Variable¶

class paddle.static. Variable ( block, type=<VarType.LOD_TENSOR: 7>, name=None, shape=None, dtype=None, lod_level=None, capacity=None, persistable=None, error_clip=None, stop_gradient=False, is_data=False, need_check_feed=False, belong_to_optimizer=False, **kwargs ) [source]

Notes

The constructor of Variable should not be invoked directly.

In Static Graph Mode: Please use ** Block.create_var ** to create a Static variable which has no data until being feed.

In Dygraph Mode: Please use ** api_fluid_dygraph_to_variable ** to create a dygraph variable with real data.

In Fluid, every input and output of an OP is a variable. In most cases, variables are used for holding different kinds of data or training labels. A variable belongs to a Block . All variable has its own name and two variables in different Block could have the same name.

There are many kinds of variables. Each kind of them has its own attributes and usages. Please refer to the framework.proto for details.

Most of a Variable’s member variables can be set to be None. It mean it is not available or will be specified later.

Examples

In Static Graph Mode:

           import paddle.fluid as fluid
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')

          

In Dygraph Mode:

           import paddle.fluid as fluid
import numpy as np

with fluid.dygraph.guard():
    new_variable = fluid.dygraph.to_variable(np.arange(10))

detach ( ) detach¶

Returns a new Variable, detached from the current graph. It will share data with origin Variable and without tensor copy. In addition, the detached Variable doesn’t provide gradient propagation.

Returns: ( Variable | dtype is same as current Variable), The detached Variable.

Examples

             import paddle

paddle.enable_static()

# create a static Variable
x = paddle.static.data(name='x', shape=[3, 2, 1])

# create a detached Variable
y = x.detach()

numpy ( ) numpy¶

Notes:: This API is ONLY available in Dygraph mode

Returns a numpy array shows the value of current Variable

Returns: The numpy value of current Variable.
Return type: ndarray

Returns type:: ndarray: dtype is same as current Variable

Examples

             import paddle.fluid as fluid
from paddle.fluid.dygraph.base import to_variable
from paddle.fluid.dygraph import Linear
import numpy as np

data = np.random.uniform(-1, 1, [30, 10, 32]).astype('float32')
with fluid.dygraph.guard():
    linear = Linear(32, 64)
    data = to_variable(data)
    x = linear(data)
    print(x.numpy())

            

backward ( retain_graph=False ) backward¶

Notes:: This API is ONLY available in Dygraph mode

Run backward of current Graph which starts from current Tensor.

Parameters: retain_graph (bool, optional) – If False, the graph used to compute grads will be freed. If you would like to add more ops to the built graph after calling this method( backward ), set the parameter retain_graph to True, then the grads will be retained. Thus, seting it to False is much more memory-efficient. Defaults to False.
Returns: None
Return type: NoneType

Examples

             import numpy as np
import paddle
paddle.disable_static()

x = np.ones([2, 2], np.float32)
inputs = []
for _ in range(10):
    tmp = paddle.to_tensor(x)
    # if we don't set tmp's stop_gradient as False then, all path to loss will has no gradient since
    # there is no one need gradient on it.
    tmp.stop_gradient=False
    inputs.append(tmp)
ret = paddle.add_n(inputs)
loss = paddle.sum(ret)
loss.backward()

            

gradient ( ) gradient¶

Notes:: This API is ONLY available in Dygraph mode

Get the Gradient of Current Variable

Returns: if Variable’s type is LoDTensor, return numpy value of the gradient of current Variable, if Variable’s type is SelectedRows, return tuple of ndarray, first element of tuple is numpy value of the gradient of current Variable, second element of tuple is numpy value of the rows of current Variable.
Return type: ndarray or tuple of ndarray

Examples

             import paddle
import paddle.fluid as fluid
import numpy as np

# example1: return ndarray
x = np.ones([2, 2], np.float32)
with fluid.dygraph.guard():
    inputs2 = []
    for _ in range(10):
        tmp = fluid.dygraph.base.to_variable(x)
        tmp.stop_gradient=False
        inputs2.append(tmp)
    ret2 = paddle.add_n(inputs2)
    loss2 = paddle.sum(ret2)
    loss2.backward()
    print(loss2.gradient())

# example2: return tuple of ndarray
with fluid.dygraph.guard():
    embedding = paddle.nn.Embedding(
        20,
        32,
        weight_attr='emb.w',
        sparse=True)
    x_data = np.arange(12).reshape(4, 3).astype('int64')
    x_data = x_data.reshape((-1, 3, 1))
    x = fluid.dygraph.base.to_variable(x_data)
    out = embedding(x)
    out.backward()
    print(embedding.weight.gradient())

            

clear_gradient ( ) clear_gradient¶

Notes:

1. This API is ONLY available in Dygraph mode

2. Use it only Variable has gradient, normally we use this for Parameters since other temporal Variable will be deleted by Python’s GC

Clear (set to 0 ) the Gradient of Current Variable

Returns: None

Examples

             import paddle
import paddle.fluid as fluid
import numpy as np

x = np.ones([2, 2], np.float32)
with fluid.dygraph.guard():
    inputs2 = []
    for _ in range(10):
        tmp = fluid.dygraph.base.to_variable(x)
        tmp.stop_gradient=False
        inputs2.append(tmp)
    ret2 = paddle.add_n(inputs2)
    loss2 = paddle.sum(ret2)
    loss2.backward()
    print(loss2.gradient())
    loss2.clear_gradient()
    print("After clear {}".format(loss2.gradient()))

            

to_string ( throw_on_error, with_details=False ) to_string¶

Get debug string.

Parameters

throw_on_error (bool) – True if raise an exception when self is not initialized.
with_details (bool) – more details about variables and parameters (e.g. trainable, optimize_attr, …) will be printed when with_details is True. Default value is False;

Returns

The debug string.

Return type

str

Examples

             import paddle.fluid as fluid
import paddle

paddle.enable_static()
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print(new_variable.to_string(True))
print("=============with detail===============")
print(new_variable.to_string(True, True))

            

element_size ( ) element_size¶

Returns the size in bytes of an element in the Tensor.

Examples

             import paddle
paddle.enable_static()

x = paddle.static.data(name='x1', shape=[3, 2], dtype='bool')
x.element_size() # 1

x = paddle.static.data(name='x2', shape=[3, 2], dtype='int16')
x.element_size() # 2

x = paddle.static.data(name='x3', shape=[3, 2], dtype='float16')
x.element_size() # 2

x = paddle.static.data(name='x4', shape=[3, 2], dtype='float32')
x.element_size() # 4

x = paddle.static.data(name='x5', shape=[3, 2], dtype='float64')
x.element_size() # 8

            

property stop_gradient

Indicating if we stop gradient from current Variable

Notes: This Property has default value as True in Dygraph mode, while Parameter’s default value is False. However, in Static Graph Mode all Variable’s default stop_gradient value is False

Examples

             import paddle.fluid as fluid
import numpy as np

with fluid.dygraph.guard():
    value0 = np.arange(26).reshape(2, 13).astype("float32")
    value1 = np.arange(6).reshape(2, 3).astype("float32")
    value2 = np.arange(10).reshape(2, 5).astype("float32")
    linear = fluid.Linear(13, 5, dtype="float32")
    linear2 = fluid.Linear(3, 3, dtype="float32")
    a = fluid.dygraph.to_variable(value0)
    b = fluid.dygraph.to_variable(value1)
    c = fluid.dygraph.to_variable(value2)
    out1 = linear(a)
    out2 = linear2(b)
    out1.stop_gradient = True
    out = fluid.layers.concat(input=[out1, out2, c], axis=1)
    out.backward()

    assert linear.weight.gradient() is None
    assert (out1.gradient() == 0).all()

            

property persistable

Indicating if we current Variable should be long-term alive

Notes: This Property will be deprecated and this API is just to help user understand concept

1. All Variable’s persistable is False except Parameters.

2. In Dygraph mode, this property should not be changed

Examples

             import paddle.fluid as fluid
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print("persistable of current Var is: {}".format(new_variable.persistable))

            

property is_parameter

Indicating if current Variable is a Parameter

Examples

             import paddle
new_parameter = paddle.static.create_parameter(name="X",
                                    shape=[10, 23, 48],
                                    dtype='float32')
if new_parameter.is_parameter:
    print("Current var is a Parameter")
else:
    print("Current var is not a Parameter")

# Current var is a Parameter

            

property grad_name

Indicating name of the gradient Variable of current Variable.

Notes: This is a read-only property. It simply returns name of gradient Variable from a naming convention but doesn’t guarantee the gradient exists.

Examples

import paddle

x = paddle.static.data(name=”x”, shape=[-1, 23, 48], dtype=’float32’) print(x.grad_name) # output is x@GRAD

property name

Indicating name of current Variable

Notes: If it has two or more Varaible share the same name in the same Block , it means these Variable will share content in no- Dygraph mode. This is how we achieve Parameter sharing

Examples

             import paddle.fluid as fluid
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print("name of current Var is: {}".format(new_variable.name))

            

property shape

Indicating shape of current Variable

Notes: This is a read-only property

Examples

             import paddle.fluid as fluid
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print("shape of current Var is: {}".format(new_variable.shape))

            

property dtype

Indicating data type of current Variable

Notes: This is a read-only property

Examples

             import paddle.fluid as fluid
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print("Dtype of current Var is: {}".format(new_variable.dtype))

            

property lod_level

Indicating LoD info of current Variable, please refer to api_fluid_LoDTensor_en to check the meaning of LoD

Notes:

1. This is a read-only property

2. Don’t support this property in Dygraph mode, it’s value should be 0(int)

Examples

             import paddle
import paddle.fluid as fluid

paddle.enable_static()
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print("LoD Level of current Var is: {}".format(new_variable.lod_level))

            

property type

Indicating Type of current Variable

Notes: This is a read-only property

Examples

             import paddle.fluid as fluid
cur_program = fluid.Program()
cur_block = cur_program.current_block()
new_variable = cur_block.create_var(name="X",
                                    shape=[-1, 23, 48],
                                    dtype='float32')
print("Type of current Var is: {}".format(new_variable.type))

            

property T

Permute current Variable with its dimensions reversed.

If n is the dimensions of x , x.T is equivalent to x.transpose([n-1, n-2, …, 0]).

Examples

             import paddle
paddle.enable_static()

x = paddle.ones(shape=[2, 3, 5])
x_T = x.T

exe = paddle.static.Executor()
x_T_np = exe.run(paddle.static.default_main_program(), fetch_list=[x_T])[0]
print(x_T_np.shape)
# (5, 3, 2)

            

clone ( ) clone¶

Returns a new static Variable, which is the clone of the original static Variable. It remains in the current graph, that is, the cloned Variable provides gradient propagation. Calling out = tensor.clone() is same as out = assign(tensor) .

Returns: Variable, The cloned Variable.

Examples

             import paddle

paddle.enable_static()

# create a static Variable
x = paddle.static.data(name='x', shape=[3, 2, 1])
# create a cloned Variable
y = x.clone()

            

get_value ( scope=None ) get_value¶

Get the value of variable in given scope.

Parameters: scope (Scope, optional) – If scope is None, it will be set to global scope obtained through ‘paddle.static.global_scope()’. Otherwise, use scope. Default: None
Returns: Tensor, the value in given scope.

Examples

             import paddle
import paddle.static as static
import numpy as np

paddle.enable_static()

x = static.data(name="x", shape=[10, 10], dtype='float32')

y = static.nn.fc(x, 10, name='fc')
place = paddle.CPUPlace()
exe = static.Executor(place)
prog = paddle.static.default_main_program()
exe.run(static.default_startup_program())
inputs = np.ones((10, 10), dtype='float32')
exe.run(prog, feed={'x': inputs}, fetch_list=[y, ])
path = 'temp/tensor_'
for var in prog.list_vars():
    if var.persistable:
        t = var.get_value()
        paddle.save(t, path+var.name+'.pdtensor')

for var in prog.list_vars():
    if var.persistable:
        t_load = paddle.load(path+var.name+'.pdtensor')
        var.set_value(t_load)

            

set_value ( value, scope=None ) set_value¶

Set the value to the tensor in given scope.

Parameters

value (Tensor/ndarray) – The value to be set.
scope (Scope, optional) – If scope is None, it will be set to global scope obtained through ‘paddle.static.global_scope()’. Otherwise, use scope. Default: None

Returns

None

Examples

             import paddle
import paddle.static as static
import numpy as np

paddle.enable_static()

x = static.data(name="x", shape=[10, 10], dtype='float32')

y = static.nn.fc(x, 10, name='fc')
place = paddle.CPUPlace()
exe = static.Executor(place)
prog = paddle.static.default_main_program()
exe.run(static.default_startup_program())
inputs = np.ones((10, 10), dtype='float32')
exe.run(prog, feed={'x': inputs}, fetch_list=[y, ])
path = 'temp/tensor_'
for var in prog.list_vars():
    if var.persistable:
        t = var.get_value()
        paddle.save(t, path+var.name+'.pdtensor')

for var in prog.list_vars():
    if var.persistable:
        t_load = paddle.load(path+var.name+'.pdtensor')
        var.set_value(t_load)

            

size ( ) size¶

Returns the number of elements for current Variable, which is a int64 Variable with shape [] .

Returns: Variable, the number of elements for current Variable

Examples

             import paddle

paddle.enable_static()

# create a static Variable
x = paddle.static.data(name='x', shape=[3, 2, 1])

# get the number of elements of the Variable
y = x.size()

property attr_names: Get the names of all attributes defined.

attr ( name ) attr¶

Get the attribute by name.

Parameters: name (str) – the attribute name.
Returns: int|str|list, The attribute value. The return value can be any valid attribute type.

property dist_attr: Get distributed attribute of this Variable.

abs ( name=None ) abs¶

Abs Operator. Perform elementwise abs for input X.

\[out = |x|\]

Parameters

x (Tensor) – The input tensor of abs op.
out (Tensor) – The output tensor of abs op.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.abs(x)
print(out)
# [0.4 0.2 0.1 0.3]

            

acos ( name=None ) acos¶

Acos Activation Operator.

\[out = cos^{-1}(x)\]

Parameters

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

Returns

Tensor. Output of Acos operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.acos(x)
print(out)
# [1.98231317 1.77215425 1.47062891 1.26610367]

            

acosh ( name=None ) acosh¶

Acosh Activation Operator.

\[out = acosh(x)\]

Parameters

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

Returns

Tensor. Output of Acosh operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([1., 3., 4., 5.])
out = paddle.acosh(x)
print(out)
# [0.        , 1.76274729, 2.06343699, 2.29243159]

            

add ( y, name=None ) add¶

Elementwise Add Operator. Add two tensors element-wise The equation is:

\[Out=X+Y\]

$X$ the tensor of any dimension. $Y$ the tensor whose dimensions must be less than or equal to the dimensions of $X$.

There are two cases for this operator:

The shape of $Y$ is the same with $X$.
The shape of $Y$ is a continuous subsequence of $X$.

For case 2:

Broadcast $Y$ to match the shape of $X$, where axis is the start dimension index for broadcasting $Y$ onto $X$.
If $axis$ is -1 (default), $axis$=rank($X$)-rank($Y$).

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:

                 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

                

Parameters

x (Tensor) – Tensor or LoDTensor of any dimensions. Its dtype should be int32, int64, float32, float64.
y (Tensor) – Tensor or LoDTensor of any dimensions. Its dtype should be int32, int64, float32, float64.
name (string, optional) – For details, please refer to 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

             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)  # [3., 8., 6. ]

            

add_ ( y, name=None ) add_¶: Inplace version of add API, the output Tensor will be inplaced with input x. Please refer to api_tensor_add.

add_n ( name=None ) add_n¶

Sum one or more Tensor of the input.

For example:

             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]]

            

Parameters

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: float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the sum of input $inputs$ , its shape and data types are consistent with $inputs$.

Examples

             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])
# [[8., 10., 12.],
#  [14., 16., 18.]]

            

addmm ( x, y, beta=1.0, alpha=1.0, name=None ) addmm¶

addmm

Perform matrix multiplication for input $x$ and $y$. $input$ is added to the final result. The equation is:

\[Out = alpha * x * y + beta * input\]

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

Parameters

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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output Tensor of addmm.

