multiarray.py

#!/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."""


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

from array import array as native_array
import functools
import ctypes
import sys
import datetime
import warnings
import numpy as _np
from .. import _deferred_compute as dc
from ..autograd import is_recording
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, mx_int, mx_int64
from ..base import mx_real_t, c_array_buf, mx_uint, numeric_types, integer_types
from ..runtime import Features
from ..device import Device
from ..util import set_module, wrap_np_unary_func, wrap_np_binary_func,\
                   is_np_default_dtype, wrap_ctx_to_device_func,\
                   dtype_from_number, wrap_data_api_statical_func,\
                   wrap_sort_functions
from ..device import current_device
from ..ndarray import numpy as _mx_nd_np
from ..ndarray.numpy import _internal as _npi
from ..ndarray.ndarray import _storage_type
from ..dlpack import ndarray_from_numpy, ndarray_to_dlpack_for_write, DLDeviceType,\
                     ndarray_from_dlpack
from .utils import _get_np_op
from .fallback import *  # pylint: disable=wildcard-import,unused-wildcard-import
from . import fallback


__all__ = ['ndarray', 'empty', 'empty_like', 'array', 'shape', 'median',
           'zeros', 'zeros_like', 'ones', 'ones_like', 'full', 'full_like', 'all', 'any', 'broadcast_to',
           'add', 'subtract', 'multiply', 'divide', 'mod', 'remainder', 'fmod', 'pow', 'power', 'bitwise_not',
           'delete', 'trace', 'transpose', 'copy', 'moveaxis', 'reshape', 'dot',
           'arctan2', 'atan2', 'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'log10', 'bitwise_invert', 'invert',
           'sqrt', 'cbrt', 'abs', 'absolute', 'fabs', 'exp', 'expm1', 'arcsin', 'asin', 'arccos', 'acos', 'arctan',
           'atan', 'sign', 'log', 'degrees', 'log2', 'log1p', 'rint', 'radians', 'reciprocal', 'square',
           'negative', 'histogram', 'fix', 'ceil', 'floor', 'trunc', 'logical_not', 'arcsinh', 'asinh',
           'arccosh', 'acosh', 'arctanh', 'atanh', 'append', 'argsort', 'sort', 'tensordot', 'eye', 'linspace',
           'logspace', 'expand_dims', 'tile', 'arange', 'array_split', 'split', 'hsplit', 'vsplit',
           'dsplit', 'flatnonzero', 'tril_indices', 'concatenate', 'concat', 'stack', 'vstack', 'row_stack',
           'column_stack', 'hstack', 'dstack', 'average', 'mean', 'maximum', 'fmax', 'minimum', 'fmin',
           'amax', 'amin', 'max', 'min', 'swapaxes', 'clip', 'argmax', 'argmin', 'std', 'var', 'insert',
           'indices', 'copysign', 'ravel', 'unravel_index', 'diag_indices_from', 'hanning', 'hamming', 'blackman',
           'logical_and', 'logical_or', 'logical_xor',
           'flip', 'flipud', 'fliplr', 'around', 'round', 'round_', 'arctan2', 'hypot',
           'triu_indices_from', 'triu_indices', 'tri',
           'bitwise_and', 'bitwise_xor', 'bitwise_or', 'rad2deg', 'deg2rad',
           'unique', 'lcm', 'gcd', 'tril', 'triu', 'identity', 'take', 'ldexp', 'vdot', 'inner', 'outer',
           'cross', 'kron', 'equal', 'not_equal', 'interp',
           'greater', 'less', 'greater_equal', 'less_equal', 'roll', 'rot90', 'einsum', 'true_divide', 'nonzero',
           'quantile', 'percentile', 'shares_memory', 'may_share_memory', 'diff', 'ediff1d', 'resize', 'matmul',
           'nan_to_num', 'isnan', 'isinf', 'isposinf', 'isneginf', 'isfinite', 'polyval', 'where', 'bincount',
           'atleast_1d', 'atleast_2d', 'atleast_3d', 'fill_diagonal', 'squeeze',
           'diagflat', 'repeat', 'prod', 'pad', 'cumsum', 'sum', 'rollaxis', 'diag', 'diagonal',
           'positive', 'logaddexp', 'floor_divide', 'permute_dims', 'bitwise_left_shift', 'bitwise_right_shift',
           'asarray', 'from_dlpack']

__all__ += fallback.__all__

# Return code for dispatching indexing function call
_NDARRAY_UNSUPPORTED_INDEXING = -1
_NDARRAY_BASIC_INDEXING = 0
_NDARRAY_ADVANCED_INDEXING = 1
_NDARRAY_EMPTY_TUPLE_INDEXING = 2

# Return code for 0-d boolean array handler
_NDARRAY_NO_ZERO_DIM_BOOL_ARRAY = -1
_NDARRAY_ZERO_DIM_BOOL_ARRAY_FALSE = 0
_NDARRAY_ZERO_DIM_BOOL_ARRAY_TRUE = 1
_SIGNED_INT32_UPPER_LIMIT = (2**31 - 1)

# Caching whether MXNet was built with INT64 support or not
_INT64_TENSOR_SIZE_ENABLED = None

def _int64_enabled():
    global _INT64_TENSOR_SIZE_ENABLED
    if _INT64_TENSOR_SIZE_ENABLED is None:
        _INT64_TENSOR_SIZE_ENABLED = Features().is_enabled('INT64_TENSOR_SIZE')
    return _INT64_TENSOR_SIZE_ENABLED

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

    Empty handle is only used to hold results.

    Returns
    -------
    handle
        A new empty `ndarray` handle.
    """
    hdl = NDArrayHandle()
    if _int64_enabled():
        check_call(_LIB.MXNDArrayCreate64(
            c_array_buf(mx_int64, native_array('q', shape)),
            ctypes.c_int(len(shape)),
            ctypes.c_int(device.device_typeid),
            ctypes.c_int(device.device_id),
            ctypes.c_int(int(delay_alloc)),
            ctypes.c_int(int(dtype_np_to_mx(dtype))),
            ctypes.byref(hdl)))
    else:
        # When shape is larger than uint32 then there is an overflow error at python end itself.
        # It needs to be caught here since the call doesn't even reach backend.
        array_size = 1
        for idx in shape:
            array_size = array_size * idx
        if array_size > _SIGNED_INT32_UPPER_LIMIT:
            raise Exception("[_new_alloc_handle] Size of tensor you are trying to allocate is " +
                            "larger than 2^31 elements. Please build with flag " +
                            "USE_INT64_TENSOR_SIZE=1")
        check_call(_LIB.MXNDArrayCreate(
            c_array_buf(mx_uint, native_array('I', shape)),
            mx_uint(len(shape)),
            ctypes.c_int(device.device_typeid),
            ctypes.c_int(device.device_id),
            ctypes.c_int(int(delay_alloc)),
            ctypes.c_int(int(dtype_np_to_mx(dtype))),
            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)

def _as_mx_np_array(object, device=None, zero_copy=False):
    """Convert arrays or any array member of container to mxnet.numpy.ndarray on device."""
    if object is None or isinstance(object, ndarray):
        return object
    elif isinstance(object, _np.ndarray):
        from_numpy = ndarray_from_numpy(ndarray, array)
        return from_numpy(object, zero_copy and object.flags['C_CONTIGUOUS'])
    elif isinstance(object, (integer_types, numeric_types)):
        return object
    elif isinstance(object, (_np.bool_, _np.bool)):
        return array(object, dtype=_np.bool_, device=device)
    elif isinstance(object, (list, tuple)):
        tmp = [_as_mx_np_array(arr, device=device, zero_copy=zero_copy) for arr in object]
        return object.__class__(tmp)
    else:
        raise TypeError('Does not support converting {} to mx.np.ndarray.'.format(str(type(object))))


def _as_onp_array(object, cur_device=None):
    """Convert object to numpy.ndarray."""
    def _update_device(cur_device, tmp_device):
        if cur_device is None:
            cur_device = tmp_device
        elif tmp_device is not None and cur_device != tmp_device:
            raise ValueError('Ambiguous to set the device for the output ndarray since'  # pylint: disable=too-few-format-args
                             ' input ndarrays are allocated on different devices: {} and {}'
                             .format(str(cur_device, tmp_device)))
        return cur_device

    if isinstance(object, ndarray):
        return object.asnumpy(), object.device
    elif isinstance(object, (list, tuple)):
        tmp = []
        for arr in object:
            arr, tmp_device = _as_onp_array(arr, cur_device)
            tmp.append(arr)
            cur_device = _update_device(cur_device, tmp_device)
        return object.__class__(tmp), cur_device
    elif isinstance(object, dict):
        tmp = dict()
        for key, value in object.items():
            value, tmp_device = _as_onp_array(value, cur_device)
            tmp[key] = value
            cur_device = _update_device(cur_device, tmp_device)
        return object.__class__(tmp), cur_device
    else:
        return object, cur_device


# 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 == -1:
        stype = _storage_type(handle)
    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 = {}
_FALLBACK_ARRAY_FUNCTION_WARNED_RECORD = {}
_FALLBACK_ARRAY_UFUNC_WARNED_RECORD = {}

def wrap_mxnp_np_ufunc(func):
    """
    A convenience decorator for wrapping for python overload-able ops to provide type
    casting for mixed use of mx_np and onp inputs.

    Parameters
    ----------
    func : a python overload-able binary function to be wrapped for type casting.

    Returns
    -------
    Function
        A function wrapped with type casted.
    """
    @functools.wraps(func)
    def _wrap_mxnp_np_ufunc(x1, x2):
        if isinstance(x2, _np.ndarray):
            x2 = _as_mx_np_array(x2, device=x1.device)
        return func(x1, x2)
    return _wrap_mxnp_np_ufunc

@set_module('mxnet.numpy')
class ndarray(NDArray):  # pylint: disable=invalid-name
    """
    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.
        Casting rules for operator with mx_np and onp (inplace op will keep its type)
        | Expression | a type | b type | out type|
        | --- | --- | --- | --- |
        | `a += b` | onp | mx_np | onp |
        | `a += b` | mx_np | onp | mx_np |
        | `c = a + b` | onp | mx_np | mx_np |
        | `c = a + b` | mx_np | onp | mx_np |
        """
        ufunc_list = ["add", "subtract", "multiply", "divide", "true_divide", "floor_divide", "power",
                      "remainder", "bitwise_and", "bitwise_or", "bitwise_xor", "left_shift", "right_shift",
                      "greater", "greater_equal", "less", "less_equal", "not_equal", "equal", "matmul"]
        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__':
            name = ufunc.__name__
            mx_ufunc = _NUMPY_ARRAY_UFUNC_DICT.get(name, None)
            onp_op = _get_np_op(name)
            if mx_ufunc is None:
                # try to fallback to official NumPy op
                if is_recording():
                    raise ValueError("Falling back to NumPy operator {} with autograd active is not supported."
                                     "Please consider moving the operator to the outside of the autograd scope.")\
                                     .format(name)
                new_inputs = [arg.asnumpy() if isinstance(arg, ndarray) else arg for arg in inputs]
                if onp_op not in _FALLBACK_ARRAY_UFUNC_WARNED_RECORD:
                    import logging
                    logging.warning("np.%s is a fallback operator, "
                                    "which is actually using official numpy's implementation", name)
                    _FALLBACK_ARRAY_UFUNC_WARNED_RECORD[onp_op] = True
                out = onp_op(*new_inputs, **kwargs)
                return _as_mx_np_array(out, device=inputs[0].device)
            # ops with np mx_np
            elif name in ufunc_list and isinstance(inputs[0], _np.ndarray):
                # inplace
                if 'out' in kwargs:
                    new_inputs = [arg.asnumpy() if isinstance(arg, ndarray) else arg for arg in inputs]
                    return onp_op(*new_inputs, **kwargs)
                else:
                    new_inputs = [_as_mx_np_array(arg, device=inputs[1].device)
                                  if isinstance(arg, _np.ndarray) else arg for arg in inputs]
                    return mx_ufunc(*new_inputs, **kwargs)
            else:
                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)
        func_name = func.__name__
        if mx_np_func is None:
            # try to fallback to official NumPy op
            if is_recording():
                raise ValueError("Falling back to NumPy operator {} with autograd active is not supported."
                                 "Please consider moving the operator to the outside of the autograd scope.")\
                                 .format(func)
            cur_device = None
            new_args, cur_device = _as_onp_array(args, cur_device)
            new_kwargs, cur_device = _as_onp_array(kwargs, cur_device)
            if cur_device is None:
                raise ValueError('Unknown device for the input ndarrays. It is probably a bug. Please'
                                 ' create an issue on GitHub.')
            if func not in _FALLBACK_ARRAY_FUNCTION_WARNED_RECORD:
                import logging
                logging.warning("np.%s is a fallback operator, "
                                "which is actually using official numpy's implementation.", func_name)
                _FALLBACK_ARRAY_FUNCTION_WARNED_RECORD[func] = True
            out = func(*new_args, **new_kwargs)
            return _as_mx_np_array(out, device=cur_device)
        else:
            if py_all(issubclass(t, ndarray) for t in types):
                return mx_np_func(*args, **kwargs)
            else:
                try:
                    cur_device = next(a.device for a in args if hasattr(a, 'device'))
                except StopIteration:
                    cur_device = next(a.device for a in kwargs.values() if hasattr(a, 'device'))
                new_args = _as_mx_np_array(args, device=cur_device,
                                           zero_copy=func_name in {'may_share_memory', 'shares_memory'})
                new_kwargs = {k: _as_mx_np_array(v, cur_device) for k, v in kwargs.items()}
                return mx_np_func(*new_args, **new_kwargs)


    def __array_namespace__(self, api_version=None):
        """
        Returns an object that has all the array API functions on it.

        Notes
        -----
        This is a standard API in
        https://data-apis.org/array-api/latest/API_specification/array_object.html#array-namespace-self-api-version-none.

        Parameters
        ----------
        self : ndarray
            The indexing key.
        api_version : Optional, string
            string representing the version of the array API specification to be returned, in `YYYY.MM` form.
            If it is None, it should return the namespace corresponding to latest version of the array API
            specification.
        """
        if api_version is not None:
            try:
                date = datetime.datetime.strptime(api_version, '%Y.%m')
                if date.year != 2021:
                    raise ValueError
            except ValueError:
                raise ValueError(f"Unrecognized array API version: {api_version!r}")
        return sys.modules[self.__module__]


    def __dlpack__(self, stream=None):
        """Exports the array for consumption by from_dlpack() as a DLPack capsule.

        Parameters
        ----------
        stream : int, optional
            A Python integer representing a pointer to a stream (CUDA or ROCm).
            Stream is provided by the consumer to the producer to instruct the producer
            to ensure that operations can safely be performed on the array. The pointer must
            be positive integer or -1. If stream is -1, the value must be used by the consumer
            to signal "producer must not perform any synchronization". 

        Returns
        -------
        capsule : PyCapsule
            A DLPack capsule for the array, containing a DLPackManagedTensor.
        """
        if stream is not None:
            if type(stream) is not int:
                raise TypeError('The input stream must be int or None')
            if self.device.device_type != "gpu":
                raise ValueError('Stream {} is not supported in current device {}'\
                    .format(stream, self.device.device_type))
            if stream != -1:
                check_call(_LIB.MXPushStreamDep(self.handle, ctypes.c_int64(stream)))
        to_dlpack_write = ndarray_to_dlpack_for_write()
        return to_dlpack_write(self)


    def __dlpack_device__(self):
        """Returns device type and device ID in DLPack format"""
        devtype_map = {'cpu': DLDeviceType.DLCPU,
                       'gpu': DLDeviceType.DLGPU,
                       'cpu_pinned': DLDeviceType.DLCPUPINNED}
        if self.device.device_type not in devtype_map:
            raise ValueError('Unkown device type {} for DLPack'.format(self.device.device_type))
        return (devtype_map[self.device.device_type], self.device.device_id)


    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)
            if _int64_enabled():
                check_call(
                    _LIB.MXNDArraySlice64(
                        flat_self.handle,
                        ctypes.c_int64(flat_begin),
                        ctypes.c_int64(flat_end),
                        ctypes.byref(handle),
                    )
                )
            else:
                check_call(
                    _LIB.MXNDArraySlice(
                        flat_self.handle,
                        ctypes.c_uint32(flat_begin),
                        ctypes.c_uint32(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_empty_tuple_indexing(self, key):
        new_shape = []
        num_none = 0
        for i, idx in enumerate(key):
            if idx is None:
                new_shape.append(1) # expand dimension
                num_none += 1
            elif idx == ():
                new_shape.append(0) # 0 shape
            elif idx == slice(None, None, None):
                new_shape.append(self.shape[i - num_none])
        return empty(new_shape, dtype=self.dtype)

    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 = _mx_nd_np.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 = _mx_nd_np.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=redefined-outer-name
    def _get_np_boolean_indexing(self, key, ndim, shape):
        """
        There are two types of boolean indices (which are equivalent,
        for the most part though). This function will handle single
        boolean indexing for higher speed.
        If this is not the case, it is instead expanded into (multiple)
        integer array indices and will be handled by advanced 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)
        if data.size == 0 and key.size == 0:
            return data
        return _reshape_view(_npi.boolean_mask(data, key), -1, *remaining_dims)

    def _set_np_boolean_indexing(self, key, value):
        """
        There are two types of boolean indices (which are equivalent,
        for the most part though). This function will handle single boolean assign for higher speed.
        If this is not the case, it is instead expanded into (multiple)
        integer array indices and will be handled by advanced assign.
        """
        if isinstance(value, numeric_types):
            _npi.boolean_mask_assign_scalar(data=self, mask=key,
                                            value=int(value) if isinstance(value, bool) else value,
                                            start_axis=0, out=self)
        elif isinstance(value, ndarray):
            _npi.boolean_mask_assign_tensor(data=self, mask=key, value=value, start_axis=0, out=self)
        else:
            raise NotImplementedError(f'type {type(value)} is not supported.')

    # 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.])

        For more imformation related to boolean indexing, please refer to
        https://docs.scipy.org/doc/numpy-1.17.0/reference/arrays.indexing.html.
        """
        ndim = self.ndim  # pylint: disable=redefined-outer-name
        shape = self.shape  # pylint: disable=redefined-outer-name
        if isinstance(key, bool): # otherwise will be treated as 0 and 1
            key = array(key, dtype=_np.bool, device=self.device)
        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):
            if dc.is_deferred_compute():
                raise TypeError('Indexing with a numpy array is not supported in HybridBlock.')
            if key.dtype == _np.bool_:
                key = array(key, dtype='bool', device=self.device)

        # Handle single boolean index of matching dimensionality and size first for higher speed
        # If the boolean array is mixed with other idices, it is instead expanded into (multiple)
        # integer array indices and will be handled by advanced indexing.
        # Come before the check self.dim == 0 as it also handle the 0-dim case.
        if isinstance(key, ndarray) and key.dtype == _np.bool_:
            return self._get_np_boolean_indexing(key, ndim, shape)

        all = __builtins__['all']  # `def all` below shadows the all builtin
        if ndim == 0 and 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 py_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):
            # Equivalent to isinstance(key, integer_types) case in numpy/_symbol.py
            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):
            # Unlike numpy/_symbol.py, calls MXNDArraySlice64 writable memory
            # sharing if key.step not in [None, 1]. Equivalent otherwise to
            # isinstance(key, py_slice) case in _symbol.py otherwise.
            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:
                start = [None] if key.start is None else key.start
                stop = [None] if key.stop is None else key.stop
                return _npi.slice(self, start, stop, key.step)
            else:
                raise ValueError("slice step cannot be zero")
        elif isinstance(key, tuple) and \
           all((isinstance(arr, NDArray) and _np.issubdtype(arr.dtype, _np.integer) and \
                arr.ndim > 0) for arr in key):
            # Equivalent case in numpy/_symbol.py
            return _npi.advanced_indexing_multiple(self, _mx_nd_np.stack(key))
        elif isinstance(key, tuple) and dc.is_deferred_compute():
            # Equivalent to isinstance(key, tuple) case in numpy/_symbol.py
            # Only enabled in deferred compute mode, as this codepath prevents
            # memory sharing which may be desired in non-deferred compute
            # imperative mode.
            begin = []
            end = []
            step = []
            new_shape = ()
            assert len(key)  # len(key) == 0 is handled a above
            unsupported = False
            for index in key:
                if isinstance(index, py_slice):
                    if index.step is not None and index.step == 0:
                        raise ValueError("slice step cannot be zero")
                    begin.append(index.start)
                    end.append(index.stop)
                    step.append(index.step)
                    new_shape += (-2,)
                elif isinstance(index, integer_types):
                    if index >= 0:
                        begin.append(index)
                        end.append(index+1)
                        step.append(1)
                    else:
                        begin.append(index)
                        end.append(index - 1)
                        step.append(-1)
                    new_shape += (-3,)
                else:
                    unsupported = True
                    break
            if not unsupported:
                new_shape += (-4,)
                sliced = _npi.slice(self, begin, end, step)
                return _mx_nd_np.reshape(sliced, new_shape)

