# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from __future__ import annotations import math import warnings from typing import TYPE_CHECKING, Literal import numpy as np import paddle from paddle import _C_ops from paddle._C_ops import ( # noqa: F401 all, amax, amin, any, isfinite, isinf, isnan, log, logsumexp, maximum, minimum, multiply, sign, sin, ) from paddle.base.libpaddle import DataType from paddle.common_ops_import import VarDesc, dygraph_utils from paddle.pir import Value from paddle.utils.decorator_utils import ( ParamAliasDecorator, param_one_alias, param_two_alias, sum_decorator, ) from paddle.utils.inplace_utils import inplace_apis_in_dygraph_only from ..base.data_feeder import ( check_dtype, check_type, check_variable_and_dtype, convert_dtype, ) from ..common_ops_import import Variable from ..framework import ( LayerHelper, convert_np_dtype_to_dtype_, core, in_dynamic_mode, in_dynamic_or_pir_mode, in_pir_mode, ) from .creation import _complex_to_real_dtype from .layer_function_generator import generate_layer_fn from .manipulation import cast, cast_ from .ops import ( # noqa: F401 abs, abs_, acos, acos_, acosh, acosh_, asin, asin_, asinh, asinh_, atan, atan_, atanh, atanh_, ceil, ceil_, cos, cos_, cosh, cosh_, erf, erf_, exp, exp_, expm1, expm1_, floor, floor_, reciprocal, reciprocal_, round, round_, rsqrt, rsqrt_, sigmoid, sigmoid_, sin_, sinh, sinh_, sqrt, sqrt_, square, square_, tan, tan_, ) if TYPE_CHECKING: from collections.abc import Sequence from numbers import Number from paddle import Tensor from paddle._typing import DTypeLike from paddle.utils.decorator_utils import ForbidKeywordsDecorator __all__ = [] _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, ] def _get_reduce_axis(axis, x): """ Internal function for max, min, amax and amin. It computes the attribute reduce_all value based on axis. """ if axis is not None and not isinstance(axis, list): if isinstance(axis, (tuple, range)): axis = list(axis) elif isinstance(axis, int): axis = [axis] else: raise TypeError( f"The type of axis must be int, list or tuple, but received {type(axis)}" ) if axis is None: axis = [] if axis == [] or len(axis) == len(x.shape): reduce_all = True else: reduce_all = False return reduce_all, axis def _get_reduce_axis_with_tensor(axis, x): if isinstance(axis, (Variable, paddle.pir.Value)): if axis.shape != [] and axis.shape[0] == len(x.shape): reduce_all = True else: reduce_all = False else: reduce_all, axis = _get_reduce_axis(axis, x) if paddle.utils._contain_var(axis): axis = paddle.utils._convert_to_tensor_list(axis) return reduce_all, axis @inplace_apis_in_dygraph_only def log_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``log`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_log`. """ if in_dynamic_mode(): return _C_ops.log_(x) def scale( x: Tensor, scale: float | Tensor = 1.0, bias: float = 0.0, bias_after_scale: bool = True, act: str | None = None, name: str | None = None, ) -> Tensor: """ Scale operator. Putting scale and bias to the input Tensor as following: ``bias_after_scale`` is True: .. math:: Out=scale*X+bias ``bias_after_scale`` is False: .. math:: Out=scale*(X+bias) Args: x (Tensor): Input N-D Tensor of scale operator. Data type can be bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8, complex64, complex128. scale (float|Tensor): The scale factor of the input, it should be a float number or a 0-D Tensor with shape [] and data type as float32. bias (float): The bias to be put on the input. bias_after_scale (bool): Apply bias addition after or before scaling. It is useful for numeric stability in some circumstances. act (str|None, optional): Activation applied to the output such as tanh, softmax, sigmoid, relu. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: Output Tensor of scale operator, with shape and data type same as input. Examples: .. code-block:: python >>> # scale as a float32 number >>> import paddle >>> data = paddle.arange(6).astype("float32").reshape([2, 3]) >>> print(data) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[0., 1., 2.], [3., 4., 5.]]) >>> res = paddle.scale(data, scale=2.0, bias=1.0) >>> print(res) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[1. , 3. , 5. ], [7. , 9. , 11.]]) .. code-block:: python >>> # scale with parameter scale as a Tensor >>> import paddle >>> data = paddle.arange(6).astype("float32").reshape([2, 3]) >>> print(data) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[0., 1., 2.], [3., 4., 5.]]) >>> factor = paddle.to_tensor([2], dtype='float32') >>> res = paddle.scale(data, scale=factor, bias=1.0) >>> print(res) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[1. , 3. , 5. ], [7. , 9. , 11.]]) """ if in_dynamic_mode(): if act is None: return _C_ops.scale(x, scale, float(bias), bias_after_scale) out = _C_ops.scale(x, scale, float(bias), bias_after_scale) return dygraph_utils._append_activation_in_dygraph(out, act) elif in_pir_mode(): out = _C_ops.scale(x, scale, float(bias), bias_after_scale) return paddle.pir_utils.append_activation_in_pir(out, act) else: check_variable_and_dtype( x, "x", [ 'float16', 'bfloat16', 'uint16', 'float32', 'float64', 'int8', 'int16', 'int32', 'int64', 'uint8', 'complex64', 'complex128', ], "scale", ) inputs = {'X': [x]} attrs = { 'bias': float(bias), 'bias_after_scale': bias_after_scale, } if isinstance(scale, Variable): inputs['ScaleTensor'] = [scale] else: attrs['scale'] = float(scale) helper = LayerHelper('scale', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='scale', inputs=inputs, outputs={'Out': out}, attrs=attrs ) return helper.append_activation(out) def stanh( x: Tensor, scale_a: float = 0.67, scale_b: float = 1.7159, name: str | None = None, ) -> Tensor: r""" stanh activation. .. math:: out = b * \frac{e^{a * x} - e^{-a * x}}{e^{a * x} + e^{-a * x}} Parameters: x (Tensor): The input Tensor with data type bfloat16, float16, float32, float64, uint8, int8, int16, int32, int64. scale_a (float, optional): The scale factor a of the input. Default is 0.67. scale_b (float, optional): The scale factor b of the output. Default is 1.7159. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: A Tensor with the same shape and data type as ``x`` (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([1.0, 2.0, 3.0, 4.0]) >>> out = paddle.stanh(x, scale_a=0.67, scale_b=1.72) >>> print(out) Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [1.00616539, 1.49927628, 1.65933096, 1.70390463]) """ if in_dynamic_or_pir_mode(): return _C_ops.stanh(x, scale_a, scale_b) else: check_variable_and_dtype( x, 'x', [ 'float16', 'uint16', 'float32', 'float64', 'uint8', 'int8', 'int16', 'int32', 'int64', ], 'stanh', ) helper = LayerHelper('stanh', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='stanh', inputs={'X': x}, outputs={'Out': out}, attrs={'scale_a': scale_a, 'scale_b': scale_b}, ) return out def multiplex( inputs: Sequence[Tensor], index: Tensor, name: str | None = None ) -> Tensor: """ Based on the given index parameter, the OP selects a specific row from each input Tensor to construct the output Tensor. If the input of this OP contains :math:`m` Tensors, where :math:`I_{i}` means the i-th input Tensor, :math:`i` between :math:`[0,m)` . And :math:`O` means the output, where :math:`O[i]` means the i-th row of the output, then the output satisfies that :math:`O[i] = I_{index[i]}[i]` . For Example: .. code-block:: text Given: inputs = [[[0,0,3,4], [0,1,3,4], [0,2,4,4], [0,3,3,4]], [[1,0,3,4], [1,1,7,8], [1,2,4,2], [1,3,3,4]], [[2,0,3,4], [2,1,7,8], [2,2,4,2], [2,3,3,4]], [[3,0,3,4], [3,1,7,8], [3,2,4,2], [3,3,3,4]]] index = [[3],[0],[1],[2]] out = [[3,0,3,4], # out[0] = inputs[index[0]][0] = inputs[3][0] = [3,0,3,4] [0,1,3,4], # out[1] = inputs[index[1]][1] = inputs[0][1] = [0,1,3,4] [1,2,4,2], # out[2] = inputs[index[2]][2] = inputs[1][2] = [1,2,4,2] [2,3,3,4]] # out[3] = inputs[index[3]][3] = inputs[2][3] = [2,3,3,4] Args: inputs (list[Tensor]|tuple[Tensor, ...]): The input Tensor list. The list elements are N-D Tensors of data types float32, float64, int32, int64, complex64, complex128. All input Tensor shapes should be the same and rank must be at least 2. index (Tensor): Used to select some rows in the input Tensor to construct an index of the output Tensor. It is a 2-D Tensor with data type int32 or int64 and shape [M, 1], where M is the number of input Tensors. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: Output of multiplex OP, with data type being float32, float64, int32, int64. Examples: .. code-block:: python >>> import paddle >>> img1 = paddle.to_tensor([[1, 2], [3, 4]], dtype=paddle.float32) >>> img2 = paddle.to_tensor([[5, 6], [7, 8]], dtype=paddle.float32) >>> inputs = [img1, img2] >>> index = paddle.to_tensor([[1], [0]], dtype=paddle.int32) >>> res = paddle.multiplex(inputs, index) >>> print(res) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[5., 6.], [3., 4.]]) """ if in_dynamic_mode(): return _C_ops.multiplex(inputs, index) elif in_pir_mode(): check_variable_and_dtype( index, "index", ['int32', 'int64'], 'multiplex' ) return _C_ops.multiplex(inputs, index) else: helper = LayerHelper('multiplex', **locals()) check_type(inputs, 'inputs', (list), 'multiplex') if len(inputs) < 2: raise ValueError( "inputs should be a list object with at least 2 elements." ) for id, x in enumerate(inputs): check_variable_and_dtype( x, 'input[' + str(id) + ']', [ 'float32', 'float64', 'int32', 'int64', 'complex64', 'complex128', ], 'multiplex', ) check_variable_and_dtype( index, "index", ['int32', 'int64'], 'multiplex' ) out = helper.create_variable_for_type_inference(inputs[0].dtype) helper.append_op( type='multiplex', inputs={'X': inputs, 'Ids': index}, outputs={'Out': [out]}, ) return out @inplace_apis_in_dygraph_only def scale_( x: Tensor, scale: float = 1.0, bias: float = 0.0, bias_after_scale: bool = True, act: str | None = None, name: str | None = None, ) -> Tensor: """ Inplace version of ``scale`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_scale`. """ if in_dynamic_mode(): return _C_ops.scale_(x, scale, float(bias), bias_after_scale) @ParamAliasDecorator({"x": ["input"], "y": ["exponent"]}) def pow( x: Tensor, y: float | Tensor, name: str | None = None, *, out: Tensor | None = None, ) -> Tensor: """ Compute the power of Tensor elements. The equation is: .. math:: out = x^{y} Note: ``paddle.pow`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, The parameter name ``exponent`` can be used as an alias for ``y``. For example, ``pow(input=2, exponent=1.1)`` is equivalent to ``pow(x=2, y=1.1)``. Args: x (Tensor): An N-D Tensor, the data type is bfloat16, float16, float32, float64, int32, int64, complex64 or complex128. input: An alias for ``x`` , with identical behavior. y (float|int|Tensor): If it is an N-D Tensor, its data type should be the same as `x`. exponent: An alias for ``y`` , with identical behavior. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. out (Tensor, optional): The output tensor. If set, the result will be stored in this tensor. Default is None. Returns: N-D Tensor. A location into which the result is stored. Its dimension and data type are the same as `x`. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([1, 2, 3], dtype='float32') >>> # example 1: y is a float or int >>> res = paddle.pow(x, 2) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [1., 4., 9.]) >>> res = paddle.pow(x, 2.5) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [1. , 5.65685415 , 15.58845711]) >>> # example 2: y is a Tensor >>> y = paddle.to_tensor([2], dtype='float32') >>> res = paddle.pow(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [1., 4., 9.]) """ # in dynamic graph mode if in_dynamic_or_pir_mode(): if isinstance(y, (int, float)): return _C_ops.pow(x, y, out=out) elif isinstance(y, (paddle.Tensor, Variable, paddle.pir.Value)): return _C_ops.elementwise_pow(x, y, out=out) else: raise TypeError( f"y must be scalar, Tensor(in dygraph mode), Value(in pir mode) but received: {type(y)}" ) else: # in static graph mode 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()) out = helper.create_variable_for_type_inference(dtype=x.dtype) return _elementwise_op(LayerHelper('elementwise_pow', **locals())) else: raise TypeError( f"y must be scalar or tensor type, but received: {type(y)}" ) @inplace_apis_in_dygraph_only def pow_(x: Tensor, y: float | Tensor, name: str | None = None) -> Tensor: """ Inplace version of ``pow`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_pow`. """ if isinstance(y, (int, float)): return _C_ops.pow_(x, y) else: raise TypeError(f'y must be scalar type, but received: {type(y)} ') OP_NAMEMAPPING = { 'elementwise_max': 'maximum', 'elementwise_min': 'minimum', 'elementwise_pow': 'elementwise_pow', 'elementwise_floordiv': 'floor_divide', 'elementwise_add': 'add', 'elementwise_sub': 'subtract', 'elementwise_mul': 'multiply', 'elementwise_div': 'divide', 'elementwise_mod': 'remainder', } 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) out = helper.kwargs.get('out', None) assert x is not None, f'x cannot be None in {original_op_type}' assert y is not None, f'y cannot be None in {original_op_type}' bf16_and_complex_supported_ops = [ "elementwise_add", "elementwise_sub", "elementwise_mul", "elementwise_div", "elementwise_max", "elementwise_pow", ] if original_op_type in bf16_and_complex_supported_ops: data_type = [ 'uint16', 'float16', 'float32', 'float64', 'int32', 'int64', 'bool', 'complex64', 'complex128', ] else: data_type = [ 'float16', 'uint16', 'float32', 'float64', 'int32', 'int64', 'bool', ] check_variable_and_dtype( x, 'x', data_type, original_op_type, ) check_variable_and_dtype( y, 'y', data_type, original_op_type, ) axis = helper.kwargs.get('axis', -1) name = helper.kwargs.get('name', None) 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 ) helper.append_op( type=op_type, inputs={'X': x, 'Y': y}, outputs={'Out': out}, attrs={'axis': axis}, ) return helper.append_activation(out) @param_two_alias(["x", "input"], ["y", "other"]) def add( x: Tensor, y: Tensor, name: str | None = None, *, alpha: Number = 1, out: Tensor | None = None, ) -> Tensor: """ Elementwise Add Operator. Add two tensors element-wise. The equation is: .. math:: Out=X+Y $X$ the tensor of any dimension. $Y$ the tensor whose dimensions must be less than or equal to the dimensions of $X$. This operator is used in the following cases: 1. The shape of $Y$ is the same with $X$. 2. The shape of $Y$ is a continuous subsequence of $X$. For example: .. code-block:: text shape(X) = (2, 3, 4, 5), shape(Y) = (,) shape(X) = (2, 3, 4, 5), shape(Y) = (5,) shape(X) = (2, 3, 4, 5), shape(Y) = (4, 5), with axis=-1(default) or axis=2 shape(X) = (2, 3, 4, 5), shape(Y) = (3, 4), with axis=1 shape(X) = (2, 3, 4, 5), shape(Y) = (2), with axis=0 shape(X) = (2, 3, 4, 5), shape(Y) = (2, 1), with axis=0 .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, and ``other`` can be used as an alias for ``y``. For example, ``add(input=tensor_x, other=tensor_y)`` is equivalent to ``add(x=tensor_x, y=tensor_y)``. Args: x (Tensor): Tensor of any dimensions. Its dtype should be bool, bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8, complex64, complex128. alias: ``input``. y (Tensor): Tensor of any dimensions. Its dtype should be bool, bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8, complex64, complex128. alias: ``other``. alpha (Number, optional): Scaling factor for Y. Default: 1. out (Tensor, optional): The output tensor. Default: None. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: N-D Tensor. A location into which the result is stored. It's dimension equals with x. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([2, 3, 4], 'float64') >>> y = paddle.to_tensor([1, 5, 2], 'float64') >>> z = paddle.add(x, y) >>> print(z) Tensor(shape=[3], dtype=float64, place=Place(cpu), stop_gradient=True, [3., 8., 6.]) """ if in_dynamic_or_pir_mode(): scaled_y = y * alpha if alpha != 1 else y return _C_ops.add(x, scaled_y, out=out) else: helper = LayerHelper('elementwise_add', **locals()) scaled_y = ( helper.create_variable_for_type_inference(y.dtype) if alpha != 1 else y ) if alpha != 1: helper.append_op( type='scale', inputs={'X': [y]}, outputs={'Out': [scaled_y]}, attrs={'scale': alpha, 'bias': 0.0}, ) output = helper.create_variable_for_type_inference(x.dtype) helper.append_op( type='elementwise_add', inputs={'X': x, 'Y': scaled_y}, outputs={'Out': output}, attrs={'axis': -1}, ) return output @param_two_alias(["x", "input"], ["y", "other"]) @inplace_apis_in_dygraph_only def add_( x: Tensor, y: Tensor, name: str | None = None, *, alpha: Number = 1, ) -> Tensor: """ Inplace version of ``add`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_add`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) scaled_y = y * alpha if alpha != 1 else y return _C_ops.add_(x, scaled_y) def logaddexp(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Elementwise LogAddExp Operator. Add of exponentiations of the inputs The equation is: .. math:: Out=log(X.exp()+Y.exp()) $X$ the tensor of any dimension. $Y$ the tensor whose dimensions must be less than or equal to the dimensions of $X$. There are two cases for this operator: 1. The shape of $Y$ is the same with $X$. 2. The shape of $Y$ is a continuous subsequence of $X$. For case 2: 1. Broadcast $Y$ to match the shape of $X$, where axis is the start dimension index for broadcasting $Y$ onto $X$. 2. If $axis$ is -1 (default), $axis$=rank($X$)-rank($Y$). 3. The trailing dimensions of size 1 for $Y$ will be ignored for the consideration of subsequence, such as shape($Y$) = (2, 1) => (2). For example: .. code-block:: text shape(X) = (2, 3, 4, 5), shape(Y) = (,) shape(X) = (2, 3, 4, 5), shape(Y) = (5,) shape(X) = (2, 3, 4, 5), shape(Y) = (4, 5), with axis=-1(default) or axis=2 shape(X) = (2, 3, 4, 5), shape(Y) = (3, 4), with axis=1 shape(X) = (2, 3, 4, 5), shape(Y) = (2), with axis=0 shape(X) = (2, 3, 4, 5), shape(Y) = (2, 1), with axis=0 Args: x (Tensor): Tensor of any dimensions. Its dtype should be int32, int64, bfloat16, float16, float32, float64. y (Tensor): Tensor of any dimensions. Its dtype should be int32, int64, bfloat16, float16, float32, float64. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: N-D Tensor. A location into which the result is stored. It's dimension equals with x. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-1, -2, -3], 'float64') >>> y = paddle.to_tensor([-1], 'float64') >>> z = paddle.logaddexp(x, y) >>> print(z) Tensor(shape=[3], dtype=float64, place=Place(cpu), stop_gradient=True, [-0.30685282, -0.68673831, -0.87307199]) """ log_1p = paddle.log1p(paddle.exp(-paddle.abs(x - y))) _maximum = paddle.maximum(x, y) if _maximum.dtype == paddle.int32 or _maximum.dtype == paddle.int64: _maximum = _maximum.astype(log_1p.dtype) return log_1p + _maximum def subtract(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Subtract 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 `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int16, int32, int64, complex64, complex128. y (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int16, int32, int64, complex64, complex128. name (str|None, 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 paddle >>> x = paddle.to_tensor([[1, 2], [7, 8]]) >>> y = paddle.to_tensor([[5, 6], [3, 4]]) >>> res = paddle.subtract(x, y) >>> print(res) Tensor(shape=[2, 2], dtype=int64, place=Place(cpu), stop_gradient=True, [[-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) Tensor(shape=[1, 2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[[ 0, 2, -1], [ 0, 2, -1]]]) >>> x = paddle.to_tensor([2, float('nan'), 5], dtype='float32') >>> y = paddle.to_tensor([1, 4, float('nan')], dtype='float32') >>> res = paddle.subtract(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [1. , nan, nan]) >>> x = paddle.to_tensor([5, float('inf'), -float('inf')], dtype='float64') >>> y = paddle.to_tensor([1, 4, 5], dtype='float64') >>> res = paddle.subtract(x, y) >>> print(res) Tensor(shape=[3], dtype=float64, place=Place(cpu), stop_gradient=True, [ 4. , inf., -inf.]) """ if in_dynamic_or_pir_mode(): return _C_ops.subtract(x, y) else: return _elementwise_op(LayerHelper('elementwise_sub', **locals())) @inplace_apis_in_dygraph_only def subtract_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Inplace version of ``subtract`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_subtract`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) return _C_ops.subtract_(x, y) @param_two_alias(["x", "input"], ["y", "other"]) def divide( x: Tensor, y: Tensor, name: str | None = None, *, rounding_mode: str | None = None, out: Tensor | None = None, ) -> Tensor: """ Divide two tensors element-wise. The equation is: .. math:: out = x / y Note: ``paddle.divide`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, and ``other`` can be used as an alias for ``y``. For example, ``divide(input=tensor_x, other=tensor_y)`` is equivalent to ``divide(x=tensor_x, y=tensor_y)``. Args: x (Tensor): the input tensor, it's data type should be bool, bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8, complex64, complex128. alias: ``input``. y (Tensor): the input tensor, it's data type should be bool, bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8, complex64, complex128. alias: ``other``. rounding_mode (str|None, optional): The rounding mode. Can be None (default), "trunc" (truncate toward zero), or "floor" (round down toward negative infinity). out (Tensor, optional): The output tensor. Default: None. name (str|None, 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 paddle >>> x = paddle.to_tensor([2, 3, 4], dtype='float64') >>> y = paddle.to_tensor([1, 5, 2], dtype='float64') >>> z = paddle.divide(x, y) >>> print(z) Tensor(shape=[3], dtype=float64, place=Place(cpu), stop_gradient=True, [2. , 0.60000000, 2. ]) """ if rounding_mode is None: if in_dynamic_or_pir_mode(): res = _C_ops.divide(x, y, out=out) else: res = _elementwise_op(LayerHelper('elementwise_div', **locals())) return res elif rounding_mode == "trunc": if in_dynamic_or_pir_mode(): tmp = _C_ops.divide(x, y) res = _C_ops.trunc(tmp, out=out) if x.dtype in ( paddle.uint8, paddle.int8, paddle.int16, paddle.int32, paddle.int64, ) and y.dtype in ( paddle.uint8, paddle.int8, paddle.int16, paddle.int32, paddle.int64, ): if x.dtype == paddle.int64 or y.dtype == paddle.int64: target_dtype = paddle.int64 elif x.dtype == paddle.int32 or y.dtype == paddle.int32: target_dtype = paddle.int32 elif x.dtype == paddle.int16 or y.dtype == paddle.int16: target_dtype = paddle.int16 elif x.dtype == paddle.int8 or y.dtype == paddle.int8: target_dtype = paddle.int8 else: target_dtype = paddle.uint8 _C_ops.cast_(res, target_dtype) else: tmp = _elementwise_op(LayerHelper('elementwise_div', **locals())) inputs = {"X": tmp} attrs = {} helper = LayerHelper("trunc", **locals()) check_variable_and_dtype( tmp, 'X', ['int32', 'int64', 'float32', 'float64'], 'trunc' ) res = helper.create_variable_for_type_inference(dtype=tmp.dtype) helper.append_op( type="trunc", inputs=inputs, attrs=attrs, outputs={"Out": res} ) return res elif rounding_mode == "floor": if in_dynamic_or_pir_mode(): res = _C_ops.floor_divide(x, y, out=out) else: res = _elementwise_op( LayerHelper('elementwise_floordiv', **locals()) ) return res else: msg = f"div expected rounding_mode to be one of None, 'trunc', or 'floor' but found {rounding_mode}." raise ValueError(msg) @param_two_alias(["x", "input"], ["y", "other"]) @inplace_apis_in_dygraph_only def divide_( x: Tensor, y: Tensor, name: str | None = None, *, rounding_mode: str | None = None, ) -> Tensor: r""" Inplace version of ``divide`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_divide`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) if rounding_mode is None: res = _C_ops.divide_(x, y) elif rounding_mode == "trunc": x_dtype = x.dtype y_dtype = y.dtype tmp = _C_ops.divide_(x, y) res = _C_ops.trunc_(tmp) if x_dtype in ( paddle.uint8, paddle.int8, paddle.int16, paddle.int32, paddle.int64, ) and y_dtype in ( paddle.uint8, paddle.int8, paddle.int16, paddle.int32, paddle.int64, ): _C_ops.cast_(res, x_dtype) elif rounding_mode == "floor": res = _C_ops.floor_divide_(x, y) else: msg = f"div_ expected rounding_mode to be one of None, 'trunc', or 'floor' but found {rounding_mode}." raise ValueError(msg) return res def true_divide( input: Tensor, other: Tensor, *, out: Tensor | None = None, ) -> Tensor: """ Alias for paddle.divide with rounding_mode=None. Please refer to :ref:`api_paddle_divide`. """ return divide(input, other, out=out) def floor_divide(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Floor divide two tensors element-wise and rounds the quotinents to the nearest integer toward negative infinite. The equation is: .. math:: out = floor(x / y) - :math:`x`: Multidimensional Tensor. - :math:`y`: Multidimensional Tensor. Note: ``paddle.floor_divide`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): the input tensor, it's data type should be uint8, int8, int32, int64, float32, float64, float16, bfloat16. y (Tensor): the input tensor, it's data type should be uint8, int8, int32, int64, float32, float64, float16, bfloat16. name (str|None, 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. It's dimension equals with $x$. