`
        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. Default is `float32`.
    ctx : device context, optional
        Device context on which the memory is allocated. Default is
        `mxnet.context.current_context()`.

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

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

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

    >>> np.array([[1, 0], [0, 1]], dtype=bool)
    array([[ True, False],
           [False,  True]])
    """
    if ctx is None:
        ctx = current_context()
    if isinstance(object, (ndarray, _np.ndarray)):
        dtype = object.dtype if dtype is None else dtype
    elif isinstance(object, NDArray):
        raise ValueError("If you're trying to create a mxnet.numpy.ndarray "
                         "from mx.nd.NDArray, please use the zero-copy as_np_ndarray function.")
    else:
        if dtype is None:
            dtype = object.dtype if hasattr(object, "dtype") else _np.float32
        try:
            object = _np.array(object, dtype=dtype)
        except Exception as e:
            # printing out the error raised by official NumPy's array function
            # for transparency on users' side
            raise TypeError('{}'.format(str(e)))
    ret = empty(object.shape, dtype=dtype, ctx=ctx)
    if len(object.shape) == 0:
        ret[()] = object
    else:
        ret[:] = object
    return ret


@set_module('mxnet.numpy')
def shape(a):
    """
    Return the shape of an array.
    Parameters
    ----------
    a : array_like
        Input array.
    Returns
    -------
    shape : tuple of ints
        The elements of the shape tuple give the lengths of the
        corresponding array dimensions.
    See Also
    --------
    ndarray.shape : Equivalent array method.
    Examples
    --------
    >>> np.shape(np.eye(3))
    (3, 3)
    >>> np.shape([[1, 2]])
    (1, 2)
    >>> np.shape([0])
    (1,)
    >>> np.shape(0)
    ()
    """
    return _mx_nd_np.shape(a)


@set_module('mxnet.numpy')
def zeros(shape, dtype=_np.float32, order='C', ctx=None):  # pylint: disable=redefined-outer-name
    """Return a new array of given shape and type, filled with zeros.
    This function currently only supports storing multi-dimensional data
    in row-major (C-style).

    Parameters
    ----------
    shape : int or tuple of int
        The shape of the empty array.
    dtype : str or numpy.dtype, optional
        An optional value type (default is `numpy.float32`). Note that this
        behavior is different from NumPy's `zeros` function where `float64`
        is the default value, because `float32` is considered as the default
        data type in deep learning.
    order : {'C'}, optional, default: 'C'
        How to store multi-dimensional data in memory, currently only row-major
        (C-style) is supported.
    ctx : Context, optional
        An optional device context (default is the current default context).

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

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

    >>> np.zeros((5,), dtype=int)
    array([0, 0, 0, 0, 0], dtype=int64)

    >>> np.zeros((2, 1))
    array([[0.],
           [0.]])
    """
    return _mx_nd_np.zeros(shape, dtype, order, ctx)


@set_module('mxnet.numpy')
def ones(shape, dtype=_np.float32, order='C', ctx=None):  # pylint: disable=redefined-outer-name
    """Return a new array of given shape and type, filled with ones.
    This function currently only supports storing multi-dimensional data
    in row-major (C-style).

    Parameters
    ----------
    shape : int or tuple of int
        The shape of the empty array.
    dtype : str or numpy.dtype, optional
        An optional value type. Default is `numpy.float32`. Note that this
        behavior is different from NumPy's `ones` function where `float64`
        is the default value, because `float32` is considered as the default
        data type in deep learning.
    order : {'C'}, optional, default: 'C'
        How to store multi-dimensional data in memory, currently only row-major
        (C-style) is supported.
    ctx : Context, optional
        An optional device context (default is the current default context).

    Returns
    -------
    out : ndarray
        Array of ones with the given shape, dtype, and ctx.

    Examples
    --------
    >>> np.ones(5)
    array([1., 1., 1., 1., 1.])

    >>> np.ones((5,), dtype=int)
    array([1, 1, 1, 1, 1], dtype=int64)

    >>> np.ones((2, 1))
    array([[1.],
           [1.]])

    >>> s = (2,2)
    >>> np.ones(s)
    array([[1., 1.],
           [1., 1.]])
    """
    return _mx_nd_np.ones(shape, dtype, order, ctx)


# pylint: disable=too-many-arguments, redefined-outer-name
@set_module('mxnet.numpy')
def full(shape, fill_value, dtype=None, order='C', ctx=None, out=None):
    """
    Return a new array of given shape and type, filled with `fill_value`.

    Parameters
    ----------
    shape : int or sequence of ints
        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
    fill_value : scalar
        Fill value.
    dtype : data-type, optional
        The desired data-type for the array. The default, `None`, means
        `np.array(fill_value).dtype`.
    order : {'C'}, optional
        Whether to store multidimensional data in C- or Fortran-contiguous
        (row- or column-wise) order in memory. Currently only supports C order.
    ctx: to specify the device, e.g. the i-th GPU.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape and dtype as input ndarray.
        If not provided or `None`, a freshly-allocated array is returned.

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

    Notes
    -----
    This function differs from the original `numpy.full
    https://docs.scipy.org/doc/numpy/reference/generated/numpy.full.html`_ in
    the following way(s):

    - Has an additional `ctx` argument to specify the device
    - Has an additional `out` argument
    - Currently does not support `order` selection

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

    Examples
    --------
    >>> np.full((2, 2), 10)
    array([[10., 10.],
           [10., 10.]])
    >>> np.full((2, 2), 2, dtype=np.int32, ctx=mx.cpu(0))
    array([[2, 2],
           [2, 2]], dtype=int32)
    """
    return _mx_nd_np.full(shape, fill_value, order=order, ctx=ctx, dtype=dtype, out=out)
# pylint: enable=too-many-arguments, redefined-outer-name


@set_module('mxnet.numpy')
def identity(n, dtype=None, ctx=None):
    """
    Return the identity array.

    The identity array is a square array with ones on
    the main diagonal.

    Parameters
    ----------
    n : int
        Number of rows (and columns) in `n` x `n` output.
    dtype : data-type, optional
        Data-type of the output.  Defaults to ``numpy.float32``.
    ctx : Context, optional
        An optional device context (default is the current default context).

    Returns
    -------
    out : ndarray
        `n` x `n` array with its main diagonal set to one,
        and all other elements 0.

    Examples
    --------
    >>> np.identity(3)
    >>> np.identity(3)
    array([[1., 0., 0.],
           [0., 1., 0.],
           [0., 0., 1.]])
    """
    return _mx_nd_np.identity(n, dtype, ctx)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def take(a, indices, axis=None, mode='raise', out=None):
    r"""
    Take elements from an array along an axis.

    When axis is not None, this function does the same thing as "fancy"
    indexing (indexing arrays using arrays); however, it can be easier to use
    if you need elements along a given axis. A call such as
    ``np.take(arr, indices, axis=3)`` is equivalent to
    ``arr[:,:,:,indices,...]``.

    Explained without fancy indexing, this is equivalent to the following use
    of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of
    indices::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        Nj = indices.shape
        for ii in ndindex(Ni):
            for jj in ndindex(Nj):
                for kk in ndindex(Nk):
                    out[ii + jj + kk] = a[ii + (indices[jj],) + kk]

    Parameters
    ----------
    a : ndarray
        The source array.
    indices : ndarray
        The indices of the values to extract. Also allow scalars for indices.
    axis : int, optional
        The axis over which to select values. By default, the flattened
        input array is used.
    out : ndarray, optional
        If provided, the result will be placed in this array. It should
        be of the appropriate shape and dtype.
    mode : {'clip', 'wrap'}, optional
        Specifies how out-of-bounds indices will behave.

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

        'clip' mode means that all indices that are too large are replaced
        by the index that addresses the last element along that axis. Note
        that this disables indexing with negative numbers.

    Returns
    -------
    out : ndarray
        The returned array has the same type as `a`.

    Notes
    -----

    This function differs from the original `numpy.take
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.take.html>`_ in
    the following way(s):

    - Only ndarray or scalar ndarray is accepted as valid input.

    Examples
    --------
    >>> a = np.array([4, 3, 5, 7, 6, 8])
    >>> indices = np.array([0, 1, 4])
    >>> np.take(a, indices)
    array([4., 3., 6.])

    In this example for `a` is an ndarray, "fancy" indexing can be used.

    >>> a[indices]
    array([4., 3., 6.])

    If `indices` is not one dimensional, the output also has these dimensions.

    >>> np.take(a, np.array([[0, 1], [2, 3]]))
    array([[4., 3.],
           [5., 7.]])
    """
    return _mx_nd_np.take(a, indices, axis, mode, out)
# pylint: enable=redefined-outer-name


@set_module('mxnet.numpy')
def unique(ar, return_index=False, return_inverse=False, return_counts=False, axis=None):
    """
    Find the unique elements of an array.

    Returns the sorted unique elements of an array. There are three optional
    outputs in addition to the unique elements:

    * the indices of the input array that give the unique values
    * the indices of the unique array that reconstruct the input array
    * the number of times each unique value comes up in the input array

    Parameters
    ----------
    ar : ndarray
        Input array. Unless `axis` is specified, this will be flattened if it
        is not already 1-D.
    return_index : bool, optional
        If True, also return the indices of `ar` (along the specified axis,
        if provided, or in the flattened array) that result in the unique array.
    return_inverse : bool, optional
        If True, also return the indices of the unique array (for the specified
        axis, if provided) that can be used to reconstruct `ar`.
    return_counts : bool, optional
        If True, also return the number of times each unique item appears
        in `ar`.
    axis : int or None, optional
        The axis to operate on. If None, `ar` will be flattened. If an integer,
        the subarrays indexed by the given axis will be flattened and treated
        as the elements of a 1-D array with the dimension of the given axis,
        see the notes for more details. The default is None.

    Returns
    -------
    unique : ndarray
        The sorted unique values.
    unique_indices : ndarray, optional
        The indices of the first occurrences of the unique values in the
        original array. Only provided if `return_index` is True.
    unique_inverse : ndarray, optional
        The indices to reconstruct the original array from the
        unique array. Only provided if `return_inverse` is True.
    unique_counts : ndarray, optional
        The number of times each of the unique values comes up in the
        original array. Only provided if `return_counts` is True.

    Notes
    -----
    When an axis is specified the subarrays indexed by the axis are sorted.
    This is done by making the specified axis the first dimension of the array
    and then flattening the subarrays in C order. The flattened subarrays are
    then viewed as a structured type with each element given a label, with the
    effect that we end up with a 1-D array of structured types that can be
    treated in the same way as any other 1-D array. The result is that the
    flattened subarrays are sorted in lexicographic order starting with the
    first element.

    This function differs from the original `numpy.unique
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.unique.html>`_ in
    the following aspects:

    - Only support ndarray as input.
    - Object arrays or structured arrays are not supported.

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

    Return the unique rows of a 2D array

    >>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
    >>> np.unique(a, axis=0)
    array([[1., 0., 0.],
           [2., 3., 4.]])

    Return the indices of the original array that give the unique values:

    >>> a = np.array([1, 2, 6, 4, 2, 3, 2])
    >>> u, indices = np.unique(a, return_index=True)
    >>> u
    array([1., 2., 3., 4., 6.])
    >>> indices
    array([0, 1, 5, 3, 2], dtype=int64)
    >>> a[indices]
    array([1., 2., 3., 4., 6.])

    Reconstruct the input array from the unique values:

    >>> a = np.array([1, 2, 6, 4, 2, 3, 2])
    >>> u, indices = np.unique(a, return_inverse=True)
    >>> u
    array([1., 2., 3., 4., 6.])
    >>> indices
    array([0, 1, 4, 3, 1, 2, 1], dtype=int64)
    >>> u[indices]
    array([1., 2., 6., 4., 2., 3., 2.])
    """
    return _mx_nd_np.unique(ar, return_index, return_inverse, return_counts, axis)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def add(x1, x2, out=None, **kwargs):
    """
    Add arguments element-wise.

    Parameters
    ----------
    x1, x2 : ndarrays or scalar values
        The arrays to be added. If x1.shape != x2.shape, they must be broadcastable to
        a common shape (which may be the shape of one or the other).

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    add : ndarray or scalar
        The sum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

    Notes
    -----
    This operator now supports automatic type promotion. The resulting type will be determined
    according to the following rules:
        * If both inputs are of floating number types, the output is the more precise type.
        * If only one of the inputs is floating number type, the result is that type.
        * If both inputs are of integer types (including boolean), not supported yet.

    Examples
    --------
    >>> np.add(1.0, 4.0)
    5.0
    >>>
    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.add(x1, x2)
    array([[ 0.,  2.,  4.],
           [ 3.,  5.,  7.],
           [ 6.,  8., 10.]])
    """
    return _mx_nd_np.add(x1, x2, out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def subtract(x1, x2, out=None, **kwargs):
    """
    Subtract arguments element-wise.

    Parameters
    ----------
    x1, x2 : ndarrays or scalar values
        The arrays to be subtracted from each other. If x1.shape != x2.shape,
        they must be broadcastable to a common shape (which may be the shape
        of one or the other).

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    subtract : ndarray or scalar
        The difference of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

    Notes
    -----
    This operator now supports automatic type promotion. The resulting type will be determined
    according to the following rules:
        * If both inputs are of floating number types, the output is the more precise type.
        * If only one of the inputs is floating number type, the result is that type.
        * If both inputs are of integer types (including boolean), not supported yet.

    Examples
    --------
    >>> np.subtract(1.0, 4.0)
    -3.0
    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.subtract(x1, x2)
    array([[0., 0., 0.],
           [3., 3., 3.],
           [6., 6., 6.]])
    """
    return _mx_nd_np.subtract(x1, x2, out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def multiply(x1, x2, out=None, **kwargs):
    """
    Multiply arguments element-wise.

    Parameters
    ----------
    x1, x2 : ndarrays or scalar values
        The arrays to be multiplied. If x1.shape != x2.shape, they must be broadcastable to
        a common shape (which may be the shape of one or the other).

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    out : ndarray or scalar
        The difference of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

    Notes
    -----
    This operator now supports automatic type promotion. The resulting type will be determined
    according to the following rules:
        * If both inputs are of floating number types, the output is the more precise type.
        * If only one of the inputs is floating number type, the result is that type.
        * If both inputs are of integer types (including boolean), not supported yet.

    Examples
    --------
    >>> np.multiply(2.0, 4.0)
    8.0
    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.multiply(x1, x2)
    array([[ 0.,  1.,  4.],
           [ 0.,  4., 10.],
           [ 0.,  7., 16.]])
    """
    return _mx_nd_np.multiply(x1, x2, out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def divide(x1, x2, out=None, **kwargs):
    """
    Returns a true division of the inputs, element-wise.

    Parameters
    ----------
    x1 : ndarray or scalar
        Dividend array.

    x2 : ndarray or scalar
        Divisor array.

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    out : ndarray or scalar
        This is a scalar if both x1 and x2 are scalars.

    Notes
    -----
    This operator now supports automatic type promotion. The resulting type will be determined
    according to the following rules:
        * If both inputs are of floating number types, the output is the more precise type.
        * If only one of the inputs is floating number type, the result is that type.
        * If both inputs are of integer types (including boolean), the output is of float32 type.

    Examples
    --------
    >>> np.true_divide(x, 4)
    array([0.  , 0.25, 0.5 , 0.75, 1.  ])
    """
    return _mx_nd_np.divide(x1, x2, out=out)


@set_module('mxnet.numpy')
def true_divide(x1, x2, out=None):
    """Returns a true division of the inputs, element-wise.