        # Special handling for cases only supported in imperative mode
        if dc.is_deferred_compute():
            raise TypeError('The type of indexing used is not supported in HybridBlock.')
        # For 0-d boolean indices: A new axis is added,
        # but at the same time no axis is "used". So if we have True,
        # we add a new axis (a bit like with np.newaxis). If it is
        # False, we add a new axis, but this axis has 0 entries.
        # prepend is defined to handle this case.
        # prepend = _NDARRAY_NO_ZERO_DIM_BOOL_ARRAY/-1 means there is no 0-d boolean scalar
        # prepend = _NDARRAY_ZERO_DIM_BOOL_ARRAY_FALSE/0 means an zero dim must be expanded
        # prepend = _NDARRAY_ZERO_DIM_BOOL_ARRAY_TRUE/1 means a new axis must be prepended
        key, prepend = indexing_key_expand_implicit_axes(key, self.shape)
        indexing_dispatch_code = get_indexing_dispatch_code(key)
        if indexing_dispatch_code == _NDARRAY_EMPTY_TUPLE_INDEXING:
            # won't be affected by zero-dim boolean indices
            return self._get_np_empty_tuple_indexing(key)
        elif indexing_dispatch_code == _NDARRAY_BASIC_INDEXING:
            if prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_FALSE:
                return empty((0,) + self._get_np_basic_indexing(key).shape,
                             dtype=self.dtype, device=self.device)
            if prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_TRUE:
                key = (_np.newaxis,) + key
            return self._get_np_basic_indexing(key)
        elif indexing_dispatch_code == _NDARRAY_ADVANCED_INDEXING:
            if prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_FALSE:
                return empty((0,) + self._get_np_adanced_indexing(key).shape,
                             dtype=self.dtype, device=self.device)
            if prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_TRUE:
                key = (_np.newaxis,) + key
            return self._get_np_advanced_indexing(key)
        else:
            raise RuntimeError

    # pylint: disable=inconsistent-return-statements
    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.]])

        For imformation related to boolean indexing, please refer to
        https://docs.scipy.org/doc/numpy-1.17.0/reference/arrays.indexing.html.
        """
        if isinstance(value, NDArray) and not isinstance(value, ndarray):
            raise TypeError('Cannot assign mx.nd.NDArray to mxnet.numpy.ndarray')
        if isinstance(key, bool): # otherwise will be treated as 0 and 1
            key = array(key, dtype=_np.bool)

        # Handle single boolean assign of matching dimensionality and size first for higher speed
        # If the boolean array is mixed with other idices, it is instead expanded into (multiple)
        # integer array indices and will be handled by advanced assign.
        # Come before the check self.dim == 0 as it also handle the 0-dim case.
        if isinstance(key, ndarray) and key.dtype == _np.bool:
            return self._set_np_boolean_indexing(key, value)

        # 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:
            # For 0-d boolean indices: A new axis is added,
            # but at the same time no axis is "used". So if we have True,
            # we add a new axis (a bit like with np.newaxis). If it is
            # False, we add a new axis, but this axis has 0 entries.
            # prepend is defined to handle this case.
            # prepend == _NDARRAY_NO_ZERO_DIM_BOOL_ARRAY/-1 means there is no 0-d boolean scalar
            # prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_FALSE/0 means an zero dim must be expanded
            # prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_TRUE/1 means a new axis must be expanded
            # prepend actually has no influence on __setitem__
            key, prepend = indexing_key_expand_implicit_axes(key, self.shape)
            if prepend == _NDARRAY_ZERO_DIM_BOOL_ARRAY_FALSE:
                return # no action is needed
            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_EMPTY_TUPLE_INDEXING:
                pass # no action needed
            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 device 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, device=self.device, dtype=self.dtype)
        elif isinstance(value, self.__class__):
            value_nd = value.to_device(self.device)
            if value_nd.dtype != self.dtype:
                value_nd = value_nd.astype(self.dtype)
        else:
            try:
                value_nd = array(value, device=self.device, 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

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

    @wrap_mxnp_np_ufunc
    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)

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

    def __invert__(self):
        """x.__invert__() <=> ~x"""
        return invert(self)

    @wrap_mxnp_np_ufunc
    def __and__(self, other):
        """x.__and__(y) <=> x & y"""
        return bitwise_and(self, other)

    @wrap_mxnp_np_ufunc
    def __rand__(self, other):
        """x.__rand__(y) <=> y & x"""
        return bitwise_and(other, self)

    @wrap_mxnp_np_ufunc
    def __or__(self, other):
        """x.__or__(y) <=> x | y"""
        return bitwise_or(self, other)

    @wrap_mxnp_np_ufunc
    def __ror__(self, other):
        """x.__ror__(y) <=> y | x"""
        return bitwise_or(other, self)

    @wrap_mxnp_np_ufunc
    def __xor__(self, other):
        """x.__xor__(y) <=> x ^ y"""
        return bitwise_xor(self, other)

    @wrap_mxnp_np_ufunc
    def __rxor__(self, other):
        """x.__rxor__(y) <=> y ^ x"""
        return bitwise_xor(other, self)

    @wrap_mxnp_np_ufunc
    def __lshift__(self, other):
        """x.__lshift__(y) <=> x << y"""
        return bitwise_left_shift(self, other)

    @wrap_mxnp_np_ufunc
    def __rshift__(self, other):
        """x.__rshift__(y) <=> x >> y"""
        return bitwise_right_shift(self, other)

    @wrap_mxnp_np_ufunc
    def __iand__(self, other):
        """x.__iand__(y) <=> x &= y"""
        return bitwise_and(self, other, out=self)

    @wrap_mxnp_np_ufunc
    def __ior__(self, other):
        r"""x.__ior__(y) <=> x \|= y"""
        return bitwise_or(self, other, out=self)

    @wrap_mxnp_np_ufunc
    def __ixor__(self, other):
        """x.__ixor__(y) <=> x ^= y"""
        return bitwise_xor(self, other, out=self)

    @wrap_mxnp_np_ufunc
    def __ilshift__(self, other):
        """x.__ilshift__(y) <=> x <<= y"""
        return bitwise_left_shift(self, other, out=self)

    @wrap_mxnp_np_ufunc
    def __irshift__(self, other):
        """x.__irshift__(y) <=> x >>= y"""
        return bitwise_right_shift(self, other, out=self)

    @wrap_mxnp_np_ufunc
    def __rlshift__(self, other):
        """x.__rlshift__(y) <=> y << x"""
        return bitwise_left_shift(other, self)

    @wrap_mxnp_np_ufunc
    def __rrshift__(self, other):
        """x.__rrshift__(y) <=> y >> x"""
        return bitwise_right_shift(other, self)

    def __round__(self, n=0):
        """x.__round__(n)"""
        return round(self, decimals=n)

    def __abs__(self):
        """x.__abs__()"""
        return absolute(self)

    def __ceil__(self):
        """x.__ceil__()"""
        return ceil(self)

    def __floor__(self):
        """x.__floor__()"""
        return floor(self)

    def __trunc__(self):
        """x.__trunc__()"""
        return trunc(self)

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

    @wrap_mxnp_np_ufunc
    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)

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

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

    @wrap_mxnp_np_ufunc
    def __floordiv__(self, other):
        """x.__floordiv__(y) <=> x // y"""
        return floor_divide(self, other)

    @wrap_mxnp_np_ufunc
    def __ifloordiv__(self, other):
        """x.__ifloordiv__(y) <=> x //= y"""
        if not self.writable:
            raise ValueError('trying to divide from a readonly ndarray')
        return floor_divide(self, other, out=self)

    @wrap_mxnp_np_ufunc
    def __rfloordiv__(self, other):
        """x.__rfloordiv__(y) <=> y // x"""
        return floor_divide(other, self)

    def __neg__(self):
        """x.__neg__() <=> -x"""
        return negative(self)

    def __pos__(self):
        """x.__pos__() <=> +x"""
        return positive(self)

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

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

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

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

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

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

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

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

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

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

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

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

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

    @wrap_mxnp_np_ufunc
    def __ipow__(self, other):
        """x.__ipow__(y) <=> x **= y"""
        return power(self, other, out=self)

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

    def __hash__(self):
        raise NotImplementedError

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

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

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

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

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

    @wrap_mxnp_np_ufunc
    def __matmul__(self, other):
        """x.__matmul__(y) <=> x @ y"""
        return matmul(self, other)

    @wrap_mxnp_np_ufunc
    def __rmatmul__(self, other):
        """x.__rmatmul__(y) <=> y @ x"""
        return matmul(other, self)

    @wrap_mxnp_np_ufunc
    def __imatmul__(self, other):
        """x.__imatmul__(y) <=> x @= y"""
        return matmul(self, other, out=self)

    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 __index__(self):
        if self.ndim == 0 and _np.issubdtype(self.dtype, _np.integer):
            return self.item()
        raise TypeError('only integer scalar arrays can be converted to a scalar index')

    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."""
        if self.ndim != 2:
            warnings.warn('x.T requires x to have 2 dimensions. '
                          'Use x.mT to transpose stacks of matrices and '
                          'permute_dims() to permute dimensions.')
        return self.transpose()
    # pylint: enable= invalid-name, undefined-variable

    @property
    # pylint: disable= invalid-name, undefined-variable
    def mT(self):
        """Same as self.transpose(). This always returns a copy of self."""
        if self.ndim < 2:
            raise ValueError("x must be at least 2-dimensional for matrix_transpose")
        return _mx_nd_np.swapaxes(self, -1, -2)
    # pylint: enable= invalid-name, undefined-variable

    def all(self, axis=None, out=None, keepdims=False):
        return _mx_nd_np.all(self, axis=axis, out=out, keepdims=keepdims)

    def any(self, axis=None, out=None, keepdims=False):
        return _mx_nd_np.any(self, axis=axis, out=out, keepdims=keepdims)

    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 be appended if it's inconsistent with current dtype.
        The device 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
        dtype('float32')
        >>> npx.set_np_float64()
        >>> a
        array([[0.5488135 , 0.5928446 , 0.71518934],
               [0.84426576, 0.60276335, 0.8579456 ]], dtype=float32)
        >>> npx.set_np_float64(default_float64=False)
        >>> a
        array([[0.5488135 , 0.5928446 , 0.71518934],
               [0.84426576, 0.60276335, 0.8579456 ]])
        >>> 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
        dtype('float64')
        >>> c = a.copyto(npx.gpu(0))
        >>> c
        array([[0.5488135 , 0.5928446 , 0.71518934],
               [0.84426576, 0.60276335, 0.8579456 ]], device=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, device=gpu(0))
        >>> print(d)
        [[0.54881352 0.59284461 0.71518934]
         [0.84426576 0.60276335 0.85794562]] @gpu(0)

        """
        if self._alive:
            array_str = self.asnumpy().__repr__()
            dtype = self.dtype
            default_dtype = _np.float64 if is_np_default_dtype() else _np.float32
            if 'dtype=' in array_str:
                if dtype == default_dtype:
                    array_str = array_str[:array_str.rindex(',')] + ')'
            elif dtype not in (default_dtype, _np.bool_):
                array_str = array_str[:-1] + ', dtype={})'.format(dtype)

            device = self.device
            if device.device_type == 'cpu':
                return array_str
            return array_str[:-1] + ', device={})'.format(str(device))
        else:
            return '<FREED {}>'.format(self.__class__.__name__)

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

    def __format__(self, fmt):
        """Return value.__format__(format_spec). Overwrite to include 0-d array"""
        if self.ndim == 0:
            return self.item().__format__(fmt)
        elif len(fmt) == 0:
            return self.__str__().__format__(fmt)
        else:
            raise TypeError("Cannot format mxnet.numpy.ndarray with format_spec")

    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_nd_np.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)))

    def drop_grad(self):
        """Free the memory of the marked ndarray."""
        check_call(_LIB.MXAutogradDropGrads(
            1, ctypes.pointer(self.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, order='K', casting='unsafe', subok=True, copy=True):  # pylint: disable=arguments-differ,unused-argument, too-many-arguments
        """
        Copy of the array, cast to a specified type.

        Parameters
        ----------
        dtype : str or dtype
            Typecode or data-type to which the array is cast.
        order : {'C', 'F', 'A', 'K'}, optional
            Controls the memory layout order of the result.
            'C' means C order, 'F' means Fortran order, 'A'
            means 'F' order if all the arrays are Fortran contiguous,
            'C' order otherwise, and 'K' means as close to the
            order the array elements appear in memory as possible.
            Default is 'K'.
        casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
            Controls what kind of data casting may occur. Defaults to 'unsafe'
            for backwards compatibility.

              * 'no' means the data types should not be cast at all.
              * 'equiv' means only byte-order changes are allowed.
              * 'safe' means only casts which can preserve values are allowed.
              * 'same_kind' means only safe casts or casts within a kind,
                like float64 to float32, are allowed.
              * 'unsafe' means any data conversions may be done.
        subok : bool, optional
            If True, then sub-classes will be passed-through (default), otherwise
            the returned array will be forced to be a base-class array.
        copy : bool, optional
            Default `True`. By default, astype always returns a newly
            allocated ndarray on the same device. 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`.

        Notes
        -----
        This function differs from the official `ndarray`'s ``astype`` function in the following
        aspects:
            * `order` only supports 'C' and 'K'.
            * `casting` only supports 'unsafe'.
            * `subok` only supports ``True``.
        """
        if order is not None and order != 'K' and order != 'C':
            raise ValueError('order must be either \'K\' or \'C\'')
        if casting != 'unsafe':
            raise ValueError('casting must be equal to \'unsafe\'')
        if not subok:
            raise ValueError('subok must be equal to True')
        if dtype is None:
            dtype = _np.float32
        if not copy and _np.dtype(dtype) == self.dtype:
            return self

        return _npi.cast(self, dtype=dtype)

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

        Parameters
        ----------
        other : ndarray or Device
            The destination array or device.

        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), device=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, Device):
            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, keepdims=False):  # 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, keepdims)

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

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

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


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

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

        Parameters
        ----------
        device : Device
            The target device.

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

    @property
    def device(self):
        """Hardware device the array data resides on.

        Examples
        --------
        >>> x = np.array([1, 2, 3, 4])
        >>> x.device
        cpu(0)
        >>> type(x.device)
        <class 'mxnet.device.Device'>
        >>> y = np.zeros((2, 3), npx.gpu(0))
        >>> y.device
        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 Device(Device.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 device.

        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.device)

    def dot(self, b, out=None):
        """Dot product of two arrays.
        Refer to ``numpy.dot`` for full documentation."""
        return 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(list(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_nd_np.reshape(self, newshape=args[0], order=order)
        else:
            return _mx_nd_np.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 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, axis=-1, descending=False, stable=True):  # pylint: disable=arguments-differ
        """Convenience fluent method for :py:func:`sort`.

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

    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, axis=-1, descending=False, stable=True):  # pylint: disable=arguments-differ
        """Convenience fluent method for :py:func:`argsort`.

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

    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, keepdims=False):  # 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, keepdims)

    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, reps):  # pylint: disable=arguments-differ
        """Construct an array by repeating A the number of times given by reps.
        Refer to `mxnet.numpy.tile` for full documentation."""
        return tile(self, reps=reps)

    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 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 diagonal(self, offset=0, axis1=0, axis2=1):  # pylint: disable=arguments-differ
        """Return the diagonal with the given offset.

        If array has more than two dimensions, then the axes specified by axis1 and
        axis2 are used to determine the 2-D sub-array whose diagonal is returned.

        Refer to `mxnet.numpy.diagonal` for full documents.
        """
        return diagonal(self, offset=offset, axis1=axis1, axis2=axis2)

    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 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

    @wrap_data_api_statical_func
    def std(self, axis=None, dtype=None, out=None, correction=0, keepdims=False):
        """Returns the standard deviation of the array elements along given axis."""
        return std(self, axis=axis, dtype=dtype, correction=correction, keepdims=keepdims, out=out)

    @wrap_data_api_statical_func
    def var(self, axis=None, dtype=None, out=None, correction=0, keepdims=False):
        """Returns the variance of the array elements, along given axis."""
        return var(self, axis=axis, dtype=dtype, out=out, correction=correction, 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_nd_np.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_nd_np.max(self, axis=axis, out=out, keepdims=keepdims)

    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_nd_np.min(self, axis=axis, out=out, keepdims=keepdims)

    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, decimals=0, out=None, **kwargs): # pylint: disable=arguments-differ
        """Convenience fluent method for :py:func:`round`.

        The arguments are the same as for :py:func:`round`, with
        this array as data.
        """
        return round(self, decimals=decimals, out=out, **kwargs)

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

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

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

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

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

    def broadcast_to(self, shape):  # pylint: disable=redefined-outer-name
        return _mx_nd_np.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, device=self.device, 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):
        """Tuple of array dimensions.

        Examples
        --------
        >>> x = mx.np.array([1, 2, 3, 4])
        >>> x.shape
        (4L,)
        >>> y = mx.np.zeros((2, 3, 4))
        >>> y.shape
        (2L, 3L, 4L)
        >>> z = mx.np.array(3)
        >>> z.shape
        ()
        """
        num_dim = mx_int()
        if _int64_enabled():
            pdata = ctypes.POINTER(mx_int64)()
            check_call(_LIB.MXNDArrayGetShape64(
                self.handle, ctypes.byref(num_dim), ctypes.byref(pdata)))
        else:
            pdata = ctypes.POINTER(mx_int)()
            check_call(_LIB.MXNDArrayGetShape(
                self.handle, ctypes.byref(num_dim), ctypes.byref(pdata)))
        if num_dim.value == -1:
            return None
        else:
            return tuple(pdata[:num_dim.value])  # pylint: disable=invalid-slice-index

    @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')
@wrap_ctx_to_device_func
def empty(shape, dtype=None, order='C', device=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`.
        Note that this behavior is different from NumPy's `empty` function where `float64`
        is the default value, here you can set your default dtype as 'float32' or 'float64'
        because `float32` is considered as the default data type in deep learning.
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
    order : {'C'}, optional, default: 'C'
        How to store multi-dimensional data in memory, currently only row-major
        (C-style) is supported.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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 device is None:
        device = current_device()
    if dtype is None or dtype is float:
        dtype = _np.float64 if is_np_default_dtype() else _np.float32
    if isinstance(shape, int):
        shape = (shape,)
    return ndarray(handle=_new_alloc_handle(shape, device, False, dtype))


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def array(object, dtype=None, device=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.
        The default dtype is ``object.dtype`` if `object` is an `ndarray`, `float32` otherwise.
        Default dtype can be set to be consistent with offical numpy by `npx.set_np(dtype=True)`.

        * When npx.is_np_default_dtype() returns False, default dtype is float32;
        * When npx.is_np_default_dtype() returns True, default dtype is float64.

    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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]])

    >>> np.array([1, 2, 3]).dtype
    dtype('float32')

    >>> npx.set_np(dtype=True)
    >>> np.array([1, 2, 3]).dtype
    dtype('float64')
    """
    if device is None:
        device = current_device()
    if isinstance(object, _np.ndarray):
        if is_np_default_dtype():
            dtype = object.dtype if dtype is None else dtype
        else:
            dtype = _np.float32 if dtype is None or object.dtype is _np.float64 else dtype
    if isinstance(object, 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:
            default_dtype = _np.float64 if is_np_default_dtype() else _np.float32
            dtype = object.dtype if hasattr(object, "dtype") else default_dtype
        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, device=device)
    if len(object.shape) == 0:
        ret[()] = object
    else:
        ret[:] = object
    return ret
# pylint: enable=redefined-outer-name


@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')
@wrap_ctx_to_device_func
def zeros(shape, dtype=None, order='C', device=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,
        When npx.is_np_default_dtype() returns False, default dtype is float32,
        When npx.is_np_default_dtype() returns True, default dtype is float64.
        Note that this behavior is different from NumPy's `zeros` function where `float64`
        is the default value, here we can set 'float32' or 'float64' as your default dtype,
        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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

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

    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, device)


@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def ones(shape, dtype=None, order='C', device=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 depend on your current default dtype.
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
        Note that this behavior is different from NumPy's `ones` function where
        `float64` is the default value.
    order : {'C'}, optional, default: 'C'
        How to store multi-dimensional data in memory, currently only row-major
        (C-style) is supported.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

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

    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, device)


@set_module('mxnet.numpy')
def broadcast_to(array, shape):  # pylint: disable=redefined-outer-name
    """
    Broadcast an array to a new shape.

    Parameters
    ----------
    array : ndarray or scalar
        The array to broadcast.
    shape : tuple
        The shape of the desired array.

    Returns
    -------
    broadcast : array
        A readonly view on the original array with the given shape. It is
        typically not contiguous. Furthermore, more than one element of a
        broadcasted array may refer to a single memory location.

    Raises
    ------
    MXNetError
        If the array is not compatible with the new shape according to NumPy's
        broadcasting rules.
    """
    return _mx_nd_np.broadcast_to(array, shape)


# pylint: disable=too-many-arguments, redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def full(shape, fill_value, dtype=None, order='C', device=None, out=None):
    r"""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 or ndarray
        Fill value.
    dtype : data-type, optional
        If dtype is None, the output array data type must be inferred from fill_value.
        If it’s an int, the output array dtype must be the default integer dtype;
        If it’s a float, then the output array dtype must be the default floating-point data type;
        If it’s a bool then the output array must have boolean dtype. Default: None.
    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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.
    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.
        If `fill_value` is an ndarray, out will have the same device as `fill_value`
        regardless of the provided `device`.

    .. note::
       This function differs from the original numpy.full in the following way(s):

       * Has an additional `device` 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, device=mx.cpu(0))
    array([[2, 2],
           [2, 2]], dtype=int32)
    """
    return _mx_nd_np.full(shape, fill_value, order=order, device=device, dtype=dtype, out=out)
# pylint: enable=too-many-arguments, redefined-outer-name


# pylint: disable=redefined-outer-name, too-many-arguments
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def empty_like(prototype, dtype=None, device=None, order='C', subok=False, shape=None): # pylint: disable=W0621
    """
    Return a new array with the same shape and type as a given array.

