math.py 80.6 KB
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# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
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#
# 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.
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"""
math functions
"""
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from __future__ import print_function
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import numpy as np
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from paddle.common_ops_import import *
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from paddle.tensor import cast
import paddle
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from ..fluid import layers
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from ..fluid.framework import core, _varbase_creator, in_dygraph_mode, Variable, convert_np_dtype_to_dtype_
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from ..fluid.layer_helper import LayerHelper
from ..fluid.data_feeder import check_variable_and_dtype, check_type, check_dtype, convert_dtype
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from ..fluid.layers.layer_function_generator import _generate_doc_string_, generate_activation_fn, generate_layer_fn
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# TODO: define math functions
# yapf: disable
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from ..fluid.layers import abs    #DEFINE_ALIAS
from ..fluid.layers import acos    #DEFINE_ALIAS
from ..fluid.layers import asin    #DEFINE_ALIAS
from ..fluid.layers import ceil    #DEFINE_ALIAS
from ..fluid.layers import cos    #DEFINE_ALIAS
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from ..fluid.layers import sinh    #DEFINE_ALIAS
from ..fluid.layers import cosh    #DEFINE_ALIAS
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# from ..fluid.layers import elementwise_add    #DEFINE_ALIAS
# from ..fluid.layers import elementwise_div    #DEFINE_ALIAS
# from ..fluid.layers import elementwise_floordiv    #DEFINE_ALIAS
# from ..fluid.layers import elementwise_mod    #DEFINE_ALIAS
# from ..fluid.layers import elementwise_mul    #DEFINE_ALIAS
# from ..fluid.layers import elementwise_pow    #DEFINE_ALIAS
# from ..fluid.layers import elementwise_sub    #DEFINE_ALIAS
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from ..fluid.layers import exp    #DEFINE_ALIAS
from ..fluid.layers import floor    #DEFINE_ALIAS
from ..fluid.layers import log    #DEFINE_ALIAS
from ..fluid.layers import reciprocal    #DEFINE_ALIAS
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from ..fluid.layers import reduce_all    #DEFINE_ALIAS
from ..fluid.layers import reduce_any    #DEFINE_ALIAS
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# from ..fluid.layers import reduce_max    #DEFINE_ALIAS
# from ..fluid.layers import reduce_min    #DEFINE_ALIAS
# from ..fluid.layers import reduce_prod    #DEFINE_ALIAS
# from ..fluid.layers import reduce_sum    #DEFINE_ALIAS
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from ..fluid.layers import round    #DEFINE_ALIAS
from ..fluid.layers import rsqrt    #DEFINE_ALIAS
from ..fluid.layers import scale    #DEFINE_ALIAS
from ..fluid.layers import square    #DEFINE_ALIAS
from ..fluid.layers import stanh    #DEFINE_ALIAS
from ..fluid.layers import atan    #DEFINE_ALIAS
from ..fluid.layers import erf    #DEFINE_ALIAS
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from ..fluid.layers import sqrt    #DEFINE_ALIAS
from ..fluid.layers import sin    #DEFINE_ALIAS
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from ..fluid.layers import multiplex    #DEFINE_ALIAS
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from ..fluid import layers
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__all__ = [
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        'abs',
        'acos',
        'asin',
        'atan',
        'ceil',
        'cos',
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        'cosh',
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        'cumsum',
        'exp',
        'floor',
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        'increment',
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        'log',
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        'log2',
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        'log10',
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        'logsumexp',
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        'mul',
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        'multiplex',
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        'pow',
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        'prod',
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        'reciprocal',
        'round',
        'rsqrt',
        'scale',
        'sign',
        'sin',
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        'sinh',
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        'sqrt',
        'square',
        'stanh',
        'sum',
        'tanh',
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        'add_n',
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        'max',
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        'maximum',
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        'min',
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        'minimum',
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        'mm',
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        'divide',
        'floor_divide',
        'remainder',
        'mod',
        'floor_mod',
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        'multiply',
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        'add',
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        'subtract',
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        'atan',
        'logsumexp',
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        'inverse',
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        'log1p',
        'erf',
        'addcmul',
        'addmm',
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        'clip',
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        'trace',
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        'kron',
        'isfinite',
        'isinf',
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        'isnan',
        'broadcast_shape'
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]
# yapf: enable.

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_supported_int_dtype_ = [
    VarDesc.VarType.UINT8,
    VarDesc.VarType.INT8,
    VarDesc.VarType.INT16,
    VarDesc.VarType.INT32,
    VarDesc.VarType.INT64,
]

_supported_float_dtype_ = [
    VarDesc.VarType.FP32,
    VarDesc.VarType.FP64,
]

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def pow(x, y, name=None):
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    """
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    Compute the power of tensor elements. The equation is:
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    .. math::
        out = x^{y} 
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    **Note**:
    ``paddle.pow`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .
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    Args:
        x (Tensor): An N-D Tensor, the data type is float32, float64, int32 or int64.
        y (Tensor): An N-D Tensor with type float32, float64, int32 or int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
    
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    Returns:
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        N-D Tensor. A location into which the result is stored. Its dimension equals with $x$.
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    Examples:

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        ..  code-block:: python
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            import paddle

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            # example 1: y is a float
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            x = paddle.to_tensor([1, 2, 3])
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            y = 2
            res = paddle.pow(x, y)
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            print(res) # [1 4 9]
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            # example 2: y is a Tensor
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            y = paddle.full(shape=[1], fill_value=2, dtype='float32')
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            res = paddle.pow(x, y)
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            print(res) # [1 4 9]
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    """
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    # in dynamic graph mode
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    if in_dygraph_mode():
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        if isinstance(y, (int, float)):
            return core.ops.pow(x, 'factor', y)
        elif isinstance(y, (paddle.Tensor, Variable)):
            return _elementwise_op_in_dygraph(
                x, y, axis=-1, act=None, op_name='elementwise_pow')
        else:
            raise TypeError('y must be scalar or tensor type, but received: %s '% (y.dtype))
    # in static graph mode
    else:
        if isinstance(y, (int, float)):
            helper = LayerHelper('pow', **locals())
            inputs = {'X': x}
            attrs = {'factor': y}
            out = helper.create_variable_for_type_inference(dtype=x.dtype)
            helper.append_op(
                type='pow', inputs=inputs, outputs={'Out': out}, attrs=attrs)
            return out
        elif isinstance(y, (paddle.Tensor, Variable)):
            # TODO A potential speed improvement is supporting different types in C++ and removing the cast ops here
            helper = LayerHelper('elementwise_pow', **locals())
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            out = helper.create_variable_for_type_inference(dtype=x.dtype)
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            return _elementwise_op(LayerHelper('elementwise_pow', **locals()))
        else:
            raise TypeError('y must be scalar or tensor type, but received: %s '% (type(y)))
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@dygraph_only
def _elementwise_op_in_dygraph(x,
                               y,
                               axis=-1,
                               act=None,
                               use_mkldnn=False,
                               op_name=None):
    op = getattr(core.ops, op_name)
    out = op(x, y, 'axis', axis, 'use_mkldnn', use_mkldnn)

    return dygraph_utils._append_activation_in_dygraph(
        out, act, use_mkldnn=use_mkldnn)


def _elementwise_op(helper):
    op_type = helper.layer_type
    original_op_type = helper.kwargs.get('original_op_type', op_type)
    x = helper.kwargs.get('x', None)
    y = helper.kwargs.get('y', None)

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    out = helper.kwargs.get('out', None)

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    assert x is not None, 'x cannot be None in {}'.format(original_op_type)
    assert y is not None, 'y cannot be None in {}'.format(original_op_type)
    check_variable_and_dtype(
        x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64'],
        original_op_type)
    check_variable_and_dtype(
        y, 'y', ['float16', 'float32', 'float64', 'int32', 'int64'],
        original_op_type)

    axis = helper.kwargs.get('axis', -1)
    use_mkldnn = helper.kwargs.get('use_mkldnn', False)
    name = helper.kwargs.get('name', None)
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    if out is None:
        if name is None:
            out = helper.create_variable_for_type_inference(dtype=x.dtype)
        else:
            out = helper.create_variable(name=name, dtype=x.dtype, persistable=False)
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    helper.append_op(
        type=op_type,
        inputs={'X': x,
                'Y': y},
        outputs={'Out': out},
        attrs={'axis': axis,
               'use_mkldnn': use_mkldnn})
    return helper.append_activation(out)


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def add(x, y, name=None):
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    """
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    Examples:
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    ..  code-block:: python

        import paddle
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        x = paddle.to_tensor([2, 3, 4], 'float64')
        y = paddle.to_tensor([1, 5, 2], 'float64')
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        z = paddle.add(x, y)
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        print(z)  # [3., 8., 6. ]
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    """
    op_type = 'elementwise_add'
    axis = -1
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
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            x, y, axis=axis, op_name=op_type)
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    return _elementwise_op(LayerHelper(op_type, **locals()))


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def subtract(x, y, name=None):
    """
    Substract two tensors element-wise. The equation is: 

    .. math::
        out = x - y

    **Note**:
    ``paddle.subtract`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .

    Args:
        x (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        y (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        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. A location into which the result is stored. If x, y have different shapes and are "broadcastable", the resulting tensor shape is the shape of x and y after broadcasting. If x, y have the same shape,  its shape is the same as x and y.