    Instead of the Python traditional 'floor division', this returns a true
    division.  True division adjusts the output type to present the best
    answer, regardless of input types.

    Parameters
    ----------
    x1 : ndarray or scalar
        Dividend array.

    x2 : ndarray or scalar
        Divisor array.

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    out : ndarray or scalar
        This is a scalar if both x1 and x2 are scalars.

    Notes
    -----
    This operator now supports automatic type promotion. The resulting type will be determined
    according to the following rules:
        * If both inputs are of floating number types, the output is the more precise type.
        * If only one of the inputs is floating number type, the result is that type.
        * If both inputs are of integer types (including boolean), the output is of float32 type.

    Examples
    --------
    >>> x = np.arange(5)
    >>> np.true_divide(x, 4)
    array([0.  , 0.25, 0.5 , 0.75, 1.  ])
    """
    return _mx_nd_np.true_divide(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def mod(x1, x2, out=None, **kwargs):
    """
    Return element-wise remainder of division.

    Parameters
    ----------
    x1 : ndarray or scalar
        Dividend array.

    x2 : ndarray or scalar
        Divisor array.

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    out : ndarray or scalar
        This is a scalar if both x1 and x2 are scalars.

    Examples
    --------
    >>> np.mod(np.arange(7), 5)
    array([0., 1., 2., 3., 4., 0., 1.])
    """
    return _mx_nd_np.mod(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def remainder(x1, x2, out=None, **kwargs):
    """
    Return element-wise remainder of division.

    Parameters
    ----------
    x1 : ndarray or scalar
        Dividend array.

    x2 : ndarray or scalar
        Divisor array.

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    out : ndarray or scalar
        This is a scalar if both x1 and x2 are scalars.

    Examples
    --------
    >>> np.remainder(np.arange(7), 5)
    array([0., 1., 2., 3., 4., 0., 1.])
    """
    return _mx_nd_np.remainder(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def power(x1, x2, out=None, **kwargs):
    """
    First array elements raised to powers from second array, element-wise.

    Parameters
    ----------
    x1 : ndarray or scalar
        The bases.

    x2 : ndarray or scalar
        The exponent.

    out : ndarray
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    out : ndarray or scalar
        The bases in x1 raised to the exponents in x2.
        This is a scalar if both x1 and x2 are scalars.

    Examples
    --------
    >>> x1 = np.arange(6)
    >>> np.power(x1, 3)
    array([  0.,   1.,   8.,  27.,  64., 125.])

    Raise the bases to different exponents.

    >>> x2 = np.array([1.0, 2.0, 3.0, 3.0, 2.0, 1.0])
    >>> np.power(x1, x2)
    array([ 0.,  1.,  8., 27., 16.,  5.])

    The effect of broadcasting.

    >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
    >>> x2
    array([[1., 2., 3., 3., 2., 1.],
           [1., 2., 3., 3., 2., 1.]])

    >>> np.power(x1, x2)
    array([[ 0.,  1.,  8., 27., 16.,  5.],
           [ 0.,  1.,  8., 27., 16.,  5.]])
    """
    return _mx_nd_np.power(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def lcm(x1, x2, out=None, **kwargs):
    """
    Returns the lowest common multiple of ``|x1|`` and ``|x2|``

    Parameters
    ----------
    x1, x2 : ndarrays or scalar values
        The arrays for computing lowest common multiple. If x1.shape != x2.shape,
        they must be broadcastable to a common shape (which may be the shape of
        one or the other).

    out : ndarray or None, optional
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array
        is returned.

    Returns
    -------
    y : ndarray or scalar
        The lowest common multiple of the absolute value of the inputs
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    gcd : The greatest common divisor

    Examples
    --------
    >>> np.lcm(12, 20)
    60
    >>> np.lcm(np.arange(6, dtype=int), 20)
    array([ 0, 20, 20, 60, 20, 20], dtype=int64)
    """
    return _mx_nd_np.lcm(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def sin(x, out=None, **kwargs):
    r"""
    Trigonometric sine, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Angle, in radians (:math:`2 \pi` rad equals 360 degrees).
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs broadcast to. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output is the same as that of the input if the input is an ndarray.

    Returns
    -------
    y : ndarray or scalar
        The sine of each element of x. This is a scalar if `x` is a scalar.

    Notes
    ----
    This function only supports input type of float.

    Examples
    --------
    >>> np.sin(np.pi/2.)
    1.0
    >>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180.)
    array([0.        , 0.5       , 0.70710677, 0.86602545, 1.        ])
    """
    return _mx_nd_np.sin(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def cos(x, out=None, **kwargs):
    r"""
    Cosine, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Angle, in radians (:math:`2 \pi` rad equals 360 degrees).
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs broadcast to. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output is the same as that of the input if the input is an ndarray.

    Returns
    -------
    y : ndarray or scalar
        The corresponding cosine values. This is a scalar if x is a scalar.

    Notes
    ----
    This function only supports input type of float.

    Examples
    --------
    >>> np.cos(np.array([0, np.pi/2, np.pi]))
    array([ 1.000000e+00, -4.371139e-08, -1.000000e+00])
    >>> # Example of providing the optional output parameter
    >>> out1 = np.array([0], dtype='f')
    >>> out2 = np.cos(np.array([0.1]), out1)
    >>> out2 is out1
    True
    """
    return _mx_nd_np.cos(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def sinh(x, out=None, **kwargs):
    """
    Hyperbolic sine, element-wise.
    Equivalent to ``1/2 * (np.exp(x) - np.exp(-x))`` or ``-1j * np.sin(1j*x)``.

    Parameters
    ----------
    x : ndarray or scalar
        Input array or scalar.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs broadcast to. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output is the same as that of the input if the input is an ndarray.

    Returns
    -------
    y : ndarray or scalar
        The corresponding hyperbolic sine values. This is a scalar if `x` is a scalar.

    Notes
    ----
    This function only supports input type of float.

    Examples
    --------
    >>> np.sinh(0)
    0.0
    >>> # Example of providing the optional output parameter
    >>> out1 = np.array([0], dtype='f')
    >>> out2 = np.sinh(np.array([0.1]), out1)
    >>> out2 is out1
    True
    """
    return _mx_nd_np.sinh(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def cosh(x, out=None, **kwargs):
    """
    Hyperbolic cosine, element-wise.
    Equivalent to ``1/2 * (np.exp(x) + np.exp(-x))`` and ``np.cos(1j*x)``.

    Parameters
    ----------
    x : ndarray or scalar
        Input array or scalar.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs broadcast to. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output is the same as that of the input if the input is an ndarray.

    Returns
    -------
    y : ndarray or scalar
        The corresponding hyperbolic cosine values. This is a scalar if `x` is a scalar.

    Notes
    ----
    This function only supports input type of float.

    Examples
    --------
    >>> np.cosh(0)
    1.0
    """
    return _mx_nd_np.cosh(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def tanh(x, out=None, **kwargs):
    """
    Compute hyperbolic tangent element-wise.
    Equivalent to ``np.sinh(x)/np.cosh(x)``.

    Parameters
    ----------
    x : ndarray or scalar.
        Input array.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs fill into. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output and input must be the same.

    Returns
    ----------
    y : ndarray or scalar
       The corresponding hyperbolic tangent values.

    Notes
    -----
    If `out` is provided, the function writes the result into it,
    and returns a reference to `out`.  (See Examples)
    - input x does not support complex computation (like imaginary number)
    >>> np.tanh(np.pi*1j)
    TypeError: type <type 'complex'> not supported

    Examples
    --------
    >>> np.tanh(np.array[0, np.pi]))
    array([0.       , 0.9962721])
    >>> np.tanh(np.pi)
    0.99627207622075
    >>> # Example of providing the optional output parameter illustrating
    >>> # that what is returned is a reference to said parameter
    >>> out1 = np.array(1)
    >>> out2 = np.tanh(np.array(0.1), out1)
    >>> out2 is out1
    True
    """
    return _mx_nd_np.tanh(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def log10(x, out=None, **kwargs):
    """
    Return the base 10 logarithm of the input array, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Input array or scalar.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs broadcast to. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output is the same as that of the input if the input is an ndarray.

    Returns
    -------
    y : ndarray or scalar
        The logarithm to the base 10 of `x`, element-wise. NaNs are
        returned where x is negative. This is a scalar if `x` is a scalar.

    Notes
    ----
    This function only supports input type of float.

    Examples
    --------
    >>> np.log10(np.array([1e-15, -3.]))
    array([-15.,  nan])
    """
    return _mx_nd_np.log10(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def sqrt(x, out=None, **kwargs):
    """
    Return the non-negative square-root of an array, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        The values whose square-roots are required.
    out : ndarray, or None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray or scalar
        An array of the same shape as `x`, containing the positive
        square-root of each element in `x`. This is a scalar if `x` is a scalar.

    Notes
    ----
    This function only supports input type of float.

    Examples
    --------
    >>> np.sqrt(np.array([1,4,9]))
    array([1., 2., 3.])
    >>> np.sqrt(np.array([4, -1, _np.inf]))
    array([ 2., nan, inf])
    """
    return _mx_nd_np.sqrt(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def cbrt(x, out=None, **kwargs):
    """
    Return the cube-root of an array, element-wise.

    Parameters
    ----------
    x : ndarray
        The values whose cube-roots are required.
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have a shape that the
        inputs broadcast to. If not provided or None, a freshly-allocated array is returned.
        A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

    Returns
    ----------
    y : ndarray
        An array of the same shape as x, containing the cube cube-root of each element in x.
        If out was provided, y is a reference to it. This is a scalar if x is a scalar.

    Examples
    ----------
    >>> np.cbrt([1,8,27])
    array([ 1.,  2.,  3.])
    """
    return _mx_nd_np.cbrt(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def abs(x, out=None, **kwargs):
    r"""
    Calculate the absolute value element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    absolute : ndarray
        An ndarray containing the absolute value of
        each element in `x`. This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> x = np.array([-1.2, 1.2])
    >>> np.abs(x)
    array([1.2, 1.2])
    """
    return _mx_nd_np.abs(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def absolute(x, out=None, **kwargs):
    """
    Calculate the absolute value element-wise.
    np.abs is a shorthand for this function.

    Parameters
    ----------
    x : ndarray
        Input array.
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have a shape
        that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned.
        A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

    Returns
    ----------
    absolute : ndarray
        An ndarray containing the absolute value of each element in x.

    Examples
    ----------
    >>> x = np.array([-1.2, 1.2])
    >>> np.absolute(x)
    array([ 1.2,  1.2])
    """
    return _mx_nd_np.absolute(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def exp(x, out=None, **kwargs):
    r"""
    Calculate the exponential of all elements in the input array.

    Parameters
    ----------
    x : ndarray or scalar
        Input values.
    out : ndarray or None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise exponential of `x`.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> np.exp(1)
    2.718281828459045
    >>> x = np.array([-1, 1, -2, 2])
    >>> np.exp(x)
    array([0.36787945, 2.7182817 , 0.13533528, 7.389056  ])
    """
    return _mx_nd_np.exp(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def expm1(x, out=None, **kwargs):
    r"""
    Calculate `exp(x) - 1` for all elements in the array.

    Parameters
    ----------
    x : ndarray or scalar
        Input values.
    out : ndarray or None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise exponential minus one: `out = exp(x) - 1`.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> np.expm1(1)
    1.718281828459045
    >>> x = np.array([-1, 1, -2, 2])
    >>> np.exp(x)
    array([-0.63212056,  1.71828183, -0.86466472,  6.3890561])
    """
    return _mx_nd_np.expm1(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def arcsin(x, out=None, **kwargs):
    r"""
    Inverse sine, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        `y`-coordinate on the unit circle.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape as the input.
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    angle : ndarray or scalar
        Output array is same shape and type as x. This is a scalar if x is a scalar.
        The inverse sine of each element in `x`, in radians and in the
        closed interval ``[-pi/2, pi/2]``.

    Examples
    --------
    >>> np.arcsin(1)     # pi/2
    1.5707963267948966
    >>> np.arcsin(-1)    # -pi/2
    -1.5707963267948966
    >>> np.arcsin(0)
    0.0

    Notes
    -----
    `arcsin` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that :math:`sin(z) = x`.  The convention is to
    return the angle `z` whose real part lies in [-pi/2, pi/2].
    For real-valued input data types, *arcsin* always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.
    The inverse sine is also known as `asin` or sin^{-1}.
    The output `ndarray` has the same `ctx` as the input `ndarray`.
    This function differs from the original `numpy.arcsin
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.arcsin.html>`_ in
    the following aspects:
    - Only support ndarray or scalar now.
    - `where` argument is not supported.
    - Complex input is not supported.

    References
    ----------
    Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
    10th printing, New York: Dover, 1964, pp. 79ff.
    http://www.math.sfu.ca/~cbm/aands/
    """
    return _mx_nd_np.arcsin(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def arccos(x, out=None, **kwargs):
    """
    Trigonometric inverse cosine, element-wise.
    The inverse of cos so that, if y = cos(x), then x = arccos(y).

    Parameters
    ----------
    x : ndarray
        x-coordinate on the unit circle. For real arguments, the domain is [-1, 1].
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have a shape that
        the inputs broadcast to. If not provided or None, a freshly-allocated array is returned.
        A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

    Returns
    ----------
    angle : ndarray
        The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi].
        This is a scalar if x is a scalar.

    Notes
    ----------
    arccos is a multivalued function: for each x there are infinitely many numbers z such that
    cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi].
    For real-valued input data types, arccos always returns real output.
    For each value that cannot be expressed as a real number or infinity, it yields nan and sets
    the invalid floating point error flag.
    The inverse cos is also known as acos or cos^-1.

    Examples
    ----------
    >>> np.arccos([1, -1])
    array([ 0.        ,  3.14159265])
    """
    return _mx_nd_np.arccos(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def arctan(x, out=None, **kwargs):
    r"""
    Trigonometric inverse tangent, element-wise.
    The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``.

    Parameters
    ----------
    x : ndarray or scalar
        Input values.
    out : ndarray or None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray or scalar
        Out has the same shape as `x`. It lies is in
        ``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``).
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `arctan` is a multi-valued function: for each `x` there are infinitely
    many numbers `z` such that tan(`z`) = `x`.  The convention is to return
    the angle `z` whose real part lies in [-pi/2, pi/2].
    For real-valued input data types, `arctan` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.
    For complex-valued input, we do not have support for them yet.
    The inverse tangent is also known as `atan` or tan^{-1}.

    Examples
    --------
    >>> x = np.array([0, 1])
    >>> np.arctan(x)
    array([0.       , 0.7853982])
    >>> np.pi/4
    0.7853981633974483
    """
    return _mx_nd_np.arctan(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def sign(x, out=None, **kwargs):
    """
    Returns an element-wise indication of the sign of a number.
    The `sign` function returns ``-1 if x < 0, 0 if x==0, 1 if x > 0``. Only supports real number.

    Parameters
    ----------
    x : ndarray or a scalar
        Input values.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape and dtype as input ndarray.
        If not provided or `None`, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray
        The sign of `x`.
        This is a scalar if `x` is a scalar.

    Note
    -------
    - Only supports real number as input elements.
    - Input type does not support Python native iterables(list, tuple, ...).
    - ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
    - ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
    - ``out`` param does not support scalar input case.