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([2, 3, 8, 7]) >>> y = paddle.to_tensor([1, 5, 3, 3]) >>> z = paddle.floor_divide(x, y) >>> print(z) Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [2, 0, 2, 2]) >>> x = paddle.to_tensor([2, 3, 8, 7]) >>> y = paddle.to_tensor([1, -5, -3, -3]) >>> z = paddle.floor_divide(x, y) >>> print(z) Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [2, -1, -3, -3]) """ if in_dynamic_or_pir_mode(): return _C_ops.floor_divide(x, y) else: return _elementwise_op(LayerHelper('elementwise_floordiv', **locals())) @inplace_apis_in_dygraph_only def floor_divide_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``floor_divide`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_floor_divide`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) return _C_ops.floor_divide_(x, y) def remainder(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Mod two tensors element-wise. The equation is: .. math:: out = x \% y Note: ``paddle.remainder`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor And `mod`, `floor_mod` are all functions with the same name Args: x (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int32, int64. y (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int32, int64. name (str|None, 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 paddle >>> x = paddle.to_tensor([2, 3, 8, 7]) >>> y = paddle.to_tensor([1, 5, 3, 3]) >>> z = paddle.remainder(x, y) >>> print(z) Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 3, 2, 1]) >>> z = paddle.floor_mod(x, y) >>> print(z) Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 3, 2, 1]) >>> z = paddle.mod(x, y) >>> print(z) Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 3, 2, 1]) """ if in_dynamic_or_pir_mode(): return _C_ops.remainder(x, y) else: return _elementwise_op(LayerHelper('elementwise_mod', **locals())) @inplace_apis_in_dygraph_only def remainder_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``remainder`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_remainder`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) return _C_ops.remainder_(x, y) mod = remainder floor_mod = remainder mod_ = remainder_ mod_.__doc__ = r""" Inplace version of ``mod`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_mod`. """ floor_mod_ = remainder_ floor_mod_.__doc__ = r""" Inplace version of ``floor_mod_`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_floor_mod_`. """ @param_two_alias(["x", "input"], ["y", "other"]) def mul( x: Tensor, y: Tensor, name: str | None = None, *, out: Tensor | None = None ) -> Tensor: """ multiply two tensors element-wise. The equation is: .. math:: out = x * y Note: Supported shape of :attr:`x` and :attr:`y` for this operator: 1. `x.shape` == `y.shape`. 2. `x.shape` could be the continuous subsequence of `y.shape`. ``paddle.mul`` supports broadcasting. If you would like to know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): the input tensor, its data type should be one of bfloat16, float16, float32, float64, int32, int64, bool, complex64, complex128. y (Tensor): the input tensor, its data type should be one of bfloat16, float16, float32, float64, int32, int64, bool, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. out (Tensor|None, optional): The output tensor. If set, the result will be stored in this tensor. Default is None. Returns: N-D Tensor. A location into which the result is stored. If :attr:`x`, :attr:`y` have different shapes and are "broadcastable", the resulting tensor shape is the shape of :attr:`x` and :attr:`y` after broadcasting. If :attr:`x`, :attr:`y` have the same shape, its shape is the same as :attr:`x` and :attr:`y`. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([[1, 2], [3, 4]]) >>> y = paddle.to_tensor([[5, 6], [7, 8]]) >>> res = paddle.mul(x, y) >>> print(res) Tensor(shape=[2, 2], dtype=int64, place=Place(cpu), stop_gradient=True, [[5 , 12], [21, 32]]) >>> x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]]) >>> y = paddle.to_tensor([2]) >>> res = paddle.mul(x, y) >>> print(res) Tensor(shape=[1, 2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[[2, 4, 6], [2, 4, 6]]]) """ if in_dynamic_or_pir_mode(): return _C_ops.multiply(x, y, out=out) else: return _elementwise_op(LayerHelper('elementwise_mul', **locals())) @param_two_alias(["x", "input"], ["y", "other"]) @inplace_apis_in_dygraph_only def multiply_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Inplace version of ``multiply`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_multiply`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) return _C_ops.multiply_(x, y) def _elementwise_op_with_axis(x, y, axis=-1, name=None, op_type="Undefined"): assert in_dynamic_or_pir_mode(), ( "You can only call `_elementwise_op_with_axis` function within in_dynamic_or_pir_mode" ) assert op_type in [ "add", "subtract", "multiply", "divide", ], ( f"op_name input error! _elementwise_op_with_axis is an inner function to replace elementwise_add/sub/mul/div. Input op_name={op_type}, Expect op_name=[add|subtract|multiply|divide]\n" ) op = getattr(_C_ops, op_type) x_shape = list(x.shape) y_shape = list(y.shape) if axis == -1 or len(x_shape) == len(y_shape): return op(x, y) if len(x_shape) > len(y_shape): padding = len(x_shape) - len(y_shape) - axis y = paddle.reshape(y, [1] * axis + y_shape + [1] * padding) else: padding = len(y_shape) - len(x_shape) - axis x = paddle.reshape(x, [1] * axis + y_shape + [1] * padding) return op(x, y) def _add_with_axis(x, y, axis=-1, name=None): # opt performance, only dynamic mode needs reshape if in_dynamic_or_pir_mode(): return _elementwise_op_with_axis(x, y, axis, name, "add") else: op_type = 'elementwise_add' return _elementwise_op(LayerHelper(op_type, **locals())) def _subtract_with_axis(x, y, axis=-1, name=None): # opt performance, only dynamic mode needs reshape if in_dynamic_or_pir_mode(): return _elementwise_op_with_axis(x, y, axis, name, "subtract") else: op_type = 'elementwise_sub' return _elementwise_op(LayerHelper(op_type, **locals())) def _multiply_with_axis(x, y, axis=-1, name=None): # opt performance, only dynamic mode needs reshape if in_dynamic_or_pir_mode(): return _elementwise_op_with_axis(x, y, axis, name, "multiply") else: op_type = 'elementwise_mul' return _elementwise_op(LayerHelper(op_type, **locals())) def _divide_with_axis(x, y, axis=-1, name=None): # opt performance, only dynamic mode needs reshape if in_dynamic_or_pir_mode(): return _elementwise_op_with_axis(x, y, axis, name, "divide") else: op_type = 'elementwise_div' return _elementwise_op(LayerHelper(op_type, **locals())) def fmax(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Compares the elements at the corresponding positions of the two tensors and returns a new tensor containing the maximum value of the element. If one of them is a nan value, the other value is directly returned, if both are nan values, then the first nan value is returned. The equation is: .. math:: out = fmax(x, y) Note: ``paddle.fmax`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int32, int64. y (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int32, int64. name (str|None, 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 paddle >>> x = paddle.to_tensor([[1, 2], [7, 8]]) >>> y = paddle.to_tensor([[3, 4], [5, 6]]) >>> res = paddle.fmax(x, y) >>> print(res) Tensor(shape=[2, 2], dtype=int64, place=Place(cpu), stop_gradient=True, [[3, 4], [7, 8]]) >>> x = paddle.to_tensor([[1, 2, 3], [1, 2, 3]]) >>> y = paddle.to_tensor([3, 0, 4]) >>> res = paddle.fmax(x, y) >>> print(res) Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[3, 2, 4], [3, 2, 4]]) >>> x = paddle.to_tensor([2, 3, 5], dtype='float32') >>> y = paddle.to_tensor([1, float("nan"), float("nan")], dtype='float32') >>> res = paddle.fmax(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [2., 3., 5.]) >>> x = paddle.to_tensor([5, 3, float("inf")], dtype='float32') >>> y = paddle.to_tensor([1, -float("inf"), 5], dtype='float32') >>> res = paddle.fmax(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [5. , 3. , inf.]) """ if in_dynamic_or_pir_mode(): return _C_ops.fmax(x, y) else: return _elementwise_op(LayerHelper('elementwise_fmax', **locals())) def fmin(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Compares the elements at the corresponding positions of the two tensors and returns a new tensor containing the minimum value of the element. If one of them is a nan value, the other value is directly returned, if both are nan values, then the first nan value is returned. The equation is: .. math:: out = fmin(x, y) Note: ``paddle.fmin`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int32, int64. y (Tensor): the input tensor, it's data type should be bfloat16, float16, float32, float64, int32, int64. name (str|None, 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 paddle >>> x = paddle.to_tensor([[1, 2], [7, 8]]) >>> y = paddle.to_tensor([[3, 4], [5, 6]]) >>> res = paddle.fmin(x, y) >>> print(res) Tensor(shape=[2, 2], dtype=int64, place=Place(cpu), stop_gradient=True, [[1, 2], [5, 6]]) >>> x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]]) >>> y = paddle.to_tensor([3, 0, 4]) >>> res = paddle.fmin(x, y) >>> print(res) Tensor(shape=[1, 2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[[1, 0, 3], [1, 0, 3]]]) >>> x = paddle.to_tensor([2, 3, 5], dtype='float32') >>> y = paddle.to_tensor([1, float("nan"), float("nan")], dtype='float32') >>> res = paddle.fmin(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [1., 3., 5.]) >>> x = paddle.to_tensor([5, 3, float("inf")], dtype='float64') >>> y = paddle.to_tensor([1, -float("inf"), 5], dtype='float64') >>> res = paddle.fmin(x, y) >>> print(res) Tensor(shape=[3], dtype=float64, place=Place(cpu), stop_gradient=True, [ 1. , -inf., 5. ]) """ if in_dynamic_or_pir_mode(): return _C_ops.fmin(x, y) else: return _elementwise_op(LayerHelper('elementwise_fmin', **locals())) @sum_decorator() def sum( x: Tensor, axis: int | Sequence[int] | None = None, dtype: DTypeLike | None = None, keepdim: bool = False, name: str | None = None, ) -> Tensor: """ Computes the sum of tensor elements over the given dimension. .. note:: Parameter order support: When passing positional parameters, it is possible to support swapping the positional order of dtype and axis. For example, ``sum(x, axis, keepdim, dtype)`` is equivalent to ``sum(x, axis, dtype, keepdim)``. Alias Support: The parameter name ``input`` can be used as an alias for ``x`` and the parameter name ``dim`` can be used as an alias for ``axis``. For example, ``sum(input=tensor_x, dim=1)`` is equivalent to ``sum(x=tensor_x, axis=1)``. Args: x (Tensor): An N-D Tensor, the data type is bool, bfloat16, float16, float32, float64, uint8, int8, int16, int32, int64, complex64, complex128. alias: ``input``. axis (int|list|tuple|None, optional): The dimensions along which the sum is performed. If :attr:`None`, sum all elements of :attr:`x` and return a Tensor with a single element, otherwise must be in the range :math:`[-rank(x), rank(x))`. If :math:`axis[i] < 0`, the dimension to reduce is :math:`rank + axis[i]`. alias: ``dim``. dtype (str|paddle.dtype|np.dtype, 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 value is False. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: Results of summation operation on the specified axis of input Tensor `x`, if `x.dtype='bool'`, `x.dtype='int32'`, it's data type is `'int64'`, otherwise it's data type is the same as `x`. Examples: .. code-block:: python >>> import paddle >>> # x is a Tensor with following elements: >>> # [[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. >>> x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9], ... [0.1, 0.2, 0.6, 0.7]]) >>> out1 = paddle.sum(x) >>> out1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 3.50000000) >>> out2 = paddle.sum(x, axis=0) >>> out2 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [0.30000001, 0.50000000, 1.10000002, 1.59999990]) >>> out3 = paddle.sum(x, axis=-1) >>> out3 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [1.89999998, 1.60000002]) >>> out4 = paddle.sum(x, axis=1, keepdim=True) >>> out4 Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[1.89999998], [1.60000002]]) >>> # y is a Tensor with shape [2, 2, 2] and elements as below: >>> # [[[1, 2], [3, 4]], >>> # [[5, 6], [7, 8]]] >>> # Each example is followed by the corresponding output tensor. >>> y = paddle.to_tensor([[[1, 2], [3, 4]], ... [[5, 6], [7, 8]]]) >>> out5 = paddle.sum(y, axis=[1, 2]) >>> out5 Tensor(shape=[2], dtype=int64, place=Place(cpu), stop_gradient=True, [10, 26]) >>> out6 = paddle.sum(y, axis=[0, 1]) >>> out6 Tensor(shape=[2], dtype=int64, place=Place(cpu), stop_gradient=True, [16, 20]) >>> # x is a Tensor with following elements: >>> # [[True, True, True, True] >>> # [False, False, False, False]] >>> # Each example is followed by the corresponding output tensor. >>> x = paddle.to_tensor([[True, True, True, True], ... [False, False, False, False]]) >>> out7 = paddle.sum(x) >>> out7 Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 4) >>> out8 = paddle.sum(x, axis=0) >>> out8 Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [1, 1, 1, 1]) >>> out9 = paddle.sum(x, axis=1) >>> out9 Tensor(shape=[2], dtype=int64, place=Place(cpu), stop_gradient=True, [4, 0]) """ dtype_flag = False if dtype is not None: dtype_flag = True if not isinstance(dtype, paddle.dtype): dtype = convert_np_dtype_to_dtype_(dtype) if in_dynamic_mode(): return _C_ops.sum(x, axis, dtype, keepdim) else: reduce_all, axis = _get_reduce_axis_with_tensor(axis, x) if in_pir_mode(): return _C_ops.sum(x, axis, dtype, keepdim) else: attrs = {'dim': axis, 'keep_dim': keepdim} if dtype_flag: attrs.update({'in_dtype': x.dtype, 'out_dtype': dtype}) check_variable_and_dtype( x, 'x', [ 'bool', 'uint16', 'int8', 'uint8', 'float16', 'float32', 'float64', 'int16', 'int32', 'int64', 'complex64', 'complex128', ], 'sum', ) check_type( axis, 'axis', (int, list, tuple, type(None), Variable), 'sum' ) helper = LayerHelper('sum', **locals()) if dtype_flag: out = helper.create_variable_for_type_inference(dtype=dtype) else: out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='reduce_sum', inputs={'X': x}, outputs={'Out': out}, attrs=attrs, ) return out def reduce_as(x: Tensor, target: Tensor, name: str | None = None) -> Tensor: """ Computes the sum of tensor elements make the shape of its result equal to the shape of target. Args: x (Tensor): An N-D Tensor, the data type is bool, float16, float32, float64, int8, uint8, int16, uint16, int32, int64, complex64 or complex128. target (Tensor): An N-D Tensor, the length of x shape must greater than or equal to the length of target shape. The data type is bool, float16, float32, float64, int8, uint8, int16, uint16, int32, int64, complex64 or complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The sum of the input tensor x along some axis has the same shape as the shape of the input tensor target, if `x.dtype='bool'`, `x.dtype='int32'`, it's data type is `'int64'`, otherwise it's data type is the same as `x`. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([[1, 2, 3, 4], [5, 6, 7, 8]]) >>> x Tensor(shape=[2, 4], dtype=int64, place=Place(gpu:0), stop_gradient=True, [[1, 2, 3, 4], [5, 6, 7, 8]]) >>> target = paddle.to_tensor([1, 2, 3, 4]) >>> target Tensor(shape=[4], dtype=int64, place=Place(gpu:0), stop_gradient=True, [1, 2, 3, 4]) >>> res = paddle.reduce_as(x, target) >>> res Tensor(shape=[4], dtype=int64, place=Place(gpu:0), stop_gradient=True, [6 , 8 , 10, 12]) """ if in_dynamic_or_pir_mode(): return _C_ops.reduce_as(x, target) else: check_variable_and_dtype( x, 'x', [ 'bool', 'float16', 'float32', 'float64', 'int8', 'uint8', 'int16', 'uint16', 'int32', 'int64', 'complex64', 'complex128', ], 'reduce_as', ) check_variable_and_dtype( target, 'target', [ 'bool', 'float16', 'float32', 'float64', 'int8', 'uint8', 'int16', 'uint16', 'int32', 'int64', 'complex64', 'complex128', ], 'reduce_as', ) helper = LayerHelper('reduce_as', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='reduce_as', inputs={'x': x, 'target': target}, outputs={'out': out}, ) return out def nan_to_num( x: Tensor, nan: float = 0.0, posinf: float | None = None, neginf: float | None = None, name: str | None = None, ) -> Tensor: """ Replaces NaN, positive infinity, and negative infinity values in input tensor. Args: x (Tensor): An N-D Tensor, the data type is float32, float64. nan (float, optional): the value to replace NaNs with. Default is 0. posinf (float|None, optional): if a Number, the value to replace positive infinity values with. If None, positive infinity values are replaced with the greatest finite value representable by input’s dtype. Default is None. neginf (float|None, optional): if a Number, the value to replace negative infinity values with. If None, negative infinity values are replaced with the lowest finite value representable by input’s dtype. Default is None. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: Results of nan_to_num operation input Tensor ``x``. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([float('nan'), 0.3, float('+inf'), float('-inf')], dtype='float32') >>> out1 = paddle.nan_to_num(x) >>> out1 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [ 0. , 0.30000001 , 340282346638528859811704183484516925440., -340282346638528859811704183484516925440.]) >>> out2 = paddle.nan_to_num(x, nan=1) >>> out2 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [ 1. , 0.30000001 , 340282346638528859811704183484516925440., -340282346638528859811704183484516925440.]) >>> out3 = paddle.nan_to_num(x, posinf=5) >>> out3 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [ 0. , 0.30000001 , 5. , -340282346638528859811704183484516925440.]) >>> out4 = paddle.nan_to_num(x, nan=10, neginf=-99) >>> out4 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [ 10. , 0.30000001 , 340282346638528859811704183484516925440., -99. ]) """ # NOTE(tiancaishaonvjituizi): it seems that paddle handles the dtype of python float number # incorrectly, so we have to explicitly construct tensors here posinf_value = paddle.full_like(x, float("+inf")) neginf_value = paddle.full_like(x, float("-inf")) nan = paddle.full_like(x, nan) assert x.dtype in [ paddle.float32, paddle.float64, paddle.base.core.DataType.FLOAT32, paddle.base.core.DataType.FLOAT64, ] is_float32 = ( x.dtype == paddle.float32 or x.dtype == paddle.base.core.DataType.FLOAT32 ) if posinf is None: posinf = ( np.finfo(np.float32).max if is_float32 else np.finfo(np.float64).max ) posinf = paddle.full_like(x, posinf) if neginf is None: neginf = ( np.finfo(np.float32).min if is_float32 else np.finfo(np.float64).min ) neginf = paddle.full_like(x, neginf) x = paddle.where(paddle.isnan(x), nan, x) x = paddle.where(paddle.equal(x, posinf_value), posinf, x) x = paddle.where(paddle.equal(x, neginf_value), neginf, x) return x @inplace_apis_in_dygraph_only def nan_to_num_( x: Tensor, nan: float = 0.0, posinf: float | None = None, neginf: float | None = None, name: str | None = None, ) -> Tensor: r""" Inplace version of ``nan_to_num`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_nan_to_num`. """ # NOTE(tiancaishaonvjituizi): it seems that paddle handles the dtype of python float number # incorrectly, so we have to explicitly construct tensors here posinf_value = paddle.full_like(x, float("+inf")) neginf_value = paddle.full_like(x, float("-inf")) nan = paddle.full_like(x, nan) assert x.dtype in [paddle.float32, paddle.float64] is_float32 = x.dtype == paddle.float32 if posinf is None: posinf = ( np.finfo(np.float32).max if is_float32 else np.finfo(np.float64).max ) posinf = paddle.full_like(x, posinf) if neginf is None: neginf = ( np.finfo(np.float32).min if is_float32 else np.finfo(np.float64).min ) neginf = paddle.full_like(x, neginf) x_not_nan = paddle.logical_not(paddle.isnan(x)) x = paddle.where_(x_not_nan, x, nan) x = paddle.where_(x != posinf_value, x, posinf) x = paddle.where_(x != neginf_value, x, neginf) return x def nansum( x: Tensor, axis: int | Sequence[int] | None = None, dtype: DTypeLike | None = None, keepdim: bool = False, name: str | None = None, ) -> Tensor: """ Computes the sum of tensor elements over the given axis, treating Not a Numbers (NaNs) as zero. Args: x (Tensor): An N-D Tensor, the data type is bfloat16, float16, float32, float64, int32 or int64. axis (int|list|tuple, optional): The dimensions along which the nansum is performed. If :attr:`None`, nansum all elements of :attr:`x` and return a Tensor with a single element, otherwise must be in the range :math:`[-rank(x), rank(x))`. If :math:`axis[i] < 0`, the dimension to reduce is :math:`rank + axis[i]`. dtype (str|paddle.dtype|np.dtype, 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 value is False. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: Results of summation operation on the specified axis of input Tensor `x`, Examples: .. code-block:: python >>> import paddle >>> # x is a Tensor with following elements: >>> # [[nan, 0.3, 0.5, 0.9] >>> # [0.1, 0.2, -nan, 0.7]] >>> # Each example is followed by the corresponding output tensor. >>> x = paddle.to_tensor([[float('nan'), 0.3, 0.5, 0.9], ... [0.1, 0.2, float('-nan'), 0.7]],dtype="float32") >>> out1 = paddle.nansum(x) >>> out1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 2.69999981) >>> out2 = paddle.nansum(x, axis=0) >>> out2 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [0.10000000, 0.50000000, 0.50000000, 1.59999990]) >>> out3 = paddle.nansum(x, axis=-1) >>> out3 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [1.70000005, 1. ]) >>> out4 = paddle.nansum(x, axis=1, keepdim=True) >>> out4 Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[1.70000005], [1. ]]) >>> # y is a Tensor with shape [2, 2, 2] and elements as below: >>> # [[[1, nan], [3, 4]], >>> # [[5, 6], [-nan, 8]]] >>> # Each example is followed by the corresponding output tensor. >>> y = paddle.to_tensor([[[1, float('nan')], [3, 4]], ... [[5, 6], [float('-nan'), 8]]]) >>> out5 = paddle.nansum(y, axis=[1, 2]) >>> out5 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [8. , 19.]) >>> out6 = paddle.nansum(y, axis=[0, 1]) >>> out6 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [9. , 18.]) """ check_variable_and_dtype( x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64', 'uint16'], 'nansum', ) check_type(axis, 'axis', (int, list, tuple, type(None)), 'nansum') zero_tensor = paddle.zeros_like(x) tmp_tensor = paddle.where(isnan(x), zero_tensor, x) return sum(tmp_tensor, axis, dtype, keepdim, name) def nanmean( x: Tensor, axis: int | Sequence[int] | None = None, keepdim: bool = False, name: str | None = None, ) -> Tensor: r""" Compute the arithmetic mean along the specified axis, ignoring NaNs. Args: x (Tensor): The input Tensor with data type uint16, float16, float32, float64. axis (int|list|tuple, optional):The axis along which to perform nanmean calculations. ``axis`` should be int, list(int) or tuple(int). If ``axis`` is a list/tuple of dimension(s), nanmean 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, nanmean is calculated over all elements of ``x``. Default is None. keepdim (bool, optional): Whether to reserve the reduced dimension(s) in the output Tensor. If ``keepdim`` 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|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, results of arithmetic mean along ``axis`` of ``x``, with the same data type as ``x``. Examples: .. code-block:: python >>> import paddle >>> # x is a 2-D Tensor: >>> x = paddle.to_tensor([[float('nan'), 0.3, 0.5, 0.9], ... [0.1, 0.2, float('-nan'), 0.7]]) >>> out1 = paddle.nanmean(x) >>> out1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.44999996) >>> out2 = paddle.nanmean(x, axis=0) >>> out2 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [0.10000000, 0.25000000, 0.50000000, 0.79999995]) >>> out3 = paddle.nanmean(x, axis=0, keepdim=True) >>> out3 Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.10000000, 0.25000000, 0.50000000, 0.79999995]]) >>> out4 = paddle.nanmean(x, axis=1) >>> out4 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [0.56666666, 0.33333334]) >>> out5 = paddle.nanmean(x, axis=1, keepdim=True) >>> out5 Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.56666666], [0.33333334]]) >>> # y is a 3-D Tensor: >>> y = paddle.to_tensor([[[1, float('nan')], [3, 4]], ... [[5, 6], [float('-nan'), 8]]]) >>> out6 = paddle.nanmean(y, axis=[1, 2]) >>> out6 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [2.66666675, 6.33333349]) >>> out7 = paddle.nanmean(y, axis=[0, 1]) >>> out7 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [3., 6.]) """ if isinstance(axis, int): axis = [axis] check_variable_and_dtype( x, 'x/input', ['uint16', 'float16', 'float32', 'float64'], 'nanmean' ) if axis is not None: check_type(axis, 'axis/dim', (int, list, tuple), 'nanmean') cnt = paddle.sum(~paddle.isnan(x), axis=axis, keepdim=keepdim) return paddle.divide( paddle.nansum(x, axis=axis, keepdim=keepdim, name=name), cnt.astype(x.dtype), ) def count_nonzero( x: Tensor, axis: int | Sequence[int] | None = None, keepdim: bool = False, name: str | None = None, ) -> Tensor: r""" Counts the number of non-zero values in the tensor x along the specified axis. Args: x (Tensor): An N-D Tensor, the data type is bool, float16, 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 Tensor with a single element, otherwise must be in the 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|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: Results of count operation on the specified axis of input Tensor `x`, it's data type is `'int64'`. Examples: .. code-block:: python >>> import paddle >>> # x is a 2-D Tensor: >>> x = paddle.to_tensor([[0., 1.1, 1.2], [0., 0., 1.3], [0., 0., 0.]]) >>> out1 = paddle.count_nonzero(x) >>> out1 Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 3) >>> out2 = paddle.count_nonzero(x, axis=0) >>> out2 Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 1, 2]) >>> out3 = paddle.count_nonzero(x, axis=0, keepdim=True) >>> out3 Tensor(shape=[1, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[0, 1, 2]]) >>> out4 = paddle.count_nonzero(x, axis=1) >>> out4 Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [2, 1, 0]) >>> out5 = paddle.count_nonzero(x, axis=1, keepdim=True) >>> out5 Tensor(shape=[3, 1], dtype=int64, place=Place(cpu), stop_gradient=True, [[2], [1], [0]]) >>> # y is a 3-D Tensor: >>> y = paddle.to_tensor([[[0., 1.1, 1.2], [0., 0., 1.3], [0., 0., 0.]], ... [[0., 2.5, 2.6], [0., 0., 2.4], [2.1, 2.2, 