    Examples:

        .. code-block:: python
        
            import numpy as np
            import paddle

            x = paddle.to_tensor([[1, 2], [7, 8]])
            y = paddle.to_tensor([[5, 6], [3, 4]])
            res = paddle.subtract(x, y)
            print(res)
            #       [[-4, -4],
            #        [4, 4]]

            x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]])
            y = paddle.to_tensor([1, 0, 4])
            res = paddle.subtract(x, y)
            print(res)
            #       [[[ 0,  2, -1],
            #         [ 0,  2, -1]]]

            x = paddle.to_tensor([2, np.nan, 5], dtype='float32')
            y = paddle.to_tensor([1, 4, np.nan], dtype='float32')
            res = paddle.subtract(x, y)
            print(res)
            #       [ 1., nan, nan]

            x = paddle.to_tensor([5, np.inf, -np.inf], dtype='float64')
            y = paddle.to_tensor([1, 4, 5], dtype='float64')
            res = paddle.subtract(x, y)
            print(res)
            #       [   4.,  inf., -inf.]

    """
    op_type = 'elementwise_sub'
    axis = -1
    act = None
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
            x, y, axis=axis, act=act, op_name=op_type)
    return _elementwise_op(LayerHelper(op_type, **locals()))


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def divide(x, y, name=None):
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    """
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    Divide two tensors element-wise. The equation is:
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    .. math::
        out = x / y
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    **Note**:
    ``paddle.divide`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .
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    Args:
        x (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        y (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
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    Returns:
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        N-D Tensor. A location into which the result is stored. If x, y have different shapes and are "broadcastable", the resulting tensor shape is the shape of x and y after broadcasting. If x, y have the same shape,  its shape is the same as x and y.
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    Examples:
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        ..  code-block:: python
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            import paddle
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            x = paddle.to_tensor([2, 3, 4], dtype='float64')
            y = paddle.to_tensor([1, 5, 2], dtype='float64')
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            z = paddle.divide(x, y)
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            print(z)  # [2., 0.6, 2.]
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    """
    op_type = 'elementwise_div'
    axis = -1
    act = None
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
            x, y, axis=axis, act=act, op_name=op_type)
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    return _elementwise_op(LayerHelper(op_type, **locals()))
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def floor_divide(x, y, name=None):
    """
    Floor divide two tensors element-wise. The equation is:
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    .. math::
        out = x // y
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    **Note**:
    ``paddle.floor_divide`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .
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    Args:
        x (Tensor): the input tensor, it's data type should be int32, int64.
        y (Tensor): the input tensor, it's data type should be int32, int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
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    Returns:
        N-D Tensor. A location into which the result is stored. It's dimension equals with $x$.
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    Examples:
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        ..  code-block:: python
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            import paddle
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            x = paddle.to_tensor([2, 3, 8, 7])
            y = paddle.to_tensor([1, 5, 3, 3])
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            z = paddle.floor_divide(x, y)
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            print(z)  # [2, 0, 2, 2]
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    """
    op_type = 'elementwise_floordiv'
    axis = -1
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
            x, y, axis=axis, op_name=op_type)
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    return _elementwise_op(LayerHelper(op_type, **locals()))
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def remainder(x, y, name=None):
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    r"""
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    Mod two tensors element-wise. The equation is:

    .. math::
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        out = x \% y

    **Note**:
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    ``paddle.remainder`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .
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    Args:
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        x (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        y (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
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        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
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        N-D Tensor. A location into which the result is stored. If x, y have different shapes and are "broadcastable", the resulting tensor shape is the shape of x and y after broadcasting. If x, y have the same shape,  its shape is the same as x and y.
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    Examples:

        ..  code-block:: python

            import paddle

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            x = paddle.to_tensor([2, 3, 8, 7])
            y = paddle.to_tensor([1, 5, 3, 3])
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            z = paddle.remainder(x, y)
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            print(z)  # [0, 3, 2, 1]
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    """
    op_type = 'elementwise_mod'
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    axis = -1
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
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            x, y, axis=axis, op_name=op_type)
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    return _elementwise_op(LayerHelper(op_type, **locals()))


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mod = remainder  #DEFINE_ALIAS
floor_mod = remainder  #DEFINE_ALIAS


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def multiply(x, y, name=None):
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    """
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    multiply two tensors element-wise. The equation is:
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    .. math::
        out = x * y
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    **Note**:
    ``paddle.multiply`` supports broadcasting. If you would like to know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .
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    Args:
        x (Tensor): the input tensor, its data type should be float32, float64, int32, int64.
        y (Tensor): the input tensor, its data type should be float32, float64, int32, int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
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    Returns:
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        N-D Tensor. A location into which the result is stored. If x, y have different shapes and are "broadcastable", the resulting tensor shape is the shape of x and y after broadcasting. If x, y have the same shape,  its shape is the same as x and y.
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    Examples:

        ..  code-block:: python

            import paddle

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            x = paddle.to_tensor([[1, 2], [3, 4]])
            y = paddle.to_tensor([[5, 6], [7, 8]])
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            res = paddle.multiply(x, y)
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            print(res) # [[5, 12], [21, 32]]
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            x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]])
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            y = paddle.to_tensor([2])
            res = paddle.multiply(x, y)
            print(res) # [[[2, 4, 6], [2, 4, 6]]]
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    """
    op_type = 'elementwise_mul'
    act = None
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    axis = -1
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    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
            x, y, axis=axis, act=act, op_name=op_type)

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    if x.dtype != y.dtype:
        raise TypeError(
            'Input tensors must be same type, but received type of x: %s, type of y: %s '
            % (x.dtype, y.dtype))

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    return _elementwise_op(LayerHelper(op_type, **locals()))

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def maximum(x, y, name=None):
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    """
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    Compare two tensors and returns a new tensor containing the element-wise maxima. The equation is: 
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    .. math::
        out = max(x, y)
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    **Note**:
    ``paddle.maximum`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .

    Args:
        x (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        y (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        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. A location into which the result is stored. If x, y have different shapes and are "broadcastable", the resulting tensor shape is the shape of x and y after broadcasting. If x, y have the same shape,  its shape is the same as x and y.

    Examples:

        .. code-block:: python

            import numpy as np
            import paddle

            x = paddle.to_tensor([[1, 2], [7, 8]])
            y = paddle.to_tensor([[3, 4], [5, 6]])
            res = paddle.maximum(x, y)
            print(res)
            #    [[3, 4],
            #     [7, 8]]

            x = paddle.to_tensor([[1, 2, 3], [1, 2, 3]])
            y = paddle.to_tensor([3, 0, 4])
            res = paddle.maximum(x, y)
            print(res)
            #    [[3, 2, 4],
            #     [3, 2, 4]]

            x = paddle.to_tensor([2, 3, 5], dtype='float32')
            y = paddle.to_tensor([1, np.nan, np.nan], dtype='float32')
            res = paddle.maximum(x, y)
            print(res)
            #    [ 2., nan, nan]

            x = paddle.to_tensor([5, 3, np.inf], dtype='float32')
            y = paddle.to_tensor([1, -np.inf, 5], dtype='float32')
            res = paddle.maximum(x, y)
            print(res)
            #    [  5.,   3., inf.]
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    """
    op_type = 'elementwise_max'
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    axis = -1
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    act = None
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
            x, y, axis=axis, act=act, op_name=op_type)
    return _elementwise_op(LayerHelper(op_type, **locals()))

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def minimum(x, y, name=None):
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    """
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    Compare two tensors and returns a new tensor containing the element-wise minima. The equation is: 
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    .. math::
        out = min(x, y)
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    **Note**:
    ``paddle.minimum`` supports broadcasting. If you want know more about broadcasting, please refer to :ref:`user_guide_broadcasting` .

    Args:
        x (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        y (Tensor): the input tensor, it's data type should be float32, float64, int32, int64.
        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. A location into which the result is stored. If x, y have different shapes and are "broadcastable", the resulting tensor shape is the shape of x and y after broadcasting. If x, y have the same shape,  its shape is the same as x and y.

    Examples:

        .. code-block:: python

            import numpy as np
            import paddle

            x = paddle.to_tensor([[1, 2], [7, 8]])
            y = paddle.to_tensor([[3, 4], [5, 6]])
            res = paddle.minimum(x, y)
            print(res)
            #       [[1, 2],
            #        [5, 6]]

            x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]])
            y = paddle.to_tensor([3, 0, 4])
            res = paddle.minimum(x, y)
            print(res)
            #       [[[1, 0, 3],
            #         [1, 0, 3]]]

            x = paddle.to_tensor([2, 3, 5], dtype='float32')
            y = paddle.to_tensor([1, np.nan, np.nan], dtype='float32')
            res = paddle.minimum(x, y)
            print(res)
            #       [ 1., nan, nan]

            x = paddle.to_tensor([5, 3, np.inf], dtype='float64')
            y = paddle.to_tensor([1, -np.inf, 5], dtype='float64')
            res = paddle.minimum(x, y)
            print(res)
            #       [   1., -inf.,    5.]
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    """
    op_type = 'elementwise_min'
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    axis = -1
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    act = None
    if in_dygraph_mode():
        return _elementwise_op_in_dygraph(
            x, y, axis=axis, act=act, op_name=op_type)
    return _elementwise_op(LayerHelper(op_type, **locals()))
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for func in [
        add,
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        multiply
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]:
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    proto_dict = {'add': 'elementwise_add', 'multiply': 'elementwise_mul'}
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    op_proto = OpProtoHolder.instance().get_op_proto(proto_dict[func.__name__])

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    additional_args_lines = [
        "name (string, optional): Name of the output. \
        Default is None. It's used to print debug info for developers. Details: \
        :ref:`api_guide_Name` "
    ]

    func.__doc__ = _generate_doc_string_(
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        op_proto,
        additional_args_lines=additional_args_lines,
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        skip_attrs_set={"x_data_format", "y_data_format", "axis",
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            "use_quantizer", "mkldnn_data_type", "Scale_x", "Scale_y", "Scale_out"
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        }) + """\n""" + str(func.__doc__)
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def sum(x, axis=None, dtype=None, keepdim=False, name=None):
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    """
    Computes the sum of tensor elements over the given dimension.