    Parameters
    ----------
    prototype : ndarray
        The shape and data-type of `prototype` define these same attributes
        of the returned array.
    dtype : data-type, optional
        Overrides the data type of the result.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.
    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.
    subok : {False}, optional
        If True, then the newly created array will use the sub-class
        type of 'a', otherwise it will be a base-class array. Defaults
        to False.
        (Only support False at this moment)
    shape : int or sequence of ints, optional.
        Overrides the shape of the result. If order='K' and the number of
        dimensions is unchanged, will try to keep order, otherwise,
        order='C' is implied.
        (Not supported at this moment)

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

    See Also
    --------
    ones_like : Return an array of ones with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full_like : Return a new array with shape of input filled with value.
    empty : Return a new uninitialized array.

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

    Examples
    --------
    >>> a = np.array([[1,2,3], [4,5,6]])
    >>> np.empty_like(a)
    array([[-5764607523034234880, -2305834244544065442,           4563075075], # uninitialized
           [          4567052944, -5764607523034234880,      844424930131968]])
    >>> a = np.array([[1., 2., 3.],[4.,5.,6.]])
    >>> np.empty_like(a)
    array([[4.9e-324, 9.9e-324, 1.5e-323], # uninitialized
           [2.0e-323, 2.5e-323, 3.0e-323]])
    """
    ret = _mx_nd_np.empty_like(prototype, dtype=dtype, order=order, subok=subok, shape=shape)
    if device is not None:
        ret.to_device(device)
    return ret
# pylint: enable=redefined-outer-name


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def all(a, axis=None, out=None, keepdims=False):
    """
    Test whether all array elements along a given axis evaluate to True.

    Parameters
    ----------
    a : ndarray
        Input array or object that can be converted to an array.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a logical AND reduction is performed.
        The default (axis = None) is to perform a logical AND over
        all the dimensions of the input array.
    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.
    out : ndarray, optional
        Alternate output array in which to place the result. It must have
        the same shape as the expected output and its type is preserved

    Returns
    --------
    all : ndarray, bool
        A new boolean or array is returned unless out is specified,
        in which case a reference to out is returned.

    Examples:
    ---------
    >>> np.all([[True,False],[True,True]])
    False

    >>> np.all([[True,False],[True,True]], axis=0)
    array([ True, False])

    >>> np.all([-1, 4, 5])
    True

    >>> np.all([1.0, np.nan])
    True

    >>> o=np.array(False)
    >>> z=np.all([-1, 4, 5], out=o)
    >>> id(z), id(o), z
    (28293632, 28293632, array(True)) # may vary
    """
    return _mx_nd_np.all(a, axis=axis, out=out, keepdims=keepdims)


@set_module('mxnet.numpy')
def any(a, axis=None, out=None, keepdims=False):
    """
    Test whether any array element along a given axis evaluates to True.
    Returns single boolean unless axis is not None

    Parameters
    ----------
    a : ndarray
        Input array or object that can be converted to an array.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a logical AND reduction is performed.
        The default (axis = None) is to perform a logical AND over
        all the dimensions of the input array.
    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.
    out : ndarray, optional
        Alternate output array in which to place the result. It must have
        the same shape as the expected output and its type is preserved

    Returns
    --------
    any : bool or ndarray
        A new boolean or ndarray is returned unless out is specified,
        in which case a reference to out is returned.

    Examples:
    ---------
    >>> np.any([[True, False], [True, True]])
    True

    >>> np.any([[True, False], [False, False]], axis=0)
    array([ True, False])

    >>> np.any([-1, 0, 5])
    True

    >>> np.any(np.nan)
    True

    >>> o=np.array(False)
    >>> z=np.any([-1, 4, 5], out=o)
    >>> z, o
    (array(True), array(True))
    >>> # Check now that z is a reference to o
    >>> z is o
    True
    >>> id(z), id(o) # identity of z and o              # doctest: +SKIP
    (191614240, 191614240)
    """
    return _mx_nd_np.any(a, axis=axis, out=out, keepdims=keepdims)


@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def identity(n, dtype=None, device=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.
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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, device)
# pylint: enable=redefined-outer-name


# 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`.

    .. note::

       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.

    .. note::

       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
    -------
    The sum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

    .. note::

       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):
    r"""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.

    .. note::
       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.

    .. note::
       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.

    .. note::
       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 or
         float64 type, which depends on your current default dtype:

         * When ``npx.is_np_default_dtype()`` returns False, default dtype is float32.
         * When ``npx.is_np_default_dtype()`` returns True, default dtype is float64.

    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.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.

    .. note::

       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 or
         float64 type, which depends on your current default dtype.
         When npx.is_np_default_dtype() returns False, default dtype is float32;
         When npx.is_np_default_dtype() returns True, default dtype is float64.

    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 floor_divide(x1, x2, out=None):
    """Return the largest integer smaller or equal to the division of the inputs.

    It is equivalent to the Python // operator and pairs with the Python % (remainder),
    function so that a = a % b + b * (a // b) up to roundoff.

    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.

    .. note::

       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 the more
         precise type

    Examples
    --------
    >>> np.floor_divide(7,3)
    2
    >>> np.floor_divide([1., 2., 3., 4.], 2.5)
    array([ 0.,  0.,  1.,  1.])
    """
    return _mx_nd_np.floor_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 fmod(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.fmod(np.arange(7), 5)
    array([0., 1., 2., 3., 4., 0., 1.])
    """
    return _mx_nd_np.fmod(x1, x2, out=out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def matmul(a, b, out=None, **kwargs):
    r"""Matrix product of two arrays.

    Parameters
    ----------
    a, b : ndarray
        Input arrays, scalars not allowed.
    out : ndarray, optional
        A location into which the result is stored.
        If provided, it must have a shape that matches the signature (n,k),(k,m)->(n,m).
        If not provided or None, a freshly-allocated array is returned.

    Returns
    -------
    y : ndarray
        The matrix product of the inputs.
        This is a scalar only when both x1, x2 are 1-d vectors.

    Raises
    ------
    MXNetError
        If the last dimension of a is not the same size as the second-to-last dimension of b.
        If a scalar value is passed in.

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

    .. note::

       The behavior depends on the arguments in the following way.

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

       matmul differs from dot in two important ways:

       * Multiplication by scalars is not allowed, use multiply instead.
       * Stacks of matrices are broadcast together as if the matrices were elements,
         respecting the signature ``(n,k),(k,m)->(n,m)``:

       >>> a = np.ones([9, 5, 7, 4])
       >>> c = np.ones([9, 5, 4, 3])
       >>> np.dot(a, c).shape
       (9, 5, 7, 9, 5, 3)
       >>> np.matmul(a, c).shape
       (9, 5, 7, 3)
       >>> # n is 7, k is 4, m is 3

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

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

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

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

    Broadcasting is conventional for stacks of arrays

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

    Scalar multiplication raises an error.

    >>> np.matmul([1, 2], 3)
    Traceback (most recent call last):
    ...
    mxnet.base.MXNetError: ... : Multiplication by scalars is not allowed.

    """
    return _mx_nd_np.matmul(a, b, 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)

pow = power
pow.__doc_ = """
    First array elements raised to powers from second array, element-wise.
    
    Notes 
    ----- 
    `pow` is an alias for `power`. It is a standard API in 
    https://data-apis.org/array-api/latest/API_specification/elementwise_functions.html#pow-x1-x2 
    instead of an official NumPy operator. 
    
    >>> np.pow is np.power 
    True 

    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.pow(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.pow(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.pow(x1, x2)
    array([[ 0.,  1.,  8., 27., 16.,  5.],
           [ 0.,  1.,  8., 27., 16.,  5.]])
    """

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

    Parameters
    ----------
    x1, x2 : ndarrays or scalar values
        The arrays for computing greatest common divisor. 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 greatest common divisor of the absolute value of the inputs
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    gcd : The lowest common multiple

    Examples
    --------
    >>> np.gcd(12, 20)
    4
    >>> np.gcd(np.arange(6, dtype=int), 20)
    array([20,  1,  2,  1,  4,  5], dtype=int64)
    """
    return _mx_nd_np.gcd(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.

    .. note::
       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 fabs(x, out=None, **kwargs):
    r"""
    Calculate the absolute value element-wise.

    This function returns the absolute values (positive magnitude) of the
    data in `x`. Complex values are not handled, use `absolute` to find the
    absolute values of complex data.

    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
    --------
    >>> np.fabs(-1)
    1.0
    >>> np.fabs(np.array([-1.2, 1.2]))s
    array([ 1.2,  1.2])
    """
    return _mx_nd_np.fabs(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

    .. note::
       `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 `device` as the input `ndarray`.
       This function differs from the original `numpy.arcsin
       <https://numpy.org/doc/stable/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)

asin = arcsin
asin.__doc__ = """
    Inverse sine, element-wise.
    
    >>>np.asin is np.asin
    True

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

    .. note::
       `asin` is a alias for `arcsin`. It is a standard API in
       https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.asin.html
       instead of an official NumPy operator.
       
       `asin` 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, *asin* 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://numpy.org/doc/stable/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/
    """


@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)

acos = arccos
acos.__doc__ = """
    Trigonometric inverse cosine, element-wise.
    The inverse of cos so that, if y = cos(x), then x = acos(y).
    
    >>>np.acos is np.arccos
    True

    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
    ----------
    `acos` is a alias for `arccos`. It is a standard API in
    https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.acos.html
    instead of an official NumPy operator.
    
    acos 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, acos 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.acos([1, -1])
    array([ 0.        ,  3.14159265])
    """

@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)

atan = arctan
atan.__doc__ = """
    Trigonometric inverse tangent, element-wise.
    The inverse of tan, so that if ``y = tan(x)`` then ``x = atan(y)``.
    
    >>>np.atan is np.arctan
    True
    
    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]`` (``atan(+/-inf)`` returns ``+/-pi/2``).
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `atan` is a alias for `arctan`. It is a standard API in
    https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.atan.html
    instead of an official NumPy operator.
    
    `atan` 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, `atan` 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.atan(x)
    array([0.       , 0.7853982])
    >>> np.pi/4
    0.7853981633974483
    """


@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.

    .. note::
       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.

    .. note::
       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.

    .. note::
       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.

    .. note::
       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.

    .. note::

       "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.

    .. note::
       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.

    .. note::
       "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])

    .. 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 `device` 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.])

    .. note::
       The output `ndarray` has the same `device` 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 positive(x, out=None, **kwargs):
    r"""
    Computes the numerical positive of each element `x_i` (i.e.,`y_i = +x_i`)
    of the input array x .

    Parameters
    ----------
    x : ndarray or scalar
        Input array.

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

    Notes
    -----
    Equivalent to `x.copy()`, but only defined for types that support arithmetic.

    Examples
    --------
    >>> x1 = np.array(([1., -1.]))
    >>> np.positive(x1)
    array([ 1., -1.])
    >>> +x1
    array([ 1., -1.])
    """
    return _mx_nd_np.positive(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 bitwise_invert(x, out=None, **kwargs):
    r"""
    Compute bit-wise inversion, or bit-wise NOT, element-wise.
    Computes the bit-wise NOT of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``~``.

    Parameters
    ----------
    x : array_like
        Only integer and boolean types are handled.
    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
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    bitwise_and, bitwise_or, bitwise_xor
    logical_not
    binary_repr :
        Return the binary representation of the input number as a string.

    Examples
    --------
    We've seen that 13 is represented by ``00001101``.
    The invert or bit-wise NOT of 13 is then:

    >>> x = np.bitwise_invert(np.array(13, dtype=np.uint8))
    >>> x
    242
    >>> np.binary_repr(x, width=8)
    '11110010'

    Notes
    -----
    `bitwise_not` is an alias for `invert`:

    >>> np.bitwise_not is np.invert
    True
    """
    return _mx_nd_np.bitwise_not(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def invert(x, out=None, **kwargs):
    r"""
    Compute bit-wise inversion, or bit-wise NOT, element-wise.
    Computes the bit-wise NOT of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``~``.

    Parameters
    ----------
    x : array_like
        Only integer and boolean types are handled.
    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
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    bitwise_and, bitwise_or, bitwise_xor
    logical_not
    binary_repr :
        Return the binary representation of the input number as a string.

    Examples
    --------
    We've seen that 13 is represented by ``00001101``.
    The invert or bit-wise NOT of 13 is then:

    >>> x = np.invert(np.array(13, dtype=np.uint8))
    >>> x
    242
    >>> np.binary_repr(x, width=8)
    '11110010'

    Notes
    -----
    `bitwise_not` is an alias for `invert`:

    >>> np.bitwise_not is np.invert
    True
    """
    return _mx_nd_np.bitwise_not(x, out=out, **kwargs)

@set_module('mxnet.numpy')
@wrap_np_unary_func
def bitwise_not(x, out=None, **kwargs):
    r"""
    Compute bit-wise inversion, or bit-wise NOT, element-wise.
    Computes the bit-wise NOT of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``~``.

    Parameters
    ----------
    x : array_like
        Only integer and boolean types are handled.
    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
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    bitwise_and, bitwise_or, bitwise_xor
    logical_not
    binary_repr :
        Return the binary representation of the input number as a string.

    Examples
    --------
    We've seen that 13 is represented by ``00001101``.
    The invert or bit-wise NOT of 13 is then:

    >>> x = np.invert(np.array(13, dtype=np.uint8))
    >>> x
    242
    >>> np.binary_repr(x, width=8)
    '11110010'

    Notes
    -----
    `bitwise_not` is an alias for `invert`:

    >>> np.bitwise_not is np.invert
    True
    """
    return _mx_nd_np.bitwise_not(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.

    .. note::
       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.

    .. note::
       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.

    .. note::
       `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)

asinh = arcsinh
asinh.__doc__ = """
    Inverse hyperbolic cosine, element-wise.
    
    >>>np.asinh is np.arcsinh
    True

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

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

    .. note::
       `asinh` is a alias for `arcsinh`. It is a standard API in
       https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.asinh.html
       instead of an official NumPy operator.
       
       `asinh` is a multivalued function: for each `x` there are infinitely
       many numbers `z` such that `sinh(z) = x`.

       For real-valued input data types, `asinh` 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.asinh(a)
    array([1.8309381, 2.2924316])

    >>> np.asinh(1)
    0.0
    """


@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.

    .. note::
       `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)

acosh = arccosh
acosh.__doc__ = """
    Inverse hyperbolic cosine, element-wise.
    
    >>>np.acosh is np.arccosh
    True

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

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

    .. note::
       `acosh` is a alias for `arccosh`. It is a standard API in
       https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.acosh.html
       instead of an official NumPy operator.
       
       `acosh` is a multivalued function: for each `x` there are infinitely
       many numbers `z` such that `cosh(z) = x`.

       For real-valued input data types, `acosh` 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.acosh(a)
    array([1.8309381, 2.2924316])

    >>> np.acosh(1)
    0.0
    """

@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.

    .. note::
       `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)

atanh = arctanh
atanh.__doc__ = """
    Inverse hyperbolic tangent, element-wise.

    >>>np.atanh is np.arctanh
    True

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

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

    .. note::
       `atanh` is a alias for `arctanh`. It is a standard API in
       https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.atanh.html
       instead of an official NumPy operator.
    
       `atanh` is a multivalued function: for each `x` there are infinitely
       many numbers `z` such that `tanh(z) = x`.

       For real-valued input data types, `atanh` 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.atanh(a)
    array([0., -0.54930615])

    >>> np.atanh(1)
    0.0
    """


@set_module('mxnet.numpy')
@wrap_sort_functions
def argsort(a, axis=-1, descending=False, stable=True):
    """
    Returns the indices that sort an array `x` along a specified axis.

    Notes
    -----
    `argsort` is a standard API in
    https://data-apis.org/array-api/latest/API_specification/generated/signatures.sorting_functions.argsort.html
    instead of an official NumPy operator.

    Parameters
    ----------
    a : ndarray
        Array to sort.
    axis : int or None, optional
        Axis along which to sort.  The default is -1 (the last axis). If None,
        the flattened array is used.
    descending : bool, optional
        sort order. If `True`, the returned indices sort x in descending order (by value).
        If `False`, the returned indices sort x in ascending order (by value).Default: False.
    stable : bool, optional
        sort stability. If `True`, the returned indices must maintain the relative order
        of x values which compare as equal. If `False`, the returned indices may or may not
        maintain the relative order of x values which compare as equal. Default: True.

    Returns
    -------
    index_array : ndarray, int
        Array of indices that sort `a` along the specified `axis`.
        If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`.
        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
        always yields the sorted `a`, irrespective of dimensionality.

    Notes
    -----
    This operator does not support different sorting algorithms.

    Examples
    --------
    One dimensional array:

    >>> x = np.array([3, 1, 2])
    >>> np.argsort(x)
    array([1, 2, 0])

    Two-dimensional array:

    >>> x = np.array([[0, 3], [2, 2]])
    >>> x
    array([[0, 3],
           [2, 2]])
    >>> ind = np.argsort(x, axis=0)  # sorts along first axis (down)
    >>> ind
    array([[0, 1],
           [1, 0]])
    >>> np.take_along_axis(x, ind, axis=0)  # same as np.sort(x, axis=0)
    array([[0, 2],
           [2, 3]])
    >>> ind = np.argsort(x, axis=1)  # sorts along last axis (across)
    >>> ind
    array([[0, 1],
           [0, 1]])
    >>> np.take_along_axis(x, ind, axis=1)  # same as np.sort(x, axis=1)
    array([[0, 3],
           [2, 2]])

    Indices of the sorted elements of a N-dimensional array:

    >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
    >>> ind
    (array([0, 1, 1, 0]), array([0, 0, 1, 1]))
    >>> x[ind]  # same as np.sort(x, axis=None)
    array([0, 2, 2, 3])
    """
    if stable:
        warnings.warn("Currently, MXNet only support quicksort in backend, which is not stable")
    return _mx_nd_np.argsort(a, axis=axis, descending=descending)


@set_module('mxnet.numpy')
@wrap_sort_functions
def sort(a, axis=-1, descending=False, stable=True):
    """
    Return a sorted copy of an array.

    Notes
    -----
    `sort` is a standard API in
    https://data-apis.org/array-api/latest/API_specification/generated/signatures.sorting_functions.sort.html
    instead of an official NumPy operator.

    Parameters
    ----------
    a : ndarray
        Array to sort.
    axis : int or None, optional
        Axis along which to sort.  The default is -1 (the last axis). If None,
        the flattened array is used.
    descending : bool, optional
        sort order. If `True`, the returned indices sort x in descending order (by value).
        If `False`, the returned indices sort x in ascending order (by value).Default: False.
    stable : bool, optional
        sort stability. If `True`, the returned indices must maintain the relative order
        of x values which compare as equal. If `False`, the returned indices may or may not
        maintain the relative order of x values which compare as equal. Default: True.

    Returns
    -------
    sorted_array : ndarray
        Array of the same type and shape as `a`.

    Notes
    -----
    This operator does not support different sorting algorithms.

    Examples
    --------
    >>> a = np.array([[1,4],[3,1]])
    >>> np.sort(a)                # sort along the last axis
    array([[1, 4],
           [1, 3]])
    >>> np.sort(a, axis=None)     # sort the flattened array
    array([1, 1, 3, 4])
    >>> np.sort(a, axis=0)        # sort along the first axis
    array([[1, 1],
           [3, 4]])
    """
    return _mx_nd_np.sort(a, axis=axis, descending=descending)


@set_module('mxnet.numpy')
def tensordot(a, b, axes=2):
    r"""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

    .. note::

       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)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def eye(N, M=None, k=0, dtype=None, device=None, **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.
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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, device=device, **kwargs)
# pylint: enable=redefined-outer-name


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0, device=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 : int or float
        The starting value of the sequence.
    stop : int or float
        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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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()

    .. note::

       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 `device` argument to specify the device, e.g. the i-th
         GPU.
    """
    return _mx_nd_np.linspace(start, stop, num, endpoint, retstep, dtype, axis, device)
# pylint: enable=redefined-outer-name


# pylint: disable=too-many-arguments, redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0, device=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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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, device=npx.gpu(0))
    array([ 100.     ,  215.44347,  464.15887, 1000.     ], device=gpu(0))
    """
    return _mx_nd_np.logspace(start, stop, num, endpoint, base, dtype, axis, device=device)
# pylint: enable=too-many-arguments, redefined-outer-name


@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 _mx_nd_np.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.tile(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 trace(a, offset=0, axis1=0, axis2=1, out=None):
    """
    Return the sum along diagonals of the array.
    If `a` is 2-D, the sum along its diagonal with the given offset
    is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.
    If `a` has more than two dimensions, then the axes specified by axis1 and
    axis2 are used to determine the 2-D sub-arrays whose traces are returned.
    The shape of the resulting array is the same as that of `a` with `axis1`
    and `axis2` removed.

    Parameters
    ----------
    a : ndarray
        Input array, from which the diagonals are taken.
    offset : int, optional
        Offset of the diagonal from the main diagonal. Can be both positive
        and negative. Defaults to 0.
    axis1, axis2 : int, optional
        Axes to be used as the first and second axis of the 2-D sub-arrays
        from which the diagonals should be taken. Defaults are the first two
        axes of `a`.
    out : ndarray, optional
        Array into which the output is placed. It must be of the right shape
        and right type to hold the output.

    Returns
    -------
    sum_along_diagonals : ndarray
        If `a` is 2-D, the sum along the diagonal is returned.  If `a` has
        larger dimensions, then an array of sums along diagonals is returned.

    Examples
    --------
    >>> a = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
    >>> np.trace(a)
    array(3.)
    >>> a = np.arange(8).reshape((2, 2, 2))
    >>> np.trace(a)
    array([6., 8.])
    >>> a = np.arange(24).reshape((2, 2, 2, 3))
    >>> np.trace(a).shape
    (2, 3)
    """
    return _mx_nd_np.trace(a, offset, axis1, axis2, out)


@set_module('mxnet.numpy')
def transpose(a, axes=None):
    """
    Permute the dimensions of an array.