Return type

Tensor

Examples

             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)
# [[10.5 10.5]
# [10.5 10.5]]

            

all ( axis=None, keepdim=False, name=None ) all¶

Computes the logical and of tensor elements over the given dimension.

Parameters

x (Tensor) – An N-D Tensor, the input data type should be bool.
axis (int|list|tuple, optional) – The dimensions along which the logical and is compute. If None, and all elements of x and return a Tensor with a single element, otherwise must be in the range $[-rank(x), rank(x))$. If $axis[i] < 0$, the dimension to reduce is $rank + axis[i]$.
keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result Tensor will have one fewer dimension than the x unless keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Results the logical and on the specified axis of input Tensor x, it’s data type is bool.

Return type

Tensor

Examples

             import paddle

# x is a bool Tensor with following elements:
#    [[True, False]
#     [True, True]]
x = paddle.to_tensor([[1, 0], [1, 1]], dtype='int32')
print(x)
x = paddle.cast(x, 'bool')

# out1 should be False
out1 = paddle.all(x)          # False
print(out1)

# out2 should be [True, False]
out2 = paddle.all(x, axis=0)  # [True, False]
print(out2)

# keepdim=False, out3 should be [False, True], out.shape should be (2,)
out3 = paddle.all(x, axis=-1) # [False, True]
print(out3)

# keepdim=True, out4 should be [[False], [True]], out.shape should be (2,1)
out4 = paddle.all(x, axis=1, keepdim=True) # [[False], [True]]
print(out4)

            

allclose ( y, rtol=1e-05, atol=1e-08, equal_nan=False, name=None ) allclose¶

Check if all $x$ and $y$ satisfy the condition:

\[\left| x - y \right| \leq atol + rtol \times \left| y \right|\]

elementwise, for all elements of $x$ and $y$. This is analogous to $numpy.allclose$, namely that it returns $True$ if two tensors are elementwise equal within a tolerance.

Parameters

x (Tensor) – The input tensor, it’s data type should be float16, float32, float64..
y (Tensor) – The input tensor, it’s data type should be float16, float32, float64..
rtol (rtoltype, optional) – The relative tolerance. Default: $1e-5$ .
atol (atoltype, optional) – The absolute tolerance. Default: $1e-8$ .
equal_nan (equalnantype, optional) – (bool), attribute 2 for allclose op.
name (str, optional) – Name for the operation. For more information, please refer to Name. Default: None.

Returns

The output tensor, it’s data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([10000., 1e-07])
y = paddle.to_tensor([10000.1, 1e-08])
result1 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
                        equal_nan=False, name="ignore_nan")
# False

result2 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
                            equal_nan=True, name="equal_nan")
# False

x = paddle.to_tensor([1.0, float('nan')])
y = paddle.to_tensor([1.0, float('nan')])
result1 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
                        equal_nan=False, name="ignore_nan")
# False

result2 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
                            equal_nan=True, name="equal_nan")
# True

            

amax ( axis=None, keepdim=False, name=None ) amax¶

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.

Parameters

x (Tensor) – A tensor, the data type is float32, float64, int32, int64, the dimension is no more than 4.
axis (int|list|tuple, optional) – The axis along which the maximum is computed. If None, compute the maximum over all elements of x and return a Tensor with a single element, otherwise must be in the range $[-x.ndim(x), x.ndim(x))$. If $axis[i] < 0$, the axis to reduce is $x.ndim + axis[i]$.
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 keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of maximum on the specified axis of input tensor, it’s data type is the same as x.

Examples

             import paddle
# data_x is a Tensor with shape [2, 4] with multiple maximum elements
# the axis is a int element

x = paddle.to_tensor([[0.1, 0.9, 0.9, 0.9],
                      [0.9, 0.9, 0.6, 0.7]],
                     dtype='float64', stop_gradient=False)
# There are 5 maximum elements:
# 1) amax evenly distributes gradient between these equal values,
#    thus the corresponding gradients are 1/5=0.2;
# 2) while max propagates gradient to all of them,
#    thus the corresponding gradient are 1.
result1 = paddle.amax(x)
result1.backward()
print(result1, x.grad)
# 0.9, [[0., 0.2, 0.2, 0.2], [0.2, 0.2, 0., 0.]]

x.clear_grad()
result1_max = paddle.max(x)
result1_max.backward()
print(result1_max, x.grad)
# 0.9, [[0., 1.0, 1.0, 1.0], [1.0, 1.0, 0., 0.]]

###############################

x.clear_grad()
result2 = paddle.amax(x, axis=0)
result2.backward()
print(result2, x.grad)
#[0.9, 0.9, 0.9, 0.9], [[0., 0.5, 1., 1.], [1., 0.5, 0., 0.]]

x.clear_grad()
result3 = paddle.amax(x, axis=-1)
result3.backward()
print(result3, x.grad)
#[0.9, 0.9], [[0., 0.3333, 0.3333, 0.3333], [0.5, 0.5, 0., 0.]]

x.clear_grad()
result4 = paddle.amax(x, axis=1, keepdim=True)
result4.backward()
print(result4, x.grad)
#[[0.9], [0.9]], [[0., 0.3333, 0.3333, 0.3333.], [0.5, 0.5, 0., 0.]]

# data_y is a Tensor with shape [2, 2, 2]
# the axis is list
y = paddle.to_tensor([[[0.1, 0.9], [0.9, 0.9]],
                      [[0.9, 0.9], [0.6, 0.7]]],
                     dtype='float64', stop_gradient=False)
result5 = paddle.amax(y, axis=[1, 2])
result5.backward()
print(result5, y.grad)
#[0.9., 0.9], [[[0., 0.3333], [0.3333, 0.3333]], [[0.5, 0.5], [0., 1.]]]

y.clear_grad()
result6 = paddle.amax(y, axis=[0, 1])
result6.backward()
print(result6, y.grad)
#[0.9., 0.9], [[[0., 0.3333], [0.5, 0.3333]], [[0.5, 0.3333], [1., 1.]]]

            

amin ( axis=None, keepdim=False, name=None ) amin¶

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.

Parameters

x (Tensor) – A tensor, the data type is float32, float64, int32, int64, the dimension is no more than 4.
axis (int|list|tuple, optional) – The axis along which the minimum is computed. If None, compute the minimum over all elements of x and return a Tensor with a single element, otherwise must be in the range $[-x.ndim, x.ndim)$. If $axis[i] < 0$, the axis to reduce is $x.ndim + axis[i]$.
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 keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             import paddle
# data_x is a Tensor with shape [2, 4] with multiple minimum elements
# the axis is a int element

x = paddle.to_tensor([[0.2, 0.1, 0.1, 0.1],
                      [0.1, 0.1, 0.6, 0.7]],
                     dtype='float64', stop_gradient=False)
# There are 5 minimum elements:
# 1) amin evenly distributes gradient between these equal values,
#    thus the corresponding gradients are 1/5=0.2;
# 2) while min propagates gradient to all of them,
#    thus the corresponding gradient are 1.
result1 = paddle.amin(x)
result1.backward()
print(result1, x.grad)
# 0.1, [[0., 0.2, 0.2, 0.2], [0.2, 0.2, 0., 0.]]

x.clear_grad()
result1_min = paddle.min(x)
result1_min.backward()
print(result1_min, x.grad)
# 0.1, [[0., 1.0, 1.0, 1.0], [1.0, 1.0, 0., 0.]]

###############################

x.clear_grad()
result2 = paddle.amin(x, axis=0)
result2.backward()
print(result2, x.grad)
#[0.1, 0.1, 0.1, 0.1], [[0., 0.5, 1., 1.], [1., 0.5, 0., 0.]]

x.clear_grad()
result3 = paddle.amin(x, axis=-1)
result3.backward()
print(result3, x.grad)
#[0.1, 0.1], [[0., 0.3333, 0.3333, 0.3333], [0.5, 0.5, 0., 0.]]

x.clear_grad()
result4 = paddle.amin(x, axis=1, keepdim=True)
result4.backward()
print(result4, x.grad)
#[[0.1], [0.1]], [[0., 0.3333, 0.3333, 0.3333.], [0.5, 0.5, 0., 0.]]

# data_y is a Tensor with shape [2, 2, 2]
# the axis is list
y = paddle.to_tensor([[[0.2, 0.1], [0.1, 0.1]],
                      [[0.1, 0.1], [0.6, 0.7]]],
                     dtype='float64', stop_gradient=False)
result5 = paddle.amin(y, axis=[1, 2])
result5.backward()
print(result5, y.grad)
#[0.1., 0.1], [[[0., 0.3333], [0.3333, 0.3333]], [[0.5, 0.5], [0., 1.]]]

y.clear_grad()
result6 = paddle.amin(y, axis=[0, 1])
result6.backward()
print(result6, y.grad)
#[0.1., 0.1], [[[0., 0.3333], [0.5, 0.3333]], [[0.5, 0.3333], [1., 1.]]]

            

angle ( name=None ) angle¶

Element-wise angle of complex numbers. For non-negative real numbers, the angle is 0 while for negative real numbers, the angle is $\pi$.

Equation:: \[angle(x)=arctan2(x.imag, x.real)\]

Parameters

x (Tensor) – An N-D Tensor, the data type is complex64, complex128, or float32, float64 .
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

An N-D Tensor of real data type with the same precision as that of x’s data type.

Return type

Tensor

Examples

             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
print(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)
print(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]])

            

any ( axis=None, keepdim=False, name=None ) any¶

Computes the logical or of tensor elements over the given dimension, and return the result.

Parameters

x (Tensor) – An N-D Tensor, the input data type should be bool.
axis (int|list|tuple, optional) – The dimensions along which the logical or is compute. If None, and all elements of x and return a Tensor with a single element, otherwise must be in the range $[-rank(x), rank(x))$. If $axis[i] < 0$, the dimension to reduce is $rank + axis[i]$.
keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result Tensor will have one fewer dimension than the x unless keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Results the logical or on the specified axis of input Tensor x, it’s data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[1, 0], [1, 1]], dtype='int32')
x = paddle.assign(x)
print(x)
x = paddle.cast(x, 'bool')
# x is a bool Tensor with following elements:
#    [[True, False]
#     [True, True]]

# out1 should be True
out1 = paddle.any(x)           # True
print(out1)

# out2 should be [True, True]
out2 = paddle.any(x, axis=0)   # [True, True]
print(out2)

# keepdim=False, out3 should be [True, True], out.shape should be (2,)
out3 = paddle.any(x, axis=-1)  # [True, True]
print(out3)

# keepdim=True, result should be [[True], [True]], out.shape should be (2,1)
out4 = paddle.any(x, axis=1, keepdim=True)  # [[True], [True]]
print(out4)

            

append ( var ) append¶

Notes:: **The type variable must be LoD Tensor Array.

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.fluid.layers.math_op_patch.monkey_patch_variable.<locals>.append, line 2); backlink

Inline strong start-string without end-string.

argmax ( axis=None, keepdim=False, dtype='int64', name=None ) argmax¶

Computes the indices of the max elements of the input tensor’s element along the provided axis.

Parameters

x (Tensor) – An input N-D Tensor with type float16, float32, float64, int16, int32, int64, uint8.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is x.ndim. when axis < 0, it works the same way as axis + R. Default is None, the input x will be into the flatten tensor, and selecting the min value index.
keepdim (bool, optional) – Whether to keep the given axis in output. If it is True, the dimensions will be same as input x and with size one in the axis. Otherwise the output dimentions is one fewer than x since the axis is squeezed. Default is False.
dtype (str|np.dtype, optional) – Data type of the output tensor which can be int32, int64. The default value is int64 , and it will return the int64 indices.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, return the tensor of int32 if set dtype is int32, otherwise return the tensor of int64.

Examples

             import paddle

x = paddle.to_tensor([[5,8,9,5],
                     [0,0,1,7],
                     [6,9,2,4]])
out1 = paddle.argmax(x)
print(out1) # 2
out2 = paddle.argmax(x, axis=0)
print(out2)
# [2, 2, 0, 1]
out3 = paddle.argmax(x, axis=-1)
print(out3)
# [2, 3, 1]
out4 = paddle.argmax(x, axis=0, keepdim=True)
print(out4)
# [[2, 2, 0, 1]]

            

argmin ( axis=None, keepdim=False, dtype='int64', name=None ) argmin¶

Computes the indices of the min elements of the input tensor’s element along the provided axis.

Parameters

x (Tensor) – An input N-D Tensor with type float16, float32, float64, int16, int32, int64, uint8.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is x.ndim. when axis < 0, it works the same way as axis + R. Default is None, the input x will be into the flatten tensor, and selecting the min value index.
keepdim (bool, optional) – Whether to keep the given axis in output. If it is True, the dimensions will be same as input x and with size one in the axis. Otherwise the output dimentions is one fewer than x since the axis is squeezed. Default is False.
dtype (str, optional) – Data type of the output tensor which can be int32, int64. The default value is ‘int64’, and it will return the int64 indices.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, return the tensor of int32 if set dtype is int32, otherwise return the tensor of int64.

Examples

             import paddle

x =  paddle.to_tensor([[5,8,9,5],
                         [0,0,1,7],
                         [6,9,2,4]])
out1 = paddle.argmin(x)
print(out1) # 4
out2 = paddle.argmin(x, axis=0)
print(out2)
# [1, 1, 1, 2]
out3 = paddle.argmin(x, axis=-1)
print(out3)
# [0, 0, 2]
out4 = paddle.argmin(x, axis=0, keepdim=True)
print(out4)
# [[1, 1, 1, 2]]

            

argsort ( axis=- 1, descending=False, name=None ) argsort¶

Sorts the input along the given axis, and returns the corresponding index tensor for the sorted output values. The default sort algorithm is ascending, if you want the sort algorithm to be descending, you must set the descending as True.

Parameters

x (Tensor) – An input N-D Tensor with type float16, float32, float64, int16, int32, int64, uint8.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is Rank(x). when axis<0, it works the same way as axis+R. Default is -1.
descending (bool, optional) – Descending is a flag, if set to true, algorithm will sort by descending order, else sort by ascending order. Default is false.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

sorted indices(with the same shape as x and with data type int64).

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[[5,8,9,5],
                       [0,0,1,7],
                       [6,9,2,4]],
                      [[5,2,4,2],
                       [4,7,7,9],
                       [1,7,0,6]]],
                    dtype='float32')
out1 = paddle.argsort(x, axis=-1)
out2 = paddle.argsort(x, axis=0)
out3 = paddle.argsort(x, axis=1)

print(out1)
#[[[0 3 1 2]
#  [0 1 2 3]
#  [2 3 0 1]]
# [[1 3 2 0]
#  [0 1 2 3]
#  [2 0 3 1]]]

print(out2)
#[[[0 1 1 1]
#  [0 0 0 0]
#  [1 1 1 0]]
# [[1 0 0 0]
#  [1 1 1 1]
#  [0 0 0 1]]]

print(out3)
#[[[1 1 1 2]
#  [0 0 2 0]
#  [2 2 0 1]]
# [[2 0 2 0]
#  [1 1 0 2]
#  [0 2 1 1]]]

            

as_complex ( name=None ) as_complex¶

Transform a real tensor to a complex tensor.

The data type of the input tensor is ‘float32’ or ‘float64’, and the data type of the returned tensor is ‘complex64’ or ‘complex128’, respectively.

The shape of the input tensor is (* ,2), (* means arbitary shape), i.e. the size of the last axis shoule be 2, which represent the real and imag part of a complex number. The shape of the returned tensor is (*,).

Parameters

x (Tensor) – The input tensor. Data type is ‘float32’ or ‘float64’.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, The output. Data type is ‘complex64’ or ‘complex128’, with the same precision as the input.

Examples

             import paddle
x = paddle.arange(12, dtype=paddle.float32).reshape([2, 3, 2])
y = paddle.as_complex(x)
print(y)

# Tensor(shape=[2, 3], dtype=complex64, place=Place(gpu:0), stop_gradient=True,
#        [[1j      , (2+3j)  , (4+5j)  ],
#         [(6+7j)  , (8+9j)  , (10+11j)]])

            

as_real ( name=None ) as_real¶

Transform a complex tensor to a real tensor.

The data type of the input tensor is ‘complex64’ or ‘complex128’, and the data type of the returned tensor is ‘float32’ or ‘float64’, respectively.