    Args:
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        x (Tensor): An N-D Tensor, the data type is float32, float64, int32 or int64.
        axis (int|list|tuple, optional): The dimensions along which the sum is performed. If
            :attr:`None`, sum all elements of :attr:`x` and return a
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            Tensor with a single element, otherwise must be in the
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            range :math:`[-rank(x), rank(x))`. If :math:`axis[i] < 0`,
            the dimension to reduce is :math:`rank + axis[i]`.
        dtype (str, optional): The dtype of output Tensor. The default value is None, the dtype
            of output is the same as input Tensor `x`.
        keepdim (bool, optional): Whether to reserve the reduced dimension in the
            output Tensor. The result Tensor will have one fewer dimension
            than the :attr:`x` unless :attr:`keepdim` is true, default
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            value is False.
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        name (str, optional): The default value is None. Normally there is no need for
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            user to set this property.  For more information, please refer to :ref:`api_guide_Name`

    Returns:
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        Tensor: Results of summation operation on the specified axis of input Tensor `x`,
        it's data type is the same as `x`.
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    Raises:
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        ValueError: If the data type of `x` is float64, :attr:`dtype` can not be float32 or int32.
        ValueError: If the data type of `x` is int64, :attr:`dtype` can not be int32.
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        TypeError: The type of :attr:`axis` must be int, list or tuple.
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    Examples:
        .. code-block:: python

            import paddle
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            # x is a Tensor with following elements:
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            #    [[0.2, 0.3, 0.5, 0.9]
            #     [0.1, 0.2, 0.6, 0.7]]
            # Each example is followed by the corresponding output tensor.
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            x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9],
                                  [0.1, 0.2, 0.6, 0.7]])
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            out1 = paddle.sum(x)  # [3.5]
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            out2 = paddle.sum(x, axis=0)  # [0.3, 0.5, 1.1, 1.6]
            out3 = paddle.sum(x, axis=-1)  # [1.9, 1.6]
            out4 = paddle.sum(x, axis=1, keepdim=True)  # [[1.9], [1.6]]
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            # y is a Tensor with shape [2, 2, 2] and elements as below:
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            #      [[[1, 2], [3, 4]],
            #      [[5, 6], [7, 8]]]
            # Each example is followed by the corresponding output tensor.
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            y = paddle.to_tensor([[[1, 2], [3, 4]], 
                                  [[5, 6], [7, 8]]])
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            out5 = paddle.sum(y, axis=[1, 2]) # [10, 26]
            out6 = paddle.sum(y, axis=[0, 1]) # [16, 20]
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    """
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    if axis is not None and not isinstance(axis, (list, tuple)):
        axis = [axis]

    if not axis:
        reduce_all_flag = True
    else:
        if len(axis) == len(x.shape):
            reduce_all_flag = True
        else:
            reduce_all_flag = False

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    attrs = {
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        'dim': axis if axis != None and axis != [] and axis != () else [0],
        'keep_dim': keepdim,
        'reduce_all': reduce_all_flag
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    }
    dtype_flag = False
    if dtype is not None:
        if dtype in ['float64', 'int64']:
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            if (convert_dtype(x.dtype) == "float32" and dtype == "float64") or \
               (convert_dtype(x.dtype) == "int32" and dtype == "int64"):
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                attrs.update({
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                    'in_dtype': x.dtype,
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                    'out_dtype': convert_np_dtype_to_dtype_(dtype)
                })
                dtype_flag = True

    if in_dygraph_mode():
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        axis = axis if axis != None and axis != [] else [0]
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        if dtype_flag:
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            return core.ops.reduce_sum(x, 'dim', axis, 'keep_dim', keepdim,
                                       'reduce_all', reduce_all_flag, 'in_dtype',
                                       x.dtype, 'out_dtype',
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                                       convert_np_dtype_to_dtype_(dtype))
        else:
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            return core.ops.reduce_sum(x, 'dim', axis, 'keep_dim', keepdim,
                                       'reduce_all', reduce_all_flag)
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    check_variable_and_dtype(
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        x, 'x', ['float32', 'float64', 'int32', 'int64'], 'sum')
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    if dtype is not None:
        check_dtype(dtype, 'dtype', ['float32', 'float64', 'int32', 'int64'], 'sum')
        x_dtype = convert_dtype(x.dtype)

        if (x_dtype == "float64" and dtype in ["float32", "int32"]) or \
                (x_dtype == "int64" and dtype == "int32"):
            raise ValueError("The input(x)'s dtype is {} but the attr(dtype) of sum is {}, "
                             "which may cause data type overflows. Please reset attr(dtype) of sum."
                             .format(x_dtype, dtype))

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    check_type(axis, 'axis', (int, list, tuple, type(None)), 'sum')

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    helper = LayerHelper('sum', **locals())
    if dtype_flag:
        out = helper.create_variable_for_type_inference(
            dtype=convert_np_dtype_to_dtype_(dtype))
    else:
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        out = helper.create_variable_for_type_inference(dtype=x.dtype)
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    helper.append_op(
        type='reduce_sum',
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        inputs={'X': x},
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        outputs={'Out': out},
        attrs=attrs)
    return out
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@templatedoc(op_type="sum")
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def add_n(inputs, name=None):
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    """
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    This OP is used to sum one or more Tensor of the input.
    
    For example:

    .. code-block:: text
    
        Case 1:

            Input:
                input.shape = [2, 3]
                input = [[1, 2, 3],
                         [4, 5, 6]]

            Output:
                output.shape = [2, 3]
                output = [[1, 2, 3],
                          [4, 5, 6]]

        Case 2:
       
            Input:
                First input:
                    input1.shape = [2, 3]
                    Input1 = [[1, 2, 3],
                              [4, 5, 6]]

                The second input:
                    input2.shape = [2, 3]
                    input2 = [[7, 8, 9],
                              [10, 11, 12]]

                Output:
                    output.shape = [2, 3]
                    output = [[8, 10, 12],
                              [14, 16, 18]]
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    Args:
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        inputs (Tensor|list(Tensor)):  A Tensor list. The shape and data type of the list elements should be consistent.
            Input can be multi-dimensional Tensor, and data types can be: float32, float64, int32, int64.
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        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:
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        Tensor, the sum of input :math:`inputs` , its shape and data types are consistent with :math:`inputs`.
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    Examples:
        .. code-block:: python

            import paddle

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            input0 = paddle.to_tensor([[1, 2, 3], [4, 5, 6]], dtype='float32')
            input1 = paddle.to_tensor([[7, 8, 9], [10, 11, 12]], dtype='float32')
            output = paddle.add_n([input0, input1])
            # [[8., 10., 12.], 
            #  [14., 16., 18.]]
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    """
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    if in_dygraph_mode():
        if isinstance(inputs, Variable):
            inputs = [inputs]
        return core.ops.sum(inputs, 'use_mkldnn', False)
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    helper = LayerHelper('add_n', **locals())
    check_type(inputs, 'inputs', (Variable, tuple, list), 'add_n')
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    if isinstance(inputs, list) or isinstance(inputs, tuple):
        if len(inputs) > 0:
            for input in inputs:
                check_variable_and_dtype(input, "inputs", \
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                   ['float32', 'float64', 'int32', 'int64'], 'add_n')
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    else:
        check_variable_and_dtype(inputs, "inputs", \
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                ['float32', 'float64', 'int32', 'int64'], 'add_n')
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    out = helper.create_variable_for_type_inference(
        dtype=helper.input_dtype('inputs'))
    helper.append_op(
        type='sum',
        inputs={'X': inputs},
        outputs={'Out': out},
        attrs={'use_mkldnn': False})

    return out


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def mm(input, mat2, name=None):
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    """
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    Applies matrix multiplication to two tensors.

    Currently, the input tensors' rank can be any, but when the rank of any
    inputs is bigger than 3, this two inputs' rank should be equal.


    Also note that if the raw tensor :math:`x` or :math:`mat2` is rank-1 and
    nontransposed, the prepended or appended dimension :math:`1` will be
    removed after matrix multiplication.

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    This op does not support broadcasting. See paddle.matmul.

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    Args:
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        input (Tensor): The input tensor which is a Tensor.
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        mat2 (Tensor): The input tensor which is a Tensor.
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        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:
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        Tensor: The product Tensor.
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    Examples:
        .. code-block:: python

            import paddle
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            input = paddle.arange(1, 7).reshape((3, 2)).astype('float32')
            mat2 = paddle.arange(1, 9).reshape((2, 4)).astype('float32')
            out = paddle.mm(input, mat2)
            print(out)
            #        [[11., 14., 17., 20.],
            #         [23., 30., 37., 44.],
            #         [35., 46., 57., 68.]])