    Parameters
    ----------
    a : ndarray
        Input array.
    axes : list of ints, optional
        By default, reverse the dimensions,
        otherwise permute the axes according to the values given.

    Returns
    -------
    p : ndarray
        a with its axes permuted.

    .. note::

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

       * only ndarray is accepted as valid input, python iterables are not supported
       * the operator always returns an `ndarray` that does not share the memory with the input

    Examples
    --------
    >>> x = np.arange(4).reshape((2,2))
    >>> x
    array([[0., 1.],
           [2., 3.]])
    >>> np.transpose(x)
    array([[0., 2.],
           [1., 3.]])
    >>> x = np.ones((1, 2, 3))
    >>> np.transpose(x, (1, 0, 2)).shape
    (2, 1, 3)
    """
    return _mx_nd_np.transpose(a, axes)


@set_module('mxnet.numpy')
def permute_dims(a, axes=None):
    """
    Permute the dimensions of an array.

    Parameters
    ----------
    a : ndarray
        Input array.
    axes : list of ints, optional
        By default, reverse the dimensions,
        otherwise permute the axes according to the values given.

    Returns
    -------
    p : ndarray
        a with its axes permuted.

    Note
    --------
    `permute_dims` is a alias for `transpose`. It is a standard API in
    https://data-apis.org/array-api/latest/API_specification/manipulation_functions.html#permute-dims-x-axes
    instead of an official NumPy operator.

    Examples
    --------
    >>> x = np.arange(4).reshape((2,2))
    >>> x
    array([[0., 1.],
           [2., 3.]])
    >>> np.permute_dims(x)
    array([[0., 2.],
           [1., 3.]])
    >>> x = np.ones((1, 2, 3))
    >>> np.permute_dims(x, (1, 0, 2)).shape
    (2, 1, 3)
    """
    return _mx_nd_np.transpose(a, axes)


@set_module('mxnet.numpy')
def repeat(a, repeats, axis=None):
    """
    Repeat elements of an array.

    Parameters
    ----------
    a : array_like
        Input array.
    repeats : int
        The number of repetitions for each element.
    axis : int, optional
        The axis along which to repeat values.  By default, use the
        flattened input array, and return a flat output array.

    Returns
    -------
    repeated_array : ndarray
        Output array which has the same shape as `a`, except along
        the given axis.

    See Also
    --------
    tile : Tile an array.

    Examples
    --------
    >>> np.repeat(3, 4)
    array([3, 3, 3, 3])
    >>> x = np.array([[1,2],[3,4]])
    >>> np.repeat(x, 2)
    array([1, 1, 2, 2, 3, 3, 4, 4])
    >>> np.repeat(x, 3, axis=1)
    array([[1, 1, 1, 2, 2, 2],
           [3, 3, 3, 4, 4, 4]])
    >>> np.repeat(x, [1, 2], axis=0)
    array([[1, 2],
           [3, 4],
           [3, 4]])
    """
    return _mx_nd_np.repeat(a, repeats, axis)


@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')
@wrap_ctx_to_device_func
def tri(N, M=None, k=0, dtype=None, device=None):    # pylint: disable=redefined-outer-name
    r"""
    An array with ones at and below the given diagonal and zeros elsewhere.
    Parameters
    ----------
    N : int
        Number of rows in the array.
    M : int, optional
        Number of columns in the array.
        By default, `M` is taken equal to `N`.
    k : int, optional
        The sub-diagonal at and below which the array is filled.
        `k` = 0 is the main diagonal, while `k` < 0 is below it,
        and `k` > 0 is above.  The default is 0.
    dtype : dtype, optional
        Data type of the returned array.  The default is float.
    Returns
    -------
    tri : ndarray of shape (N, M)
        Array with its lower triangle filled with ones and zero elsewhere;
        in other words ``T[i,j] == 1`` for ``i <= j + k``, 0 otherwise.
    Examples
    --------
    >>> np.tri(3, 5, 2, dtype=int)
    array([[1, 1, 1, 0, 0],
           [1, 1, 1, 1, 0],
           [1, 1, 1, 1, 1]])
    >>> np.tri(3, 5, -1)
    array([[0.,  0.,  0.,  0.,  0.],
           [1.,  0.,  0.,  0.,  0.],
           [1.,  1.,  0.,  0.,  0.]])
    """
    return _mx_nd_np.tri(N, M, k, dtype, device)


@set_module('mxnet.numpy')
def triu_indices(n, k=0, m=None, device=None):    # pylint: disable=redefined-outer-name
    r"""
    Return the indices for the upper-triangle of an (n, m) array.
    Parameters
    ----------
    n : int
        The size of the arrays for which the returned indices will
        be valid.
    k : int, optional
        Diagonal offset (see `triu` for details).
    m : int, optional
        .. versionadded:: 1.9.0
        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.
    Returns
    -------
    inds : tuple, shape(2) of ndarrays, shape(`n`)
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.  Can be used
        to slice a ndarray of shape(`n`, `n`).
    See also
    --------
    tril_indices : similar function, for lower-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    triu, tril
    Examples
    --------
    Compute two different sets of indices to access 4x4 arrays, one for the
    upper triangular part starting at the main diagonal, and one starting two
    diagonals further right:
    >>> iu1 = np.triu_indices(4)
    >>> iu2 = np.triu_indices(4, 2)
    Here is how they can be used with a sample array:
    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])
    Both for indexing:
    >>> a[iu1]
    array([ 0,  1,  2, ..., 10, 11, 15])
    And for assigning values:
    >>> a[iu1] = -1
    >>> a
    array([[-1, -1, -1, -1],
           [ 4, -1, -1, -1],
           [ 8,  9, -1, -1],
           [12, 13, 14, -1]])
    These cover only a small part of the whole array (two diagonals right
    of the main one):
    >>> a[iu2] = -10
    >>> a
    array([[ -1,  -1, -10, -10],
           [  4,  -1,  -1, -10],
           [  8,   9,  -1,  -1],
           [ 12,  13,  14,  -1]])
        """
    return _mx_nd_np.triu_indices(n, k, m, device)


@set_module('mxnet.numpy')
def triu_indices_from(arr, k=0):
    """
    Return the indices for the upper-triangle of arr.
    See `triu_indices` for full details.
    Parameters
    ----------
    arr : ndarray, shape(N, N)
        The indices will be valid for square arrays.
    k : int, optional
        Diagonal offset (see `triu` for details).
    Returns
    -------
    triu_indices_from : tuple, shape(2) of ndarray, shape(N)
        Indices for the upper-triangle of `arr`.
    See Also
    --------
    triu_indices, triu
    """
    return _mx_nd_np.triu_indices_from(arr, k)


@set_module('mxnet.numpy')
def tril_indices(n, k=0, m=None):
    """
    Return the indices for the lower-triangle of an (n, m) array.

    Parameters
    ----------
    n : int
        The row dimension of the arrays for which the returned
        indices will be valid.
    k : int, optional
        Diagonal offset (see `tril` for details).
    m : int, optional
        .. versionadded:: 1.9.0

        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.

    Returns
    -------
    inds : tuple of arrays
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.

    See also
    --------
    triu_indices : similar function, for upper-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    tril, triu

    Examples
    --------
    Compute two different sets of indices to access 4x4 arrays, one for the
    lower triangular part starting at the main diagonal, and one starting two
    diagonals further right:

    >>> il1 = np.tril_indices(4)
    >>> il2 = np.tril_indices(4, 2)

    Here is how they can be used with a sample array:

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

    Both for indexing:

    >>> a[il1]
    array([ 0,  4,  5,  8,  9, 10, 12, 13, 14, 15])

    And for assigning values:

    >>> a[il1] = -1
    >>> a
    array([[-1,  1,  2,  3],
           [-1, -1,  6,  7],
           [-1, -1, -1, 11],
           [-1, -1, -1, -1]])

    These cover almost the whole array (two diagonals right of the main one):

    >>> a[il2] = -10
    >>> a
    array([[-10, -10, -10,   3],
           [-10, -10, -10, -10],
           [-10, -10, -10, -10],
           [-10, -10, -10, -10]])

    """
    if m is None:
        m = n
    return _mx_nd_np.tril_indices(n, k, m)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def triu(m, k=0):
    r"""
    Upper triangle of an array.

    Return a copy of a matrix with the elements below the `k`-th diagonal
    zeroed.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

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


@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def arange(start, stop=None, step=1, dtype=None, device=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.
        Default dtype can be set to be consistent with offical numpy by `npx.set_np(dtype=True)`.
        * When npx.is_np_default_dtype() returns False, default dtype is float32;
        * When npx.is_np_default_dtype() returns True, default dtype is int64.
    device : device context, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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.])

    >>> np.arange(3).dtype
    dtype('float32')
    >>> npx.set_np(dtype=True)
    >>> np.arange(3).dtype
    dtype('int64')
    """
    return _mx_nd_np.arange(start, stop, step, dtype, device)
# pylint: enable=redefined-outer-name


@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 array_split(ary, indices_or_sections, axis=0):
    """Split an array into multiple sub-arrays.

    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 array of length l that should be split into n sections, it returns
    l % n sub-arrays of size l//n + 1 and the rest of size l//n.

    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.

    Parameters
    ----------
    ary : ndarray
        Array to be divided into sub-arrays.
    indices_or_sections : int or 1-D Python tuple, list or set.
        Param used to determine the number and size of the subarray.
    axis : int, optional
        The axis along which to split, default is 0.

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

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

    >>> np.array_split(x, [3, 5, 6, 8])
    [array([0., 1., 2.]), array([3., 4.]), array([5.]), array([6., 7.]), array([])]

    >>> x = np.arange(8.0)
    >>> np.array_split(x, 3)
    [array([0.,  1.,  2.]), array([3.,  4.,  5.]), array([6.,  7.])]

    >>> x = np.arange(7.0)
    >>> np.array_split(x, 3)
    [array([0.,  1.,  2.]), array([3.,  4.]), array([5.,  6.])]
    """
    return _mx_nd_np.array_split(ary, indices_or_sections, axis=axis)


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

    .. note::
       This function differs from the original `numpy.vsplit
       <https://docs.scipy.org/doc/numpy/reference/generated/numpy.vsplit.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 _mx_nd_np.vsplit(ary, indices_or_sections)


@set_module('mxnet.numpy')
def dsplit(ary, indices_or_sections):
    r"""
    Split array into multiple sub-arrays along the 3rd axis (depth).
    Please refer to the `split` documentation.  `dsplit` is equivalent
    to `split` with ``axis=2``, the array is always split along the third
    axis provided the array dimension is greater than or equal to 3.

    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 2.  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 2 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 2, 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.

    .. note::
       This function differs from the original `numpy.dsplit
       <https://docs.scipy.org/doc/numpy/reference/generated/numpy.dsplit.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 2,
       an error will be thrown.

    Examples
    --------
    >>> x = np.arange(16.0).reshape(2, 2, 4)
    >>> x
    array([[[ 0.,   1.,   2.,   3.],
            [ 4.,   5.,   6.,   7.]],
           [[ 8.,   9.,  10.,  11.],
            [12.,  13.,  14.,  15.]]])
    >>> np.dsplit(x, 2)
    [array([[[ 0.,  1.],
            [ 4.,  5.]],
           [[ 8.,  9.],
            [12., 13.]]]), array([[[ 2.,  3.],
            [ 6.,  7.]],
           [[10., 11.],
            [14., 15.]]])]
    >>> np.dsplit(x, np.array([3, 6]))
    [array([[[ 0.,   1.,   2.],
            [ 4.,   5.,   6.]],
           [[ 8.,   9.,  10.],
            [12.,  13.,  14.]]]),
     array([[[ 3.],
            [ 7.]],
           [[11.],
            [15.]]]),
    array([], shape=(2, 2, 0), dtype=float64)]

    """
    return _mx_nd_np.dsplit(ary, indices_or_sections)

@set_module('mxnet.numpy')
def concat(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.

    Note
    --------
    `concate` is a alias for `concatante`. It is a standard API in
    https://data-apis.org/array-api/latest/API_specification/manipulation_functions.html#concat-arrays-axis-0
    instead of an official NumPy operator.

    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.concat((a, b), axis=0)
    array([[1., 2.],
           [3., 4.],
           [5., 6.]])

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

    >>> np.concat((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 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 row_stack(arrays):
    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.row_stack(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 hstack(arrays):
    """
    Stack arrays in sequence horizontally (column wise).
    This is equivalent to concatenation along the second axis,
    except for 1-D arrays where it concatenates along the first axis.
    Rebuilds arrays divided by hsplit.
    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 ndarrays
        The arrays must have the same shape along all but the second axis, except 1-D arrays which can be any length.

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

    Examples
    --------
    >>> from mxnet import np,npx
    >>> a = np.array((1,2,3))
    >>> b = np.array((2,3,4))
    >>> np.hstack((a,b))
    array([1., 2., 3., 2., 3., 4.])
    >>> a = np.array([[1],[2],[3]])
    >>> b = np.array([[2],[3],[4]])
    >>> np.hstack((a,b))
    array([[1., 2.],
           [2., 3.],
           [3., 4.]])
    """
    return _mx_nd_np.hstack(arrays)


@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 fmax(x1, x2, out=None, **kwargs):
    """
    Returns element-wise maximum of the input arrays with broadcasting. (Ignores NaNs)

    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.fmax(np.array([2, 3, 4]), np.array([1, 5, 2]))
    array([2., 5., 4.])

    >>> np.fmax(np.eye(2), np.array([0.5, 2])) # broadcasting
    array([[1. , 2. ],
           [0.5, 2. ]])
    """
    return _mx_nd_np.fmax(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')
@wrap_np_binary_func
def fmin(x1, x2, out=None, **kwargs):
    """
    Returns element-wise minimum of the input arrays with broadcasting. (Ignores NaNs)

    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 fmin of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

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

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


@set_module('mxnet.numpy')
def max(a, axis=None, out=None, keepdims=False):
    """
    Return the maximum of an array or maximum along an axis.

    Parameters
    ----------
    a : ndarray
        Input data.
    axis : int, optional
        Axis along which to operate.  By default, flattened input is used.
    out : ndarray, optional
        Alternative output array in which to place the result.  Must
        be of the same shape and buffer length as the expected output.
        See `doc.ufuncs` (Section "Output arguments") for more details.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

    Returns
    -------
    max : ndarray
        Maximum of `a`. If `axis` is None, the result is an array of dimension 1.
        If `axis` is given, the result is an array of dimension
        ``a.ndim - 1``.

    See Also
    --------
    min :
        The minimum value of an array along a given axis, ignoring any nan.
    maximum :
        Element-wise maximum of two arrays, ignoring any nan.
    argmax :
        Return the indices of the maximum values.

    Notes
    -----
    NaN in the orginal `numpy` is denoted as nan and will be ignored.

    Don't use `max` for element-wise comparison of 2 arrays; when
    ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
    ``max(a, axis=0)``.

    Examples
    --------
    >>> a = np.arange(4).reshape((2,2))
    >>> a
    array([[0., 1.],
        [2., 3.]])
    >>> np.max(a)            # Maximum of the flattened array
    array(3.)
    >>> np.max(a, axis=0)    # Maxima along the first axis
    array([2., 3.])
    >>> np.max(a, axis=1)    # Maxima along the second axis
    array([1., 3.])

    >>> b = np.arange(5, dtype=np.float32)
    >>> b[2] = np.nan
    >>> np.max(b)
    array(4.)
    """
    return _mx_nd_np.max(a, axis=axis, out=out, keepdims=keepdims)


@set_module('mxnet.numpy')
def min(a, axis=None, out=None, keepdims=False):
    """
    Return the minimum of an array or minimum along an axis.

    Parameters
    ----------
    a : ndarray
        Input data.
    axis : int, optional
        Axis along which to operate.  By default, flattened input is used.
    out : ndarray, optional
        Alternative output array in which to place the result.  Must
        be of the same shape and buffer length as the expected output.
        See `doc.ufuncs` (Section "Output arguments") for more details.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

    Returns
    -------
    min : ndarray
        Minimum of `a`. If `axis` is None, the result is an array of dimension 1.
        If `axis` is given, the result is an array of dimension
        ``a.ndim - 1``.

    See Also
    --------
    max :
        The maximum value of an array along a given axis, ignoring any nan.
    minimum :
        Element-wise minimum of two arrays, ignoring any nan.

    Notes
    -----
    NaN in the orginal `numpy` is denoted as nan and will be ignored.

    Don't use `min` for element-wise comparison of 2 arrays; when
    ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
    ``min(a, axis=0)``.

    Examples
    --------
    >>> a = np.arange(4).reshape((2,2))
    >>> a
    array([[0., 1.],
        [2., 3.]])
    >>> np.min(a)           # Minimum of the flattened array
    array(0.)
    >>> np.min(a, axis=0)   # Minima along the first axis
    array([0., 1.])
    >>> np.min(a, axis=1)   # Minima along the second axis
    array([0., 2.])
    >>> b = np.arange(5, dtype=np.float32)
    >>> b[2] = np.nan
    >>> np.min(b)
    array(0.) # nan will be ignored
    """
    return _mx_nd_np.min(a, axis=axis, out=out, keepdims=keepdims)


@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.])
    >>> a
    array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])
    >>> np.clip(a, 3, 6, out=a)
    array([3., 3., 3., 3., 4., 5., 6., 6., 6., 6.])
    """
    from numbers import Number
    if isinstance(a, Number):
        # In case input is a scalar, the computation would fall back to native numpy.
        # The value returned would be a python scalar.
        return _np.clip(a, a_min, a_max, out=None)
    return _mx_nd_np.clip(a, a_min, a_max, out=out)


@set_module('mxnet.numpy')
def argmax(a, axis=None, out=None, keepdims=False):
    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.
    keepdims : bool
        If True, the reduced axes (dimensions) must be included in the result as
        singleton dimensions, and, accordingly, the result must be compatible with
        the input array. Otherwise, if False, the reduced axes (dimensions) must
        not be included in the result. Default: False .

    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.

    .. note::
       ``keepdims`` param is part of request in data-api-standard
       <https://data-apis.org/array-api/latest/API_specification/generated/signatures.searching_functions.argmax.html>`_,
       which is not the parameter in official NumPy

       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://numpy.org/doc/stable/reference/generated/numpy.argmax.html>`_ in
       the following aspects:

       * 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.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, keepdims)


@set_module('mxnet.numpy')
def argmin(a, axis=None, out=None, keepdims=False):
    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.
    keepdims : bool
        If True, the reduced axes (dimensions) must be included in the result as
        singleton dimensions, and, accordingly, the result must be compatible with
        the input array. Otherwise, if False, the reduced axes (dimensions) must
        not be included in the result. Default: False .

    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.

    .. note::
       ``keepdims`` param is part of request in data-api-standard
       <https://data-apis.org/array-api/latest/API_specification/generated/signatures.searching_functions.argmin.html>`_,
       which is not the parameter in official NumPy

       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://numpy.org/doc/stable/reference/generated/numpy.argmin.html>`_ in
       the following aspects:

       * 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.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, keepdims)


@set_module('mxnet.numpy')
def amax(a, axis=None, out=None, keepdims=False):
    """
    Return the maximum of an array or maximum along an axis.

    Parameters
    ----------
    a : ndarray
        Input data.
    axis : int, optional
        Axis along which to operate.  By default, flattened input is used.
    out : ndarray, optional
        Alternative output array in which to place the result.  Must
        be of the same shape and buffer length as the expected output.
        See `doc.ufuncs` (Section "Output arguments") for more details.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

    Returns
    -------
    max : ndarray
        Maximum of `a`. If `axis` is None, the result is an array of dimension 1.
        If `axis` is given, the result is an array of dimension
        ``a.ndim - 1``.

    See Also
    --------
    min :
        The minimum value of an array along a given axis, ignoring any nan.
    maximum :
        Element-wise maximum of two arrays, ignoring any nan.
    argmax :
        Return the indices of the maximum values.

    Notes
    -----
    NaN in the orginal `numpy` is denoted as nan and will be ignored.

    Don't use `max` for element-wise comparison of 2 arrays; when
    ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
    ``max(a, axis=0)``.

    Examples
    --------
    >>> a = np.arange(4).reshape((2,2))
    >>> a
    array([[0., 1.],
        [2., 3.]])
    >>> np.max(a)            # Maximum of the flattened array
    array(3.)
    >>> np.max(a, axis=0)    # Maxima along the first axis
    array([2., 3.])
    >>> np.max(a, axis=1)    # Maxima along the second axis
    array([1., 3.])

    >>> b = np.arange(5, dtype=np.float32)
    >>> b[2] = np.nan
    >>> np.max(b)
    array(4.)
    """
    return _mx_nd_np.amax(a, axis=axis, out=out, keepdims=keepdims)


@set_module('mxnet.numpy')
def amin(a, axis=None, out=None, keepdims=False):
    """
    Return the minimum of an array or minimum along an axis.

    Parameters
    ----------
    a : ndarray
        Input data.
    axis : int, optional
        Axis along which to operate.  By default, flattened input is used.
    out : ndarray, optional
        Alternative output array in which to place the result.  Must
        be of the same shape and buffer length as the expected output.
        See `doc.ufuncs` (Section "Output arguments") for more details.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

    Returns
    -------
    min : ndarray
        Minimum of `a`. If `axis` is None, the result is an array of dimension 1.
        If `axis` is given, the result is an array of dimension
        ``a.ndim - 1``.

    See Also
    --------
    max :
        The maximum value of an array along a given axis, ignoring any nan.
    minimum :
        Element-wise minimum of two arrays, ignoring any nan.