When the shape of the input tensor is (*, ), (* means arbitary shape), the shape of the output tensor is (*, 2), i.e. the shape of the output is the shape of the input appended by an extra 2.

Parameters

x (Tensor) – The input tensor. Data type is ‘complex64’ or ‘complex128’.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, The output. Data type is ‘float32’ or ‘float64’, with the same precision as the input.

Examples

             import paddle
x = paddle.arange(12, dtype=paddle.float32).reshape([2, 3, 2])
y = paddle.as_complex(x)
z = paddle.as_real(y)
print(z)

# Tensor(shape=[2, 3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[[0. , 1. ],
#          [2. , 3. ],
#          [4. , 5. ]],

#         [[6. , 7. ],
#          [8. , 9. ],
#          [10., 11.]]])

            

asin ( name=None ) asin¶

Arcsine Operator.

\[out = sin^{-1}(x)\]

Parameters

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

Returns

Tensor. Same shape and dtype as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.asin(x)
print(out)
# [-0.41151685 -0.20135792  0.10016742  0.30469265]

            

asinh ( name=None ) asinh¶

Asinh Activation Operator.

\[out = asinh(x)\]

Parameters

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

Returns

Tensor. Output of Asinh operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.asinh(x)
print(out)
# [-0.39003533, -0.19869010,  0.09983408,  0.29567307]

            

astype ( dtype ) astype¶

Notes:: The variable must be a api_fluid_Tensor

Cast a variable to a specified data type.

Parameters

self (Variable) – The source variable
dtype – The target data type

Returns

Variable with new dtype

Return type

Variable

Examples

In Static Graph Mode:

System Message: ERROR/3 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.fluid.layers.math_op_patch.monkey_patch_variable.<locals>.astype, line 17)

Error in “code-block” directive: maximum 1 argument(s) allowed, 32 supplied.

              .. code-block:: python
    import paddle
    import paddle.fluid as fluid
    paddle.enable_static()
    startup_prog = fluid.Program()
    main_prog = fluid.Program()
    with fluid.program_guard(startup_prog, main_prog):
        original_variable = paddle.static.data(name = "new_variable", shape=[2,2], dtype='float32')
        new_variable = original_variable.astype('int64')
        print("new var's dtype is: {}".format(new_variable.dtype))

             

In Dygraph Mode:

             import paddle.fluid as fluid
import numpy as np

x = np.ones([2, 2], np.float32)
with fluid.dygraph.guard():
    original_variable = fluid.dygraph.to_variable(x)
    print("original var's dtype is: {}, numpy dtype is {}".format(original_variable.dtype, original_variable.numpy().dtype))
    new_variable = original_variable.astype('int64')
    print("new var's dtype is: {}, numpy dtype is {}".format(new_variable.dtype, new_variable.numpy().dtype))

            

atan ( name=None ) atan¶

Arctangent Operator.

\[out = tan^{-1}(x)\]

Parameters

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

Returns

Tensor. Same shape and dtype as input x.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.atan(x)
print(out)
# [-0.38050638 -0.19739556  0.09966865  0.29145679]

            

atanh ( name=None ) atanh¶

Atanh Activation Operator.

\[out = atanh(x)\]

Parameters

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

Returns

Tensor. Output of Atanh operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.atanh(x)
print(out)
# [-0.42364895, -0.20273256,  0.10033535,  0.30951962]

            

bincount ( weights=None, minlength=0, name=None ) bincount¶

Computes frequency of each value in the input tensor.

Parameters

x (Tensor) – A Tensor with non-negative integer. Should be 1-D tensor.
weights (Tensor, optional) – Weight for each value in the input tensor. Should have the same shape as input. Default is None.
minlength (int, optional) – Minimum number of bins. Should be non-negative integer. Default is 0.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The tensor of frequency.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 1, 4, 5])
result1 = paddle.bincount(x)
print(result1) # [0, 2, 1, 0, 1, 1]

w = paddle.to_tensor([2.1, 0.4, 0.1, 0.5, 0.5])
result2 = paddle.bincount(x, weights=w)
print(result2) # [0., 2.19999981, 0.40000001, 0., 0.50000000, 0.50000000]

            

bitwise_and ( y, out=None, name=None ) bitwise_and¶

Apply bitwise_and on Tensor X and Y .

\[Out = X \& Y\]

Note

paddle.bitwise_and supports broadcasting. If you want know more about broadcasting, please refer to please refer to `Introduction to Tensor`_ .

Parameters

x (Tensor) – Input Tensor of bitwise_and . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
y (Tensor) – Input Tensor of bitwise_and . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
out (Tensor) – Result of bitwise_and . It is a N-D Tensor with the same data type of input Tensor.

Returns

Result of bitwise_and . It is a N-D Tensor with the same data type of input Tensor.

Return type

Tensor

Examples

             import paddle
x = paddle.to_tensor([-5, -1, 1])
y = paddle.to_tensor([4,  2, -3])
res = paddle.bitwise_and(x, y)
print(res)  # [0, 2, 1]

            

bitwise_not ( out=None, name=None ) bitwise_not¶

Apply bitwise_not on Tensor X.

\[Out = \sim X\]

Note

paddle.bitwise_not supports broadcasting. If you want know more about broadcasting, please refer to please refer to `Introduction to Tensor`_ .

Parameters

x (Tensor) – Input Tensor of bitwise_not . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
out (Tensor) – Result of bitwise_not . It is a N-D Tensor with the same data type of input Tensor.

Returns

Result of bitwise_not . It is a N-D Tensor with the same data type of input Tensor.

Return type

Tensor

Examples

             import paddle
x = paddle.to_tensor([-5, -1, 1])
res = paddle.bitwise_not(x)
print(res) # [4, 0, -2]

            

bitwise_or ( y, out=None, name=None ) bitwise_or¶

Apply bitwise_or on Tensor X and Y .

\[Out = X | Y\]

Note

paddle.bitwise_or supports broadcasting. If you want know more about broadcasting, please refer to please refer to `Introduction to Tensor`_ .

Parameters

x (Tensor) – Input Tensor of bitwise_or . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
y (Tensor) – Input Tensor of bitwise_or . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
out (Tensor) – Result of bitwise_or . It is a N-D Tensor with the same data type of input Tensor.

Returns

Result of bitwise_or . It is a N-D Tensor with the same data type of input Tensor.

Return type

Tensor

Examples

             import paddle
x = paddle.to_tensor([-5, -1, 1])
y = paddle.to_tensor([4,  2, -3])
res = paddle.bitwise_or(x, y)
print(res)  # [-1, -1, -3]

            

bitwise_xor ( y, out=None, name=None ) bitwise_xor¶

Apply bitwise_xor on Tensor X and Y .

\[Out = X ^\wedge Y\]

Note

paddle.bitwise_xor supports broadcasting. If you want know more about broadcasting, please refer to please refer to `Introduction to Tensor`_ .

Parameters

x (Tensor) – Input Tensor of bitwise_xor . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
y (Tensor) – Input Tensor of bitwise_xor . It is a N-D Tensor of bool, uint8, int8, int16, int32, int64.
out (Tensor) – Result of bitwise_xor . It is a N-D Tensor with the same data type of input Tensor.

Returns

Result of bitwise_xor . It is a N-D Tensor with the same data type of input Tensor.

Return type

Tensor

Examples

             import paddle
x = paddle.to_tensor([-5, -1, 1])
y = paddle.to_tensor([4,  2, -3])
res = paddle.bitwise_xor(x, y)
print(res) # [-1, -3, -4]

            

bmm ( y, name=None ) bmm¶

Applies batched matrix multiplication to two tensors.

Both of the two input tensors must be three-dementional and share the same batch size.

if x is a (b, m, k) tensor, y is a (b, k, n) tensor, the output will be a (b, m, n) tensor.

Parameters

x (Tensor) – The input Tensor.
y (Tensor) – The input Tensor.
name (str|None) – A name for this layer(optional). If set None, the layer will be named automatically.

Returns

The product Tensor.

Return type

Tensor

Examples

             import paddle

# In imperative mode:
# size x: (2, 2, 3) and y: (2, 3, 2)
x = paddle.to_tensor([[[1.0, 1.0, 1.0],
                    [2.0, 2.0, 2.0]],
                    [[3.0, 3.0, 3.0],
                    [4.0, 4.0, 4.0]]])
y = paddle.to_tensor([[[1.0, 1.0],[2.0, 2.0],[3.0, 3.0]],
                    [[4.0, 4.0],[5.0, 5.0],[6.0, 6.0]]])
out = paddle.bmm(x, y)
# Tensor(shape=[2, 2, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[[6. , 6. ],
#          [12., 12.]],

#         [[45., 45.],
#          [60., 60.]]])

            

broadcast_shape ( y_shape ) broadcast_shape¶

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`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.broadcast_shape, line 7); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

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

             import paddle

shape = paddle.broadcast_shape([2, 1, 3], [1, 3, 1])
# [2, 3, 3]

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

broadcast_tensors ( name=None ) broadcast_tensors¶

Broadcast a list of tensors following broadcast semantics

Note

If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.manipulation.broadcast_tensors, line 5); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

input (list|tuple) – input is a Tensor list or Tensor tuple which is with data type bool, float16, float32, float64, int32, int64. All the Tensors in input must have same data type. Currently we only support tensors with rank no greater than 5.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

list(Tensor), The list of broadcasted tensors following the same order as input.

Examples

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

            

broadcast_to ( shape, name=None ) broadcast_to¶

Broadcast the input tensor to a given shape.

Both the number of dimensions of x and the number of elements in shape should be less than or equal to 6. The dimension to broadcast to must have a value 0.

Parameters

x (Tensor) – The input tensor, its data type is bool, float16, float32, float64, int32 or int64.
shape (list|tuple|Tensor) – The result shape after broadcasting. The data type is int32. If shape is a list or tuple, all its elements should be integers or 0-D or 1-D Tensors with the data type int32. If shape is a Tensor, it should be an 1-D Tensor with the data type int32. The value -1 in shape means keeping the corresponding dimension unchanged.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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

Examples

             import paddle

data = paddle.to_tensor([1, 2, 3], dtype='int32')
out = paddle.broadcast_to(data, shape=[2, 3])
print(out)
# [[1, 2, 3], [1, 2, 3]]

            

bucketize ( sorted_sequence, out_int32=False, right=False, name=None ) bucketize¶

This API is used to find the index of the corresponding 1D tensor sorted_sequence in the innermost dimension based on the given x.

Parameters

x (Tensor) – An input N-D tensor value with type int32, int64, float32, float64.
sorted_sequence (Tensor) – An input 1-D tensor with type int32, int64, float32, float64. The value of the tensor monotonically increases in the innermost dimension.
out_int32 (bool, optional) – Data type of the output tensor which can be int32, int64. The default value is False, and it indicates that the output data type is int64.
right (bool, optional) – Find the upper or lower bounds of the sorted_sequence range in the innermost dimension based on the given x. If the value of the sorted_sequence is nan or inf, return the size of the innermost dimension. The default value is False and it shows the lower bounds.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

Tensor (the same sizes of the x), return the tensor of int32 if set out_int32 is True, otherwise return the tensor of int64.

Examples

             import paddle

sorted_sequence = paddle.to_tensor([2, 4, 8, 16], dtype='int32')
x = paddle.to_tensor([[0, 8, 4, 16], [-1, 2, 8, 4]], dtype='int32')
out1 = paddle.bucketize(x, sorted_sequence)
print(out1)
# Tensor(shape=[2, 4], dtype=int64, place=CPUPlace, stop_gradient=True,
#        [[0, 2, 1, 3],
#         [0, 0, 2, 1]])
out2 = paddle.bucketize(x, sorted_sequence, right=True)
print(out2)
# Tensor(shape=[2, 4], dtype=int64, place=CPUPlace, stop_gradient=True,
#        [[0, 3, 2, 4],
#         [0, 1, 3, 2]])
out3 = x.bucketize(sorted_sequence)
print(out3)
# Tensor(shape=[2, 4], dtype=int64, place=CPUPlace, stop_gradient=True,
#        [[0, 2, 1, 3],
#         [0, 0, 2, 1]])
out4 = x.bucketize(sorted_sequence, right=True)
print(out4)
# Tensor(shape=[2, 4], dtype=int64, place=CPUPlace, stop_gradient=True,
#        [[0, 3, 2, 4],
#         [0, 1, 3, 2]])

            

cast ( dtype ) cast¶

Take in the Tensor x with x.dtype and cast it to the output with dtype. It’s meaningless if the output dtype equals the input dtype, but it’s fine if you do so.

Parameters

x (Tensor) – An input N-D Tensor with data type bool, float16, float32, float64, int32, int64, uint8.
dtype (np.dtype|str) – Data type of the output: bool, float16, float32, float64, int8, int32, int64, uint8.

Returns

Tensor, A Tensor with the same shape as input’s.

Examples

             import paddle

x = paddle.to_tensor([2, 3, 4], 'float64')
y = paddle.cast(x, 'uint8')

cdist ( y, p=2.0, compute_mode='use_mm_for_euclid_dist_if_necessary', name=None ) cdist¶

Compute the p-norm distance between each pair of the two collections of inputs.

This function is equivalent to scipy.spatial.distance.cdist(input,’minkowski’, p=p) if $p \in (0, \infty)$. When $p = 0$ it is equivalent to scipy.spatial.distance.cdist(input, ‘hamming’) * M. When $p = \infty$, the closest scipy function is scipy.spatial.distance.cdist(xn, lambda x, y: np.abs(x - y).max()).

Parameters

x (Tensor) – A tensor with shape $B \times P \times M$.
y (Tensor) – A tensor with shape $B \times R \times M$.
p (float, optional) – The value for the p-norm distance to calculate between each vector pair. Default: $2.0$.
compute_mode (str, optional) –
The mode for compute distance.
- use_mm_for_euclid_dist_if_necessary , for p = 2.0 and (P > 25 or R > 25), it will use matrix multiplication to calculate euclid distance if possible.
- use_mm_for_euclid_dist , for p = 2.0, it will use matrix multiplication to calculate euclid distance.
- donot_use_mm_for_euclid_dist , it will not use matrix multiplication to calculate euclid distance.
Default: use_mm_for_euclid_dist_if_necessary.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, the dtype is same as input tensor.

If x has shape $B \times P \times M$ and y has shape $B \times R \times M$ then the output will have shape $B \times P \times R$.

Examples

             import paddle
x = paddle.to_tensor([[0.9041,  0.0196], [-0.3108, -2.4423], [-0.4821,  1.059]], dtype=paddle.float32)
y = paddle.to_tensor([[-2.1763, -0.4713], [-0.6986,  1.3702]], dtype=paddle.float32)
distance = paddle.cdist(x, y)
print(distance)
# Tensor(shape=[3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
# [[3.1193, 2.0959], [2.7138, 3.8322], [2.2830, 0.3791]])

            

ceil ( name=None ) ceil¶

Ceil Operator. Computes ceil of x element-wise.

\[out = \left \lceil x \right \rceil\]

Parameters

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

Returns

Tensor. Output of Ceil operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.ceil(x)
print(out)
# [-0. -0.  1.  1.]

            

ceil_ ( name=None ) ceil_¶: Inplace version of ceil API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_ceil.

cholesky ( upper=False, name=None ) cholesky¶

Computes the Cholesky decomposition of one symmetric positive-definite matrix or batches of symmetric positive-definite matrice.

If upper is True, the decomposition has the form $A = U^{T}U$ , and the returned matrix $U$ is upper-triangular. Otherwise, the decomposition has the form $A = LL^{T}$ , and the returned matrix $L$ is lower-triangular.

Parameters

x (Tensor) – The input tensor. Its shape should be [*, M, M], where * is zero or more batch dimensions, and matrices on the inner-most 2 dimensions all should be symmetric positive-definite. Its data type should be float32 or float64.
upper (bool) – The flag indicating whether to return upper or lower triangular matrices. Default: False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, A Tensor with same shape and data type as x. It represents triangular matrices generated by Cholesky decomposition.

Examples

             import paddle

a = paddle.rand([3, 3], dtype="float32")
a_t = paddle.transpose(a, [1, 0])
x = paddle.matmul(a, a_t) + 1e-03

out = paddle.linalg.cholesky(x, upper=False)
print(out)

            

cholesky_solve ( y, upper=False, name=None ) cholesky_solve¶

Solves a linear system of equations A @ X = B, given A’s Cholesky factor matrix u and matrix B.