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    """
    if in_dygraph_mode():
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        out = _varbase_creator(dtype=input.dtype)
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        core.ops.matmul(input, mat2, out)
        return out
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    def __check_input(x, y):
        var_names = {'x': x, 'y': y}
        for name, val in var_names.items():
            check_variable_and_dtype(val, name,
                                     ['float16', 'float32', 'float64'], 'mm')
        x_shape = list(x.shape)
        y_shape = list(y.shape)
        if len(x_shape) == 1:
            x_shape = [1] + x_shape
        if len(y_shape) == 1:
            y_shape = y_shape + [1]

        # check the inner 2 dimensions
        if x_shape[-1] != y_shape[-2]:
            if not ((x_shape[-1] == -1) or (y_shape[-2] == -1)):
                raise ValueError(
                    "After performing an optional transpose, Input X's width should be "
                    "equal to Y's width for multiplication "
                    "prerequisites. But received X's shape: %s, Y's shape: %s\n"
                    % (x_shape, y_shape))

        if len(y_shape) > 2 and len(x_shape) > 2:
            for i, dim_x in enumerate(x_shape[:-2]):
                # don't check neg shape
                if dim_x < 0 or y_shape[i] < 0:
                    continue
                if dim_x != y_shape[i]:
                    raise ValueError(
                        "When the matrix is larger than 2 dimensions, the higher "
                        "dimensional values of the two matrices need to be equal. "
                        "But received x_shape[%d] != y_shape[%d]. X's shape: %s, "
                        "Y's shape: %s.\n" % (i, i, x_shape, y_shape))

    __check_input(input, mat2)

    helper = LayerHelper('mm', **locals())
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    out = helper.create_variable_for_type_inference(dtype=input.dtype)
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    helper.append_op(
        type='matmul', inputs={'X': input,
                               'Y': mat2}, outputs={'Out': out})
    return out
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def addmm(input, x, y, beta=1.0, alpha=1.0, name=None):
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    """
    **addmm**

    This operator is used to perform matrix multiplication for input $x$ and $y$.
    $input$ is added to the final result.
    The equation is:

    ..  math::
        Out = alpha * x * y + beta * input

    $Input$, $x$ and $y$ can carry the LoD (Level of Details) information, or not. But the output only shares the LoD information with input $input$.

    Args:
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        input (Tensor): The input Tensor to be added to the final result.
        x (Tensor): The first input Tensor for matrix multiplication.
        y (Tensor): The second input Tensor for matrix multiplication.
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        beta (float): Coefficient of $input$.
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        alpha (float): Coefficient of $x*y$.
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        name (str, optional): Name of the output. Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name`. Default is None.

    Returns:
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        Tensor: The output Tensor of addmm op.
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    Examples:
        ..  code-block:: python
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            import paddle

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            x = paddle.ones([2,2])
            y = paddle.ones([2,2])
            input = paddle.ones([2,2])
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            out = paddle.addmm( input=input, x=x, y=y, beta=0.5, alpha=5.0 )
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            print(out)
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            # [[10.5 10.5]
            # [10.5 10.5]]
    """
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    input_shape = input.shape
    x_shape = x.shape
    y_shape = y.shape
    if not len(input_shape) == len(x_shape) == len(y_shape) == 2:
        raise ValueError("The dimention of input, x, y should be 2 but receive input's shape: {}, x's shape: {}, y's shape: {}".format(input_shape, x_shape, y_shape))
    if input_shape[0] != x_shape[0]:
        if input_shape[0] != 1:
            raise ValueError( "When x's dimension[0] is not equal with input's dimension[0], input's dimension[0] must be 1 but got {}".format(input_shape[0]))
        if input_shape[1] != y_shape[1] and input_shape[1] != 1:
            raise ValueError( "When y's dimension[1] is not equal with input's dimension[1], input's dimension[1] must be 1 but got {}".format(input_shape[1]))
    if input_shape[1] != y_shape[1]:
        if input_shape[1] != 1:
            raise ValueError( "When y's dimension[1] is not equal with input's dimension[1], input's dimension[1] must be 1 but got {}".format(input_shape[1]))
        if input_shape[0] != x_shape[0] and input_shape[0] != 1:
            raise ValueError( "When x's dimension[0] is not equal with input's dimension[0], input's dimension[0] must be 1 but got {}".format(input_shape[0]))
    if x_shape[1] != y_shape[0]:
        raise ValueError("The input Variable x's width must be equal with Variable y' height. But received x's shape = {}, y's shape = {}.".format(x_shape, y_shape))



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    if in_dygraph_mode():
        out = core.ops.addmm(input, x, y, "Alpha", alpha, "Beta", beta)
        return out

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    inputs = {'Input': input, "X": x, "Y": y}
    attrs = {'Alpha': alpha, 'Beta': beta}

    helper = LayerHelper("addmm", **locals())
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    check_variable_and_dtype(input, 'Input', ['float32', 'float64'], 'addmm')
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    check_variable_and_dtype(x, 'X', ['float32', 'float64'], 'addmm')
    check_variable_and_dtype(y, 'Y', ['float32', 'float64'], 'addmm')
    out = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(
        type="addmm", inputs=inputs, attrs=attrs, outputs={"Out": out})
    return out
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1027
def logsumexp(x, axis=None, keepdim=False, name=None):
1028
    r"""
1029
    This OP calculates the log of the sum of exponentials of ``x`` along ``axis`` .
1030

1031
    .. math::
1032
       logsumexp(x) = \\log\\sum exp(x)
1033

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    Args:
        x (Tensor): The input Tensor with data type float32, float64.
        axis (int|list|tuple, optional): The axis along which to perform
            logsumexp calculations. ``axis`` should be int, list(int) or
            tuple(int). If ``axis`` is a list/tuple of dimension(s), logsumexp
            is calculated along all element(s) of ``axis`` . ``axis`` or
            element(s) of ``axis`` should be in range [-D, D), where D is the
            dimensions of ``x`` . If ``axis`` or element(s) of ``axis`` is
            less than 0, it works the same way as :math:`axis + D` . If
            ``axis`` is None, logsumexp is calculated along all elements of
            ``x``. Default is None.
        keepdim (bool, optional): Whether to reserve the reduced dimension(s)
            in the output Tensor. If ``keep_dim`` is True, the dimensions of
            the output Tensor is the same as ``x`` except in the reduced
            dimensions(it is of size 1 in this case). Otherwise, the shape of
            the output Tensor is squeezed in ``axis`` . Default is False.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.
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    Returns:
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        Tensor, results of logsumexp along ``axis`` of ``x``, with the same data
        type as ``x``.
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    Examples:
1058

1059
    .. code-block:: python
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        import paddle

1063
        x = paddle.to_tensor([[-1.5, 0., 2.], [3., 1.2, -2.4]])
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        out1 = paddle.logsumexp(x) # [3.4691226]
        out2 = paddle.logsumexp(x, 1) # [2.15317821, 3.15684602]
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    """
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    if isinstance(axis, int):
        axis = [axis]
    reduce_all = True if axis is None \
        or len(axis)==0 \
        or len(axis) == len(x.shape) else False
    if axis is None or len(axis) == 0:
        axis = [0]
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1076
    if in_dygraph_mode():
1077
        return core.ops.logsumexp(x, 'axis', axis, 'keepdim', keepdim, 'reduce_all', reduce_all)
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    check_variable_and_dtype(x, 'x',
                             ['float32', 'float64'],
                             'logsumexp')
1082

1083
    helper = LayerHelper('logsumexp', **locals())
1084
    attrs = {'axis': axis, 'keepdim': keepdim, 'reduce_all':reduce_all}
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    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='logsumexp', inputs={'X': x}, outputs={'Out': out}, attrs=attrs)
    return out
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def inverse(x, name=None):
    """
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    Takes the inverse of the square matrix. A square matrix is a matrix with
    the same number of rows and columns. The input can be a square matrix
    (2-D Tensor) or batches of square matrices.

    Args:
1098
        x (Tensor): The input tensor. The last two
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            dimensions should be equal. When the number of dimensions is
            greater than 2, it is treated as batches of square matrix. The data
            type can be float32 and float64.
        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:
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        Tensor: A Tensor holds the inverse of x. The shape and data type
1108
                        is the same as x.
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    Examples:
        .. code-block:: python

            import paddle
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            mat = paddle.to_tensor([[2, 0], [0, 2]], dtype='float32')
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            inv = paddle.inverse(mat)
            print(inv) # [[0.5, 0], [0, 0.5]]
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    """
    if in_dygraph_mode():
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        return core.ops.inverse(x)
1122

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    def _check_input(x):
        check_variable_and_dtype(x, 'x',
1125
                                 ['float32', 'float64'], 'inverse')
1126
        if len(x.shape) < 2:
1127 1128 1129
            raise ValueError(
                "The input of inverse is expected to be a Tensor whose number "
                "of dimensions is no less than 2. But reviced: %d, "
1130 1131
                "x's shape: %s." % (len(x.shape), x.shape))
    _check_input(x)
1132
    helper = LayerHelper('inverse', **locals())
1133
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
1134
    helper.append_op(
1135
        type='inverse', inputs={'Input': [x] }, outputs={'Output': [out]})
1136 1137 1138
    return out


1139
def max(x, axis=None, keepdim=False, name=None):
1140
    """
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1142
    Computes the maximum of tensor elements over the given axis.
1143 1144

