manipulation.py

#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed 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.

from __future__ import print_function

from ..fluid.layers import core
from ..fluid.layer_helper import LayerHelper
from ..fluid.framework import Variable, OpProtoHolder, in_dygraph_mode, convert_np_dtype_to_dtype_, device_guard, dygraph_only
from ..fluid.data_feeder import convert_dtype, check_variable_and_dtype, check_type, check_dtype
from ..fluid.layers.tensor import fill_constant
from ..fluid.layers import utils
import numpy as np
# TODO: define functions to manipulate a tensor  
from ..fluid.layers import cast  # noqa: F401
from ..fluid.layers import slice  # noqa: F401
from ..fluid.layers import transpose  # noqa: F401
from ..fluid.layers import unstack  # noqa: F401

from ..fluid.layers import scatter_nd  # noqa: F401
from ..fluid.layers import shard_index  # noqa: F401
from ..fluid.layers.nn import _elementwise_op_in_dygraph
from ..fluid import layers
from ..fluid.dygraph.inplace_utils import inplace_apis_in_dygraph_only
import paddle
from paddle import _C_ops

__all__ = []


@dygraph_only
def fill_(x, value):
    """
    **Notes**:
        **This API is ONLY available in Dygraph mode**

    This function fill the Tensor with value inplace.

    Args:
        x(Tensor): ``x`` is the Tensor we want to filled data inplace
        value(Scale): ``value`` is the value to be filled in x

    Returns:
        x(Tensor): Tensor x filled with value inplace

    Examples:
        .. code-block:: python

            import paddle

            tensor = paddle.to_tensor([0, 1, 2, 3, 4])

            tensor.fill_(0)
            print(tensor.tolist())   #[0, 0, 0, 0, 0]

    """
    if not isinstance(value, (float, int)):
        raise TypeError(
            "The type of 'value'  must be int or float, but received %s." %
            (type(value)))
    return core.ops.fill_any_(x, "value_float",
                              float(value), "value_int", int(value))


setattr(core.VarBase, 'fill_', fill_)


@dygraph_only
def zero_(x):
    """
    **Notes**:
        **This API is ONLY available in Dygraph mode**

    This function fill the Tensor with zero inplace.

    Args:
        x(Tensor): ``x`` is the Tensor we want to filled with zero inplace

    Returns:
        x(Tensor): Tensor x filled with zero inplace

    Examples:
        .. code-block:: python

            import paddle

            tensor = paddle.to_tensor([0, 1, 2, 3, 4])

            tensor.zero_()
            print(tensor.tolist())   #[0, 0, 0, 0, 0]

    """
    return core.ops.fill_any_(x, "value_float", 0., "value_int", int(0))


setattr(core.VarBase, 'zero_', zero_)


@dygraph_only
def fill_diagonal_(x, value, offset=0, wrap=False, name=None):
    """
    **Notes**:
        **This API is ONLY available in Dygraph mode**
    This function fill the value into the x Tensor's diagonal inplace.
    Args:
        x(Tensor): ``x`` is the original Tensor
        value(Scale): ``value`` is the value to filled in x
        offset(int,optional): the offset to the main diagonal. Default: 0 (main diagonal).
        wrap(bool,optional): the diagonal 'wrapped' after N columns for tall matrices.
        name(str,optional): Name for the operation (optional, default is None)
    Returns:
        Tensor: Tensor with diagonal filled with value.
    Returns type:
        dtype is same as x Tensor
    Examples:
        .. code-block:: python
            import paddle
            x = paddle.ones((4, 3)) * 2
            x.fill_diagonal_(1.0)
            print(x.tolist())   #[[1.0, 2.0, 2.0], [2.0, 1.0, 2.0], [2.0, 2.0, 1.0], [2.0, 2.0, 2.0]]
    """
    helper = LayerHelper("fill_diagonal_", **locals())
    check_type(x, 'X', (Variable), 'fill_diagonal_')
    dtype = helper.input_dtype('x')
    check_dtype(dtype, 'X',
                ['bool', 'float16', 'float32', 'float64', 'int32', 'int64'],
                'fill_diagonal_')
    check_type(value, 'value', (bool, int, float), 'fill_diagonal_')
    check_type(wrap, 'wrap', (bool), 'fill_diagonal_')

    inshape = x.shape
    inshapeset = set(inshape)
    assert len(inshape) >= 2, ('Tensor dims should >= 2 in fill_diagonal_ API')
    if len(inshape) > 2:
        assert len(inshapeset) == 1, (
            'Tensor dims should be equal while input dims > 2 in fill_diagonal_ API'
        )
    if len(inshape) == 2:
        return core.ops.fill_diagonal_(x, 'value', value, 'offset', offset,
                                       'wrap', wrap)
    return core.ops.fill_diagonal_(x, 'value', value, 'offset', offset, 'wrap',
                                   True)


setattr(core.VarBase, 'fill_diagonal_', fill_diagonal_)


def _fill_diagonal_tensor_impl(x, y, offset=0, dim1=0, dim2=1, inplace=False):
    inshape = x.shape
    assert dim1 < len(inshape) and dim1 >= -len(inshape), (
        'dim1 should between [-rank,rank) in fill_diagonal_tensor_')
    assert dim2 < len(inshape) and dim2 >= -len(inshape), (
        'dim2 should between [-rank,rank) in fill_diagonal_tensor_')
    assert len(inshape) >= 2, (
        'Tensor dims should >= 2 in fill_diagonal_tensor_')
    dim1 %= len(inshape)
    dim2 %= len(inshape)

    predshape = []
    for i in range(len(inshape)):
        if i != dim1 and i != dim2:
            predshape.append(inshape[i])
    diaglen = min(
        min(inshape[dim1], inshape[dim1] + offset),
        min(inshape[dim2], inshape[dim2] - offset))
    predshape.append(diaglen)
    assert tuple(predshape) == tuple(y.shape), (
        "the y shape should be {}".format(predshape))
    if len(y.shape) == 1:
        y = y.reshape([1, -1])

    if inplace:
        return core.ops.fill_diagonal_tensor_(x, y, 'dim1', dim1, 'dim2', dim2,
                                              'offset', offset)
    return core.ops.fill_diagonal_tensor(x, y, 'dim1', dim1, 'dim2', dim2,
                                         'offset', offset)


def fill_diagonal_tensor_(x, y, offset=0, dim1=0, dim2=1, name=None):
    """
    **Notes**:
        **This API is ONLY available in Dygraph mode**

    This function fill the source Tensor y into the x Tensor's diagonal inplace.

    Args:
        x(Tensor): ``x`` is the original Tensor
        y(Tensor): ``y`` is the Tensor to filled in x
        dim1(int,optional): first dimension with respect to which to fill diagonal. Default: 0.
        dim2(int,optional): second dimension with respect to which to fill diagonal. Default: 1.
        offset(int,optional): the offset to the main diagonal. Default: 0 (main diagonal).
        name(str,optional): Name for the operation (optional, default is None)

    Returns:
        Tensor: Tensor with diagonal filled with y.

    Returns type:
        list: dtype is same as x Tensor

    Examples:
        .. code-block:: python

            import paddle

            x = paddle.ones((4, 3)) * 2
            y = paddle.ones((3,))
            x.fill_diagonal_tensor_(y)
            print(x.tolist())   #[[1.0, 2.0, 2.0], [2.0, 1.0, 2.0], [2.0, 2.0, 1.0], [2.0, 2.0, 2.0]]

    """
    return _fill_diagonal_tensor_impl(
        x, y, offset=offset, dim1=dim1, dim2=dim2, inplace=True)


setattr(core.VarBase, 'fill_diagonal_tensor_', fill_diagonal_tensor_)


def fill_diagonal_tensor(x, y, offset=0, dim1=0, dim2=1, name=None):
    """
    This function fill the source Tensor y into the x Tensor's diagonal.

    Args:
        x(Tensor): ``x`` is the original Tensor
        y(Tensor): ``y`` is the Tensor to filled in x
        dim1(int,optional): first dimension with respect to which to fill diagonal. Default: 0.
        dim2(int,optional): second dimension with respect to which to fill diagonal. Default: 1.
        offset(int,optional): the offset to the main diagonal. Default: 0 (main diagonal).
        name(str,optional): Name for the operation (optional, default is None)

    Returns:
        Tensor: Tensor with diagonal filled with y.

    Returns type:
        list: dtype is same as x Tensor

    Examples:
        .. code-block:: python

            import paddle

            x = paddle.ones((4, 3)) * 2
            y = paddle.ones((3,))
            nx = x.fill_diagonal_tensor(y)
            print(nx.tolist())   #[[1.0, 2.0, 2.0], [2.0, 1.0, 2.0], [2.0, 2.0, 1.0], [2.0, 2.0, 2.0]]

    """
    return _fill_diagonal_tensor_impl(
        x, y, offset=offset, dim1=dim1, dim2=dim2, inplace=False)


setattr(core.VarBase, 'fill_diagonal_tensor', fill_diagonal_tensor)


@dygraph_only
def tolist(x):
    """
    **Notes**:
        **This API is ONLY available in Dygraph mode**

    This function translate the paddle.Tensor to python list.

    Args:
        x(Tensor): ``x`` is the Tensor we want to translate to list

    Returns:
        list: A list that contain the same value of current Tensor.

    Returns type:
        list: dtype is same as current Tensor

    Examples:
        .. code-block:: python

            import paddle

            t = paddle.to_tensor([0,1,2,3,4])
            expectlist = t.tolist()
            print(expectlist)   #[0, 1, 2, 3, 4]

            expectlist = paddle.tolist(t)
            print(expectlist)   #[0, 1, 2, 3, 4]

    """
    return x.numpy().tolist()


setattr(core.VarBase, 'tolist', tolist)


def concat(x, axis=0, name=None):
    """

    This OP concatenates the input along the axis.

    Args:
        x(list|tuple): ``x`` is a Tensor list or Tensor tuple which is with data type bool, float16,
            float32, float64, int32, int64, uint8. All the Tensors in ``x`` must have same data type.
        axis(int|Tensor, optional): Specify the axis to operate on the input Tensors.
            It's a scalar with data type int or a Tensor with shape [1] and data type int32 
            or int64. The effective range is [-R, R), where R is Rank(x). When ``axis < 0``,
            it works the same way as ``axis+R``. Default is 0.
        name (str, optional): The default value is None. Normally there is no
            need for user to set this property. For more information, please
            refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: A Tensor with the same data type as ``x``.