    Notes
    -----
    NaN in the orginal `numpy` is denoted as nan and will be ignored.

    Don't use `min` for element-wise comparison of 2 arrays; when
    ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
    ``min(a, axis=0)``.

    Examples
    --------
    >>> a = np.arange(4).reshape((2,2))
    >>> a
    array([[0., 1.],
        [2., 3.]])
    >>> np.min(a)           # Minimum of the flattened array
    array(0.)
    >>> np.min(a, axis=0)   # Minima along the first axis
    array([0., 1.])
    >>> np.min(a, axis=1)   # Minima along the second axis
    array([0., 2.])
    >>> b = np.arange(5, dtype=np.float32)
    >>> b[2] = np.nan
    >>> np.min(b)
    array(0.) # nan will be ignored
    """
    return _mx_nd_np.amin(a, axis=axis, out=out, keepdims=keepdims)


@set_module('mxnet.numpy')
def average(a, axis=None, weights=None, returned=False, out=None):
    """
    Compute the weighted average along the specified axis.

    Parameters
    --------
    a : ndarray
        Array containing data to be averaged.
    axis : None or int or tuple of ints, optional
        Axis or axes along which to average a.
        The default, axis=None, will average over
        all of the elements of the input array.
        If axis is negative it counts from the last to the first axis.
        New in version 1.7.0.
        If axis is a tuple of ints, averaging is
        performed on all of the axes specified in the tuple
        instead of a single axis or all the axes as before.
    weights : ndarray, optional
        An array of weights associated with the values in a, must be the same dtype with a.
        Each value in a contributes to the average according to its associated weight.
        The weights array can either be 1-D (in which case its length must be
        the size of a along the given axis) or of the same shape as a.
        If weights=None, then all data in a are assumed to have a weight equal to one.
        The 1-D calculation is: avg = sum(a * weights) / sum(weights)
        The only constraint on weights is that sum(weights) must not be 0.
    returned : bool, optional
        Default is False.
        If True, the tuple (average, sum_of_weights) is returned,
        otherwise only the average is returned.
        If weights=None, sum_of_weights is equivalent to
        the number of elements over which the average is taken.
    out : ndarray, optional
        If provided, the calculation is done into this array.

    Returns
    --------
    retval, [sum_of_weights] : ndarray
        Return the average along the specified axis.
        When returned is True, return a tuple with the average as the first element
        and the sum of the weights as the second element. sum_of_weights is of the same type as retval.
        If a is integral, the result dtype will be current default dtype,
        When npx.is_np_default_dtype() returns False, default dtype is float32,
        When npx.is_np_default_dtype() returns True, default dtype is float64;
        otherwise it will be the same as dtype of a.

    Raises
    --------
        MXNetError
        * When all weights along axis sum to zero.
        * When the length of 1D weights is not the same as the shape of a along axis.
        * When given 1D weights, the axis is not specified or is not int.
        * When the shape of weights and a differ, but weights are not 1D.

    See also
    --------
        mean

    .. note::
       This function differs from the original `numpy.average`
       <https://numpy.org/devdocs/reference/generated/numpy.average.html>`_ in
       the following way(s):

       * Does not guarantee the same behavior with numpy when given float16 dtype and overflow happens
       * Does not support complex dtype
       * The dtypes of a and weights must be the same
       * Integral a results in float32 or float64 returned dtype:

         * When npx.is_np_default_dtype() returns False, default dtype is float32,
         * When npx.is_np_default_dtype() returns True, default dtype is float64;

    Examples
    --------
    >>> data = np.arange(1, 5)
    >>> data
    array([1., 2., 3., 4.])
    >>> np.average(data)
    array(2.5)
    >>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1))
    array(4.)
    >>> data = np.arange(6).reshape((3,2))
    >>> data
    array([[0., 1.],
           [2., 3.],
           [4., 5.]])
    >>> weights = np.array([0.25, 0.75])
    array([0.25, 0.75])
    >>> np.average(data, axis=1, weights=weights)
    array([0.75, 2.75, 4.75])
    """
    return _mx_nd_np.average(a, axis=axis, weights=weights, returned=returned, out=out)


# pylint: disable=redefined-outer-name
@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 of your current default dtype,
        When npx.is_np_default_dtype() returns False, default dtype is float32,
        When npx.is_np_default_dtype() returns True, default dtype is float64;
        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.

    .. note::

       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 or float64, which depends on your current default dtype

    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, dtype=float64)
    """
    return _mx_nd_np.mean(a, axis=axis, dtype=dtype, keepdims=keepdims, out=out)
# pylint: enable=redefined-outer-name


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_data_api_statical_func
def std(a, axis=None, dtype=None, out=None, correction=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.
    correction : int, optional
        Means Delta Degrees of Freedom.  The divisor used in calculations
        is ``N - correction``, where ``N`` represents the number of elements.
        By default `correction` 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 _mx_nd_np.std(a, axis=axis, dtype=dtype, ddof=correction, keepdims=keepdims, out=out)
# pylint: enable=redefined-outer-name


@set_module('mxnet.numpy')
def delete(arr, obj, axis=None):
    """
    Return a new array with sub-arrays along an axis deleted. For a one
    dimensional array, this returns those entries not returned by
    `arr[obj]`.

    Parameters
    ----------
    arr : ndarray
      Input array.
    obj : slice, int or ndarray of ints
      Indicate indices of sub-arrays to remove along the specified axis.
    axis : int, optional
      The axis along which to delete the subarray defined by `obj`.
      If `axis` is None, `obj` is applied to the flattened array.

    Returns
    -------
    out : ndarray
        A copy of `arr` with the elements specified by `obj` removed. Note
        that `delete` does not occur in-place. If `axis` is None, `out` is
        a flattened array.

    Examples
    --------
    >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
    >>> arr
    array([[ 1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.],
           [ 9., 10., 11., 12.]])

    >>> np.delete(arr, 1, 0)
    array([[ 1.,  2.,  3.,  4.],
           [ 9., 10., 11., 12.]])

    >>> np.delete(arr, slice(None, None, 2), 1)
    array([[ 2.,  4.],
           [ 6.,  8.],
           [10., 12.]])

    >>> np.delete(arr, np.array([1,3,5]), None)
    array([ 1.,  3.,  5.,  7.,  8.,  9., 10., 11., 12.])
    >>> np.delete(arr, np.array([1,1,5]), None)
    array([ 1.,  3.,  4.,  5.,  7.,  8.,  9., 10., 11., 12.])
    """
    return _mx_nd_np.delete(arr, obj, axis=axis)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_data_api_statical_func
def var(a, axis=None, dtype=None, out=None, correction=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 of your current default dtype,
        When npx.is_np_default_dtype() returns False, default dtype is float32,
        When npx.is_np_default_dtype() returns True, default dtype is float64.
        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.
    correction : int, optional
        "Delta Degrees of Freedom": the divisor used in the calculation is
        ``N - correction``, where ``N`` represents the number of elements. By
        default `correction` 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 _mx_nd_np.var(a, axis=axis, dtype=dtype, ddof=correction, keepdims=keepdims, out=out)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def indices(dimensions, dtype=None, device=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 `int64`.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    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]], dtype=int64)
    >>> grid[1]        # column indices
    array([[0, 0, 0],
           [1, 1, 1]], dtype=int64)

    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, device=device)
# 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.

    .. note::
       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.

    .. note::
       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 unravel_index(indices, shape, order='C'): # pylint: disable=redefined-outer-name
    """
    Converts a flat index or array of flat indices into a tuple of coordinate arrays.

    Parameters
    ----------
    indices : array_like
            An integer array whose elements are indices into the flattened version of an array of dimensions shape.
            Before version 1.6.0, this function accepted just one index value.
    shape : tuple of ints
            The shape of the array to use for unraveling indices.
    order : Only row-major is supported currently.

    Returns
    -------
    unraveled_coords : ndarray
            Each row in the ndarray has the same shape as the indices array.
            Each column in the ndarray represents the unravelled index

    Examples:
    -------------
    >>> np.unravel_index([22, 41, 37], (7,6))
    [[3. 6. 6.]
      [4. 5. 1.]]
    >>> np.unravel_index(1621, (6,7,8,9))
    [3, 1, 4, 1]
    """
    return _mx_nd_np.unravel_index(indices, shape, order=order)


@set_module('mxnet.numpy')
def flatnonzero(a):
    r"""
    Return indices that are non-zero in the flattened version of a.

    This is equivalent to np.nonzero(np.ravel(a))[0].

    Parameters
    ----------
    a : array_like
        Input data.

    Returns
    -------
    res : ndarray
        Output array, containing the indices of the elements of `a.ravel()`
        that are non-zero.

    See Also
    --------
    nonzero : Return the indices of the non-zero elements of the input array.
    ravel : Return a 1-D array containing the elements of the input array.

    Examples
    --------
    >>> x = np.arange(-2, 3)
    >>> x
    array([-2, -1,  0,  1,  2])
    >>> np.flatnonzero(x)
    array([0, 1, 3, 4])

    Use the indices of the non-zero elements as an index array to extract
    these elements:

    >>> x.ravel()[np.flatnonzero(x)]
    array([-2, -1,  1,  2])
    """
    return _mx_nd_np.flatnonzero(a)


@set_module('mxnet.numpy')
def diag_indices_from(arr):
    """
    This returns a tuple of indices that can be used to access the main diagonal of an array
    a with a.ndim >= 2 dimensions and shape (n, n, ..., n). For a.ndim = 2 this is
    the usual diagonal, for a.ndim > 2 this is the set of indices to access
    a[i, i, ..., i] for i = [0..n-1].

    Parameters
    ----------
    arr : ndarray
        Input array for acessing the main diagonal. All dimensions
        should have equal length.

    Return:
    -------------
    diag: tuple of ndarray
        indices of the main diagonal.

    Examples:
    -------------
    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11],
        [12, 13, 14, 15]])
    >>> idx = np.diag_indices_from(a)
    >>> idx
    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))
    >>> a[idx] = 100
    >>> a
    array([[100,   1,   2,   3],
        [  4, 100,   6,   7],
        [  8,   9, 100,  11],
        [ 12,  13,  14, 100]])
    """
    return _mx_nd_np.diag_indices_from(arr)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def hanning(M, dtype=None, device=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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    Returns
    -------
    out : ndarray, shape(M,)
        The window, with the maximum value normalized to one (the value
        one appears only if `M` is odd).
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
        Note that you need select numpy.float32 or float64 in this operator.

    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, device=device)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def hamming(M, dtype=None, device=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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    Returns
    -------
    out : ndarray, shape(M,)
        The window, with the maximum value normalized to one (the value
        one appears only if `M` is odd).
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
        Note that you need select numpy.float32 or float64 in this operator.

    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, device=device)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def blackman(M, dtype=None, device=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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.

    Returns
    -------
    out : ndarray
        The window, with the maximum value normalized to one (the value one
        appears only if the number of samples is odd).
        When npx.is_np_default_dtype() returns False, default dtype is float32;
        When npx.is_np_default_dtype() returns True, default dtype is float64.
        Note that you need select numpy.float32 or float64 in this operator.

    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, device=device)


@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 flipud(m):
    r"""
    flipud(*args, **kwargs)

    Flip array in the up/down direction.

    Flip the entries in each column in the up/down direction.
    Rows are preserved, but appear in a different order than before.

    Parameters
    ----------
    m : array_like
        Input array.

    Returns
    -------
    out : array_like
        A view of `m` with the rows reversed.  Since a view is
        returned, this operation is :math:`\mathcal O(1)`.

    See Also
    --------
    fliplr : Flip array in the left/right direction.
    rot90 : Rotate array counterclockwise.

    Notes
    -----
    Equivalent to ``m[::-1,...]``.
    Does not require the array to be two-dimensional.

    Examples
    --------
    >>> A = np.diag(np.array([1.0, 2, 3]))
    >>> A
    array([[1.,  0.,  0.],
           [0.,  2.,  0.],
           [0.,  0.,  3.]])
    >>> np.flipud(A)
    array([[0.,  0.,  3.],
           [0.,  2.,  0.],
           [1.,  0.,  0.]])

    >>> A = np.random.randn(2,3,5)
    >>> np.all(np.flipud(A) == A[::-1,...])
    array(True)

    >>> np.flipud(np.array([1,2]))
    array([2., 1.])
    """
    return flip(m, 0)


@set_module('mxnet.numpy')
def fliplr(m):
    r"""
    fliplr(*args, **kwargs)

    Flip array in the left/right direction.

    Flip the entries in each row in the left/right direction.
    Columns are preserved, but appear in a different order than before.

    Parameters
    ----------
    m : array_like
        Input array, must be at least 2-D.

    Returns
    -------
    f : ndarray
        A view of `m` with the columns reversed.  Since a view
        is returned, this operation is :math:`\mathcal O(1)`.

    See Also
    --------
    flipud : Flip array in the up/down direction.
    rot90 : Rotate array counterclockwise.

    Notes
    -----
    Equivalent to m[:,::-1]. Requires the array to be at least 2-D.

    Examples
    --------
    >>> A = np.diag([1.,2.,3.])
    >>> A
    array([[1.,  0.,  0.],
        [0.,  2.,  0.],
        [0.,  0.,  3.]])
    >>> np.fliplr(A)
    array([[0.,  0.,  1.],
        [0.,  2.,  0.],
        [3.,  0.,  0.]])

    >>> A = np.random.randn(2,3,5)
    >>> np.all(np.fliplr(A) == A[:,::-1,...])
    array(True)
    """
    return flip(m, 1)


@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.

    .. note::
       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')
def round(x, decimals=0, out=None, **kwargs):
    r"""
    round(a, decimals=0, out=None)
    Round an array to the given number of decimals.

    See Also
    --------
    around : equivalent function; see for details.
    """
    return _mx_nd_np.round(x, decimals, out=out, **kwargs)


@set_module('mxnet.numpy')
def round_(x, decimals=0, out=None, **kwargs):
    r"""
    round_(a, decimals=0, out=None)
    Round an array to the given number of decimals.

    See Also
    --------
    around : equivalent function; see for details.
    """
    return _mx_nd_np.round_(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)

atan2 = arctan2
atan2.__doc__ = """
    Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly.

    The quadrant (i.e., branch) is chosen so that ``atan2(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`.
    
    >>>np.atan2 is np.arctan2
    True

    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::
       `atan2` is a alias for `arctan2`. It is a standard API in
       https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.atan2.html
       instead of an official NumPy operator.
       
       *atan2* is identical to the ``atan2`` function of the underlying
       C library.  The following special values are defined in the C
       standard: [1]_

       +========+========+==================+
       | `x1`   | `x2`   | `atan2(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.atan2(y, x) * 180 / np.pi
    array([-135.,  -45.,   45.,  135.])

    Note the order of the parameters. `atan2` 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.atan2(x, y)
    array([ 1.5707964, -1.5707964])
    """

@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.

    .. note::
       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_and(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_and(13, 17)
    1

    >>> np.bitwise_and(14, 13)
    12
    >>> np.bitwise_and(np.array([14,3], dtype='int32'), 13)
    array([26,  5], dtype=int32)

    >>> np.bitwise_and(np.array([11,7], dtype='int32'), np.array([4,25], dtype='int32'))
    array([0, 1], dtype=int32)
    >>> np.bitwise_and(np.array([2,5,255], dtype='int32'), np.array([3,14,16], dtype='int32'))
    array([ 2,  4, 16], dtype=int32)
    >>> np.bitwise_and(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
    array([False,  True])
    """
    return _mx_nd_np.bitwise_and(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], dtype=int32)

    >>> np.bitwise_xor(np.array([31,3], dtype='int32'), np.array([5,6], dtype='int32'))
    array([26,  5], dtype=int32)
    >>> 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 bitwise_or(x1, x2, out=None, **kwargs):
    r"""
    Compute the bit-wise OR 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_or(13, 17)
    29

    >>> np.bitwise_or(31, 5)
    31
    >>> np.bitwise_or(np.array([31,3], dtype=np.int32), 5)
    array([31,  7])

    >>> np.bitwise_or(np.array([31,3], dtype='int32'), np.array([5,6], dtype='int32'))
    array([31,  7])
    >>> np.bitwise_or(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
    array([ True, True])
    """
    return _mx_nd_np.bitwise_or(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')
@wrap_np_binary_func
def logaddexp(x1, x2, out=None, **kwargs):
    """
    Logarithm of the sum of exponentiations of the inputs.

    Calculates log(exp(x1) + exp(x2)). This function is useful in statistics where
    the calculated probabilities of events may be so small as to exceed the range of
    normal floating point numbers. In such cases the logarithm of the calculate
    probability is stored. This function allows adding probabilities stored
    in such a fashion.

    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
        Logarithm of exp(x1) + exp(x2). This is a scalar if both x1 and x2 are scalars.

    Examples
    --------
    >>> prob1 = np.log(1e-50)
    >>> prob2 = np.log(2.5e-50)
    >>> prob12 = np.logaddexp(prob1, prob2)
    >>> prob12
    -113.87649168120691
    >>> np.exp(prob12)
    3.5000000000000057e-50
    """
    return _mx_nd_np.logaddexp(x1, x2, out)


@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 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.

    .. note::

       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 cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None): # pylint: disable=too-many-arguments
    """
    Return the cross product of two (arrays of) vectors.

    The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular
    to both `a` and `b`.  If `a` and `b` are arrays of vectors, the vectors
    are defined by the last axis of `a` and `b` by default, and these axes
    can have dimensions 2 or 3.  Where the dimension of either `a` or `b` is
    2, the third component of the input vector is assumed to be zero and the
    cross product calculated accordingly.  In cases where both input vectors
    have dimension 2, the z-component of the cross product is returned.

    Parameters
    ----------
    a : ndarray
        Components of the first vector(s).
    b : ndarray
        Components of the second vector(s).
    axisa : int, optional
        Axis of `a` that defines the vector(s).  By default, the last axis.
    axisb : int, optional
        Axis of `b` that defines the vector(s).  By default, the last axis.
    axisc : int, optional
        Axis of `c` containing the cross product vector(s).  Ignored if
        both input vectors have dimension 2, as the return is scalar.
        By default, the last axis.
    axis : int, optional
        If defined, the axis of `a`, `b` and `c` that defines the vector(s)
        and cross product(s).  Overrides `axisa`, `axisb` and `axisc`.

    Returns
    -------
    c : ndarray
        Vector cross product(s).

    Raises
    ------
    ValueError
        When the dimension of the vector(s) in `a` and/or `b` does not
        equal 2 or 3.

    Notes
    -----
    Supports full broadcasting of the inputs.

    Examples
    --------
    Vector cross-product.

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

    One vector with dimension 2.

    >>> x = np.array([1., 2.])
    >>> y = np.array([4., 5., 6.])
    >>> np.cross(x, y)
    array([12., -6., -3.])

    Equivalently:

    >>> x = np.array([1., 2., 0.])
    >>> y = np.array([4., 5., 6.])
    >>> np.cross(x, y)
    array([12., -6., -3.])

    Both vectors with dimension 2.

    >>> x = np.array([1., 2.])
    >>> y = np.array([4., 5.])
    >>> np.cross(x, y)
    array(-3.)

    Multiple vector cross-products. Note that the direction of the cross
    product vector is defined by the `right-hand rule`.

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

    The orientation of `c` can be changed using the `axisc` keyword.

    >>> np.cross(x, y, axisc=0)
    array([[-3.,  3.],
           [ 6., -6.],
           [-3.,  3.]])

    Change the vector definition of `x` and `y` using `axisa` and `axisb`.

    >>> x = np.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])
    >>> y = np.array([[7., 8., 9.], [4., 5., 6.], [1., 2., 3.]])
    >>> np.cross(x, y)
    array([[ -6.,  12.,  -6.],
           [  0.,   0.,   0.],
           [  6., -12.,   6.]])
    >>> np.cross(x, y, axisa=0, axisb=0)
    array([[-24.,  48., -24.],
           [-30.,  60., -30.],
           [-36.,  72., -36.]])
    """
    return _mx_nd_np.cross(a, b, axisa=axisa, axisb=axisb, axisc=axisc, axis=axis)


@set_module('mxnet.numpy')
def kron(a, b):
    r"""Kronecker product of two arrays.

    Computes the Kronecker product, a composite array made of blocks of the
    second array scaled by the first.