    Args:
1145
        x(Tensor): A tensor, the data type is float32,
1146
            float64, int32, int64.
1147
        axis(list|int, optional): The axis along which the maximum is computed.
1148
            If :attr:`None`, compute the maximum over all elements of
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            `x` and return a Tensor with a single element,
1150 1151 1152
            otherwise must be in the range :math:`[-x.ndim(x), x.ndim(x))`.
            If :math:`axis[i] < 0`, the axis to reduce is :math:`x.ndim + axis[i]`.
        keepdim(bool, optional): Whether to reserve the reduced dimension in the
1153
            output Tensor. The result tensor will have one fewer dimension
1154
            than the `x` unless :attr:`keepdim` is true, default
1155
            value is False.
1156
        name(str, optional): The default value is None.  Normally there is no need for
1157 1158 1159
            user to set this property.  For more information, please refer to :ref:`api_guide_Name`

    Returns:
1160
        Tensor, results of maximum on the specified axis of input tensor,
1161
        it's data type is the same as `x`.
1162 1163 1164

    Examples:
        .. code-block:: python
1165

1166
            import paddle
1167

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1168
            # data_x is a Tensor with shape [2, 4]
1169
            # the axis is a int element
1170 1171 1172

            x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9],
                                  [0.1, 0.2, 0.6, 0.7]])
1173
            result1 = paddle.max(x)
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            print(result1)
1175 1176
            #[0.9]
            result2 = paddle.max(x, axis=0)
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            print(result2) 
1178 1179
            #[0.2 0.3 0.6 0.9]
            result3 = paddle.max(x, axis=-1)
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            print(result3)
1181 1182
            #[0.9 0.7]
            result4 = paddle.max(x, axis=1, keepdim=True)
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            print(result4)
1184 1185 1186
            #[[0.9]
            # [0.7]]

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            # data_y is a Tensor with shape [2, 2, 2]
1188
            # the axis is list 
1189 1190 1191

            y = paddle.to_tensor([[[1.0, 2.0], [3.0, 4.0]],
                                  [[5.0, 6.0], [7.0, 8.0]]])
1192
            result5 = paddle.max(y, axis=[1, 2])
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            print(result5)
1194 1195
            #[4. 8.]
            result6 = paddle.max(y, axis=[0, 1])
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            print(result6)
1197
            #[7. 8.]
1198 1199
    """

1200
    if axis is not None and not isinstance(axis, list):
1201 1202 1203 1204 1205 1206 1207 1208
        if isinstance(axis, tuple):
            axis = list(axis)
        elif isinstance(axis, int):
            axis= [axis]
        else:
            raise TypeError(
                "The type of axis must be int, list or tuple, but received {}".format(type(axis)))

1209 1210 1211 1212 1213
    reduce_all = True if axis == None or axis == [] else False
    axis = axis if axis != None and axis != [] else [0]
    if in_dygraph_mode():
        return core.ops.reduce_max(x, 'dim', axis, 'keep_dim', keepdim,
                                   'reduce_all', reduce_all)
1214

1215
    helper = LayerHelper('max', **locals())
1216
    check_variable_and_dtype(
1217
        x, 'x', ['float32', 'float64', 'int32', 'int64'], 'max')
1218

1219
    out = helper.create_variable_for_type_inference(
1220
            dtype=x.dtype)
1221 1222
    helper.append_op(
        type='reduce_max',
1223
        inputs={'X': x},
1224 1225
        outputs={'Out': out},
        attrs={
1226 1227
            'dim': axis,
            'keep_dim': keepdim,
1228 1229 1230 1231
            'reduce_all': reduce_all
        })
    return out

1232
def min(x, axis=None, keepdim=False, name=None):
1233
    """
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1235
    Computes the minimum of tensor elements over the given axis
1236

1237
    Args:
1238 1239
        x(Tensor): A tensor, the data type is float32, float64, int32, int64.
        axis(list|int, optional): The axis along which the minimum is computed.
1240
            If :attr:`None`, compute the minimum over all elements of
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            `x` and return a Tensor with a single element,
1242 1243 1244
            otherwise must be in the range :math:`[-x.ndim, x.ndim)`.
            If :math:`axis[i] < 0`, the axis to reduce is :math:`x.ndim + axis[i]`.
        keepdim(bool, optional): Whether to reserve the reduced dimension in the
1245
            output Tensor. The result tensor will have one fewer dimension
1246
            than the `x` unless :attr:`keepdim` is true, default
1247
            value is False.
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        name(str, optional): The default value is None.  Normally there is no need for 
1249
            user to set this property.  For more information, please refer to :ref:`api_guide_Name`
1250

1251
    Returns:
1252
        Tensor, results of minimum on the specified axis of input tensor,
1253
        it's data type is the same as input's Tensor.
1254

1255 1256 1257
    Examples:
        .. code-block:: python

1258
            import paddle
1259

1260
            # x is a tensor with shape [2, 4]
1261
            # the axis is a int element
1262 1263
            x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9],
                                  [0.1, 0.2, 0.6, 0.7]])
1264
            result1 = paddle.min(x)
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            print(result1)
1266 1267
            #[0.1]
            result2 = paddle.min(x, axis=0)
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            print(result2)
1269 1270
            #[0.1 0.2 0.5 0.7]
            result3 = paddle.min(x, axis=-1)
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            print(result3) 
1272 1273
            #[0.2 0.1]
            result4 = paddle.min(x, axis=1, keepdim=True)
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            print(result4)
1275 1276 1277
            #[[0.2]
            # [0.1]]

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            # y is a Tensor with shape [2, 2, 2]
1279
            # the axis is list 
1280 1281
            y = paddle.to_tensor([[[1.0, 2.0], [3.0, 4.0]],
                                  [[5.0, 6.0], [7.0, 8.0]]])
1282
            result5 = paddle.min(y, axis=[1, 2])
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            print(result5) 
1284 1285
            #[1. 5.]
            result6 = paddle.min(y, axis=[0, 1])
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            print(result6)
1287 1288
            #[1. 2.]
    """
1289

1290
    if axis is not None and not isinstance(axis, list):
1291 1292 1293 1294 1295 1296 1297
        if isinstance(axis, tuple):
            axis = list(axis)
        elif isinstance(axis, int):
            axis= [axis]
        else:
            raise TypeError(
                "The type of axis must be int, list or tuple, but received {}".format(type(axis)))
1298 1299
    reduce_all = True if axis == None or axis == [] else False
    axis = axis if axis != None and axis != [] else [0]
1300
    if in_dygraph_mode():
1301
        return core.ops.reduce_min(x, 'dim', axis, 'keep_dim', keepdim,
1302
                                   'reduce_all', reduce_all)
1303 1304 1305 1306 1307 1308

    helper = LayerHelper('min', **locals())
    check_variable_and_dtype(
        x, 'x', ['float32', 'float64', 'int32', 'int64'], 'min')

    out = helper.create_variable_for_type_inference(
1309
            dtype=x.dtype)
1310 1311
    helper.append_op(
        type='reduce_min',
1312
        inputs={'X': x},
1313 1314
        outputs={'Out': out},
        attrs={
1315 1316
            'dim': axis,
            'keep_dim': keepdim,
1317 1318 1319 1320 1321
            'reduce_all': reduce_all
        })
    return out


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def log1p(x, name=None):
1323
    r"""
1324
    Calculates the natural log of the given input tensor, element-wise.
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1326 1327
    .. math::
        Out = \\ln(x+1)
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1329
    Args:
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        x (Tensor): Input Tensor. Must be one of the following types: float32, float64.
1331 1332 1333
        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:
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        Tensor, the natural log of the input Tensor computed element-wise.
1335

1336 1337
    Examples:
        .. code-block:: python
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1338

1339
            import paddle
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            data = paddle.to_tensor([[0], [1]], dtype='float32')
            res = paddle.log1p(data)
            # [[0.], [0.6931472]]
1344 1345 1346 1347 1348 1349 1350 1351 1352
    """

    if in_dygraph_mode():
        return core.ops.log1p(x)

    check_variable_and_dtype(x, 'x', ['float32', 'float64'], "log1p")
    inputs = {'X': [x]}
    helper = LayerHelper('log1p', **locals())
    dtype = helper.input_dtype(input_param_name='x')
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    out = helper.create_variable_for_type_inference(dtype)
1354 1355
    helper.append_op(type="log1p", inputs={"X": x}, outputs={"Out": out})
    return out
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def log2(x, name=None):
1358
    r"""
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    Calculates the log to the base 2 of the given input tensor, element-wise.

    .. math::

        Out = \\log_2x

    Args:
        x (Tensor): Input tensor must be one of the following types: float32, float64.
        name (str|None): 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 log to the base 2 of the input Tensor computed element-wise.

    Examples:

        .. code-block:: python
        
            import paddle

            # example 1: x is a float
            x_i = paddle.to_tensor([[1.0], [2.0]])
            res = paddle.log2(x_i) # [[0.], [1.0]]

            # example 2: x is float32
            x_i = paddle.full(shape=[1], fill_value=2, dtype='float32')
            paddle.to_tensor(x_i)
            res = paddle.log2(x_i)
            print(res) # [1.0]

            # example 3: x is float64
            x_i = paddle.full(shape=[1], fill_value=2, dtype='float64')
            paddle.to_tensor(x_i)
            res = paddle.log2(x_i)
            print(res) # [1.0]
    """
    if in_dygraph_mode():
        return core.ops.log2(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], "log2")
    inputs = {'X': [x]}
    helper = LayerHelper('log2', **locals())
    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(type="log2", inputs={"X": x}, outputs={"Out": out})
    return out
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def log10(x, name=None):
1408
    r"""
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    Calculates the log to the base 10 of the given input tensor, element-wise.