    Examples:
        .. code-block:: python
            
            import paddle
            
            x1 = paddle.to_tensor([[1, 2, 3],
                                   [4, 5, 6]])
            x2 = paddle.to_tensor([[11, 12, 13],
                                   [14, 15, 16]])
            x3 = paddle.to_tensor([[21, 22],
                                   [23, 24]])
            zero = paddle.full(shape=[1], dtype='int32', fill_value=0)
            # When the axis is negative, the real axis is (axis + Rank(x))
            # As follow, axis is -1, Rank(x) is 2, the real axis is 1
            out1 = paddle.concat(x=[x1, x2, x3], axis=-1)
            out2 = paddle.concat(x=[x1, x2], axis=0)
            out3 = paddle.concat(x=[x1, x2], axis=zero)
            # out1
            # [[ 1  2  3 11 12 13 21 22]
            #  [ 4  5  6 14 15 16 23 24]]
            # out2 out3
            # [[ 1  2  3]
            #  [ 4  5  6]
            #  [11 12 13]
            #  [14 15 16]]
    """
    return paddle.fluid.layers.concat(input=x, axis=axis, name=name)


def broadcast_tensors(input, name=None):
    """
    This OP broadcast a list of tensors following broadcast semantics

    .. note::
        If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting`.

    Args:
        input(list|tuple): ``input`` is a Tensor list or Tensor tuple which is with data type bool,
            float16, float32, float64, int32, int64. All the Tensors in ``input`` must have same data type.
            Currently we only support tensors with rank no greater than 5.

        name (str, optional): The default value is None. Normally there is no need for user to set this property. 
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        list(Tensor): The list of broadcasted tensors following the same order as ``input``.

    Examples:
        .. code-block:: python

            import paddle
            x1 = paddle.rand([1, 2, 3, 4]).astype('float32')
            x2 = paddle.rand([1, 2, 1, 4]).astype('float32')
            x3 = paddle.rand([1, 1, 3, 1]).astype('float32')
            out1, out2, out3 = paddle.broadcast_tensors(input=[x1, x2, x3])
            # out1, out2, out3: tensors broadcasted from x1, x2, x3 with shape [1,2,3,4]
    """

    num_inputs = len(input)
    if in_dygraph_mode():
        return _C_ops.broadcast_tensors(input, num_inputs)

    check_type(input, 'input', (list, tuple), 'broadcast_tensors')
    if num_inputs < 1:
        raise TypeError(
            "At least 1 tensor is needed to perform broadcast_tensors")

    # Check input types
    for id, x in enumerate(input):
        check_variable_and_dtype(
            x, 'input[' + str(id) + ']',
            ['bool', 'float32', 'float64', 'int32', 'int64'],
            'broadcast_tensors')
        if x.dtype != input[0].dtype:
            raise TypeError(
                "All the Tensors in the input must have the same data type.")

    # Check bcast semantics
    output_shape_r_last_tensor_index = []
    output_shape_r = []

    # Use while loop due to weird behaviour of "range()"
    j = 0
    while j < len(input):
        tensor = input[j]
        shape = list(reversed(tensor.shape))

        i = 0
        while i < len(shape):
            if len(output_shape_r) <= i:
                output_shape_r.append(shape[i])
                output_shape_r_last_tensor_index.append(j)
            else:
                invalid = (output_shape_r[i] != shape[i] and
                           output_shape_r[i] != 1 and shape[i] != 1)
                if invalid:
                    last_index = output_shape_r_last_tensor_index[i]
                    raise TypeError(
                        "Input tensors to broadcast_tensors does not follow bcast semantics"
                        "Tensor {last_index} conflicts with Tensor {j} in reversed dimension {i}"
                    )
                if output_shape_r[i] <= shape[i]:
                    output_shape_r[i] = shape[i]
                    output_shape_r_last_tensor_index[i] = j
            i += 1  # while i < len(shape)
        j += 1  # while j < len(input)

    helper = LayerHelper('broadcast_tensors', **locals())
    i = 0
    out = []
    while i < num_inputs:
        out.append(
            helper.create_variable_for_type_inference(dtype=helper.input_dtype(
            )))
        i += 1

    inputs = {'X': input}
    helper.append_op(
        type='broadcast_tensors', inputs=inputs, outputs={'Out': out},
        attrs={})

    return out


def flip(x, axis, name=None):
    """
    Reverse the order of a n-D tensor along given axis in axis.

    Args:
        x (Tensor): A Tensor(or LoDTensor) with shape :math:`[N_1, N_2,..., N_k]` . The data type of the input Tensor x
            should be float32, float64, int32, int64, bool.
        axis (list|tuple|int): The axis(axes) to flip on. Negative indices for indexing from the end are accepted.
        name (str, optional): The default value is None.  Normally there is no need for user to set this property.
            For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        Tensor: Tensor or LoDTensor calculated by flip layer. The data type is same with input x.

    Examples:
        .. code-block:: python

          import paddle
          import numpy as np

          image_shape=(3, 2, 2)
          x = np.arange(image_shape[0] * image_shape[1] * image_shape[2]).reshape(image_shape)
          x = x.astype('float32')
          img = paddle.to_tensor(x)
          tmp = paddle.flip(img, [0,1])
          print(tmp) # [[[10,11],[8, 9]], [[6, 7],[4, 5]], [[2, 3],[0, 1]]]

          out = paddle.flip(tmp,-1)
          print(out) # [[[11,10],[9, 8]], [[7, 6],[5, 4]], [[3, 2],[1, 0]]]
    """
    if isinstance(axis, int):
        axis = [axis]
    if in_dygraph_mode():
        return core.ops.flip(x, "axis", axis)

    helper = LayerHelper("flip", **locals())
    check_type(x, 'X', (Variable), 'flip')
    dtype = helper.input_dtype('x')
    check_dtype(dtype, 'X',
                ['float16', 'float32', 'float64', 'int32', 'int64', 'bool'],
                'flip')
    check_type(axis, 'axis', (list, tuple), 'flip')
    if name is None:
        out = helper.create_variable_for_type_inference(dtype)
    else:
        out = helper.create_variable(name=name, dtype=dtype, persistable=False)

    helper.append_op(
        type="flip",
        inputs={"X": x},
        outputs={"Out": out},
        attrs={"axis": axis})
    return out


def flatten(x, start_axis=0, stop_axis=-1, name=None):
    r"""
    **Flatten op**

    Flattens a contiguous range of axes in a tensor according to start_axis and stop_axis.

    Note that the output Tensor will share data with origin Tensor and doesn't have a 
    Tensor copy in ``dygraph`` mode. If you want to use the Tensor copy version, please 
    use `Tensor.clone` like ``flatten_clone_x = x.flatten().clone()``.

    For Example:

    .. code-block:: text

        Case 1:

          Given
            X.shape = (3, 100, 100, 4)

          and
            start_axis = 1
            end_axis = 2

          We get:
            Out.shape = (3, 1000 * 100, 2)

        Case 2:

          Given
            X.shape = (3, 100, 100, 4)

          and
            start_axis = 0
            stop_axis = -1

          We get:
            Out.shape = (3 * 100 * 100 * 4)

    Args:
        x (Tensor): A tensor of number of dimentions >= axis. A tensor with data type float32,
                      float64, int8, int32, int64, uint8.
        start_axis (int): the start axis to flatten
        stop_axis (int): the stop axis to flatten
        name(str, Optional): For details, please refer to :ref:`api_guide_Name`.
                        Generally, no setting is required. Default: None.

    Returns:
        Tensor: A tensor with the contents of the input tensor, with input \
                  axes flattened by indicated start axis and end axis. \
                  A Tensor with data type same as input x.

    Raises:
        ValueError: If x is not a Tensor.
        ValueError: If start_axis or stop_axis is illegal.

    Examples:

        .. code-block:: python

            import paddle

            image_shape=(2, 3, 4, 4)

            x = paddle.arange(end=image_shape[0] * image_shape[1] * image_shape[2] * image_shape[3])
            img = paddle.reshape(x, image_shape)

            out = paddle.flatten(img, start_axis=1, stop_axis=2)
            # out shape is [2, 12, 4]

            # out shares data with img in dygraph mode
            img[0, 0, 0, 0] = -1
            print(out[0, 0, 0]) # [-1]
    """
    if not (isinstance(x, Variable)):
        raise ValueError("The input x should be a Tensor")

    if not in_dygraph_mode():
        check_variable_and_dtype(
            x, 'x', ['float32', 'float64', 'int8', 'int32', 'int64', 'uint8'],
            'flatten')

    x_dim = len(x.shape)
    if not (isinstance(start_axis, int)) or (
            start_axis > x_dim - 1) or start_axis < -x_dim:
        raise ValueError(
            "The start_axis should be a int, and in range [-rank(x), rank(x))")
    if not (isinstance(stop_axis, int)) or (
            stop_axis > x_dim - 1) or stop_axis < -x_dim:
        raise ValueError(
            "The stop_axis should be a int, and in range [-rank(x), rank(x))")
    if start_axis < 0:
        start_axis = start_axis + x_dim
    if stop_axis < 0:
        stop_axis = stop_axis + x_dim
    if start_axis > stop_axis:
        raise ValueError("The stop_axis should be larger than stat_axis")

    if in_dygraph_mode():
        dy_out, _ = _C_ops.flatten_contiguous_range(x, 'start_axis', start_axis,
                                                    'stop_axis', stop_axis)
        return dy_out

    helper = LayerHelper('flatten', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    x_shape = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='flatten_contiguous_range',
        inputs={"X": x},
        outputs={'Out': out,
                 'XShape': x_shape},
        attrs={"start_axis": start_axis,
               "stop_axis": stop_axis})
    return out


@inplace_apis_in_dygraph_only
def flatten_(x, start_axis=0, stop_axis=-1, name=None):
    """
    Inplace version of ``flatten`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_tensor_flatten`.
    """
    if not (isinstance(x, Variable)):
        raise ValueError("The input x should be a Tensor")

    x_dim = len(x.shape)
    if not (isinstance(start_axis, int)) or (
            start_axis > x_dim - 1) or start_axis < -x_dim:
        raise ValueError(
            "The start_axis should be a int, and in range [-rank(x), rank(x))")
    if not (isinstance(stop_axis, int)) or (
            stop_axis > x_dim - 1) or stop_axis < -x_dim:
        raise ValueError(
            "The stop_axis should be a int, and in range [-rank(x), rank(x))")
    if start_axis < 0:
        start_axis = start_axis + x_dim
    if stop_axis < 0:
        stop_axis = stop_axis + x_dim
    if start_axis > stop_axis:
        raise ValueError("The stop_axis should be larger than stat_axis")

    dy_out, _ = _C_ops.flatten_contiguous_range_(x, 'start_axis', start_axis,
                                                 'stop_axis', stop_axis)
    return dy_out


def roll(x, shifts, axis=None, name=None):
    """
    Roll the `x` tensor along the given axis(axes). With specific 'shifts', Elements that 
    roll beyond the last position are re-introduced at the first according to 'shifts'. 
    If a axis is not specified, 
    the tensor will be flattened before rolling and then restored to the original shape.