2.3]]]) >>> out6 = paddle.count_nonzero(y, axis=[1, 2]) >>> out6 Tensor(shape=[2], dtype=int64, place=Place(cpu), stop_gradient=True, [3, 6]) >>> out7 = paddle.count_nonzero(y, axis=[0, 1]) >>> out7 Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [1, 3, 5]) """ if isinstance(axis, int): axis = [axis] bool_tensor = paddle.cast(x, 'bool') int_tensor = paddle.cast(bool_tensor, 'int64') return paddle.sum(int_tensor, axis=axis, keepdim=keepdim, name=name) def add_n(inputs: Tensor | Sequence[Tensor], name: str | None = None) -> Tensor: """ 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]] Args: inputs (Tensor|list[Tensor]|tuple[Tensor]): A Tensor or a list/tuple of Tensors. The shape and data type of the list/tuple elements should be consistent. Input can be multi-dimensional Tensor, and data types can be: bfloat16, float16, float32, float64, int32, int64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the sum of input :math:`inputs` , its shape and data types are consistent with :math:`inputs`. Examples: .. code-block:: python >>> import paddle >>> 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]) >>> output Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[8. , 10., 12.], [14., 16., 18.]]) """ if in_dynamic_or_pir_mode(): if isinstance(inputs, (Variable, paddle.pir.Value)): inputs = [inputs] return _C_ops.add_n(inputs) else: helper = LayerHelper('add_n', **locals()) check_type(inputs, 'inputs', (Variable, tuple, list), 'add_n') if isinstance(inputs, (list, tuple)): if len(inputs) > 0: for input in inputs: check_variable_and_dtype( input, "inputs", [ 'float16', 'float32', 'float64', 'int32', 'int64', 'uint16', 'complex64', 'complex128', ], 'add_n', ) else: check_variable_and_dtype( inputs, "inputs", [ 'float16', 'float32', 'float64', 'int32', 'int64', 'uint16', 'complex64', 'complex128', ], 'add_n', ) out = helper.create_variable_for_type_inference( dtype=helper.input_dtype('inputs') ) helper.append_op( type='sum', inputs={'X': inputs}, outputs={'Out': out}, attrs={}, ) return out def trunc(input: Tensor, name: str | None = None) -> Tensor: ''' This API is used to returns a new tensor with the truncated integer values of input. Args: input (Tensor): The input tensor, it's data type should be int32, int64, float32, float64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The output Tensor of trunc. Examples: .. code-block:: python >>> import paddle >>> input = paddle.to_tensor([[0.1, 1.5], [-0.2, -2.4]], 'float32') >>> output = paddle.trunc(input) >>> output Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[ 0., 1.], [-0., -2.]]) ''' if in_dynamic_or_pir_mode(): return _C_ops.trunc(input) else: inputs = {"X": input} attrs = {} helper = LayerHelper("trunc", **locals()) check_variable_and_dtype( input, 'X', ['int32', 'int64', 'float32', 'float64'], 'trunc' ) out = helper.create_variable_for_type_inference(dtype=input.dtype) helper.append_op( type="trunc", inputs=inputs, attrs=attrs, outputs={"Out": out} ) return out @inplace_apis_in_dygraph_only def trunc_(input: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``trunc`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_trunc`. """ if in_dynamic_mode(): return _C_ops.trunc_(input) def mm(input: Tensor, mat2: Tensor, name: str | None = None) -> Tensor: """ 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. Args: input (Tensor): The input tensor which is a Tensor. Support data types: bfloat16, float16, float32, float64, int8, int32, int64, complex64, complex128. mat2 (Tensor): The input tensor which is a Tensor. Support data types: bfloat16, float16, float32, float64, int8, int32, int64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The product Tensor, with same data type of the input Tensor. :: * example 1: input: [B, ..., M, K], mat2: [B, ..., K, N] out: [B, ..., M, N] * example 2: input: [B, M, K], mat2: [B, K, N] out: [B, M, N] * example 3: input: [B, M, K], mat2: [K, N] out: [B, M, N] * example 4: input: [M, K], mat2: [K, N] out: [M, N] * example 5: input: [B, M, K], mat2: [K] out: [B, M] * example 6: input: [K], mat2: [K] out: [1] Examples: .. code-block:: python >>> import paddle >>> 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) >>> out Tensor(shape=[3, 4], dtype=float32, place=Place(cpu), stop_gradient=True, [[11., 14., 17., 20.], [23., 30., 37., 44.], [35., 46., 57., 68.]]) """ if in_dynamic_mode(): return _C_ops.matmul(input, mat2, False, False) 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 " f"prerequisites. But received X's shape: {x_shape}, Y's shape: {y_shape}\n" ) 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. " f"But received x_shape[{i}] != y_shape[{i}]. X's shape: {x_shape}, " f"Y's shape: {y_shape}.\n" ) __check_input(input, mat2) if in_pir_mode(): return _C_ops.matmul(input, mat2, False, False) else: helper = LayerHelper('mm', **locals()) out = helper.create_variable_for_type_inference(dtype=input.dtype) helper.append_op( type='matmul_v2', inputs={'X': input, 'Y': mat2}, outputs={'Out': out}, ) return out def addmm( input: Tensor, x: Tensor, y: Tensor, beta: float = 1.0, alpha: float = 1.0, name: str | None = None, ) -> Tensor: """ **addmm** 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: 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. beta (float, optional): Coefficient of $input$, default is 1. alpha (float, optional): Coefficient of $x*y$, default is 1. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The output Tensor of addmm. Examples: .. code-block:: python >>> import paddle >>> x = paddle.ones([2, 2]) >>> y = paddle.ones([2, 2]) >>> input = paddle.ones([2, 2]) >>> out = paddle.addmm(input=input, x=x, y=y, beta=0.5, alpha=5.0) >>> print(out) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[10.50000000, 10.50000000], [10.50000000, 10.50000000]]) """ input_shape = input.shape x_shape = x.shape y_shape = y.shape if not len(x_shape) == len(y_shape) == 2: raise ValueError( f"The dimension of x, y should be 2 but receive x's shape: {x_shape}, y's shape: {y_shape}" ) if x_shape[1] != y_shape[0]: raise ValueError( f"The input Variable x's width must be equal with Variable y' height. But received x's shape = {x_shape}, y's shape = {y_shape}." ) if len(input_shape) == 2: if input_shape[0] != x_shape[0]: if input_shape[0] != 1: raise ValueError( f"When x's dimension[0] is not equal with input's dimension[0], input's dimension[0] must be 1 but got {input_shape[0]}" ) if input_shape[1] != y_shape[1] and input_shape[1] != 1: raise ValueError( f"When y's dimension[1] is not equal with input's dimension[1], input's dimension[1] must be 1 but got {input_shape[1]}" ) if input_shape[1] != y_shape[1]: if input_shape[1] != 1: raise ValueError( f"When y's dimension[1] is not equal with input's dimension[1], input's dimension[1] must be 1 but got {input_shape[1]}" ) elif len(input_shape) == 1: if input_shape[0] not in (y_shape[1], 1): raise ValueError( f"The input's shape: {input_shape} is not broadcastable with [x.shape[0], y.shape[1]]: [{x_shape[0]},{y_shape[1]}]" ) else: raise ValueError( f"The dimension of input should be 2 or 1 but receive input's shape: {input_shape}" ) if in_dynamic_or_pir_mode(): return _C_ops.addmm(input, x, y, beta, alpha) else: inputs = {'Input': input, "X": x, "Y": y} attrs = {'Alpha': alpha, 'Beta': beta} helper = LayerHelper("addmm", **locals()) check_variable_and_dtype( input, 'Input', ['float16', 'float32', 'float64', 'uint16'], 'addmm' ) check_variable_and_dtype( x, 'X', ['float16', 'float32', 'float64', 'uint16'], 'addmm' ) check_variable_and_dtype( y, 'Y', ['float16', 'float32', 'float64', 'uint16'], '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 @inplace_apis_in_dygraph_only def addmm_( input: Tensor, x: Tensor, y: Tensor, beta: float = 1.0, alpha: float = 1.0, name: str | None = None, ) -> Tensor: """ Inplace version of ``addmm`` API, the output Tensor will be inplaced with input ``input``. Please refer to :ref:`api_paddle_addmm`. """ input_shape = input.shape x_shape = x.shape y_shape = y.shape if not len(x_shape) == len(y_shape) == 2: raise ValueError( f"The dimension of x, y should be 2 but receive x's shape: {x_shape}, y's shape: {y_shape}" ) if x_shape[1] != y_shape[0]: raise ValueError( f"The input Variable x's width must be equal with Variable y' height. But received x's shape = {x_shape}, y's shape = {y_shape}." ) if len(input_shape) == 2: if input_shape[0] != x_shape[0]: if input_shape[0] != 1: raise ValueError( f"When x's dimension[0] is not equal with input's dimension[0], input's dimension[0] must be 1 but got {input_shape[0]}" ) if input_shape[1] != y_shape[1] and input_shape[1] != 1: raise ValueError( f"When y's dimension[1] is not equal with input's dimension[1], input's dimension[1] must be 1 but got {input_shape[1]}" ) if input_shape[1] != y_shape[1]: if input_shape[1] != 1: raise ValueError( f"When y's dimension[1] is not equal with input's dimension[1], input's dimension[1] must be 1 but got {input_shape[1]}" ) elif len(input_shape) == 1: if input_shape[0] not in (y_shape[1], 1): raise ValueError( f"The input's shape: {input_shape} is not broadcastable with [x.shape[0], y.shape[1]]: [{x_shape[0]},{y_shape[1]}]" ) else: raise ValueError( f"The dimension of input should be 2 or 1 but receive input's shape: {input_shape}" ) if in_dynamic_mode(): return _C_ops.addmm_(input, x, y, beta, alpha) def baddbmm( input: Tensor, x: Tensor, y: Tensor, beta: float = 1.0, alpha: float = 1.0, name: str | None = None, ) -> Tensor: """ **baddbmm** Perform batch 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: input (Tensor): The input Tensor to be added to the final result. x (Tensor): The first input Tensor for batch matrix multiplication. y (Tensor): The second input Tensor for batch matrix multiplication. beta (float, optional): Coefficient of $input$, default is 1. alpha (float, optional): Coefficient of $x*y$, default is 1. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The output Tensor of baddbmm. Examples: .. code-block:: python >>> import paddle >>> x = paddle.ones([2, 2, 2]) >>> y = paddle.ones([2, 2, 2]) >>> input = paddle.ones([2, 2, 2]) >>> out = paddle.baddbmm(input=input, x=x, y=y, beta=0.5, alpha=5.0) >>> out Tensor(shape=[2, 2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[[10.50000000, 10.50000000], [10.50000000, 10.50000000]], [[10.50000000, 10.50000000], [10.50000000, 10.50000000]]]) """ input_shape = input.shape x_shape = x.shape y_shape = y.shape if not len(x_shape) == len(y_shape) == 3: raise ValueError( f"The dimension of x, y should be 3 but receive x's shape: {x_shape}, y's shape: {y_shape}" ) if x_shape[2] != y_shape[1]: raise ValueError( f"The input Variable x's width must be equal with Variable y's height. But received x's shape = {x_shape}, y's shape = {y_shape}." ) if len(input_shape) == 3: if input_shape[0] != x_shape[0]: if input_shape[0] != 1: raise ValueError( f"If input's dimension[0] is not equal to x's dimension[0], input's dimension[0] must be 1. But received input's dimension[0] = {input_shape[0]}, x's dimension[0] = {x_shape[0]}" ) else: if not ( input_shape[1] == x_shape[1] or input_shape[1] == 1 ) or not (input_shape[2] == y_shape[2] or input_shape[2] == 1): raise ValueError( f"If input's dimension[0] is 1, input's dimension[1] and dimension[2] must be equal to x's dimension[1] and y's dimension[2] respectively, or they must be 1. But received input's shape = {input_shape}, x's shape = {x_shape}, y's shape = {y_shape}" ) if input_shape[1] != x_shape[1]: if input_shape[1] != 1: raise ValueError( f"If input's dimension[1] is not equal to x's dimension[1], input's dimension[1] must be 1. But received input's dimension[1] = {input_shape[1]}, x's dimension[1] = {x_shape[1]}" ) else: if not ( input_shape[0] == x_shape[0] or input_shape[0] == 1 ) or not (input_shape[2] == y_shape[2] or input_shape[2] == 1): raise ValueError( f"If input's dimension[1] is 1, input's dimension[0] and dimension[2] must be equal to x's dimension[0] and y's dimension[2] respectively, or they must be 1. But received input's shape = {input_shape}, x's shape = {x_shape}, y's shape = {y_shape}" ) if input_shape[2] != y_shape[2]: if input_shape[2] != 1: raise ValueError( f"If input's dimension[2] is not equal to y's dimension[2], input's dimension[2] must be 1. But received input's dimension[2] = {input_shape[2]}, y's dimension[2] = {y_shape[2]}" ) elif len(input_shape) == 2: if input_shape[0] != x_shape[0]: raise ValueError( f"The batch size of input must be equal to the batch size of x. But received input's batch size = {input_shape[0]}, x's batch size = {x_shape[0]}" ) if input_shape[1] not in (y_shape[2], 1): raise ValueError( f"The input's shape: {input_shape} is not broadcastable with [x.shape[0], x.shape[1], y.shape[2]]: [{x_shape[0]},{x_shape[1]},{y_shape[2]}]" ) else: raise ValueError( f"The dimension of input should be 3 or 2 but received input's shape: {input_shape}" ) if in_dynamic_or_pir_mode(): return _C_ops.baddbmm(input, x, y, beta, alpha) else: inputs = {'Input': input, "X": x, "Y": y} attrs = {'Alpha': alpha, 'Beta': beta} helper = LayerHelper("baddbmm", **locals()) check_variable_and_dtype( input, 'Input', ['float16', 'float32', 'float64', 'uint16'], 'baddbmm', ) check_variable_and_dtype( x, 'X', ['float16', 'float32', 'float64', 'uint16'], 'baddbmm' ) check_variable_and_dtype( y, 'Y', ['float16', 'float32', 'float64', 'uint16'], 'baddbmm' ) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type="baddbmm", inputs=inputs, attrs=attrs, outputs={"Out": out} ) return out @inplace_apis_in_dygraph_only def baddbmm_( input: Tensor, x: Tensor, y: Tensor, beta: float = 1.0, alpha: float = 1.0, name: str | None = None, ) -> Tensor: """ Inplace version of ``baddbmm`` API, the output Tensor will be inplaced with input ``input``. Please refer to :ref:`api_paddle_baddbmm`. """ input_shape = input.shape x_shape = x.shape y_shape = y.shape if not len(x_shape) == len(y_shape) == 3: raise ValueError( f"The dimension of x, y should be 3 but receive x's shape: {x_shape}, y's shape: {y_shape}" ) if x_shape[2] != y_shape[1]: raise ValueError( f"The input Variable x's width must be equal with Variable y's height. But received x's shape = {x_shape}, y's shape = {y_shape}." ) if len(input_shape) == 3: if input_shape[0] != x_shape[0]: if input_shape[0] != 1: raise ValueError( f"If input's dimension[0] is not equal to x's dimension[0], input's dimension[0] must be 1. But received input's dimension[0] = {input_shape[0]}, x's dimension[0] = {x_shape[0]}" ) else: if not ( input_shape[1] == x_shape[1] or input_shape[1] == 1 ) or not (input_shape[2] == y_shape[2] or input_shape[2] == 1): raise ValueError( f"If input's dimension[0] is 1, input's dimension[1] and dimension[2] must be equal to x's dimension[1] and y's dimension[2] respectively, or they must be 1. But received input's shape = {input_shape}, x's shape = {x_shape}, y's shape = {y_shape}" ) if input_shape[1] != x_shape[1]: if input_shape[1] != 1: raise ValueError( f"If input's dimension[1] is not equal to x's dimension[1], input's dimension[1] must be 1. But received input's dimension[1] = {input_shape[1]}, x's dimension[1] = {x_shape[1]}" ) else: if not ( input_shape[0] == x_shape[0] or input_shape[0] == 1 ) or not (input_shape[2] == y_shape[2] or input_shape[2] == 1): raise ValueError( f"If input's dimension[1] is 1, input's dimension[0] and dimension[2] must be equal to x's dimension[0] and y's dimension[2] respectively, or they must be 1. But received input's shape = {input_shape}, x's shape = {x_shape}, y's shape = {y_shape}" ) if input_shape[2] != y_shape[2]: if input_shape[2] != 1: raise ValueError( f"If input's dimension[2] is not equal to y's dimension[2], input's dimension[2] must be 1. But received input's dimension[2] = {input_shape[2]}, y's dimension[2] = {y_shape[2]}" ) elif len(input_shape) == 2: if input_shape[0] != x_shape[0]: raise ValueError( f"The batch size of input must be equal to the batch size of x. But received input's batch size = {input_shape[0]}, x's batch size = {x_shape[0]}" ) if input_shape[1] not in (y_shape[2], 1): raise ValueError( f"The input's shape: {input_shape} is not broadcastable with [x.shape[0], x.shape[1], y.shape[2]]: [{x_shape[0]},{x_shape[1]},{y_shape[2]}]" ) else: raise ValueError( f"The dimension of input should be 3 or 2 but received input's shape: {input_shape}" ) if in_dynamic_mode(): return _C_ops.baddbmm_(input, x, y, beta, alpha) def renorm(x: Tensor, p: float, axis: int, max_norm: float) -> Tensor: """ **renorm** This operator is used to calculate the p-norm along the axis, suppose the input-shape on axis dimension has the value of T, then the tensor is split into T parts, the p-norm should be calculated for each part, if the p-norm for part i is larger than max-norm, then each element in part i should be re-normalized at the same scale so that part-i' p-norm equals max-norm exactly, otherwise part-i stays unchanged. Args: x (Tensor): The input Tensor p (float): The power of the norm operation. axis (int): the dimension to slice the tensor. max-norm (float): the maximal norm limit. Returns: Tensor: the renorm Tensor. Examples: .. code-block:: python >>> import paddle >>> input = [[[2.0, 2.0, -2.0], [3.0, 0.3, 3.0]], ... [[2.0, -8.0, 2.0], [3.1, 3.7, 3.0]]] >>> x = paddle.to_tensor(input,dtype='float32') >>> y = paddle.renorm(x, 1.0, 2, 2.05) >>> print(y) Tensor(shape=[2, 2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[[ 0.40594056, 0.29285714, -0.41000000], [ 0.60891086, 0.04392857, 0.61500001]], [[ 0.40594056, -1.17142856, 0.41000000], [ 0.62920785, 0.54178572, 0.61500001]]]) """ input_shape = x.shape if not axis < len(input_shape): raise ValueError( f"the axis:{axis} should be less then the shape's size {len(input_shape)}:{input_shape}" ) if not axis >= 0: if not axis >= -1 * len(input_shape): raise ValueError( f"the axis:{axis} should not be less than -1 * length of input_shape:{-1 * len(input_shape)}" ) axis = axis + len(input_shape) if in_dynamic_or_pir_mode(): out = _C_ops.renorm(x, p, axis, max_norm) return out else: check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'renorm') inputs = {'X': x} attrs = {'p': p, 'axis': axis, 'max_norm': max_norm} helper = LayerHelper("renorm", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type="renorm", inputs=inputs, attrs=attrs, outputs={"Out": out} ) return out @inplace_apis_in_dygraph_only def renorm_(x: Tensor, p: float, axis: int, max_norm: float) -> Tensor: """ Inplace version of ``renorm`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_renorm`. """ input_shape = x.shape if not axis < len(input_shape): raise ValueError( f"the axis:{axis} should be less then the shape's size {len(input_shape)}:{input_shape}" ) if not axis >= 0: if not axis >= -1 * len(input_shape): raise ValueError( f"the axis:{axis} should not be less than -1 * length of input_shape:{-1 * len(input_shape)}" ) axis = axis + len(input_shape) if in_dynamic_mode(): out = _C_ops.renorm_(x, p, axis, max_norm) return out def inner(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Inner product of two input Tensor. Ordinary inner product for 1-D Tensors, in higher dimensions a sum product over the last axes. Args: x (Tensor): An N-D Tensor or a Scalar Tensor. If its not a scalar Tensor, its last dimensions must match y's. y (Tensor): An N-D Tensor or a Scalar Tensor. If its not a scalar Tensor, its last dimensions must match x's. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The inner-product Tensor, the output shape is x.shape[:-1] + y.shape[:-1]. Examples: .. code-block:: python >>> import paddle >>> x = paddle.arange(1, 7).reshape((2, 3)).astype('float32') >>> y = paddle.arange(1, 10).reshape((3, 3)).astype('float32') >>> out = paddle.inner(x, y) >>> print(out) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[14. , 32. , 50. ], [32. , 77. , 122.]]) """ xshape = x.shape yshape = y.shape if in_dynamic_mode() and (x.size == 1 or y.size == 1): return multiply(x, y) else: dstshape = list(xshape[:-1]) + list(yshape[:-1]) if xshape[-1] == 0: # If the last dimension is 0 if len(xshape) == 1: # shape is [0] nx = x.reshape((1, 0)) else: nx = x.reshape((math.prod(xshape[:-1]), 0)) else: nx = x.reshape((-1, xshape[-1])) if yshape[-1] == 0: # If the last dimension is 0 if len(yshape) == 1: # shape is [0] ny = y.reshape((1, 0)) else: ny = y.reshape((math.prod(yshape[:-1]), 0)) else: ny = y.reshape((-1, yshape[-1])) 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'], 'inner' ) x_shape = list(xshape) y_shape = list(yshape) # check the inner 2 dimensions if x_shape[-1] != y_shape[-1]: if not ((x_shape[-1] == -1) or (y_shape[-1] == -1)): raise ValueError( "After performing an optional transpose, Input X's last dim should be " "equal to Y's last dim for multiplication " f"prerequisites. But received X's shape: {x_shape}, Y's shape: {y_shape}\n" ) __check_input(nx, ny) if in_dynamic_or_pir_mode(): return _C_ops.matmul(nx, ny, False, True).reshape(dstshape) else: helper = LayerHelper('inner', **locals()) out = helper.create_variable_for_type_inference(dtype=nx.dtype) helper.append_op( type='matmul_v2', inputs={'X': nx, 'Y': ny.T}, outputs={'Out': out}, ) return out.reshape(dstshape) @ParamAliasDecorator({"x": ["input"], "y": ["vec2"]}) def outer( x: Tensor, y: Tensor, name: str | None = None, *, out: Tensor | None = None, ) -> Tensor: """ Outer product of two Tensors. Input is flattened if not already 1-dimensional. .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, and ``vec2`` can be used as an alias for ``y``. For example, ``outer(input=tensor_x, vec2=tensor_y, ...)`` is equivalent to ``outer(x=tensor_x, y=tensor_y, ...)``. Args: x (Tensor): An N-D Tensor or a Scalar Tensor. alias: ``input``. y (Tensor): An N-D Tensor or a Scalar Tensor. alias: ``vec2``. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. out (Tensor|None, optional): The output Tensor. If set, the result will be stored in this Tensor. Returns: Tensor: The outer-product Tensor. Examples: .. code-block:: python >>> import paddle >>> x = paddle.arange(1, 4).astype('float32') >>> y = paddle.arange(1, 6).astype('float32') >>> out = paddle.outer(x, y) >>> print(out) Tensor(shape=[3, 5], dtype=float32, place=Place(cpu), stop_gradient=True, [[1. , 2. , 3. , 4. , 5. ], [2. , 4. , 6. , 8. , 10.], [3. , 6. , 9. , 12., 15.]]) """ xshape = x.shape yshape = y.shape if math.prod(xshape) == 0: # If the size is 0 nx = x.reshape((0, 0)) else: nx = x.reshape((-1, 1)) if math.prod(yshape) == 0: # If the size is 0 ny = y.reshape((0, 0)) else: ny = y.reshape((1, -1)) if in_dynamic_mode(): return _C_ops.multiply(nx, ny, out=out) 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', 'int32', 'int64'], 'outer', ) __check_input(nx, ny) if in_pir_mode(): return _C_ops.multiply(nx, ny, out=out) else: helper = LayerHelper('outer', **locals()) out = helper.create_variable_for_type_inference(dtype=nx.dtype) helper.append_op( type='matmul_v2', inputs={'X': nx, 'Y': ny}, outputs={'Out': out} ) return out def inverse(x: Tensor, name: str | None = None) -> Tensor: """ 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: x (Tensor): The input tensor. The last two 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, float64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: A Tensor holds the inverse of x. The shape and data type is the same as x. Examples: .. code-block:: python >>> import paddle >>> mat = paddle.to_tensor([[2, 0], [0, 2]], dtype='float32') >>> inv = paddle.inverse(mat) >>> print(inv) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.50000000, 0. ], [0. , 0.50000000]]) """ if in_dynamic_or_pir_mode(): return _C_ops.inverse(x) else: def _check_input(x): check_variable_and_dtype( x, 'x', ['float32', 'float64', 'complex64', 'complex128'], 'inverse', ) if len(x.shape) < 2: raise ValueError( "The input of inverse is expected to be a Tensor whose number " f"of dimensions is no less than 2. But received: {len(x.shape)}, " f"x's shape: {x.shape}." ) _check_input(x) helper = LayerHelper('inverse', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='inverse', inputs={'Input': [x]}, outputs={'Output': [out]} ) return out @ForbidKeywordsDecorator( illegal_keys={"input", "dim", "other"}, func_name="paddle.max", correct_name="paddle.compat.max", url_suffix="torch/torch.max", ) def max( x: Tensor, axis: int | Sequence[int] | None = None, keepdim: bool = False, name: str | None = None, ) -> Tensor: """ Computes the maximum of tensor elements over the given axis. Note: The difference between max and amax is: If there are multiple maximum elements, amax evenly distributes gradient between these equal values, while max propagates gradient to all of them. Args: x (Tensor): A tensor, the data type is float8_e4m3fn, float8_e5m2, bfloat16, float16, float32, float64, int32, int64. axis (int|list|tuple|None, optional): The axis along which the maximum is computed. If :attr:`None`, compute the maximum over all elements of `x` and return a Tensor with a single element, 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 output Tensor. The result tensor will have one fewer dimension than the `x` unless :attr:`keepdim` is true, default value is False. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, results of maximum on the specified axis of input tensor, it's data type is the same as `x`. Examples: .. code-block:: python >>> import paddle >>> # data_x is a Tensor with shape [2, 4] >>> # the axis is a int element >>> x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9], ... [0.1, 0.2, 0.6, 0.7]], ... dtype='float64', stop_gradient=False) >>> result1 = paddle.max(x) >>> result1.backward() >>> result1 Tensor(shape=[], dtype=float64, place=Place(cpu), stop_gradient=False, 0.90000000) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[0., 0., 0., 1.], [0., 0., 0., 0.]]) >>> x.clear_grad() >>> result2 = paddle.max(x, axis=0) >>> result2.backward() >>> result2 Tensor(shape=[4], dtype=float64, place=Place(cpu), stop_gradient=False, [0.20000000, 0.30000000, 0.60000000, 0.90000000]) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[1., 1., 0., 1.], [0., 0., 1., 0.]]) >>> x.clear_grad() >>> result3 = paddle.max(x, axis=-1) >>> result3.backward() >>> result3 Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=False, [0.90000000, 0.70000000]) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[0., 0., 0., 1.], [0., 0., 0., 1.]]) >>> x.clear_grad() >>> result4 = paddle.max(x, axis=1, keepdim=True) >>> result4.backward() >>> result4 Tensor(shape=[2, 1], dtype=float64, place=Place(cpu), stop_gradient=False, [[0.90000000], [0.70000000]]) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[0., 0., 0., 1.], [0., 0., 0., 1.]]) >>> # data_y is a Tensor with shape [2, 2, 2] >>> # the axis is list >>> y = paddle.to_tensor([[[1.0, 2.0], [3.0, 4.0]], ... [[5.0, 6.0], [7.0, 8.0]]], ... dtype='float64', stop_gradient=False) >>> result5 = paddle.max(y, axis=[1, 2]) >>> result5.backward() >>> result5 Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=False, [4., 8.]) >>> y.grad Tensor(shape=[2, 2, 2], dtype=float64, place=Place(cpu), stop_gradient=False, [[[0., 0.], [0., 1.]], [[0., 0.], [0., 1.]]]) >>> y.clear_grad() >>> result6 = paddle.max(y, axis=[0, 1]) >>> result6.backward() >>> result6 Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=False, [7., 8.]) >>> y.grad Tensor(shape=[2, 2, 2], dtype=float64, place=Place(cpu), stop_gradient=False, [[[0., 0.], [0., 0.]], [[0., 0.], [1., 1.]]]) """ if in_dynamic_mode(): return _C_ops.max(x, axis, keepdim) else: reduce_all, axis = _get_reduce_axis_with_tensor(axis, x) if in_pir_mode(): return _C_ops.max(x, axis, keepdim) else: helper = LayerHelper('max', **locals()) check_variable_and_dtype( x, 'x', [ 'float16', 'uint16', 'float32', 'float64', 'int32', 'int64', 'float8_e4m3fn', 'float8_e5m2', ], 'max', ) if not isinstance(axis, Variable) and paddle.utils._contain_var( axis ): axis = paddle.utils._convert_to_tensor_list(axis) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='reduce_max', inputs={'X': x}, outputs={'Out': out}, attrs={ 'dim': axis, 'keep_dim': keepdim, 'reduce_all': reduce_all, }, ) return out @ForbidKeywordsDecorator( illegal_keys={"input", "dim", "other"}, func_name="paddle.min", correct_name="paddle.compat.min", url_suffix="torch/torch.min", ) def min( x: Tensor, axis: int | Sequence[int] | None = None, keepdim: bool = False, name: str | None = None, ) -> Tensor: """ Computes the minimum of tensor elements over the given axis Note: The difference between min and amin is: If there are multiple minimum elements, amin evenly distributes gradient between these equal values, while min propagates gradient to all of them. Args: x (Tensor): A tensor, the data type is bfloat16, float16, float32, float64, int32, int64. axis (int|list|tuple|None, optional): The axis along which the minimum is computed. If :attr:`None`, compute the minimum over 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]`. keepdim (bool, optional): Whether to reserve the reduced dimension in the output Tensor. The result tensor will have one fewer dimension than the `x` unless :attr:`keepdim` is true, default value is False. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, results of minimum on the specified axis of input tensor, it's data type is the same as input's Tensor. Examples: .. code-block:: python >>> import paddle >>> # data_x is a Tensor with shape [2, 4] >>> # the axis is a int element >>> x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9], ... [0.1, 0.2, 0.6, 0.7]], ... dtype='float64', stop_gradient=False) >>> result1 = paddle.min(x) >>> result1.backward() >>> result1 Tensor(shape=[], dtype=float64, place=Place(cpu), stop_gradient=False, 0.10000000) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[0., 0., 0., 0.], [1., 0., 0., 0.]]) >>> x.clear_grad() >>> result2 = paddle.min(x, axis=0) >>> result2.backward() >>> result2 Tensor(shape=[4], dtype=float64, place=Place(cpu), stop_gradient=False, [0.10000000, 0.20000000, 0.50000000, 0.70000000]) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[0., 0., 1., 0.], [1., 1., 0., 1.]]) >>> x.clear_grad() >>> result3 = paddle.min(x, axis=-1) >>> result3.backward() >>> result3 Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=False, [0.20000000, 0.10000000]) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[1., 0., 0., 0.], [1., 0., 0., 0.]]) >>> x.clear_grad() >>> result4 = paddle.min(x, axis=1, keepdim=True) >>> result4.backward() >>> result4 Tensor(shape=[2, 1], dtype=float64, place=Place(cpu), stop_gradient=False, [[0.20000000], [0.10000000]]) >>> x.grad Tensor(shape=[2, 4], dtype=float64, place=Place(cpu), stop_gradient=False, [[1., 0., 0., 0.], [1., 0., 0., 0.]]) >>> # data_y is a Tensor with shape [2, 2, 2] >>> # the axis is list >>> y = paddle.to_tensor([[[1.0, 2.0], [3.0, 4.0]], ... [[5.0, 6.0], [7.0, 8.0]]], ... dtype='float64', stop_gradient=False) >>> result5 = paddle.min(y, axis=[1, 2]) >>> result5.backward() >>> result5 Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=False, [1., 5.]) >>> y.grad Tensor(shape=[2, 2, 2], dtype=float64, place=Place(cpu), stop_gradient=False, [[[1., 0.], [0., 0.]], [[1., 0.], [0., 0.]]]) >>> y.clear_grad() >>> result6 = paddle.min(y, axis=[0, 1]) >>> result6.backward() >>> result6 Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=False, [1., 2.]) >>> y.grad Tensor(shape=[2, 2, 2], dtype=float64, place=Place(cpu), stop_gradient=False, [[[1., 1.], [0., 0.]], [[0., 0.], [0., 0.]]]) """ if in_dynamic_mode(): return _C_ops.min(x, axis, keepdim) else: reduce_all, axis = _get_reduce_axis_with_tensor(axis, x) if in_pir_mode(): return _C_ops.min(x, axis, keepdim) else: helper = LayerHelper('min', **locals()) check_variable_and_dtype( x, 'x', ['float16', 'uint16', 'float32', 'float64', 'int32', 'int64'], 'min', ) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='reduce_min', inputs={'X': x}, outputs={'Out': out}, attrs={ 'dim': axis, 'keep_dim': keepdim, 'reduce_all': reduce_all, }, ) return out def log1p(x: Tensor, name: str | None = None) -> Tensor: r""" Calculates the natural log of the given input tensor, element-wise. .. math:: Out = \ln(x+1) Args: x (Tensor): Input Tensor. Must be one of the following types: int32, int64, float16, bfloat16, float32, float64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the natural log of the input Tensor computed element-wise. Examples: .. code-block:: python >>> import paddle >>> data = paddle.to_tensor([[0], [1]], dtype='float32') >>> res = paddle.log1p(data) >>> res Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[0. ], [0.69314718]]) """ if in_dynamic_or_pir_mode(): return _C_ops.log1p(x) else: check_variable_and_dtype( x, 'x', [ 'int32', 'int64', 'float16', 'uint16', 'float32', 'float64', 'complex64', 'complex128', ], "log1p", ) inputs = {'X': [x]} helper = LayerHelper('log1p', **locals()) dtype = helper.input_dtype(input_param_name='x') out = helper.create_variable_for_type_inference(dtype) helper.append_op(type="log1p", inputs={"X": x}, outputs={"Out": out}) return out @inplace_apis_in_dygraph_only def log1p_(x: Tensor, name: str | None = None) -> None: r""" Inplace version of ``log1p`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_log1p`. """ if in_dynamic_mode(): return _C_ops.log1p_(x) def log2(x: Tensor, name: str | None = None) -> Tensor: r""" 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: int32, int64, float16, bfloat16, float32, float64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). 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) >>> res Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.], [1.]]) >>> # 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) >>> res Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.]) >>> # 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) >>> res Tensor(shape=[1], dtype=float64, place=Place(cpu), stop_gradient=True, [1.]) """ if in_dynamic_or_pir_mode(): return _C_ops.log2(x) else: check_variable_and_dtype( x, 'x', [ 'int32', 'int64', 'float16', 'uint16', 'float32', 'float64', 'complex64', 'complex128', ], "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 @inplace_apis_in_dygraph_only def log2_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``log2`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_log2`. """ if in_dynamic_mode(): return _C_ops.log2_(x) def log10(x: Tensor, name: str | None = None) -> Tensor: r""" 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: int32, int64, float16, bfloat16, float32, float64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). 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) >>> res Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.], [1.]]) >>> # 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) >>> res Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.]) >>> # 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) >>> res Tensor(shape=[1], dtype=float64, place=Place(cpu), stop_gradient=True, [1.]) """ if in_dynamic_or_pir_mode(): return _C_ops.log10(x) else: check_variable_and_dtype( x, 'x', [ 'int32', 'int64', 'float16', 'uint16', 'float32', 'float64', 'complex64', 'complex128', ], "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 @inplace_apis_in_dygraph_only def log10_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``log10`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_log10`. """ if in_dynamic_mode(): return _C_ops.log10_(x) @param_one_alias(["x", "input"]) def clip( x: Tensor, min: float | None = None, max: float | None = None, name: str | None = None, *, out: Tensor | None = None, ) -> Tensor: """ This operator clip all elements in input into the range [ min, max ] and return a resulting tensor as the following equation: .. math:: Out = MIN(MAX(x, min), max) .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``. For example, ``clip(input=tensor_x)`` is equivalent to ``clip(x=tensor_x)``. Args: x (Tensor): An N-D Tensor with data type bfloat16, float16, float32, float64, int32 or int64. alias: ``input``. min (float|int|Tensor, optional): The lower bound with type ``float`` , ``int`` or a ``0-D Tensor`` with shape [] and type ``bfloat16``, ``float16``, ``float32``, ``float64``, ``int32``. max (float|int|Tensor, optional): The upper bound with type ``float``, ``int`` or a ``0-D Tensor`` with shape [] and type ``bfloat16``, ``float16``, ``float32``, ``float64``, ``int32``. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. out (Tensor, optional): The output Tensor. If set, the result will be stored in this Tensor. Default: None. Returns: Tensor: A Tensor with the same data shape as input. If either min or max is a floating-point value/Tensor, the output tensor will have a data type of ``float32``. Otherwise, the output tensor will inherit the same data type as the input. Examples: .. code-block:: python >>> import paddle >>> x1 = paddle.to_tensor([[1.2, 3.5], [4.5, 6.4]], 'float32') >>> out1 = paddle.clip(x1, min=3.5, max=5.0) >>> out1 Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[3.50000000, 3.50000000], [4.50000000, 5. ]]) >>> out2 = paddle.clip(x1, min=2.5) >>> out2 Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[2.50000000, 3.50000000], [4.50000000, 6.40000010]]) """ x_dtype = str(x.dtype) if x_dtype == 'paddle.int32': min_ = np.iinfo(np.int32).min max_ = np.iinfo(np.int32).max - 2**7 elif x_dtype == 'paddle.int64': min_ = np.iinfo(np.int64).min max_ = np.iinfo(np.int64).max - 2**39 elif x_dtype == 'paddle.float16': min_ = float(np.finfo(np.float16).min) max_ = float(np.finfo(np.float16).max) elif x_dtype == 'paddle.float64': min_ = float(np.finfo(np.float64).min) max_ = float(np.finfo(np.float64).max) else: min_ = float(np.finfo(np.float32).min) max_ = float(np.finfo(np.float32).max) min = min_ if min is None else min max = max_ if max is None else max if in_dynamic_mode(): if x_dtype in ['paddle.int32', 'paddle.int64']: if isinstance(min, paddle.Tensor): min = min.item(0) if isinstance(max, paddle.Tensor): max = max.item(0) if isinstance(min, float) or isinstance(max, float): x = paddle.cast(x, paddle.float32) return _C_ops.clip(x, min, max, out=out) elif in_pir_mode(): if x_dtype in ['paddle.int32', 'paddle.int64']: if ( isinstance(min, float) or isinstance(max, float) or ( isinstance(min, paddle.pir.Value) and min.dtype in [paddle.float32, paddle.float64] ) or ( isinstance(max, paddle.pir.Value) and max.dtype in [paddle.float32, paddle.float64] ) ): x = paddle.cast(x, paddle.float32) return _C_ops.clip(x, min, max, out=out) else: if min is not None: check_type(min, 'min', (float, int, Variable), 'clip') if isinstance(min, Variable): check_dtype( min.dtype, 'min', ['float16', 'float32', 'float64', 'int32', 'uint16'], 'clip', '(When the type of min in clip is Variable.)', ) if max is not None: check_type(max, 'max', (float, int, Variable), 'clip') if isinstance(max, Variable): check_dtype( max.dtype, 'max', ['float16', 'float32', 'float64', 'int32', 'uint16'], 'clip', '(When the type of max in clip is Variable.)', ) check_variable_and_dtype( x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64', 'uint16'], 'clip', ) inputs = {'X': x} attrs = {'min': min_, 'max': max_} 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 helper = LayerHelper('clip', **locals()) output = helper.create_variable_for_type_inference( dtype=helper.input_dtype('x') ) helper.append_op( type='clip', inputs=inputs, outputs={'Out': [output]}, attrs=attrs ) return output @inplace_apis_in_dygraph_only def clip_( x: Tensor, min: float | None = None, max: float | None = None, name: str | None = None, ) -> Tensor: """ Inplace version of ``clip`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_clip`. """ fmin = float(np.finfo(np.float32).min) fmax = float(np.finfo(np.float32).max) if isinstance(min, Variable): min = min.item(0) if isinstance(max, Variable): max = max.item(0) min = fmin if min is None else min max = fmax if max is None else max if in_dynamic_mode(): return _C_ops.clip_(x, min, max) def trace( x: Tensor, offset: int = 0, axis1: int = 0, axis2: int = 1, name: str | None = None, ) -> Tensor: """ Computes the sum along diagonals of the input tensor x. If ``x`` is 2D, returns the sum of diagonal. If ``x`` has larger dimensions, then returns an tensor of diagonals sum, diagonals be taken from the 2D planes specified by axis1 and axis2. By default, the 2D planes formed by the first and second axes of the input tensor x. The argument ``offset`` determines where diagonals are taken from input tensor x: - 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. - Note that if offset is out of input's shape indicated by axis1 and axis2, 0 will be returned. Args: x (Tensor): The input tensor x. Must be at least 2-dimensional. The input data type should be float16, float32, float64, int32, int64. 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. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: the output data type is the same as input data type. Examples: .. code-block:: python >>> import paddle >>> case1 = paddle.randn([2, 3]) >>> case2 = paddle.randn([3, 10, 10]) >>> case3 = paddle.randn([3, 10, 5, 10]) >>> data1 = paddle.trace(case1) >>> data1.shape [] >>> data2 = paddle.trace(case2, offset=1, axis1=1, axis2=2) >>> data2.shape [3] >>> data3 = paddle.trace(case3, offset=-3, axis1=1, axis2=-1) >>> data3.shape [3, 5] """ def __check_input(x, offset, axis1, axis2): check_dtype( x.dtype, 'Input', ['int32', 'int64', 'float16', 'float32', 'float64'], 'trace', ) input_shape = list(x.shape) assert len(input_shape) >= 2, ( "The x must be at least 2-dimensional, " f"But received Input x's dimensional: {len(input_shape)}.\n" ) axis1_ = axis1 if axis1 >= 0 else len(input_shape) + axis1 axis2_ = axis2 if axis2 >= 0 else len(input_shape) + axis2 assert (0 <= axis1_) and (axis1_ < len(input_shape)), ( f"The argument axis1 is out of range (expected to be in range of [{-(len(input_shape))}, {len(input_shape) - 1}], but got {axis1}).\n" ) assert (0 <= axis2_) and (axis2_ < len(input_shape)), ( f"The argument axis2 is out of range (expected to be in range of [{-(len(input_shape))}, {len(input_shape) - 1}], but got {axis2}).\n" ) assert axis1_ != axis2_, ( "axis1 and axis2 cannot be the same axis." f"But received axis1 = {axis1}, axis2 = {axis2}\n" ) if in_dynamic_or_pir_mode(): return _C_ops.trace(x, offset, axis1, axis2) else: __check_input(x, offset, axis1, axis2) helper = LayerHelper('trace', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='trace', inputs={'Input': [x]}, attrs={'offset': offset, 'axis1': axis1, 'axis2': axis2}, outputs={'Out': [out]}, ) return out def kron(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Compute the Kronecker product of two tensors, a composite tensor made of blocks of the second tensor scaled by the first. Assume that the rank of the two tensors, $X$ and $Y$ are the same, if necessary prepending the smallest with ones. If the shape of $X$ is [$r_0$, $r_1$, ..., $r_N$] and the shape of $Y$ is [$s_0$, $s_1$, ..., $s_N$], then the shape of the output tensor is [$r_{0}s_{0}$, $r_{1}s_{1}$, ..., $r_{N}s_{N}$]. The elements are products of elements from $X$ and $Y$. The equation is: $$ output[k_{0}, k_{1}, ..., k_{N}] = X[i_{0}, i_{1}, ..., i_{N}] * Y[j_{0}, j_{1}, ..., j_{N}] $$ where $$ k_{t} = i_{t} * s_{t} + j_{t}, t = 0, 1, ..., N $$ Args: x (Tensor): the fist operand of kron op, data type: bfloat16, float16, float32, float64, int32 or int64. y (Tensor): the second operand of kron op, data type: bfloat16, float16, float32, float64, int32 or int64. Its data type should be the same with x. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The output of kron, data type: bfloat16, float16, float32, float64, int32 or int64. Its data is the same with x. Examples: .. code-block:: python >>> 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) >>> out Tensor(shape=[6, 6], dtype=int64, place=Place(cpu), stop_gradient=True, [[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]]) """ if in_dynamic_or_pir_mode(): return _C_ops.kron(x, y) else: helper = LayerHelper('kron', **locals()) check_variable_and_dtype( x, 'x', ['float16', 'float32', 'float64', 'int32', 'int64', 'uint16'], 'kron', ) check_variable_and_dtype( y, 'y', ['float16', 'float32', 'float64', 'int32', 'int64', 'uint16'], 'kron', ) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type="kron", inputs={"X": x, "Y": y}, outputs={"Out": out} ) return out @param_two_alias(["x", "input"], ["axis", "dim"]) def cumsum( x: Tensor, axis: int | None = None, dtype: DTypeLike | None = None, name: str | None = None, *, out: Tensor | None = None, ) -> Tensor: """ The cumulative sum of the elements along a given axis. Note: The first element of the result is the same as the first element of the input. .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, and ``dim`` can be used as an alias for ``axis``. For example, ``cumsum(input=tensor_x, dim=1, ...)`` is equivalent to ``cumsum(x=tensor_x, axis=1, ...)``. Args: x (Tensor): The input tensor needed to be cumsumed. alias: ``input``. 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. alias: ``dim``. dtype (str|paddle.dtype|np.dtype|None, optional): The data type of the output tensor, can be bfloat16, float16, float32, float64, int32, int64, complex64, complex128. By default, it is int64 if the input x is int8/int16/int32; otherwise, it is None. If it is not None, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. out (Tensor, optional): The output tensor. If provided, the result will be stored in this tensor. Returns: Tensor, the result of cumsum operator. Examples: .. code-block:: python >>> import paddle >>> data = paddle.arange(12) >>> data = paddle.reshape(data, (3, 4)) >>> y = paddle.cumsum(data) >>> y Tensor(shape=[12], dtype=int64, place=Place(cpu), stop_gradient=True, [0 , 1 , 3 , 6 , 10, 15, 21, 28, 36, 45, 55, 66]) >>> y = paddle.cumsum(data, axis=0) >>> y Tensor(shape=[3, 4], dtype=int64, place=Place(cpu), stop_gradient=True, [[0 , 1 , 2 , 3 ], [4 , 6 , 8 , 10], [12, 15, 18, 21]]) >>> y = paddle.cumsum(data, axis=-1) >>> y Tensor(shape=[3, 4], dtype=int64, place=Place(cpu), stop_gradient=True, [[0 , 1 , 3 , 6 ], [4 , 9 , 15, 22], [8 , 17, 27, 38]]) >>> y = paddle.cumsum(data, dtype='float64') >>> assert y.dtype == paddle.float64 """ if axis is None: flatten = True else: flatten = False if dtype is None: if x.dtype in [ paddle.uint8, paddle.int8, paddle.int16, paddle.int32, ]: x = cast(x, "int64") else: dtype = convert_np_dtype_to_dtype_(dtype) if x.dtype != dtype: x = cast(x, dtype) if in_dynamic_or_pir_mode(): if axis is None: axis = -1 return _C_ops.cumsum(x, axis, flatten, False, False, out=out) else: check_variable_and_dtype( x, 'x', [ 'float16', 'uint16', 'float32', 'float64', 'int32', 'int64', 'complex64', 'complex128', ], 'cumsum', ) check_type(x, 'x', (Variable), 'cumsum') locals_var = locals().copy() kwargs = {} 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) @inplace_apis_in_dygraph_only def cumsum_( x: Tensor, axis: int | None = None, dtype: DTypeLike | None = None, name: str | None = None, ) -> Tensor: r""" Inplace version of ``cumprod`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_cumprod`. """ if axis is None: flatten = True else: flatten = False if dtype is not None: if not isinstance(dtype, (core.VarDesc.VarType, core.DataType)): dtype = convert_np_dtype_to_dtype_(dtype) if x.dtype != dtype: x = cast_(x, dtype) if in_dynamic_mode(): if axis is None: axis = -1 return _C_ops.cumsum_(x, axis, flatten, False, False) def cummax( x: Tensor, axis: int | None = None, dtype: DTypeLike = 'int64', name: str | None = None, ) -> tuple[Tensor, Tensor]: """ The cumulative max of the elements along a given axis. Note: The first element of the result is the same as the first element of the input. Args: x (Tensor): The input tensor needed to be cummaxed. axis (int, optional): The dimension to accumulate along. -1 means the last dimension. The default (None) is to compute the cummax over the flattened array. dtype (str|paddle.dtype|np.dtype, optional): The data type of the indices tensor, can be int32, int64. The default value is int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The result of cummax operation. The dtype of cummax result is same with input x. indices (Tensor), The corresponding index results of cummax operation. Examples: .. code-block:: python >>> import paddle >>> data = paddle.to_tensor([-1, 5, 0, -2, -3, 2]) >>> data = paddle.reshape(data, (2, 3)) >>> value, indices = paddle.cummax(data) >>> value Tensor(shape=[6], dtype=int64, place=Place(cpu), stop_gradient=True, [-1, 5, 5, 5, 5, 5]) >>> indices Tensor(shape=[6], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 1, 1, 1, 1, 1]) >>> value, indices = paddle.cummax(data, axis=0) >>> value Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[-1, 5, 0], [-1, 5, 2]]) >>> indices Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[0, 0, 0], [0, 0, 1]]) >>> value, indices = paddle.cummax(data, axis=-1) >>> value Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[-1, 5, 5], [-2, -2, 2]]) >>> indices Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[0, 1, 1], [0, 0, 2]]) >>> value, indices = paddle.cummax(data, dtype='int64') >>> assert indices.dtype == paddle.int64 """ if axis is None: axis = -1 x = x.flatten(0, len(x.shape) - 1) check_dtype(dtype, 'dtype', ['int32', 'int64'], 'cummax') if not isinstance(dtype, (core.VarDesc.VarType, core.DataType)): dtype = convert_np_dtype_to_dtype_(dtype) if in_dynamic_or_pir_mode(): return _C_ops.cummax(x, axis, dtype) else: check_variable_and_dtype( x, 'x', ['float32', 'float64', 'int32', 'int64'], 'cummax', ) check_type(x, 'x', (Variable), 'cummax') helper = LayerHelper('cummax', **locals()) out = helper.create_variable_for_type_inference(x.dtype) indices = helper.create_variable_for_type_inference(dtype='int64') helper.append_op( type='cummax', inputs={'x': x}, outputs={'out': out, 'indices': indices}, attrs={'axis': axis, 'dtype': dtype}, ) return out, indices def cummin( x: Tensor, axis: int | None = None, dtype: DTypeLike = 'int64', name: str | None = None, ) -> tuple[Tensor, Tensor]: """ The cumulative min of the elements along a given axis. Note: The first element of the result is the same as the first element of the input. Args: x (Tensor): The input tensor needed to be cummined. axis (int, optional): The dimension to accumulate along. -1 means the last dimension. The default (None) is to compute the cummin over the flattened array. dtype (str|paddle.dtype|np.dtype, optional): The data type of the indices tensor, can be int32, int64. The default value is int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The result of cummin operation. The dtype of cummin result is same with input x. indices (Tensor), The corresponding index results of cummin operation. Examples: .. code-block:: python >>> import paddle >>> data = paddle.to_tensor([-1, 5, 0, -2, -3, 2]) >>> data = paddle.reshape(data, (2, 3)) >>> value, indices = paddle.cummin(data) >>> value Tensor(shape=[6], dtype=int64, place=Place(cpu), stop_gradient=True, [-1, -1, -1, -2, -3, -3]) >>> indices Tensor(shape=[6], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 0, 0, 3, 4, 4]) >>> value, indices = paddle.cummin(data, axis=0) >>> value Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[-1, 5, 0], [-2, -3, 0]]) >>> indices Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[0, 0, 0], [1, 1, 0]]) >>> value, indices = paddle.cummin(data, axis=-1) >>> value Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[-1, -1, -1], [-2, -3, -3]]) >>> indices Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[0, 0, 0], [0, 1, 1]]) >>> value, indices = paddle.cummin(data, dtype='int64') >>> assert indices.dtype == paddle.int64 """ if axis is None: axis = -1 x = x.flatten(0, len(x.shape) - 1) check_dtype(dtype, 'dtype', ['int32', 'int64'], 'cummin') if not isinstance(dtype, (core.VarDesc.VarType, core.DataType)): dtype = convert_np_dtype_to_dtype_(dtype) if in_dynamic_or_pir_mode(): return _C_ops.cummin(x, axis, dtype) else: check_variable_and_dtype( x, 'x', ['float32', 'float64', 'int32', 'int64'], 'cummin', ) check_type(x, 'x', (Variable), 'cummin') helper = LayerHelper('cummin', **locals()) out = helper.create_variable_for_type_inference(x.dtype) indices = helper.create_variable_for_type_inference(dtype='int64') helper.append_op( type='cummin', inputs={'x': x}, outputs={'out': out, 'indices': indices}, attrs={'axis': axis, 'dtype': dtype}, ) return out, indices def logcumsumexp( x: Tensor, axis: int | None = None, dtype: DTypeLike | None = None, name: str | None = None, ) -> Tensor: r""" The logarithm of the cumulative summation of the exponentiation of the elements along a given axis. For summation index j given by `axis` and other indices i, the result is .. math:: logcumsumexp(x)_{ij} = log \sum_{i=0}^{j}exp(x_{ij}) Note: The first element of the result is the same as the first element of the input. Args: x (Tensor): The input tensor, with data type float32, float64, float16, bfloat16, uint8, int8, int16, int32, int64 axis (int, optional): The dimension to do the operation along. -1 means the last dimension. The default (None) is to compute the cumsum over the flattened array. dtype (str|core.VarDesc.VarType|core.DataType|np.dtype, optional): The data type of the output tensor, can be float16, float32, float64. 