    Parameters
    ----------
    a, b : ndarray

    Returns
    -------
    out : ndarray

    See Also
    --------
    outer : The outer product

    .. note::
       The function assumes that the number of dimensions of `a` and `b`
       are the same, if necessary prepending the smallest with ones.
       If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`,
       the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`.
       The elements are products of elements from `a` and `b`, organized
       explicitly by::

           kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]

       where::

           kt = it * st + jt,  t = 0,...,N

       In the common 2-D case (N=1), the block structure can be visualized::

           [[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
           [  ...                              ...   ],
           [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]


    Examples
    --------
    >>> np.kron([1,10,100], [5,6,7])
    array([  5,   6,   7,  50,  60,  70, 500, 600, 700])
    >>> np.kron([5,6,7], [1,10,100])
    array([  5,  50, 500,   6,  60, 600,   7,  70, 700])
    """
    return _mx_nd_np.kron(a, b)


@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')
@wrap_np_binary_func
def logical_and(x1, x2, out=None):
    r"""
    Compute the truth value of x1 AND x2 element-wise.
    Parameters
    ----------
    x1, x2 : array_like
        Logical AND is applied to the elements of `x1` and `x2`.
        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. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    Returns
    -------
    y : ndarray or bool
        Boolean result of the logical AND operation applied to the elements
        of `x1` and `x2`; the shape is determined by broadcasting.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    logical_or, logical_not, logical_xor, bitwise_or
    Examples
    --------
    >>> np.logical_and(True, False)
    False
    >>> np.logical_and(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
    array([False,  True])
    """
    return _mx_nd_np.logical_and(x1, x2, out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def logical_or(x1, x2, out=None):
    r"""
    Compute the truth value of x1 OR x2 element-wise.
    Parameters
    ----------
    x1, x2 : array_like
        Logical OR is applied to the elements of `x1` and `x2`.
        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. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    Returns
    -------
    y : ndarray or bool
        Boolean result of the logical OR operation applied to the elements
        of `x1` and `x2`; the shape is determined by broadcasting.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    logical_and, logical_not, logical_xor, bitwise_or
    Examples
    --------
    >>> np.logical_or(True, False)
    True
    >>> np.logical_or(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
    array([True,  True])
    """
    return _mx_nd_np.logical_or(x1, x2, out)


@set_module('mxnet.numpy')
@wrap_np_binary_func
def logical_xor(x1, x2, out=None):
    r"""
    Compute the truth value of x1 XOR x2 element-wise.
    Parameters
    ----------
    x1, x2 : array_like
        Logical XOR is applied to the elements of `x1` and `x2`.
        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. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    Returns
    -------
    y : ndarray or bool
        Boolean result of the logical XOR operation applied to the elements
        of `x1` and `x2`; the shape is determined by broadcasting.
        This is a scalar if both `x1` and `x2` are scalars.
    See Also
    --------
    logical_and, logical_not, logical_or, bitwise_or
    Examples
    --------
    >>> np.logical_xor(True, False)
    True
    >>> np.logical_xor(np.array([True, True], dtype='bool'), np.array([False, True], dtype='bool'))
    array([ True, False])
    """
    return _mx_nd_np.logical_xor(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 roll(a, shift, axis=None):
    """
    Roll array elements along a given axis.

    Elements that roll beyond the last position are re-introduced at
    the first.

    Parameters
    ----------
    a : ndarray
        Input array.
    shift : int or tuple of ints
        The number of places by which elements are shifted.  If a tuple,
        then `axis` must be a tuple of the same size, and each of the
        given axes is shifted by the corresponding number.  If an int
        while `axis` is a tuple of ints, then the same value is used for
        all given axes.
    axis : int or tuple of ints, optional
        Axis or axes along which elements are shifted.  By default, the
        array is flattened before shifting, after which the original
        shape is restored.

    Returns
    -------
    res : ndarray
        Output array, with the same shape as `a`.

    Notes
    -----
    Supports rolling over multiple dimensions simultaneously.

    Examples
    --------
    >>> x = np.arange(10)
    >>> np.roll(x, 2)
    array([8., 9., 0., 1., 2., 3., 4., 5., 6., 7.])
    >>> np.roll(x, -2)
    array([2., 3., 4., 5., 6., 7., 8., 9., 0., 1.])

    >>> x2 = np.reshape(x, (2,5))
    >>> x2
    array([[0., 1., 2., 3., 4.],
           [5., 6., 7., 8., 9.]])
    >>> np.roll(x2, 1)
    array([[9., 0., 1., 2., 3.],
           [4., 5., 6., 7., 8.]])
    >>> np.roll(x2, -1)
    array([[1., 2., 3., 4., 5.],
           [6., 7., 8., 9., 0.]])
    >>> np.roll(x2, 1, axis=0)
    array([[5., 6., 7., 8., 9.],
           [0., 1., 2., 3., 4.]])
    >>> np.roll(x2, -1, axis=0)
    array([[5., 6., 7., 8., 9.],
           [0., 1., 2., 3., 4.]])
    >>> np.roll(x2, 1, axis=1)
    array([[4., 0., 1., 2., 3.],
           [9., 5., 6., 7., 8.]])
    >>> np.roll(x2, -1, axis=1)
    array([[1., 2., 3., 4., 0.],
           [6., 7., 8., 9., 5.]])
   """
    return _mx_nd_np.roll(a, shift, axis=axis)


@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.

    .. note::
       * 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.

    .. note::
       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 insert(arr, obj, values, axis=None):
    r"""Insert values along the given axis before the given indices.

    Parameters
    ----------
    arr : ndarray
        Input array.
    obj : int, slice or ndarray of int64
        Object that defines the index or indices before which `values` is
        inserted.
        Support for multiple insertions when `obj` is a single scalar or a
        sequence with one element (only support int32 and int64 element).
    values : ndarray
        Values to insert into `arr`.
        If the type of values is different from that of arr, values is converted
        to the type of arr.
    axis : int, optional
        Axis along which to insert `values`.  If `axis` is None then `arr`
        is flattened first.

    Returns
    -------
    out : ndarray
        A copy of `arr` with `values` inserted.  Note that `insert`
        does not occur in-place: a new array is returned. If
        `axis` is None, `out` is a flattened array.

    .. note::
       * Note that for higher dimensional inserts `obj=0` behaves very different
         from `obj=[0]` just like `arr[:,0,:] = values` is different from
         `arr[:,[0],:] = values`.
       * If obj is a ndarray, it's dtype only supports int64

    Examples
    --------
    >>> a = np.array([[1, 1], [2, 2], [3, 3]])
    >>> a
    array([[1., 1.],
           [2., 2.],
           [3., 3.]])
    >>> np.insert(a, 1, np.array(5))
    array([1., 5., 1., 2., 2., 3., 3.])
    >>> np.insert(a, 1, np.array(5), axis=1)
    array([[1., 5., 1.],
           [2., 5., 2.],
           [3., 5., 3.]])

    Difference between sequence and scalars:

    >>> np.insert(a, np.array([1], dtype=np.int64), np.array([[1],[2],[3]]), axis=1)
    array([[1., 1., 1.],
           [2., 2., 2.],
           [3., 3., 3.]])
    >>> np.insert(a, 1, np.array([1, 2, 3]), axis=1)
    array([[1., 1., 1.],
           [2., 2., 2.],
           [3., 3., 3.]])

    >>> b = a.flatten()
    >>> b
    array([1., 1., 2., 2., 3., 3.])
    >>> np.insert(b, np.array([2, 2], dtype=np.int64), np.array([5, 6]))
    array([1., 1., 5., 6., 2., 2., 3., 3.])

    >>> np.insert(b, slice(2, 4), np.array([5, 6]))
    array([1., 1., 5., 2., 6., 2., 3., 3.])

    # type casting
    >>> np.insert(b.astype(np.int32), np.array([2, 2],dtype='int64'), np.array([7.13, False]))
    array([1, 1, 7, 0, 2, 2, 3, 3], dtype=int32)

    >>> x = np.arange(8).reshape(2, 4)
    >>> idx = np.array([1, 3], dtype=np.int64)
    >>> np.insert(x, idx, np.array([999]), axis=1)
    array([[  0., 999.,   1.,   2., 999.,   3.],
           [  4., 999.,   5.,   6., 999.,   7.]])
    """
    return _mx_nd_np.insert(arr, obj, values, axis=axis)


@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 percentile(a, q, axis=None, out=None, overwrite_input=None, interpolation='linear', keepdims=False): # pylint: disable=too-many-arguments
    """
    Compute the q-th percentile of the data along the specified axis.
    Returns the q-th percentile(s) of the array elements.

    Parameters
    ----------
    a : array_like
        Input array
    q : array_like
        Percentile or sequence of percentiles to compute.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the percentiles are computed. The default is to
        compute the percentile(s) along a flattened version of the array.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have the same
        shape and buffer length as the expected output, but the type (of the output)
        will be cast if necessary.
    overwrite_input : bool, optional (Not supported yet)
        If True, then allow the input array a to be modified by intermediate calculations,
        to save memory. In this case, the contents of the input a after this function
        completes is undefined.
    interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
        This optional parameter specifies the interpolation method to use when the
        desired percentile lies between two data points i < j:
        'linear': i + (j - i) * fraction, where fraction is the fractional part of the
        index surrounded by i and j.
        'lower': i.
        'higher': j.
        'nearest': i or j, whichever is nearest.
        'midpoint': (i + j) / 2.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in the result as
        dimensions with size one. With this option, the result will broadcast
        correctly against the original array a.

    Returns
    -------
    percentile : scalar or ndarray
        Output array.

    Examples
    --------
    >>> a = np.array([[10, 7, 4], [3, 2, 1]])
    >>> a
    array([[10,  7,  4],
        [ 3,  2,  1]])
    >>> np.percentile(a, np.array(50))
    array(3.5)
    >>> np.percentile(a, np.array(50), axis=0)
    array([6.5, 4.5, 2.5])
    >>> np.percentile(a, np.array(50), axis=1)
    array([7.,  2.])
    >>> np.percentile(a, np.array(50), axis=1, keepdims=True)
    array([[7.],
        [2.]])

    >>> m = np.percentile(a, np.array(50), axis=0)
    >>> out = np.zeros_like(m)
    >>> np.percentile(a, np.array(50), axis=0, out=out)
    array([6.5, 4.5, 2.5])
    >>> m
    array([6.5, 4.5, 2.5])
    """
    return _mx_nd_np.percentile(a, q, axis=axis, out=out, overwrite_input=overwrite_input,
                                interpolation=interpolation, keepdims=keepdims)


@set_module('mxnet.numpy')
def median(a, axis=None, out=None, overwrite_input=None, keepdims=False):
    r"""Compute the median along the specified axis.
    Returns the median of the array elements.

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array.
    axis : {int, sequence of int, None}, optional
        Axis or axes along which the medians are computed. The default
        is to compute the median along a flattened version of the array.
        A sequence of axes is supported since version 1.9.0.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output,
        but the type (of the output) will be cast if necessary.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

    Returns
    -------
    median : ndarray
        A new array holding the result. If the input contains integers
        or floats smaller than ``float32``, then the output data-type is
        ``np.float32``.  Otherwise, the data-type of the output is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    mean, percentile

    Examples
    --------
    >>> a = np.array([[10, 7, 4], [3, 2, 1]])
    >>> a
    array([[10,  7,  4],
        [ 3,  2,  1]])
    >>> np.median(a)
    3.5
    >>> np.median(a, axis=0)
    array([6.5, 4.5, 2.5])
    >>> np.median(a, axis=1)
    array([7.,  2.])
    """
    return _mx_nd_np.median(a, axis=axis, overwrite_input=overwrite_input,
                            keepdims=keepdims, out=out)


@set_module('mxnet.numpy')
def quantile(a, q, axis=None, out=None, overwrite_input=None, interpolation='linear', keepdims=False): # pylint: disable=too-many-arguments
    """Compute the q-th quantile of the data along the specified axis.
    New in version 1.15.0.

    Parameters
    ----------
    a : ndarray
        Input array or object that can be converted to an array.
    q : ndarray
        Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the quantiles are computed.
        The default is to compute the quantile(s) along a flattened version of the array.
    out : ndarray, optional
        Alternative output array in which to place the result.
        It must have the same shape and buffer length as the expected output,
        but the type (of the output) will be cast if necessary.
    interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
        This optional parameter specifies the interpolation method to use
        when the desired quantile lies between two data points i < j:

        * linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.
        * lower: i.
        * higher: j.
        * nearest: i or j, whichever is nearest.
        * midpoint: (i + j) / 2.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in the result as dimensions with size one.
        With this option, the result will broadcast correctly against the original array a.

    Returns
    -------
    quantile : ndarray
        If q is a single quantile and axis=None, then the result is a scalar.
        If multiple quantiles are given, first axis of the result corresponds to the quantiles.
        The other axes are the axes that remain after the reduction of a.
        If out is specified, that array is returned instead.

    See also
    --------
    mean

    .. note::
       Given a vector V of length N, the q-th quantile of V is the value q of the way from the minimum
       to the maximum in a sorted copy of V. The values and distances of the two nearest neighbors
       as well as the interpolation parameter will determine the quantile if the normalized ranking
       does not match the location of q exactly. This function is the same as the median if q=0.5,
       the same as the minimum if q=0.0 and the same as the maximum if q=1.0.
       This function differs from the original `numpy.quantile
       <https://numpy.org/devdocs/reference/generated/numpy.quantile.html>`_ in
       the following aspects:

       * q must be ndarray type even if it is a scalar
       * do not support overwrite_input

    Examples
    --------
    >>> a = np.array([[10, 7, 4], [3, 2, 1]])
    >>> a
    array([[10., 7., 4.],
           [3., 2., 1.]])
    >>> q = np.array(0.5)
    >>> q
    array(0.5)
    >>> np.quantile(a, q)
    array(3.5)
    >>> np.quantile(a, q, axis=0)
    array([6.5, 4.5, 2.5])
    >>> np.quantile(a, q, axis=1)
    array([7., 2.])
    >>> np.quantile(a, q, axis=1, keepdims=True)
    array([[7.],
           [2.]])
    >>> m = np.quantile(a, q, axis=0)
    >>> out = np.zeros_like(m)
    >>> np.quantile(a, q, axis=0, out=out)
    array([6.5, 4.5, 2.5])
    >>> out
    array([6.5, 4.5, 2.5])
    """
    return _mx_nd_np.quantile(a, q, axis=axis, out=out, overwrite_input=overwrite_input,
                              interpolation=interpolation, keepdims=keepdims)


@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

    .. note::
       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 np
    """
    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

    .. note::
       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 np
    """
    return _mx_nd_np.may_share_memory(a, b, max_work)


@set_module('mxnet.numpy')
def diff(a, n=1, axis=-1, prepend=None, append=None):  # pylint: disable=redefined-outer-name
    r"""
    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)


@set_module('mxnet.numpy')
def ediff1d(ary, to_end=None, to_begin=None):
    """
    The differences between consecutive elements of an array.

    Parameters
    ----------
    ary : ndarray
        If necessary, will be flattened before the differences are taken.
    to_end : ndarray or scalar, optional
        Number(s) to append at the end of the returned differences.
    to_begin : ndarray or scalar, optional
        Number(s) to prepend at the beginning of the returned differences.

    Returns
    -------
    ediff1d : ndarray
        The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.

    Examples
    --------
    >>> x = np.array([1, 2, 4, 7, 0])
    >>> np.ediff1d(x)
    array([ 1.,  2.,  3., -7.])

    >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
    rray([-99.,   1.,   2.,   3.,  -7.,  88.,  99.])

    The returned array is always 1D.

    >>> y = np.array([[1, 2, 4], [1, 6, 24]])
    >>> np.ediff1d(y)
    array([ 1.,  2., -3.,  5., 18.])

    >>> np.ediff1d(x, to_begin=y)
    array([ 1.,  2.,  4.,  1.,  6., 24.,  1.,  2.,  3., -7.])
    """
    return _mx_nd_np.ediff1d(ary, to_end=to_end, to_begin=to_begin)


@set_module('mxnet.numpy')
def resize(a, new_shape):
    """
    Return a new array with the specified shape.
    If the new array is larger than the original array, then the new
    array is filled with repeated copies of `a`.  Note that this behavior
    is different from a.resize(new_shape) which fills with zeros instead
    of repeated copies of `a`.

    Parameters
    ----------
    a : ndarray
        Array to be resized.
    new_shape : int or tuple of int
        Shape of resized array.

    Returns
    -------
    reshaped_array : ndarray
        The new array is formed from the data in the old array, repeated
        if necessary to fill out the required number of elements.  The
        data are repeated in the order that they are stored in memory.

    See Also
    --------
    ndarray.resize : resize an array in-place.

    Notes
    -----
    Warning: This functionality does **not** consider axes separately,
    i.e. it does not apply interpolation/extrapolation.
    It fills the return array with the required number of elements, taken
    from `a` as they are laid out in memory, disregarding strides and axes.
    (This is in case the new shape is smaller. For larger, see above.)
    This functionality is therefore not suitable to resize images,
    or data where each axis represents a separate and distinct entity.

    Examples
    --------
    >>> a = np.array([[0, 1], [2, 3]])
    >>> np.resize(a, (2, 3))
    array([[0., 1., 2.],
           [3., 0., 1.]])
    >>> np.resize(a, (1, 4))
    array([[0., 1., 2., 3.]])
    >>> np.resize(a,(2, 4))
    array([[0., 1., 2., 3.],
           [0., 1., 2., 3.]])
    """
    return _mx_nd_np.resize(a, new_shape)


@set_module('mxnet.numpy')
def interp(x, xp, fp, left=None, right=None, period=None):  # pylint: disable=too-many-arguments
    r"""One-dimensional linear interpolation.

    Returns the one-dimensional piecewise linear interpolant to a function
    with given values at discrete data-points.

    Parameters
    ----------
    x : ndarray
        The x-coordinates of the interpolated values.
    xp : 1-D array of floats
        The x-coordinates of the data points, must be increasing if argument
        `period` is not specified. Otherwise, `xp` is internally sorted after
        normalizing the periodic boundaries with ``xp = xp % period``.
    fp : 1-D array of floats
        The y-coordinates of the data points, same length as `xp`.
    left : optional float corresponding to fp
        Value to return for `x < xp[0]`, default is `fp[0]`.
    right : optional float corresponding to fp
        Value to return for `x > xp[-1]`, default is `fp[-1]`.
    period : None or float, optional
        A period for the x-coordinates. This parameter allows the proper
        interpolation of angular x-coordinates. Parameters `left` and `right`
        are ignored if `period` is specified.

    Returns
    -------
    y : float (corresponding to fp) or ndarray
        The interpolated values, same shape as `x`.

    Raises
    ------
    ValueError
        If `xp` and `fp` have different length
        If `xp` or `fp` are not 1-D sequences
        If `period == 0`

    .. note::
       Does not check that the x-coordinate sequence `xp` is increasing.
       If `xp` is not increasing, the results are nonsense.
       A simple check for increasing is::

           np.all(np.diff(xp) > 0)


    Examples
    --------
    >>> xp = [1, 2, 3]
    >>> fp = [3, 2, 0]
    >>> np.interp(2.5, xp, fp)
    1.0
    >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)
    array([ 3. ,  3. ,  2.5 ,  0.56,  0. ])
    >>> UNDEF = -99.0
    >>> np.interp(3.14, xp, fp, right=UNDEF)
    -99.0
    Plot an interpolant to the sine function:
    >>> x = np.linspace(0, 2*np.pi, 10)
    >>> y = np.sin(x)
    >>> xvals = np.linspace(0, 2*np.pi, 50)
    >>> yinterp = np.interp(xvals, x, y)
    >>> import matplotlib.pyplot as plt
    >>> plt.plot(x, y, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.plot(xvals, yinterp, '-x')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.show()
    Interpolation with periodic x-coordinates:
    >>> x = [-180, -170, -185, 185, -10, -5, 0, 365]
    >>> xp = [190, -190, 350, -350]
    >>> fp = [5, 10, 3, 4]
    >>> np.interp(x, xp, fp, period=360)
    array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75])
    """
    return _mx_nd_np.interp(x, xp, fp, left=left, right=right, period=period)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def full_like(a, fill_value, dtype=None, order='C', device=None, out=None): # pylint: disable=too-many-arguments
    """
    Return a full array with the same shape and type as a given array.

    Parameters
    ----------
    a : ndarray
        The shape and data-type of `a` define these same attributes of
        the returned array.
    fill_value : scalar
        Fill value.
    dtype : data-type, optional
        Overrides the data type of the result.
        Temporarily do not support boolean type.
    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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.
    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 same shape and type as `a`.

    See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones_like : Return an array of ones with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full : Return a new array of given shape filled with value.

    Examples
    --------
    >>> x = np.arange(6, dtype=int)
    >>> np.full_like(x, 1)
    array([1, 1, 1, 1, 1, 1], dtype=int64)
    >>> np.full_like(x, 0.1)
    array([0, 0, 0, 0, 0, 0], dtype=int64)
    >>> np.full_like(x, 0.1, dtype=np.float64)
    array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1], dtype=float64)
    >>> np.full_like(x, np.nan, dtype=np.float64)
    array([nan, nan, nan, nan, nan, nan], dtype=float64)
    >>> y = np.arange(6, dtype=np.float32)
    >>> np.full_like(y, 0.1)
    array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
    """
    return _mx_nd_np.full_like(a, fill_value=fill_value, dtype=dtype, order=order, device=device, out=out)
# pylint: enable=redefined-outer-name


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def zeros_like(a, dtype=None, order='C', device=None, out=None):
    """
    Return an array of zeros with the same shape and type as a given array.

    Parameters
    ----------
    a : ndarray
        The shape and data-type of `a` define these same attributes of
        the returned array.
    dtype : data-type, optional
        Overrides the data type of the result.
        Temporarily do not support boolean type.
    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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.
    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 zeros with the same shape and type as a.

    See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones_like : Return an array of ones with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full : Return a new array of given shape filled with value.

    Examples
    --------
    >>> x = np.arange(6)
    >>> x = x.reshape((2, 3))
    >>> x
    array([[0., 1., 2.],
           [3., 4., 5.]])
    >>> np.zeros_like(x)
    array([[0., 0., 0.],
           [0., 0., 0.]])
    >>> np.zeros_like(x, int)
    array([[0, 0, 0],
           [0, 0, 0]], dtype=int64)
    >>> y = np.arange(3, dtype=float)
    >>> y
    array([0., 1., 2.], dtype=float64)
    >>> np.zeros_like(y)
    array([0., 0., 0.], dtype=float64)
    """
    return _mx_nd_np.full_like(a, fill_value=0, dtype=dtype, order=order, device=device, out=out)
# pylint: enable=redefined-outer-name


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def ones_like(a, dtype=None, order='C', device=None, out=None):
    """
    Return an array of ones with the same shape and type as a given array.

    Parameters
    ----------
    a : ndarray
        The shape and data-type of `a` define these same attributes of
        the returned array.
    dtype : data-type, optional
        Overrides the data type of the result.
        Temporarily do not support boolean type.
    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.
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.
    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 ones with the same shape and type as a.