    Examples
    --------
    >>> a = np.array([-5., 4.5])
    >>> np.sign(a)
    array([-1.,  1.])
    Scalars as input:
    >>> np.sign(4.0)
    1.0
    >>> np.sign(0)
    0
    Use ``out`` parameter:
    >>> b = np.zeros((2, ))
    >>> np.sign(a, out=b)
    array([-1.,  1.])
    >>> b
    array([-1.,  1.])
    """
    return _mx_nd_np.sign(x, out=out)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def log(x, out=None, **kwargs):
    """
    Natural logarithm, element-wise.
    The natural logarithm `log` is the inverse of the exponential function,
    so that `log(exp(x)) = x`. The natural logarithm is logarithm in base
    `e`.

    Parameters
    ----------
    x : ndarray
        Input value. Elements must be of real value.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape and dtype as input ndarray.
        If not provided or `None`, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray
        The natural logarithm of `x`, element-wise.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    Currently only supports data of real values and ``inf`` as input. Returns data of real value, ``inf``, ``-inf`` and
    ``nan`` according to the input.
    This function differs from the original `numpy.log
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html>`_ in
    the following aspects:
    - Does not support complex number for now
    - Input type does not support Python native iterables(list, tuple, ...).
    - ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
    - ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
    - ``out`` param does not support scalar input case.

    Examples
    --------
    >>> a = np.array([1, np.exp(1), np.exp(2), 0], dtype=np.float64)
    >>> np.log(a)
    array([  0.,   1.,   2., -inf], dtype=float64)
    >>> # Using the default float32 dtype leads to slightly different behavior
    >>> a = np.array([1, np.exp(1), np.exp(2), 0])
    >>> np.log(a)
    array([  0.,  0.99999994,   2., -inf])
    >>> np.log(1)
    0.0
    """
    return _mx_nd_np.log(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def rint(x, out=None, **kwargs):
    """
    Round elements of the array to the nearest integer.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None
        A location into which the result is stored.
        If provided, it must have the same shape and type as the input.
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray or scalar
        Output array is same shape and type as x. This is a scalar if x is a scalar.

    Notes
    -----
    This function differs from the original `numpy.rint
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.rint.html>`_ in
    the following way(s):
    - only ndarray or scalar is accpted as valid input, tuple of ndarray is not supported
    - broadcasting to `out` of different shape is currently not supported
    - when input is plain python numerics, the result will not be stored in the `out` param

    Examples
    --------
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.rint(a)
    array([-2., -2., -0.,  0.,  1.,  2.,  2.])
    """
    return _mx_nd_np.rint(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def log2(x, out=None, **kwargs):
    """
    Base-2 logarithm of x.

    Parameters
    ----------
    x : ndarray or scalar
        Input values.
    out : ndarray or None
        A location into which the result is stored.
        If provided, it must have the same shape and type as the input.
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray
        The logarithm base two of `x`, element-wise.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    This function differs from the original `numpy.log2
    <https://www.google.com/search?q=numpy+log2>`_ in
    the following way(s):
    - only ndarray or scalar is accpted as valid input, tuple of ndarray is not supported
    - broadcasting to `out` of different shape is currently not supported
    - when input is plain python numerics, the result will not be stored in the `out` param

    Examples
    --------
    >>> x = np.array([0, 1, 2, 2**4])
    >>> np.log2(x)
    array([-inf,   0.,   1.,   4.])
    """
    return _mx_nd_np.log2(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def log1p(x, out=None, **kwargs):
    """
    Return the natural logarithm of one plus the input array, element-wise.
    Calculates ``log(1 + x)``.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs fill into. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output and input must be the same.

    Returns
    -------
    y : ndarray or scalar
        Natural logarithm of 1 + x, element-wise. This is a scalar
        if x is a scalar.

    Notes
    -----
    For real-valued input, `log1p` is accurate also for `x` so small
    that `1 + x == 1` in floating-point accuracy.
    Logarithm is a multivalued function: for each `x` there is an infinite
    number of `z` such that `exp(z) = 1 + x`. The convention is to return
    the `z` whose imaginary part lies in `[-pi, pi]`.
    For real-valued input data types, `log1p` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.
    cannot support complex-valued input.

    Examples
    --------
    >>> np.log1p(1e-99)
    1e-99
    >>> a = np.array([3, 4, 5])
    >>> np.log1p(a)
    array([1.3862944, 1.609438 , 1.7917595])
    """
    return _mx_nd_np.log1p(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def degrees(x, out=None, **kwargs):
    """
    Convert angles from radians to degrees.

    Parameters
    ----------
    x : ndarray
        Input value. Elements must be of real value.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape and dtype as input ndarray.
        If not provided or `None`, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray
        The corresponding degree values; if `out` was supplied this is a
        reference to it.
        This is a scalar if `x` is a scalar.

    Notes
    -------
    This function differs from the original `numpy.degrees
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.degrees.html>`_ in
    the following aspects:
    - Input type does not support Python native iterables(list, tuple, ...). Only ndarray is supported.
    - ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
    - ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
    - ``out`` param does not support scalar input case.

    Examples
    --------
    >>> rad = np.arange(12.) * np.pi / 6
    >>> np.degrees(rad)
    array([  0.,  30.,  60.,  90., 120., 150., 180., 210., 240., 270., 300., 330.])
    >>> # Use specified ``out`` ndarray:
    >>> out = np.zeros((rad.shape))
    >>> np.degrees(rad, out)
    array([  0.,  30.,  60.,  90., 120., 150., 180., 210., 240., 270., 300., 330.])
    >>> out
    array([  0.,  30.,  60.,  90., 120., 150., 180., 210., 240., 270., 300., 330.])
    """
    return _mx_nd_np.degrees(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def rad2deg(x, out=None, **kwargs):
    r"""
    Convert angles from radians to degrees.
    Parameters
    ----------
    x : ndarray or scalar
        Angles in degrees.
    out : ndarray or None, optional
        A location into which the result is stored. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray or scalar
        The corresponding angle in radians.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    "rad2deg(x)" is "x * 180 / pi".

    This function differs from the original numpy.arange in the following aspects:
        - Only support float32 and float64.
        - `out` must be in the same size of input.

    Examples
    --------
    >>> np.rad2deg(np.pi/2)
    90.0
    """
    return _mx_nd_np.rad2deg(x, out=out)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def radians(x, out=None, **kwargs):
    """
    Convert angles from degrees to radians.

    Parameters
    ----------
    x : ndarray or scalar
        Input array in degrees.
    out : ndarray or None
        A location into which the result is stored.
        If provided, it must have the same shape and type as the input.
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray
        The corresponding radian values. This is a scalar if x is a scalar.

    Notes
    -----
    This function differs from the original `numpy.radians
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.radians.html>`_ in
    the following way(s):
    - only ndarray or scalar is accpted as valid input, tuple of ndarray is not supported
    - broadcasting to `out` of different shape is currently not supported
    - when input is plain python numerics, the result will not be stored in the `out` param

    Examples
    --------
    >>> deg = np.arange(12.) * 30.
    >>> np.radians(deg)
    array([0.       , 0.5235988, 1.0471976, 1.5707964, 2.0943952, 2.6179938,
           3.1415927, 3.6651914, 4.1887903, 4.712389 , 5.2359877, 5.7595863],
           dtype=float32)
    """
    return _mx_nd_np.radians(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def deg2rad(x, out=None, **kwargs):
    r"""
    Convert angles from degrees to radians.

    Parameters
    ----------
    x : ndarray or scalar
        Angles in degrees.
    out : ndarray or None, optional
        A location into which the result is stored. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray or scalar
        The corresponding angle in radians.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    "deg2rad(x)" is "x * pi / 180".

    This function differs from the original numpy.arange in the following aspects:
        - Only support float32 and float64.
        - `out` must be in the same size of input.

    Examples
    --------
    >>> np.deg2rad(180)
    3.1415927
    """
    return _mx_nd_np.deg2rad(x, out=out)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def reciprocal(x, out=None, **kwargs):
    r"""
    Return the reciprocal of the argument, element-wise.
    Calculates ``1/x``.

    Parameters
    ----------
    x : ndarray or scalar
        The values whose reciprocals are required.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape as the input.
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray or scalar
        Output array is same shape and type as x. This is a scalar if x is a scalar.

    Examples
    --------
    >>> np.reciprocal(2.)
    0.5
    >>> x = np.array([1, 2., 3.33])
    >>> np.reciprocal(x)
    array([1.       , 0.5      , 0.3003003])

    Notes
    -----
    .. note::
        This function is not designed to work with integers.
    For integer arguments with absolute value larger than 1 the result is
    always zero because of the way Python handles integer division.  For
    integer zero the result is an overflow.
    The output `ndarray` has the same `ctx` as the input `ndarray`.
    This function differs from the original `numpy.reciprocal
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.reciprocal.html>`_ in
    the following aspects:
    - Only support ndarray and scalar now.
    - `where` argument is not supported.
    """
    return _mx_nd_np.reciprocal(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def square(x, out=None, **kwargs):
    r"""
    Return the element-wise square of the input.

    Parameters
    ----------
    x : ndarray or scalar
        The values whose squares are required.
    out : ndarray or None, optional
        A location into which the result is stored.
        If provided, it must have the same shape as the input.
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray or scalar
        Output array is same shape and type as x. This is a scalar if x is a scalar.

    Examples
    --------
    >>> np.square(2.)
    4.0
    >>> x = np.array([1, 2., -1])
    >>> np.square(x)
    array([1., 4., 1.])

    Notes
    -----
    The output `ndarray` has the same `ctx` as the input `ndarray`.
    This function differs from the original `numpy.square
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.square.html>`_ in
    the following aspects:
    - Only support ndarray and scalar now.
    - `where` argument is not supported.
    - Complex input is not supported.
    """
    return _mx_nd_np.square(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def negative(x, out=None, **kwargs):
    r"""
    Numerical negative, element-wise.

    Parameters:
    ------------
    x : ndarray or scalar
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
          A location into which the result is stored.
          If provided, it must have a shape that the inputs broadcast to.
          If not provided or None, a freshly-allocated array is returned.
          A tuple (possible only as a keyword argument) must have length
          equal to the number of outputs.

    Returns:
    -------
    y : ndarray or scalar
        Returned array or scalar: y = -x. This is a scalar if x is a scalar.

    Examples
    --------
    >>> np.negative(1)
    -1
    """
    return _mx_nd_np.negative(x, out=out)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def fix(x, out=None, **kwargs):
    """
    Round an array of floats element-wise to nearest integer towards zero.
    The rounded values are returned as floats.

    Parameters:
    ----------
    x : ndarray
        An array of floats to be rounded
    out : ndarray, optional
        Output array

    Returns:
    -------
    y : ndarray or scalar
    Returned array or scalar: y = -x. This is a scalar if x is a scalar.ndarray of floats

    Examples
    ---------
    >>> np.fix(3.14)
    3
    """
    return _mx_nd_np.fix(x, out=out)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def tan(x, out=None, **kwargs):
    r"""
    Compute tangent element-wise.
    Equivalent to np.sin(x)/np.cos(x) element-wise.

    Parameters:
    ----------
    x : ndarray
        Input array.
    out : ndarray or none, optional
          A location into which the result is stored. If provided,
          it must have a shape that the inputs broadcast to. If not provided or None,
          a freshly-allocated array is returned. A tuple (possible only as a keyword argument)
          must have length equal to the number of outputs.

    Returns:
    -------
    y : ndarray
    The corresponding tangent values. This is a scalar if x is a scalar.

    Examples
    ---------
    >>> np.tan(np.array([-np.pi, np.pi/2, np.pi]))
    array([-8.7422777e-08, -2.2877332e+07,  8.7422777e-08])
    """

    return _mx_nd_np.tan(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def ceil(x, out=None, **kwargs):
    r"""
    Return the ceiling of the input, element-wise.
    The ceil of the ndarray `x` is the smallest integer `i`, such that
    `i >= x`.  It is often denoted as :math:`\lceil x \rceil`.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs fill into. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output and input must be the same.

    Returns
    -------
    y : ndarray or scalar
        The ceiling of each element in `x`, with `float` dtype.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.ceil(a)
    array([-1., -1., -0.,  1.,  2.,  2.,  2.])
    >>> # if you use parameter out, x and out must be ndarray.
    >>> a = np.array(1)
    >>> np.ceil(np.array(3.5), a)
    array(4.)
    >>> a
    array(4.)
    """
    return _mx_nd_np.ceil(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def floor(x, out=None, **kwargs):
    r"""
    Return the floor of the input, element-wise.
    The ceil of the ndarray `x` is the largest integer `i`, such that
    `i <= x`.  It is often denoted as :math:`\lfloor x \rfloor`.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None
        A location into which the result is stored. If provided, it
        must have a shape that the inputs fill into. If not provided
        or None, a freshly-allocated array is returned. The dtype of the
        output and input must be the same.

    Returns
    -------
    y : ndarray or scalar
        The floor of each element in `x`, with `float` dtype.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.floor(a)
    array([-2., -2., -1.,  0.,  1.,  1.,  2.])
    >>> # if you use parameter out, x and out must be ndarray.
    >>> a = np.array(1)
    >>> np.floor(np.array(3.5), a)
    array(3.)
    >>> a
    array(3.)
    """
    return _mx_nd_np.floor(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def trunc(x, out=None, **kwargs):
    r"""
    Return the truncated value of the input, element-wise.
    The truncated value of the scalar `x` is the nearest integer `i` which
    is closer to zero than `x` is. In short, the fractional part of the
    signed number `x` is discarded.

    Parameters
    ----------
    x : ndarray or scalar
        Input data.
    out : ndarray or None, optional
        A location into which the result is stored.

    Returns
    -------
    y : ndarray or scalar
        The truncated value of each element in `x`.
        This is a scalar if `x` is a scalar.
    Notes
    -----
    This function differs from the original numpy.trunc in the following aspects:
        - Do not support `where`, a parameter in numpy which indicates where to calculate.
        - Cannot cast type automatically. Dtype of `out` must be same as the expected one.
        - Cannot broadcast automatically. Shape of `out` must be same as the expected one.
        - If `x` is plain python numeric, the result won't be stored in out.

    Examples
    --------
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.trunc(a)
    array([-1., -1., -0.,  0.,  1.,  1.,  2.])
    """
    return _mx_nd_np.trunc(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def logical_not(x, out=None, **kwargs):
    r"""
    Compute the truth value of NOT x element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Logical NOT is applied to the elements of `x`.
    out : ndarray or None, optional
        A location into which the result is stored.

    Returns
    -------
    y : bool or ndarray of bool
        Boolean result with the same shape as `x` of the NOT operation
        on elements of `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    This function differs from the original numpy.logical_not in the following aspects:
        - Do not support `where`, a parameter in numpy which indicates where to calculate.
        - Cannot cast type automatically. Dtype of `out` must be same as the expected one.
        - Cannot broadcast automatically. Shape of `out` must be same as the expected one.
        - If `x` is plain python numeric, the result won't be stored in out.

    Examples
    --------
    >>> x= np.array([True, False, 0, 1])
    >>> np.logical_not(x)
    array([False,  True,  True, False])

    >>> x = np.arange(5)
    >>> np.logical_not(x<3)
    array([False, False, False,  True,  True])
    """
    return _mx_nd_np.logical_not(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def arcsinh(x, out=None, **kwargs):
    r"""
    Inverse hyperbolic cosine, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None, optional
        A location into which the result is stored.

    Returns
    -------
    arcsinh : ndarray
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `arcsinh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `sinh(z) = x`.

    For real-valued input data types, `arcsinh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    yields ``nan`` and sets the `invalid` floating point error flag.