Input x and y is 2D matrices or batches of 2D matrices. If the inputs are batches, the outputs is also batches.

Parameters

x (Tensor) – The input matrix which is upper or lower triangular Cholesky factor of square matrix A. Its shape should be [*, M, M], where * is zero or more batch dimensions. Its data type should be float32 or float64.
y (Tensor) – Multiple right-hand sides of system of equations. Its shape should be [*, M, K], where * is zero or more batch dimensions. Its data type should be float32 or float64.
upper (bool, optional) – whether to consider the Cholesky factor as a lower or upper triangular matrix. Default: False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The solution of the system of equations. Its data type is the same as that of x.

Return type

Tensor

Examples

             import paddle

u = paddle.to_tensor([[1, 1, 1],
                        [0, 2, 1],
                        [0, 0,-1]], dtype="float64")
b = paddle.to_tensor([[0], [-9], [5]], dtype="float64")
out = paddle.linalg.cholesky_solve(b, u, upper=True)

print(out)
# [-2.5, -7, 9.5]

            

chunk ( chunks, axis=0, name=None ) chunk¶

Split the input tensor into multiple sub-Tensors.

Parameters

x (Tensor) – A N-D Tensor. The data type is bool, float16, float32, float64, int32 or int64.
chunks (int) – The number of tensor to be split along the certain axis.
axis (int|Tensor, optional) – The axis along which to split, it can be a integer or a 0-D Tensor with shape [] and data type int32 or int64. If :math::axis < 0, the axis to split along is $rank(x) + axis$. Default is 0.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

list(Tensor), The list of segmented Tensors.

Examples

             import paddle

x = paddle.rand([3, 9, 5])

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


# axis is negative, the real axis is (rank(x) + axis) which real
# value is 1.
out0, out1, out2 = paddle.chunk(x, chunks=3, axis=-2)
# out0.shape [3, 3, 5]
# out1.shape [3, 3, 5]
# out2.shape [3, 3, 5]

            

clip ( min=None, max=None, name=None ) clip¶

This operator clip all elements in input into the range [ min, max ] and return a resulting tensor as the following equation:

\[Out = MIN(MAX(x, min), max)\]

Parameters

x (Tensor) – An N-D Tensor with data type float16, float32, float64, int32 or int64.
min (float|int|Tensor, optional) – The lower bound with type float , int or a 0-D Tensor with shape [] and type int32, float16, float32, float64.
max (float|int|Tensor, optional) – The upper bound with type float, int or a 0-D Tensor with shape [] and type int32, float16, float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

A Tensor with the same data type and data shape as input.

Return type

Tensor

Examples

             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)
out2 = paddle.clip(x1, min=2.5)
print(out1)
# [[3.5, 3.5]
# [4.5, 5.0]]
print(out2)
# [[2.5, 3.5]
# [[4.5, 6.4]

            

clip_ ( min=None, max=None, name=None ) clip_¶: Inplace version of clip API, the output Tensor will be inplaced with input x. Please refer to api_tensor_clip.

concat ( axis=0, name=None ) concat¶

Concatenates the input along the axis. It doesn’t support 0-D Tensor because it requires a certain axis, and 0-D Tensor doesn’t have any axis.

Parameters

x (list|tuple) – x is a Tensor list or Tensor tuple which is with data type bool, float16, float32, float64, int32, int64, int8, uint8. All the Tensors in x must have same data type.
axis (int|Tensor, optional) – Specify the axis to operate on the input Tensors. Tt should be integer or 0-D int Tensor with shape []. The effective range is [-R, R), where R is Rank(x). When axis < 0, it works the same way as axis+R. Default is 0.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, A Tensor with the same data type as x.

Examples

             import paddle

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

            

cond ( p=None, name=None ) cond¶

Computes the condition number of a matrix or batches of matrices with respect to a matrix norm p.

Parameters

x (Tensor) – The input tensor could be tensor of shape (*, m, n) where * is zero or more batch dimensions for p in (2, -2), or of shape (*, n, n) where every matrix is invertible for any supported p. And the input data type could be float32 or float64.
p (float|string, optional) – Order of the norm. Supported values are fro, nuc, 1, -1, 2, -2, inf, -inf. Default value is None, meaning that the order of the norm is 2.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

computing results of condition number, its data type is the same as input Tensor x.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[1., 0, -1], [0, 1, 0], [1, 0, 1]])

# compute conditional number when p is None
out = paddle.linalg.cond(x)
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        1.41421342)

# compute conditional number when order of the norm is 'fro'
out_fro = paddle.linalg.cond(x, p='fro')
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        3.16227770)

# compute conditional number when order of the norm is 'nuc'
out_nuc = paddle.linalg.cond(x, p='nuc')
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        9.24263859)

# compute conditional number when order of the norm is 1
out_1 = paddle.linalg.cond(x, p=1)
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        2.)

# compute conditional number when order of the norm is -1
out_minus_1 = paddle.linalg.cond(x, p=-1)
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        1.)

# compute conditional number when order of the norm is 2
out_2 = paddle.linalg.cond(x, p=2)
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        1.41421342)

# compute conditional number when order of the norm is -1
out_minus_2 = paddle.linalg.cond(x, p=-2)
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        0.70710683)

# compute conditional number when order of the norm is inf
out_inf = paddle.linalg.cond(x, p=float("inf"))
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        2.)

# compute conditional number when order of the norm is -inf
out_minus_inf = paddle.linalg.cond(x, p=-float("inf"))
# Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        1.)

a = paddle.randn([2, 4, 4])
# Tensor(shape=[2, 4, 4], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[[-0.06784091, -0.07095790,  1.31792855, -0.58959651],
#          [ 0.20818676, -0.85640615, -0.89998871, -1.47439921],
#          [-0.49132481,  0.42250812, -0.77383220, -2.19794774],
#          [-0.33551720, -1.70003879, -1.09795380, -0.63737559]],

#         [[ 1.12026262, -0.16119350, -1.21157813,  2.74383283],
#          [-0.15999718,  0.18798758, -0.69392562,  1.35720372],
#          [-0.53013402, -2.26304483,  1.40843511, -1.02288902],
#          [ 0.69533503,  2.05261683, -0.02251151, -1.43127477]]])

a_cond_fro = paddle.linalg.cond(a, p='fro')
# Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [8.86691189 , 75.23817444])

b = paddle.randn([2, 3, 4])
# Tensor(shape=[2, 3, 4], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[[-0.43754861,  1.80796063, -0.78729683, -1.82264030],
#          [-0.27670753,  0.06620564,  0.29072434, -0.31155765],
#          [ 0.34123746, -0.05444612,  0.05001324, -1.46877074]],

#         [[-0.64331555, -1.51103854, -1.26277697, -0.68024760],
#          [ 2.59375715, -1.06665540,  0.96575671, -0.73330832],
#          [-0.47064447, -0.23945692, -0.95150250, -1.07125998]]])
b_cond_2 = paddle.linalg.cond(b, p=2)
# Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [6.64228773, 3.89068866])

            

conj ( name=None ) conj¶

This function computes the conjugate of the Tensor elementwisely.

Parameters

x (Tensor) – The input Tensor which hold the complex numbers. Optional data types are:float16, complex64, complex128, float32, float64, int32 or int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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.

Return type

out (Tensor)

Examples

             import paddle

data=paddle.to_tensor([[1+1j, 2+2j, 3+3j], [4+4j, 5+5j, 6+6j]])
#Tensor(shape=[2, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
#       [[(1+1j), (2+2j), (3+3j)],
#        [(4+4j), (5+5j), (6+6j)]])

conj_data=paddle.conj(data)
#Tensor(shape=[2, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
#       [[(1-1j), (2-2j), (3-3j)],
#        [(4-4j), (5-5j), (6-6j)]])

            

corrcoef ( rowvar=True, name=None ) corrcoef¶

A correlation coefficient matrix indicate the correlation of each pair variables in the input matrix. For example, for an N-dimensional samples X=[x1,x2,…xN]T, then the correlation coefficient matrix element Rij is the correlation of xi and xj. The element Rii is the covariance of xi itself.

The relationship between the correlation coefficient matrix R and the covariance matrix C, is

\[R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }\]

The values of R are between -1 and 1.

Parameters

x (Tensor) – A N-D(N<=2) Tensor containing multiple variables and observations. By default, each row of x represents a variable. Also see rowvar below.
rowvar (Bool, optional) – If rowvar is True (default), then each row represents a variable, with observations in the columns. Default: True.
name (str, optional) – Name of the output. Default is None. It’s used to print debug info for developers. Details: Name.

Returns

The correlation coefficient matrix of the variables.

Examples

             import paddle

xt = paddle.rand((3,4))
print(paddle.linalg.corrcoef(xt))

# Tensor(shape=[3, 3], dtype=float32, place=Place(cpu), stop_gradient=True,
# [[ 1.        , -0.73702252,  0.66228950],
# [-0.73702258,  1.        , -0.77104872],
# [ 0.66228974, -0.77104825,  1.        ]])

            

cos ( name=None ) cos¶

Cosine Operator. Computes cosine of x element-wise.

Input range is (-inf, inf) and output range is [-1,1].

\[out = cos(x)\]

Parameters

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

Returns

Tensor. Output of Cos operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.cos(x)
print(out)
# [0.92106099 0.98006658 0.99500417 0.95533649]

            

cosh ( name=None ) cosh¶

Cosh Activation Operator.

Input range (-inf, inf), output range (1, inf).

\[out = \frac{exp(x)+exp(-x)}{2}\]

Parameters

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

Returns

Tensor. Output of Cosh operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.cosh(x)
print(out)
# [1.08107237 1.02006676 1.00500417 1.04533851]

            

count_nonzero ( axis=None, keepdim=False, name=None ) count_nonzero¶

Counts the number of non-zero values in the tensor x along the specified axis.

Parameters

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 None, sum all elements of x and return a Tensor with a single element, otherwise must be in the range $[-rank(x), rank(x))$. If $axis[i] < 0$, the dimension to reduce is $rank + axis[i]$.
keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result Tensor will have one fewer dimension than the x unless keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Results of count operation on the specified axis of input Tensor x, it’s data type is ‘int64’.

Return type

Tensor

Examples

             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)
# 3
out2 = paddle.count_nonzero(x, axis=0)
# [0, 1, 2]
out3 = paddle.count_nonzero(x, axis=0, keepdim=True)
# [[0, 1, 2]]
out4 = paddle.count_nonzero(x, axis=1)
# [2, 1, 0]
out5 = paddle.count_nonzero(x, axis=1, keepdim=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])
# [3, 6]
out7 = paddle.count_nonzero(y, axis=[0, 1])
# [1, 3, 5]

            

cov ( rowvar=True, ddof=True, fweights=None, aweights=None, name=None ) cov¶

Estimate the covariance matrix of the input variables, given data and weights.

A covariance matrix is a square matrix, indicate the covariance of each pair variables in the input matrix. For example, for an N-dimensional samples X=[x1,x2,…xN]T, then the covariance matrix element Cij is the covariance of xi and xj. The element Cii is the variance of xi itself.

Parameters

x (Tensor) – A N-D(N<=2) Tensor containing multiple variables and observations. By default, each row of x represents a variable. Also see rowvar below.
rowvar (Bool, optional) – If rowvar is True (default), then each row represents a variable, with observations in the columns. Default: True
ddof (Bool, optional) – If ddof=True will return the unbiased estimate, and ddof=False will return the simple average. Default: True
fweights (Tensor, optional) – 1-D Tensor of integer frequency weights; The number of times each observation vector should be repeated. Default: None
aweights (Tensor, optional) – 1-D Tensor of observation vector weights. How important of the observation vector, larger data means this element is more important. Default: None
name (str, optional) – Name of the output. Default is None. It’s used to print debug info for developers. Details: Name

Returns

The covariance matrix Tensor of the variables.

Return type

Tensor

Examples:

             import paddle

xt = paddle.rand((3, 4))
paddle.linalg.cov(xt)

'''
Tensor(shape=[3, 3], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
    [[0.07918842, 0.06127326, 0.01493049],
        [0.06127326, 0.06166256, 0.00302668],
        [0.01493049, 0.00302668, 0.01632146]])
'''

            

cpu ( ) cpu¶: Variable should not have cpu() and cuda() interface. But this interface can greatly facilitate dy2static. We do nothing here.

create_parameter ( dtype, name=None, attr=None, is_bias=False, default_initializer=None ) [source] create_parameter¶

This function creates a parameter. The parameter is a learnable variable, which can have gradient, and can be optimized.

Note

This is a very low-level API. This API is useful when you create operator by your self, instead of using layers.

Parameters

shape (list of int) – Shape of the parameter
dtype (str) – Data type of the parameter
name (str, optional) – For detailed information, please refer to Name . Usually name is no need to set and None by default.
attr (ParamAttr, optional) – Attributes of the parameter
is_bias (bool, optional) – This can affect which default initializer is chosen when default_initializer is None. If is_bias, initializer.Constant(0.0) will be used. Otherwise, Xavier() will be used.
default_initializer (Initializer, optional) – Initializer for the parameter

Returns

The created parameter.

Examples

             import paddle
paddle.enable_static()
W = paddle.create_parameter(shape=[784, 200], dtype='float32')

            

create_tensor ( name=None, persistable=False ) create_tensor¶

Create a variable, which will hold a Tensor with data type dtype.

Parameters

dtype (string|numpy.dtype) – the data type of Tensor to be created, the data type is bool, float16, float32, float64, int8, int16, int32 and int64.
name (string, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name
persistable (bool) – Set the persistable flag of the create tensor. default value is False.

Returns

The tensor to be created according to dtype.

Return type

Variable

Examples

             import paddle
tensor = paddle.tensor.create_tensor(dtype='float32')

cross ( y, axis=9, name=None ) cross¶

Computes the cross product between two tensors along an axis.

Inputs must have the same shape, and the length of their axes should be equal to 3. If axis is not given, it defaults to the first axis found with the length 3.

Parameters

x (Tensor) – The first input tensor, the data type is float16, float32, float64, int32, int64.
y (Tensor) – The second input tensor, the data type is float16, float32, float64, int32, int64.
axis (int, optional) – The axis along which to compute the cross product. It defaults to be 9 which indicates using the first axis found with the length 3.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor. A Tensor with same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 1.0, 1.0],
                      [2.0, 2.0, 2.0],
                      [3.0, 3.0, 3.0]])
y = paddle.to_tensor([[1.0, 1.0, 1.0],
                      [1.0, 1.0, 1.0],
                      [1.0, 1.0, 1.0]])

z1 = paddle.cross(x, y)
# [[-1. -1. -1.]
#  [ 2.  2.  2.]
#  [-1. -1. -1.]]

z2 = paddle.cross(x, y, axis=1)
# [[0. 0. 0.]
#  [0. 0. 0.]
#  [0. 0. 0.]]

            

cuda ( ) cuda¶: Variable should not have cpu() and cuda() interface. But this interface can greatly facilitate dy2static. We do nothing here.

cumprod ( dim=None, dtype=None, name=None ) cumprod¶

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.

Parameters

x (Tensor) – the input tensor need to be cumproded.
dim (int, optional) – the dimension along which the input tensor will be accumulated. It need to be in the range of [-x.rank, x.rank), where x.rank means the dimensions of the input tensor x and -1 means the last dimension.
dtype (str, optional) – The data type of the output tensor, can be 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the result of cumprod operator.

Examples

             import paddle

data = paddle.arange(12)
data = paddle.reshape(data, (3, 4))
# [[ 0  1  2  3 ]
#  [ 4  5  6  7 ]
#  [ 8  9  10 11]]

y = paddle.cumprod(data, dim=0)
# [[ 0  1   2   3]
#  [ 0  5  12  21]
#  [ 0 45 120 231]]

y = paddle.cumprod(data, dim=-1)
# [[ 0   0   0    0]
#  [ 4  20 120  840]
#  [ 8  72 720 7920]]

y = paddle.cumprod(data, dim=1, dtype='float64')
# [[ 0.   0.   0.    0.]
#  [ 4.  20. 120.  840.]
#  [ 8.  72. 720. 7920.]]

print(y.dtype)
# paddle.float64

            

cumsum ( axis=None, dtype=None, name=None ) cumsum¶

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.