    Args:
        x (Tensor): The x tensor as input.
        shifts (int|list|tuple): The number of places by which the elements
                           of the `x` tensor are shifted.
        axis (int|list|tuple|None): axis(axes) along which to roll.

    Returns:
        Tensor: A Tensor with same data type as `x`.

    Examples:
        .. code-block:: python
            
            import paddle

            x = paddle.to_tensor([[1.0, 2.0, 3.0],
                                  [4.0, 5.0, 6.0],
                                  [7.0, 8.0, 9.0]])
            out_z1 = paddle.roll(x, shifts=1)
            print(out_z1)
            #[[9. 1. 2.]
            # [3. 4. 5.]
            # [6. 7. 8.]]
            out_z2 = paddle.roll(x, shifts=1, axis=0)
            print(out_z2)
            #[[7. 8. 9.]
            # [1. 2. 3.]
            # [4. 5. 6.]]
    """
    origin_shape = x.shape
    if type(shifts) == int:
        shifts = [shifts]
    if type(axis) == int:
        axis = [axis]

    len_origin_shape = len(origin_shape)
    if axis is not None:
        for i in range(len(axis)):
            if axis[i] >= len_origin_shape or axis[i] < -len_origin_shape:
                raise ValueError(
                    "axis is out of range, it should be in range [{}, {}), but received {}".
                    format(-len_origin_shape, len_origin_shape, axis))
    else:
        axis = []

    if in_dygraph_mode():
        return _C_ops.roll(x, 'axis', axis, 'shifts', shifts)

    helper = LayerHelper("roll", **locals())
    check_type(axis, 'axis', (list, tuple), 'roll')
    check_type(shifts, 'shifts', (list, tuple), 'roll')
    out = helper.create_variable_for_type_inference(x.dtype)

    helper.append_op(
        type='roll',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'axis': axis,
               'shifts': shifts})
    return out


def stack(x, axis=0, name=None):
    """
    This OP stacks all the input tensors ``x`` along ``axis`` dimemsion. 
    All tensors must be of the same shape and same dtype.
    
    For example, given N tensors of shape [A, B], if ``axis == 0``, the shape of stacked 
    tensor is [N, A, B]; if ``axis == 1``, the shape of stacked 
    tensor is [A, N, B], etc.
    

    .. code-block:: text

        Case 1:

          Input:
            x[0].shape = [1, 2]
            x[0].data = [ [1.0 , 2.0 ] ]
            x[1].shape = [1, 2]
            x[1].data = [ [3.0 , 4.0 ] ]
            x[2].shape = [1, 2]
            x[2].data = [ [5.0 , 6.0 ] ]

          Attrs:
            axis = 0

          Output:
            Out.dims = [3, 1, 2]
            Out.data =[ [ [1.0, 2.0] ],
                        [ [3.0, 4.0] ],
                        [ [5.0, 6.0] ] ]


        Case 2:

          Input:
            x[0].shape = [1, 2]
            x[0].data = [ [1.0 , 2.0 ] ]
            x[1].shape = [1, 2]
            x[1].data = [ [3.0 , 4.0 ] ]
            x[2].shape = [1, 2]
            x[2].data = [ [5.0 , 6.0 ] ]


          Attrs:
            axis = 1 or axis = -2  # If axis = -2, axis = axis+ndim(x[0])+1 = -2+2+1 = 1.

          Output:
            Out.shape = [1, 3, 2]
            Out.data =[ [ [1.0, 2.0]
                          [3.0, 4.0]
                          [5.0, 6.0] ] ]

    Args:
        x (list[Tensor]|tuple[Tensor]): Input ``x`` can be a ``list`` or ``tuple`` of tensors, the Tensors in ``x``
                                     must be of the same shape and dtype. Supported data types: float32, float64, int32, int64.
        axis (int, optional): The axis along which all inputs are stacked. ``axis`` range is ``[-(R+1), R+1)``,
                              where ``R`` is the number of dimensions of the first input tensor ``x[0]``. 
                              If ``axis < 0``, ``axis = axis+R+1``. The default value of axis is 0.
        name (str, optional): Please refer to :ref:`api_guide_Name`, Default None.
        
    Returns:
        Tensor: The stacked tensor with same data type as input.

    Example:    
        .. code-block:: python

            import paddle
            
            x1 = paddle.to_tensor([[1.0, 2.0]])
            x2 = paddle.to_tensor([[3.0, 4.0]])
            x3 = paddle.to_tensor([[5.0, 6.0]])
            out = paddle.stack([x1, x2, x3], axis=0)
            print(out.shape)  # [3, 1, 2]
            print(out)
            # [[[1., 2.]],
            #  [[3., 4.]],
            #  [[5., 6.]]]
    """
    return layers.stack(x, axis, name)


def split(x, num_or_sections, axis=0, name=None):
    """
    Split the input tensor into multiple sub-Tensors.
    
    Args:
        x (Tensor): A N-D Tensor. The data type is bool, float16, float32, float64, int32 or int64.
        num_or_sections (int|list|tuple): If ``num_or_sections`` is an int, then ``num_or_sections`` 
            indicates the number of equal sized sub-Tensors that the ``x`` will be divided into.
            If ``num_or_sections`` is a list or tuple, the length of it indicates the number of
            sub-Tensors and the elements in it indicate the sizes of sub-Tensors'  dimension orderly.
            The length of the list must not  be larger than the ``x`` 's size of specified ``axis``.
        axis (int|Tensor, optional): The axis along which to split, it can be a scalar with type 
            ``int`` or a ``Tensor`` with shape [1] and data type  ``int32`` or ``int64``.
            If :math::`axis < 0`, the axis to split along is :math:`rank(x) + axis`. Default is 0.
        name (str, optional): The default value is None.  Normally there is no need for user to set this property.
            For more information, please refer to :ref:`api_guide_Name` .
    Returns:
        list(Tensor): The list of segmented Tensors.
    
    Example:
        .. code-block:: python
            
            import paddle
            
            # x is a Tensor of shape [3, 9, 5]
            x = paddle.rand([3, 9, 5])

            out0, out1, out2 = paddle.split(x, num_or_sections=3, axis=1)
            print(out0.shape)  # [3, 3, 5]
            print(out1.shape)  # [3, 3, 5]
            print(out2.shape)  # [3, 3, 5]

            out0, out1, out2 = paddle.split(x, num_or_sections=[2, 3, 4], axis=1)
            print(out0.shape)  # [3, 2, 5]
            print(out1.shape)  # [3, 3, 5]
            print(out2.shape)  # [3, 4, 5]

            out0, out1, out2 = paddle.split(x, num_or_sections=[2, 3, -1], axis=1)
            print(out0.shape)  # [3, 2, 5]
            print(out1.shape)  # [3, 3, 5]
            print(out2.shape)  # [3, 4, 5]
            
            # axis is negative, the real axis is (rank(x) + axis)=1
            out0, out1, out2 = paddle.split(x, num_or_sections=3, axis=-2)
            print(out0.shape)  # [3, 3, 5]
            print(out1.shape)  # [3, 3, 5]
            print(out2.shape)  # [3, 3, 5]
    """
    return paddle.fluid.layers.split(
        input=x, num_or_sections=num_or_sections, dim=axis, name=name)


def squeeze(x, axis=None, name=None):
    """
    This OP will squeeze the dimension(s) of size 1 of input tensor x's shape. 
    
    Note that the output Tensor will share data with origin Tensor and doesn't have a 
    Tensor copy in ``dygraph`` mode. If you want to use the Tensor copy version, 
    please use `Tensor.clone` like ``squeeze_clone_x = x.squeeze().clone()``.

    If axis is provided, it will remove the dimension(s) by given axis that of size 1. 
    If the dimension of given axis is not of size 1, the dimension remain unchanged. 
    If axis is not provided, all dims equal of size 1 will be removed.

    .. code-block:: text

        Case1:

          Input:
            x.shape = [1, 3, 1, 5]  # If axis is not provided, all dims equal of size 1 will be removed.
            axis = None
          Output:
            out.shape = [3, 5]

        Case2:

          Input:
            x.shape = [1, 3, 1, 5]  # If axis is provided, it will remove the dimension(s) by given axis that of size 1.
            axis = 0
          Output:
            out.shape = [3, 1, 5]
        
        Case4:

          Input:
            x.shape = [1, 3, 1, 5]  # If the dimension of one given axis (3) is not of size 1, the dimension remain unchanged. 
            axis = [0, 2, 3]
          Output:
            out.shape = [3, 5]

        Case4:

          Input:
            x.shape = [1, 3, 1, 5]  # If axis is negative, axis = axis + ndim (number of dimensions in x). 
            axis = [-2]
          Output:
            out.shape = [1, 3, 5]

    Args:
        x (Tensor): The input Tensor. Supported data type: float32, float64, bool, int8, int32, int64.
        axis (int|list|tuple, optional): An integer or list/tuple of integers, indicating the dimensions to be squeezed. Default is None.
                          The range of axis is :math:`[-ndim(x), ndim(x))`.
                          If axis is negative, :math:`axis = axis + ndim(x)`.
                          If axis is None, all the dimensions of x of size 1 will be removed.
        name (str, optional): Please refer to :ref:`api_guide_Name`, Default None.

    Returns:
        Tensor: Squeezed Tensor with the same data type as input Tensor.

    Examples:
        .. code-block:: python

            import paddle
            
            x = paddle.rand([5, 1, 10])
            output = paddle.squeeze(x, axis=1)

            print(x.shape)  # [5, 1, 10]
            print(output.shape)  # [5, 10]

            # output shares data with x in dygraph mode
            x[0, 0, 0] = 10.
            print(output[0, 0]) # [10.]

    """
    if axis is None:
        axis = []
    elif isinstance(axis, int):
        axis = [axis]
    elif isinstance(axis, tuple):
        axis = list(axis)

    return layers.squeeze(x, axis, name)


@inplace_apis_in_dygraph_only
def squeeze_(x, axis=None, name=None):
    """
    Inplace version of ``squeeze`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_paddle_tensor_squeeze`.
    """
    if axis is None:
        axis = []
    elif isinstance(axis, int):
        axis = [axis]
    elif isinstance(axis, tuple):
        axis = list(axis)

    out, _ = _C_ops.squeeze2_(x, 'axes', axis)
    return out


def unique_consecutive(x,
                       return_inverse=False,
                       return_counts=False,
                       axis=None,
                       dtype="int64",
                       name=None):
    r"""
    Eliminates all but the first element from every consecutive group of equivalent elements.

    .. note:: This function is different from :func:`paddle.unique` in the sense that this function
        only eliminates consecutive duplicate values. This semantics is similar to `std::unique` in C++.