    This function differs from the original numpy.arcsinh in the following aspects:
        - Do not support `where`, a parameter in numpy which indicates where to calculate.
        - Do not support complex-valued input.
        - Cannot cast type automatically. DType of `out` must be same as the expected one.
        - Cannot broadcast automatically. Shape of `out` must be same as the expected one.
        - If `x` is plain python numeric, the result won't be stored in out.

    Examples
    --------
    >>> a = np.array([3.2, 5.0])
    >>> np.arcsinh(a)
    array([1.8309381, 2.2924316])

    >>> np.arcsinh(1)
    0.0
    """
    return _mx_nd_np.arcsinh(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def arccosh(x, out=None, **kwargs):
    r"""
    Inverse hyperbolic cosine, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None, optional
        A location into which the result is stored.

    Returns
    -------
    arccosh : ndarray
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `arccosh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `cosh(z) = x`.

    For real-valued input data types, `arccosh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    yields ``nan`` and sets the `invalid` floating point error flag.

    This function differs from the original numpy.arccosh in the following aspects:
        - Do not support `where`, a parameter in numpy which indicates where to calculate.
        - Do not support complex-valued input.
        - Cannot cast type automatically. Dtype of `out` must be same as the expected one.
        - Cannot broadcast automatically. Shape of `out` must be same as the expected one.
        - If `x` is plain python numeric, the result won't be stored in out.

    Examples
    --------
    >>> a = np.array([3.2, 5.0])
    >>> np.arccosh(a)
    array([1.8309381, 2.2924316])

    >>> np.arccosh(1)
    0.0
    """
    return _mx_nd_np.arccosh(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def arctanh(x, out=None, **kwargs):
    r"""
    Inverse hyperbolic tangent, element-wise.

    Parameters
    ----------
    x : ndarray or scalar
        Input array.
    out : ndarray or None, optional
        A location into which the result is stored.

    Returns
    -------
    arctanh : ndarray
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `arctanh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `tanh(z) = x`.

    For real-valued input data types, `arctanh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    yields ``nan`` and sets the `invalid` floating point error flag.

    This function differs from the original numpy.arctanh in the following aspects:
        - Do not support `where`, a parameter in numpy which indicates where to calculate.
        - Do not support complex-valued input.
        - Cannot cast type automatically. Dtype of `out` must be same as the expected one.
        - Cannot broadcast automatically. Shape of `out` must be same as the expected one.
        - If `x` is plain python numeric, the result won't be stored in out.

    Examples
    --------
    >>> a = np.array([0.0, -0.5])
    >>> np.arctanh(a)
    array([0., -0.54930615])

    >>> np.arctanh(1)
    0.0
    """
    return _mx_nd_np.arctanh(x, out=out, **kwargs)


@set_module('mxnet.numpy')
def tensordot(a, b, axes=2):
    r"""
    tensordot(a, b, axes=2)
    Compute tensor dot product along specified axes for arrays >= 1-D.
    Given two tensors (arrays of dimension greater than or equal to one),
    `a` and `b`, and an ndarray object containing two ndarray
    objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s
    elements (components) over the axes specified by ``a_axes`` and
    ``b_axes``. The third argument can be a single non-negative
    integer_like scalar, ``N``; if it is such, then the last ``N``
    dimensions of `a` and the first ``N`` dimensions of `b` are summed
    over.

    Parameters
    ----------
    a, b : ndarray, len(shape) >= 1
        Tensors to "dot".
    axes : int or (2,) ndarray
        * integer_like
        If an int N, sum over the last N axes of `a` and the first N axes
        of `b` in order. The sizes of the corresponding axes must match.
        * (2,) ndarray
        Or, a list of axes to be summed over, first sequence applying to `a`,
        second to `b`. Both elements ndarray must be of the same length.

    See Also
    --------
    dot, einsum

    Notes
    -----
    Three common use cases are:
        * ``axes = 0`` : tensor product :math:`a\otimes b`
        * ``axes = 1`` : tensor dot product :math:`a\cdot b`
        * ``axes = 2`` : (default) tensor double contraction :math:`a:b`
    When `axes` is integer_like, the sequence for evaluation will be: first
    the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and
    Nth axis in `b` last.
    When there is more than one axis to sum over - and they are not the last
    (first) axes of `a` (`b`) - the argument `axes` should consist of
    two sequences of the same length, with the first axis to sum over given
    first in both sequences, the second axis second, and so forth.

    Examples
    --------
    >>> a = np.arange(60.).reshape(3,4,5)
    >>> b = np.arange(24.).reshape(4,3,2)
    >>> c = np.tensordot(a,b, axes=([1,0],[0,1]))
    >>> c.shape
    (5, 2)
    >>> c
    array([[ 4400.,  4730.],
           [ 4532.,  4874.],
           [ 4664.,  5018.],
           [ 4796.,  5162.],
           [ 4928.,  5306.]])
    """
    return _mx_nd_np.tensordot(a, b, axes)


@set_module('mxnet.numpy')
def histogram(a, bins=10, range=None, normed=None, weights=None, density=None):  # pylint: disable=too-many-arguments
    """
    Compute the histogram of a set of data.

    Parameters
    ----------
    a : ndarray
        Input data. The histogram is computed over the flattened array.
    bins : int or ndarray
        If `bins` is an int, it defines the number of equal-width
        bins in the given range (10, by default). If `bins` is a
        sequence, it defines a monotonically increasing array of bin edges,
        including the rightmost edge, allowing for non-uniform bin widths.
        .. versionadded:: 1.11.0
        If `bins` is a string, it defines the method used to calculate the
        optimal bin width, as defined by `histogram_bin_edges`.
    range : (float, float)
        The lower and upper range of the bins. Required when `bins` is an integer.
        Values outside the range are ignored. The first element of the range must
        be less than or equal to the second.
    normed : bool, optional
        Not supported yet, coming soon.
    weights : array_like, optional
        Not supported yet, coming soon.
    density : bool, optional
        Not supported yet, coming soon.

    Examples
    --------
    >>> np.histogram(np.arange(4), bins=np.arange(5))
    [array([1, 1, 1, 1], dtype=int64), array([0., 1., 2., 3., 4.])]
    """
    return _mx_nd_np.histogram(a, bins=bins, range=range, normed=normed, weights=weights, density=density)


@set_module('mxnet.numpy')
def eye(N, M=None, k=0, dtype=_np.float32, **kwargs):
    """
    Return a 2-D array with ones on the diagonal and zeros elsewhere.

    Parameters
    ----------
    N : int
        Number of rows in the output.
    M : int, optional
        Number of columns in the output. If None, defaults to N.
    k : int, optional
        Index of the diagonal: 0 (the default) refers to the main diagonal,
        a positive value refers to an upper diagonal,
        and a negative value to a lower diagonal.
    dtype : data-type, optional
        Data-type of the returned array.

    Returns
    -------
    I : ndarray of shape (N,M)
        An array where all elements are equal to zero,
        except for the k-th diagonal, whose values are equal to one.

    Examples
    --------
    >>> np.eye(2, dtype=int)
    array([[1, 0],
           [0, 1]], dtype=int64)
    >>> np.eye(3, k=1)
    array([[0., 1., 0.],
           [0., 0., 1.],
           [0., 0., 0.]])
    """
    return _mx_nd_np.eye(N, M, k, dtype, **kwargs)


@set_module('mxnet.numpy')
def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0, ctx=None):  # pylint: disable=too-many-arguments
    r"""
    Return evenly spaced numbers over a specified interval.

    Returns num evenly spaced samples, calculated over the interval [start, stop].
    The endpoint of the interval can optionally be excluded.

    Parameters
    ----------
    start : real number
        The starting value of the sequence.
    stop : real number
        The end value of the sequence, unless endpoint is set to False. In
        that case, the sequence consists of all but the last of num + 1
        evenly spaced samples, so that stop is excluded. Note that the step
        size changes when endpoint is False.
    num : int, optional
        Number of samples to generate. Default is 50. Must be non-negative.
    endpoint : bool, optional
        If True, stop is the last sample. Otherwise, it is not included.
        Default is True.
    retstep : bool, optional
        If True, return (samples, step), where step is the spacing between samples.
    dtype : dtype, optional
        The type of the output array. If dtype is not given, infer the data
        type from the other input arguments.
    axis : int, optional
        The axis in the result to store the samples. Relevant only if start or
        stop are array-like. By default (0), the samples will be along a new
        axis inserted at the beginning. Use -1 to get an axis at the end.

    Returns
    -------
    samples : ndarray
        There are num equally spaced samples in the closed interval
        `[start, stop]` or the half-open interval `[start, stop)`
        (depending on whether endpoint is True or False).
    step : float, optional
        Only returned if retstep is True
        Size of spacing between samples.


    See Also
    --------
    arange : Similar to `linspace`, but uses a step size (instead of the
             number of samples).

    Examples
    --------
    >>> np.linspace(2.0, 3.0, num=5)
    array([2.  , 2.25, 2.5 , 2.75, 3.  ])
    >>> np.linspace(2.0, 3.0, num=5, endpoint=False)
    array([2. , 2.2, 2.4, 2.6, 2.8])
    >>> np.linspace(2.0, 3.0, num=5, retstep=True)
    (array([2.  , 2.25, 2.5 , 2.75, 3.  ]), 0.25)

    Graphical illustration:

    >>> import matplotlib.pyplot as plt
    >>> N = 8
    >>> y = np.zeros(N)
    >>> x1 = np.linspace(0, 10, N, endpoint=True)
    >>> x2 = np.linspace(0, 10, N, endpoint=False)
    >>> plt.plot(x1.asnumpy(), y.asnumpy(), 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.plot(x2.asnumpy(), (y + 0.5).asnumpy(), 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.ylim([-0.5, 1])
    (-0.5, 1)
    >>> plt.show()

    Notes
    -----

    This function differs from the original `numpy.linspace
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html>`_ in
    the following aspects:

    - `start` and `stop` do not support list, numpy ndarray and mxnet ndarray
    - axis could only be 0
    - There could be an additional `ctx` argument to specify the device, e.g. the i-th
      GPU.
    """
    return _mx_nd_np.linspace(start, stop, num, endpoint, retstep, dtype, axis, ctx)


# pylint: disable=too-many-arguments
@set_module('mxnet.numpy')
def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0, ctx=None):
    r"""Return numbers spaced evenly on a log scale.

    In linear space, the sequence starts at ``base ** start``
    (`base` to the power of `start`) and ends with ``base ** stop``
    (see `endpoint` below).

        Non-scalar `start` and `stop` are now supported.

    Parameters
    ----------
    start : int or float
        ``base ** start`` is the starting value of the sequence.
    stop : int or float
        ``base ** stop`` is the final value of the sequence, unless `endpoint`
        is False.  In that case, ``num + 1`` values are spaced over the
        interval in log-space, of which all but the last (a sequence of
        length `num`) are returned.
    num : integer, optional
        Number of samples to generate.  Default is 50.
    endpoint : boolean, optional
        If true, `stop` is the last sample. Otherwise, it is not included.
        Default is True.
    base : float, optional
        The base of the log space. The step size between the elements in
        ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.
        Default is 10.0.
    dtype : dtype
        The type of the output array.  If `dtype` is not given, infer the data
        type from the other input arguments.
    axis : int, optional
        The axis in the result to store the samples.  Relevant only if start
        or stop are array-like.  By default (0), the samples will be along a
        new axis inserted at the beginning. Now, axis only support axis = 0.
    ctx : Context, optional
        An optional device context (default is the current default context).

    Returns
    -------
    samples : ndarray
        `num` samples, equally spaced on a log scale.

    See Also
    --------
    arange : Similar to linspace, with the step size specified instead of the
             number of samples. Note that, when used with a float endpoint, the
             endpoint may or may not be included.
    linspace : Similar to logspace, but with the samples uniformly distributed
               in linear space, instead of log space.

    Notes
    -----
    Logspace is equivalent to the code

    >>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
    ...
    >>> power(base, y).astype(dtype)
    ...

    Examples
    --------
    >>> np.logspace(2.0, 3.0, num=4)
    array([ 100.     ,  215.44347,  464.15887, 1000.     ])
    >>> np.logspace(2.0, 3.0, num=4, endpoint=False)
    array([100.     , 177.82794, 316.22775, 562.3413 ])
    >>> np.logspace(2.0, 3.0, num=4, base=2.0)
    array([4.       , 5.0396843, 6.349604 , 8.       ])
    >>> np.logspace(2.0, 3.0, num=4, base=2.0, dtype=np.int32)
    array([4, 5, 6, 8], dtype=int32)
    >>> np.logspace(2.0, 3.0, num=4, ctx=npx.gpu(0))
    array([ 100.     ,  215.44347,  464.15887, 1000.     ], ctx=gpu(0))
    """
    return _mx_nd_np.logspace(start, stop, num, endpoint, base, dtype, axis, ctx=ctx)
# pylint: enable=too-many-arguments


@set_module('mxnet.numpy')
def expand_dims(a, axis):
    """Expand the shape of an array.

    Insert a new axis that will appear at the `axis` position in the expanded array shape.

    Parameters
    ----------
    a : ndarray
        Input array.
    axis : int
        Position in the expanded axes where the new axis is placed.

    Returns
    -------
    res : ndarray
        Output array. The number of dimensions is one greater than that of
        the input array.

    See Also
    --------
    squeeze : The inverse operation, removing singleton dimensions
    reshape : Insert, remove, and combine dimensions, and resize existing ones

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

    >>> y = np.expand_dims(x, axis=0)
    >>> y
    array([[1., 2.]])

    >>> y.shape
    (1, 2)

    >>> y = np.expand_dims(x, axis=1)  # Equivalent to x[:,np.newaxis]
    >>> y
    array([[1.],
           [2.]])

    >>> y.shape
    (2, 1)

    Note that some examples may use None instead of np.newaxis. These are the same objects:

    >>> np.newaxis is None
    True
    """
    return _npi.expand_dims(a, axis)


@set_module('mxnet.numpy')
def tile(A, reps):
    r"""
    Construct an array by repeating A the number of times given by reps.

    If `reps` has length ``d``, the result will have dimension of
    ``max(d, A.ndim)``.

    If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new
    axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,
    or shape (1, 1, 3) for 3-D replication. If this is not the desired
    behavior, promote `A` to d-dimensions manually before calling this
    function.

    If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it.
    Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as
    (1, 1, 2, 2).

    Parameters
    ----------
    A : ndarray or scalar
        An input array or a scalar to repeat.
    reps : a single integer or tuple of integers
        The number of repetitions of `A` along each axis.

    Returns
    -------
    c : ndarray
        The tiled output array.

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

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

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

    Scalar as input:

    >>> np.tile(2, 3)
    array([2, 2, 2]) # repeating integer `2`

    """
    return _mx_nd_np.tile(A, reps)


@set_module('mxnet.numpy')
def tril(m, k=0):
    r"""
    Lower triangle of an array.

    Return a copy of an array with elements above the `k`-th diagonal zeroed.

    Parameters
    ----------
    m : ndarray, shape (M, N)
        Input array.
    k : int, optional
        Diagonal above which to zero elements.  `k = 0` (the default) is the
        main diagonal, `k < 0` is below it and `k > 0` is above.

    Returns
    -------
    tril : ndarray, shape (M, N)
        Lower triangle of `m`, of same shape and data-type as `m`.