Parameters

x (Tensor) – The input tensor needed to be cumsumed.
axis (int, optional) – The dimension to accumulate along. -1 means the last dimension. The default (None) is to compute the cumsum over the flattened array.
dtype (str, optional) – The data type of the output tensor, can be float16, float32, float64, int32, int64. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. The default value is None.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the result of cumsum operator.

Examples

             import paddle

data = paddle.arange(12)
data = paddle.reshape(data, (3, 4))

y = paddle.cumsum(data)
# [ 0  1  3  6 10 15 21 28 36 45 55 66]

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

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

y = paddle.cumsum(data, dtype='float64')
print(y.dtype)
# paddle.float64

            

cumulative_trapezoid ( x=None, dx=None, axis=- 1, name=None ) cumulative_trapezoid¶

Integrate along the given axis using the composite trapezoidal rule. Use the cumsum method

Parameters

y (Tensor) – Input tensor to integrate. It’s data type should be float16, float32, float64.
x (Tensor, optional) – The sample points corresponding to the y values, the same type as y. It is known that the size of y is [d_1, d_2, … , d_n] and $axis=k$, then the size of x can only be [d_k] or [d_1, d_2, … , d_n ]. If x is None, the sample points are assumed to be evenly spaced dx apart. The default is None.
dx (float, optional) – The spacing between sample points when x is None. If neither x nor dx is provided then the default is $dx = 1$.
axis (int, optional) – The axis along which to integrate. The default is -1.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, Definite integral of y is N-D tensor as approximated along a single axis by the trapezoidal rule. The result is an N-D tensor.

Examples

             import paddle

y = paddle.to_tensor([4, 5, 6], dtype='float32')

print(paddle.cumulative_trapezoid(y))
# Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [4.50000000, 10.       ])

print(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')

print(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')

print(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')

print(paddle.cumulative_trapezoid(y, axis=0))
# Tensor(shape=[1, 3], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[1.50000000, 2.50000000, 3.50000000]])
print(paddle.cumulative_trapezoid(y, axis=1))
# Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[0.50000000, 2.        ],
#         [3.50000000, 8.        ]])

            

deg2rad ( name=None ) deg2rad¶

Convert each of the elements of input x from degrees to angles in radians.

\[deg2rad(x)=\pi * x / 180\]

Parameters

x (Tensor) – An N-D Tensor, the data type is float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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).

Return type

out (Tensor)

Examples

             import paddle

x1 = paddle.to_tensor([180.0, -180.0, 360.0, -360.0, 90.0, -90.0])
result1 = paddle.deg2rad(x1)
print(result1)
# Tensor(shape=[6], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#         [3.14159274, -3.14159274,  6.28318548, -6.28318548,  1.57079637,
#           -1.57079637])

x2 = paddle.to_tensor(180)
result2 = paddle.deg2rad(x2)
print(result2)
# Tensor(shape=[], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        3.14159274)

            

diagonal ( offset=0, axis1=0, axis2=1, name=None ) diagonal¶

Computes the diagonals of the input tensor x.

If x is 2D, returns the diagonal. If x has larger dimensions, diagonals be taken from the 2D planes specified by axis1 and axis2. By default, the 2D planes formed by the first and second axis 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.

Parameters

x (Tensor) – The input tensor x. Must be at least 2-dimensional. The input data type should be bool, int32, int64, float16, float32, float64.
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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

a partial view of input tensor in specify two dimensions, the output data type is the same as input data type.

Return type

Tensor

Examples

             import paddle

x = paddle.rand([2,2,3],'float32')
print(x)
# Tensor(shape=[2, 2, 3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        [[[0.45661032, 0.03751532, 0.90191704],
#          [0.43760979, 0.86177313, 0.65221709]],

#         [[0.17020577, 0.00259554, 0.28954273],
#          [0.51795638, 0.27325270, 0.18117726]]])

out1 = paddle.diagonal(x)
print(out1)
#Tensor(shape=[3, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [[0.45661032, 0.51795638],
#        [0.03751532, 0.27325270],
#        [0.90191704, 0.18117726]])

out2 = paddle.diagonal(x, offset=0, axis1=2, axis2=1)
print(out2)
#Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [[0.45661032, 0.86177313],
#        [0.17020577, 0.27325270]])

out3 = paddle.diagonal(x, offset=1, axis1=0, axis2=1)
print(out3)
#Tensor(shape=[3, 1], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [[0.43760979],
#        [0.86177313],
#        [0.65221709]])

out4 = paddle.diagonal(x, offset=0, axis1=1, axis2=2)
print(out4)
#Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [[0.45661032, 0.86177313],
#        [0.17020577, 0.27325270]])

            

diff ( n=1, axis=- 1, prepend=None, append=None, name=None ) diff¶

Computes the n-th forward difference along the given axis. The first-order differences is computed by using the following formula:

\[out[i] = x[i+1] - x[i]\]

Higher-order differences are computed by using paddle.diff() recursively. Only n=1 is currently supported.

Parameters

x (Tensor) – The input tensor to compute the forward difference on, the data type is float16, float32, float64, bool, int32, int64.
n (int, optional) – The number of times to recursively compute the difference. Only support n=1. Default:1
axis (int, optional) – The axis to compute the difference along. Default:-1
prepend (Tensor, 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, 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output tensor with same dtype with x.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 4, 5, 2])
out = paddle.diff(x)
print(out)
# out:
# [3, 1, -3]

y = paddle.to_tensor([7, 9])
out = paddle.diff(x, append=y)
print(out)
# out:
# [3, 1, -3, 5, 2]

z = paddle.to_tensor([[1, 2, 3], [4, 5, 6]])
out = paddle.diff(z, axis=0)
print(out)
# out:
# [[3, 3, 3]]
out = paddle.diff(z, axis=1)
print(out)
# out:
# [[1, 1], [1, 1]]

            

digamma ( name=None ) digamma¶

Calculates the digamma of the given input tensor, element-wise.

\[Out = \Psi(x) = \frac{ \Gamma^{'}(x) }{ \Gamma(x) }\]

Parameters

x (Tensor) – Input Tensor. Must be one of the following types: float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the digamma of the input Tensor, the shape and data type is the same with input.

Examples

             import paddle

data = paddle.to_tensor([[1, 1.5], [0, -2.2]], dtype='float32')
res = paddle.digamma(data)
print(res)
# Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [[-0.57721591,  0.03648996],
#        [ nan       ,  5.32286835]])

            

dist ( y, p=2, name=None ) dist¶

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.search.where, line 45); backlink

Duplicate explicit target name: “introduction to tensor”.

Returns the p-norm of (x - y). It is not a norm in a strict sense, only as a measure of distance. The shapes of x and y must be broadcastable. The definition is as follows, for details, please refer to the Introduction to Tensor:

Each input has at least one dimension.
Match the two input dimensions from back to front, the dimension sizes must either be equal, one of them is 1, or one of them does not exist.

Where, z = x - y, the shapes of x and y are broadcastable, then the shape of z can be obtained as follows:

1. If the number of dimensions of x and y are not equal, prepend 1 to the dimensions of the tensor with fewer dimensions.

For example, The shape of x is [8, 1, 6, 1], the shape of y is [7, 1, 5], prepend 1 to the dimension of y.

x (4-D Tensor): 8 x 1 x 6 x 1

y (4-D Tensor): 1 x 7 x 1 x 5

2. Determine the size of each dimension of the output z: choose the maximum value from the two input dimensions.

z (4-D Tensor): 8 x 7 x 6 x 5

If the number of dimensions of the two inputs are the same, the size of the output can be directly determined in step 2. When p takes different values, the norm formula is as follows:

When p = 0, defining $0^0=0$, the zero-norm of z is simply the number of non-zero elements of z.

\[\begin{split}||z||_{0}=\lim_{p \\rightarrow 0}\sum_{i=1}^{m}|z_i|^{p}\end{split}\]

When p = inf, the inf-norm of z is the maximum element of the absolute value of z.

\[||z||_\infty=\max_i |z_i|\]

When p = -inf, the negative-inf-norm of z is the minimum element of the absolute value of z.

\[||z||_{-\infty}=\min_i |z_i|\]

Otherwise, the p-norm of z follows the formula,

\[\begin{split}||z||_{p}=(\sum_{i=1}^{m}|z_i|^p)^{\\frac{1}{p}}\end{split}\]

Parameters

x (Tensor) – 1-D to 6-D Tensor, its data type is float32 or float64.
y (Tensor) – 1-D to 6-D Tensor, its data type is float32 or float64.
p (float, optional) – The norm to be computed, its data type is float32 or float64. Default: 2.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

Tensor that is the p-norm of (x - y).

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[3, 3],[3, 3]], dtype="float32")
y = paddle.to_tensor([[3, 3],[3, 1]], dtype="float32")
out = paddle.dist(x, y, 0)
print(out) # out = 1.

out = paddle.dist(x, y, 2)
print(out) # out = 2.

out = paddle.dist(x, y, float("inf"))
print(out) # out = 2.

out = paddle.dist(x, y, float("-inf"))
print(out) # out = 0.

            

divide ( y, name=None ) divide¶

Divide two tensors element-wise. The equation is:

\[out = x / y\]

Note

paddle.divide supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.divide, line 10); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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)  # [2., 0.6, 2.]

            

dot ( y, name=None ) dot¶

This operator calculates inner product for vectors.

Note

Support 1-d and 2-d Tensor. When it is 2d, the first dimension of this matrix is the batch dimension, which means that the vectors of multiple batches are dotted.

Parameters

x (Tensor) – 1-D or 2-D Tensor. Its dtype should be float32, float64, int32, int64
y (Tensor) – 1-D or 2-D Tensor. Its dtype soulde be float32, float64, int32, int64
name (str, optional) – Name of the output. Default is None. It’s used to print debug info for developers. Details: Name

Returns

the calculated result Tensor.

Return type

Tensor

Examples:

             import paddle

# 1-D Tensor * 1-D Tensor
x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([4, 5, 6])
z = paddle.dot(x, y)
print(z)  # 32

# 2-D Tensor * 2-D Tensor
x = paddle.to_tensor([[1, 2, 3], [2, 4, 6]])
y = paddle.to_tensor([[4, 5, 6], [4, 5, 6]])
z = paddle.dot(x, y)
print(z)  # [32, 64]

            

eig ( name=None ) eig¶

Performs the eigenvalue decomposition of a square matrix or a batch of square matrices.

Note

If the matrix is a Hermitian or a real symmetric matrix, please use paddle.linalg.eigh instead, which is much faster.
If only eigenvalues is needed, please use paddle.linalg.eigvals instead.
If the matrix is of any shape, please use paddle.linalg.svd.
This API is only supported on CPU device.
The output datatype is always complex for both real and complex input.

Parameters

x (Tensor) – A tensor with shape math:[*, N, N], The data type of the x should be one of float32, float64, compplex64 or complex128.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

A tensor with shape math:[*, N] refers to the eigen values. Eigenvectors(Tensors): A tensor with shape math:[*, N, N] refers to the eigen vectors.

Return type

Eigenvalues(Tensors)

Examples

             import paddle

paddle.device.set_device("cpu")

x = paddle.to_tensor([[1.6707249, 7.2249975, 6.5045543],
                   [9.956216,  8.749598,  6.066444 ],
                   [4.4251957, 1.7983172, 0.370647 ]])
w, v = paddle.linalg.eig(x)
print(v)
# Tensor(shape=[3, 3], dtype=complex128, place=CPUPlace, stop_gradient=False,
#       [[(-0.5061363550800655+0j) , (-0.7971760990842826+0j) ,
#         (0.18518077798279986+0j)],
#        [(-0.8308237755993192+0j) ,  (0.3463813401919749+0j) ,
#         (-0.6837005269141947+0j) ],
#        [(-0.23142567697893396+0j),  (0.4944999840400175+0j) ,
#         (0.7058765252952796+0j) ]])

print(w)
# Tensor(shape=[3], dtype=complex128, place=CPUPlace, stop_gradient=False,
#       [ (16.50471283351188+0j)  , (-5.5034820550763515+0j) ,
#         (-0.21026087843552282+0j)])

            

eigvals ( name=None ) eigvals¶

Compute the eigenvalues of one or more general matrices.

Warning

The gradient kernel of this operator does not yet developed. If you need back propagation through this operator, please replace it with paddle.linalg.eig.

Parameters

x (Tensor) – A square matrix or a batch of square matrices whose eigenvalues will be computed. Its shape should be [*, M, M], where * is zero or more batch dimensions. Its data type should be float32, float64, complex64, or complex128.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, A tensor containing the unsorted eigenvalues which has the same batch dimensions with x. The eigenvalues are complex-valued even when x is real.

Examples

             import paddle

paddle.set_device("cpu")
paddle.seed(1234)

x = paddle.rand(shape=[3, 3], dtype='float64')
# [[0.02773777, 0.93004224, 0.06911496],
#  [0.24831591, 0.45733623, 0.07717843],
#  [0.48016702, 0.14235102, 0.42620817]])

print(paddle.linalg.eigvals(x))
# [(-0.27078833542132674+0j), (0.29962280156230725+0j), (0.8824477020120244+0j)] #complex128

            

eigvalsh ( UPLO='L', name=None ) eigvalsh¶

Computes the eigenvalues of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.

Parameters

x (Tensor) – A tensor with shape $[*, M, M]$ , where * is zero or greater batch dimension. The data type of the input Tensor x should be one of float32, float64, complex64, complex128.
UPLO (str, optional) – Lower triangular part of a (‘L’, default) or the upper triangular part (‘U’).
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The tensor eigenvalues in ascending order.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[1, -2j], [2j, 5]])
out_value = paddle.eigvalsh(x, UPLO='L')
print(out_value)
# Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [0.17157286, 5.82842731])

            

equal ( y, name=None ) equal¶

This layer returns the truth value of $x == y$ elementwise.

Note

The output has no gradient.

Parameters

x (Tensor) – Tensor, data type is bool, float16, float32, float64, int32, int64.
y (Tensor) – Tensor, data type is bool, float16, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

output Tensor, it’s shape is the same as the input’s Tensor, and the data type is bool. The result of this op is stop_gradient.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 3, 2])
result1 = paddle.equal(x, y)
print(result1)  # result1 = [True False False]

            

equal_all ( y, name=None ) equal_all¶

Returns the truth value of $x == y$. True if two inputs have the same elements, False otherwise.

Note

The output has no gradient.

Parameters

x (Tensor) – Tensor, data type is bool, float32, float64, int32, int64.
y (Tensor) – Tensor, data type is bool, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

output Tensor, data type is bool, value is [False] or [True].

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 2, 3])
z = paddle.to_tensor([1, 4, 3])
result1 = paddle.equal_all(x, y)
print(result1) # result1 = True
result2 = paddle.equal_all(x, z)
print(result2) # result2 = False

            

erf ( name=None ) erf¶

Erf Operator For more details, see Error function.

Equation:: \[out = \frac{2}{\sqrt{\pi}} \int_{0}^{x}e^{- \eta^{2}}d\eta\]

Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output of Erf, dtype: float32 or float64, the same as the input, shape: the same as the input.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.erf(x)
print(out)
# [-0.42839236 -0.22270259  0.11246292  0.32862676]

            

erfinv ( name=None ) erfinv¶

The inverse error function of x. Please refer to erf

\[erfinv(erf(x)) = x.\]

Parameters

x (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 Name.

Returns

out (Tensor), an N-D Tensor, the shape and data type is the same with input.

Example

             import paddle

x = paddle.to_tensor([0, 0.5, -1.], dtype="float32")
out = paddle.erfinv(x)
# out: [0, 0.4769, -inf]

erfinv_ ( name=None ) erfinv_¶: Inplace version of erfinv API, the output Tensor will be inplaced with input x. Please refer to api_tensor_erfinv.

exp ( name=None ) exp¶

Computes exp of x element-wise with a natural number e as the base.

\[out = e^x\]

Parameters

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

Returns

Tensor. Output of Exp operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.exp(x)
print(out)
# [0.67032005 0.81873075 1.10517092 1.34985881]

            

exp_ ( name=None ) exp_¶: Inplace version of exp API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_exp.

expand ( shape, name=None ) expand¶

Expand the input tensor to a given shape.

Both the number of dimensions of x and the number of elements in shape should be less than or equal to 6. And the number of dimensions of x should be less than the number of elements in shape. The dimension to expand must have a value 0.