    Args:
        x(Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        return_inverse(bool, optional): If True, also return the indices for where elements in
            the original input ended up in the returned unique consecutive tensor. Default is False.
        return_counts(bool, optional): If True, also return the counts for each unique consecutive element.
            Default is False.
        axis(int, optional): The axis to apply unique consecutive. If None, the input will be flattened.
            Default is None.
        dtype(np.dtype|str, optional): The data type `inverse` tensor: int32 or int64.
            Default: int64.
        name(str, optional): Name for the operation. For more information, please refer to
            :ref:`api_guide_Name`. Default is None.

    Returns:
        tuple: (out, inverse, counts). `out` is the unique consecutive tensor for `x`. `inverse` is provided only if `return_inverse` is True. `counts` is provided only if `return_counts` is True.

    Example:
        .. code-block:: python

            import paddle 

            x = paddle.to_tensor([1, 1, 2, 2, 3, 1, 1, 2])
            output = paddle.unique_consecutive(x) # 
            np_output = output.numpy() # [1 2 3 1 2]
            _, inverse, counts = paddle.unique_consecutive(x, return_inverse=True, return_counts=True)
            np_inverse = inverse.numpy() # [0 0 1 1 2 3 3 4]
            np_counts = inverse.numpy() # [2 2 1 2 1]

            x = paddle.to_tensor([[2, 1, 3], [3, 0, 1], [2, 1, 3], [2, 1, 3]])
            output = paddle.unique_consecutive(x, axis=0) # 
            np_output = output.numpy() # [2 1 3 0 1 2 1 3 2 1 3]

            x = paddle.to_tensor([[2, 1, 3], [3, 0, 1], [2, 1, 3], [2, 1, 3]])
            output = paddle.unique_consecutive(x, axis=0) # 
            np_output = output.numpy()
            # [[2 1 3]
            #  [3 0 1]
            #  [2 1 3]]
    """

    if axis is None:
        axis = []
    else:
        axis = [axis]
    attr_dtype = convert_np_dtype_to_dtype_(dtype)
    if in_dygraph_mode():
        out, inverse, counts = core.ops.unique_consecutive(
            x, 'dtype', attr_dtype, 'return_inverse', return_inverse,
            'return_counts', return_counts, 'axis', axis)
        outs = [out]
        if return_inverse:
            outs.append(inverse)
        if return_counts:
            outs.append(counts)
        if len(outs) == 1:
            return outs[0]
        return tuple(outs)
    check_variable_and_dtype(x, "input",
                             ['float32', 'float64', 'int32', 'int64'],
                             'unique_consecutive')
    check_type(return_inverse, 'return_inverse', bool, 'unique_consecutive')
    check_type(return_counts, 'return_counts', bool, 'unique_consecutive')
    check_dtype(dtype, 'dtype', ['int32', 'int64'], 'unique_consecutive')
    if len(axis) != 0:
        check_type(axis[0], 'axis', int, 'unique_consecutive')
    helper = LayerHelper('unique_consecutive', **locals())
    attrs = {
        'dtype': attr_dtype,
        "return_inverse": return_inverse,
        "return_counts": return_counts,
        "axis": axis,
    }
    out = helper.create_variable_for_type_inference(
        dtype=x.dtype, stop_gradient=True)
    inverse = helper.create_variable_for_type_inference(
        dtype=attr_dtype, stop_gradient=True)
    counts = helper.create_variable_for_type_inference(
        dtype=attr_dtype, stop_gradient=True)
    outputs = {"Out": out, "Index": inverse, "Counts": counts}
    outs = [out]
    if return_inverse:
        outs.append(inverse)
    if return_counts:
        outs.append(counts)
    helper.append_op(
        type="unique_consecutive",
        inputs={"X": x},
        attrs=attrs,
        outputs=outputs)
    if len(outs) == 1:
        return outs[0]
    return tuple(outs)


def unique(x,
           return_index=False,
           return_inverse=False,
           return_counts=False,
           axis=None,
           dtype="int64",
           name=None):
    r"""
    Returns the unique elements of `x` in ascending order.

    Args:
        x(Tensor): The input tensor, it's data type should be float32, float64, int32, int64.
        return_index(bool, optional): If True, also return the indices of the input tensor that
            result in the unique Tensor.
        return_inverse(bool, optional): If True, also return the indices for where elements in
            the original input ended up in the returned unique tensor.
        return_counts(bool, optional): If True, also return the counts for each unique element.
        axis(int, optional): The axis to apply unique. If None, the input will be flattened.
            Default: None.
        dtype(np.dtype|str, optional): The date type of `indices` or `inverse` tensor: int32 or int64.
            Default: int64.
        name(str, optional): Name for the operation. For more information, please refer to
            :ref:`api_guide_Name`. Default: None.

    Returns: 
        tuple: (out, indices, inverse, counts). `out` is the unique tensor for `x`. `indices` is \
            provided only if `return_index` is True. `inverse` is provided only if `return_inverse` \
            is True. `counts` is provided only if `return_counts` is True.

    Examples:
        .. code-block:: python

            import paddle

            x = paddle.to_tensor([2, 3, 3, 1, 5, 3])
            unique = paddle.unique(x)
            np_unique = unique.numpy() # [1 2 3 5]
            _, indices, inverse, counts = paddle.unique(x, return_index=True, return_inverse=True, return_counts=True)
            np_indices = indices.numpy() # [3 0 1 4]
            np_inverse = inverse.numpy() # [1 2 2 0 3 2]
            np_counts = counts.numpy() # [1 1 3 1]

            x = paddle.to_tensor([[2, 1, 3], [3, 0, 1], [2, 1, 3]])
            unique = paddle.unique(x)
            np_unique = unique.numpy() # [0 1 2 3]

            unique = paddle.unique(x, axis=0)
            np_unique = unique.numpy() 
            # [[2 1 3]
            #  [3 0 1]]
    """
    if axis is None:
        axis = []
    else:
        axis = [axis]
    attr_dtype = convert_np_dtype_to_dtype_(dtype)
    if in_dygraph_mode():
        out, inverse, indices, counts = _C_ops.unique(
            x, 'dtype', attr_dtype, 'return_index', return_index,
            'return_inverse', return_inverse, 'return_counts', return_counts,
            'axis', axis, "is_sorted", True)
        outs = [out]
        if return_index:
            outs.append(indices)
        if return_inverse:
            outs.append(inverse)
        if return_counts:
            outs.append(counts)

        if len(outs) == 1:
            return outs[0]

        return tuple(outs)

    check_variable_and_dtype(x, "input",
                             ['float32', 'float64', 'int32', 'int64'], 'unique')
    check_type(return_index, 'return_index', bool, 'unique')
    check_type(return_inverse, 'return_inverse', bool, 'unique')
    check_type(return_counts, 'return_counts', bool, 'unique')
    check_dtype(dtype, 'dtype', ['int32', 'int64'], 'unique')
    if len(axis) != 0:
        check_type(axis[0], 'axis', int, 'unique')

    helper = LayerHelper('unique', **locals())
    attrs = {
        'dtype': attr_dtype,
        "return_index": return_index,
        "return_inverse": return_inverse,
        "return_counts": return_counts,
        "axis": axis,
        "is_sorted": True
    }
    out = helper.create_variable_for_type_inference(
        dtype=x.dtype, stop_gradient=True)
    indices = helper.create_variable_for_type_inference(
        dtype=attr_dtype, stop_gradient=True)
    inverse = helper.create_variable_for_type_inference(
        dtype=attr_dtype, stop_gradient=True)
    counts = helper.create_variable_for_type_inference(
        dtype=attr_dtype, stop_gradient=True)
    outputs = {
        "Out": out,
        "Indices": indices,
        "Index": inverse,
        "Counts": counts
    }
    outs = [out]
    if return_index:
        outs.append(indices)
    if return_inverse:
        outs.append(inverse)
    if return_counts:
        outs.append(counts)

    helper.append_op(
        type="unique", inputs={"X": x}, attrs=attrs, outputs=outputs)

    if len(outs) == 1:
        return outs[0]

    return tuple(outs)


def unsqueeze(x, axis, name=None):
    """
    Insert single-dimensional entries to the shape of input Tensor ``x``. Takes one
    required argument axis, a dimension or list of dimensions that will be inserted.
    Dimension indices in axis are as seen in the output tensor.

    Note that the output Tensor will share data with origin Tensor and doesn't have a 
    Tensor copy in ``dygraph`` mode. If you want to use the Tensor copy version, 
    please use `Tensor.clone` like ``unsqueeze_clone_x = x.unsqueeze(-1).clone()``.

    Args:
        x (Tensor): The input Tensor to be unsqueezed. Supported data type: float32, float64, bool, int8, int32, int64.
        axis (int|list|tuple|Tensor): Indicates the dimensions to be inserted. The data type is ``int32`` . 
                                    If ``axis`` is a list or tuple, the elements of it should be integers or Tensors with shape [1]. 
                                    If ``axis`` is a Tensor, it should be an 1-D Tensor .
                                    If ``axis`` is negative, ``axis = axis + ndim(x) + 1``.
        name (str|None): Name for this layer. Please refer to :ref:`api_guide_Name`, Default None.

    Returns:
        Tensor: Unsqueezed Tensor with the same data type as input Tensor.

    Examples:
        .. code-block:: python

            import paddle

            x = paddle.rand([5, 10])
            print(x.shape)  # [5, 10]
            
            out1 = paddle.unsqueeze(x, axis=0)
            print(out1.shape)  # [1, 5, 10]
            
            out2 = paddle.unsqueeze(x, axis=[0, 2]) 
            print(out2.shape)  # [1, 5, 1, 10]

            axis = paddle.to_tensor([0, 1, 2])
            out3 = paddle.unsqueeze(x, axis=axis) 
            print(out3.shape)  # [1, 1, 1, 5, 10]

            # out1, out2, out3 share data with x in dygraph mode
            x[0, 0] = 10.
            print(out1[0, 0, 0]) # [10.]
            print(out2[0, 0, 0, 0]) # [10.]
            print(out3[0, 0, 0, 0, 0]) # [10.]
            
    """

    return layers.unsqueeze(x, axis, name)


@inplace_apis_in_dygraph_only
def unsqueeze_(x, axis, name=None):
    """
    Inplace version of ``unsqueeze`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_paddle_tensor_unsqueeze`.
    """
    if isinstance(axis, int):
        axis = [axis]
    elif isinstance(axis, Variable):
        axis = axis.numpy().tolist()
    elif isinstance(axis, (list, tuple)):
        axis = [
            item.numpy().item(0) if isinstance(item, Variable) else item
            for item in axis
        ]
    out, _ = _C_ops.unsqueeze2_(x, 'axes', axis)
    return out


def gather(x, index, axis=None, name=None):
    """
    Output is obtained by gathering entries of ``axis``
    of ``x`` indexed by ``index`` and concatenate them together.