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

    Examples
    --------
    >>> x = np.arange(6)
    >>> x = x.reshape((2, 3))
    >>> x
    array([[0., 1., 2.],
           [3., 4., 5.]])
    >>> np.ones_like(x)
    array([[1., 1., 1.],
           [1., 1., 1.]])
    >>> np.ones_like(x, int)
    array([[1, 1, 1],
           [1, 1, 1]], dtype=int64)
    >>> y = np.arange(3, dtype=float)
    >>> y
    array([0., 1., 2.], dtype=float64)
    >>> np.ones_like(y)
    array([1., 1., 1.], dtype=float64)
    """
    return _mx_nd_np.full_like(a, fill_value=1, dtype=dtype, order=order, device=device, out=out)
# pylint: enable=redefined-outer-name


@set_module('mxnet.numpy')
def fill_diagonal(a, val, wrap=False):
    """
    Fill the main diagonal of the given array of any dimensionality.
    For an array `a` with ``a.ndim >= 2``, the diagonal is the list of
    locations with indices ``a[i, ..., i]`` all identical. This function
    modifies the input array in-place, it does not return a value.
    Parameters
    ----------
    a : array, at least 2-D.
      Array whose diagonal is to be filled, it gets modified in-place.
    val : scalar
      Value to be written on the diagonal, its type must be compatible with
      that of the array a.
    wrap : bool
      For tall matrices in NumPy version up to 1.6.2, the
      diagonal "wrapped" after N columns. You can have this behavior
      with this option. This affects only tall matrices.

    Examples
    --------
    >>> a = np.zeros((3, 3), int)
    >>> np.fill_diagonal(a, 5)
    >>> a
    array([[5, 0, 0],
           [0, 5, 0],
           [0, 0, 5]])
    The same function can operate on a 4-D array:
    >>> a = np.zeros((3, 3, 3, 3), int)
    >>> np.fill_diagonal(a, 4)
    We only show a few blocks for clarity:
    >>> a[0, 0]
    array([[4, 0, 0],
           [0, 0, 0],
           [0, 0, 0]])
    >>> a[1, 1]
    array([[0, 0, 0],
           [0, 4, 0],
           [0, 0, 0]])
    >>> a[2, 2]
    array([[0, 0, 0],
           [0, 0, 0],
           [0, 0, 4]])
    The wrap option affects only tall matrices:
    >>> # tall matrices no wrap
    >>> a = np.zeros((5, 3), int)
    >>> np.fill_diagonal(a, 4)
    >>> a
    array([[4, 0, 0],
           [0, 4, 0],
           [0, 0, 4],
           [0, 0, 0],
           [0, 0, 0]])
    >>> # tall matrices wrap
    >>> a = np.zeros((5, 3), int)
    >>> np.fill_diagonal(a, 4, wrap=True)
    >>> a
    array([[4, 0, 0],
           [0, 4, 0],
           [0, 0, 4],
           [0, 0, 0],
           [4, 0, 0]])
    >>> # wide matrices
    >>> a = np.zeros((3, 5), int)
    >>> np.fill_diagonal(a, 4, wrap=True)
    >>> a
    array([[4, 0, 0, 0, 0],
           [0, 4, 0, 0, 0],
           [0, 0, 4, 0, 0]])
    The anti-diagonal can be filled by reversing the order of elements
    using either `numpy.flipud` or `numpy.fliplr`.
    >>> a = np.zeros((3, 3), int);
    >>> np.fill_diagonal(np.fliplr(a), [1,2,3])  # Horizontal flip
    >>> a
    array([[0, 0, 1],
           [0, 2, 0],
           [3, 0, 0]])
    >>> np.fill_diagonal(np.flipud(a), [1,2,3])  # Vertical flip
    >>> a
    array([[0, 0, 3],
           [0, 2, 0],
           [1, 0, 0]])
    Note that the order in which the diagonal is filled varies depending
    on the flip function.
    """
    _mx_nd_np.fill_diagonal(a, val=val, wrap=wrap)

# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def nan_to_num(x, copy=True, nan=0.0, posinf=None, neginf=None, **kwargs):
    """
    Replace NaN with zero and infinity with large finite numbers (default
    behaviour) or with the numbers defined by the user using the `nan`,
    `posinf` and/or `neginf` keywords.

    If `x` is inexact, NaN is replaced by zero or by the user defined value in
    `nan` keyword, infinity is replaced by the largest finite floating point
    values representable by ``x.dtype`` or by the user defined value in
    `posinf` keyword and -infinity is replaced by the most negative finite
    floating point values representable by ``x.dtype`` or by the user defined
    value in `neginf` keyword.

    For complex dtypes, the above is applied to each of the real and
    imaginary components of `x` separately.

    If `x` is not inexact, then no replacements are made.

    Parameters
    ----------
    x : scalar
        ndarray
        Input data.
    copy : bool, optional
        Whether to create a copy of `x` (True) or to replace values
        in-place (False). The in-place operation only occurs if
        casting to an array does not require a copy.
        Default is True.
        Gluon does not support copy = False.
    nan : int, float, optional
        Value to be used to fill NaN values. If no value is passed
        then NaN values will be replaced with 0.0.
    posinf : int, float, optional
        Value to be used to fill positive infinity values. If no value is
        passed then positive infinity values will be replaced with a very
        large number.
    neginf : int, float, optional
        Value to be used to fill negative infinity values. If no value is
        passed then negative infinity values will be replaced with a very
        small (or negative) number.

        .. versionadded:: 1.13

    Returns
    -------
    out : ndarray
        `x`, with the non-finite values replaced. If `copy` is False, this may
        be `x` itself.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.

    Examples
    --------
    >>> np.nan_to_num(np.inf)
    1.7976931348623157e+308
    >>> np.nan_to_num(-np.inf)
    -1.7976931348623157e+308
    >>> np.nan_to_num(np.nan)
    0.0
    >>> x = np.array([np.inf, -np.inf, np.nan, -128, 128])
    >>> np.nan_to_num(x)
    array([ 3.4028235e+38, -3.4028235e+38,  0.0000000e+00, -1.2800000e+02,
            1.2800000e+02])
    >>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333)
    array([ 3.3333332e+07,  3.3333332e+07, -9.9990000e+03, -1.2800000e+02,
            1.2800000e+02])
    >>> y = np.array([[-1, 0, 1],[9999,234,-14222]],dtype="float64")/0
    array([[-inf,  nan,  inf],
        [ inf,  inf, -inf]], dtype=float64)
    >>> np.nan_to_num(y)
    array([[-1.79769313e+308,  0.00000000e+000,  1.79769313e+308],
        [ 1.79769313e+308,  1.79769313e+308, -1.79769313e+308]], dtype=float64)
    >>> np.nan_to_num(y, nan=111111, posinf=222222)
    array([[-1.79769313e+308,  1.11111000e+005,  2.22222000e+005],
        [ 2.22222000e+005,  2.22222000e+005, -1.79769313e+308]], dtype=float64)
    >>> y
    array([[-inf,  nan,  inf],
       [ inf,  inf, -inf]], dtype=float64)
    >>> np.nan_to_num(y, copy=False, nan=111111, posinf=222222)
    array([[-1.79769313e+308,  1.11111000e+005,  2.22222000e+005],
       [ 2.22222000e+005,  2.22222000e+005, -1.79769313e+308]], dtype=float64)
    >>> y
    array([[-1.79769313e+308,  1.11111000e+005,  2.22222000e+005],
       [ 2.22222000e+005,  2.22222000e+005, -1.79769313e+308]], dtype=float64)
    """
    return _mx_nd_np.nan_to_num(x, copy=copy, nan=nan, posinf=posinf, neginf=neginf)


@set_module('mxnet.numpy')
def squeeze(x, axis=None):
    r"""Remove single-dimensional entries from the shape of an array.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : None or int or tuple of ints, optional
        Selects a subset of the single-dimensional entries in the
        shape. If an axis is selected with shape entry greater than
        one, an error is raised.

    Returns
    -------
    squeezed : ndarray
        The input array, but with all or a subset of the
        dimensions of length 1 removed. This is always `a` itself
        or a view into `a`.

    Raises
    ------
    ValueError
        If `axis` is not `None`, and an axis being squeezed is not of length 1

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

    Examples
    --------
    >>> x = np.array([[[0], [1], [2]]])
    >>> x.shape
    (1, 3, 1)
    >>> np.squeeze(x).shape
    (3,)
    >>> np.squeeze(x, axis=0).shape
    (3, 1)
    >>> np.squeeze(x, axis=1).shape
    Traceback (most recent call last):
    ...
    ValueError: cannot select an axis to squeeze out which has size not equal to one
    >>> np.squeeze(x, axis=2).shape
    (1, 3)
    """
    return _mx_nd_np.squeeze(x, axis=axis)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def isnan(x, out=None, **kwargs):
    """
    Test element-wise for NaN and return result as a boolean array.

    Parameters
    ----------
    x : ndarray
        Input array.
    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 or bool
        True where x is NaN, false otherwise.
        This is a scalar if x is a scalar.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).

    .. note::

       This function differs from the original `numpy.isinf
       <https://docs.scipy.org/doc/numpy/reference/generated/numpy.isnan.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
    --------
    >>> np.isnan(np.nan)
    True
    >>> np.isnan(np.inf)
    False
    >>> np.isnan(np.array([np.log(-1.),1.,np.log(0)]))
    array([ True, False, False])
    """
    return _mx_nd_np.isnan(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def isinf(x, out=None, **kwargs):
    """
    Test element-wise for positive or negative infinity.

    Parameters
    ----------
    x : ndarray
        Input array.
    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 or bool
        True where x is positive or negative infinity, false otherwise.
        This is a scalar if x is a scalar.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
    This means that Not a Number is not equivalent to infinity.

    .. note::

       This function differs from the original `numpy.isnan
       <https://docs.scipy.org/doc/numpy/reference/generated/numpy.isnan.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
    --------
    >>> np.isinf(np.inf)
    True
    >>> np.isinf(np.nan)
    False
    >>> np.isinf(np.array([np.inf, -np.inf, 1.0, np.nan]))
    array([ True,  True, False, False])
    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([True, True, True], dtype=np.bool_)
    >>> np.isinf(x, y)
    array([ True, False,  True])
    >>> y
    array([ True, False,  True])
    """
    return _mx_nd_np.isinf(x, out=out, **kwargs)


@set_module('mxnet.ndarray.numpy')
@wrap_np_unary_func
def isposinf(x, out=None, **kwargs):
    """
    Test element-wise for positive infinity, return result as bool array.

    Parameters
    ----------
    x : ndarray
        Input array.
    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 or bool
        True where x is positive infinity, false otherwise.
        This is a scalar if x is a scalar.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
    This means that Not a Number is not equivalent to infinity.

    Examples
    --------
    >>> np.isposinf(np.inf)
    True
    >>> np.isposinf(-np.inf)
    False
    >>> np.isposinf(np.nan)
    False
    >>> np.isposinf(np.array([-np.inf, 0., np.inf]))
    array([False, False,  True])
    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([True, True, True], dtype=np.bool)
    >>> np.isposinf(x, y)
    array([False, False,  True])
    >>> y
    array([False, False,  True])
    """
    return _mx_nd_np.isposinf(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def isneginf(x, out=None, **kwargs):
    """
    Test element-wise for negative infinity, return result as bool array.

    Parameters
    ----------
    x : ndarray
        Input array.
    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 or bool
        True where x is negative infinity, false otherwise.
        This is a scalar if x is a scalar.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
    This means that Not a Number is not equivalent to infinity.

    Examples
    --------
    >>> np.isneginf(-np.inf)
    True
    >>> np.isneginf(np.inf)
    False
    >>> np.isneginf(float('-inf'))
    True
    >>> np.isneginf(np.array([-np.inf, 0., np.inf]))
    array([ True, False, False])
    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([True, True, True], dtype=np.bool)
    >>> np.isneginf(x, y)
    array([ True, False, False])
    >>> y
    array([ True, False, False])
    """
    return _mx_nd_np.isneginf(x, out=out, **kwargs)


@set_module('mxnet.numpy')
@wrap_np_unary_func
def isfinite(x, out=None, **kwargs):
    """
    Test element-wise for finiteness (not infinity or not Not a Number).

    Parameters
    ----------
    x : ndarray
        Input array.
    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 or bool
        True where x is negative infinity, false otherwise.
        This is a scalar if x is a scalar.

    Notes
    -----
    Not a Number, positive infinity and negative infinity are considered to be non-finite.

    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).
    This means that Not a Number is not equivalent to infinity.
    Also that positive infinity is not equivalent to negative infinity.
    But infinity is equivalent to positive infinity. Errors result if the second argument
    is also supplied when x is a scalar input, or if first and second arguments have different shapes.

    Examples
    --------
    >>> np.isfinite(1)
    True
    >>> np.isfinite(0)
    True
    >>> np.isfinite(np.nan)
    False
    >>> np.isfinite(np.inf)
    False
    >>> np.isfinite(-np.inf)
    False
    >>> np.isfinite(np.array([np.log(-1.),1.,np.log(0)]))
    array([False,  True, False])
    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([True, True, True], dtype=np.bool)
    >>> np.isfinite(x, y)
    array([False,  True, False])
    >>> y
    array([False,  True, False])
    """
    return _mx_nd_np.isfinite(x, out=out, **kwargs)


@set_module('mxnet.numpy')
def where(condition, x=None, y=None):
    """where(condition, [x, y])
    Return elements chosen from `x` or `y` depending on `condition`.

    .. note::
        When only `condition` is provided, this function is a shorthand for
        ``np.asarray(condition).nonzero()``. The rest of this documentation
        covers only the case where all three arguments are provided.

    Parameters
    ----------
    condition : ndarray
        Where True, yield `x`, otherwise yield `y`.
    x, y : ndarray
        Values from which to choose. `x`, `y` and `condition` need to be
        broadcastable to some shape. `x` and `y` must have the same dtype.

    Returns
    -------
    out : ndarray
        An array with elements from `x` where `condition` is True, and elements
        from `y` elsewhere.

    Notes
    -----
    If all the arrays are 1-D, `where` is equivalent to::

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

    Examples
    --------
    >>> a = np.arange(10)
    >>> a
    array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])
    >>> np.where(a < 5, a, 10*a)
    array([ 0.,  1.,  2.,  3.,  4., 50., 60., 70., 80., 90.])

    This can be used on multidimensional arrays too:

    >>> cond = np.array([[True, False], [True, True]])
    >>> x = np.array([[1, 2], [3, 4]])
    >>> y = np.array([[9, 8], [7, 6]])
    >>> np.where(cond, x, y)
    array([[1., 8.],
           [3., 4.]])

    The shapes of x, y, and the condition are broadcast together:

    >>> x, y = onp.ogrid[:3, :4]
    >>> x = np.array(x)
    >>> y = np.array(y)
    >>> np.where(x < y, x, 10 + y)  # both x and 10+y are broadcast
    array([[10,  0,  0,  0],
           [10, 11,  1,  1],
           [10, 11, 12,  2]], dtype=int64)

    >>> a = np.array([[0, 1, 2],
    ...               [0, 2, 4],
    ...               [0, 3, 6]])
    >>> np.where(a < 4, a, -1)  # -1 is broadcast
    array([[ 0.,  1.,  2.],
           [ 0.,  2., -1.],
           [ 0.,  3., -1.]])
    """
    return _mx_nd_np.where(condition, x, y)


@set_module('mxnet.numpy')
def polyval(p, x):
    """
    Evaluate a polynomial at specific values.
    If p is of length N, this function returns the value:
    p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]
    If x is a sequence, then p(x) is returned for each element of x.
    If x is another polynomial then the composite polynomial p(x(t)) is returned.

    Parameters
    ----------
    p : ndarray
        1D array of polynomial coefficients (including coefficients equal to zero)
        from highest degree to the constant term.
    x : ndarray
        An array of numbers, at which to evaluate p.

    Returns
    -------
    values : ndarray
        Result array of polynomials

    .. note::
       This function differs from the original `numpy.polyval
       <https://numpy.org/devdocs/reference/generated/numpy.polyval.html>`_ in
       the following way(s):

       * Does not support poly1d.
       * X should be ndarray type even if it contains only one element.

    Examples
    --------
    >>> p = np.array([3, 0, 1])
    array([3., 0., 1.])
    >>> x = np.array([5])
    array([5.])
    >>> np.polyval(p, x)  # 3 * 5**2 + 0 * 5**1 + 1
    array([76.])
    >>> x = np.array([5, 4])
    array([5., 4.])
    >>> np.polyval(p, x)
    array([76., 49.])
    """
    return _mx_nd_np.polyval(p, x)


@set_module('mxnet.numpy')
def bincount(x, weights=None, minlength=0):
    """
    Count number of occurrences of each value in array of non-negative ints.

    Parameters
    ----------
    x : ndarray
        input array, 1 dimension, nonnegative ints.
    weights: ndarray
        input weigths same shape as x. (Optional)
    minlength: int
        A minimum number of bins for the output. (Optional)

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

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

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

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

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

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


@set_module('mxnet.numpy')
def atleast_1d(*arys):
    """
    Convert inputs to arrays with at least one dimension.

    Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved.

    Parameters
    ----------
    arys1, arys2, ... : ndarray
        One or more input arrays.

    Returns
    -------
    ret : ndarray
        An array, or list of arrays, each with a.ndim >= 1. Copies are made only if necessary.

    See also
    --------
    atleast_2d, atleast_3d

    Examples
    --------
    >>> np.atleast_1d(1.0)
    array([1.])
    >>> x = np.arange(9.0).reshape(3,3)
    >>> np.atleast_1d(x)
    array([[0., 1., 2.],
           [3., 4., 5.],
           [6., 7., 8.]])
    >>> np.atleast_1d(np.array(1), np.array([3, 4]))
    [array([1.]), array([3., 4.])]
    """
    res = []
    for ary in arys:
        if not isinstance(ary, NDArray):
            ary = array(ary)
        res.append(ary)
    return _mx_nd_np.atleast_1d(*res)


@set_module('mxnet.numpy')
def atleast_2d(*arys):
    """
    Convert inputs to arrays with at least two dimensions.

    Parameters
    ----------
    arys1, arys2, ... : ndarray
        One or more input arrays.

    Returns
    -------
    ret : ndarray
        An array, or list of arrays, each with a.ndim >= 2. Copies are made only if necessary.

    See also
    --------
    atleast_1d, atleast_3d

    Examples
    --------
    >>> np.atleast_2d(3.0)
    array([[3.]])
    >>> x = np.arange(3.0)
    >>> np.atleast_2d(x)
    array([[0., 1., 2.]])
    >>> np.atleast_2d(np.array(1), np.array([1, 2]), np.array([[1, 2]]))
    [array([[1.]]), array([[1., 2.]]), array([[1., 2.]])]
    """
    res = []
    for ary in arys:
        if not isinstance(ary, NDArray):
            ary = array(ary)
        res.append(ary)
    return _mx_nd_np.atleast_2d(*res)


@set_module('mxnet.numpy')
def atleast_3d(*arys):
    """
    Convert inputs to arrays with at least three dimension.

    Parameters
    ----------
    arys1, arys2, ... : ndarray
        One or more input arrays.

    Returns
    -------
    ret : ndarray
        An array, or list of arrays, each with a.ndim >= 3.
        For example, a 1-D array of shape (N,) becomes a view of shape (1, N, 1),
        and a 2-D array of shape (M, N) becomes a view of shape (M, N, 1).

    See also
    --------
    atleast_1d, atleast_2d

    Examples
    --------
    >>> np.atleast_3d(3.0)
    array([[[3.]]])
    >>> x = np.arange(3.0)
    >>> np.atleast_3d(x).shape
    (1, 3, 1)
    >>> x = np.arange(12.0).reshape(4,3)
    >>> np.atleast_3d(x).shape
    (4, 3, 1)
    >>> for arr in np.atleast_3d(np.array([1, 2]), np.array([[1, 2]]), np.array([[[1, 2]]])):
    ...     print(arr, arr.shape)
    ...
    [[[1.]
      [2.]]] (1, 2, 1)
    [[[1.]
      [2.]]] (1, 2, 1)
    [[[1. 2.]]] (1, 1, 2)
    """
    res = []
    for ary in arys:
        if not isinstance(ary, NDArray):
            ary = array(ary)
        res.append(ary)
    return _mx_nd_np.atleast_3d(*res)


@set_module('mxnet.numpy')
def pad(x, pad_width=None, mode="constant", **kwargs): # pylint: disable=too-many-arguments
    # pylint: disable=too-many-return-statements
    """
    Pad an array.

    Parameters
    ----------
    array : array_like of rank N
        The array to pad.
    pad_width : {sequence, array_like, int}
        Number of values padded to the edges of each axis.
        ((before_1, after_1), ... (before_N, after_N)) unique pad widths
        for each axis.
        ((before, after),) yields same before and after pad for each axis.
        (pad,) or int is a shortcut for before = after = pad width for all
        axes.
    mode : str or function, optional
        One of the following string values or a user supplied function.
        'constant' (default)
            Pads with a constant value.
        'edge'
            Pads with the edge values of array.
        'linear_ramp'
            not supported yet
        'maximum'
            Pads with the maximum value of all of the
            vector along each axis.
        'mean'
            not supported yet
        'median'
            not supported yet
        'minimum'
            Pads with the minimum value of all of the
            vector along each axis.
        'reflect'
            Pads with the reflection of the vector mirrored on
            the first and last values of the vector along each
            axis.
        'symmetric'
            Pads with the reflection of the vector mirrored
            along the edge of the array.
        'wrap'
            not supported yet.
        'empty'
            not supported yet.
        <function>
            not supported yet.
    stat_length : not supported yet
    constant_values : scalar, optional
        Used in 'constant'.  The values to set the padded values for each
        axis.
        Default is 0.

    end_values : not supported yet
    reflect_type : {'even', 'odd'}, optional
        only support even now

    Returns
    -------
    pad : ndarray
        Padded array of rank equal to `array` with shape increased
        according to `pad_width`.