Parameters

x (Tensor) – The input Tensor, its data type is bool, float32, float64, int32 or int64.
shape (list|tuple|Tensor) – The result shape after expanding. The data type is int32. If shape is a list or tuple, all its elements should be integers or 0-D or 1-D Tensors with the data type int32. If shape is a Tensor, it should be an 1-D Tensor with the data type int32. The value -1 in shape means keeping the corresponding dimension unchanged.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

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

Examples

             import paddle

data = paddle.to_tensor([1, 2, 3], dtype='int32')
out = paddle.expand(data, shape=[2, 3])
print(out)
# [[1, 2, 3], [1, 2, 3]]

            

expand_as ( y, name=None ) expand_as¶

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

Both the number of dimensions of x and y must be less than or equal to 6, and the number of dimensions of y must be greather than or equal to that of x. The dimension to expand must have a value of 0.

Parameters

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

Returns

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

Examples

             import paddle

data_x = paddle.to_tensor([1, 2, 3], 'int32')
data_y = paddle.to_tensor([[1, 2, 3], [4, 5, 6]], 'int32')
out = paddle.expand_as(data_x, data_y)
print(out)
# Tensor(shape=[2, 3], dtype=int32, place=Place(gpu:0), stop_gradient=True,
#        [[1, 2, 3],
#         [1, 2, 3]])

            

expm1 ( name=None ) expm1¶

Expm1 Operator. Computes expm1 of x element-wise with a natural number $e$ as the base.

\[out = e^x - 1\]

Parameters

x (Tensor) – Input of Expm1 operator, an N-D Tensor, with data type float32, float64 or float16.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor. Output of Expm1 operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.expm1(x)
print(out)
# [-0.32967997, -0.18126924,  0.10517092,  0.34985882]

            

exponential_ ( lam=1.0, name=None ) exponential_¶

This inplace OP fill input Tensor x with random number from a Exponential Distribution.

lam is $\lambda$ parameter of Exponential Distribution.

\[f(x) = \lambda e^{-\lambda x}\]

Parameters

x (Tensor) – Input tensor. The data type should be float32, float64.
lam (float, optional) – $\lambda$ parameter of Exponential Distribution. Default, 1.0.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

Input Tensor x.

Return type

Tensor

Examples

             import paddle
paddle.set_device('cpu')
paddle.seed(100)

x = paddle.empty([2,3])
x.exponential_()
# [[0.80643415, 0.23211166, 0.01169797],
#  [0.72520673, 0.45208144, 0.30234432]]

            

flatten ( start_axis=0, stop_axis=- 1, name=None ) flatten¶

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

Note

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

For Example:

             Case 1:

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

  and
    start_axis = 1
    end_axis = 2

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

Case 2:

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

  and
    start_axis = 0
    stop_axis = -1

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

            

Parameters

x (Tensor) – A tensor of number of dimentions >= axis. A tensor with data type float16, float32, float64, int8, int32, int64, uint8.
start_axis (int) – the start axis to flatten
stop_axis (int) – the stop axis to flatten
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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

Examples

             import paddle

image_shape=(2, 3, 4, 4)

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

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

# out shares data with img in dygraph mode
img[0, 0, 0, 0] = -1
print(out[0, 0, 0]) # [-1]

            

flatten_ ( start_axis=0, stop_axis=- 1, name=None ) flatten_¶: Inplace version of flatten API, the output Tensor will be inplaced with input x. Please refer to api_tensor_flatten.

flip ( axis, name=None ) flip¶

Reverse the order of a n-D tensor along given axis in axis.

Parameters

x (Tensor) – A Tensor(or LoDTensor) with shape $[N_1, N_2,..., N_k]$ . The data type of the input Tensor x should be float32, float64, int32, int64, bool.
axis (list|tuple|int) – The axis(axes) to flip on. Negative indices for indexing from the end are accepted.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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

Examples

             import paddle

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

out = paddle.flip(tmp,-1)
print(out) # [[[11,10],[9, 8]], [[7, 6],[5, 4]], [[3, 2],[1, 0]]]

            

floor ( name=None ) floor¶

Floor Activation Operator. Computes floor of x element-wise.

\[out = \lfloor x \rfloor\]

Parameters

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

Returns

Tensor. Output of Floor operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.floor(x)
print(out)
# [-1. -1.  0.  0.]

            

floor_ ( name=None ) floor_¶: Inplace version of floor API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_floor.

floor_divide ( y, name=None ) floor_divide¶

Floor divide two tensors element-wise and rounds the quotinents to the nearest integer toward zero. The equation is:

\[out = trunc(x / y)\]

$x$: Multidimensional Tensor.
$y$: Multidimensional Tensor.

Note

paddle.floor_divide supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.floor_divide, line 13); backlink

Duplicate explicit target name: “introduction to tensor”.

Also note that the name floor_divide can be misleading, as the quotinents are actually rounded toward zero, not toward negative infinite.

Parameters

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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

N-D Tensor. A location into which the result is stored. It’s dimension equals with $x$.

Examples

             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)  # [2, 0, 2, 2]

            

floor_mod ( y, name=None ) floor_mod¶

Mod two tensors element-wise. The equation is:

\[out = x \% y\]

Note

paddle.remainder supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.remainder, line 11); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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)  # [0, 3, 2, 1]

            

fmax ( y, name=None ) fmax¶

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:

\[out = fmax(x, y)\]

Note

paddle.fmax supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.fmax, line 12); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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.])

            

fmin ( y, name=None ) fmin¶

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:

\[out = fmin(x, y)\]

Note

paddle.fmin supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.fmin, line 12); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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.  ])

            

frac ( name=None ) frac¶

This API is used to return the fractional portion of each element in input.

Parameters

x (Tensor) – The input tensor, which data type should be int32, int64, float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output Tensor of frac.

Return type

Tensor

Examples

             import paddle

input = paddle.to_tensor([[12.22000003, -1.02999997],
                        [-0.54999995, 0.66000003]])
output = paddle.frac(input)
print(output)
# Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[ 0.22000003, -0.02999997],
#         [-0.54999995,  0.66000003]])

            

frexp ( name=None ) frexp¶

The function used to decompose a floating point number into mantissa and exponent.

Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.
name (str, optional) – For details, please refer to 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

             import paddle

x = paddle.to_tensor([[1, 2, 3, 4]], dtype="float32")
print(paddle.tensor.math.frexp(x))
# (Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True,[[0.50000000, 0.50000000, 0.75000000, 0.50000000]]),
#  Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True,[[1., 2., 2., 3.]]))

            

gather ( index, axis=None, name=None ) gather¶

Output is obtained by gathering entries of axis of x indexed by index and concatenate them together.

             Given:

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

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

Then:

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

            

Parameters

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

Returns

output (Tensor), If the index is a 1-D tensor, the output is a tensor with the same shape as x. If the index is a 0-D tensor, the output will reduce the dimension where the axis pointing.

Examples

             import paddle

input = paddle.to_tensor([[1,2],[3,4],[5,6]])
index = paddle.to_tensor([0,1])
output = paddle.gather(input, index, axis=0)
# expected output: [[1,2],[3,4]]

            

gather_nd ( index, name=None ) gather_nd¶

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

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

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

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

* Case 1:
    index = [[1]]

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

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

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

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

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

            

Parameters

x (Tensor) – The input Tensor which it’s data type should be bool, float16, float32, float64, int32, int64.
index (Tensor) – The index input with rank > 1, index.shape[-1] <= input.rank. Its dtype should be int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

-1] + input.shape[index.shape[-1]:]

Return type

output (Tensor), A tensor with the shape index.shape[

Examples

             import paddle

x = paddle.to_tensor([[[1, 2], [3, 4], [5, 6]],
                      [[7, 8], [9, 10], [11, 12]]])
index = paddle.to_tensor([[0, 1]])

output = paddle.gather_nd(x, index) #[[3, 4]]

gcd ( y, name=None ) gcd¶

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).

Parameters

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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

An N-D Tensor, the data type is the same with input.

Return type

out (Tensor)

Examples

             import paddle

x1 = paddle.to_tensor(12)
x2 = paddle.to_tensor(20)
paddle.gcd(x1, x2)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        4)

x3 = paddle.arange(6)
paddle.gcd(x3, x2)
# Tensor(shape=[6], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        [20, 1 , 2 , 1 , 4 , 5])

x4 = paddle.to_tensor(0)
paddle.gcd(x4, x2)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        20)

paddle.gcd(x4, x4)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        0)

x5 = paddle.to_tensor(-20)
paddle.gcd(x1, x5)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        4)

            

greater_equal ( y, name=None ) greater_equal¶

Returns the truth value of $x >= y$ elementwise, which is equivalent function to the overloaded operator >=.

Note

The output has no gradient.

Parameters

x (Tensor) – First input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
y (Tensor) – Second input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The output shape is same as input x. The output data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 3, 2])
result1 = paddle.greater_equal(x, y)
print(result1)  # result1 = [True False True]

            

greater_than ( y, name=None ) greater_than¶

Returns the truth value of $x > y$ elementwise, which is equivalent function to the overloaded operator >.

Note

The output has no gradient.

Parameters

x (Tensor) – First input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
y (Tensor) – Second input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The output shape is same as input x. The output data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 3, 2])
result1 = paddle.greater_than(x, y)
print(result1)  # result1 = [False False True]

            

heaviside ( y, name=None ) heaviside¶

Computes the Heaviside step function determined by corresponding element in y for each element in x. The equation is

\[\begin{split}heaviside(x, y)= \left\{ \begin{array}{lcl} 0,& &\text{if} \ x < 0, \\ y,& &\text{if} \ x = 0, \\ 1,& &\text{if} \ x > 0. \end{array} \right.\end{split}\]

Note

paddle.heaviside supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.heaviside, line 17); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – The input tensor of Heaviside step function, it’s data type should be float16, float32, float64, int32 or int64.
y (Tensor) – The tensor that determines a Heaviside step function, it’s data type should be float16, float32, float64, int32 or int64.
name (str, 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 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

             import paddle
x = paddle.to_tensor([-0.5, 0, 0.5])
y = paddle.to_tensor([0.1])
paddle.heaviside(x, y)
#    [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)
#    [[0.        , 0.20000000, 1.        ],
#     [0.        , 1.        , 0.30000001]]

            

histogram ( bins=100, min=0, max=0, name=None ) histogram¶

Computes the histogram of a tensor. The elements are sorted into equal width bins between min and max. If min and max are both zero, the minimum and maximum values of the data are used.

Parameters

input (Tensor) – A Tensor(or LoDTensor) with shape $[N_1, N_2,..., N_k]$ . The data type of the input Tensor should be float32, float64, int32, int64.
bins (int, optional) – number of histogram bins.
min (int, optional) – lower end of the range (inclusive).
max (int, optional) – upper end of the range (inclusive).
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

data type is int64, shape is (nbins,).

Return type

Tensor

Examples

             import paddle

inputs = paddle.to_tensor([1, 2, 1])
result = paddle.histogram(inputs, bins=4, min=0, max=3)
print(result) # [0, 2, 1, 0]

i0 ( name=None ) i0¶

The function used to calculate modified bessel function of order 0.

Equation:: \[I_0(x) = \sum^{\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2}\]

Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.
name (str, optional) – For details, please refer to 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.

Examples

             import paddle

x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32")
print(paddle.i0(x))
# (Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True, [0.99999994 , 1.26606596 , 2.27958512 , 4.88079262 , 11.30192089]),

i0e ( name=None ) i0e¶

The function used to calculate exponentially scaled modified Bessel function of order 0.

Equation:: \[\begin{split}I_0(x) = \sum^{\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2} \\ I_{0e}(x) = e^{-|x|}I_0(x)\end{split}\]

Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.
name (str, optional) – For details, please refer to 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.

Examples

             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, [1., 0.46575961, 0.30850832, 0.24300035, 0.20700192]),

i1 ( name=None ) i1¶

The function is used to calculate modified bessel function of order 1.

Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.
name (str, optional) – For details, please refer to 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.

Examples

             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., 0.5651591 , 1.59063685 , 3.95337022 , 9.75946515]),

i1e ( name=None ) i1e¶

The function is used to calculate exponentially scaled modified Bessel function of order 1.

Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.
name (str, optional) – For details, please refer to 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.

Examples

             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, 0.21526929, 0.24300035, 0.17875084]),

imag ( name=None ) imag¶

Returns a new tensor containing imaginary values of input tensor.

Parameters

x (Tensor) – the input tensor, its data type could be complex64 or complex128.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

a tensor containing imaginary values of the input tensor.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor(
    [[1 + 6j, 2 + 5j, 3 + 4j], [4 + 3j, 5 + 2j, 6 + 1j]])
# Tensor(shape=[2, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
#        [[(1+6j), (2+5j), (3+4j)],
#         [(4+3j), (5+2j), (6+1j)]])

imag_res = paddle.imag(x)
# Tensor(shape=[2, 3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        [[6., 5., 4.],
#         [3., 2., 1.]])

imag_t = x.imag()
# Tensor(shape=[2, 3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        [[6., 5., 4.],
#         [3., 2., 1.]])

            

increment ( value=1.0, name=None ) increment¶

The API is usually used for control flow to increment the data of x by an amount value. Notice that the number of elements in x must be equal to 1.

Parameters

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 x. Default: 1.0.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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

Examples

             import paddle

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

index_add ( index, axis, value, name=None ) index_add¶

Adds the elements of the input tensor with value tensor by selecting the indices in the order given in index.

Parameters

x (Tensor) – The Destination Tensor. Supported data types are int32, int64, float16, float32, float64.
index (Tensor) – The 1-D Tensor containing the indices to index. The data type of index must be int32 or int64.
axis (int) – The dimension in which we index.
value (Tensor) – The tensor used to add the elements along the target axis.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, same dimention and dtype with x.

Examples

             # required: gpu
import paddle

input_tensor = paddle.to_tensor(paddle.ones((3, 3)), dtype="float32")
index = paddle.to_tensor([0, 2], dtype="int32")
value = paddle.to_tensor([[1, 1, 1], [1, 1, 1]], dtype="float32")
outplace_res = paddle.index_add(input_tensor, index, 0, value)
print(outplace_res)
# Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[2., 2., 2.],
#         [1., 1., 1.],
#         [2., 2., 2.]])

            

index_add_ ( index, axis, value, name=None ) index_add_¶

Inplace version of index_add API, the output Tensor will be inplaced with input x. Please refer to index_add.

Examples

             # required: gpu
import paddle

input_tensor = paddle.to_tensor(paddle.ones((3, 3)), dtype="float32")
index = paddle.to_tensor([0, 2], dtype="int32")
value = paddle.to_tensor([[1, 1], [1, 1], [1, 1]], dtype="float32")
inplace_res = paddle.index_add_(input_tensor, index, 1, value)
print(inplace_res)
# Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[2., 1., 2.],
#         [2., 1., 2.],
#         [2., 1., 2.]])

            

index_put ( indices, value, accumulate=False, name=None ) index_put¶

Outplace version of index_put_ API, the output Tensor will be inplaced with input x. Please refer to index_put.

Examples

             import paddle

x = paddle.zeros([3, 3])
value = paddle.ones([3])
ix1 = paddle.to_tensor([0,1,2])
ix2 = paddle.to_tensor([1,2,1])
indices=(ix1,ix2)

out = paddle.index_put(x,indices,value)
print(x)
# Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[0., 0., 0.],
#         [0., 0., 0.],
#         [0., 0., 0.]])
print(out)
# Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[0., 1., 0.],
#         [0., 0., 1.],
#         [0., 1., 0.]])

            

index_put_ ( indices, value, accumulate=False, name=None ) index_put_¶

Puts values from the tensor values into the tensor x using the indices specified in indices (which is a tuple of Tensors). The expression paddle.index_put_(x, indices, values) is equivalent to tensor[indices] = values. Returns x. If accumulate is True, the elements in values are added to x. If accumulate is False, the behavior is undefined if indices contain duplicate elements.

Parameters

x (Tensor) – The Source Tensor. Supported data types are int32, int64, float16, float32, float64, bool.
indices (Tuple of Tensor) – The tuple of Tensor containing the indices to index. The data type of tensor in indices must be int32, int64 or bool.
value (Tensor) – The tensor used to be assigned to x.
accummulate (Bool, optional) – Whether the elements in values are added to x. Default: False.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, same dimention and dtype with x.