    See Also
    --------
    triu : same thing, only for the upper triangle

    Examples
    --------
    >>> a = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
    >>> np.tril(a, -1)
    array([[ 0.,  0.,  0.],
           [ 4.,  0.,  0.],
           [ 7.,  8.,  0.],
           [10., 11., 12.]])
    """
    return _mx_nd_np.tril(m, k)


@set_module('mxnet.numpy')
def arange(start, stop=None, step=1, dtype=None, ctx=None):
    """Return evenly spaced values within a given interval.

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

    Parameters
    ----------
    start : number, optional
        Start of interval. The interval includes this value.  The default
        start value is 0.
    stop : number
        End of interval. The interval does not include this value, except
        in some cases where `step` is not an integer and floating point
        round-off affects the length of `out`.
    step : number, optional
        Spacing between values. For any output `out`, this is the distance
        between two adjacent values, ``out[i+1] - out[i]``.  The default
        step size is 1.  If `step` is specified as a position argument,
        `start` must also be given.
    dtype : dtype
        The type of the output array. The default is `float32`.

    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`.

    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.])
    """
    return _mx_nd_np.arange(start, stop, step, dtype, ctx)


@set_module('mxnet.numpy')
def split(ary, indices_or_sections, axis=0):
    """Split an array into multiple sub-arrays.

    Parameters
    ----------
    ary : ndarray
        Array to be divided into sub-arrays.
    indices_or_sections : int or 1-D Python tuple, list or set.
        If `indices_or_sections` is an integer, N, the array will be divided
        into N equal arrays along `axis`.  If such a split is not possible,
        an error is raised.
        If `indices_or_sections` is a 1-D array of sorted integers, the entries
        indicate where along `axis` the array is split.  For example,
        ``[2, 3]`` would, for ``axis=0``, result in
          - ary[:2]
          - ary[2:3]
          - ary[3:]
        If an index exceeds the dimension of the array along `axis`,
        an empty sub-array is returned correspondingly.
    axis : int, optional
        The axis along which to split, default is 0.

    Returns
    -------
    sub-arrays : list of ndarrays
        A list of sub-arrays.

    Raises
    ------
    ValueError
        If `indices_or_sections` is given as an integer, but
        a split does not result in equal division.

    See Also
    --------
    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).
    concatenate : Join a sequence of arrays along an existing axis.
    stack : Join 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).

    Examples
    --------
    >>> x = np.arange(9.0)
    >>> np.split(x, 3)
    [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7., 8.])]

    >>> np.split(x, [3, 5, 6, 8])
    [array([0., 1., 2.]), array([3., 4.]), array([5.]), array([6., 7.]), array([])]
    """
    return _mx_nd_np.split(ary, indices_or_sections, axis=axis)


@set_module('mxnet.numpy')
def vsplit(ary, indices_or_sections):
    r"""
    vsplit(ary, indices_or_sections)

    Split an array into multiple sub-arrays vertically (row-wise).

    ``vsplit`` is equivalent to ``split`` with `axis=0` (default): the array is always split
    along the first axis regardless of the array dimension.

    Parameters
    ----------
    ary : ndarray
        Array to be divided into sub-arrays.
    indices_or_sections : int or 1 - D Python tuple, list or set.
        If `indices_or_sections` is an integer, N, the array will be divided into N equal arrays
        along axis 0.  If such a split is not possible, an error is raised.

        If `indices_or_sections` is a 1-D array of sorted integers, the entries indicate where
        along axis 0 the array is split.  For example, ``[2, 3]`` would result in

          - ary[:2]
          - ary[2:3]
          - ary[3:]

        If an index exceeds the dimension of the array along axis 0, an error will be thrown.

    Returns
    -------
    sub-arrays : list of ndarrays
        A list of sub-arrays.

    See Also
    --------
    split : Split an array into multiple sub-arrays of equal size.

    Notes
    -------
    This function differs from the original `numpy.degrees
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.degrees.html>`_ in
    the following aspects:

    - Currently parameter ``indices_or_sections`` does not support ndarray, but supports scalar,
    tuple and list.
    - In ``indices_or_sections``, if an index exceeds the dimension of the array along axis 0,
    an error will be thrown.

    Examples
    --------
    >>> x = np.arange(16.0).reshape(4, 4)
    >>> x
    array([[  0.,   1.,   2.,   3.],
           [  4.,   5.,   6.,   7.],
           [  8.,   9.,  10.,  11.],
           [ 12.,  13.,  14.,  15.]])
    >>> np.vsplit(x, 2)
    [array([[0., 1., 2., 3.],
            [4., 5., 6., 7.]]), array([[ 8.,  9., 10., 11.],
            [12., 13., 14., 15.]])]

    >>> # With a higher dimensional array the split is still along the first axis.
    >>> x = np.arange(8.0).reshape(2, 2, 2)
    >>> x
    array([[[ 0.,  1.],
            [ 2.,  3.]],
           [[ 4.,  5.],
            [ 6.,  7.]]])
    >>> np.vsplit(x, 2)
    [array([[[0., 1.],
            [2., 3.]]]), array([[[4., 5.],
            [6., 7.]]])]

    """
    return split(ary, indices_or_sections, 0)


@set_module('mxnet.numpy')
def concatenate(seq, axis=0, out=None):
    """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.  If axis is None,
        arrays are flattened before use.  Default is 0.
    out : ndarray, optional
        If provided, the destination to place the result. The shape must be
        correct, matching that of what concatenate would have returned if no
        out argument were specified.

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

    See Also
    --------
    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)

    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.]])

    >>> np.concatenate((a, b), axis=None)
    array([1., 2., 3., 4., 5., 6.])
    """
    return _mx_nd_np.concatenate(seq, axis=axis, out=out)


@set_module('mxnet.numpy')
def append(arr, values, axis=None):  # pylint: disable=redefined-outer-name
    """
    Append values to the end of an array.

    Parameters
    ----------
    arr : ndarray
        Values are appended to a copy of this array.
    values : ndarray
        These values are appended to a copy of `arr`.  It must be of the
        correct shape (the same shape as `arr`, excluding `axis`).  If
        `axis` is not specified, `values` can be any shape and will be
        flattened before use.
    axis : int, optional
        The axis along which `values` are appended.  If `axis` is not
        given, both `arr` and `values` are flattened before use.

    Returns
    -------
    append : ndarray
        A copy of `arr` with `values` appended to `axis`.  Note that
        `append` does not occur in-place: a new array is allocated and
        filled.  If `axis` is None, `out` is a flattened array.

    Examples
    --------
    >>> np.append(np.array([1, 2, 3]), np.array([[4, 5, 6],[7, 8, 9]]))
    array([1., 2., 3., 4., 5., 6., 7., 8., 9.])

    When `axis` is specified, `values` must have the correct shape.

    >>> np.append(np.array([[1, 2, 3], [4, 5, 6]]), np.array([[7, 8, 9]]), axis=0)
    array([[1., 2., 3.],
           [4., 5., 6.],
           [7., 8., 9.]])
    """
    return _mx_nd_np.append(arr, values, axis=axis)


@set_module('mxnet.numpy')
def stack(arrays, axis=0, out=None):
    """Join a sequence of arrays along a new axis.
        The axis parameter specifies the index of the new axis in the dimensions of the result.
        For example, if `axis=0` it will be the first dimension and if `axis=-1` it will be the last dimension.

    Parameters
    ----------
    arrays : sequence of array_like
        Each array must have the same shape.
    axis : int, optional
        The axis in the result array along which the input arrays are stacked.
    out : ndarray, optional
        If provided, the destination to place the result. The shape must be correct,
        matching that of what stack would have returned if no out argument were specified.

    Returns
    -------
    stacked : ndarray
        The stacked array has one more dimension than the input arrays.

    See Also
    --------
    concatenate : Join a sequence of arrays along an existing axis.
    split : Split array into a list of multiple sub-arrays of equal size.

    Examples
    --------
    >>> arrays = [np.random.rand(3, 4) for _ in range(10)]
    >>> np.stack(arrays, axis=0).shape
    (10, 3, 4)

    >>> np.stack(arrays, axis=1).shape
    (3, 10, 4)

    >>> np.stack(arrays, axis=2).shape
    (3, 4, 10)

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

    >>> np.stack((a, b), axis=-1)
    array([[1., 2.],
           [2., 3.],
           [3., 4.]])
    """
    return _mx_nd_np.stack(arrays, axis=axis, out=out)


@set_module('mxnet.numpy')
def vstack(arrays, out=None):
    r"""Stack arrays in sequence vertically (row wise).

    This is equivalent to concatenation along the first axis after 1-D arrays
    of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by
    `vsplit`.

    This function makes most sense for arrays with up to 3 dimensions. For
    instance, for pixel-data with a height (first axis), width (second axis),
    and r/g/b channels (third axis). The functions `concatenate` and `stack`
    provide more general stacking and concatenation operations.

    Parameters
    ----------
    tup : sequence of ndarrays
        The arrays must have the same shape along all but the first axis.
        1-D arrays must have the same length.

    Returns
    -------
    stacked : ndarray
        The array formed by stacking the given arrays, will be at least 2-D.

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

    >>> a = np.array([[1], [2], [3]])
    >>> b = np.array([[2], [3], [4]])
    >>> np.vstack((a, b))
    array([[1.],
           [2.],
           [3.],
           [2.],
           [3.],
           [4.]])
    """
    return _mx_nd_np.vstack(arrays)


@set_module('mxnet.numpy')
def column_stack(tup):
    """
    Stack 1-D arrays as columns into a 2-D array.

    Take a sequence of 1-D arrays and stack them as columns
    to make a single 2-D array. 2-D arrays are stacked as-is,
    just like with `hstack`.  1-D arrays are turned into 2-D columns
    first.

    Parameters
    ----------
    tup : sequence of 1-D or 2-D arrays.
        Arrays to stack. All of them must have the same first dimension.

    Returns
    --------
    stacked : 2-D array
        The array formed by stacking the given arrays.

    See Also
    --------
    stack, hstack, vstack, concatenate

    Examples
    --------
    >>> a = np.array((1,2,3))
    >>> b = np.array((2,3,4))
    >>> np.column_stack((a,b))
    array([[1., 2.],
           [2., 3.],
           [3., 4.]])
    """
    return _mx_nd_np.column_stack(tup)


@set_module('mxnet.numpy')
def dstack(arrays):
    """
    Stack arrays in sequence depth wise (along third axis).

    This is equivalent to concatenation along the third axis after 2-D arrays
    of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape
    `(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by
    `dsplit`.

    This function makes most sense for arrays with up to 3 dimensions. For
    instance, for pixel-data with a height (first axis), width (second axis),
    and r/g/b channels (third axis). The functions `concatenate`, `stack` and
    `block` provide more general stacking and concatenation operations.

    Parameters
    ----------
    tup : sequence of arrays
        The arrays must have the same shape along all but the third axis.
        1-D or 2-D arrays must have the same shape.

    Returns
    -------
    stacked : ndarray
        The array formed by stacking the given arrays, will be at least 3-D.

    Examples
    --------
    >>> a = np.array((1,2,3))
    >>> b = np.array((2,3,4))
    >>> np.dstack((a,b))
    array([[[1, 2],
            [2, 3],
            [3, 4]]])
    >>> a = np.array([[1],[2],[3]])
    >>> b = np.array([[2],[3],[4]])
    >>> np.dstack((a,b))
    array([[[1, 2]],
           [[2, 3]],
           [[3, 4]]])
    """
    return _npi.dstack(*arrays)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def maximum(x1, x2, out=None, **kwargs):
    """
    Returns element-wise maximum of the input arrays with broadcasting.

    Parameters
    ----------
    x1, x2 : scalar or mxnet.numpy.ndarray
        The arrays holding the elements to be compared. They must have the same shape,
        or shapes that can be broadcast to a single shape.

    Returns
    -------
    out : mxnet.numpy.ndarray or scalar
        The maximum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

    Examples
    --------
    >>> np.maximum(np.array([2, 3, 4]), np.array([1, 5, 2]))
    array([2., 5., 4.])

    >>> np.maximum(np.eye(2), np.array([0.5, 2])) # broadcasting
    array([[1. , 2. ],
           [0.5, 2. ]])
    """
    return _mx_nd_np.maximum(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def minimum(x1, x2, out=None, **kwargs):
    """
    Returns element-wise minimum of the input arrays with broadcasting.

    Parameters
    ----------
    x1, x2 : scalar or mxnet.numpy.ndarray
        The arrays holding the elements to be compared. They must have the same shape,
        or shapes that can be broadcast to a single shape.

    Returns
    -------
    out : mxnet.numpy.ndarray or scalar
        The minimum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

    Examples
    --------
    >>> np.minimum(np.array([2, 3, 4]), np.array([1, 5, 2]))
    array([1., 3., 2.])

    >>> np.minimum(np.eye(2), np.array([0.5, 2])) # broadcasting
    array([[0.5, 0. ],
           [0. , 1. ]])
    """
    return _mx_nd_np.minimum(x1, x2, out=out)


@set_module('mxnet.numpy')
def swapaxes(a, axis1, axis2):
    """Interchange two axes of an array.

    Parameters
    ----------
    a : ndarray
        Input array.
    axis1 : int
        First axis.
    axis2 : int
        Second axis.

    Returns
    -------
    a_swapped : ndarray
        Swapped array. This is always a copy of the input array.

    Examples
    --------
    >>> x = np.array([[1,2,3]])
    >>> np.swapaxes(x,0,1)
    array([[1.],
           [2.],
           [3.]])

    >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
    >>> x
    array([[[0., 1.],
            [2., 3.]],

           [[4., 5.],
            [6., 7.]]])

    >>> np.swapaxes(x,0,2)
    array([[[0., 4.],
            [2., 6.]],

           [[1., 5.],
            [3., 7.]]])
    """
    return _npi.swapaxes(a, dim1=axis1, dim2=axis2)


@set_module('mxnet.numpy')
def clip(a, a_min, a_max, out=None):
    """clip(a, a_min, a_max, out=None)

    Clip (limit) the values in an array.
    Given an interval, values outside the interval are clipped to
    the interval edges.  For example, if an interval of ``[0, 1]``
    is specified, values smaller than 0 become 0, and values larger
    than 1 become 1.

    Parameters
    ----------
    a : ndarray
        Array containing elements to clip.
    a_min : scalar or `None`
        Minimum value. If `None`, clipping is not performed on lower
        interval edge. Not more than one of `a_min` and `a_max` may be
        `None`.
    a_max : scalar or `None`
        Maximum value. If `None`, clipping is not performed on upper
        interval edge. Not more than one of `a_min` and `a_max` may be
        `None`.
    out : ndarray, optional
        The results will be placed in this array. It may be the input
        array for in-place clipping.  `out` must be of the right shape
        to hold the output.  Its type is preserved.

    Returns
    -------
    clipped_array : ndarray
        An array with the elements of `a`, but where values
        < `a_min` are replaced with `a_min`, and those > `a_max`
        with `a_max`.

    Notes
    -----
    array_like `a_min` and `a_max` are not supported.

    Examples
    --------
    >>> a = np.arange(10)
    >>> np.clip(a, 1, 8)
    array([1., 1., 2., 3., 4., 5., 6., 7., 8., 8.], dtype=float32)
    >>> a
    array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.], dtype=float32)
    >>> np.clip(a, 3, 6, out=a)
    array([3., 3., 3., 3., 4., 5., 6., 6., 6., 6.], dtype=float32)
    """
    return _mx_nd_np.clip(a, a_min, a_max, out=out)


@set_module('mxnet.numpy')
def argmax(a, axis=None, out=None):
    r"""
    Returns the indices of the maximum values along an axis.