    .. code-block:: text


                Given:

                x = [[1, 2],
                     [3, 4],
                     [5, 6]]

                index = [1, 2]
                axis=[0]

                Then:

                out = [[3, 4],
                       [5, 6]] 

    Args:
        x (Tensor): The source input tensor with rank>=1. Supported data type is
            int32, int64, float32, float64 and uint8 (only for CPU),
            float16 (only for GPU).
        index (Tensor): The index input tensor with rank=1. Data type is int32 or int64.
        axis (Tensor|int, optional): The axis of input to be gathered, it's can be int or a Tensor with data type is int32 or int64. The default value is None, if None, the ``axis`` is 0.
        name (str, optional): The default value is None.  Normally there is no need for user to set this property.
            For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        output (Tensor): The output is a tensor with the same rank as ``x``.
    
    Examples:

        .. code-block:: python

            import paddle

            input = paddle.to_tensor([[1,2],[3,4],[5,6]])
            index = paddle.to_tensor([0,1])
            output = paddle.gather(input, index, axis=0)
            # expected output: [[1,2],[3,4]]
    """
    if axis is None:
        axis = 0

    if in_dygraph_mode():
        axis = axis.item() if isinstance(axis, paddle.Tensor) else axis
        return _C_ops.gather(x, index, None, "axis", axis, "overwrite", False)

    check_variable_and_dtype(
        x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64', 'uint8'],
        'gather')
    check_variable_and_dtype(index, 'index', ['int32', 'int64'], 'gather')

    if isinstance(axis, Variable):
        check_variable_and_dtype(axis, 'axis', ['int32', 'int64'], 'gather')

    helper = LayerHelper('gather', **locals())
    dtype = helper.input_dtype('x')
    out = helper.create_variable_for_type_inference(dtype)
    if not isinstance(axis, Variable):
        helper.append_op(
            type="gather",
            inputs={"X": x,
                    "Index": index},
            attrs={'axis': axis,
                   'overwrite': False},
            outputs={"Out": out})
    else:
        helper.append_op(
            type="gather",
            inputs={"X": x,
                    "Index": index,
                    "Axis": axis},
            attrs={"overwrite": False},
            outputs={"Out": out})

    return out


def unbind(input, axis=0):
    """

    Removes a tensor dimension, then split the input tensor into multiple sub-Tensors.

    Args:
        input (Tensor): The input variable which is an N-D Tensor, data type being float32, float64, int32 or int64.
        axis (int32|int64, optional): A scalar with type ``int32|int64`` shape [1]. The dimension along which to unbind. 
            If :math:`axis < 0`, the dimension to unbind along is :math:`rank(input) + axis`. Default is 0.
    Returns:
        list(Tensor): The list of segmented Tensor variables.

    Example:
        .. code-block:: python

            import paddle
            import numpy as np
            # input is a variable which shape is [3, 4, 5]
            np_input = np.random.rand(3, 4, 5).astype('float32')
            input = paddle.to_tensor(np_input)
            [x0, x1, x2] = paddle.unbind(input, axis=0)
            # x0.shape [4, 5]
            # x1.shape [4, 5]
            # x2.shape [4, 5]
            [x0, x1, x2, x3] = paddle.unbind(input, axis=1)
            # x0.shape [3, 5]
            # x1.shape [3, 5]
            # x2.shape [3, 5]
            # x3.shape [3, 5]

    """
    if not isinstance(axis, (int)):
        raise TypeError("The type of 'axis'  must be int, but received %s." %
                        (type(axis)))
    if isinstance(axis, np.generic):
        axis = np.asscalar(axis)
    input_shape = input.shape
    axis_ = axis if axis >= 0 else len(input_shape) + axis
    num = input_shape[axis_]
    if in_dygraph_mode():
        return _C_ops.unbind(input, num, 'axis', axis)

    helper = LayerHelper("unbind", **locals())
    check_type(input, 'input', (Variable), 'unbind')
    dtype = helper.input_dtype()
    check_dtype(dtype, 'unbind', ['float32', 'float64', 'int32', 'int64'],
                'unbind')
    outs = [
        helper.create_variable_for_type_inference(dtype=helper.input_dtype())
        for i in range(num)
    ]
    helper.append_op(
        type="unbind",
        inputs={"X": input},
        outputs={"Out": outs},
        attrs={"axis": axis})
    return outs


def scatter(x, index, updates, overwrite=True, name=None):
    """
    **Scatter Layer**
    Output is obtained by updating the input on selected indices based on updates.
    
    .. code-block:: python
    
        import numpy as np
        #input:
        x = np.array([[1, 1], [2, 2], [3, 3]])
        index = np.array([2, 1, 0, 1])
        # shape of updates should be the same as x
        # shape of updates with dim > 1 should be the same as input
        updates = np.array([[1, 1], [2, 2], [3, 3], [4, 4]])
        overwrite = False
        # calculation:
        if not overwrite:
            for i in range(len(index)):
                x[index[i]] = np.zeros((2))
        for i in range(len(index)):
            if (overwrite):
                x[index[i]] = updates[i]
            else:
                x[index[i]] += updates[i]
        # output:
        out = np.array([[3, 3], [6, 6], [1, 1]])
        out.shape # [3, 2]

    **NOTICE**: The order in which updates are applied is nondeterministic, 
    so the output will be nondeterministic if index contains duplicates.

    Args:
        x (Tensor): The input N-D Tensor with ndim>=1. Data type can be float32, float64.
        index (Tensor): The index 1-D Tensor. Data type can be int32, int64. The length of index cannot exceed updates's length, and the value in index cannot exceed input's length.
        updates (Tensor): update input with updates parameter based on index. shape should be the same as input, and dim value with dim > 1 should be the same as input.
        overwrite (bool): The mode that updating the output when there are same indices. 
            
            If True, use the overwrite mode to update the output of the same index,
	        if False, use the accumulate mode to update the output of the same index.Default value is True.
        
        name(str, optional): The default value is None. Normally there is no need for user to set this property.  For more information, please refer to :ref:`api_guide_Name` .
 
    Returns:
        Tensor: The output is a Tensor with the same shape as x.

    Examples:
        .. code-block:: python
            
            import paddle

            x = paddle.to_tensor([[1, 1], [2, 2], [3, 3]], dtype='float32')
            index = paddle.to_tensor([2, 1, 0, 1], dtype='int64')
            updates = paddle.to_tensor([[1, 1], [2, 2], [3, 3], [4, 4]], dtype='float32')
  
            output1 = paddle.scatter(x, index, updates, overwrite=False)
            # [[3., 3.],
            #  [6., 6.],
            #  [1., 1.]]

            output2 = paddle.scatter(x, index, updates, overwrite=True)
            # CPU device:
            # [[3., 3.],
            #  [4., 4.],
            #  [1., 1.]]
            # GPU device maybe have two results because of the repeated numbers in index
            # result 1:
            # [[3., 3.],
            #  [4., 4.],
            #  [1., 1.]]
            # result 2:
            # [[3., 3.],
            #  [2., 2.],
            #  [1., 1.]]
    """
    if in_dygraph_mode():
        return _C_ops.scatter(x, index, updates, 'overwrite', overwrite)

    check_variable_and_dtype(x, 'dtype', ['float32', 'float64'], 'scatter')
    check_type(overwrite, 'overwrite', bool, 'scatter')
    helper = LayerHelper('scatter', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type="scatter",
        inputs={"X": x,
                "Ids": index,
                "Updates": updates},
        attrs={'overwrite': overwrite},
        outputs={"Out": out})
    return out


@inplace_apis_in_dygraph_only
def scatter_(x, index, updates, overwrite=True, name=None):
    """
    Inplace version of ``scatter`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_paddle_tensor_scatter`.
    """
    return _C_ops.scatter_(x, index, updates, 'overwrite', overwrite)


def scatter_nd_add(x, index, updates, name=None):
    r"""
    **Scatter_nd_add Layer**

    Output is obtained by applying sparse addition to a single value
    or slice in a Tensor.

    :attr:`x` is a Tensor with ndim :math:`R`
    and :attr:`index` is a Tensor with ndim :math:`K` . Thus, :attr:`index`
    has shape :math:`[i_0, i_1, ..., i_{K-2}, Q]` where :math:`Q \leq R` . :attr:`updates`
    is a Tensor with ndim :math:`K - 1 + R - Q` and its
    shape is :math:`index.shape[:-1] + x.shape[index.shape[-1]:]` .

    According to the :math:`[i_0, i_1, ..., i_{K-2}]` of :attr:`index` ,
    add the corresponding :attr:`updates` slice to the :attr:`x` slice
    which is obtained by the last one dimension of :attr:`index` .

    .. code-block:: text

        Given:

        * Case 1:
            x = [0, 1, 2, 3, 4, 5]
            index = [[1], [2], [3], [1]]
            updates = [9, 10, 11, 12]

          we get:

            output = [0, 22, 12, 14, 4, 5]

        * Case 2:
            x = [[65, 17], [-14, -25]]
            index = [[], []]
            updates = [[[-1, -2], [1, 2]],
                       [[3, 4], [-3, -4]]]
            x.shape = (2, 2)
            index.shape = (2, 0)
            updates.shape = (2, 2, 2)

          we get:

            output = [[67, 19], [-16, -27]]

    Args:
        x (Tensor): The x input. Its dtype should be int32, int64, float32, float64.
        index (Tensor): The index input with ndim > 1 and index.shape[-1] <= x.ndim.
                          Its dtype should be int32 or int64 as it is used as indexes.
        updates (Tensor): The updated value of scatter_nd_add op, and it must have the same dtype
                            as x. It must have the shape index.shape[:-1] + x.shape[index.shape[-1]:].
        name (str|None): The output tensor name. If set None, the layer will be named automatically.

    Returns:
        output (Tensor): The output is a tensor with the same shape and dtype as x.

    Examples:

        .. code-block:: python

            import paddle
            import numpy as np

            x = paddle.rand(shape=[3, 5, 9, 10], dtype='float32')
            updates = paddle.rand(shape=[3, 9, 10], dtype='float32')
            index_data = np.array([[1, 1],
                                   [0, 1],
                                   [1, 3]]).astype(np.int64)
            index = paddle.to_tensor(index_data)
            output = paddle.scatter_nd_add(x, index, updates)
    """
    return layers.scatter_nd_add(x, index, updates, name=None)


def chunk(x, chunks, axis=0, name=None):
    """
    Split the input tensor into multiple sub-Tensors.
    
    Args:
        x (Tensor): A N-D Tensor. The data type is bool, float16, float32, float64, int32 or int64.
        chunks(int): The number of tensor to be split along the certain axis.
        axis (int|Tensor, optional): The axis along which to split, it can be a scalar with type 
            ``int`` or a ``Tensor`` with shape [1] and data type  ``int32`` or ``int64``.
            If :math::`axis < 0`, the axis to split along is :math:`rank(x) + axis`. Default is 0.
        name (str, optional): The default value is None.  Normally there is no need for user to set this property.
            For more information, please refer to :ref:`api_guide_Name` .
    Returns:
        list(Tensor): The list of segmented Tensors.
    