Examples

             import paddle

x = paddle.zeros([3, 3])
value = paddle.ones([3])
ix1 = paddle.to_tensor([0,1,2])
ix2 = paddle.to_tensor([1,2,1])
indices=(ix1,ix2)

out = paddle.index_put_(x,indices,value)
print(x)
# Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[0., 1., 0.],
#         [0., 0., 1.],
#         [0., 1., 0.]])
print(out)
# Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[0., 1., 0.],
#         [0., 0., 1.],
#         [0., 1., 0.]])

            

index_sample ( index ) index_sample¶

IndexSample Layer

IndexSample OP returns the element of the specified location of X, and the location is specified by Index.

             Given:

X = [[1, 2, 3, 4, 5],
     [6, 7, 8, 9, 10]]

Index = [[0, 1, 3],
         [0, 2, 4]]

Then:

Out = [[1, 2, 4],
       [6, 8, 10]]

Parameters

x (Tensor) – The source input tensor with 2-D shape. Supported data type is int32, int64, bfloat16, float16, float32, float64.
index (Tensor) – The index input tensor with 2-D shape, first dimension should be same with X. Data type is int32 or int64.

Returns

The output is a tensor with the same shape as index.

Return type

output (Tensor)

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0, 3.0, 4.0],
                      [5.0, 6.0, 7.0, 8.0],
                      [9.0, 10.0, 11.0, 12.0]], dtype='float32')
index = paddle.to_tensor([[0, 1, 2],
                          [1, 2, 3],
                          [0, 0, 0]], dtype='int32')
target = paddle.to_tensor([[100, 200, 300, 400],
                           [500, 600, 700, 800],
                           [900, 1000, 1100, 1200]], dtype='int32')
out_z1 = paddle.index_sample(x, index)
print(out_z1)
#[[1. 2. 3.]
# [6. 7. 8.]
# [9. 9. 9.]]

# Use the index of the maximum value by topk op
# get the value of the element of the corresponding index in other tensors
top_value, top_index = paddle.topk(x, k=2)
out_z2 = paddle.index_sample(target, top_index)
print(top_value)
#[[ 4.  3.]
# [ 8.  7.]
# [12. 11.]]

print(top_index)
#[[3 2]
# [3 2]
# [3 2]]

print(out_z2)
#[[ 400  300]
# [ 800  700]
# [1200 1100]]

            

index_select ( index, axis=0, name=None ) index_select¶

Returns a new tensor which indexes the input tensor along dimension axis using the entries in index which is a Tensor. The returned tensor has the same number of dimensions as the original x tensor. The dim-th dimension has the same size as the length of index; other dimensions have the same size as in the x tensor.

Parameters

x (Tensor) – The input Tensor to be operated. The data of x can be one of float16, float32, float64, int32, int64.
index (Tensor) – The 1-D Tensor containing the indices to index. The data type of index must be int32 or int64.
axis (int, optional) – The dimension in which we index. Default: if None, the axis is 0.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

A Tensor with same data type as x.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0, 3.0, 4.0],
                      [5.0, 6.0, 7.0, 8.0],
                      [9.0, 10.0, 11.0, 12.0]])
index = paddle.to_tensor([0, 1, 1], dtype='int32')
out_z1 = paddle.index_select(x=x, index=index)
#[[1. 2. 3. 4.]
# [5. 6. 7. 8.]
# [5. 6. 7. 8.]]
out_z2 = paddle.index_select(x=x, index=index, axis=1)
#[[ 1.  2.  2.]
# [ 5.  6.  6.]
# [ 9. 10. 10.]]

            

inner ( y, name=None ) inner¶

Inner product of two input Tensor.

Ordinary inner product for 1-D Tensors, in higher dimensions a sum product over the last axes.

Parameters

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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The inner-product Tensor, the output shape is x.shape[:-1] + y.shape[:-1].

Return type

Tensor

Examples

             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)
#        ([[14, 32, 50],
#         [32, 77, 122]])

            

inverse ( name=None ) inverse¶

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.

Parameters

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 and float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

A Tensor holds the inverse of x. The shape and data type: is the same as x.

Return type

Tensor

Examples

             import paddle

mat = paddle.to_tensor([[2, 0], [0, 2]], dtype='float32')
inv = paddle.inverse(mat)
print(inv) # [[0.5, 0], [0, 0.5]]

is_complex ( ) is_complex¶

Return whether x is a tensor of complex data type(complex64 or complex128).

Parameters: x (Tensor) – The input tensor.
Returns: True if the data type of the input is complex data type, otherwise false.
Return type: bool

Examples

             import paddle

x = paddle.to_tensor([1 + 2j, 3 + 4j])
print(paddle.is_complex(x))
# True

x = paddle.to_tensor([1.1, 1.2])
print(paddle.is_complex(x))
# False

x = paddle.to_tensor([1, 2, 3])
print(paddle.is_complex(x))
# False

            

is_empty ( name=None ) is_empty¶

Test whether a Tensor is empty.

Parameters

x (Tensor) – The Tensor to be tested.
name (str, optional) – The default value is None . Normally users don’t have to set this parameter. For more information, please refer to Name .

Returns

A bool scalar Tensor. True if ‘x’ is an empty Tensor.

Return type

Tensor

Examples

             import paddle

input = paddle.rand(shape=[4, 32, 32], dtype='float32')
res = paddle.is_empty(x=input)
# res: Tensor(shape=[], dtype=bool, place=Place(cpu), stop_gradient=True,
#        False)

            

is_floating_point ( ) is_floating_point¶

Returns whether the dtype of x is one of paddle.float64, paddle.float32, paddle.float16, and paddle.bfloat16.

Parameters: x (Tensor) – The input tensor.
Returns: True if the dtype of x is floating type, otherwise false.
Return type: bool

Examples

             import paddle

x = paddle.arange(1., 5., dtype='float32')
y = paddle.arange(1, 5, dtype='int32')
print(paddle.is_floating_point(x))
# True
print(paddle.is_floating_point(y))
# False

            

is_integer ( ) is_integer¶

Return whether x is a tensor of integeral data type.

Parameters: x (Tensor) – The input tensor.
Returns: True if the data type of the input is integer data type, otherwise false.
Return type: bool

Examples

             import paddle

x = paddle.to_tensor([1 + 2j, 3 + 4j])
print(paddle.is_integer(x))
# False

x = paddle.to_tensor([1.1, 1.2])
print(paddle.is_integer(x))
# False

x = paddle.to_tensor([1, 2, 3])
print(paddle.is_integer(x))
# True

            

is_tensor ( ) is_tensor¶

Tests whether input object is a paddle.Tensor.

Parameters: x (object) – Object to test.
Returns: A boolean value. True if x is a paddle.Tensor, otherwise False.

Examples

             import paddle

input1 = paddle.rand(shape=[2, 3, 5], dtype='float32')
check = paddle.is_tensor(input1)
print(check)  #True

input3 = [1, 4]
check = paddle.is_tensor(input3)
print(check)  #False

            

isclose ( y, rtol=1e-05, atol=1e-08, equal_nan=False, name=None ) isclose¶

Check if all $x$ and $y$ satisfy the condition:

\[\left| x - y \right| \leq atol + rtol \times \left| y \right|\]

elementwise, for all elements of $x$ and $y$. The behaviour of this operator is analogous to $numpy.isclose$, namely that it returns $True$ if two tensors are elementwise equal within a tolerance.

Parameters

x (Tensor) – The input tensor, it’s data type should be float16, float32, float64.
y (Tensor) – The input tensor, it’s data type should be float16, float32, float64.
rtol (rtoltype, optional) – The relative tolerance. Default: $1e-5$ .
atol (atoltype, optional) – The absolute tolerance. Default: $1e-8$ .
equal_nan (equalnantype, optional) – If $True$ , then two $NaNs$ will be compared as equal. Default: $False$ .
name (str, optional) – Name for the operation. For more information, please refer to Name. Default: None.

Returns

The output tensor, it’s data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([10000., 1e-07])
y = paddle.to_tensor([10000.1, 1e-08])
result1 = paddle.isclose(x, y, rtol=1e-05, atol=1e-08,
                        equal_nan=False, name="ignore_nan")
# [True, False]
result2 = paddle.isclose(x, y, rtol=1e-05, atol=1e-08,
                            equal_nan=True, name="equal_nan")
# [True, False]

x = paddle.to_tensor([1.0, float('nan')])
y = paddle.to_tensor([1.0, float('nan')])
result1 = paddle.isclose(x, y, rtol=1e-05, atol=1e-08,
                        equal_nan=False, name="ignore_nan")
# [True, False]
result2 = paddle.isclose(x, y, rtol=1e-05, atol=1e-08,
                            equal_nan=True, name="equal_nan")
# [True, True]

            

isfinite ( name=None ) isfinite¶

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

Parameters

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

Returns

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

Examples

             import paddle

x = paddle.to_tensor([float('-inf'), -2, 3.6, float('inf'), 0, float('-nan'), float('nan')])
out = paddle.isfinite(x)
print(out)  # [False  True  True False  True False False]

isinf ( name=None ) isinf¶

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

Parameters

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

Returns

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

Examples

             import paddle

x = paddle.to_tensor([float('-inf'), -2, 3.6, float('inf'), 0, float('-nan'), float('nan')])
out = paddle.isinf(x)
print(out)  # [ True False False  True False False False]

isnan ( name=None ) isnan¶

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

Parameters

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

Returns

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

Examples

             import paddle

x = paddle.to_tensor([float('-inf'), -2, 3.6, float('inf'), 0, float('-nan'), float('nan')])
out = paddle.isnan(x)
print(out)  # [False False False False False  True  True]

item ( ) item¶: In order to be compatible with the item interface introduced by the dynamic graph, it does nothing but returns self. It will check that the shape must be a 1-D tensor

kron ( y, name=None ) kron¶

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 $$ k_{t} = i_{t} * s_{t} + j_{t}, t = 0, 1, …, N $$

Parameters

x (Tensor) – the fist operand of kron op, data type: float16, float32, float64, int32 or int64.
y (Tensor) – the second operand of kron op, data type: float16, float32, float64, int32 or int64. Its data type should be the same with x.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output of kron, data type: float16, float32, float64, int32 or int64. Its data is the same with x.

Return type

Tensor

Examples

             import paddle
x = paddle.to_tensor([[1, 2], [3, 4]], dtype='int64')
y = paddle.to_tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype='int64')
out = paddle.kron(x, y)
print(out)
#        [[1, 2, 3, 2, 4, 6],
#         [ 4,  5,  6,  8, 10, 12],
#         [ 7,  8,  9, 14, 16, 18],
#         [ 3,  6,  9,  4,  8, 12],
#         [12, 15, 18, 16, 20, 24],
#         [21, 24, 27, 28, 32, 36]])

            

kthvalue ( k, axis=None, keepdim=False, name=None ) kthvalue¶

Find values and indices of the k-th smallest at the axis.

Parameters

x (Tensor) – A N-D Tensor with type float16, float32, float64, int32, int64.
k (int) – The k for the k-th smallest number to look for along the axis.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is x.ndim. when axis < 0, it works the same way as axis + R. The default is None. And if the axis is None, it will computed as -1 by default.
keepdim (bool, optional) – Whether to keep the given axis in output. If it is True, the dimensions will be same as input x and with size one in the axis. Otherwise the output dimentions is one fewer than x since the axis is squeezed. Default is False.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

tuple(Tensor), return the values and indices. The value data type is the same as the input x. The indices data type is int64.

Examples

             import paddle

x = paddle.randn((2,3,2))
# Tensor(shape=[2, 3, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [[[ 0.22954939, -0.01296274],
#         [ 1.17135799, -0.34493217],
#         [-0.19550551, -0.17573971]],
#
#        [[ 0.15104349, -0.93965352],
#         [ 0.14745511,  0.98209465],
#         [ 0.10732264, -0.55859774]]])
y = paddle.kthvalue(x, 2, 1)
# (Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
# [[ 0.22954939, -0.17573971],
#  [ 0.14745511, -0.55859774]]), Tensor(shape=[2, 2], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#  [[0, 2],
#  [1, 2]]))

            

lcm ( y, name=None ) lcm¶

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).

Parameters

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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

An N-D Tensor, the data type is the same with input.

Return type

out (Tensor)

Examples

             import paddle

x1 = paddle.to_tensor(12)
x2 = paddle.to_tensor(20)
paddle.lcm(x1, x2)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        60)

x3 = paddle.arange(6)
paddle.lcm(x3, x2)
# Tensor(shape=[6], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        [0, 20, 20, 60, 20, 20])

x4 = paddle.to_tensor(0)
paddle.lcm(x4, x2)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        0)

paddle.lcm(x4, x4)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        0)

x5 = paddle.to_tensor(-20)
paddle.lcm(x1, x5)
# Tensor(shape=[], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#        60)

            

ldexp ( y, name=None ) ldexp¶

Compute the result of multiplying x by 2 to the power of y. The equation is:

\[out = x * 2^{y}\]

Parameters

x (Tensor) – The input Tensor, the data type is float32, float64, int32 or int64.
y (Tensor) – A Tensor of exponents, typically integers.
name (str, optional) – Name for the operation (optional, default is None).For more information, please refer to Name.

Returns

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.

Return type

out (Tensor)

Examples

             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=CUDAPlace(0), 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=CUDAPlace(0), stop_gradient=True,
#        [4., 8., 12.])

            

lerp ( y, weight, name=None ) lerp¶

Does a linear interpolation between x and y based on weight.

Equation:: \[lerp(x, y, weight) = x + weight * (y - x).\]

Parameters

x (Tensor) – An N-D Tensor with starting points, the data type is float16, float32, float64.
y (Tensor) – An N-D Tensor with ending points, the data type is float16, float32, float64.
weight (float|Tensor) – The weight for the interpolation formula. When weight is Tensor, the data type is float16, float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

An N-D Tensor, the shape and data type is the same with input.

Return type

out (Tensor)

Example

             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: [5.5, 6., 6.5, 7.]

            

lerp_ ( y, weight, name=None ) lerp_¶: Inplace version of lerp API, the output Tensor will be inplaced with input x. Please refer to api_tensor_lerp.

less_equal ( y, name=None ) less_equal¶

Returns the truth value of $x <= y$ elementwise, which is equivalent function to the overloaded operator <=.

Note

The output has no gradient.

Parameters

x (Tensor) – First input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
y (Tensor) – Second input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The output shape is same as input x. The output data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 3, 2])
result1 = paddle.less_equal(x, y)
print(result1)  # result1 = [True True False]

            

less_than ( y, name=None ) less_than¶

Returns the truth value of $x < y$ elementwise, which is equivalent function to the overloaded operator <.

Note

The output has no gradient.

Parameters

x (Tensor) – First input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
y (Tensor) – Second input to compare which is N-D tensor. The input data type should be bool, float16, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The output shape is same as input x. The output data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 3, 2])
result1 = paddle.less_than(x, y)
print(result1)  # result1 = [False True False]

            

lgamma ( name=None ) lgamma¶

Calculates the lgamma of the given input tensor, element-wise.

This operator performs elementwise lgamma for input $X$. $out = log\Gamma(x)$

Parameters

x (Tensor) – Input Tensor. Must be one of the following types: float16, float32, float64, uint16.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the lgamma of the input Tensor, the shape and data type is the same with input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.lgamma(x)
print(out)
# [1.31452441, 1.76149750, 2.25271273, 1.09579802]

            

log ( name=None ) log¶

Calculates the natural log of the given input Tensor, element-wise.

\[Out = \ln(x)\]

Parameters

x (Tensor) – Input Tensor. Must be one of the following types: float16, float32, float64.
name (str|None) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name

Returns

The natural log of the input Tensor computed element-wise.

Return type

Tensor

Examples

             import paddle

x = [[2,3,4], [7,8,9]]
x = paddle.to_tensor(x, dtype='float32')
res = paddle.log(x)
# [[0.693147, 1.09861, 1.38629], [1.94591, 2.07944, 2.19722]]

            

log10 ( name=None ) log10¶

Calculates the log to the base 10 of the given input tensor, element-wise.

\[Out = \log_10_x\]

Parameters

x (Tensor) – Input tensor must be one of the following types: float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The log to the base 10 of the input Tensor computed element-wise.