    Parameters
    ----------
    a : ndarray
        Input array. Only support ndarrays of dtype `float16`, `float32`, and `float64`.
    axis : int, optional
        By default, the index is into the flattened array, otherwise
        along the specified axis.
    out : ndarray or None, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype.

    Returns
    -------
    index_array : ndarray of indices whose dtype is same as the input ndarray.
        Array of indices into the array. It has the same shape as `a.shape`
        with the dimension along `axis` removed.

    Notes
    -----
    In case of multiple occurrences of the maximum values, the indices
    corresponding to the first occurrence are returned.

    This function differs from the original `numpy.argmax
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html>`_ in
    the following aspects:

    - Input type does not support Python native iterables(list, tuple, ...).
    - Output has dtype that is same as the input ndarray.
    - ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
    - ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
    - ``out`` param does not support scalar input case.

    Examples
    --------
    >>> a = np.arange(6).reshape(2,3) + 10
    >>> a
    array([[10., 11., 12.],
           [13., 14., 15.]])
    >>> np.argmax(a)
    array(5.)
    >>> np.argmax(a, axis=0)
    array([1., 1., 1.])
    >>> np.argmax(a, axis=1)
    array([2., 2.])

    >>> b = np.arange(6)
    >>> b[1] = 5
    >>> b
    array([0., 5., 2., 3., 4., 5.])
    >>> np.argmax(b)  # Only the first occurrence is returned.
    array(1.)

    Specify ``out`` ndarray:

    >>> a = np.arange(6).reshape(2,3) + 10
    >>> b = np.zeros((2,))
    >>> np.argmax(a, axis=1, out=b)
    array([2., 2.])
    >>> b
    array([2., 2.])
    """
    return _mx_nd_np.argmax(a, axis, out)


@set_module('mxnet.numpy')
def argmin(a, axis=None, out=None):
    r"""
    Returns the indices of the minimum values along an axis.

    Parameters
    ----------
    a : ndarray
        Input array. Only support ndarrays of dtype `float16`, `float32`, and `float64`.
    axis : int, optional
        By default, the index is into the flattened array, otherwise
        along the specified axis.
    out : ndarray or None, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype.

    Returns
    -------
    index_array : ndarray of indices whose dtype is same as the input ndarray.
        Array of indices into the array. It has the same shape as `a.shape`
        with the dimension along `axis` removed.

    Notes
    -----
    In case of multiple occurrences of the minimum values, the indices
    corresponding to the first occurrence are returned.

    This function differs from the original `numpy.argmin
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmin.html>`_ in
    the following aspects:

    - Input type does not support Python native iterables(list, tuple, ...).
    - Output has dtype that is same as the input ndarray.
    - ``out`` param: cannot perform auto broadcasting. ``out`` ndarray's shape must be the same as the expected output.
    - ``out`` param: cannot perform auto type cast. ``out`` ndarray's dtype must be the same as the expected output.
    - ``out`` param does not support scalar input case.

    Examples
    --------
    >>> a = np.arange(6).reshape(2,3) + 10
    >>> a
    array([[10., 11., 12.],
           [13., 14., 15.]])
    >>> np.argmin(a)
    array(0.)
    >>> np.argmin(a, axis=0)
    array([0., 0., 0.])
    >>> np.argmin(a, axis=1)
    array([0., 0.])

    >>> b = np.arange(6)
    >>> b[2] = 0
    >>> b
    array([0., 1., 0., 3., 4., 5.])
    >>> np.argmax(b)  # Only the first occurrence is returned.
    array(0.)

    Specify ``out`` ndarray:

    >>> a = np.arange(6).reshape(2,3) + 10
    >>> b = np.zeros((2,))
    >>> np.argmin(a, axis=1, out=b)
    array([0., 0.])
    >>> b
    array([0., 0.])
    """
    return _mx_nd_np.argmin(a, axis, out)


@set_module('mxnet.numpy')
def mean(a, axis=None, dtype=None, out=None, keepdims=False):  # pylint: disable=arguments-differ
    """
    Compute the arithmetic mean along the specified axis.
    Returns the average of the array elements.
    The average is taken over the flattened array by default, otherwise over the specified axis.

    Parameters
    ----------
    a : ndarray
        ndarray containing numbers whose mean is desired.
    axis : None or int or tuple of ints, optional
        Axis or axes along which the means are computed. The default is to compute the mean of the flattened array.
        If this is a tuple of ints, a mean is performed over multiple axes,
        instead of a single axis or all the axes as before.
    dtype : data-type, optional
        Type to use in computing the mean. For integer inputs, the default is float32;
        for floating point inputs, it is the same as the input dtype.
    out : ndarray, optional
        Alternate output array in which to place the result. The default is None; if provided,
        it must have the same shape and type as the expected output.
    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 input array.
        If the default value is passed, then keepdims will not be passed through to the mean
        method of sub-classes of ndarray, however any non-default value will be. If the sub-class
        method does not implement keepdims any exceptions will be raised.

    Returns
    -------
    m : ndarray, see dtype parameter above
        If out=None, returns a new array containing the mean values,
        otherwise a reference to the output array is returned.

    Notes
    -----
    This function differs from the original `numpy.mean
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html>`_ in
    the following way(s):
    - only ndarray is accepted as valid input, python iterables or scalar is not supported
    - default data type for integer input is float32

    Examples
    --------
    >>> a = np.array([[1, 2], [3, 4]])
    >>> np.mean(a)
    array(2.5)
    >>> a = np.zeros((2, 512*512), dtype=np.float32)
    >>> a[0,:] = 1.0
    >>> a[1,:] = 0.1
    >>> np.mean(a)
    array(0.55)
    >>> np.mean(a, dtype=np.float64)
    array(0.55)
    """
    return _npi.mean(a, axis=axis, dtype=dtype, keepdims=keepdims, out=out)


@set_module('mxnet.numpy')
def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):  # pylint: disable=too-many-arguments
    """
    Compute the standard deviation along the specified axis.
    Returns the standard deviation, a measure of the spread of a distribution,
    of the array elements. The standard deviation is computed for the
    flattened array by default, otherwise over the specified axis.

    Parameters
    ----------
    a : array_like
        Calculate the standard deviation of these values.
    axis : None or int or tuple of ints, optional
        Axis or axes along which the standard deviation is computed. The
        default is to compute the standard deviation of the flattened array.
        .. versionadded:: 1.7.0
        If this is a tuple of ints, a standard deviation is performed over
        multiple axes, instead of a single axis or all the axes as before.
    dtype : dtype, optional
        Type to use in computing the standard deviation. For arrays of
        integer type the default is float64, for arrays of float types it is
        the same as the array type.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape as the expected output but the type (of the calculated
        values) will be cast if necessary.
    ddof : int, optional
        Means Delta Degrees of Freedom.  The divisor used in calculations
        is ``N - ddof``, where ``N`` represents the number of elements.
        By default `ddof` is zero.
    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 input array.
        If the default value is passed, then `keepdims` will not be
        passed through to the `std` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    Returns
    -------
    standard_deviation : ndarray, see dtype parameter above.
        If `out` is None, return a new array containing the standard deviation,
        otherwise return a reference to the output array.

    Examples
    --------
    >>> a = np.array([[1, 2], [3, 4]])
    >>> np.std(a)
    1.1180339887498949 # may vary
    >>> np.std(a, axis=0)
    array([1.,  1.])
    >>> np.std(a, axis=1)
    array([0.5,  0.5])
    In single precision, std() can be inaccurate:
    >>> a = np.zeros((2, 512*512), dtype=np.float32)
    >>> a[0, :] = 1.0
    >>> a[1, :] = 0.1
    >>> np.std(a)
    array(0.45)
    >>> np.std(a, dtype=np.float64)
    array(0.45, dtype=float64)
    """
    return _npi.std(a, axis=axis, dtype=dtype, ddof=ddof, keepdims=keepdims, out=out)


@set_module('mxnet.numpy')
def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):  # pylint: disable=too-many-arguments
    """
    Compute the variance along the specified axis.
    Returns the variance of the array elements, a measure of the spread of a
    distribution.  The variance is computed for the flattened array by
    default, otherwise over the specified axis.

    Parameters
    ----------
    a : array_like
        Array containing numbers whose variance is desired.  If `a` is not an
        array, a conversion is attempted.
    axis : None or int or tuple of ints, optional
        Axis or axes along which the variance is computed.  The default is to
        compute the variance of the flattened array.
        .. versionadded:: 1.7.0
        If this is a tuple of ints, a variance is performed over multiple axes,
        instead of a single axis or all the axes as before.
    dtype : data-type, optional
        Type to use in computing the variance.  For arrays of integer type
        the default is `float32`; for arrays of float types it is the same as
        the array type.
    out : ndarray, optional
        Alternate output array in which to place the result.  It must have
        the same shape as the expected output, but the type is cast if
        necessary.
    ddof : int, optional
        "Delta Degrees of Freedom": the divisor used in the calculation is
        ``N - ddof``, where ``N`` represents the number of elements. By
        default `ddof` is zero.
    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 input array.
        If the default value is passed, then `keepdims` will not be
        passed through to the `var` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    Returns
    -------
    variance : ndarray, see dtype parameter above
        If ``out=None``, returns a new array containing the variance;
        otherwise, a reference to the output array is returned.

    Examples
    --------
    >>> a = np.array([[1, 2], [3, 4]])
    >>> np.var(a)
    array(1.25)
    >>> np.var(a, axis=0)
    array([1.,  1.])
    >>> np.var(a, axis=1)
    array([0.25,  0.25])

    >>> a = np.zeros((2, 512*512), dtype=np.float32)
    >>> a[0, :] = 1.0
    >>> a[1, :] = 0.1
    >>> np.var(a)
    array(0.2025)
    >>> np.var(a, dtype=np.float64)
    array(0.2025, dtype=float64)
    >>> ((1-0.55)**2 + (0.1-0.55)**2)/2
    0.2025
    """
    return _npi.var(a, axis=axis, dtype=dtype, ddof=ddof, keepdims=keepdims, out=out)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def indices(dimensions, dtype=_np.int32, ctx=None):
    """Return an array representing the indices of a grid.

    Compute an array where the subarrays contain index values 0,1,...
    varying only along the corresponding axis.

    Parameters
    ----------
    dimensions : sequence of ints
        The shape of the grid.
    dtype : data-type, optional
        The desired data-type for the array. Default is `float32`.
    ctx : device context, optional
        Device context on which the memory is allocated. Default is
        `mxnet.context.current_context()`.

    Returns
    -------
    grid : ndarray
        The array of grid indices,
        ``grid.shape = (len(dimensions),) + tuple(dimensions)``.

    Notes
    -----
    The output shape is obtained by prepending the number of dimensions
    in front of the tuple of dimensions, i.e. if `dimensions` is a tuple
    ``(r0, ..., rN-1)`` of length ``N``, the output shape is
    ``(N,r0,...,rN-1)``.

    The subarrays ``grid[k]`` contains the N-D array of indices along the
    ``k-th`` axis. Explicitly::

        grid[k,i0,i1,...,iN-1] = ik

    Examples
    --------
    >>> grid = np.indices((2, 3))
    >>> grid.shape
    (2, 2, 3)
    >>> grid[0]        # row indices
    array([[0, 0, 0],
           [1, 1, 1]])
    >>> grid[1]        # column indices
    array([[0, 0, 0],
           [1, 1, 1]], dtype=int32)

    The indices can be used as an index into an array.

    >>> x = np.arange(20).reshape(5, 4)
    >>> row, col = np.indices((2, 3))
    >>> x[row, col]
    array([[0., 1., 2.],
           [4., 5., 6.]])

    Note that it would be more straightforward in the above example to
    extract the required elements directly with ``x[:2, :3]``.
    """
    return _mx_nd_np.indices(dimensions=dimensions, dtype=dtype, ctx=ctx)
# pylint: enable=redefined-outer-name


@set_module('mxnet.numpy')
@wrap_np_binary_func
def copysign(x1, x2, out=None, **kwargs):
    r"""
    Change the sign of x1 to that of x2, element-wise.

    If `x2` is a scalar, its sign will be copied to all elements of `x1`.

    Parameters
    ----------
    x1 : ndarray or scalar
        Values to change the sign of.
    x2 : ndarray or scalar
        The sign of `x2` is copied to `x1`.
    out : ndarray or None, optional
        A location into which the result is stored. It must be of the
        right shape and right type to hold the output. If not provided
        or `None`,a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray or scalar
        The values of `x1` with the sign of `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -------
    This function differs from the original `numpy.copysign
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.copysign.html>`_ in
    the following aspects:

    - ``where`` param is not supported.

    Examples
    --------
    >>> np.copysign(1.3, -1)
    -1.3
    >>> 1/np.copysign(0, 1)
    inf
    >>> 1/np.copysign(0, -1)
    -inf

    >>> a = np.array([-1, 0, 1])
    >>> np.copysign(a, -1.1)
    array([-1., -0., -1.])
    >>> np.copysign(a, np.arange(3)-1)
    array([-1.,  0.,  1.])
    """
    return _mx_nd_np.copysign(x1, x2, out=out)


@set_module('mxnet.numpy')
def ravel(x, order='C'):
    r"""
    ravel(x)

    Return a contiguous flattened array.
    A 1-D array, containing the elements of the input, is returned.  A copy is
    made only if needed.

    Parameters
    ----------
    x : ndarray
        Input array.  The elements in `x` are read in row-major, C-style order and
        packed as a 1-D array.
    order : `C`, optional
        Only support row-major, C-style order.

    Returns
    -------
    y : ndarray
        y is an array of the same subtype as `x`, with shape ``(x.size,)``.
        Note that matrices are special cased for backward compatibility, if `x`
        is a matrix, then y is a 1-D ndarray.

    Notes
    -----
    This function differs from the original numpy.arange in the following aspects:
        - Only support row-major, C-style order.

    Examples
    --------
    It is equivalent to ``reshape(x, -1)``.

    >>> x = np.array([[1, 2, 3], [4, 5, 6]])
    >>> print(np.ravel(x))
    [1. 2. 3. 4. 5. 6.]

    >>> print(x.reshape(-1))
    [1. 2. 3. 4. 5. 6.]

    >>> print(np.ravel(x.T))
    [1. 4. 2. 5. 3. 6.]
    """
    return _mx_nd_np.ravel(x, order)


@set_module('mxnet.numpy')
def hanning(M, dtype=_np.float32, ctx=None):
    r"""Return the Hanning window.

    The Hanning window is a taper formed by using a weighted cosine.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.
    dtype : str or numpy.dtype, optional
        An optional value type. Default is `float32`. Note that you need
        select numpy.float32 or float64 in this operator.
    ctx : Context, optional
        An optional device context (default is the current default context).

    Returns
    -------
    out : ndarray, shape(M,)
        The window, with the maximum value normalized to one (the value
        one appears only if `M` is odd).

    See Also
    --------
    blackman, hamming

    Notes
    -----
    The Hanning window is defined as

    .. math::  w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right)
               \qquad 0 \leq n \leq M-1

    The Hanning was named for Julius von Hann, an Austrian meteorologist.
    It is also known as the Cosine Bell. Some authors prefer that it be
    called a Hann window, to help avoid confusion with the very similar
    Hamming window.

    Most references to the Hanning window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function.

    References
    ----------
    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
           spectra, Dover Publications, New York.
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
           The University of Alberta Press, 1975, pp. 106-108.
    .. [3] Wikipedia, "Window function",
           http://en.wikipedia.org/wiki/Window_function
    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
           "Numerical Recipes", Cambridge University Press, 1986, page 425.