    .. math::

        Out = \\log_10_x

    Args:
        x (Tensor): Input tensor must be one of the following types: float32, float64.
        name (str|None): 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 log to the base 10 of the input Tensor computed element-wise.

    Examples:

        .. code-block:: python
        
            import paddle

            # example 1: x is a float
            x_i = paddle.to_tensor([[1.0], [10.0]])
            res = paddle.log10(x_i) # [[0.], [1.0]]

            # example 2: x is float32
            x_i = paddle.full(shape=[1], fill_value=10, dtype='float32')
            paddle.to_tensor(x_i)
            res = paddle.log10(x_i)
            print(res) # [1.0]

            # example 3: x is float64
            x_i = paddle.full(shape=[1], fill_value=10, dtype='float64')
            paddle.to_tensor(x_i)
            res = paddle.log10(x_i)
            print(res) # [1.0]
    """
    if in_dygraph_mode():
        return core.ops.log10(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], "log10")
    inputs = {'X': [x]}
    helper = LayerHelper('log10', **locals())
    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(type="log10", inputs={"X": x}, outputs={"Out": out})
    return out


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def addcmul(input, tensor1, tensor2, value=1.0, name=None):
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    """
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1460 1461 1462 1463 1464
    Calculate the element-wise multiplication of tensor1 and tensor2,
    then multiply the result by value, and add it to input. The shape of input,
    tensor1, tensor2 should be broadcastable.
    The equation is:
    ..  math::
1465

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1466 1467
        out = input + value * tensor1 * tensor2
    Args:
1468 1469 1470
        input(Tensor): The input to be added. A Tensor with type float32, float64, int32, int64.
        tensor1(Tensor): The tensor to be multiplied. A Tensor with type float32, float64, int32, int64.
        tensor2(Tensor): The tensor to be multiplied. A Tensor with type float32, float64, int32, int64.
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        value(int|float): The multiplier for tensor1*tensor2. For float32 and float64 type input, value must be float, otherwise an integer.
        name(str, Optional): For details, please refer to :ref:`api_guide_Name`.
                        Generally, no setting is required. Default: None.
    Returns:
1475
        out(Tensor): The output result. A Tensor with the same data type as input's.
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    Examples:
        .. code-block:: python
1478

B
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1479
          import paddle
1480 1481 1482
          input = paddle.ones([2,2])
          tensor1 = paddle.ones([2,2])
          tensor2 = paddle.ones([2,2])
1483
          out = paddle.tensor.math.addcmul(input, tensor1, tensor2, value=0.5)
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          print(out)
1485 1486
          # [[1.5 1.5]
          # [1.5 1.5]]
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    """

    check_variable_and_dtype(input, 'input', ['float32', 'float64', 'int32', 'int64'], 'addcmul')
    check_variable_and_dtype(tensor1, 'tensor1', ['float32', 'float64', 'int32', 'int64'], 'addcmul')
    check_variable_and_dtype(tensor2, 'tensor2', ['float32', 'float64', 'int32', 'int64'], 'addcmul')
    if convert_dtype(input.dtype) in ['float32', 'float64']:
        check_type(value, 'value', float, 'addcmul')
    if convert_dtype(input.dtype) in ['int32', 'int64']:
        check_type(value, 'value', int, 'addcmul')

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    out = layers.elementwise_add(input, layers.elementwise_mul(tensor1, tensor2) * value)
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    return out
1499 1500


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def clip(x, min=None, max=None, name=None):
1502
    """
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1503
    This operator clip all elements in input into the range [ min, max ] and return
1504 1505 1506 1507
    a resulting tensor as the following equation:

    .. math::

1508
        Out = MIN(MAX(x, min), max)
1509 1510

    Args:
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        x (Tensor): An N-D Tensor with data type float32 or float64.
        min (float32|Tensor): The lower bound with type ``float32`` or a ``Tensor``
1513
            with shape [1] and type ``int32``, ``float32``, ``float64``.
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        max (float32|Tensor): The upper bound with type ``float32`` or a ``Tensor``
1515 1516 1517 1518 1519 1520
            with shape [1] and type ``int32``, ``float32``, ``float64``.
        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:
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        Tensor: A Tensor with the same data type and data shape as input.
1522 1523 1524 1525 1526

    Examples:
        .. code-block:: python

            import paddle
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1527

1528
            x1 = paddle.to_tensor([[1.2, 3.5], [4.5, 6.4]], 'float32')
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1529 1530
            out1 = paddle.clip(x1, min=3.5, max=5.0)
            out2 = paddle.clip(x1, min=2.5)
1531
            print(out1)
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1532 1533
            # [[3.5, 3.5]
            # [4.5, 5.0]]
1534
            print(out2)
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            # [[2.5, 3.5]
            # [[4.5, 6.4]
1537 1538
    """

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1539 1540
    fmin = float(np.finfo(np.float32).min)
    fmax = float(np.finfo(np.float32).max)
1541

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1542
    if in_dygraph_mode():
1543 1544 1545 1546
        if isinstance(min, Variable):
            min = min.numpy().item(0)
        if isinstance(max, Variable):
            max = max.numpy().item(0)
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        min = fmin if min is None else min
        max = fmax if max is None else max
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        return core.ops.clip(x, "min", min, "max", max)
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1550

1551
    if min is not None:
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1552
        check_type(min, 'min', (float, int, Variable), 'clip')
1553 1554
        if isinstance(min, Variable):
            check_dtype(min.dtype, 'min', ['float32', 'float64', 'int32'],
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                        'clip', '(When the type of min in clip is Variable.)')
1556
    if max is not None:
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        check_type(max, 'max', (float, int, Variable), 'clip')
1558 1559
        if isinstance(max, Variable):
            check_dtype(max.dtype, 'max', ['float32', 'float64', 'int32'],
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                        'clip', '(When the type of max in clip is Variable.)')
1561

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    check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'clip')
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1563 1564

    inputs = {'X': x}
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    attrs = {'min': fmin, 'max': fmax}
1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578

    if isinstance(min, Variable):
        min.stop_gradient = True
        inputs['Min'] = min
    elif min is not None:
        attrs['min'] = min

    if isinstance(max, Variable):
        max.stop_gradient = True
        inputs['Max'] = max
    elif max is not None:
        attrs['max'] = max

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    helper = LayerHelper('clip', **locals())
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    output = helper.create_variable_for_type_inference(
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        dtype=helper.input_dtype('x'))
1582 1583 1584 1585
    helper.append_op(
        type='clip', inputs=inputs, outputs={'Out': [output]}, attrs=attrs)

    return output
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1588
def trace(x, offset=0, axis1=0, axis2=1, name=None):
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    """
1590
    **trace**
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1592
    This OP computes the sum along diagonals of the input tensor x.
1593 1594

    If ``x`` is 2D, returns the sum of diagonal.
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1596
    If ``x`` has larger dimensions, then returns an tensor of diagonals sum, diagonals be taken from
1597
    the 2D planes specified by axis1 and axis2. By default, the 2D planes formed by the first and second axes
1598
    of the input tensor x.
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1600
    The argument ``offset`` determines where diagonals are taken from input tensor x:
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    - If offset = 0, it is the main diagonal.
    - If offset > 0, it is above the main diagonal.
    - If offset < 0, it is below the main diagonal.
1605
    - Note that if offset is out of input's shape indicated by axis1 and axis2, 0 will be returned.
1606

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    Args:
1608
        x(Tensor): The input tensor x. Must be at least 2-dimensional. The input data type should be float32, float64, int32, int64.
1609 1610 1611
        offset(int, optional): Which diagonals in input tensor x will be taken. Default: 0 (main diagonals).
        axis1(int, optional): The first axis with respect to take diagonal. Default: 0.
        axis2(int, optional): The second axis with respect to take diagonal. Default: 1.
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        name (str, optional): Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name`. Default: None.

    Returns:
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        Tensor: the output data type is the same as input data type.
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    Examples:
        .. code-block:: python

            import paddle
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            case1 = paddle.randn([2, 3])
            case2 = paddle.randn([3, 10, 10])
            case3 = paddle.randn([3, 10, 5, 10])
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            data1 = paddle.trace(case1) # data1.shape = [1]
            data2 = paddle.trace(case2, offset=1, axis1=1, axis2=2) # data2.shape = [3]
            data3 = paddle.trace(case3, offset=-3, axis1=1, axis2=-1) # data2.shape = [3, 5]
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    """
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    inputs = {'Input': [x]}
    attrs = {'offset': offset, 'axis1': axis1, 'axis2': axis2}
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    def __check_input(input, offset, dim1, dim2):
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        check_dtype(x.dtype, 'Input',
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                    ['int32', 'int64', 'float16', 'float32', 'float64'],
                    'trace')

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        input_shape = list(x.shape)
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        assert len(input_shape) >= 2,                     \
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                "The x must be at least 2-dimensional, "   \
                "But received Input x's dimensional: %s.\n" %  \
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                len(input_shape)

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        axis1_ = axis1 if axis1 >= 0 else len(input_shape) + axis1
        axis2_ = axis2 if axis2 >= 0 else len(input_shape) + axis2
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        assert axis1_ < len(input_shape),     \
            "The argument axis1 is out of range (expected to be in range of [%d, %d], but got %d).\n"  \
            % (-(len(input_shape)), len(input_shape) - 1, axis1)
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        assert axis2_ < len(input_shape),   \
            "The argument axis2 is out of range (expected to be in range of [%d, %d], but got %d).\n"   \
            % (-(len(input_shape)), len(input_shape) - 1, axis2)
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        assert  axis1_ != axis2_,   \
               "axis1 and axis2 cannot be the same axis." \
                "But received axis1 = %d, axis2 = %d\n"%(axis1, axis2)
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    if in_dygraph_mode():
        return core.ops.trace(x, 'offset', offset, 'axis1', axis1, 'axis2', axis2)

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    if not in_dygraph_mode():
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        __check_input(input, offset, axis1, axis2)
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    helper = LayerHelper('trace', **locals())

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    out = helper.create_variable_for_type_inference(dtype=x.dtype)
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    helper.append_op(
        type='trace',
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        inputs={'Input': [x]},
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        attrs={'offset': offset,
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               'axis1': axis1,
               'axis2': axis2},
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        outputs={'Out': [out]})
    return out

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@templatedoc(op_type="kron")
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def kron(x, y, name=None):
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    """

${comment}
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    Args:
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        x (Tensor): the fist operand of kron op, data type: float16, float32,
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            float64, int32 or int64.
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        y (Tensor): the second operand of kron op, data type: float16,
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            float32, float64, int32 or int64. Its data type should be the same
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            with x.
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        name(str, optional): The default value is None.  Normally there is no
            need for user to set this property.  For more information, please
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            refer to :ref:`api_guide_Name`.