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|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the result of logcumsumexp operator (integer input types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> data = paddle.arange(12, dtype='float64') >>> data = paddle.reshape(data, (3, 4)) >>> y = paddle.logcumsumexp(data) >>> y Tensor(shape=[12], dtype=float64, place=Place(cpu), stop_gradient=True, [0. , 1.31326169 , 2.40760596 , 3.44018970 , 4.45191440 , 5.45619332 , 6.45776285 , 7.45833963 , 8.45855173 , 9.45862974 , 10.45865844, 11.45866900]) >>> y = paddle.logcumsumexp(data, axis=0) >>> y Tensor(shape=[3, 4], dtype=float64, place=Place(cpu), stop_gradient=True, [[0. , 1. , 2. , 3. ], [4.01814993 , 5.01814993 , 6.01814993 , 7.01814993 ], [8.01847930 , 9.01847930 , 10.01847930, 11.01847930]]) >>> y = paddle.logcumsumexp(data, axis=-1) >>> y Tensor(shape=[3, 4], dtype=float64, place=Place(cpu), stop_gradient=True, [[0. , 1.31326169 , 2.40760596 , 3.44018970 ], [4. , 5.31326169 , 6.40760596 , 7.44018970 ], [8. , 9.31326169 , 10.40760596, 11.44018970]]) >>> y = paddle.logcumsumexp(data, dtype='float64') >>> assert y.dtype == paddle.float64 """ if axis is None: flatten = True else: flatten = False if dtype is not None and x.dtype != convert_np_dtype_to_dtype_(dtype): x = cast(x, dtype) if in_dynamic_or_pir_mode(): if axis is None: axis = -1 return _C_ops.logcumsumexp(x, axis, flatten, False, False) else: check_variable_and_dtype( x, 'x', [ 'float16', 'float32', 'float64', 'uint16', 'uint8', 'int8', 'int16', 'int32', 'int64', ], "logcumsumexp", ) helper = LayerHelper('logcumsumexp', **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op( type='logcumsumexp', inputs={'X': x}, outputs={'Out': out}, attrs={'axis': axis, 'flatten': flatten}, ) return out def cumprod( x: Tensor, dim: int | None = None, dtype: DTypeLike | None = None, name: str | None = None, ) -> Tensor: """ Compute the cumulative product of the input tensor x along a given dimension dim. Note: The first element of the result is the same as the first element of the input. Args: x (Tensor): the input tensor need to be cumproded. dim (int|None, optional): the dimension along which the input tensor will be accumulated. It need to be in the range of [-x.rank, x.rank) or None, where x.rank means the dimensions of the input tensor x and -1 means the last dimension. The default (None) is to compute the cumprod over the flattened array. dtype (str|core.VarDesc.VarType|core.DataType|np.dtype, optional): The data type of the output tensor, can be bfloat16, float16, float32, float64, int32, int64, complex64, complex128. 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|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the result of cumprod operator. Examples: .. code-block:: python >>> import paddle >>> data = paddle.arange(12) >>> data = paddle.reshape(data, (3, 4)) >>> data Tensor(shape=[3, 4], dtype=int64, place=Place(cpu), stop_gradient=True, [[0 , 1 , 2 , 3 ], [4 , 5 , 6 , 7 ], [8 , 9 , 10, 11]]) >>> y = paddle.cumprod(data, dim=0) >>> y Tensor(shape=[3, 4], dtype=int64, place=Place(cpu), stop_gradient=True, [[0 , 1 , 2 , 3 ], [0 , 5 , 12 , 21 ], [0 , 45 , 120, 231]]) >>> y = paddle.cumprod(data, dim=-1) >>> y Tensor(shape=[3, 4], dtype=int64, place=Place(cpu), stop_gradient=True, [[0 , 0 , 0 , 0 ], [4 , 20 , 120 , 840 ], [8 , 72 , 720 , 7920]]) >>> y = paddle.cumprod(data, dim=1, dtype='float64') >>> y Tensor(shape=[3, 4], dtype=float64, place=Place(cpu), stop_gradient=True, [[0. , 0. , 0. , 0. ], [4. , 20. , 120. , 840. ], [8. , 72. , 720. , 7920.]]) >>> assert y.dtype == paddle.float64 """ if dim is None: dim = -1 x = x.flatten(0, len(x.shape) - 1) if dtype is not None: if not isinstance(dtype, (core.VarDesc.VarType, core.DataType)): dtype = convert_np_dtype_to_dtype_(dtype) if x.dtype != dtype: x = cast(x, dtype) if in_dynamic_or_pir_mode(): return _C_ops.cumprod(x, dim, False, False) else: check_variable_and_dtype( x, "x", [ 'complex64', 'complex128', 'float16', 'uint16', 'float32', 'float64', 'int32', 'int64', ], 'cumprod', ) check_type(dim, 'dim', int, 'cumprod') helper = LayerHelper('cumprod', **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op( type='cumprod', inputs={'X': x}, outputs={'Out': out}, attrs={'dim': dim}, ) return out @inplace_apis_in_dygraph_only def cumprod_( x: Tensor, dim: int | None = None, dtype: DTypeLike | None = None, name: str | None = None, ) -> Tensor: r""" Inplace version of ``cumprod`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_cumprod`. """ if dim is None: dim = -1 x = _C_ops.flatten_(x, 0, len(x.shape) - 1) if dtype is not None: if not isinstance(dtype, (core.VarDesc.VarType, core.DataType)): dtype = convert_np_dtype_to_dtype_(dtype) if x.dtype != dtype: x = cast_(x, dtype) if in_dynamic_mode(): return _C_ops.cumprod_(x, dim, False, False) @param_two_alias(["x", "input"], ["axis", "dim"]) def prod( x: Tensor, axis: int | Sequence[int] | None = None, keepdim: bool = False, dtype: DTypeLike | None = None, name: str | None = None, ) -> Tensor: """ Compute the product of tensor elements over the given axis. .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, and ``dim`` can be used as an alias for ``axis``. For example, ``prod(input=tensor_x, dim=1, ...)`` is equivalent to ``prod(x=tensor_x, axis=1, ...)``. Args: x (Tensor): The input tensor, its data type should be bfloat16, float16, float32, float64, int32, int64, complex64, complex128. alias: ``input``. axis (int|list|tuple|None, 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. alias: ``dim``. keepdim (bool, optional): Whether to reserve the reduced dimension in the output Tensor. The result tensor will have one fewer dimension than the input unless `keepdim` is true. Default is False. dtype (str|core.VarDesc.VarType|core.DataType|np.dtype, optional): The desired date type of returned tensor, can be bfloat16, float16, 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`. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, result of product on the specified dim of input tensor. Examples: .. code-block:: python >>> import paddle >>> # the axis is a int element >>> x = paddle.to_tensor([[0.2, 0.3, 0.5, 0.9], ... [0.1, 0.2, 0.6, 0.7]]) >>> out1 = paddle.prod(x) >>> out1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.00022680) >>> out2 = paddle.prod(x, -1) >>> out2 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [0.02700000, 0.00840000]) >>> out3 = paddle.prod(x, 0) >>> out3 Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [0.02000000, 0.06000000, 0.30000001, 0.63000000]) >>> out4 = paddle.prod(x, 0, keepdim=True) >>> out4 Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.02000000, 0.06000000, 0.30000001, 0.63000000]]) >>> out5 = paddle.prod(x, 0, dtype='int64') >>> out5 Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 0, 0, 0]) >>> # the axis is list >>> y = paddle.to_tensor([[[1.0, 2.0], [3.0, 4.0]], ... [[5.0, 6.0], [7.0, 8.0]]]) >>> out6 = paddle.prod(y, [0, 1]) >>> out6 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [105., 384.]) >>> out7 = paddle.prod(y, (1, 2)) >>> out7 Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [24. , 1680.]) """ if dtype is not None: check_dtype( dtype, 'dtype', [ 'float32', 'float64', 'int32', 'int64', "float16", "uint16", "complex64", "complex128", ], 'prod', ) if x.dtype != convert_np_dtype_to_dtype_(dtype): x = cast(x, dtype) # axis is 0-size tensor. if paddle.is_tensor(axis) and axis.shape == [0]: return x reduce_all, axis = _get_reduce_axis_with_tensor(axis, x) if in_dynamic_or_pir_mode(): return _C_ops.prod(x, axis, keepdim, reduce_all) else: helper = LayerHelper('reduce_prod', **locals()) check_variable_and_dtype( x, 'x/input', [ 'float32', 'float64', 'int32', 'int64', "float16", "uint16", "complex64", "complex128", ], 'reduce_prod', ) out = helper.create_variable_for_type_inference( dtype=helper.input_dtype() ) helper.append_op( type='reduce_prod', inputs={'X': x}, outputs={'Out': out}, attrs={'dim': axis, 'keep_dim': keepdim, 'reduce_all': reduce_all}, ) return out def tanh(x: Tensor, name: str | None = None) -> Tensor: r""" 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 bfloat16, float32, float64, float16, uint8, int8, int16, int32, int64. name (str|None, 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 (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3]) >>> out = paddle.tanh(x) >>> out Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [-0.37994900, -0.19737528, 0.09966799, 0.29131261]) """ if in_dynamic_or_pir_mode(): return _C_ops.tanh(x) else: check_variable_and_dtype( x, 'x', [ 'uint16', 'float16', 'float32', 'float64', 'uint8', 'int8', 'int16', 'int32', 'int64', ], 'tanh', ) check_type(x, 'x', (Variable), 'tanh') 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 @inplace_apis_in_dygraph_only def tanh_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``tanh`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_tanh`. """ return _C_ops.tanh_(x) def increment(x: Tensor, value: float = 1.0, name: str | None = None) -> Tensor: """ The API 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|None, 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) >>> counter Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.]) """ if in_dynamic_mode(): return _C_ops.increment_(x, value) check_variable_and_dtype( x, 'x', ['float32', 'float64', 'int32', 'int64'], 'increment' ) if in_pir_mode(): _C_ops.increment_(x, value) return x else: helper = LayerHelper("increment", **locals()) helper.append_op( type='increment', inputs={'X': [x]}, outputs={'Out': [x]}, attrs={'step': float(value)}, ) return x def broadcast_shapes(*shapes: Sequence[int]) -> list[int]: """ The function returns the shape of doing operation with broadcasting on tensors of shape list. Note: If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: *shapes (list[int]|tuple[int]): A shape list of multiple tensors. Returns: list[int], the result shape. Examples: .. code-block:: python >>> import paddle >>> shape = paddle.broadcast_shapes([2, 1, 3], [1, 3, 1]) >>> shape [2, 3, 3] >>> # shape = paddle.broadcast_shapes([2, 1, 3], [3, 3, 1]) >>> # ValueError (terminated with error message). >>> shape = paddle.broadcast_shapes([5, 1, 3], [1, 4, 1], [1, 1, 3]) >>> shape [5, 4, 3] >>> # shape = paddle.broadcast_shapes([5, 1, 3], [1, 4, 1], [1, 2, 3]) >>> # ValueError (terminated with error message). """ if len(shapes) == 0: return [] elif len(shapes) == 1: return list(shapes[0]) else: current_shape = list(shapes[0]) for next_shape in shapes[1:]: current_shape = broadcast_shape(current_shape, next_shape) return current_shape def broadcast_shape( x_shape: Sequence[int], y_shape: Sequence[int] ) -> list[int]: """ The function returns the shape of doing operation with broadcasting on tensors of x_shape and y_shape. Note: If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor 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]) >>> shape [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) def conj(x: Tensor, name: str | None = None) -> Tensor: r""" This function computes the conjugate of the Tensor elementwisely. Args: x (Tensor): The input Tensor which hold the complex numbers. Optional data types are: bfloat16, float16, complex64, complex128, float32, float64, int32 or int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): The conjugate of input. The shape and data type is the same with input. If the elements of tensor is real type such as float32, float64, int32 or int64, the out is the same with input. Examples: .. code-block:: python >>> import paddle >>> data = paddle.to_tensor([[1+1j, 2+2j, 3+3j], [4+4j, 5+5j, 6+6j]]) >>> data Tensor(shape=[2, 3], dtype=complex64, place=Place(cpu), stop_gradient=True, [[(1+1j), (2+2j), (3+3j)], [(4+4j), (5+5j), (6+6j)]]) >>> conj_data = paddle.conj(data) >>> conj_data Tensor(shape=[2, 3], dtype=complex64, place=Place(cpu), stop_gradient=True, [[(1-1j), (2-2j), (3-3j)], [(4-4j), (5-5j), (6-6j)]]) """ if in_dynamic_or_pir_mode(): return _C_ops.conj(x) else: check_variable_and_dtype( x, "x", [ 'complex64', 'complex128', 'float16', 'uint16', 'float32', 'float64', 'int32', 'int64', ], 'conj', ) helper = LayerHelper('conj', **locals()) out = helper.create_variable_for_type_inference( dtype=helper.input_dtype() ) helper.append_op(type='conj', inputs={'X': x}, outputs={'Out': [out]}) return out def gammaln(x: Tensor, name: str | None = None) -> Tensor: r""" Calculates the logarithm of the absolute value of the gamma function elementwisely. Args: x (Tensor): Input Tensor. Must be one of the following types: float16, float32, float64, bfloat16. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, The values of the logarithm of the absolute value of the gamma at the given tensor x. Examples: .. code-block:: python >>> import paddle >>> x = paddle.arange(1.5, 4.5, 0.5) >>> out = paddle.gammaln(x) >>> print(out) Tensor(shape=[6], dtype=float32, place=Place(cpu), stop_gradient=True, [-0.12078224, 0. , 0.28468287, 0.69314718, 1.20097363, 1.79175949]) """ if in_dynamic_or_pir_mode(): return _C_ops.gammaln(x) else: check_variable_and_dtype( x, 'x', ['float16', 'float32', 'float64', 'bfloat16'], 'gammaln' ) helper = LayerHelper('gammaln', **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op(type='gammaln', inputs={'x': x}, outputs={'out': out}) return out @inplace_apis_in_dygraph_only def gammaln_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``gammaln`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_gammaln`. """ if in_dynamic_mode(): return _C_ops.gammaln_(x) def digamma(x: Tensor, name: str | None = None) -> Tensor: r""" Calculates the digamma of the given input tensor, element-wise. .. math:: Out = \Psi(x) = \frac{ \Gamma^{'}(x) }{ \Gamma(x) } Args: x (Tensor): Input Tensor. Must be one of the following types: bfloat16, float16, float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the digamma of the input Tensor, the shape and data type is the same with input (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> data = paddle.to_tensor([[1, 1.5], [0, -2.2]], dtype='float32') >>> res = paddle.digamma(data) >>> res Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[-0.57721591, 0.03648996], [ nan , 5.32286835]]) """ if in_dynamic_or_pir_mode(): return _C_ops.digamma(x) else: check_variable_and_dtype( x, 'x', [ 'float16', 'float32', 'float64', 'uint16', 'uint8', 'int8', 'int16', 'int32', 'int64', ], 'digamma', ) helper = LayerHelper('digamma', **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op(type='digamma', inputs={'X': x}, outputs={'Out': out}) return out @inplace_apis_in_dygraph_only def digamma_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``digamma`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_digamma`. """ if in_dynamic_mode(): return _C_ops.digamma_(x) def gammaincc(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Computes the regularized upper incomplete gamma function. .. math:: Q(x, y) = \frac{1}{\Gamma(x)} \int_{y}^{\infty} t^{x-1} e^{-t} dt Args: x (Tensor): The non-negative argument Tensor. Must be one of the following types: float32, float64. y (Tensor): The positive parameter Tensor. Must be one of the following types: float32, float64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the gammaincc of the input Tensor. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0.5, 0.5, 0.5, 0.5, 0.5], dtype="float32") >>> y = paddle.to_tensor([0, 1, 10, 100, 1000], dtype="float32") >>> out = paddle.gammaincc(x, y) >>> print(out) Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [1. , 0.15729916, 0.00000774, 0. , 0. ]) """ if not isinstance(x, Value) and not paddle.all( paddle.greater_equal(x, paddle.zeros_like(x)) ): raise ValueError( "The input argument x must be greater than or equal to 0." ) if not isinstance(x, Value) and not paddle.all( paddle.greater_equal(y, paddle.zeros_like(y)) ): raise ValueError( "The input argument y must be greater than or equal to 0." ) if in_dynamic_or_pir_mode(): return _C_ops.gammaincc(x, y) else: check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'gammaincc') check_variable_and_dtype(y, 'y', ['float32', 'float64'], 'gammaincc') helper = LayerHelper('gammaincc', **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op( type='gammaincc', inputs={'x': x, 'y': y}, outputs={'out': out} ) return out @inplace_apis_in_dygraph_only def gammaincc_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``gammaincc`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_gammaincc`. """ if in_dynamic_mode(): return _C_ops.gammaincc_(x, y) def gammainc(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Computes the regularized lower incomplete gamma function. .. math:: P(x, y) = \frac{1}{\Gamma(x)} \int_{0}^{y} t^{x-1} e^{-t} dt Args: x (Tensor): The non-negative argument Tensor. Must be one of the following types: float32, float64. y (Tensor): The positive parameter Tensor. Must be one of the following types: float32, float64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the gammainc of the input Tensor. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0.5, 0.5, 0.5, 0.5, 0.5], dtype="float32") >>> y = paddle.to_tensor([0, 1, 10, 100, 1000], dtype="float32") >>> out = paddle.gammainc(x, y) >>> print(out) Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [0. , 0.84270084, 0.99999225, 1. , 1. ]) """ return 1 - paddle.gammaincc(x, y) @inplace_apis_in_dygraph_only def gammainc_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``gammainc`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_gammainc`. """ return ( paddle.gammaincc_(x, y) .multiply_(paddle.full_like(x, -1.0)) .add_(paddle.full_like(x, 1.0)) ) def lgamma(x: Tensor, name: str | None = None) -> Tensor: r""" Calculates the lgamma of the given input tensor, element-wise. This operator performs elementwise lgamma for input $X$. :math:`out = log\Gamma(x)` Args: x (Tensor): Input Tensor. Must be one of the following types: bfloat16, float16, float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, the lgamma of the input Tensor, the shape and data type is the same with input (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3]) >>> out = paddle.lgamma(x) >>> out Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [1.31452453, 1.76149762, 2.25271273, 1.09579790]) """ if in_dynamic_or_pir_mode(): return _C_ops.lgamma(x) else: check_variable_and_dtype( x, 'x', [ 'float16', 'float32', 'float64', 'uint16', 'uint8', 'int8', 'int16', 'int32', 'int64', ], 'lgamma', ) helper = LayerHelper('lgamma', **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op(type='lgamma', inputs={'X': x}, outputs={'Out': out}) return out @inplace_apis_in_dygraph_only def lgamma_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``lgamma`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_lgamma`. """ if in_dynamic_mode(): return _C_ops.lgamma_(x) def multigammaln(x: Tensor, p: int, name: str | None = None) -> Tensor: """ This function computes the log of multivariate gamma, also sometimes called the generalized gamma. Args: x (Tensor): Input Tensor. Must be one of the following types: float16, float32, float64, uint16. p (int): The dimension of the space of integration. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): The values of the log multivariate gamma at the given tensor x. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([2.5, 3.5, 4, 6.5, 7.8, 10.23, 34.25]) >>> p = 2 >>> out = paddle.multigammaln(x, p) >>> print(out) Tensor(shape=[7], dtype=float32, place=Place(cpu), stop_gradient=True, [0.85704780 , 2.46648574 , 3.56509781 , 11.02241898 , 15.84497833 , 26.09257698 , 170.68318176]) """ assert p >= 1, ( f"The p must be greater than or equal to 1, But received p is {p}.\n" ) c = 0.25 * p * (p - 1) * math.log(math.pi) b = 0.5 * paddle.arange(start=(1 - p), end=1, step=1, dtype=x.dtype) return paddle.sum(paddle.lgamma(x.unsqueeze(-1) + b), axis=-1) + c @inplace_apis_in_dygraph_only def multigammaln_(x: Tensor, p: int, name: str | None = None) -> Tensor: r""" Inplace version of ``multigammaln_`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_multigammaln`. """ assert p >= 1, ( f"The p must be greater than or equal to 1, But received p is {p}.\n" ) c = 0.25 * p * (p - 1) * math.log(math.pi) c = paddle.to_tensor(c, dtype=x.dtype) b = 0.5 * paddle.arange(start=(1 - p), end=1, step=1, dtype=x.dtype) paddle.assign((x.unsqueeze(-1) + b).lgamma_().sum(-1).add_(c), x) return x def neg(x: Tensor, name: str | None = None) -> Tensor: """ This function computes the negative of the Tensor elementwisely. Args: x (Tensor): Input of neg operator, an N-D Tensor, with data type bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): The negative of input Tensor. The shape and data type are the same with input Tensor. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3]) >>> out = paddle.neg(x) >>> out Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [ 0.40000001, 0.20000000, -0.10000000, -0.30000001]) """ return scale( x, scale=-1.0, bias=0.0, bias_after_scale=True, act=None, name=name ) @inplace_apis_in_dygraph_only def neg_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``neg`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_neg`. """ return x.scale_( scale=-1.0, bias=0.0, bias_after_scale=True, act=None, name=name ) def positive(x: Tensor, name: str | None = None) -> Tensor: r""" Returns the input Tensor as it is. This is used in `Tensor.__pos__`, applying the unary `+` operator to the tensor. .. math:: Out = +X Args: x (Tensor): The input tensor. The tensor cannot be of type bool. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: A tensor with the same shape and data type as the input tensor. The returned tensor is the same. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-1, 0, 1]) >>> out = paddle.positive(x) >>> print(out) Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [-1, 0, 1]) """ # Check if the input tensor is of bool type and raise an error if x.dtype == paddle.bool: raise TypeError("The `+` operator, on a bool tensor is not supported.") return x def negative(x: Tensor, name: str | None = None) -> Tensor: r""" Returns the negated version of the input Tensor. This is used in `Tensor.__neg__`, applying the unary `-` operator to the tensor. .. math:: Out = -X Args: x (Tensor): The input tensor. The tensor cannot be of type bool. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: A tensor with the same shape and data type as the input tensor. The returned tensor is the negative. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-1, 0, 1]) >>> out = paddle.negative(x) >>> print(out) Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [1, 0, -1]) """ # Check if the input tensor is of bool type and raise an error if x.dtype == paddle.bool: raise TypeError("The `-` operator, on a bool tensor is not supported.") return -x def atan2(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Element-wise arctangent of x/y with consideration of the quadrant. Equation: .. math:: atan2(x,y)=\left\{\begin{matrix} & tan^{-1}(\frac{x}{y}) & y > 0 \\ & tan^{-1}(\frac{x}{y}) + \pi & x>=0, y < 0 \\ & tan^{-1}(\frac{x}{y}) - \pi & x<0, y < 0 \\ & +\frac{\pi}{2} & x>0, y = 0 \\ & -\frac{\pi}{2} & x<0, y = 0 \\ &\text{undefined} & x=0, y = 0 \end{matrix}\right. Args: x (Tensor): An N-D Tensor, the data type is int32, int64, float16, float32, float64. y (Tensor): An N-D Tensor, must have the same type as `x`. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the shape and data type is the same with input (The output data type is float64 when the input data type is int). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-1, +1, +1, -1]).astype('float32') >>> x Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [-1, 1, 1, -1]) >>> y = paddle.to_tensor([-1, -1, +1, +1]).astype('float32') >>> y Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [-1, -1, 1, 1]) >>> out = paddle.atan2(x, y) >>> out Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [-2.35619450, 2.35619450, 0.78539819, -0.78539819]) """ x_shape = list(x.shape) y_shape = list(y.shape) if in_dynamic_or_pir_mode(): broadcast_x = x broadcast_y = y if x_shape != y_shape: broadcast_shape = paddle.broadcast_shape(x_shape, y_shape) broadcast_x = paddle.broadcast_to(broadcast_x, broadcast_shape) broadcast_y = paddle.broadcast_to(broadcast_y, broadcast_shape) return _C_ops.atan2(broadcast_x, broadcast_y) else: check_variable_and_dtype( x, 'x', ['int32', 'int64', 'float16', 'float32', 'float64'], 'atan2', ) check_variable_and_dtype( y, 'y', ['int32', 'int64', 'float16', 'float32', 'float64'], 'atan2', ) helper = LayerHelper('atan2', **locals()) inputs = {'X1': x, 'X2': y} out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op(type='atan2', inputs=inputs, outputs={'Out': out}) return out def logit( x: Tensor, eps: float | None = None, name: str | None = None ) -> Tensor: r""" This function generates a new tensor with the logit of the elements of input x. x is clamped to [eps, 1-eps] when eps is not zero. When eps is zero and x < 0 or x > 1, the function will yields NaN. .. math:: logit(x) = ln(\frac{x}{1 - x}) where .. math:: x_i= \left\{\begin{array}{rcl} x_i & &\text{if } eps == Default \\ eps & &\text{if } x_i < eps \\ x_i & &\text{if } eps <= x_i <= 1-eps \\ 1-eps & &\text{if } x_i > 1-eps \end{array}\right. Args: x (Tensor): The input Tensor with data type bfloat16, float16, float32, float64, uint8, int8, int16, int32, int64. eps (float|None, optional): the epsilon for input clamp bound. Default is None. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out(Tensor): A Tensor with the same data type and shape as ``x`` (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0.2635, 0.0106, 0.2780, 0.2097, 0.8095]) >>> out1 = paddle.logit(x) >>> out1 Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [-1.02785587, -4.53624487, -0.95440406, -1.32673466, 1.44676447]) """ if eps is None: eps = 0.0 if in_dynamic_or_pir_mode(): return _C_ops.logit(x, eps) else: check_variable_and_dtype( x, 'x', [ 'float16', 'uint16', 'float32', 'float64', 'uint8', 'int8', 'int16', 'int32', 'int64', ], 'logit', ) helper = LayerHelper("logit", **locals()) out = helper.create_variable_for_type_inference(x.dtype) helper.append_op( type='logit', inputs={'X': x}, outputs={'Out': out}, attrs={'eps': eps}, ) return out @inplace_apis_in_dygraph_only def logit_( x: Tensor, eps: float | None = None, name: str | None = None ) -> Tensor: r""" Inplace version of ``logit`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_logit`. """ if eps is None: eps = 0.0 if in_dynamic_mode(): return _C_ops.logit_(x, eps) def lerp( x: Tensor, y: Tensor, weight: float | Tensor, name: str | None = None ) -> Tensor: r""" Does a linear interpolation between x and y based on weight. Equation: .. math:: lerp(x, y, weight) = x + weight * (y - x). Args: x (Tensor): An N-D Tensor with starting points, the data type is bfloat16, float16, float32, float64. y (Tensor): An N-D Tensor with ending points, the data type is bfloat16, float16, float32, float64. weight (float|Tensor): The weight for the interpolation formula. When weight is Tensor, the data type is bfloat16, float16, float32, float64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the shape and data type is the same with input. Example: .. code-block:: python >>> import paddle >>> x = paddle.arange(1., 5., dtype='float32') >>> y = paddle.empty([4], dtype='float32') >>> y.fill_(10.) >>> out = paddle.lerp(x, y, 0.5) >>> out Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, [5.50000000, 6. , 6.50000000, 7. ]) """ if isinstance(weight, float): weight = paddle.full(shape=[], fill_value=weight, dtype=x.dtype) if in_dynamic_or_pir_mode(): return _C_ops.lerp(x, y, weight) else: check_variable_and_dtype( x, 'x', ['uint16', 'float16', 'float32', 'float64'], 'lerp' ) check_variable_and_dtype( y, 'y', ['uint16', 'float16', 'float32', 'float64'], 'lerp' ) check_variable_and_dtype( weight, 'weight', ['uint16', 'float16', 'float32', 'float64'], 'lerp', ) helper = LayerHelper('lerp', **locals()) inputs = {'X': x, 'Y': y, 'Weight': weight} out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op(type='lerp', inputs=inputs, outputs={'Out': out}) return out @inplace_apis_in_dygraph_only def lerp_( x: Tensor, y: Tensor, weight: float | Tensor, name: str | None = None ) -> Tensor: r""" Inplace version of ``lerp`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_lerp`. """ out_shape = broadcast_shape(x.shape, y.shape) check_type(weight, 'weight', (float, paddle.Tensor, Variable), 'lerp') if isinstance(weight, float): weight = paddle.to_tensor([weight], dtype=x.dtype) elif isinstance(weight, (paddle.Tensor, Variable)): out_shape = broadcast_shape(out_shape, weight.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) return _C_ops.lerp_(x, y, weight) def erfinv(x: Tensor, name: str | None = None) -> Tensor: r""" The inverse error function of x. Please refer to :ref:`api_paddle_erf` .. math:: erfinv(erf(x)) = x. Args: x (Tensor): An N-D Tensor, the data type is float16, bfloat16, float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), an N-D Tensor, the shape and data type is the same with input (integer types are autocasted into float32). Example: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0, 0.5, -1.], dtype="float32") >>> out = paddle.erfinv(x) >>> out Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [ 0. , 0.47693631, -inf. ]) """ if in_dynamic_or_pir_mode(): return _C_ops.erfinv(x) else: check_variable_and_dtype( x, 'x', [ 'float32', 'float64', 'float16', 'uint16', 'uint8', 'int8', 'int16', 'int32', 'int64', ], 'erfinv', ) helper = LayerHelper('erfinv', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op(type='erfinv', inputs={'X': x}, outputs={'Out': out}) return out @inplace_apis_in_dygraph_only def erfinv_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``erfinv`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_erfinv`. """ check_type(x, 'x', (paddle.Tensor, Variable), 'erfinv') return _C_ops.erfinv_(x) def rad2deg(x: Tensor, name: str | None = None) -> Tensor: r""" Convert each of the elements of input x from angles in radians to degrees. Equation: .. math:: rad2deg(x)=180/ \pi * x Args: x (Tensor): An N-D Tensor, the data type is float32, float64, int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the shape and data type is the same with input (The output data type is float32 when the input data type is int). Examples: .. code-block:: python >>> import paddle >>> import math >>> x1 = paddle.to_tensor([3.142, -3.142, 6.283, -6.283, 1.570, -1.570]) >>> result1 = paddle.rad2deg(x1) >>> result1 Tensor(shape=[6], dtype=float32, place=Place(cpu), stop_gradient=True, [ 180.02334595, -180.02334595, 359.98937988, -359.98937988, 89.95437622 , -89.95437622 ]) >>> x2 = paddle.to_tensor(math.pi/2) >>> result2 = paddle.rad2deg(x2) >>> result2 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 90.) >>> x3 = paddle.to_tensor(1) >>> result3 = paddle.rad2deg(x3) >>> result3 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 57.29578018) """ rad2deg_scale = 180 / np.pi if in_dynamic_or_pir_mode(): if convert_dtype(x.dtype) in ['int32', 'int64']: x = cast(x, dtype="float32") return _C_ops.scale(x, rad2deg_scale, 0.0, True) else: check_variable_and_dtype( x, 'x', ['int32', 'int64', 'float32', 'float64'], 'rad2deg' ) helper = LayerHelper('rad2deg', **locals()) out_cast = x if convert_dtype(x.dtype) in ['int32', 'int64']: out_cast = helper.create_variable_for_type_inference( dtype=paddle.float32 ) helper.append_op( type='cast', inputs={'X': x}, outputs={'Out': out_cast}, attrs={'in_dtype': x.dtype, 'out_dtype': paddle.float32}, ) out = helper.create_variable_for_type_inference(dtype=out_cast.dtype) helper.append_op( type='scale', inputs={'X': out_cast}, outputs={'Out': out}, attrs={'scale': rad2deg_scale}, ) return out def deg2rad(x: Tensor, name: str | None = None) -> Tensor: r""" Convert each of the elements of input x from degrees to angles in radians. .. math:: deg2rad(x)=\pi * x / 180 Args: x (Tensor): An N-D Tensor, the data type is float32, float64, int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the shape and data type is the same with input (The output data type is float32 when the input data type is int). Examples: .. code-block:: python >>> import paddle >>> x1 = paddle.to_tensor([180.0, -180.0, 360.0, -360.0, 90.0, -90.0]) >>> result1 = paddle.deg2rad(x1) >>> result1 Tensor(shape=[6], dtype=float32, place=Place(cpu), stop_gradient=True, [3.14159274, -3.14159274, 6.28318548, -6.28318548, 1.57079637, -1.57079637]) >>> x2 = paddle.to_tensor(180) >>> result2 = paddle.deg2rad(x2) >>> result2 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 3.14159274) """ deg2rad_scale = np.pi / 180.0 if in_dynamic_or_pir_mode(): if convert_dtype(x.dtype) in ['int32', 'int64']: x = cast(x, dtype="float32") return _C_ops.scale(x, deg2rad_scale, 0.0, True) else: check_variable_and_dtype( x, 'x', ['int32', 'int64', 'float32', 'float64'], 'deg2rad' ) helper = LayerHelper('deg2rad', **locals()) out_cast = x if convert_dtype(x.dtype) in ['int32', 'int64']: out_cast = helper.create_variable_for_type_inference( dtype=paddle.float32 ) helper.append_op( type='cast', inputs={'X': x}, outputs={'Out': out_cast}, attrs={'in_dtype': x.dtype, 'out_dtype': paddle.float32}, ) out = helper.create_variable_for_type_inference(dtype=out_cast.dtype) helper.append_op( type='scale', inputs={'X': out_cast}, outputs={'Out': out}, attrs={'scale': deg2rad_scale}, ) return out def gcd(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Computes the element-wise greatest common divisor (GCD) of input |x| and |y|. Both x and y must have integer types. Note: gcd(0,0)=0, gcd(0, y)=|y| If x.shape != y.shape, they must be broadcastable to a common shape (which becomes the shape of the output). Args: x (Tensor): An N-D Tensor, the data type is int32, int64. y (Tensor): An N-D Tensor, the data type is int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the data type is the same with input. Examples: .. code-block:: python >>> import paddle >>> x1 = paddle.to_tensor(12) >>> x2 = paddle.to_tensor(20) >>> paddle.gcd(x1, x2) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 4) >>> x3 = paddle.arange(6) >>> paddle.gcd(x3, x2) Tensor(shape=[6], dtype=int64, place=Place(cpu), stop_gradient=True, [20, 1 , 2 , 1 , 4 , 5]) >>> x4 = paddle.to_tensor(0) >>> paddle.gcd(x4, x2) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 20) >>> paddle.gcd(x4, x4) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 0) >>> x5 = paddle.to_tensor(-20) >>> paddle.gcd(x1, x5) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 4) """ shape = paddle.broadcast_shape(x.shape, y.shape) x = paddle.broadcast_to(x, shape) y = paddle.broadcast_to(y, shape) x = paddle.abs(x) y = paddle.abs(y) def _gcd_cond_fn(x, y): return paddle.any(y != 0) def _gcd_body_fn(x, y): # paddle.mod will raise an error when any element of y is 0. To avoid # that, we change those zeros to ones. Their values don't matter because # they won't be used. y_not_equal_0 = y != 0 y_safe = paddle.where(y_not_equal_0, y, paddle.ones(y.shape, y.dtype)) x, y = ( paddle.where(y_not_equal_0, y, x), paddle.where( y_not_equal_0, paddle.mod(x, y_safe), paddle.zeros(y.shape, y.dtype), ), ) return (paddle.where(x < y, y, x), paddle.where(x < y, x, y)) if in_dynamic_mode(): while _gcd_cond_fn(x, y): x, y = _gcd_body_fn(x, y) return x else: check_variable_and_dtype(x, 'x', ['int32', 'int64'], 'gcd') check_variable_and_dtype(y, 'y', ['int32', 'int64'], 'gcd') out, _ = paddle.static.nn.while_loop(_gcd_cond_fn, _gcd_body_fn, [x, y]) return out def gcd_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``gcd`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_gcd`. """ shape = paddle.broadcast_shape(x.shape, y.shape) if shape != x.shape: raise ValueError( f"The shape of broadcast output {shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) y = paddle.broadcast_to(y, shape) x = paddle.abs_(x) y = paddle.abs(y) def _gcd_cond_fn(x, y): return paddle.any(y != 0) def _gcd_body_fn(x, y): # paddle.mod will raise an error when any element of y is 0. To avoid # that, we change those zeros to ones. Their values don't matter because # they won't be used. y_equal_0 = y == 0 y_safe = paddle.where(y_equal_0, paddle.ones(y.shape, y.dtype), y) y, x = ( paddle.where( y_equal_0, paddle.zeros(y.shape, y.dtype), paddle.mod(x, y_safe), ), paddle.where_(y_equal_0, x, y), ) return ( paddle.where(x < y, x, y), paddle.where_(x >= y, x, y), ) if in_dynamic_mode(): while _gcd_cond_fn(x, y): y, x = _gcd_body_fn(x, y) return x def lcm(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Computes the element-wise least common multiple (LCM) of input |x| and |y|. Both x and y must have integer types. Note: lcm(0,0)=0, lcm(0, y)=0 If x.shape != y.shape, they must be broadcastable to a common shape (which becomes the shape of the output). Args: x (Tensor): An N-D Tensor, the data type is int32, int64. y (Tensor): An N-D Tensor, the data type is int32, int64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the data type is the same with input. Examples: .. code-block:: python >>> import paddle >>> x1 = paddle.to_tensor(12) >>> x2 = paddle.to_tensor(20) >>> paddle.lcm(x1, x2) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 60) >>> x3 = paddle.arange(6) >>> paddle.lcm(x3, x2) Tensor(shape=[6], dtype=int64, place=Place(cpu), stop_gradient=True, [0, 20, 20, 60, 20, 20]) >>> x4 = paddle.to_tensor(0) >>> paddle.lcm(x4, x2) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 0) >>> paddle.lcm(x4, x4) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 0) >>> x5 = paddle.to_tensor(-20) >>> paddle.lcm(x1, x5) Tensor(shape=[], dtype=int64, place=Place(cpu), stop_gradient=True, 60) """ d = paddle.gcd(x, y) # paddle.mod will raise an error when any element of y is 0. To avoid # that, we change those zeros to ones. Their values don't matter because # they won't be used. d_equal_0 = paddle.equal(d, 0) d_safe = paddle.where(d_equal_0, paddle.ones(d.shape, d.dtype), d) out = paddle.where( d_equal_0, paddle.zeros(d.shape, d.dtype), paddle.abs(x * y) // d_safe ) return out def lcm_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``lcm`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_lcm`. """ d = paddle.gcd(x, y) # paddle.mod will raise an error when any element of y is 0. To avoid # that, we change those zeros to ones. Their values don't matter because # they won't be used. d_not_equal_0 = d != 0 d_safe = paddle.where(d_not_equal_0, d, paddle.ones(d.shape, d.dtype)) out = paddle.where_( d_not_equal_0, paddle.abs_(x.multiply_(y)).floor_divide_(d_safe), paddle.zeros(d.shape, d.dtype), ) return out @ParamAliasDecorator({"x": ["input"], "axis": ["dim"]}) def diff( x: Tensor, n: int = 1, axis: int = -1, prepend: Tensor | None = None, append: Tensor | None = None, name: str | None = None, *, out: Tensor | None = None, ) -> Tensor: r""" Computes the n-th forward difference along the given axis. The first-order differences is computed by using the following formula: .. math:: out[i] = x[i+1] - x[i] Higher-order differences are computed by using paddle.diff() recursively. The number of n supports any positive integer value. .. note:: Alias Support: The parameter name ``input`` can be used as an alias for ``x``, and ``dim`` can be used as an alias for ``axis``. For example, ``diff(input=tensor_x, dim=1, ...)`` is equivalent to ``diff(x=tensor_x, axis=1, ...)``. Args: x (Tensor): The input tensor to compute the forward difference on, the data type is float16, float32, float64, bool, int32, int64. alias: ``input``. n (int, optional): The number of times to recursively compute the difference. Supports any positive integer value. Default:1 axis (int, optional): The axis to compute the difference along. Default:-1 alias: ``dim``. prepend (Tensor|None, optional): The tensor to prepend to input along axis before computing the difference. It's dimensions must be equivalent to that of x, and its shapes must match x's shape except on axis. append (Tensor|None, optional): The tensor to append to input along axis before computing the difference, It's dimensions must be equivalent to that of x, and its shapes must match x's shape except on axis. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. out (Tensor, optional): The output tensor. If provided, the result will be stored in this tensor. Returns: Tensor: The output tensor with same dtype with x. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([1, 4, 5, 2]) >>> out = paddle.diff(x) >>> out Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [ 3, 1, -3]) >>> x_2 = paddle.to_tensor([1, 4, 5, 2]) >>> out = paddle.diff(x_2, n=2) >>> out Tensor(shape=[2], dtype=int64, place=Place(cpu), stop_gradient=True, [ -2, -4]) >>> y = paddle.to_tensor([7, 9]) >>> out = paddle.diff(x, append=y) >>> out Tensor(shape=[5], dtype=int64, place=Place(cpu), stop_gradient=True, [ 3, 1, -3, 5, 2]) >>> out = paddle.diff(x, n=2, append=y) >>> out Tensor(shape=[4], dtype=int64, place=Place(cpu), stop_gradient=True, [-2, -4, 8, -3]) >>> out = paddle.diff(x, n=3, append=y) >>> out Tensor(shape=[3], dtype=int64, place=Place(cpu), stop_gradient=True, [-2 , 12, -11]) >>> z = paddle.to_tensor([[1, 2, 3], [4, 5, 6]]) >>> out = paddle.diff(z, axis=0) >>> out Tensor(shape=[1, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[3, 3, 3]]) >>> out = paddle.diff(z, axis=1) >>> out Tensor(shape=[2, 2], dtype=int64, place=Place(cpu), stop_gradient=True, [[1, 1], [1, 1]]) """ if n < 1: raise ValueError( f"Diff expects input to be at least one-dimensional but got {n}" ) def _diff_handler( x, n=1, axis=-1, prepend=None, append=None, name=None, out=None ): if axis < 0: axis = axis + len(x.shape) if axis > len(x.shape): axis = len(x.shape) if axis < 0: axis = 0 dtype = x.dtype axes = [axis] infer_flags = [1 for i in range(len(axes))] if in_dynamic_or_pir_mode(): has_pend = False input_list = [] if prepend is not None and append is not None: input_list = [prepend, x, append] has_pend = True elif prepend is not None: input_list = [prepend, x] has_pend = True elif append is not None: input_list = [x, append] has_pend = True if has_pend: new_input = _C_ops.concat(input_list, axis) else: new_input = x attrs_1 = () attrs_2 = () dim_len = new_input.shape[axis] if dim_len < 0: dim_len = paddle.shape(new_input)[axis] starts_1 = [0] attrs_1 += ('starts', starts_1) ends_1 = [dim_len - 1] attrs_1 += ('ends', ends_1) input_front = _C_ops.slice( new_input, axes, starts_1, ends_1, infer_flags, [] ) starts_2 = [1] attrs_2 += ('starts', starts_2) ends_2 = [dim_len] attrs_2 += ('ends', ends_2) input_back = _C_ops.slice( new_input, axes, starts_2, ends_2, infer_flags, [] ) if x.dtype == paddle.bool or x.dtype == core.DataType.BOOL: return _C_ops.logical_xor(input_back, input_front, out=out) else: return _C_ops.subtract(input_back, input_front, out=out) else: check_variable_and_dtype( x, 'x', ['float16', 'float32', 'float64', 'bool', 'int32', 'int64'], 'diff', ) check_type(axis, 'axis', (int), 'diff') helper = LayerHelper('diff', **locals()) has_pend = False input_list = [] if prepend is not None and append is not None: input_list = [prepend, x, append] has_pend = True elif prepend is not None: input_list = [prepend, x] has_pend = True elif append is not None: input_list = [x, append] has_pend = True if has_pend: new_input = helper.create_variable_for_type_inference(dtype) helper.append_op( type='concat', inputs={'X': input_list}, outputs={'Out': [new_input]}, attrs={'axis': axis}, ) else: new_input = x dim_len = new_input.shape[axis] attrs_1 = {'axes': axes} starts_1 = [0] ends_1 = [dim_len - 1] attrs_1['starts'] = starts_1 attrs_1['ends'] = ends_1 input_front = helper.create_variable_for_type_inference(dtype) helper.append_op( type='slice', inputs={'Input': new_input}, attrs=attrs_1, outputs={'Out': input_front}, ) attrs_2 = {'axes': axes} starts_2 = [1] ends_2 = [dim_len] attrs_2['starts'] = starts_2 attrs_2['ends'] = ends_2 input_back = helper.create_variable_for_type_inference(dtype) helper.append_op( type='slice', inputs={'Input': new_input}, attrs=attrs_2, outputs={'Out': input_back}, ) if dtype == paddle.bool: out = helper.create_variable_for_type_inference(dtype) helper.append_op( type='logical_xor', inputs={"X": input_back, "Y": input_front}, outputs={"Out": out}, ) else: out = paddle.tensor.math.subtract(input_back, input_front) return out last_out = _diff_handler( x, n=1, axis=axis, prepend=prepend, append=append, name=name, out=out if n == 1 else None, ) if n > 1: for _ in range(n - 2): last_out = _diff_handler( last_out, n=1, axis=axis, prepend=None, append=None, name=name ) last_out = _diff_handler( last_out, n=1, axis=axis, prepend=None, append=None, name=name, out=out, ) return last_out def angle(x: Tensor, name: str | None = None) -> Tensor: r""" Element-wise angle of complex numbers. For non-negative real numbers, the angle is 0 while for negative real numbers, the angle is :math:`\pi`, and NaNs are propagated.. Equation: .. math:: angle(x)=arctan2(x.imag, x.real) Args: x (Tensor): An N-D Tensor, the data type is complex64, complex128, or float32, float64 . name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: An N-D Tensor of real data type with the same precision as that of x's data type. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([-2, -1, 0, 1]).unsqueeze(-1).astype('float32') >>> y = paddle.to_tensor([-2, -1, 0, 1]).astype('float32') >>> z = x + 1j * y >>> z Tensor(shape=[4, 4], dtype=complex64, place=Place(cpu), stop_gradient=True, [[(-2-2j), (-2-1j), (-2+0j), (-2+1j)], [(-1-2j), (-1-1j), (-1+0j), (-1+1j)], [-2j , -1j , 0j , 1j ], [ (1-2j), (1-1j), (1+0j), (1+1j)]]) >>> theta = paddle.angle(z) >>> theta Tensor(shape=[4, 4], dtype=float32, place=Place(cpu), stop_gradient=True, [[-2.35619450, -2.67794514, 3.14159274, 2.67794514], [-2.03444386, -2.35619450, 3.14159274, 2.35619450], [-1.57079637, -1.57079637, 0. , 1.57079637], [-1.10714877, -0.78539819, 0. , 0.78539819]]) """ if in_dynamic_or_pir_mode(): return _C_ops.angle(x) else: check_variable_and_dtype( x, 'x', [ 'float16', 'float32', 'float64', 'complex64', 'complex128', 'uint16', ], 'angle', ) op_type = "angle" helper = LayerHelper(op_type, **locals()) inputs = {"X": x} out = helper.create_variable_for_type_inference( dtype=_complex_to_real_dtype(x.dtype) ) outputs = {"Out": out} helper.append_op(type=op_type, inputs=inputs, outputs=outputs) return out def heaviside(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Computes the Heaviside step function determined by corresponding element in y for each element in x. The equation is .. math:: heaviside(x, y)= \left\{ \begin{array}{lcl} 0,& &\text{if} \ x < 0, \\ y,& &\text{if} \ x = 0, \\ 1,& &\text{if} \ x > 0. \end{array} \right. Note: ``paddle.heaviside`` supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): The input tensor of Heaviside step function, it's data type should be bfloat16, float16, float32, float64, int32 or int64. y (Tensor): The tensor that determines a Heaviside step function, it's data type should be bfloat16, float16, float32, float64, int32 or int64. name (str|None, optional): Name for the operation (optional, default is None). Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name`. Returns: N-D Tensor. A location into which the result is stored. If x and 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 paddle >>> x = paddle.to_tensor([-0.5, 0, 0.5]) >>> y = paddle.to_tensor([0.1]) >>> paddle.heaviside(x, y) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [0. , 0.10000000, 1. ]) >>> x = paddle.to_tensor([[-0.5, 0, 0.5], [-0.5, 0.5, 0]]) >>> y = paddle.to_tensor([0.1, 0.2, 0.3]) >>> paddle.heaviside(x, y) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[0. , 0.20000000, 1. ], [0. , 1. , 0.30000001]]) """ if in_dynamic_or_pir_mode(): return _C_ops.heaviside(x, y) else: op_type = 'elementwise_heaviside' return _elementwise_op(LayerHelper(op_type, **locals())) def frac(x: Tensor, name: str | None = None) -> Tensor: """ This API is used to return the fractional portion of each element in input. Args: x (Tensor): The input tensor, which data type should be int32, int64, float32, float64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: The output Tensor of frac. Examples: .. code-block:: python >>> import paddle >>> input = paddle.to_tensor([[12.22000003, -1.02999997], ... [-0.54999995, 0.66000003]]) >>> output = paddle.frac(input) >>> output Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[ 0.22000003, -0.02999997], [-0.54999995, 0.66000003]]) """ if x.dtype not in [ paddle.int32, paddle.int64, paddle.float32, paddle.float64, paddle.float16, DataType.INT32, DataType.INT64, DataType.FLOAT32, DataType.FLOAT64, DataType.FLOAT16, ]: raise TypeError( f"The data type of input must be one of ['int32', 'int64', 'float32', 'float64', 'float16'], but got {x.dtype}" ) if in_dynamic_or_pir_mode(): y = _C_ops.trunc(x) return _C_ops.subtract(x, y) else: inputs = {"X": x} attrs = {} helper = LayerHelper("trunc", **locals()) check_variable_and_dtype( x, "X", ['int32', 'int64', 'float32', 'float64', 'float16'], 'trunc' ) y = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type="trunc", inputs=inputs, attrs=attrs, outputs={"Out": y} ) return _elementwise_op(LayerHelper('elementwise_sub', **locals())) @inplace_apis_in_dygraph_only def frac_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``frac`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_frac`. """ if x.dtype not in [ paddle.int32, paddle.int64, paddle.float32, paddle.float64, paddle.float16, ]: raise TypeError( f"The data type of input must be one of ['int32', 'int64', 'float32', 'float64', 'float16'], but got {x.dtype}" ) if in_dynamic_mode(): y = _C_ops.trunc(x) return _C_ops.subtract_(x, y) def sgn(x: Tensor, name: str | None = None) -> Tensor: """ For complex tensor, this API returns a new tensor whose elements have the same angles as the corresponding elements of input and absolute values of one. For other float dtype tensor, this API returns sign of every element in `x`: 1 for positive, -1 for negative and 0 for zero, same as paddle.sign. Args: x (Tensor): The input tensor, which data type should be float16, float32, float64, complex64, complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor: A sign Tensor for real input, or normalized Tensor for complex input, shape and data type are same as input. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([[3 + 4j, 7 - 24j, 0, 1 + 2j], [6 + 8j, 3, 0, -2]]) >>> paddle.sgn(x) Tensor(shape=[2, 4], dtype=complex64, place=Place(cpu), stop_gradient=True, [[ (0.6000000238418579+0.800000011920929j), (0.2800000011920929-0.9599999785423279j), 0j , (0.4472135901451111+0.8944271802902222j)], [ (0.6000000238418579+0.800000011920929j), (1+0j) , 0j , (-1+0j) ]]) """ if x.dtype not in [ paddle.float16, paddle.float32, paddle.float64, paddle.complex64, paddle.complex128, DataType.FLOAT16, DataType.FLOAT32, DataType.FLOAT64, DataType.COMPLEX64, DataType.COMPLEX128, ]: raise TypeError( f"The data type of input must be one of ['float16', 'float32', 'float64', 'complex64', 'complex128'], but got {x.dtype}" ) if paddle.is_complex(x): expand_x = paddle.as_real(x) x_abs = paddle.abs(x) x_abs = paddle.unsqueeze(x_abs, axis=-1) output = expand_x / x_abs zeros = paddle.zeros_like(output) output = paddle.where(paddle.isnan(output), zeros, output) return paddle.as_complex(output) else: return paddle.sign(x) def take( x: Tensor, index: Tensor, mode: Literal["raise", "wrap", "clip"] = 'raise', name: str | None = None, ) -> Tensor: """ Returns a new tensor with the elements of input tensor x at the given index. The input tensor is treated as if it were viewed as a 1-D tensor. The result takes the same shape as the index. Args: x (Tensor): An N-D Tensor, its data type should be int32, int64, float32, float64. index (Tensor): An N-D Tensor, its data type should be int32, int64. mode (str, optional): Specifies how out-of-bounds index will behave. the candidates are ``'raise'``, ``'wrap'`` and ``'clip'``. - ``'raise'``: raise an error (default); - ``'wrap'``: wrap around; - ``'clip'``: clip to the range. ``'clip'`` mode means that all indices that are too large are replaced by the index that addresses the last element. Note that this disables indexing with negative numbers. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, Tensor with the same shape as index, the data type is the same with input. Examples: .. code-block:: python >>> import paddle >>> x_int = paddle.arange(0, 12).reshape([3, 4]) >>> x_float = x_int.astype(paddle.float64) >>> idx_pos = paddle.arange(4, 10).reshape([2, 3]) # positive index >>> idx_neg = paddle.arange(-2, 4).reshape([2, 3]) # negative index >>> idx_err = paddle.arange(-2, 13).reshape([3, 5]) # index out of range >>> paddle.take(x_int, idx_pos) Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[4, 5, 6], [7, 8, 9]]) >>> paddle.take(x_int, idx_neg) Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[10, 11, 0 ], [1 , 2 , 3 ]]) >>> paddle.take(x_float, idx_pos) Tensor(shape=[2, 3], dtype=float64, place=Place(cpu), stop_gradient=True, [[4., 5., 6.], [7., 8., 9.]]) >>> x_int.take(idx_pos) Tensor(shape=[2, 3], dtype=int64, place=Place(cpu), stop_gradient=True, [[4, 5, 6], [7, 8, 9]]) >>> paddle.take(x_int, idx_err, mode='wrap') Tensor(shape=[3, 5], dtype=int64, place=Place(cpu), stop_gradient=True, [[10, 11, 0 , 1 , 2 ], [3 , 4 , 5 , 6 , 7 ], [8 , 9 , 10, 11, 0 ]]) >>> paddle.take(x_int, idx_err, mode='clip') Tensor(shape=[3, 5], dtype=int64, place=Place(cpu), stop_gradient=True, [[0 , 0 , 0 , 1 , 2 ], [3 , 4 , 5 , 6 , 7 ], [8 , 9 , 10, 11, 11]]) """ if mode not in ['raise', 'wrap', 'clip']: raise ValueError( f"'mode' in 'take' should be 'raise', 'wrap', 'clip', but received {mode}." ) if in_dynamic_or_pir_mode(): if not isinstance(index, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError( f"The type of 'index' must be Tensor, but got {type(index)}" ) if index.dtype not in [ paddle.int32, paddle.int64, DataType.INT32, DataType.INT64, ]: raise TypeError( f"The data type of 'index' must be one of ['int32', 'int64'], but got {index.dtype}" ) else: check_variable_and_dtype(index, 'index', ['int32', 'int64'], 'take') input_1d = x.flatten() index_1d = index.flatten() max_index = input_1d.shape[-1] if mode == 'raise': # This processing enables 'take' to handle negative indexes within the correct range. index_1d = paddle.where(index_1d < 0, index_1d + max_index, index_1d) elif mode == 'wrap': # The out of range indices are constrained by taking the remainder. index_1d = paddle.where(index_1d < 0, index_1d % max_index, index_1d) index_1d = paddle.where( index_1d >= max_index, index_1d % max_index, index_1d ) elif mode == 'clip': # 'clip' mode disables indexing with negative numbers. if max_index > 0: # If max_index is 0, input_1d is 0-size. index_1d = clip(index_1d, 0, max_index - 1) out = input_1d.index_select(index_1d).reshape(index.shape) return out def frexp(x: Tensor, name: str | None = None) -> tuple[Tensor, Tensor]: """ The function used to decompose a floating point number into mantissa and exponent. Args: x (Tensor): The input tensor, it's data type should be float32, float64. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: - mantissa (Tensor), A mantissa Tensor. The shape and data type of mantissa tensor and exponential tensor are the same as those of input. - exponent (Tensor), A exponent Tensor. The shape and data type of mantissa tensor and exponential tensor are the same as those of input. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([[1, 2, 3, 4]], dtype="float32") >>> mantissa, exponent = paddle.tensor.math.frexp(x) >>> mantissa Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.50000000, 0.50000000, 0.75000000, 0.50000000]]) >>> exponent Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True, [[1., 2., 2., 3.]]) """ if x.dtype not in [ paddle.float32, paddle.float64, DataType.FLOAT32, DataType.FLOAT64, ]: raise TypeError( f"The data type of input must be one of ['float32', 'float64'], but got {x.dtype}" ) input_x = paddle.abs(x) exponent = paddle.floor(paddle.log2(input_x)) exponent = paddle.where( paddle.isinf(exponent), paddle.full_like(exponent, 0), exponent ) # 0填充 mantissa = paddle.divide(input_x, 2**exponent) # 计算exponent exponent = paddle.where( (mantissa >= 1), paddle.add(exponent, paddle.ones_like(exponent)), exponent, ) mantissa = paddle.where( (mantissa >= 1), paddle.divide(mantissa, 2 ** paddle.ones_like(exponent)), mantissa, ) mantissa = paddle.where((x < 0), mantissa * -1, mantissa) return mantissa, exponent def _trapezoid( y: Tensor, x: Tensor | None = None, dx: float | None = None, axis: int = -1, mode: Literal["sum", "cumsum"] = 'sum', ) -> Tensor: """ Integrate along the given axis using the composite trapezoidal rule. Args: y (Tensor): Input tensor to integrate. It's data type should be float16, float32, float64. x (Tensor|None, optional): The sample points corresponding to the :attr:`y` values, the same type as :attr:`y`. It is known that the size of :attr:`y` is `[d_1, d_2, ... , d_n]` and :math:`axis=k`, then the size of :attr:`x` can only be `[d_k]` or `[d_1, d_2, ... , d_n ]`. If :attr:`x` is None, the sample points are assumed to be evenly spaced :attr:`dx` apart. The default is None. dx (float|None, optional): The spacing between sample points when :attr:`x` is None. If neither :attr:`x` nor :attr:`dx` is provided then the default is :math:`dx = 1`. axis (int, optional): The axis along which to integrate. The default is -1. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. sum_mode (str): use a different summation. The default is `sum`. Returns: Tensor, Definite integral of :attr:`y` is N-D tensor as approximated along a single axis by the trapezoidal rule. """ if mode == 'sum': sum_mode = paddle.sum elif mode == 'cumsum': sum_mode = paddle.cumsum if not (x is None or dx is None): raise ValueError("Not permitted to specify both x and dx input args.") if y.dtype not in [ paddle.float16, paddle.float32, paddle.float64, paddle.base.core.DataType.FLOAT16, paddle.base.core.DataType.FLOAT32, paddle.base.core.DataType.FLOAT64, ]: raise TypeError( f"The data type of input must be Tensor, and dtype should be one of ['paddle.float16', 'paddle.float32', 'paddle.float64', 'paddle.base.core.DataType.FLOAT16', 'paddle.base.core.DataType.FLOAT32', 'paddle.base.core.DataType.FLOAT64'], but got {y.dtype}" ) y_shape = y.shape length = y_shape[axis] if axis < 0: axis += y.dim() if x is None: if dx is None: dx = 1.0 dx = paddle.to_tensor(dx) if dx.dim() > 1: raise ValueError(f'Expected dx to be a scalar, got dx={dx}') else: if x.dtype not in [ paddle.float16, paddle.float32, paddle.float64, paddle.base.core.DataType.FLOAT16, paddle.base.core.DataType.FLOAT32, paddle.base.core.DataType.FLOAT64, ]: raise TypeError( f"The data type of input must be Tensor, and dtype should be one of ['paddle.float16', 'paddle.float32', 'paddle.float64', 'paddle.base.core.DataType.FLOAT16', 'paddle.base.core.DataType.FLOAT32', 'paddle.base.core.DataType.FLOAT64'], but got {x.dtype}" ) # Reshape to correct shape if x.dim() == 1: dx = paddle.diff(x) shape = [1] * y.dim() shape[axis] = dx.shape[0] dx = dx.reshape(shape) else: dx = paddle.diff(x, axis=axis) return 0.5 * sum_mode( ( paddle.gather(y, paddle.arange(1, length), axis=axis) + paddle.gather(y, paddle.arange(0, length - 1), axis=axis) ) * dx, axis=axis, ) def trapezoid( y: Tensor, x: Tensor | None = None, dx: float | None = None, axis: int = -1, name: str | None = None, ) -> Tensor: """ Integrate along the given axis using the composite trapezoidal rule. Use the sum method. Args: y (Tensor): Input tensor to integrate. It's data type should be float16, float32, float64. x (Tensor|None, optional): The sample points corresponding to the :attr:`y` values, the same type as :attr:`y`. It is known that the size of :attr:`y` is `[d_1, d_2, ... , d_n]` and :math:`axis=k`, then the size of :attr:`x` can only be `[d_k]` or `[d_1, d_2, ... , d_n ]`. If :attr:`x` is None, the sample points are assumed to be evenly spaced :attr:`dx` apart. The default is None. dx (float|None, optional): The spacing between sample points when :attr:`x` is None. If neither :attr:`x` nor :attr:`dx` is provided then the default is :math:`dx = 1`. axis (int, optional): The axis along which to integrate. The default is -1. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, Definite integral of :attr:`y` is N-D tensor as approximated along a single axis by the trapezoidal rule. If :attr:`y` is a 1D tensor, then the result is a float. If N is greater than 1, then the result is an (N-1)-D tensor. Examples: .. code-block:: python >>> import paddle >>> y = paddle.to_tensor([4, 5, 6], dtype='float32') >>> paddle.trapezoid(y) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 10.) >>> paddle.trapezoid(y, dx=2.) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 20.) >>> y = paddle.to_tensor([4, 5, 6], dtype='float32') >>> x = paddle.to_tensor([1, 2, 3], dtype='float32') >>> paddle.trapezoid(y, x) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 10.) >>> y = paddle.to_tensor([1, 2, 3], dtype='float64') >>> x = paddle.to_tensor([8, 6, 4], dtype='float64') >>> paddle.trapezoid(y, x) Tensor(shape=[], dtype=float64, place=Place(cpu), stop_gradient=True, -8.) >>> y = paddle.arange(6).reshape((2, 3)).astype('float32') >>> paddle.trapezoid(y, axis=0) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [1.50000000, 2.50000000, 3.50000000]) >>> paddle.trapezoid(y, axis=1) Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [2., 8.]) """ return _trapezoid(y, x, dx, axis, mode='sum') def cumulative_trapezoid( y: Tensor, x: Tensor | None = None, dx: float | None = None, axis: int = -1, name: str | None = None, ) -> Tensor: """ Integrate along the given axis using the composite trapezoidal rule. Use the cumsum method Args: y (Tensor): Input tensor to integrate. It's data type should be float16, float32, float64. x (Tensor|None, optional): The sample points corresponding to the :attr:`y` values, the same type as :attr:`y`. It is known that the size of :attr:`y` is `[d_1, d_2, ... , d_n]` and :math:`axis=k`, then the size of :attr:`x` can only be `[d_k]` or `[d_1, d_2, ... , d_n ]`. If :attr:`x` is None, the sample points are assumed to be evenly spaced :attr:`dx` apart. The default is None. dx (float|None, optional): The spacing between sample points when :attr:`x` is None. If neither :attr:`x` nor :attr:`dx` is provided then the default is :math:`dx = 1`. axis (int, optional): The axis along which to integrate. The default is -1. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, Definite integral of :attr:`y` is N-D tensor as approximated along a single axis by the trapezoidal rule. The result is an N-D tensor. Examples: .. code-block:: python >>> import paddle >>> y = paddle.to_tensor([4, 5, 6], dtype='float32') >>> paddle.cumulative_trapezoid(y) Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [4.50000000, 10. ]) >>> paddle.cumulative_trapezoid(y, dx=2.) >>> # Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, >>> # [9. , 20.]) >>> y = paddle.to_tensor([4, 5, 6], dtype='float32') >>> x = paddle.to_tensor([1, 2, 3], dtype='float32') >>> paddle.cumulative_trapezoid(y, x) Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [4.50000000, 10. ]) >>> y = paddle.to_tensor([1, 2, 3], dtype='float64') >>> x = paddle.to_tensor([8, 6, 4], dtype='float64') >>> paddle.cumulative_trapezoid(y, x) Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=True, [-3., -8.]) >>> y = paddle.arange(6).reshape((2, 3)).astype('float32') >>> paddle.cumulative_trapezoid(y, axis=0) Tensor(shape=[1, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[1.50000000, 2.50000000, 3.50000000]]) >>> paddle.cumulative_trapezoid(y, axis=1) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.50000000, 2. ], [3.50000000, 8. ]]) """ return _trapezoid(y, x, dx, axis, mode='cumsum') def vander( x: Tensor, n: int | None = None, increasing: bool = False, name: str | None = None, ) -> Tensor: """ Generate a Vandermonde matrix. The columns of the output matrix are powers of the input vector. Order of the powers is determined by the increasing Boolean parameter. Specifically, when the increment is "false", the ith output column is a step-up in the order of the elements of the input vector to the N - i - 1 power. Such a matrix with a geometric progression in each row is named after Alexandre-Theophile Vandermonde. Args: x (Tensor): The input tensor, it must be 1-D Tensor, and it's data type should be ['complex64', 'complex128', 'float32', 'float64', 'int32', 'int64']. n (int|None): Number of columns in the output. If n is not specified, a square array is returned (n = len(x)). increasing(bool): Order of the powers of the columns. If True, the powers increase from left to right, if False (the default) they are reversed. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: Tensor, A vandermonde matrix with shape (len(x), N). If increasing is False, the first column is :math:`x^{(N-1)}`, the second :math:`x^{(N-2)}` and so forth. If increasing is True, the columns are :math:`x^0`, :math:`x^1`, ..., :math:`x^{(N-1)}`. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([1., 2., 3.], dtype="float32") >>> out = paddle.vander(x) >>> out Tensor(shape=[3, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[1., 1., 1.], [4., 2., 1.], [9., 3., 1.]]) >>> out1 = paddle.vander(x,2) >>> out1 Tensor(shape=[3, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[1., 1.], [2., 1.], [3., 1.]]) >>> out2 = paddle.vander(x, increasing = True) >>> out2 Tensor(shape=[3, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[1., 1., 1.], [1., 2., 4.], [1., 3., 9.]]) >>> real = paddle.to_tensor([2., 4.]) >>> imag = paddle.to_tensor([1., 3.]) >>> complex = paddle.complex(real, imag) >>> out3 = paddle.vander(complex) >>> out3 Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True, [[(2+1j), (1+0j)], [(4+3j), (1+0j)]]) """ check_variable_and_dtype( x, 'x', ['complex64', 'complex128', 'float32', 'float64', 'int32', 'int64'], 'vander', ) if x.dim() != 1: raise ValueError( "The input of x is expected to be a 1-D Tensor." f"But now the dims of Input(X) is {x.dim()}." ) if n is None: n = x.shape[0] if n < 0: raise ValueError("N must be non-negative.") res = paddle.empty([x.shape[0], n], dtype=x.dtype) if paddle.in_dynamic_mode(): if n > 0: res[:, 0] = paddle.to_tensor([1], dtype=x.dtype) if n > 1: res[:, 1:] = x[:, None] res[:, 1:] = paddle.cumprod(res[:, 1:], dim=-1) else: if n > 0: res = paddle.static.setitem( res, (slice(None), 0), paddle.to_tensor([1], dtype=x.dtype) ) if n > 1: res = paddle.static.setitem( res, (slice(None), slice(1, None)), x[:, None] ) res = paddle.static.setitem( res, (slice(None), slice(1, None)), paddle.cumprod(res[:, 1:], dim=-1), ) res = res[:, ::-1] if not increasing else res return res def nextafter(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Return the next floating-point value after input towards other, elementwise. The shapes of input and other must be broadcastable. Args: x (Tensor): An N-D Tensor, the data type is float32, float64. y (Tensor): An N-D Tensor, the data type is float32, float64. name(str, optional):Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor, the shape and data type is the same with input. Examples: .. code-block:: python >>> import paddle >>> out = paddle.nextafter(paddle.to_tensor([1.0,2.0]),paddle.to_tensor([2.0,1.0])) >>> out Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [1.00000012, 1.99999988]) """ if in_dynamic_or_pir_mode(): return _C_ops.nextafter(x, y) else: check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'nextafter') check_variable_and_dtype(y, 'y', ['float32', 'float64'], 'nextafter') op_type = "nextafter" helper = LayerHelper(op_type, **locals()) inputs = {"x": x, "y": y} out = helper.create_variable_for_type_inference(dtype=paddle.float32) outputs = {"out": out} helper.append_op(type=op_type, inputs=inputs, outputs=outputs) return out def i0(x: Tensor, name: str | None = None) -> Tensor: r""" The function used to calculate modified bessel function of order 0. Equation: .. math:: I_0(x) = \sum^{\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2} Args: x (Tensor): The input tensor, it's data type should be float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: - out (Tensor), A Tensor. the value of the modified bessel function of order 0 at x (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32") >>> paddle.i0(x) Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [0.99999994 , 1.26606596 , 2.27958512 , 4.88079262 , 11.30192089]) """ if in_dynamic_or_pir_mode(): return _C_ops.i0(x) else: check_variable_and_dtype( x, "x", ["float32", "float64", "uint8", "int8", "int16", "int32", "int64"], "i0", ) helper = LayerHelper("i0", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op(type='i0', inputs={'x': x}, outputs={'out': out}) return out @inplace_apis_in_dygraph_only def i0_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``i0`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_i0`. """ if in_dynamic_mode(): return _C_ops.i0_(x) def i0e(x: Tensor, name: str | None = None) -> Tensor: r""" The function used to calculate exponentially scaled modified Bessel function of order 0. Equation: .. math:: I_0(x) = \sum^{\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2} \\ I_{0e}(x) = e^{-|x|}I_0(x) Args: x (Tensor): The input tensor, it's data type should be float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: - out (Tensor), A Tensor. the value of the exponentially scaled modified Bessel function of order 0 at x (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32") >>> print(paddle.i0e(x)) Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [0.99999994, 0.46575963, 0.30850831, 0.24300036, 0.20700191]) """ if in_dynamic_or_pir_mode(): return _C_ops.i0e(x) else: check_variable_and_dtype( x, "x", ["float32", "float64", "uint8", "int8", "int16", "int32", "int64"], "i0e", ) helper = LayerHelper("i0e", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op(type='i0e', inputs={'x': x}, outputs={'out': out}) return out def i1(x: Tensor, name: str | None = None) -> Tensor: """ The function is used to calculate modified bessel function of order 1. Args: x (Tensor): The input tensor, it's data type should be float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: - out (Tensor), A Tensor. the value of the modified bessel function of order 1 at x (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32") >>> print(paddle.i1(x)) Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [0. , 0.56515908, 1.59063685, 3.95337057, 9.75946712]) """ if in_dynamic_or_pir_mode(): return _C_ops.i1(x) else: check_variable_and_dtype( x, "x", ["float32", "float64", "uint8", "int8", "int16", "int32", "int64"], "i1", ) helper = LayerHelper("i1", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='i1', inputs={'x': x}, outputs={'out': out}, attrs={} ) return out def i1e(x: Tensor, name: str | None = None) -> Tensor: """ The function is used to calculate exponentially scaled modified Bessel function of order 1. Args: x (Tensor): The input tensor, it's data type should be float32, float64, uint8, int8, int16, int32, int64. name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. Returns: - out (Tensor), A Tensor. the value of the exponentially scaled modified Bessel function of order 1 at x (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32") >>> print(paddle.i1e(x)) Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [0. , 0.20791042, 0.21526928, 0.19682673, 0.17875087]) """ if in_dynamic_or_pir_mode(): return _C_ops.i1e(x) else: check_variable_and_dtype( x, "x", ["float32", "float64", "uint8", "int8", "int16", "int32", "int64"], "i1e", ) helper = LayerHelper("i1e", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='i1e', inputs={'x': x}, outputs={'out': out}, attrs={} ) return out def polygamma(x: Tensor, n: int, name: str | None = None) -> Tensor: r""" Calculates the polygamma of the given input tensor, element-wise. The equation is: .. math:: \Phi^n(x) = \frac{d^n}{dx^n} [\ln(\Gamma(x))] Args: x (Tensor): Input Tensor. Must be one of the following types: float32, float64, uint8, int8, int16, int32, int64. n (int): Order of the derivative. Must be integral. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: - out (Tensor), A Tensor. the polygamma of the input Tensor, the shape and data type is the same with input (integer types are autocasted into float32). Examples: .. code-block:: python >>> import paddle >>> data = paddle.to_tensor([2, 3, 25.5], dtype='float32') >>> res = paddle.polygamma(data, 1) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [0.64493412, 0.39493406, 0.03999467]) """ if not isinstance(n, int): raise TypeError( f"The input of n must be int type, but received: {type(n)} " ) if n < 0: raise ValueError( f"The input of n must be greater than or equal to 0. But received n = {n}" ) if n == 0: return digamma(x) else: if in_dynamic_or_pir_mode(): return _C_ops.polygamma(x, n) else: check_variable_and_dtype( x, "x", [ "float32", "float64", "uint8", "int8", "int16", "int32", "int64", ], "polygamma", ) helper = LayerHelper("polygamma", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='polygamma', inputs={'x': x}, outputs={'out': out}, attrs={'n': n}, ) return out @inplace_apis_in_dygraph_only def polygamma_(x: Tensor, n: int, name: str | None = None) -> Tensor: r""" Inplace version of ``polygamma`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_polygamma`. """ if not isinstance(n, int): raise TypeError( f"The input of n must be int type, but received: {type(n)} " ) if n < 0: raise ValueError( f"The input of n must be greater than or equal to 0. But received n = {n}" ) if n == 0: return digamma_(x) else: if in_dynamic_mode(): return _C_ops.polygamma_(x, n) def ldexp(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Compute the result of multiplying x by 2 to the power of y. The equation is: .. math:: out = x * 2^{y} Args: x (Tensor): The input Tensor, the data type is float32, float64, int32 or int64. y (Tensor): A Tensor of exponents, typically integers. name (str|None, optional): Name for the operation (optional, default is None).For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor. 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. And the data type is float32 or float64. Examples: .. code-block:: python >>> import paddle >>> # example1 >>> x = paddle.to_tensor([1, 2, 3], dtype='float32') >>> y = paddle.to_tensor([2, 3, 4], dtype='int32') >>> res = paddle.ldexp(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [4. , 16., 48.]) >>> # example2 >>> x = paddle.to_tensor([1, 2, 3], dtype='float32') >>> y = paddle.to_tensor([2], dtype='int32') >>> res = paddle.ldexp(x, y) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [4. , 8. , 12.]