    Examples
    --------
    >>> np.hanning(12)
    array([0.        , 0.07937324, 0.29229254, 0.5711574 , 0.8274304 ,
           0.9797465 , 0.97974646, 0.82743025, 0.5711573 , 0.29229245,
           0.07937312, 0.        ])

    Plot the window and its frequency response:

    >>> import matplotlib.pyplot as plt
    >>> window = np.hanning(51)
    >>> plt.plot(window.asnumpy())
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.title("Hann window")
    Text(0.5, 1.0, 'Hann window')
    >>> plt.ylabel("Amplitude")
    Text(0, 0.5, 'Amplitude')
    >>> plt.xlabel("Sample")
    Text(0.5, 0, 'Sample')
    >>> plt.show()
    """
    return _mx_nd_np.hanning(M, dtype=dtype, ctx=ctx)


@set_module('mxnet.numpy')
def hamming(M, dtype=_np.float32, ctx=None):
    r"""Return the hamming window.

    The hamming window is a taper formed by using a weighted cosine.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.
    dtype : str or numpy.dtype, optional
        An optional value type. Default is `float32`. Note that you need
        select numpy.float32 or float64 in this operator.
    ctx : Context, optional
        An optional device context (default is the current default context).

    Returns
    -------
    out : ndarray, shape(M,)
        The window, with the maximum value normalized to one (the value
        one appears only if `M` is odd).

    See Also
    --------
    blackman, hanning

    Notes
    -----
    The Hamming window is defined as

    .. math::  w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right)
               \qquad 0 \leq n \leq M-1

    The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
    and is described in Blackman and Tukey. It was recommended for
    smoothing the truncated autocovariance function in the time domain.
    Most references to the Hamming window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function.

    References
    ----------
    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
           spectra, Dover Publications, New York.
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
           University of Alberta Press, 1975, pp. 109-110.
    .. [3] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function
    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
           "Numerical Recipes", Cambridge University Press, 1986, page 425.

    Examples
    --------
    >>> np.hamming(12)
    array([0.08000001, 0.15302339, 0.34890914, 0.6054648 , 0.841236  ,
           0.9813669 , 0.9813668 , 0.8412359 , 0.6054647 , 0.34890908,
           0.15302327, 0.08000001])

    Plot the window and its frequency response:

    >>> import matplotlib.pyplot as plt
    >>> window = np.hamming(51)
    >>> plt.plot(window.asnumpy())
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.title("hamming window")
    Text(0.5, 1.0, 'hamming window')
    >>> plt.ylabel("Amplitude")
    Text(0, 0.5, 'Amplitude')
    >>> plt.xlabel("Sample")
    Text(0.5, 0, 'Sample')
    >>> plt.show()
    """
    return _mx_nd_np.hamming(M, dtype=dtype, ctx=ctx)


@set_module('mxnet.numpy')
def blackman(M, dtype=_np.float32, ctx=None):
    r"""Return the Blackman window.

    The Blackman window is a taper formed by using the first three
    terms of a summation of cosines. It was designed to have close to the
    minimal leakage possible.  It is close to optimal, only slightly worse
    than a Kaiser window.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.
    dtype : str or numpy.dtype, optional
        An optional value type. Default is `float32`. Note that you need
        select numpy.float32 or float64 in this operator.
    ctx : Context, optional
        An optional device context (default is the current default context).

    Returns
    -------
    out : ndarray
        The window, with the maximum value normalized to one (the value one
        appears only if the number of samples is odd).

    See Also
    --------
    hamming, hanning

    Notes
    -----
    The Blackman window is defined as

    .. math::  w(n) = 0.42 - 0.5 \cos(2\pi n/{M-1}) + 0.08 \cos(4\pi n/{M-1})

    Most references to the Blackman window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function. It is known as a
    "near optimal" tapering function, almost as good (by some measures)
    as the kaiser window.

    References
    ----------
    Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
    Dover Publications, New York.

    Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
    Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.

    Examples
    --------
    >>> np.blackman(12)
    array([-1.4901161e-08,  3.2606423e-02,  1.5990365e-01,  4.1439798e-01,
            7.3604530e-01,  9.6704686e-01,  9.6704674e-01,  7.3604506e-01,
            4.1439781e-01,  1.5990359e-01,  3.2606363e-02, -1.4901161e-08])

    Plot the window and its frequency response:

    >>> import matplotlib.pyplot as plt
    >>> window = np.blackman(51)
    >>> plt.plot(window.asnumpy())
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.title("blackman window")
    Text(0.5, 1.0, 'blackman window')
    >>> plt.ylabel("Amplitude")
    Text(0, 0.5, 'Amplitude')
    >>> plt.xlabel("Sample")
    Text(0.5, 0, 'Sample')
    >>> plt.show()
    """
    return _mx_nd_np.blackman(M, dtype=dtype, ctx=ctx)


@set_module('mxnet.numpy')
def flip(m, axis=None, out=None):
    r"""
    flip(m, axis=None, out=None)

    Reverse the order of elements in an array along the given axis.

    The shape of the array is preserved, but the elements are reordered.

    Parameters
    ----------
    m : ndarray or scalar
        Input array.
    axis : None or int or tuple of ints, optional
        Axis or axes along which to flip over. The default,
        axis=None, will flip over all of the axes of the input array.
        If axis is negative it counts from the last to the first axis.

        If axis is a tuple of ints, flipping is performed on all of the axes
        specified in the tuple.
    out : ndarray or scalar, optional
        Alternative output array in which to place the result. It must have
        the same shape and type as the expected output.

    Returns
    -------
    out : ndarray or scalar
        A view of `m` with the entries of axis reversed.  Since a view is
        returned, this operation is done in constant time.

    Examples
    --------
    >>> A = np.arange(8).reshape((2,2,2))
    >>> A
    array([[[0, 1],
            [2, 3]],
           [[4, 5],
            [6, 7]]])
    >>> np.flip(A, 0)
    array([[[4, 5],
            [6, 7]],
           [[0, 1],
            [2, 3]]])
    >>> np.flip(A, 1)
    array([[[2, 3],
            [0, 1]],
           [[6, 7],
            [4, 5]]])
    >>> np.flip(A)
    array([[[7, 6],
            [5, 4]],
           [[3, 2],
            [1, 0]]])
    >>> np.flip(A, (0, 2))
    array([[[5, 4],
            [7, 6]],
           [[1, 0],
            [3, 2]]])
    """
    return _mx_nd_np.flip(m, axis, out=out)


@set_module('mxnet.numpy')
def around(x, decimals=0, out=None, **kwargs):
    r"""
    around(x, decimals=0, out=None)

    Evenly round to the given number of decimals.

    Parameters
    ----------
    x : ndarray or scalar
        Input data.
    decimals : int, optional
        Number of decimal places to round to (default: 0).  If
        decimals is negative, it specifies the number of positions to
        the left of the decimal point.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape and type as the expected output.

    Returns
    -------
    rounded_array : ndarray or scalar
        An array of the same type as `x`, containing the rounded values.
        A reference to the result is returned.

    Notes
    -----
    For values exactly halfway between rounded decimal values, NumPy
    rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
    -0.5 and 0.5 round to 0.0, etc.

    This function differs from the original numpy.prod in the following aspects:

        - Cannot cast type automatically. Dtype of `out` must be same as the expected one.
        - Cannot support complex-valued number.

    Examples
    --------
    >>> np.around([0.37, 1.64])
    array([ 0.,  2.])
    >>> np.around([0.37, 1.64], decimals=1)
    array([ 0.4,  1.6])
    >>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
    array([ 0.,  2.,  2.,  4.,  4.])
    >>> np.around([1, 2, 3, 11], decimals=1) # ndarray of ints is returned
    array([ 1,  2,  3, 11])
    >>> np.around([1, 2, 3, 11], decimals=-1)
    array([ 0,  0,  0, 10])
    """
    return _mx_nd_np.around(x, decimals, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def arctan2(x1, x2, out=None, **kwargs):
    r"""
    Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly.

    The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is
    the signed angle in radians between the ray ending at the origin and
    passing through the point (1,0), and the ray ending at the origin and
    passing through the point (`x2`, `x1`).  (Note the role reversal: the
    "`y`-coordinate" is the first function parameter, the "`x`-coordinate"
    is the second.)  By IEEE convention, this function is defined for
    `x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see
    Notes for specific values).

    This function is not defined for complex-valued arguments; for the
    so-called argument of complex values, use `angle`.

    Parameters
    ----------
    x1 : ndarray or scalar
        `y`-coordinates.
    x2 : ndarray or scalar
        `x`-coordinates. `x2` must be broadcastable to match the shape of
        `x1` or vice versa.
    out : ndarray or None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray or scalar
        Array of angles in radians, in the range ``[-pi, pi]``. This is a scalar if
        `x1` and `x2` are scalars.

    Notes
    -----
    *arctan2* is identical to the `atan2` function of the underlying
    C library.  The following special values are defined in the C
    standard: [1]_

    ====== ====== ================
    `x1`   `x2`   `arctan2(x1,x2)`
    ====== ====== ================
    +/- 0  +0     +/- 0
    +/- 0  -0     +/- pi
        > 0   +/-inf +0 / +pi
        < 0   +/-inf -0 / -pi
    +/-inf +inf   +/- (pi/4)
    +/-inf -inf   +/- (3*pi/4)
    ====== ====== ================

    Note that +0 and -0 are distinct floating point numbers, as are +inf
    and -inf.

    This function differs from the original numpy.arange in the following aspects:
        - Only support float16, float32 and float64.

    References
    ----------
    .. [1] ISO/IEC standard 9899:1999, "Programming language C."

    Examples
    --------
    Consider four points in different quadrants:

    >>> x = np.array([-1, +1, +1, -1])
    >>> y = np.array([-1, -1, +1, +1])
    >>> np.arctan2(y, x) * 180 / np.pi
    array([-135.,  -45.,   45.,  135.])

    Note the order of the parameters. `arctan2` is defined also when `x2` = 0
    and at several other special points, obtaining values in
    the range ``[-pi, pi]``:

    >>> x = np.array([1, -1])
    >>> y = np.array([0, 0])
    >>> np.arctan2(x, y)
    array([ 1.5707964, -1.5707964])
    """
    return _mx_nd_np.arctan2(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def hypot(x1, x2, out=None, **kwargs):
    r"""
    Given the "legs" of a right triangle, return its hypotenuse.

    Equivalent to ``sqrt(x1**2 + x2**2)``, element-wise.  If `x1` or
    `x2` is scalar_like (i.e., unambiguously cast-able to a scalar type),
    it is broadcast for use with each element of the other argument.

    Parameters
    ----------
    x1, x2 : array_like
        Leg of the triangle(s).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.

    Returns
    -------
    z : ndarray
        The hypotenuse of the triangle(s).
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -----
    This function differs from the original numpy.arange in the following aspects:
        - Only support float16, float32 and float64.

    Examples
    --------
    >>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3)))
    array([[ 5.,  5.,  5.],
           [ 5.,  5.,  5.],
           [ 5.,  5.,  5.]])

    Example showing broadcast of scalar_like argument:

    >>> np.hypot(3*np.ones((3, 3)), [4])
    array([[ 5.,  5.,  5.],
           [ 5.,  5.,  5.],
           [ 5.,  5.,  5.]])
    """
    return _mx_nd_np.hypot(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def bitwise_xor(x1, x2, out=None, **kwargs):
    r"""
    Compute the bit-wise XOR of two arrays element-wise.

    Parameters
    ----------
    x1, x2 : ndarray or scalar
        Only integer and boolean types are handled. If x1.shape != x2.shape,
        they must be broadcastable to a common shape (which becomes the shape of the output).
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have a shape that the
        inputs broadcast to. If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    out : ndarray
        Result.

    Examples
    --------
    >>> np.bitwise_xor(13, 17)
    28

    >>> np.bitwise_xor(31, 5)
    26
    >>> np.bitwise_xor(np.array([31,3], dtype=np.int32), 5)
    array([26,  6])

    >>> np.bitwise_xor(np.array([31,3], dtype='int32'), np.array([5,6], dtype='int32'))
    array([26,  5])
    >>> np.bitwise_xor(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
    array([ True, False])
    """
    return _mx_nd_np.bitwise_xor(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def ldexp(x1, x2, out=None, **kwargs):
    """
    Returns x1 * 2**x2, element-wise.
    The mantissas `x1` and twos exponents `x2` are used to construct
    floating point numbers ``x1 * 2**x2``.

    Parameters
    ----------
    x1 : ndarray or scalar
        Array of multipliers.
    x2 : ndarray or scalar, int
        Array of twos exponents.
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray or scalar
        The result of ``x1 * 2**x2``.
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -----
    Complex dtypes are not supported, they will raise a TypeError.
    Different from numpy, we allow x2 to be float besides int.
    `ldexp` is useful as the inverse of `frexp`, if used by itself it is
    more clear to simply use the expression ``x1 * 2**x2``.

    Examples
    --------
    >>> np.ldexp(5, np.arange(4))
    array([  5.,  10.,  20.,  40.])
    """
    return _mx_nd_np.ldexp(x1, x2, out)


@set_module('mxnet.numpy')
def inner(a, b):
    r"""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 : ndarray
        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)
    array(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.]])
    """
    return tensordot(a, b, [-1, -1])


@set_module('mxnet.numpy')
def outer(a, b):
    r"""Compute the outer product of two vectors.
    Given two vectors, ``a = [a0, a1, ..., aM]`` and
    ``b = [b0, b1, ..., bN]``,
    the outer product [1]_ is::
    [[a0*b0  a0*b1 ... a0*bN ]
    [a1*b0    .
    [ ...          .
    [aM*b0            aM*bN ]]

    Parameters
    ----------
    a : (M,) ndarray
        First input vector.  Input is flattened if
        not already 1-dimensional.
    b : (N,) ndarray
        Second input vector.  Input is flattened if
        not already 1-dimensional.

    Returns
    -------
    out : (M, N) ndarray
        ``out[i, j] = a[i] * b[j]``

    See also
    --------
    inner
    einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.
    ufunc.outer : A generalization to N dimensions and other operations.
                ``np.multiply.outer(a.ravel(), b.ravel())`` is the equivalent.

    References
    ----------
    .. [1] : G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd
            ed., Baltimore, MD, Johns Hopkins University Press, 1996,
            pg. 8.

    Examples
    --------
    Make a (*very* coarse) grid for computing a Mandelbrot set:

    >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
    >>> rl
    array([[-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.]])
    """
    return tensordot(a.flatten(), b.flatten(), 0)


@set_module('mxnet.numpy')
def vdot(a, b):
    r"""
    Return the dot product of two vectors.
    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 : ndarray
        First argument to the dot product.
    b : ndarray
        Second argument to the dot product.

    Returns
    -------
    output : ndarray
        Dot product of `a` and `b`.