    Returns:
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        Tensor: The output of kron op, data type: float16, float32, float64, int32 or int64. Its data is the same with x.
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    Examples:
        .. code-block:: python
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            import paddle
            x = paddle.to_tensor([[1, 2], [3, 4]], dtype='int64')
            y = paddle.to_tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype='int64')
            out = paddle.kron(x, y)
            print(out)
            #        [[1, 2, 3, 2, 4, 6],
            #         [ 4,  5,  6,  8, 10, 12],
            #         [ 7,  8,  9, 14, 16, 18],
            #         [ 3,  6,  9,  4,  8, 12],
            #         [12, 15, 18, 16, 20, 24],
            #         [21, 24, 27, 28, 32, 36]])
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    """
    if in_dygraph_mode():
        return core.ops.kron(x, y)

    helper = LayerHelper('kron', **locals())
    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64'], 'kron')
    check_variable_and_dtype(y, 'y', ['float16', 'float32', 'float64', 'int32', 'int64'], 'kron')

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    out = helper.create_variable_for_type_inference(dtype=x.dtype)
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    helper.append_op(type="kron", inputs={"X": x, "Y": y}, outputs={"Out": out})
    return out
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def cumsum(x, axis=None, dtype=None, name=None):
    """
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    The cumulative sum of the elements along a given axis. 
    
    **Note**:
    The first element of the result is the same of the first element of the input. 
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    Args:
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        x (Tensor): The input tensor needed to be cumsumed.
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        axis (int, optional): The dimension to accumulate along. -1 means the last dimension. The default (None) is to compute the cumsum over the flattened array.
        dtype (str, optional): The data type of the output tensor, can be float32, float64, int32, int64. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. The default value is None. 
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
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        Tensor, the result of cumsum operator. 
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    Examples:
        .. code-block:: python
            
            import paddle
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            data = paddle.arange(12)
            data = paddle.reshape(data, (3, 4))
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            y = paddle.cumsum(data)
            # [ 0  1  3  6 10 15 21 28 36 45 55 66]

            y = paddle.cumsum(data, axis=0)
            # [[ 0  1  2  3]
            #  [ 4  6  8 10]
            #  [12 15 18 21]]
            
            y = paddle.cumsum(data, axis=-1)
            # [[ 0  1  3  6]
            #  [ 4  9 15 22]
            #  [ 8 17 27 38]]

            y = paddle.cumsum(data, dtype='float64')
            print(y.dtype)
            # VarType.FP64
    """
    if axis is None:
        flatten = True
    else:
        flatten = False
    if dtype is not None and x.dtype != convert_np_dtype_to_dtype_(dtype):
        x = layers.cast(x, dtype)

    if in_dygraph_mode():
        if axis is None:
            return core.ops.cumsum(x, 'flatten', flatten)
        else:
            return core.ops.cumsum(x, 'axis', axis, 'flatten', flatten)

    check_type(x, 'x', (Variable), 'cumsum')
    locals_var = locals().copy()
    kwargs = dict()
    for name, val in locals_var.items():
        if val is not None:
            kwargs[name] = val
    _cum_sum_ = generate_layer_fn('cumsum')
    return _cum_sum_(**kwargs)
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def isfinite(x, name=None):
    """

    Return whether every element of input tensor is finite number or not.

    Args:
        x (Tensor): The input tensor, it's data type should be float16, float32, float64, int32, int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        `Tensor`, the bool result which shows every element of `x` whether it is finite number or not.

    Examples:
        .. code-block:: python

            import paddle
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            x = paddle.to_tensor([float('-inf'), -2, 3.6, float('inf'), 0, float('-nan'), float('nan')])
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            out = paddle.tensor.isfinite(x)
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            print(out)  # [False  True  True False  True False False]
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    """
    if in_dygraph_mode():
        return core.ops.isfinite_v2(x)
    helper = LayerHelper("isfinite_v2", **locals())
    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64'], 'isfinite')
    out = helper.create_variable_for_type_inference('bool')
    helper.append_op(type="isfinite_v2", inputs={"X": x}, outputs={"Out": out})
    return out

def isinf(x, name=None):
    """

    Return whether every element of input tensor is `+/-INF` or not.

    Args:
        x (Tensor): The input tensor, it's data type should be float16, float32, float64, int32, int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        `Tensor`, the bool result which shows every element of `x` whether it is `+/-INF` or not.

    Examples:
        .. code-block:: python

            import paddle
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            x = paddle.to_tensor([float('-inf'), -2, 3.6, float('inf'), 0, float('-nan'), float('nan')])
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            out = paddle.tensor.isinf(x)
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            print(out)  # [ True False False  True False False False]
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    """
    if in_dygraph_mode():
        return core.ops.isinf_v2(x)
    helper = LayerHelper("isinf_v2", **locals())
    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64'], 'isinf')
    out = helper.create_variable_for_type_inference(dtype='bool')
    helper.append_op(type="isinf_v2", inputs={"X": x}, outputs={"Out": out})
    return out

def isnan(x, name=None):
    """

    Return whether every element of input tensor is `NaN` or not.

    Args:
        x (Tensor): The input tensor, it's data type should be float16, float32, float64, int32, int64.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        `Tensor`, the bool result which shows every element of `x` whether it is `NaN` or not.

    Examples:
        .. code-block:: python

            import paddle
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            x = paddle.to_tensor([float('-inf'), -2, 3.6, float('inf'), 0, float('-nan'), float('nan')])
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            out = paddle.tensor.isnan(x)
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            print(out)  # [False False False False False  True  True]
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    """
    if in_dygraph_mode():
        return core.ops.isnan_v2(x)
    helper = LayerHelper("isnan_v2", **locals())
    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64'], 'isnan')
    out = helper.create_variable_for_type_inference(dtype='bool')
    helper.append_op(type="isnan_v2", inputs={"X": x}, outputs={"Out": out})
    return out


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def prod(x, axis=None, keepdim=False, dtype=None, name=None):
    """
    Compute the product of tensor elements over the given axis.

    Args:
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        x(Tensor): The input tensor, its data type should be float32, float64, int32, int64.
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        axis(int|list|tuple, optional): The axis along which the product is computed. If :attr:`None`, 
            multiply all elements of `x` and return a Tensor with a single element, 
            otherwise must be in the range :math:`[-x.ndim, x.ndim)`. If :math:`axis[i]<0`, 
            the axis to reduce is :math:`x.ndim + axis[i]`. Default is None.
        dtype(str|np.dtype, optional): The desired date type of returned tensor, can be float32, float64, 
            int32, int64. If specified, the input tensor is casted to dtype before operator performed. 
            This is very useful for avoiding data type overflows. The default value is None, the dtype 
            of output is the same as input Tensor `x`.
        keepdim(bool, optional): Whether to reserve the reduced dimension in the output Tensor. The result 
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            tensor will have one fewer dimension than the input unless `keepdim` is true. Default is False.
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        name(string, 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, result of product on the specified dim of input tensor.

    Raises:
        ValueError: The :attr:`dtype` must be float32, float64, int32 or int64.
        TypeError: The type of :attr:`axis` must be int, list or tuple.
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    Examples:
        .. code-block:: python

            import paddle

            # the axis is a int element
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            x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9],
                                  [0.1, 0.2, 0.6, 0.7]])
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            out1 = paddle.prod(x)
            # [0.0002268]

            out2 = paddle.prod(x, -1)
            # [0.027  0.0084]

            out3 = paddle.prod(x, 0)
            # [0.02 0.06 0.3  0.63]

            out4 = paddle.prod(x, 0, keepdim=True)
            # [[0.02 0.06 0.3  0.63]]

            out5 = paddle.prod(x, 0, dtype='int64')
            # [0 0 0 0]

            # the axis is list
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            y = paddle.to_tensor([[[1.0, 2.0], [3.0, 4.0]],
                                  [[5.0, 6.0], [7.0, 8.0]]])
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            out6 = paddle.prod(y, [0, 1])
            # [105. 384.]

            out7 = paddle.prod(y, (1, 2))
            # [  24. 1680.]