    Example:
        .. code-block:: python
            
            import numpy as np
            import paddle
            
            # x is a Tensor which shape is [3, 9, 5]
            x_np = np.random.random([3, 9, 5]).astype("int32")
            x = paddle.to_tensor(x_np)

            out0, out1, out2 = paddle.chunk(x, chunks=3, axis=1)
            # out0.shape [3, 3, 5]
            # out1.shape [3, 3, 5]
            # out2.shape [3, 3, 5]

            
            # axis is negative, the real axis is (rank(x) + axis) which real
            # value is 1.
            out0, out1, out2 = paddle.chunk(x, chunks=3, axis=-2)
            # out0.shape [3, 3, 5]
            # out1.shape [3, 3, 5]
            # out2.shape [3, 3, 5]
    """
    check_type(chunks, 'chunks', (int), 'chunk')
    return paddle.fluid.layers.split(
        input=x, num_or_sections=chunks, dim=axis, name=name)


def tile(x, repeat_times, name=None):
    """

    Construct a new Tensor by repeating ``x`` the number of times given by ``repeat_times``.
    After tiling, the value of the i'th dimension of the output is equal to ``x.shape[i]*repeat_times[i]``.

    Both the number of dimensions of ``x`` and the number of elements in ``repeat_times`` should be less than or equal to 6.

    Args:
        x (Tensor): The input tensor, its data type should be bool, float32, float64, int32 or int64.
        repeat_times (Tensor|tuple|list): The number of repeating times. If repeat_times is a list or tuple, all its elements
            should be integers or 1-D Tensors with the data type int32. If repeat_times is a Tensor, it should be an 1-D Tensor with the data type int32.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        N-D Tensor. The data type is the same as ``x``.

    Examples:
        .. code-block:: python

            import paddle

            data = paddle.to_tensor([1, 2, 3], dtype='int32')
            out = paddle.tile(data, repeat_times=[2, 1])
            np_out = out.numpy()
            # [[1, 2, 3], [1, 2, 3]]

            out = paddle.tile(data, repeat_times=[2, 2])
            np_out = out.numpy()
            # [[1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 2, 3]]

            repeat_times = paddle.to_tensor([2, 1], dtype='int32')
            out = paddle.tile(data, repeat_times=repeat_times)
            np_out = out.numpy()
            # [[1, 2, 3], [1, 2, 3]]
    """
    if in_dygraph_mode():
        return _C_ops.tile(x, 'repeat_times', repeat_times)
    check_type(repeat_times, 'repeat_times', (list, tuple, Variable), 'tile')
    if isinstance(repeat_times, Variable):
        assert len(repeat_times.shape) == 1, (
            'repeat_times must be an 1-D Tensor.')
    else:
        for elem in repeat_times:
            if isinstance(elem, Variable):
                assert len(elem.shape) == 1, (
                    'Elements in repeat_times must be 1-D Tensors or integers.')
            else:
                type_tuple = (int, np.int32, np.int64)
                assert isinstance(elem, type_tuple), (
                    'Elements in repeat_times must be 1-D Tensors or integers.')

    check_variable_and_dtype(
        x, 'x', ['bool', 'float32', 'float64', 'int32', 'int64'], 'tile')
    if convert_dtype(x.dtype) == 'bool' and x.stop_gradient == False:
        raise ValueError(
            "When the date type is bool for the input 'x' of tile op, you "
            "must set its stop_gradient to be True by "
            "some_var.stop_gradient == True supporting some_var is the input.")

    helper = LayerHelper('tile', **locals())

    inputs = {"X": [x]}
    attrs = {}

    def get_attr_repeat_times(list_repeat_times):
        attrs_repeat_times = []
        for idx, times in enumerate(list_repeat_times):
            if isinstance(times, Variable):
                attrs_repeat_times.append(-1)
            else:
                attrs_repeat_times.append(times)
                assert times > 0, (
                    "All elements in repeat_times must be positive for tile.")
        return attrs_repeat_times

    if isinstance(repeat_times, Variable):
        repeat_times.stop_gradient = True
        inputs['RepeatTimes'] = repeat_times
        attrs['repeat_times'] = [-1]
    elif isinstance(repeat_times, (list, tuple)):
        attrs['repeat_times'] = get_attr_repeat_times(repeat_times)
        if utils._contain_var(repeat_times):
            inputs['repeat_times_tensor'] = utils._convert_to_tensor_list(
                repeat_times)

    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(
        type='tile', inputs=inputs, outputs={'Out': out}, attrs=attrs)
    return out


def expand_as(x, y, name=None):
    """

    Expand the input tensor ``x`` to the same shape as the input tensor ``y``.

    Both the number of dimensions of ``x`` and ``y`` must be less than or equal to 6, and the number of dimensions of ``y`` must be greather than or equal to that of ``x``. The dimension to expand must have a value of 1.

    Args:
        x (Tensor): The input tensor, its data type is bool, float32, float64, int32 or int64.
        y (Tensor): The input tensor that gives the shape to expand to.
        name (str, optional): The default value is None. Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        N-D Tensor: A Tensor with the same shape as ``y``. The data type is the same as ``x``.

    Examples:
        .. code-block:: python

            import paddle

            data_x = paddle.to_tensor([1, 2, 3], 'int32')
            data_y = paddle.to_tensor([[1, 2, 3], [4, 5, 6]], 'int32')
            out = paddle.expand_as(data_x, data_y)
            np_out = out.numpy()
            # [[1, 2, 3], [1, 2, 3]]
    """
    if in_dygraph_mode():
        return _C_ops.expand_as_v2(x, 'target_shape', y.shape)

    check_variable_and_dtype(
        x, 'x', ['bool', 'float32', 'float64', 'int32', 'int64'], 'expand_as')
    check_type(y, 'y', Variable, 'expand_as')

    if convert_dtype(x.dtype) == 'bool' and x.stop_gradient == False:
        raise ValueError(
            "When the data type of input 'x' for expand_as is bool, "
            "you must set its stop_gradient to be False by "
            "some_var.stop_gradient = True, supporting "
            "some_var as the input 'x'.")
    inputs = {"X": [x]}

    helper = LayerHelper('expand_as', **locals())
    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(
        type='expand_as_v2',
        inputs=inputs,
        attrs={'target_shape': y.shape},
        outputs={'Out': out})
    return out


def broadcast_to(x, shape, name=None):
    """

    Broadcast the input tensor to a given shape.

    Both the number of dimensions of ``x`` and the number of elements in ``shape`` should be less than or equal to 6. The dimension to broadcast to must have a value 1.


    Args:
        x (Tensor): The input tensor, its data type is bool, float32, float64, int32 or int64.
        shape (list|tuple|Tensor): The result shape after broadcasting. The data type is int32. If shape is a list or tuple, all its elements
            should be integers or 1-D Tensors with the data type int32. If shape is a Tensor, it should be an 1-D Tensor with the data type int32. 
            The value -1 in shape means keeping the corresponding dimension unchanged.
        name (str, optional): The default value is None. Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        N-D Tensor: A Tensor with the given shape. The data type is the same as ``x``.

    Examples:
        .. code-block:: python

            import paddle

            data = paddle.to_tensor([1, 2, 3], dtype='int32')
            out = paddle.broadcast_to(data, shape=[2, 3])
            print(out)
            # [[1, 2, 3], [1, 2, 3]]
    """
    if in_dygraph_mode():
        return _C_ops.expand_v2(x, 'shape', shape)

    if isinstance(shape, Variable):
        assert len(shape.shape) == 1, ('shape must be an 1-D Tensor.')
    else:
        for elem in shape:
            if isinstance(elem, Variable):
                assert len(elem.shape) == 1, (
                    'Elements in shape must be 1-D Tensors or integers.')
            else:
                type_tuple = (int, np.int32, np.int64)
                assert isinstance(elem, type_tuple), (
                    'Elements in shape must be 1-D Tensors or integers.')

    check_variable_and_dtype(x, 'x',
                             ['bool', 'float32', 'float64', 'int32', 'int64'],
                             'broadcast_to')
    check_type(shape, 'shape', (list, tuple, Variable), 'broadcast_to')
    if convert_dtype(x.dtype) == 'bool' and x.stop_gradient == False:
        raise ValueError(
            "When the data type of input 'x' for broadcast_to is bool, "
            "you must set its stop_gradient to be False by "
            "some_var.stop_gradient = True, supporting "
            "some_var as the input.")

    inputs = {"X": [x]}
    attrs = {}

    helper = LayerHelper('expand', **locals())

    def get_attr_expand_shape(list_expand_shape):
        attrs_expand_shape = []
        for idx, shape in enumerate(list_expand_shape):
            if isinstance(shape, Variable):
                attrs_expand_shape.append(-1)
            else:
                attrs_expand_shape.append(shape)
                assert shape > 0 or shape == -1, (
                    "All elements in shape of broadcast_to must be positive or -1."
                )
        return attrs_expand_shape

    if isinstance(shape, Variable):
        shape.stop_gradient = True
        inputs['Shape'] = shape
    elif isinstance(shape, (list, tuple)):
        attrs['shape'] = get_attr_expand_shape(shape)
        if utils._contain_var(shape):
            inputs['expand_shapes_tensor'] = utils._convert_to_tensor_list(
                shape)

    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(
        type='expand_v2', inputs=inputs, outputs={'Out': out}, attrs=attrs)
    return out


def expand(x, shape, name=None):
    """

    Expand the input tensor to a given shape.

    Both the number of dimensions of ``x`` and the number of elements in ``shape`` should be less than or equal to 6. The dimension to expand must have a value 1.


    Args:
        x (Tensor): The input tensor, its data type is bool, float32, float64, int32 or int64.
        shape (list|tuple|Tensor): The result shape after expanding. The data type is int32. If shape is a list or tuple, all its elements
            should be integers or 1-D Tensors with the data type int32. If shape is a Tensor, it should be an 1-D Tensor with the data type int32. 
            The value -1 in shape means keeping the corresponding dimension unchanged.
        name (str, optional): The default value is None. Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        N-D Tensor: A Tensor with the given shape. The data type is the same as ``x``.