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

    Examples
    --------
    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)
    array(30.)
    >>> np.vdot(b, a)
    array(30.)
    >>> 1*4 + 4*1 + 5*2 + 6*2
    30
    """
    return tensordot(a.flatten(), b.flatten(), 1)


@set_module('mxnet.numpy')
def equal(x1, x2, out=None):
    """
    Return (x1 == x2) element-wise.
    Parameters
    ----------
    x1, x2 : ndarrays or scalars
        Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
        a common shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.
    Returns
    -------
    out : ndarray or scalar
        Output array of type bool, element-wise comparison of `x1` and `x2`.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    not_equal, greater_equal, less_equal, greater, less
    Examples
    --------
    >>> np.equal(np.ones(2, 1)), np.zeros(1, 3))
    array([[False, False, False],
           [False, False, False]])
    >>> np.equal(1, np.ones(1))
    array([ True])
    """
    return _mx_nd_np.equal(x1, x2, out)


@set_module('mxnet.numpy')
def not_equal(x1, x2, out=None):
    """
    Return (x1 != x2) element-wise.
    Parameters
    ----------
    x1, x2 : ndarrays or scalars
        Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
        a common shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.
    Returns
    -------
    out : ndarray or scalar
        Output array of type bool, element-wise comparison of `x1` and `x2`.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    equal, greater, greater_equal, less, less_equal
    Examples
    --------
    >>> np.not_equal(np.ones(2, 1)), np.zeros(1, 3))
    array([[ True,  True,  True],
           [ True,  True,  True]])
    >>> np.not_equal(1, np.ones(1))
    array([False])
    """
    return _mx_nd_np.not_equal(x1, x2, out)


@set_module('mxnet.numpy')
def greater(x1, x2, out=None):
    """
    Return the truth value of (x1 > x2) element-wise.
    Parameters
    ----------
    x1, x2 : ndarrays or scalars
        Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
        a common shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.
    Returns
    -------
    out : ndarray or scalar
        Output array of type bool, element-wise comparison of `x1` and `x2`.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    equal, greater, greater_equal, less, less_equal
    Examples
    --------
    >>> np.greater(np.ones(2, 1)), np.zeros(1, 3))
    array([[ True,  True,  True],
           [ True,  True,  True]])
    >>> np.greater(1, np.ones(1))
    array([False])
    """
    return _mx_nd_np.greater(x1, x2, out)


@set_module('mxnet.numpy')
def less(x1, x2, out=None):
    """
    Return the truth value of (x1 < x2) element-wise.
    Parameters
    ----------
    x1, x2 : ndarrays or scalars
        Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
        a common shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.
    Returns
    -------
    out : ndarray or scalar
        Output array of type bool, element-wise comparison of `x1` and `x2`.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    equal, greater, greater_equal, less, less_equal
    Examples
    --------
    >>> np.less(np.ones(2, 1)), np.zeros(1, 3))
    array([[ True,  True,  True],
           [ True,  True,  True]])
    >>> np.less(1, np.ones(1))
    array([False])
    """
    return _mx_nd_np.less(x1, x2, out)


@set_module('mxnet.numpy')
def greater_equal(x1, x2, out=None):
    """
    Return the truth value of (x1 >= x2) element-wise.
    Parameters
    ----------
    x1, x2 : ndarrays or scalars
        Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
        a common shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.
    Returns
    -------
    out : ndarray or scalar
        Output array of type bool, element-wise comparison of `x1` and `x2`.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    equal, greater, greater_equal, less, less_equal
    Examples
    --------
    >>> np.greater_equal(np.ones(2, 1)), np.zeros(1, 3))
    array([[ True,  True,  True],
           [ True,  True,  True]])
    >>> np.greater_equal(1, np.ones(1))
    array([True])
    """
    return _mx_nd_np.greater_equal(x1, x2, out)


@set_module('mxnet.numpy')
def less_equal(x1, x2, out=None):
    """
    Return the truth value of (x1 <= x2) element-wise.
    Parameters
    ----------
    x1, x2 : ndarrays or scalars
        Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to
        a common shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated array is returned.
    Returns
    -------
    out : ndarray or scalar
        Output array of type bool, element-wise comparison of `x1` and `x2`.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    equal, greater, greater_equal, less, less_equal
    Examples
    --------
    >>> np.less_equal(np.ones(2, 1)), np.zeros(1, 3))
    array([[False, False, False],
           [False, False, False]])
    >>> np.less_equal(1, np.ones(1))
    array([True])
    """
    return _mx_nd_np.less_equal(x1, x2, out)


@set_module('mxnet.numpy')
def rot90(m, k=1, axes=(0, 1)):
    """
    Rotate an array by 90 degrees in the plane specified by axes.
    Rotation direction is from the first towards the second axis.

    Parameters
    ----------
    m : ndarray
        Array of two or more dimensions.
    k : integer
        Number of times the array is rotated by 90 degrees.
    axes: (2,) array_like
        The array is rotated in the plane defined by the axes.
        Axes must be different.

    Returns
    -------
    y : ndarray
        A rotated view of `m`.

    Notes
    -----
    rot90(m, k=1, axes=(1,0)) is the reverse of rot90(m, k=1, axes=(0,1))
    rot90(m, k=1, axes=(1,0)) is equivalent to rot90(m, k=-1, axes=(0,1))

    Examples
    --------
    >>> m = np.array([[1,2],[3,4]], 'int')
    >>> m
    array([[1, 2],
           [3, 4]], dtype=int64)
    >>> np.rot90(m)
    array([[2, 4],
           [1, 3]], dtype=int64)
    >>> np.rot90(m, 2)
    array([[4, 3],
           [2, 1]], dtype=int64)
    >>> m = np.arange(8).reshape((2,2,2))
    >>> np.rot90(m, 1, (1,2))
    array([[[1., 3.],
            [0., 2.]],

           [[5., 7.],
            [4., 6.]]])
    """
    return _mx_nd_np.rot90(m, k=k, axes=axes)


@set_module('mxnet.numpy')
def hsplit(ary, indices_or_sections):
    """Split an array into multiple sub-arrays horizontally (column-wise).
    This is equivalent to ``split`` with ``axis=0`` if ``ary`` has one
    dimension, and otherwise that with ``axis=1``.

    Parameters
    ----------
    ary : ndarray
        Array to be divided into sub-arrays.
    indices_or_sections : int, list of ints or tuple of ints.
        If `indices_or_sections` is an integer, N, the array will be divided
        into N equal arrays along `axis`.  If such a split is not possible,
        an error is raised.
        If `indices_or_sections` is a list of sorted integers, the entries
        indicate where along `axis` the array is split.
        If an index exceeds the dimension of the array along `axis`,
        it will raises errors. so index must less than or euqal to
        the dimension of the array along axis.

    Returns
    -------
    sub-arrays : list of ndarrays
        A list of sub-arrays.

    Notes
    ------
    - If `indices_or_sections` is given as an integer, but a split
      does not result in equal division.It will raises ValueErrors.
    - If indices_or_sections is an integer, and the number is 1, it will
      raises an error. Because single output from split is not supported yet...

    See Also
    --------
    split : Split an array into multiple sub-arrays of equal size.

    Examples
    --------
    >>> x = np.arange(16.0).reshape(4, 4)
    >>> x
    array([[ 0.,  1.,  2.,  3.],
           [ 4.,  5.,  6.,  7.],
           [ 8.,  9., 10., 11.],
           [12., 13., 14., 15.]])
    >>> np.hsplit(x, 2)
    [array([[ 0.,  1.],
           [ 4.,  5.],
           [ 8.,  9.],
           [12., 13.]]),
    array([[ 2.,  3.],
           [ 6.,  7.],
           [10., 11.],
           [14., 15.]])]
    >>> np.hsplit(x, [3, 6])
    [array([[ 0.,  1.,  2.],
           [ 4.,  5.,  6.],
           [ 8.,  9., 10.],
           [12., 13., 14.]]),
    array([[ 3.],
           [ 7.],
           [11.],
           [15.]]),
    array([], shape=(4, 0), dtype=float32)]
    With a higher dimensional array the split is still along the second axis.
    >>> x = np.arange(8.0).reshape(2, 2, 2)
    >>> x
    array([[[ 0.,  1.],
            [ 2.,  3.]],
           [[ 4.,  5.],
            [ 6.,  7.]]])
    >>> np.hsplit(x, 2)
    [array([[[ 0.,  1.]],
            [[ 4.,  5.]]]),
     array([[[ 2.,  3.]],
            [[ 6.,  7.]]])]
    If ``ary`` has one dimension, 'axis' = 0.
    >>> x = np.arange(4)
    array([0., 1., 2., 3.])
    >>> np.hsplit(x, 2)
    [array([0., 1.]), array([2., 3.])]
    If you want to produce an empty sub-array, you can see an example.
    >>> np.hsplit(x, [2, 2])
    [array([0., 1.]), array([], dtype=float32), array([2., 3.])]
    """
    return _mx_nd_np.hsplit(ary, indices_or_sections)


@set_module('mxnet.numpy')
def einsum(*operands, **kwargs):
    r"""
    einsum(subscripts, *operands, out=None, optimize=False)

    Evaluates the Einstein summation convention on the operands.

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

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

    See the notes and examples for clarification.

    Parameters
    ----------
    subscripts : str
        Specifies the subscripts for summation as comma separated list of
        subscript labels. An implicit (classical Einstein summation)
        calculation is performed unless the explicit indicator '->' is
        included as well as subscript labels of the precise output form.
    operands : list of ndarray
        These are the arrays for the operation.
    out : ndarray, optional
        If provided, the calculation is done into this array.
    optimize : {False, True}, optional
        Controls if intermediate optimization should occur. No optimization
        will occur if False. Defaults to False.

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

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

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

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

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

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

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

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

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

    The ``optimize`` argument which will optimize the contraction order
    of an einsum expression. For a contraction with three or more operands this
    can greatly increase the computational efficiency at the cost of a larger
    memory footprint during computation.

    Typically a 'greedy' algorithm is applied which empirical tests have shown
    returns the optimal path in the majority of cases. 'optimal' is not supported
    for now.

    This function differs from the original `numpy.einsum
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html>`_ in
    the following way(s):

    - Does not support 'optimal' strategy
    - Does not support the alternative subscript like
        `einsum(op0, sublist0, op1, sublist1, ..., [sublistout])`
    - Does not produce view in any cases

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

    Trace of a matrix:

    >>> np.einsum('ii', a)
    array(60.)

    Extract the diagonal (requires explicit form):

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

    Sum over an axis (requires explicit form):

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

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

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

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

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

    Vector inner products:

    >>> np.einsum('i,i', b, b)
    array(30.)

    Matrix vector multiplication:

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

    Broadcasting and scalar multiplication:

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

    Vector outer product:

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

    Tensor contraction:

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

    Example of ellipsis use:

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

    Chained array operations. For more complicated contractions, speed ups
    might be achieved by repeatedly computing a 'greedy' path. Performance
    improvements can be particularly significant with larger arrays:

    >>> a = np.ones(64).reshape(2,4,8)
    # Basic `einsum`: ~42.22ms  (benchmarked on 3.4GHz Intel Xeon.)
    >>> for iteration in range(500):
    ...     np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)
    # Greedy `einsum` (faster optimal path approximation): ~0.117ms
    >>> for iteration in range(500):
    ...     np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=True)
    """
    return _mx_nd_np.einsum(*operands, **kwargs)


@set_module('mxnet.numpy')
def nonzero(a):
    """
    Return the indices of the elements that are non-zero.

    Returns a tuple of arrays, one for each dimension of `a`,
    containing the indices of the non-zero elements in that
    dimension. The values in `a` are always returned in
    row-major, C-style order.

    To group the indices by element, rather than dimension, use `argwhere`,
    which returns a row for each non-zero element.

    Parameters
    ----------
    a : ndarray
        Input array.

    Returns
    -------
    tuple_of_arrays : tuple
        Indices of elements that are non-zero.

    See Also
    --------
    ndarray.nonzero :
        Equivalent ndarray method.

    Notes
    -----
    While the nonzero values can be obtained with ``a[nonzero(a)]``, it is
    recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which
    will correctly handle 0-d arrays.

    Examples
    --------
    >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
    >>> x
    array([[3, 0, 0],
           [0, 4, 0],
           [5, 6, 0]], dtype=int32)
    >>> np.nonzero(x)
    (array([0, 1, 2, 2], dtype=int64), array([0, 1, 0, 1], dtype=int64))

    >>> x[np.nonzero(x)]
    array([3, 4, 5, 6])
    >>> np.transpose(np.stack(np.nonzero(x)))
    array([[0, 0],
           [1, 1],
           [2, 0],
           [2, 1]], dtype=int64)

    A common use for ``nonzero`` is to find the indices of an array, where
    a condition is True.  Given an array `a`, the condition `a` > 3 is a
    boolean array and since False is interpreted as 0, np.nonzero(a > 3)
    yields the indices of the `a` where the condition is true.

    >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.int32)
    >>> a > 3
    array([[False, False, False],
           [ True,  True,  True],
           [ True,  True,  True]])
    >>> np.nonzero(a > 3)
    (array([1, 1, 1, 2, 2, 2], dtype=int64), array([0, 1, 2, 0, 1, 2], dtype=int64))

    Using this result to index `a` is equivalent to using the mask directly:

    >>> a[np.nonzero(a > 3)]
    array([4, 5, 6, 7, 8, 9], dtype=int32)
    >>> a[a > 3]
    array([4, 5, 6, 7, 8, 9], dtype=int32)

    ``nonzero`` can also be called as a method of the array.

    >>> (a > 3).nonzero()
    (array([1, 1, 1, 2, 2, 2], dtype=int64), array([0, 1, 2, 0, 1, 2], dtype=int64))
    """
    return _mx_nd_np.nonzero(a)


@set_module('mxnet.numpy')
def shares_memory(a, b, max_work=None):
    """
    Determine if two arrays share memory

    Parameters
    ----------
    a, b : ndarray
        Input arrays

    Returns
    -------
    out : bool

    See Also
    --------
    may_share_memory

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

    This function differs from the original `numpy.shares_memory
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.shares_memory.html>`_ in
    the following way(s):

    - Does not support `max_work`, it is a dummy argument
    - Actually it is same as `may_share_memory` in MXNet DeepNumPy
    """
    return _mx_nd_np.shares_memory(a, b, max_work)


@set_module('mxnet.numpy')
def 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

    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

    This function differs from the original `numpy.may_share_memory
    <https://docs.scipy.org/doc/numpy/reference/generated/numpy.may_share_memory.html>`_ in
    the following way(s):

    - Does not support `max_work`, it is a dummy argument
    - Actually it is same as `shares_memory` in MXNet DeepNumPy
    """
    return _mx_nd_np.may_share_memory(a, b, max_work)


def diff(a, n=1, axis=-1, prepend=None, append=None):  # pylint: disable=redefined-outer-name
    r"""
    numpy.diff(a, n=1, axis=-1, prepend=<no value>, append=<no value>)

    Calculate the n-th discrete difference along the given axis.

    Parameters
    ----------
    a : ndarray
        Input array
    n : int, optional
        The number of times values are differenced. If zero, the input is returned as-is.
    axis : int, optional
        The axis along which the difference is taken, default is the last axis.
    prepend, append : ndarray, optional
        Not supported yet

    Returns
    -------
    diff : ndarray
        The n-th differences.
        The shape of the output is the same as a except along axis where the dimension is smaller by n.
        The type of the output is the same as the type of the difference between any two elements of a.
        This is the same as the type of a in most cases.

    Examples
    --------
    >>> x = np.array([1, 2, 4, 7, 0])
    >>> np.diff(x)
    array([ 1,  2,  3, -7])
    >>> np.diff(x, n=2)
    array([  1,   1, -10])

    >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])
    >>> np.diff(x)
    array([[2, 3, 4],
        [5, 1, 2]])
    >>> np.diff(x, axis=0)
    array([[-1,  2,  0, -2]])

    Notes
    -----
    Optional inputs `prepend` and `append` are not supported yet
    """
    if (prepend or append):
        raise NotImplementedError('prepend and append options are not supported yet')
    return _mx_nd_np.diff(a, n=n, axis=axis)