    """
    if dtype is not None:
        check_dtype(dtype, 'dtype', ['float32', 'float64', 'int32', 'int64'], 'prod')
        if x.dtype != convert_np_dtype_to_dtype_(dtype):
            x = layers.cast(x, dtype)

    return layers.reduce_prod(input=x, dim=axis, keep_dim=keepdim, name=name)
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def sign(x, name=None):
    """
    This OP returns sign of every element in `x`: 1 for positive, -1 for negative and 0 for zero.

    Args:
        x(Tensor): The input tensor. The data type can be float16, float32 or float64.
        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 sign tensor with identical shape and data type to the input :attr:`x`.

    Examples:
        .. code-block:: python

          import paddle

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          x = paddle.to_tensor([3.0, 0.0, -2.0, 1.7], dtype='float32')
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          out = paddle.sign(x=x)
          print(out)  # [1.0, 0.0, -1.0, 1.0]
    """
    if in_dygraph_mode():
        return core.ops.sign(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'sign')
    helper = LayerHelper("sign", **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(type='sign', inputs={'X': [x]}, outputs={'Out': [out]})

    return out


def tanh(x, name=None):
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    r"""
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    Tanh Activation Operator.

    .. math::
        out = \\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}

    Args:
        x (Tensor): Input of Tanh operator, an N-D Tensor, with data type float32, float64 or float16.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Output of Tanh operator, a Tensor with same data type and shape as input.

    Examples:

        .. code-block:: python

            import paddle

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            x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
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            out = paddle.tanh(x)
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            print(out)
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            # [-0.37994896 -0.19737532  0.09966799  0.29131261]
    """
    if in_dygraph_mode():
        return core.ops.tanh(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'tanh')
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    check_type(x, 'x', (Variable), 'tanh')
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    helper = LayerHelper('tanh', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='tanh', inputs={'X': x}, outputs={'Out': out})
    return out
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def increment(x, value=1.0, name=None):
    """
    The OP is usually used for control flow to increment the data of :attr:`x` by an amount :attr:`value`.
    Notice that the number of elements in :attr:`x` must be equal to 1.

    Args:
        x (Tensor): A tensor that must always contain only one element, its data type supports float32, float64, int32 and int64.
        value(float, optional): The amount to increment the data of :attr:`x`. Default: 1.0.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor, the elementwise-incremented tensor with the same shape and data type as :attr:`x`.

    Examples:
        .. code-block:: python

            import paddle

            data = paddle.zeros(shape=[1], dtype='float32')
            counter = paddle.increment(data)
            # [1.]

    """
    if in_dygraph_mode():
        return core.ops.increment(x, 'step', value)

    check_variable_and_dtype(x, 'x', ['float32', 'float64', 'int32', 'int64'],
                             'increment')
    helper = LayerHelper("increment", **locals())
    helper.append_op(
        type='increment',
        inputs={'X': [x]},
        outputs={'Out': [x]},
        attrs={'step': float(value)})
    return x
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def all(x, axis=None, keepdim=False, name=None):
    """
    Computes the the ``logical and`` of tensor elements over the given dimension.

    Args:
        x (Tensor): An N-D Tensor, the input data type should be `bool`.
        axis (int|list|tuple, optional): The dimensions along which the ``logical and`` is compute. If
            :attr:`None`, and all elements of :attr:`x` and return a
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            Tensor with a single element, otherwise must be in the
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            range :math:`[-rank(x), rank(x))`. If :math:`axis[i] < 0`,
            the dimension to reduce is :math:`rank + axis[i]`.
        keepdim (bool, optional): Whether to reserve the reduced dimension in the
            output Tensor. The result Tensor will have one fewer dimension
            than the :attr:`x` unless :attr:`keepdim` is true, default
            value is False.
        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: Results the ``logical and`` on the specified axis of input Tensor `x`,  it's data type is bool.

    Raises:
        ValueError: If the data type of `x` is not bool.
        TypeError: The type of :attr:`axis` must be int, list or tuple.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.fluid as fluid
            import paddle.fluid.layers as layers
            import numpy as np
            
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            # x is a bool Tensor with following elements:
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            #    [[True, False]
            #     [True, True]]
            x = layers.assign(np.array([[1, 0], [1, 1]], dtype='int32'))
            print(x)
            x = layers.cast(x, 'bool')
            
            # out1 should be [False]
            out1 = paddle.all(x)  # [False]
            print(out1)
            
            # out2 should be [True, False]
            out2 = paddle.all(x, axis=0)  # [True, False]
            print(out2)
            
            # keep_dim=False, out3 should be [False, True], out.shape should be (2,)
            out3 = paddle.all(x, axis=-1)  # [False, True]
            print(out3)
            
            # keep_dim=True, out4 should be [[False], [True]], out.shape should be (2,1)
            out4 = paddle.all(x, axis=1, keep_dim=True)
            out4 = layers.cast(out4, 'int32')  # [[False], [True]]
            print(out4)
            
    """
    if axis is not None and not isinstance(axis, (list, tuple)):
        axis = [axis]

    if not axis:
        reduce_all_flag = True
    else:
        if len(axis) == len(x.shape):
            reduce_all_flag = True
        else:
            reduce_all_flag = False

    attrs = {
        'dim': axis if axis != None and axis != [] and axis != () else [0],
        'keep_dim': keepdim,
        'reduce_all': reduce_all_flag
    }
    dtype_flag = False


    if in_dygraph_mode():
        axis = axis if axis != None and axis != [] else [0]
        return core.ops.reduce_all(x, 'dim', axis, 'keep_dim', keepdim,
                                       'reduce_all', reduce_all_flag)
    check_variable_and_dtype(x, 'x', ['bool'], 'all')


    check_type(axis, 'axis', (int, list, tuple, type(None)), 'all')

    helper = LayerHelper('all', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='reduce_all',
        inputs={'X': x},
        outputs={'Out': out},
        attrs=attrs)
    return out


def any(x, axis=None, keepdim=False, name=None):
    """
    Computes the the ``logical or`` of tensor elements over the given dimension.

    Args:
        x (Tensor): An N-D Tensor, the input data type should be `bool`.
        axis (int|list|tuple, optional): The dimensions along which the ``logical or`` is compute. If
            :attr:`None`, and all elements of :attr:`x` and return a
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            Tensor with a single element, otherwise must be in the
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            range :math:`[-rank(x), rank(x))`. If :math:`axis[i] < 0`,
            the dimension to reduce is :math:`rank + axis[i]`.
        keepdim (bool, optional): Whether to reserve the reduced dimension in the
            output Tensor. The result Tensor will have one fewer dimension
            than the :attr:`x` unless :attr:`keepdim` is true, default
            value is False.
        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: Results the ``logical or`` on the specified axis of input Tensor `x`,  it's data type is bool.

    Raises:
        ValueError: If the data type of `x` is not bool.
        TypeError: The type of :attr:`axis` must be int, list or tuple.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.fluid as fluid
            import paddle.fluid.layers as layers
            import numpy as np
            
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            # x is a bool Tensor with following elements:
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            #    [[True, False]
            #     [False, False]]
            x = layers.assign(np.array([[1, 0], [1, 1]], dtype='int32'))
            print(x)
            x = layers.cast(x, 'bool')
            
            # out1 should be [True]
            out1 = paddle.any(x)  # [True]
            print(out1)
            
            # out2 should be [True, False]
            out2 = paddle.any(x, axis=0)  # [True, False]
            print(out2)
            
            # keep_dim=False, out3 should be [True, False], out.shape should be (2,)
            out3 = paddle.any(x, axis=-1)  # [True, False]
            print(out3)
            
            # keep_dim=True, result should be [[True], [False]], out.shape should be (2,1)
            out4 = paddle.any(x, axis=1, keep_dim=True)
            out4 = layers.cast(out4, 'int32')  # [[True], [False]]
            print(out4)
            
    """
    if axis is not None and not isinstance(axis, (list, tuple)):
        axis = [axis]

    if not axis:
        reduce_all_flag = True
    else:
        if len(axis) == len(x.shape):
            reduce_all_flag = True
        else:
            reduce_all_flag = False

    attrs = {
        'dim': axis if axis != None and axis != [] and axis != () else [0],
        'keep_dim': keepdim,
        'reduce_all': reduce_all_flag
    }
    dtype_flag = False


    if in_dygraph_mode():
        axis = axis if axis != None and axis != [] else [0]
        return core.ops.reduce_any(x, 'dim', axis, 'keep_dim', keepdim,
                                       'reduce_all', reduce_all_flag)
    check_variable_and_dtype(x, 'x', ['bool'], 'any')


    check_type(axis, 'axis', (int, list, tuple, type(None)), 'any')

    helper = LayerHelper('any', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='reduce_any',
        inputs={'X': x},
        outputs={'Out': out},
        attrs=attrs)
    return out
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def broadcast_shape(x_shape, y_shape):
    """
    The function returns the shape of doing operation with broadcasting on tensors of x_shape and y_shape, please refer to :ref:`user_guide_broadcasting` for more details.

    Args:
        x_shape (list[int]|tuple[int]): A shape of tensor.
        y_shape (list[int]|tuple[int]): A shape of tensor.
        

    Returns:
        list[int], the result shape.

    Examples:
        .. code-block:: python

            import paddle

            shape = paddle.broadcast_shape([2, 1, 3], [1, 3, 1])
            # [2, 3, 3]
            
            # shape = paddle.broadcast_shape([2, 1, 3], [3, 3, 1])
            # ValueError (terminated with error message).

    """

    return core.broadcast_shape(x_shape, y_shape)