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") if not isinstance(y, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"y must be tensor type, but got {type(y)}") if x.dtype == paddle.float64 or y.dtype == paddle.float64: out_dtype = paddle.float64 elif x.dtype == DataType.FLOAT64 or y.dtype == DataType.FLOAT64: out_dtype = DataType.FLOAT64 else: out_dtype = paddle.get_default_dtype() x = x.astype(dtype=out_dtype) y = y.astype(dtype=out_dtype) two = paddle.to_tensor(2, dtype=out_dtype) return paddle.multiply(x, paddle.pow(two, y)) def ldexp_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``polygamma`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_polygamma`. """ if not isinstance(x, (paddle.Tensor, Variable)): raise TypeError(f"x must be tensor type, but got {type(x)}") if not isinstance(y, (paddle.Tensor, Variable)): raise TypeError(f"y must be tensor type, but got {type(y)}") if x.dtype == paddle.float64 or y.dtype == paddle.float64: out_dtype = "float64" else: out_dtype = paddle.get_default_dtype() x = paddle.cast_(x, dtype=out_dtype) y = paddle.cast(y, dtype=out_dtype) two = paddle.to_tensor(2, dtype=out_dtype) return paddle.multiply_(x, paddle.pow(two, y)) def _bitwise_op(op_name, x, y, is_arithmetic, out=None, name=None): check_variable_and_dtype( x, "x", ["uint8", "int8", "int16", "int32", "int64"], op_name, ) if y is not None: check_variable_and_dtype( y, "y", ["uint8", "int8", "int16", "int32", "int64"], op_name, ) helper = LayerHelper(op_name, **locals()) assert x.dtype == y.dtype out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type=op_name, inputs={"x": x, "y": y}, outputs={"out": out}, attrs={'is_arithmetic': is_arithmetic}, ) return out def bitwise_left_shift( x: Tensor, y: Tensor, is_arithmetic: bool = True, out: Tensor | None = None, name: str | None = None, ) -> Tensor: r""" Apply ``bitwise_left_shift`` on Tensor ``X`` and ``Y`` . .. math:: Out = X \ll Y .. note:: ``paddle.bitwise_left_shift`` supports broadcasting. If you want know more about broadcasting, please refer to please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): Input Tensor of ``bitwise_left_shift`` . It is a N-D Tensor of uint8, int8, int16, int32, int64. y (Tensor): Input Tensor of ``bitwise_left_shift`` . It is a N-D Tensor of uint8, int8, int16, int32, int64. is_arithmetic (bool, optional): A boolean indicating whether to choose arithmetic shift, if False, means logic shift. Default True. out (Tensor|None, optional): Result of ``bitwise_left_shift`` . It is a N-D Tensor with the same data type of input Tensor. Default: None. name (str|None, 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 ``bitwise_left_shift`` . It is a N-D Tensor with the same data type of input Tensor. Examples: .. code-block:: python :name: bitwise_left_shift_example1 >>> import paddle >>> x = paddle.to_tensor([[1,2,4,8],[16,17,32,65]]) >>> y = paddle.to_tensor([[1,2,3,4,], [2,3,2,1]]) >>> paddle.bitwise_left_shift(x, y, is_arithmetic=True) Tensor(shape=[2, 4], dtype=int64, place=Place(gpu:0), stop_gradient=True, [[2 , 8 , 32 , 128], [64 , 136, 128, 130]]) .. code-block:: python :name: bitwise_left_shift_example2 >>> import paddle >>> x = paddle.to_tensor([[1,2,4,8],[16,17,32,65]]) >>> y = paddle.to_tensor([[1,2,3,4,], [2,3,2,1]]) >>> paddle.bitwise_left_shift(x, y, is_arithmetic=False) Tensor(shape=[2, 4], dtype=int64, place=Place(gpu:0), stop_gradient=True, [[2 , 8 , 32 , 128], [64 , 136, 128, 130]]) """ if in_dynamic_or_pir_mode() and out is None: return _C_ops.bitwise_left_shift(x, y, is_arithmetic) return _bitwise_op( op_name="bitwise_left_shift", x=x, y=y, is_arithmetic=is_arithmetic, name=name, out=out, ) @inplace_apis_in_dygraph_only def bitwise_left_shift_( x: Tensor, y: Tensor, is_arithmetic: bool = True, out: Tensor | None = None, name: str | None = None, ) -> Tensor: r""" Inplace version of ``bitwise_left_shift`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_bitwise_left_shift`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) if in_dynamic_or_pir_mode(): return _C_ops.bitwise_left_shift_(x, y, is_arithmetic) def bitwise_right_shift( x: Tensor, y: Tensor, is_arithmetic: bool = True, out: Tensor | None = None, name: str | None = None, ) -> Tensor: r""" Apply ``bitwise_right_shift`` on Tensor ``X`` and ``Y`` . .. math:: Out = X \gg Y .. note:: ``paddle.bitwise_right_shift`` supports broadcasting. If you want know more about broadcasting, please refer to please refer to `Introduction to Tensor`_ . .. _Introduction to Tensor: ../../guides/beginner/tensor_en.html#chapter5-broadcasting-of-tensor Args: x (Tensor): Input Tensor of ``bitwise_right_shift`` . It is a N-D Tensor of uint8, int8, int16, int32, int64. y (Tensor): Input Tensor of ``bitwise_right_shift`` . It is a N-D Tensor of uint8, int8, int16, int32, int64. is_arithmetic (bool, optional): A boolean indicating whether to choose arithmetic shift, if False, means logic shift. Default True. out (Tensor|None, optional): Result of ``bitwise_right_shift`` . It is a N-D Tensor with the same data type of input Tensor. Default: None. name (str|None, 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 ``bitwise_right_shift`` . It is a N-D Tensor with the same data type of input Tensor. Examples: .. code-block:: python :name: bitwise_right_shift_example1 >>> import paddle >>> x = paddle.to_tensor([[10,20,40,80],[16,17,32,65]]) >>> y = paddle.to_tensor([[1,2,3,4,], [2,3,2,1]]) >>> paddle.bitwise_right_shift(x, y, is_arithmetic=True) Tensor(shape=[2, 4], dtype=int64, place=Place(gpu:0), stop_gradient=True, [[5 , 5 , 5 , 5 ], [4 , 2 , 8 , 32]]) .. code-block:: python :name: bitwise_right_shift_example2 >>> import paddle >>> x = paddle.to_tensor([[-10,-20,-40,-80],[-16,-17,-32,-65]], dtype=paddle.int8) >>> y = paddle.to_tensor([[1,2,3,4,], [2,3,2,1]], dtype=paddle.int8) >>> paddle.bitwise_right_shift(x, y, is_arithmetic=False) # logic shift Tensor(shape=[2, 4], dtype=int8, place=Place(gpu:0), stop_gradient=True, [[123, 59 , 27 , 11 ], [60 , 29 , 56 , 95 ]]) """ if in_dynamic_or_pir_mode() and out is None: return _C_ops.bitwise_right_shift(x, y, is_arithmetic) return _bitwise_op( op_name="bitwise_right_shift", x=x, y=y, is_arithmetic=is_arithmetic, name=name, out=out, ) @inplace_apis_in_dygraph_only def bitwise_right_shift_( x: Tensor, y: Tensor, is_arithmetic: bool = True, out: Tensor | None = None, name: str | None = None, ) -> Tensor: r""" Inplace version of ``bitwise_right_shift`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_bitwise_left_shift`. """ out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) if in_dynamic_or_pir_mode(): return _C_ops.bitwise_right_shift_(x, y, is_arithmetic) def __lshift__( x: Tensor, y: Tensor | int, is_arithmetic: bool = True, ) -> Tensor: if isinstance(y, int): y = paddle.to_tensor(y, dtype=x.dtype) elif isinstance(y, float): raise TypeError( "unsupported operand type(s) for <<: 'Tensor' and 'float'" ) return bitwise_left_shift(x, y, is_arithmetic, None, None) def __rshift__( x: Tensor, y: Tensor | int, is_arithmetic: bool = True, ) -> Tensor: if isinstance(y, int): y = paddle.to_tensor(y, dtype=x.dtype) elif isinstance(y, float): raise TypeError( "unsupported operand type(s) for <<: 'Tensor' and 'float'" ) return bitwise_right_shift(x, y, is_arithmetic, None, None) def __rlshift__( x: Tensor, y: Tensor | int, is_arithmetic: bool = True, ): if isinstance(y, int): y = paddle.to_tensor(y, dtype=x.dtype) elif isinstance(y, float): raise TypeError( "unsupported operand type(s) for <<: 'float' and 'Tensor'" ) return bitwise_left_shift(y, x, is_arithmetic, None, None) def __rrshift__( x: Tensor, y: Tensor | int, is_arithmetic: bool = True, ): if isinstance(y, int): y = paddle.to_tensor(y, dtype=x.dtype) elif isinstance(y, float): raise TypeError( "unsupported operand type(s) for <<: 'float' and 'Tensor'" ) return bitwise_right_shift(y, x, is_arithmetic, None, None) def copysign(x: Tensor, y: Tensor | float, name: str | None = None) -> Tensor: r""" Create a new floating-point tensor with the magnitude of input ``x`` and the sign of ``y``, elementwise. Equation: .. math:: copysign(x_{i},y_{i})=\left\{\begin{matrix} & -|x_{i}| & if \space y_{i} <= -0.0\\ & |x_{i}| & if \space y_{i} >= 0.0 \end{matrix}\right. Args: x (Tensor): The input Tensor, magnitudes, the data type is bool, uint8, int8, int16, int32, int64, bfloat16, float16, float32, float64. y (Tensor|float): contains value(s) whose signbit(s) are applied to the magnitudes in input. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), the output tensor. The data type is the same as the input tensor. Examples: .. code-block:: python :name: example1 >>> import paddle >>> x = paddle.to_tensor([1, 2, 3], dtype='float64') >>> y = paddle.to_tensor([-1, 1, -1], dtype='float64') >>> out = paddle.copysign(x, y) >>> print(out) Tensor(shape=[3], dtype=float64, place=Place(gpu:0), stop_gradient=True, [-1., 2., -3.]) .. code-block:: python :name: example2 >>> import paddle >>> x = paddle.to_tensor([1, 2, 3], dtype='float64') >>> y = paddle.to_tensor([-2], dtype='float64') >>> res = paddle.copysign(x, y) >>> print(res) Tensor(shape=[3], dtype=float64, place=Place(gpu:0), stop_gradient=True, [-1., -2., -3.]) .. code-block:: python :name: example_zero1 >>> import paddle >>> x = paddle.to_tensor([1, 2, 3], dtype='float64') >>> y = paddle.to_tensor([0.0], dtype='float64') >>> out = paddle.copysign(x, y) >>> print(out) Tensor(shape=[3], dtype=float64, place=Place(gpu:0), stop_gradient=True, [1., 2., 3.]) .. code-block:: python :name: example_zero2 >>> import paddle >>> x = paddle.to_tensor([1, 2, 3], dtype='float64') >>> y = paddle.to_tensor([-0.0], dtype='float64') >>> out = paddle.copysign(x, y) >>> print(out) Tensor(shape=[3], dtype=float64, place=Place(gpu:0), stop_gradient=True, [-1., -2., -3.]) """ if isinstance(y, (float, int)): y = paddle.to_tensor(y, dtype=x.dtype) out_shape = broadcast_shape(x.shape, y.shape) if out_shape != list(x.shape): warnings.warn( f"The shape of broadcast output {out_shape} is different from the input tensor x with shape: {x.shape}, please make sure you are using copysign api correctly." ) if in_dynamic_or_pir_mode(): return _C_ops.copysign(x, y) else: helper = LayerHelper("copysign", **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='copysign', inputs={'x': x, 'y': y}, outputs={'out': out} ) return out @inplace_apis_in_dygraph_only def copysign_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``copysign`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_copysign`. """ if isinstance(y, (float, int)): y = paddle.to_tensor(y, dtype=x.dtype) out_shape = broadcast_shape(x.shape, y.shape) if out_shape != x.shape: raise ValueError( f"The shape of broadcast output {out_shape} is different from that of inplace tensor {x.shape} in the Inplace operation." ) return _C_ops.copysign_(x, y) def hypot(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: """ Calculate the length of the hypotenuse of a right-angle triangle. The equation is: .. math:: out = {\\sqrt{x^2 + y^2}} Args: x (Tensor): The input Tensor, the data type is float32, float64, int32 or int64. y (Tensor): The input Tensor, the data type is float32, float64, int32 or int64. name (str|None, optional): Name for the operation (optional, default is None).For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): An N-D Tensor. 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. And the data type is float32 or float64. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([3], dtype='float32') >>> y = paddle.to_tensor([4], dtype='float32') >>> res = paddle.hypot(x, y) >>> print(res) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [5.]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") if not isinstance(y, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"y must be tensor type, but got {type(y)}") out = (paddle.pow(x, 2) + paddle.pow(y, 2)).sqrt() return out @inplace_apis_in_dygraph_only def hypot_(x: Tensor, y: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``hypot`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_hypot`. """ if not isinstance(x, (paddle.Tensor, Variable)): raise TypeError(f"x must be tensor type, but got {type(x)}") if not isinstance(y, (paddle.Tensor, Variable)): raise TypeError(f"y must be tensor type, but got {type(y)}") out = x.pow_(2).add_(y.pow(2)).sqrt_() return out def combinations( x: Tensor, r: int = 2, with_replacement: bool = False, name: str | None = None, ) -> Tensor: """ Compute combinations of length r of the given tensor. The behavior is similar to python's itertools.combinations when with_replacement is set to False, and itertools.combinations_with_replacement when with_replacement is set to True. Args: x (Tensor): 1-D input Tensor, the data type is float16, float32, float64, int32 or int64. r (int, optional): number of elements to combine, default value is 2. with_replacement (bool, optional): whether to allow duplication in combination, default value is False. name (str|None, optional): Name for the operation (optional, default is None).For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor). Tensor concatenated by combinations, same dtype with x. Examples: .. code-block:: python >>> import paddle >>> x = paddle.to_tensor([1, 2, 3], dtype='int32') >>> res = paddle.combinations(x) >>> print(res) Tensor(shape=[3, 2], dtype=int32, place=Place(gpu:0), stop_gradient=True, [[1, 2], [1, 3], [2, 3]]) """ if len(x.shape) != 1: raise TypeError(f"Expect a 1-D vector, but got x shape {x.shape}") if not isinstance(r, int) or r < 0: raise ValueError(f"Expect a non-negative int, but got r={r}") if r == 0: return paddle.empty(shape=[0], dtype=x.dtype) if r > 1: t_l = [x for i in range(r)] grids = paddle.meshgrid(t_l) else: grids = [x] num_elements = x.numel() t_range = paddle.arange(num_elements, dtype='int64') if r > 1: t_l = [t_range for i in range(r)] index_grids = paddle.meshgrid(t_l) else: index_grids = [t_range] mask = paddle.full(x.shape * r, True, dtype='bool') if with_replacement: for i in range(r - 1): mask *= index_grids[i] <= index_grids[i + 1] else: for i in range(r - 1): mask *= index_grids[i] < index_grids[i + 1] for i in range(r): grids[i] = grids[i].masked_select(mask) return paddle.stack(grids, 1) def signbit(x: Tensor, name: str | None = None) -> Tensor: r""" Tests if each element of input has its sign bit set or not. Args: x (Tensor): The input Tensor. Must be one of the following types: float16, float32, float64, bfloat16, uint8, int8, int16, int32, int64. name (str|None, optional): Name for the operation (optional, default is None).For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor): The output Tensor. The sign bit of the corresponding element of the input tensor, True means negative, False means positive. Examples: .. code-block:: python :name: signbit-example-1 >>> import paddle >>> paddle.set_device('cpu') >>> x = paddle.to_tensor([-0., 1.1, -2.1, 0., 2.5], dtype='float32') >>> res = paddle.signbit(x) >>> print(res) Tensor(shape=[5], dtype=bool, place=Place(cpu), stop_gradient=True, [True, False, True, False, False]) .. code-block:: python :name: signbit-example-2 >>> import paddle >>> paddle.set_device('cpu') >>> x = paddle.to_tensor([-5, -2, 3], dtype='int32') >>> res = paddle.signbit(x) >>> print(res) Tensor(shape=[3], dtype=bool, place=Place(cpu), stop_gradient=True, [True , True , False]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") check_variable_and_dtype( x, "x", [ 'float16', 'float32', 'float64', 'bfloat16', 'uint8', 'int8', 'int16', 'int32', 'int64', ], "signbit", ) ones = [1.0] * math.prod(x.shape) ones = paddle.to_tensor(ones, x.dtype).reshape(x.shape) neg_zero_x = paddle.copysign(ones, x) x = paddle.sign(neg_zero_x) out = paddle.cast(x < 0, dtype='bool') return out def isposinf(x: Tensor, name: str | None = None) -> Tensor: r""" Tests if each element of input is positive infinity or not. Args: x (Tensor): The input Tensor. Must be one of the following types: bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The output Tensor. Each element of output indicates whether the input element is positive infinity or not. Examples: .. code-block:: python >>> import paddle >>> paddle.set_device('cpu') >>> x = paddle.to_tensor([-0., float('inf'), -2.1, -float('inf'), 2.5], dtype='float32') >>> res = paddle.isposinf(x) >>> print(res) Tensor(shape=[5], dtype=bool, place=Place(cpu), stop_gradient=True, [False, True, False, False, False]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") check_variable_and_dtype( x, "x", [ 'bfloat16', 'float16', 'float32', 'float64', 'int8', 'int16', 'int32', 'int64', 'uint8', ], "isposinf", ) ## dtype is the intersection of dtypes supported by isinf and signbit is_inf = paddle.isinf(x) signbit = ~paddle.signbit(x) return paddle.logical_and(is_inf, signbit) def isneginf(x: Tensor, name: str | None = None) -> Tensor: r""" Tests if each element of input is negative infinity or not. Args: x (Tensor): The input Tensor. Must be one of the following types: bfloat16, float16, float32, float64, int8, int16, int32, int64, uint8. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The output Tensor. Each element of output indicates whether the input element is negative infinity or not. Examples: .. code-block:: python >>> import paddle >>> paddle.set_device('cpu') >>> x = paddle.to_tensor([-0., float('inf'), -2.1, -float('inf'), 2.5], dtype='float32') >>> res = paddle.isneginf(x) >>> print(res) Tensor(shape=[5], dtype=bool, place=Place(cpu), stop_gradient=True, [False, False, False, True, False]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") check_variable_and_dtype( x, "x", [ 'bfloat16', 'float16', 'float32', 'float64', 'int8', 'int16', 'int32', 'int64', 'uint8', ], "isneginf", ) is_inf = paddle.isinf(x) signbit = paddle.signbit(x) return paddle.logical_and(is_inf, signbit) def isreal(x: Tensor, name: str | None = None) -> Tensor: r""" Tests if each element of input is a real number or not. Args: x (Tensor): The input Tensor. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The output Tensor. Each element of output indicates whether the input element is a real number or not. Examples: .. code-block:: python >>> import paddle >>> paddle.set_device('cpu') >>> x = paddle.to_tensor([-0., -2.1, 2.5], dtype='float32') >>> res = paddle.isreal(x) >>> print(res) Tensor(shape=[3], dtype=bool, place=Place(cpu), stop_gradient=True, [True, True, True]) >>> x = paddle.to_tensor([(-0.+1j), (-2.1+0.2j), (2.5-3.1j)]) >>> res = paddle.isreal(x) >>> print(res) Tensor(shape=[3], dtype=bool, place=Place(cpu), stop_gradient=True, [False, False, False]) >>> x = paddle.to_tensor([(-0.+1j), (-2.1+0j), (2.5-0j)]) >>> res = paddle.isreal(x) >>> print(res) Tensor(shape=[3], dtype=bool, place=Place(cpu), stop_gradient=True, [False, True, True]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") dtype = x.dtype is_real_dtype = not ( dtype == core.VarDesc.VarType.COMPLEX64 or dtype == core.VarDesc.VarType.COMPLEX128 or dtype == core.DataType.COMPLEX64 or dtype == core.DataType.COMPLEX128 ) if is_real_dtype: return paddle.ones_like(x, dtype='bool') return paddle.equal(paddle.imag(x), 0) def sinc(x: Tensor, name: str | None = None) -> Tensor: r""" Calculate the normalized sinc of ``x`` elementwise. .. math:: out_i = \left\{ \begin{aligned} &1 & \text{ if $x_i = 0$} \\ &\frac{\sin(\pi x_i)}{\pi x_i} & \text{ otherwise} \end{aligned} \right. Args: x (Tensor): The input Tensor. Must be one of the following types: bfloat16, float16, float32, float64. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The Tensor of elementwise-computed normalized sinc result. Examples: .. code-block:: python >>> import paddle >>> paddle.set_device('cpu') >>> paddle.seed(100) >>> x = paddle.rand([2,3], dtype='float32') >>> res = paddle.sinc(x) >>> print(res) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.56691176, 0.93089867, 0.99977750], [0.61639023, 0.79618412, 0.89171958]]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") check_variable_and_dtype( x, "x", [ 'uint16', 'float16', 'float32', 'float64', ], "sinc", ) tmp = paddle.where(x != 0, x, paddle.full_like(x, 1.0e-20)) tmp = paddle.multiply(tmp, paddle.to_tensor(math.pi, dtype=x.dtype)) tmp = paddle.divide(tmp.sin(), tmp) return paddle.where(~paddle.isnan(tmp), tmp, paddle.full_like(x, 1.0)) @inplace_apis_in_dygraph_only def sinc_(x: Tensor, name: str | None = None) -> Tensor: r""" Inplace version of ``sinc`` API, the output Tensor will be inplaced with input ``x``. Please refer to :ref:`api_paddle_sinc`. """ if not isinstance(x, (paddle.Tensor, Variable)): raise TypeError(f"x must be tensor type, but got {type(x)}") check_variable_and_dtype( x, "x", [ 'uint16', 'float16', 'float32', 'float64', ], "sinc_", ) paddle.where_(x != 0, x, paddle.full_like(x, 1.0e-20)) paddle.multiply_(x, paddle.to_tensor(math.pi, dtype=x.dtype)) tmp = paddle.clone(x) paddle.sin_(x) paddle.divide_(x, tmp) return paddle.where(~paddle.isnan(x), x, paddle.full_like(x, 1.0)) def isin( x: Tensor, test_x: Tensor, assume_unique: bool = False, invert: bool = False, name: str | None = None, ) -> Tensor: r""" Tests if each element of `x` is in `test_x`. Args: x (Tensor): The input Tensor. Supported data type: 'bfloat16', 'float16', 'float32', 'float64', 'int32', 'int64'. test_x (Tensor): Tensor values against which to test for each input element. Supported data type: 'bfloat16', 'float16', 'float32', 'float64', 'int32', 'int64'. assume_unique (bool, optional): If True, indicates both `x` and `test_x` contain unique elements, which could make the calculation faster. Default: False. invert (bool, optional): Indicate whether to invert the boolean return tensor. If True, invert the results. Default: False. name (str|None, optional): Name for the operation (optional, default is None).For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), The output Tensor with the same shape as `x`. Examples: .. code-block:: python >>> import paddle >>> paddle.set_device('cpu') >>> x = paddle.to_tensor([-0., -2.1, 2.5, 1.0, -2.1], dtype='float32') >>> test_x = paddle.to_tensor([-2.1, 2.5], dtype='float32') >>> res = paddle.isin(x, test_x) >>> print(res) Tensor(shape=[5], dtype=bool, place=Place(cpu), stop_gradient=True, [False, True, True, False, True]) >>> x = paddle.to_tensor([-0., -2.1, 2.5, 1.0, -2.1], dtype='float32') >>> test_x = paddle.to_tensor([-2.1, 2.5], dtype='float32') >>> res = paddle.isin(x, test_x, invert=True) >>> print(res) Tensor(shape=[5], dtype=bool, place=Place(cpu), stop_gradient=True, [True, False, False, True, False]) >>> # Set `assume_unique` to True only when `x` and `test_x` contain unique values, otherwise the result may be incorrect. >>> x = paddle.to_tensor([0., 1., 2.]*20).reshape([20, 3]) >>> test_x = paddle.to_tensor([0., 1.]*20) >>> correct_result = paddle.isin(x, test_x, assume_unique=False) >>> print(correct_result) Tensor(shape=[20, 3], dtype=bool, place=Place(cpu), stop_gradient=True, [[True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False], [True , True , False]]) >>> incorrect_result = paddle.isin(x, test_x, assume_unique=True) >>> print(incorrect_result) Tensor(shape=[20, 3], dtype=bool, place=Place(gpu:0), stop_gradient=True, [[True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , True ], [True , True , False]]) """ if not isinstance(x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(x)}") if not isinstance(test_x, (paddle.Tensor, Variable, paddle.pir.Value)): raise TypeError(f"x must be tensor type, but got {type(test_x)}") check_variable_and_dtype( x, "x", [ 'uint16', 'float16', 'float32', 'float64', 'int32', 'int64', ], "isin", ) check_variable_and_dtype( test_x, "test_x", [ 'uint16', 'float16', 'float32', 'float64', 'int32', 'int64', ], "isin", ) x_zero_dim = False if len(x.shape) == 0: x = x.reshape([1]) x_zero_dim = True size_x = math.prod(x.shape) size_t = math.prod(test_x.shape) if size_t < math.pow(size_x, 0.145) * 10.0: # use brute-force searching if the test_x size is small if len(x.shape) == 0: return paddle.zeros([], dtype='bool') tmp = x.reshape(tuple(x.shape) + ((1,) * test_x.ndim)) cmp = tmp == test_x dim = tuple(range(-1, -test_x.ndim - 1, -1)) cmp = cmp.any(axis=dim) if invert: cmp = ~cmp else: x_flat = x.flatten() test_x_flat = test_x.flatten() if assume_unique: # if x and test_x both contain unique elements, use stable argsort method which could be faster all_elements = paddle.concat([x_flat, test_x_flat]) sorted_index = paddle.argsort(all_elements, stable=True) sorted_x = all_elements[sorted_index] duplicate_mask = paddle.full_like(sorted_index, False, dtype='bool') if not in_dynamic_mode(): duplicate_mask = paddle.static.setitem( duplicate_mask, paddle.arange(duplicate_mask.numel() - 1), sorted_x[1:] == sorted_x[:-1], ) else: duplicate_mask[:-1] = sorted_x[1:] == sorted_x[:-1] if invert: duplicate_mask = duplicate_mask.logical_not() mask = paddle.empty_like(duplicate_mask) if not in_dynamic_or_pir_mode(): mask = paddle.static.setitem(mask, sorted_index, duplicate_mask) else: mask[sorted_index] = duplicate_mask cmp = mask[0 : x.numel()].reshape(x.shape) else: # otherwise use searchsorted method sorted_test_x = paddle.sort(test_x_flat) idx = paddle.searchsorted(sorted_test_x, x_flat) test_idx = paddle.where( idx < sorted_test_x.numel(), idx, paddle.zeros_like(idx, 'int64'), ) cmp = sorted_test_x[test_idx] == x_flat cmp = cmp.logical_not() if invert else cmp cmp = cmp.reshape(x.shape) if x_zero_dim: return cmp.reshape([]) else: return cmp def cartesian_prod(x: Sequence[Tensor], name: str | None = None) -> Tensor: """ Perform Cartesian product on a given tensor sequence. This behavior is similar to the itertools.product in Python. Equivalent to converting all input tensors into lists, performing itertools.product on these lists, and finally converting the resulting list into tensors. Args: x (list[Tensor]|tuple[Tensor]): Any number of 1-D input Tensors. Supported data types: bfloat16, float16, float32, float64, int32, int64, complex64 or complex128. name (str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: out (Tensor), cartesian product of input tensors with the same data type. Examples: .. code-block:: python >>> import paddle >>> a = paddle.to_tensor([1, 2, 3], dtype='int32') >>> b = paddle.to_tensor([5, 6], dtype='int32') >>> res = paddle.cartesian_prod([a, b]) >>> print(res) Tensor(shape=[6, 2], dtype=int32, place=Place(cpu), stop_gradient=True, [[1, 5], [1, 6], [2, 5], [2, 6], [3, 5], [3, 6]]) >>> c = paddle.to_tensor([7, 8, 9], dtype='float32') >>> res = paddle.cartesian_prod([c]) >>> print(res) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [7., 8., 9.]) >>> d = paddle.empty([0], dtype='float64') >>> e = paddle.to_tensor([1, 2], dtype='float64') >>> f = paddle.to_tensor([3, 4, 5, 6, 7], dtype='float64') >>> res = paddle.cartesian_prod([d, e, f]) >>> print(res) Tensor(shape=[0, 3], dtype=float64, place=Place(cpu), stop_gradient=True, []) """ for tensor in x: if len(tensor.shape) != 1: raise ValueError( f"Expect a 1D vector, but got shape {tensor.shape}" ) if len(x) == 1: return x[0] coordinates = paddle.stack(paddle.meshgrid(x), axis=-1) return paddle.reshape(coordinates, [-1, len(x)])