    Examples
    --------
    >>> a = [1, 2, 3, 4, 5]
    >>> np.pad(a, (2, 3), 'edge')
    array([1, 1, 1, ..., 5, 5, 5])
    >>> np.pad(a, (2, 2), 'maximum')
    array([5, 5, 1, 2, 3, 4, 5, 5, 5])
    >>> np.pad(a, (2, 2), 'mean')
    array([3, 3, 1, 2, 3, 4, 5, 3, 3])
    >>> a = [[1, 2], [3, 4]]
    >>> np.pad(a, ((3, 2), (2, 3)), 'minimum')
    array([[1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [3, 3, 3, 4, 3, 3, 3],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1]])
    >>> a = [1, 2, 3, 4, 5]
    >>> np.pad(a, (2, 3), 'reflect')
    array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])
    >>> np.pad(a, (2, 3), 'symmetric')
    array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])
    >>> a = np.arange(6)
    >>> a = a.reshape((2, 3))
    >>> np.pad(a, ((2, 2), (2, 2)), pad_with)
    array([[10, 10, 10, 10, 10, 10, 10],
           [10, 10, 10, 10, 10, 10, 10],
           [10, 10,  0,  1,  2, 10, 10],
           [10, 10,  3,  4,  5, 10, 10],
           [10, 10, 10, 10, 10, 10, 10],
           [10, 10, 10, 10, 10, 10, 10]])
    """
    return _mx_nd_np.pad(x, pad_width=pad_width, mode=mode, **kwargs)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def prod(a, axis=None, dtype=None, out=None, keepdims=False, initial=None): # pylint: disable=too-many-arguments
    """
    Return the product of array elements over a given axis.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a product is performed.  The default,
        axis=None, will calculate the product of all the elements in the
        input array. If axis is negative it counts from the last to the
        first axis.
        .. versionadded:: 1.7.0
        If axis is a tuple of ints, a product is performed on all of the
        axes specified in the tuple instead of a single axis or all the
        axes as before.
    dtype : dtype, optional
        The type of the returned array, as well as of the accumulator in
        which the elements are multiplied.  The dtype of `a` is used by
        default unless `a` has an integer dtype of less precision than the
        default platform integer.  In that case, if `a` is signed then the
        platform integer is used while if `a` is unsigned then an unsigned
        integer of the same precision as the platform integer is used.
    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 output
        values will be cast if necessary.
    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 `prod` 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.
    initial : scalar, optional
        The starting value for this product. See `~numpy.ufunc.reduce` for details.
    where : not supported

    Returns
    -------
    product_along_axis : ndarray, see `dtype` parameter above.
        An array shaped as `a` but with the specified axis removed.
        Returns a reference to `out` if specified.

    Examples
    --------
    By default, calculate the product of all elements:
    >>> np.prod([1.,2.])
    2.0
    Even when the input array is two-dimensional:
    >>> np.prod([[1.,2.],[3.,4.]])
    24.0
    But we can also specify the axis over which to multiply:
    >>> np.prod([[1.,2.],[3.,4.]], axis=1)
    array([  2.,  12.])
    Or select specific elements to include:
    >>> np.prod([1., np.nan, 3.], where=[True, False, True])
    3.0
    If the type of `x` is unsigned, then the output type is
    the unsigned platform integer:
    >>> x = np.array([1, 2, 3], dtype=np.uint8)
    >>> np.prod(x).dtype == np.uint
    True
    If `x` is of a signed integer type, then the output type
    is the default platform integer:
    >>> x = np.array([1, 2, 3], dtype=np.int8)
    >>> np.prod(x).dtype == int
    True
    You can also start the product with a value other than one:
    >>> np.prod([1, 2], initial=5)
    10
    """
    return _mx_nd_np.prod(a, axis=axis, dtype=dtype, keepdims=keepdims, initial=initial, out=out)

@set_module('mxnet.numpy')
def dot(a, b, out=None):
    """
    Dot product of two arrays. Specifically,

    * If both `a` and `b` are 1-D arrays, it is inner product of vectors

    * If both `a` and `b` are 2-D arrays, it is matrix multiplication,

    * If either `a` or `b` is 0-D (scalar), it is equivalent to :func:`multiply`
      and using ``np.multiply(a, b)`` or ``a * b`` is preferred.

    * If `a` is an N-D array and `b` is a 1-D array, it is a sum product over
      the last axis of `a` and `b`.

    * If `a` is an N-D array and `b` is a 2-D array, it is a
      sum product over the last axis of `a` and the second-to-last axis of `b`::

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

    Parameters
    ----------
    a : ndarray
        First argument.
    b : ndarray
        Second argument.

    out : ndarray, optional
        Output argument. It must have the same shape and type as the expected output.

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

    Examples
    --------
    >>> a = np.array(3)
    >>> b = np.array(4)
    >>> np.dot(a, b)
    array(12.)

    For 2-D arrays it is the matrix product:

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

    >>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
    >>> b = np.arange(5*6)[::-1].reshape((6,5))
    >>> np.dot(a, b)[2,3,2,2]
    array(29884.)
    >>> np.sum(a[2,3,2,:] * b[:,2])
    array(29884.)
    """
    return _mx_nd_np.dot(a, b, out=out)

# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def cumsum(a, axis=None, dtype=None, out=None):
    """
    Return the cumulative sum of the elements along a given axis.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative sum is computed. The default
        (None) is to compute the cumsum over the flattened array.
    dtype : dtype, optional
        Type of the returned array and of the accumulator in which the
        elements are summed.  If `dtype` is not specified, it defaults
        to the dtype of `a`, unless `a` has an integer dtype with a
        precision less than that of the default platform integer.  In
        that case, the default platform integer is used.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type will be cast if necessary. See `doc.ufuncs`
        (Section "Output arguments") for more details.

    Returns
    -------
    cumsum_along_axis : ndarray.
        A new array holding the result is returned unless `out` is
        specified, in which case a reference to `out` is returned. The
        result has the same size as `a`, and the same shape as `a` if
        `axis` is not None or `a` is a 1-d array.

    Examples
    --------
    >>> a = np.array([[1,2,3], [4,5,6]])
    >>> a
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> np.cumsum(a)
    array([ 1,  3,  6, 10, 15, 21])
    >>> np.cumsum(a, dtype=float)     # specifies type of output value(s)
    array([  1.,   3.,   6.,  10.,  15.,  21.])
    >>> np.cumsum(a,axis=0)      # sum over rows for each of the 3 columns
    array([[1, 2, 3],
           [5, 7, 9]])
    >>> np.cumsum(a,axis=1)      # sum over columns for each of the 2 rows
    array([[ 1,  3,  6],
           [ 4,  9, 15]])
    """
    return _mx_nd_np.cumsum(a, axis=axis, dtype=dtype, out=out)

@set_module('mxnet.numpy')
def reshape(a, newshape, order='C'):
    """
    Gives a new shape to an array without changing its data.
    This function always returns a copy of the input array if
    ``out`` is not provided.

    Parameters
    ----------
    a : ndarray
        Array to be reshaped.

    newshape : int or tuple of ints
        The new shape should be compatible with the original shape. If
        an integer, then the result will be a 1-D array of that length.
        One shape dimension can be -1. In this case, the value is
        inferred from the length of the array and remaining dimensions.

    order : {'C'}, optional
        Read the elements of `a` using this index order, and place the
        elements into the reshaped array using this index order.  'C'
        means to read / write the elements using C-like index order,
        with the last axis index changing fastest, back to the first
        axis index changing slowest. Other order types such as 'F'/'A'
        may be added in the future.

    Returns
    -------
    reshaped_array : ndarray
        It will be always a copy of the original array. This behavior is different
        from the official NumPy ``reshape`` operator where views of the original array may be
        generated.

    See Also
    --------
    ndarray.reshape : Equivalent method.

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

    >>> np.reshape(a, (2, 3)) # C-like index ordering
    array([[0., 1., 2.],
           [3., 4., 5.]])

    >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
    array([[0., 1., 2.],
           [3., 4., 5.]])

    >>> a = np.array([[1,2,3], [4,5,6]])
    >>> np.reshape(a, 6)
    array([1., 2., 3., 4., 5., 6.])

    >>> np.reshape(a, (3,-1))       # the unspecified value is inferred to be 2
    array([[1., 2.],
           [3., 4.],
           [5., 6.]])
    """
    return _mx_nd_np.reshape(a, newshape, order)

@set_module('mxnet.numpy')
def moveaxis(a, source, destination):
    """Move axes of an array to new positions.
    Other axes remain in their original order.

    Parameters
    ----------
    a : ndarray
        The array whose axes should be reordered.
        source : int or sequence of int
        Original positions of the axes to move. These must be unique.
        destination : int or sequence of int
        Destination positions for each of the original axes. These must also be
        unique.

    Returns
    -------
    result : ndarray
        Array with moved axes. This array is a view of the input array.

    See Also
    --------
        transpose: Permute the dimensions of an array.
        swapaxes: Interchange two axes of an array.

    Examples
    --------
    >>> x = np.zeros((3, 4, 5))
    >>> np.moveaxis(x, 0, -1).shape
    (4, 5, 3)
    >>> np.moveaxis(x, -1, 0).shape
    (5, 3, 4)
    These all achieve the same result:
    >>> np.transpose(x).shape
    (5, 4, 3)
    >>> np.swapaxes(x, 0, -1).shape
    (5, 4, 3)
    >>> np.moveaxis(x, [0, 1], [-1, -2]).shape
    (5, 4, 3)
    >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape
    (5, 4, 3)
    """
    return _mx_nd_np.moveaxis(a, source, destination)

@set_module('mxnet.numpy')
def copy(a): # pylint: disable=redefined-outer-name
    """
    Return an array copy of the given object.

    Parameters
    ----------
    a : _Symbol
        Input array.

    Returns
    -------
    arr : _Symbol
        Array interpretation of a.

    -----
    Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> y = x
    >>> z = np.copy(x)
    >>> x[0] = 10
    >>> x[0] == y[0]
        True
    >>> x[0] == z[0]
        False
    """
    return _mx_nd_np.copy(a)

# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def rollaxis(a, axis, start=0):
    """
    Roll the specified axis backwards, until it lies in a given position.

    Parameters
    ----------
    a : ndarray
        Input array.
    axis : integer
        The axis to roll backwards. The positions of the other axes do not
        change relative to one another.
    start: int, optional
        The axis is rolled until it lies before this position.
        The default, 0, results in a “complete” roll.

    Returns
    -------
    res : ndarray
        A view after applying rollaxis to `a` is returned.

    -----
    Examples
    --------
    >>> a = np.ones((3,4,5,6))
    >>> np.rollaxis(a, 3, 1).shape
    (3, 6, 4, 5)
    >>> np.rollaxis(a, 2).shape
    (5, 3, 4, 6)
    >>> np.rollaxis(a, 1, 4).shape
    (3, 5, 6, 4)
    """
    return _mx_nd_np.rollaxis(a, axis, start)


@set_module('mxnet.numpy')
def diag(v, k=0):
    """
    Extracts a diagonal or constructs a diagonal array.
    * 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
    * 2-D arrays: extracts the k-th Diagonal

    Parameters
    ----------
    array : ndarray
        The array to apply diag method.
    k : offset
        extracts or constructs kth diagonal given input array

    Returns
    ----------
    out : ndarray
    The extracted diagonal or constructed diagonal array.

    Examples
    --------
    >>> x = np.arange(9).reshape((3,3))
    >>> x
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])
    >>> np.diag(x)
    array([0, 4, 8])
    >>> np.diag(x, k=1)
    array([1, 5])
    >>> np.diag(x, k=-1)
    array([3, 7])

    >>> np.diag(np.diag(x))
    array([[0, 0, 0],
           [0, 4, 0],
           [0, 0, 8]])
    """
    return _mx_nd_np.diag(v, k=k)


@set_module('mxnet.numpy')
def diagflat(v, k=0):
    """
    Create a two-dimensional array with the flattened input as a diagonal.

    Parameters
    ----------
    v : array_like
        Input data, which is flattened and set as the `k`-th
        diagonal of the output.
    k : int, optional
        Diagonal to set; 0, the default, corresponds to the "main" diagonal,
        a positive (negative) `k` giving the number of the diagonal above
        (below) the main.

    Returns
    -------
    out : ndarray
        The 2-D output array.

    See Also
    --------
    diag : MATLAB work-alike for 1-D and 2-D arrays.
    diagonal : Return specified diagonals.
    trace : Sum along diagonals.

    Examples
    --------
    >>> np.diagflat([[1,2], [3,4]])
    array([[1, 0, 0, 0],
           [0, 2, 0, 0],
           [0, 0, 3, 0],
           [0, 0, 0, 4]])
    >>> np.diagflat([1,2], 1)
    array([[0, 1, 0],
           [0, 0, 2],
           [0, 0, 0]])
    """
    return _mx_nd_np.diagflat(v, k=k)


@set_module('mxnet.numpy')
def diagonal(a, offset=0, axis1=0, axis2=1):
    """
    If a is 2-D, returns the diagonal of a with the given offset, i.e., the collection of elements of
    the form a[i, i+offset]. If a has more than two dimensions, then the axes specified by axis1 and
    axis2 are used to determine the 2-D sub-array whose diagonal is returned. The shape of the
    resulting array can be determined by removing axis1 and axis2 and appending an index to the
    right equal to the size of the resulting diagonals.

    Parameters
    ----------
    a : ndarray
        Input data from which diagonal are taken.
    offset: int, Optional
        Offset of the diagonal from the main diagonal
    axis1: int, Optional
        Axis to be used as the first axis of the 2-D sub-arrays
    axis2: int, Optional
        Axis to be used as the second axis of the 2-D sub-arrays

    Returns
    -------
    out : ndarray
        Output result

    Raises
    -------
    ValueError:  If the dimension of a is less than 2.

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

    >>> a = np.arange(8).reshape(2,2,2)
    >>>a
    array([[[0, 1],
            [2, 3]],
            [[4, 5],
            [6, 7]]])
    >>> np.diagonal(a, 0, 0, 1)
    array([[0, 6],
            [1, 7]])
    """
    return _mx_nd_np.diagonal(a, offset=offset, axis1=axis1, axis2=axis2)


# pylint: disable=redefined-outer-name, too-many-arguments
@set_module('mxnet.numpy')
def sum(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None):
    r"""
    Sum of array elements over a given axis.

    Parameters
    ----------
    a : ndarray
        Input data.
    axis : None or int, optional
        Axis or axes along which a sum is performed.  The default,
        axis=None, will sum all of the elements of the input array.  If
        axis is negative it counts from the last to the first axis.
    dtype : dtype, optional
        The type of the returned array and of the accumulator in which the
        elements are summed. The default type is float32.
    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 `sum` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-classes `sum` method does not implement `keepdims` any
        exceptions will be raised.
    initial: Currently only supports None as input, optional
        Starting value for the sum.
        Currently not implemented. Please use ``None`` as input or skip this argument.
    out : ndarray or None, optional
        Alternative output array in which to place the result. It must have
        the same shape and dtype as the expected output.

    Returns
    -------
    sum_along_axis : ndarray
        An ndarray with the same shape as `a`, with the specified
        axis removed. If an output array is specified, a reference to
        `out` is returned.

    Notes
    -----
    * Input type does not support Python native iterables.
    * "out" param: cannot perform auto type change. out ndarray's dtype must be the same as the expected output.
    * "initial" param is not supported yet. Please use None as input.
    * Arithmetic is modular when using integer types, and no error is raised on overflow.
    * The sum of an empty array is the neutral element 0:

    >>> a = np.empty(1)
    >>> np.sum(a)
    array(0.)

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

    * Input type does not support Python native iterables(list, tuple, ...).
    * "out" param: cannot perform auto type cast. out ndarray's dtype must be the same as the expected output.
    * "initial" param is not supported yet. Please use ``None`` as input or skip it.
    * The default type is float32.

    Examples
    --------
    >>> a = np.array([0.5, 1.5])
    >>> np.sum(a)
    array(2.)
    >>> a = np.array([0.5, 0.7, 0.2, 1.5])
    >>> np.sum(a, dtype=np.int32)
    array(2, dtype=int32)
    >>> a = np.array([[0, 1], [0, 5]])
    >>> np.sum(a)
    array(6.)
    >>> np.sum(a, axis=0)
    array([0., 6.])
    >>> np.sum(a, axis=1)
    array([1., 5.])

    With output ndarray:

    >>> a = np.array([[0, 1], [0, 5]])
    >>> b = np.ones((2,), dtype=np.float32)
    >>> np.sum(a, axis = 0, out=b)
    array([0., 6.])
    >>> b
    array([0., 6.])

    If the accumulator is too small, overflow occurs:

    >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
    array(-128, dtype=int8)
    """
    return _mx_nd_np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims, initial=initial, where=where)


@set_module('mxnet.numpy')
def bitwise_left_shift(x1, x2, out=None):
    r"""
    Shift the bits of and integer to the left. Bits are shifted to the left by
    appending x2 0s at the right of x1. Since the internal representation of numbers
    is in binary format, this operation is equivalent to ``x1 * 2**x2``

    Parameters
    ----------
    x1 : ndarray or scalar
        Input values.
    x2 : ndarray or scalar
        Number of zeros to append to x1. Has to be non-negative. 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.binary_repr(5)
    '101'
    >>> np.left_shift(5, 2)
    20
    >>> np.binary_repr(20)
    '10100'
    """
    return _mx_nd_np.bitwise_left_shift(x1, x2, out)


@set_module('mxnet.numpy')
def bitwise_right_shift(x1, x2, out=None):
    r"""
    Shift the bits of and integer to the right. Bits are shifted to the right by
    x2. Because the internal representation of numbers is in binary format,
    this operation is equivalent to ``x1 / 2**x2``

    Parameters
    ----------
    x1 : ndarray or scalar
        Input values.
    x1 : ndarray or scalar
        Number of bits to remove at the right of x1. 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.binary_repr(10)
    '1010'
    >>> np.right_shift(10, 1)
    5
    >>> np.binary_repr(5)
    '101'
    >>> np.right_shift(10, np.array([1,2,3]))
    array([5, 2, 1])
    """
    return _mx_nd_np.bitwise_right_shift(x1, x2, out)


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
@wrap_ctx_to_device_func
def asarray(obj, dtype=None, device=None, copy=None):
    """
    Convert the input to an array.

    Parameters
    ----------
    obj : <array>, bool, int, float, NestedSequence[ bool | int | float ]
        Object to be converted to an array. Can be a Python scalar,
        a (possibly nested) sequence of Python scalars,
        or an object supporting DLPack or the Python buffer protocol.
    dtype : dtype, Optional
        output array data type. Default: None .
    device : Device, optional
        Device context on which the memory is allocated. Default is
        `mxnet.device.current_device()`.
    copy : bool, Optional
        Whether or not to make a copy of the input.
        If True, always copies.
        If False, never copies for input which supports DLPack or the buffer protocol,
        and raises ValueError in case that would be necessary.
        If None, reuses existing memory buffer if possible, copies otherwise. Default: None .

        An array containing the data from obj.

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

    >>> np.asarray([[1, 2], [3, 4]], dtype=np.int32)
    array([[1, 2],
           [3, 4]], dtype=int32)

    >>> np.asarray([1.2], device=mx.gpu())
    array([1.2], device=gpu(0))
    """
    if isinstance(obj, numeric_types):
        dtype = dtype_from_number(obj) if dtype is None else dtype
        obj = _np.asarray(obj, dtype=dtype)
    elif isinstance(obj, _np.ndarray):
        if is_np_default_dtype():
            dtype = obj.dtype if dtype is None else dtype
        else:
            dtype = _np.float32 if dtype is None or obj.dtype is _np.float64 else dtype
    elif isinstance(obj, ndarray):
        if dtype is not None:
            obj = obj.astype(dtype, copy=copy)
        if device is not None:
            obj = obj.to_device(device)
        return obj
    elif hasattr(obj, '__dlpack__'):
        return from_dlpack(obj)
    else:
        if dtype is None:
            default_dtype = _np.float64 if is_np_default_dtype() else _np.float32
            dtype = obj.dtype if hasattr(obj, "dtype") else default_dtype
        try:
            obj = _np.array(obj, 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)))
    if device is None:
        device = current_device()
    ret = empty(obj.shape, dtype=dtype, device=device)
    if len(obj.shape) == 0:
        ret[()] = obj
    else:
        ret[:] = obj
    return ret


# pylint: disable=redefined-outer-name
@set_module('mxnet.numpy')
def from_dlpack(x):
    """
    Returns a np.ndarray backed by a dlpack tensor.

    Parameters
    ----------
    dlpack : an object with __dlpack__ method or PyCapsule (the pointer of DLManagedTensor)
        input data

    Returns
    -------
    out : np.ndarray
        an ndarray backed by a dlpack tensor

    Examples
    --------
    >>> x = mx.np.ones((2,3))
    >>> y = mx.np.from_dlpack(x)
    >>> y
    array([[1., 1., 1.],
           [1., 1., 1.]])
    >>> y += 1
    >>> x
    array([[2., 2., 2.],
           [2., 2., 2.]])
    """
    from_dlpack = ndarray_from_dlpack(ndarray)
    return from_dlpack(x)