    Examples:
        .. code-block:: python

            import paddle

            data = paddle.to_tensor([1, 2, 3], dtype='int32')
            out = paddle.expand(data, shape=[2, 3])
            print(out)
            # [[1, 2, 3], [1, 2, 3]]
    """
    if in_dygraph_mode():
        return _C_ops.expand_v2(x, 'shape', shape)

    if isinstance(shape, Variable):
        assert len(shape.shape) == 1, ('shape must be an 1-D Tensor.')
    else:
        for elem in shape:
            if isinstance(elem, Variable):
                assert len(elem.shape) == 1, (
                    'Elements in shape must be 1-D Tensors or integers.')
            else:
                type_tuple = (int, np.int32, np.int64)
                assert isinstance(elem, type_tuple), (
                    'Elements in shape must be 1-D Tensors or integers.')

    check_variable_and_dtype(
        x, 'x', ['bool', 'float16', 'float32', 'float64', 'int32', 'int64'],
        'expand')
    check_type(shape, 'shape', (list, tuple, Variable), 'expand')
    if convert_dtype(x.dtype) == 'bool' and x.stop_gradient == False:
        raise ValueError("When the data type of input 'x' for expand is bool, "
                         "you must set its stop_gradient to be False by "
                         "some_var.stop_gradient = True, supporting "
                         "some_var as the input.")

    inputs = {"X": [x]}
    attrs = {}

    helper = LayerHelper('expand', **locals())

    def get_attr_expand_shape(list_expand_shape):
        attrs_expand_shape = []
        for idx, shape in enumerate(list_expand_shape):
            if isinstance(shape, Variable):
                attrs_expand_shape.append(-2)
            else:
                attrs_expand_shape.append(shape)
                assert shape > 0 or shape == -1, (
                    "All elements in shape of expand must be positive or -1.")
        return attrs_expand_shape

    if isinstance(shape, Variable):
        shape.stop_gradient = True
        inputs['Shape'] = shape
    elif isinstance(shape, (list, tuple)):
        attrs['shape'] = get_attr_expand_shape(shape)
        if utils._contain_var(shape):
            inputs['expand_shapes_tensor'] = utils._convert_to_tensor_list(
                shape)

    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(
        type='expand_v2', inputs=inputs, outputs={'Out': out}, attrs=attrs)
    return out


def reshape(x, shape, name=None):
    """
    This operator changes the shape of ``x`` without changing its data.

    Note that the output Tensor will share data with origin Tensor and doesn't
    have a Tensor copy in ``dygraph`` mode. 
    If you want to use the Tensor copy version, please use `Tensor.clone` like 
    ``reshape_clone_x = x.reshape([-1]).clone()``.

    Some tricks exist when specifying the target shape.

    1. -1 means the value of this dimension is inferred from the total element
    number of x and remaining dimensions. Thus one and only one dimension can
    be set -1.

    2. 0 means the actual dimension value is going to be copied from the
    corresponding dimension of x. The index of 0s in shape can not exceed
    the dimension of x.

    Here are some examples to explain it.

    1. Given a 3-D tensor x with a shape [2, 4, 6], and the target shape
    is [6, 8], the reshape operator will transform x into a 2-D tensor with
    shape [6, 8] and leaving x's data unchanged.

    2. Given a 3-D tensor x with a shape [2, 4, 6], and the target shape
    specified is [2, 3, -1, 2], the reshape operator will transform x into a
    4-D tensor with shape [2, 3, 4, 2] and leaving x's data unchanged. In this
    case, one dimension of the target shape is set to -1, the value of this
    dimension is inferred from the total element number of x and remaining
    dimensions.

    3. Given a 3-D tensor x with a shape [2, 4, 6], and the target shape
    is [-1, 0, 3, 2], the reshape operator will transform x into a 4-D tensor
    with shape [2, 4, 3, 2] and leaving x's data unchanged. In this case,
    besides -1, 0 means the actual dimension value is going to be copied from
    the corresponding dimension of x.

    Args:
        x(Tensor): An N-D Tensor. The data type is ``float32``, ``float64``, ``int32``, ``int64`` or ``bool``
        shape(list|tuple|Tensor): Define the target shape. At most one dimension of the target shape can be -1.
                        The data type is ``int32`` . If ``shape`` is a list or tuple, the elements of it should be integers or Tensors with shape [1].
                        If ``shape`` is an Tensor, it should be an 1-D Tensor .
        name(str, optional): The default value is None. Normally there is no need for user to set this property.
                            For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        Tensor: A reshaped Tensor with the same data type as ``x``.

    Examples:
        .. code-block:: python

            import numpy as np
            import paddle

            x = paddle.rand([2, 4, 6], dtype="float32")
            positive_four = paddle.full([1], 4, "int32")

            out = paddle.reshape(x, [-1, 0, 3, 2])
            print(out)
            # the shape is [2,4,3,2].

            out = paddle.reshape(x, shape=[positive_four, 12])
            print(out)
            # the shape of out_2 is [4, 12].

            shape_tensor = paddle.to_tensor(np.array([8, 6]).astype("int32"))
            out = paddle.reshape(x, shape=shape_tensor)
            print(out)
            # the shape is [8, 6].
            # out shares data with x in dygraph mode
            x[0, 0, 0] = 10.
            print(out[0, 0])
            # the value is [10.]

    """
    return paddle.fluid.layers.reshape(x=x, shape=shape, name=name)


@inplace_apis_in_dygraph_only
def reshape_(x, shape, name=None):
    """
    Inplace version of ``reshape`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_paddle_tensor_reshape`.
    """
    if isinstance(shape, (list, tuple)):
        shape = [
            item.numpy().item(0) if isinstance(item, Variable) else item
            for item in shape
        ]
        out, _ = _C_ops.reshape2_(x, None, 'shape', shape)
        return out
    elif isinstance(shape, Variable):
        shape.stop_gradient = True
        out, _ = _C_ops.reshape2_(x, shape)
        return out


def gather_nd(x, index, name=None):
    """

    This function is actually a high-dimensional extension of :code:`gather`
    and supports for simultaneous indexing by multiple axes. :attr:`index` is a
    K-dimensional integer tensor, which is regarded as a (K-1)-dimensional
    tensor of :attr:`index` into :attr:`input`, where each element defines
    a slice of params:

    .. math::

        output[(i_0, ..., i_{K-2})] = input[index[(i_0, ..., i_{K-2})]]

    Obviously, :code:`index.shape[-1] <= input.rank` . And, the output tensor has
    shape :code:`index.shape[:-1] + input.shape[index.shape[-1]:]` .

    .. code-block:: text

            Given:
                x =  [[[ 0,  1,  2,  3],
                       [ 4,  5,  6,  7],
                       [ 8,  9, 10, 11]],
                      [[12, 13, 14, 15],
                       [16, 17, 18, 19],
                       [20, 21, 22, 23]]]
                x.shape = (2, 3, 4)

            * Case 1:
                index = [[1]]

                gather_nd(x, index)
                         = [x[1, :, :]]
                         = [[12, 13, 14, 15],
                            [16, 17, 18, 19],
                            [20, 21, 22, 23]]

            * Case 2:
                index = [[0,2]]

                gather_nd(x, index)
                         = [x[0, 2, :]]
                         = [8, 9, 10, 11]

            * Case 3:
                index = [[1, 2, 3]]

                gather_nd(x, index)
                         = [x[1, 2, 3]]
                         = [23]

    Args:
        x (Tensor): The input Tensor which it's data type should be bool, float32, float64, int32, int64.
        index (Tensor): The index input with rank > 1, index.shape[-1] <= input.rank.
                        Its dtype should be int32, int64.
        name(str, optional): The default value is None.  Normally there is no need for user to set this property.
                        For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        output (Tensor): A tensor with the shape index.shape[:-1] + input.shape[index.shape[-1]:]
    
    Examples:

        .. code-block:: python
            
            import paddle
            
            x = paddle.to_tensor([[[1, 2], [3, 4], [5, 6]],
                                  [[7, 8], [9, 10], [11, 12]]])
            index = paddle.to_tensor([[0, 1]])
            
            output = paddle.gather_nd(x, index) #[[3, 4]]

    """

    return paddle.fluid.layers.gather_nd(input=x, index=index, name=name)


def strided_slice(x, axes, starts, ends, strides, name=None):
    """
    This operator produces a slice of ``x`` along multiple axes. Similar to numpy:
    https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html
    Slice uses ``axes``, ``starts`` and ``ends`` attributes to specify the start and
    end dimension for each axis in the list of axes and Slice uses this information
    to slice the input data tensor. If a negative value is passed to
    ``starts`` or ``ends`` such as :math:`-i`,  it represents the reverse position of the
    axis :math:`i-1` th(here 0 is the initial position). The ``strides`` represents steps of
    slicing and if the ``strides`` is negative, slice operation is in the opposite direction.
    If the value passed to ``starts`` or ``ends`` is greater than n
    (the number of elements in this dimension), it represents n.
    For slicing to the end of a dimension with unknown size, it is recommended
    to pass in INT_MAX. The size of ``axes`` must be equal to ``starts`` , ``ends`` and ``strides``.
    Following examples will explain how strided_slice works:

    .. code-block:: text

        Case1:
            Given:
                data = [ [1, 2, 3, 4], [5, 6, 7, 8], ]
                axes = [0, 1]
                starts = [1, 0]
                ends = [2, 3]
                strides = [1, 1]
            Then:
                result = [ [5, 6, 7], ]

        Case2:
            Given:
                data = [ [1, 2, 3, 4], [5, 6, 7, 8], ]
                axes = [0, 1]
                starts = [0, 1]
                ends = [2, 0]
                strides = [1, -1]
            Then:
                result = [ [8, 7, 6], ]
        Case3:
            Given:
                data = [ [1, 2, 3, 4], [5, 6, 7, 8], ]
                axes = [0, 1]
                starts = [0, 1]
                ends = [-1, 1000]
                strides = [1, 3]
            Then:
                result = [ [2], ]

    Args:
        x (Tensor): An N-D ``Tensor``. The data type is ``float32``, ``float64``, ``int32`` or ``int64``.
        axes (list|tuple): The data type is ``int32`` . Axes that `starts` and `ends` apply to.
                            It's optional. If it is not provides, it will be treated as :math:`[0,1,...,len(starts)-1]`.
        starts (list|tuple|Tensor): The data type is ``int32`` . If ``starts`` is a list or tuple, the elements of                                                                                          it should be integers or Tensors with shape [1]. If ``starts`` is an Tensor, it should be an 1-D Tensor.                                                                                    It represents starting indices of corresponding axis in ``axes``.
        ends (list|tuple|Tensor): The data type is ``int32`` . If ``ends`` is a list or tuple, the elements of
                it should be integers or Tensors with shape [1]. If ``ends`` is an Tensor, it should be an 1-D Tensor .                                                                                     It represents ending indices of corresponding axis in ``axes``.
        strides (list|tuple|Tensor): The data type is ``int32`` . If ``strides`` is a list or tuple, the elements of
                it should be integers or Tensors with shape [1]. If ``strides`` is an Tensor, it should be an 1-D Tensor .                                                                                  It represents slice step of corresponding axis in ``axes``.
        name(str, optional): The default value is None.  Normally there is no need for user to set this property.
                        For more information, please refer to :ref:`api_guide_Name` .

    Returns:
        Tensor:  A ``Tensor`` with the same dimension as ``x``. The data type is same as ``x``.

    Examples:
        .. code-block:: python

            import paddle
            x = paddle.zeros(shape=[3,4,5,6], dtype="float32")
            # example 1:
            # attr starts is a list which doesn't contain Tensor.
            axes = [1, 2, 3]
            starts = [-3, 0, 2]
            ends = [3, 2, 4]
            strides_1 = [1, 1, 1]
            strides_2 = [1, 1, 2]
            sliced_1 = paddle.strided_slice(x, axes=axes, starts=starts, ends=ends, strides=strides_1)
            # sliced_1 is x[:, 1:3:1, 0:2:1, 2:4:1].                                
            # example 2:
            # attr starts is a list which contain tensor Tensor.
            minus_3 = paddle.full(shape=[1], fill_value=-3, dtype='int32')
            sliced_2 = paddle.strided_slice(x, axes=axes, starts=[minus_3, 0, 2], ends=ends, strides=strides_2)
            # sliced_2 is x[:, 1:3:1, 0:2:1, 2:4:2].
    """

    return paddle.fluid.layers.strided_slice(
        input=x, axes=axes, starts=starts, ends=ends, strides=strides)


def tensordot(x, y, axes=2, name=None):
    r"""
    This function computes a contraction, which sum the product of elements from two tensors along the given axes. 

    Args:
        x (Tensor): The left tensor for contraction with data type ``float32`` or ``float64``.
        y (Tensor): The right tensor for contraction with the same data type as ``x``.
        axes (int|tuple|list|Tensor, optional):  The axes to contract for ``x`` and ``y``, defaulted to integer ``2``.

            1. It could be a non-negative integer ``n``, 
               in which the function will sum over the last ``n`` axes of ``x`` and the first ``n`` axes of ``y`` in order.
        
            2. It could be a 1-d tuple or list with data type ``int``, in which ``x`` and ``y`` will be contracted along the same given axes. 
               For example, ``axes`` =[0, 1] applies contraction along the first two axes for ``x`` and the first two axes for ``y``.
        
            3. It could be a tuple or list containing one or two 1-d tuple|list|Tensor with data type ``int``. 
               When containing one tuple|list|Tensor, the data in tuple|list|Tensor specified the same axes for ``x`` and ``y`` to contract. 
               When containing two tuple|list|Tensor, the first will be applied to ``x`` and the second to ``y``. 
               When containing more than two tuple|list|Tensor, only the first two axis sequences will be used while the others will be ignored.
        
            4. It could be a tensor, in which the ``axes`` tensor will be translated to a python list 
               and applied the same rules described above to determine the contraction axes. 
               Note that the ``axes`` with Tensor type is ONLY available in Dygraph mode.
        name(str, optional): The default value is None.  Normally there is no need for user to set this property. 
                             For more information, please refer to :ref:`api_guide_Name` .

    Return: 
        Output (Tensor): The contraction result with the same data type as ``x`` and ``y``. 
        In general, :math:`output.ndim = x.ndim + y.ndim - 2 \times n_{axes}`, where :math:`n_{axes}` denotes the number of axes to be contracted.
    
    NOTES:
        1. This function supports tensor broadcast, 
           the size in the corresponding dimensions of ``x`` and ``y`` should be equal, or applies to the broadcast rules.
        2. This function also supports axes expansion, 
           when the two given axis sequences for ``x`` and ``y`` are of different lengths, 
           the shorter sequence will expand the same axes as the longer one at the end. 
           For example, if ``axes`` =[[0, 1, 2, 3], [1, 0]], 
           the axis sequence for ``x`` is [0, 1, 2, 3], 
           while the corresponding axis sequences for ``y`` will be expanded from [1, 0] to [1, 0, 2, 3].
  
    Examples:
        .. code-block:: python

            import paddle

            data_type = 'float64'

            # For two 2-d tensor x and y, the case axes=0 is equivalent to outer product.
            # Note that tensordot supports empty axis sequence, so all the axes=0, axes=[], axes=[[]], and axes=[[],[]] are equivalent cases.   
            x = paddle.arange(4, dtype=data_type).reshape([2, 2])
            y = paddle.arange(4, dtype=data_type).reshape([2, 2])
            z = paddle.tensordot(x, y, axes=0)
            # z = [[[[0., 0.],
            #        [0., 0.]],
            #
            #       [[0., 1.],
            #        [2., 3.]]],
            #
            #
            #      [[[0., 2.],
            #        [4., 6.]],
            #
            #       [[0., 3.],
            #        [6., 9.]]]]


            # For two 1-d tensor x and y, the case axes=1 is equivalent to inner product.
            x = paddle.arange(10, dtype=data_type)
            y = paddle.arange(10, dtype=data_type)
            z1 = paddle.tensordot(x, y, axes=1)
            z2 = paddle.dot(x, y)
            # z1 = z2 = [285.]


            # For two 2-d tensor x and y, the case axes=1 is equivalent to matrix multiplication.
            x = paddle.arange(6, dtype=data_type).reshape([2, 3])
            y = paddle.arange(12, dtype=data_type).reshape([3, 4])
            z1 = paddle.tensordot(x, y, axes=1)
            z2 = paddle.matmul(x, y)
            # z1 = z2 =  [[20., 23., 26., 29.],
            #             [56., 68., 80., 92.]]


            # When axes is a 1-d int list, x and y will be contracted along the same given axes.
            # Note that axes=[1, 2] is equivalent to axes=[[1, 2]], axes=[[1, 2], []], axes=[[1, 2], [1]], and axes=[[1, 2], [1, 2]].
            x = paddle.arange(24, dtype=data_type).reshape([2, 3, 4])
            y = paddle.arange(36, dtype=data_type).reshape([3, 3, 4])
            z = paddle.tensordot(x, y, axes=[1, 2])
            # z =  [[506. , 1298., 2090.],
            #       [1298., 3818., 6338.]]


            # When axes is a list containing two 1-d int list, the first will be applied to x and the second to y.
            x = paddle.arange(60, dtype=data_type).reshape([3, 4, 5])
            y = paddle.arange(24, dtype=data_type).reshape([4, 3, 2])
            z = paddle.tensordot(x, y, axes=([1, 0], [0, 1]))
            # z =  [[4400., 4730.],
            #       [4532., 4874.],
            #       [4664., 5018.],
            #       [4796., 5162.],
            #       [4928., 5306.]]


            # Thanks to the support of axes expansion, axes=[[0, 1, 3, 4], [1, 0, 3, 4]] can be abbreviated as axes= [[0, 1, 3, 4], [1, 0]].
            x = paddle.arange(720, dtype=data_type).reshape([2, 3, 4, 5, 6])
            y = paddle.arange(720, dtype=data_type).reshape([3, 2, 4, 5, 6])
            z = paddle.tensordot(x, y, axes=[[0, 1, 3, 4], [1, 0]])
            # z = [[23217330., 24915630., 26613930., 28312230.],
            #      [24915630., 26775930., 28636230., 30496530.],
            #      [26613930., 28636230., 30658530., 32680830.],
            #      [28312230., 30496530., 32680830., 34865130.]] 
    """
    op_type = 'tensordot'
    input_dtype = ['float32', 'float64']

    check_variable_and_dtype(x, 'x', input_dtype, op_type)
    check_variable_and_dtype(y, 'y', input_dtype, op_type)
    check_type(axes, 'axes', (int, tuple, list, Variable), op_type)

    def _var_to_list(var):
        if in_dygraph_mode():
            return tolist(var)
        raise TypeError(
            "The 'axes' with type 'Tensor' in " + op_type +
            " is not available in static graph mode, "
            "please convert its type to int|Tuple|List, or use dynamic graph mode."
        )

    axes_x = []
    axes_y = []
    if np.issubdtype(type(axes), np.integer):
        assert axes >= 0, (
            "The 'axes' in " + op_type +
            f" should not be negative, but received axes={axes}.")
        axes_x = range(x.ndim - axes, x.ndim)
        axes_y = range(axes)
    else:
        if isinstance(axes, Variable):
            axes = _var_to_list(axes)

        if not axes or np.issubdtype(type(axes[0]), np.integer):
            axes_x = axes
        else:
            axes_x = axes[0]
            if len(axes) > 1:
                axes_y = axes[1]

            if isinstance(axes_x, Variable):
                axes_x = _var_to_list(axes_x)
            if isinstance(axes_y, Variable):
                axes_y = _var_to_list(axes_y)

    axes_x, axes_y = list(axes_x), list(axes_y)
    len_axes_x, len_axes_y = len(axes_x), len(axes_y)
    if len_axes_x < len_axes_y:
        axes_x.extend(axes_y[len_axes_x:])
    elif len_axes_y < len_axes_x:
        axes_y.extend(axes_x[len_axes_y:])

    shape_x, shape_y = list(x.shape), list(y.shape)
    need_contracted_dim_x = np.zeros((x.ndim), dtype=bool)
    need_contracted_dim_y = np.zeros((y.ndim), dtype=bool)
    contraction_size = 1
    for i in range(len(axes_x)):
        dim_x, dim_y = axes_x[i], axes_y[i]
        sx, sy = shape_x[dim_x], shape_y[dim_y]
        if sx == 1:
            shape_y[dim_y] = 1
            y = y.sum(dim_y).reshape(shape_y)
        elif sy == 1:
            shape_x[dim_x] = 1
            x = x.sum(dim_x).reshape(shape_x)
        else:
            assert sx == sy, "The dimensional size for 'x' and 'y' in " + op_type + f" should match each other, but 'x' has size {sx} in dim {dim_x} while 'y' has size {sy} in dim {dim_y}."

        need_contracted_dim_x[dim_x] = True
        need_contracted_dim_y[dim_y] = True
        contraction_size *= shape_x[dim_x]

    perm_x = []
    perm_y = []
    shape_out = []
    not_contraction_size_x = 1
    not_contraction_size_y = 1
    for i in range(x.ndim):
        if not need_contracted_dim_x[i]:
            perm_x.append(i)
            shape_out.append(shape_x[i])
            not_contraction_size_x *= shape_x[i]
    perm_x.extend(axes_x)
    perm_y.extend(axes_y)
    for i in range(y.ndim):
        if not need_contracted_dim_y[i]:
            perm_y.append(i)
            shape_out.append(shape_y[i])
            not_contraction_size_y *= shape_y[i]

    if not shape_out:
        shape_out = [1]

    x = x.transpose(perm=perm_x).reshape(
        [not_contraction_size_x, contraction_size])
    y = y.transpose(perm=perm_y).reshape(
        [contraction_size, not_contraction_size_y])
    out = x.matmul(y).reshape(shape_out)
    return out