Return type

Tensor

Examples

             import paddle

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

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

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

            

log1p ( name=None ) log1p¶

Calculates the natural log of the given input tensor, element-wise.

\[Out = \ln(x+1)\]

Parameters

x (Tensor) – Input Tensor. Must be one of the following types: float16, float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the natural log of the input Tensor computed element-wise.

Examples

             import paddle

data = paddle.to_tensor([[0], [1]], dtype='float32')
res = paddle.log1p(data)
# [[0.], [0.6931472]]

log2 ( name=None ) log2¶

Calculates the log to the base 2 of the given input tensor, element-wise.

\[Out = \log_2x\]

Parameters

x (Tensor) – Input tensor must be one of the following types: float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The log to the base 2 of the input Tensor computed element-wise.

Return type

Tensor

Examples

             import paddle

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

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

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

            

logaddexp ( y, name=None ) logaddexp¶

Elementwise LogAddExp Operator. Add of exponentiations of the inputs The equation is:

\[Out=log(X.exp()+Y.exp())\]

$X$ 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:

The shape of $Y$ is the same with $X$.
The shape of $Y$ is a continuous subsequence of $X$.

For case 2:

Broadcast $Y$ to match the shape of $X$, where axis is the start dimension index for broadcasting $Y$ onto $X$.
If $axis$ is -1 (default), $axis$=rank($X$)-rank($Y$).

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:

                 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

                

Parameters

x (Tensor) – Tensor or LoDTensor of any dimensions. Its dtype should be float32, float64, float16.
y (Tensor) – Tensor or LoDTensor of any dimensions. Its dtype should be float32, float64, float16.
name (string, optional) – For details, please refer to 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

             import paddle

x = paddle.to_tensor([-1, -2, -3], 'float64')
y = paddle.to_tensor([-1], 'float64')
z = paddle.logaddexp(x, y)
print(z)  # [-0.30685282, -0.68673831, -0.87307199]

            

logcumsumexp ( axis=None, dtype=None, name=None ) logcumsumexp¶

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

\[logcumsumexp(x)_{ij} = log \sum_{i=0}^{j}exp(x_{ij})\]

Note

The first element of the result is the same as the first element of the input.

Parameters

x (Tensor) – The input tensor.
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, 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the result of logcumsumexp operator.

Examples

             import paddle

data = paddle.arange(12, dtype='float64')
data = paddle.reshape(data, (3, 4))

y = paddle.logcumsumexp(data)
# [ 0.         1.3132617  2.4076061  3.4401898  4.4519143  5.4561934
#   6.4577627  7.4583397  8.458551   9.45863   10.458658  11.458669 ]

y = paddle.logcumsumexp(data, axis=0)
# [[ 0.        1.        2.        3.      ]
#  [ 4.01815   5.01815   6.01815   7.01815 ]
#  [ 8.018479  9.018479 10.018479 11.018479]]

y = paddle.logcumsumexp(data, axis=-1)
# [[ 0.         1.3132617  2.4076061  3.4401898]
#  [ 4.         5.3132615  6.407606   7.44019  ]
#  [ 8.         9.313262  10.407606  11.440189 ]]

y = paddle.logcumsumexp(data, dtype='float64')
print(y.dtype)
# paddle.float64

            

logical_and ( y, out=None, name=None ) logical_and¶

Compute element-wise logical AND on x and y, and return out. out is N-dim boolean Tensor. Each element of out is calculated by

\[out = x \&\& y\]

Note

paddle.logical_and supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.logic.logical_and, line 12); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be one of bool, int8, int16, in32, in64, float16, float32, float64.
y (Tensor) – the input tensor, it’s data type should be one of bool, int8, int16, in32, in64, float16, float32, float64.
out (Tensor, optional) – The Tensor that specifies the output of the operator, which can be any Tensor that has been created in the program. The default value is None, and a new Tensor will be created to save the output.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

N-D Tensor. A location into which the result is stored. It’s dimension equals with x.

Examples

             import paddle

x = paddle.to_tensor([True])
y = paddle.to_tensor([True, False, True, False])
res = paddle.logical_and(x, y)
print(res) # [True False True False]

            

logical_not ( out=None, name=None ) logical_not¶

logical_not operator computes element-wise logical NOT on x, and returns out. out is N-dim boolean Variable. Each element of out is calculated by

\[out = !x\]

Note

paddle.logical_not supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.logic.logical_not, line 12); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – Operand of logical_not operator. Must be a Tensor of type bool, int8, int16, in32, in64, float16, float32, or float64.
out (Tensor) – The Tensor that specifies the output of the operator, which can be any Tensor that has been created in the program. The default value is None, and a new ``Tensor` will be created to save the output.
name (str|None) – The default value is None. Normally there is no need for users to set this property. For more information, please refer to Name.

Returns

N-D Tensor. A location into which the result is stored. It’s dimension equals with x.

Examples

             import paddle

x = paddle.to_tensor([True, False, True, False])
res = paddle.logical_not(x)
print(res) # [False  True False  True]

logical_or ( y, out=None, name=None ) logical_or¶

logical_or operator computes element-wise logical OR on x and y, and returns out. out is N-dim boolean Tensor. Each element of out is calculated by

\[out = x || y\]

Note

paddle.logical_or supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.logic.logical_or, line 12); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be one of bool, int8, int16, in32, in64, float16, float32, float64.
y (Tensor) – the input tensor, it’s data type should be one of bool, int8, int16, in32, in64, float16, float32, float64.
out (Tensor) – The Variable that specifies the output of the operator, which can be any Tensor that has been created in the program. The default value is None, and a new Tensor will be created to save the output.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

N-D Tensor. A location into which the result is stored. It’s dimension equals with x.

Examples

             import paddle

x = paddle.to_tensor([True, False], dtype="bool").reshape([2, 1])
y = paddle.to_tensor([True, False, True, False], dtype="bool").reshape([2, 2])
res = paddle.logical_or(x, y)
print(res)
# Tensor(shape=[2, 2], dtype=bool, place=Place(cpu), stop_gradient=True,
#        [[True , True ],
#         [True , False]])

            

logical_xor ( y, out=None, name=None ) logical_xor¶

logical_xor operator computes element-wise logical XOR on x and y, and returns out. out is N-dim boolean Tensor. Each element of out is calculated by

\[out = (x || y) \&\& !(x \&\& y)\]

Note

paddle.logical_xor supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.logic.logical_xor, line 12); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be one of bool, int8, int16, in32, in64, float16, float32, float64.
y (Tensor) – the input tensor, it’s data type should be one of bool, int8, int16, in32, in64, float16, float32, float64.
out (Tensor) – The Tensor that specifies the output of the operator, which can be any Tensor that has been created in the program. The default value is None, and a new Tensor will be created to save the output.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

N-D Tensor. A location into which the result is stored. It’s dimension equals with x.

Examples

             import paddle

x = paddle.to_tensor([True, False], dtype="bool").reshape([2, 1])
y = paddle.to_tensor([True, False, True, False], dtype="bool").reshape([2, 2])
res = paddle.logical_xor(x, y)
print(res)
# Tensor(shape=[2, 2], dtype=bool, place=Place(cpu), stop_gradient=True,
#        [[False, True ],
#         [True , False]])

            

logit ( eps=None, name=None ) logit¶

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.

\[logit(x) = ln(\frac{x}{1 - x})\]

where

\[\begin{split}x_i= \left\{\begin{array}{rcl} x_i & &\text{if } eps == Default \\ eps & &\text{if } x_i < eps \\ x_i & &\text{if } eps <= x_i <= 1-eps \\ 1-eps & &\text{if } x_i > 1-eps \end{array}\right.\end{split}\]

Parameters

x (Tensor) – The input Tensor with data type float32, float64.
eps (float, optional) – the epsilon for input clamp bound. Default is None.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

A Tensor with the same data type and shape as x .

Return type

out(Tensor)

Examples

             import paddle

x = paddle.to_tensor([0.2635, 0.0106, 0.2780, 0.2097, 0.8095])
out1 = paddle.logit(x)
print(out1)
# [-1.0277, -4.5365, -0.9544, -1.3269,  1.4468]

            

logsumexp ( axis=None, keepdim=False, name=None ) logsumexp¶

Calculates the log of the sum of exponentials of x along axis .

\[logsumexp(x) = \log\sum exp(x)\]

Parameters

x (Tensor) – The input Tensor with data type float16, float32 or float64, which have no more than 4 dimensions.
axis (int|list|tuple, optional) – The axis along which to perform logsumexp calculations. axis should be int, list(int) or tuple(int). If axis is a list/tuple of dimension(s), logsumexp is calculated along all element(s) of axis . axis or element(s) of axis should be in range [-D, D), where D is the dimensions of x . If axis or element(s) of axis is less than 0, it works the same way as $axis + D$ . If axis is None, logsumexp is calculated along all elements of x. Default is None.
keepdim (bool, optional) – Whether to reserve the reduced dimension(s) in the output Tensor. If keep_dim is True, the dimensions of the output Tensor is the same as x except in the reduced dimensions(it is of size 1 in this case). Otherwise, the shape of the output Tensor is squeezed in axis . Default is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of logsumexp along axis of x, with the same data type as x.

Examples:

             import paddle

x = paddle.to_tensor([[-1.5, 0., 2.], [3., 1.2, -2.4]])
out1 = paddle.logsumexp(x)    # 3.4691226
out2 = paddle.logsumexp(x, 1) # [2.15317821, 3.15684602]

lstsq ( y, rcond=None, driver=None, name=None ) lstsq¶

Computes a solution to the least squares problem of a system of linear equations.

Parameters

x (Tensor) – A tensor with shape (*, M, N) , the data type of the input Tensor x should be one of float32, float64.
y (Tensor) – A tensor with shape (*, M, K) , the data type of the input Tensor y should be one of float32, float64.
rcond (float, optional) – The default value is None. A float pointing number used to determine the effective rank of x. If rcond is None, it will be set to max(M, N) times the machine precision of x_dtype.
driver (str, optional) – The default value is None. The name of LAPACK method to be used. For CPU inputs the valid values are ‘gels’, ‘gelsy’, ‘gelsd, ‘gelss’. For CUDA input, the only valid driver is ‘gels’. If driver is None, ‘gelsy’ is used for CPU inputs and ‘gels’ for CUDA inputs.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

A tuple of 4 Tensors which is (solution, residuals, rank, singular_values). solution is a tensor with shape (*, N, K), meaning the least squares solution. residuals is a tensor with shape (*, K), meaning the squared residuals of the solutions, which is computed when M > N and every matrix in x is full-rank, otherwise return an empty tensor. rank is a tensor with shape (*), meaning the ranks of the matrices in x, which is computed when driver in (‘gelsy’, ‘gelsd’, ‘gelss’), otherwise return an empty tensor. singular_values is a tensor with shape (*, min(M, N)), meaning singular values of the matrices in x, which is computed when driver in (‘gelsd’, ‘gelss’), otherwise return an empty tensor.

Return type

Tuple

Examples

             import paddle

paddle.set_device("cpu")
x = paddle.to_tensor([[1, 3], [3, 2], [5, 6.]])
y = paddle.to_tensor([[3, 4, 6], [5, 3, 4], [1, 2, 1.]])
results = paddle.linalg.lstsq(x, y, driver="gelsd")
print(results[0])
# [[ 0.78350395, -0.22165027, -0.62371236],
# [-0.11340097,  0.78866047,  1.14948535]]
print(results[1])
# [19.81443405, 10.43814468, 30.56185532])
print(results[2])
# 2
print(results[3])
# [9.03455734, 1.54167950]

x = paddle.to_tensor([[10, 2, 3], [3, 10, 5], [5, 6, 12.]])
y = paddle.to_tensor([[4, 2, 9], [2, 0, 3], [2, 5, 3.]])
results = paddle.linalg.lstsq(x, y, driver="gels")
print(results[0])
# [[ 0.39386186,  0.10230173,  0.93606132],
# [ 0.10741687, -0.29028133,  0.11892585],
# [-0.05115091,  0.51918161, -0.19948854]]
print(results[1])
# []

            

lu ( pivot=True, get_infos=False, name=None ) lu¶

Computes the LU factorization of an N-D(N>=2) matrix x.

Returns the LU factorization(inplace x) and Pivots. low triangular matrix L and upper triangular matrix U are combined to a single LU matrix.

Pivoting is done if pivot is set to True. P mat can be get by pivots:

System Message: ERROR/3 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.linalg.lu, line 9)

Error in “code-block” directive: maximum 1 argument(s) allowed, 17 supplied.

              .. code-block:: text
    ones = eye(rows) #eye matrix of rank rows
    for i in range(cols):
        swap(ones[i], ones[pivots[i]])
    return ones

             

Parameters

X (Tensor) – the tensor to factor of N-dimensions(N>=2).
pivot (bool, optional) – controls whether pivoting is done. Default: True.
get_infos (bool, optional) – if set to True, returns an info IntTensor. Default: False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

factorization (Tensor), LU matrix, the factorization of input X.

pivots (IntTensor), the pivots of size(∗(N-2), min(m,n)). pivots stores all the intermediate transpositions of rows. The final permutation perm could be reconstructed by this, details refer to upper example.

infos (IntTensor, optional), if get_infos is True, this is a tensor of size (∗(N-2)) where non-zero values indicate whether factorization for the matrix or each minibatch has succeeded or failed.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]).astype('float64')
lu,p,info = paddle.linalg.lu(x, get_infos=True)

# >>> lu:
# Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
#    [[5.        , 6.        ],
#        [0.20000000, 0.80000000],
#        [0.60000000, 0.50000000]])
# >>> p
# Tensor(shape=[2], dtype=int32, place=CUDAPlace(0), stop_gradient=True,
#    [3, 3])
# >>> info
# Tensor(shape=[], dtype=int32, place=CUDAPlace(0), stop_gradient=True,
#    0)

P,L,U = paddle.linalg.lu_unpack(lu,p)

# >>> P
# (Tensor(shape=[3, 3], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
# [[0., 1., 0.],
# [0., 0., 1.],
# [1., 0., 0.]]),
# >>> L
# Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
# [[1.        , 0.        ],
# [0.20000000, 1.        ],
# [0.60000000, 0.50000000]]),
# >>> U
# Tensor(shape=[2, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
# [[5.        , 6.        ],
# [0.        , 0.80000000]]))


# one can verify : X = P @ L @ U ;

            

lu_unpack ( y, unpack_ludata=True, unpack_pivots=True, name=None ) lu_unpack¶

Unpack L U and P to single matrix tensor . unpack L and U matrix from LU, unpack permutation matrix P from Pivtos .

P mat can be get by pivots:

System Message: ERROR/3 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.linalg.lu_unpack, line 6)

Error in “code-block” directive: maximum 1 argument(s) allowed, 15 supplied.

              .. code-block:: text
    ones = eye(rows) #eye matrix of rank rows
    for i in range(cols):
        swap(ones[i], ones[pivots[i]])

Parameters

x (Tensor) – The LU tensor get from paddle.linalg.lu, which is combined by L and U.
y (Tensor) – Pivots get from paddle.linalg.lu.
unpack_ludata (bool,optional) – whether to unpack L and U from x. Default: True.
unpack_pivots (bool, optional) – whether to unpack permutation matrix P from Pivtos. Default: True.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

P (Tensor), Permutation matrix P of lu factorization.

L (Tensor), The lower triangular matrix tensor of lu factorization.

U (Tensor), The upper triangular matrix tensor of lu factorization.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]).astype('float64')
lu,p,info = paddle.linalg.lu(x, get_infos=True)

# >>> lu:
# Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
#    [[5.        , 6.        ],
#        [0.20000000, 0.80000000],
#        [0.60000000, 0.50000000]])
# >>> p
# Tensor(shape=[2], dtype=int32, place=CUDAPlace(0), stop_gradient=True,
#    [3, 3])
# >>> info
# Tensor(shape=[], dtype=int32, place=CUDAPlace(0), stop_gradient=True,
#    0)

P,L,U = paddle.linalg.lu_unpack(lu,p)

# >>> P
# (Tensor(shape=[3, 3], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
# [[0., 1., 0.],
# [0., 0., 1.],
# [1., 0., 0.]]),
# >>> L
# Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
# [[1.        , 0.        ],
# [0.20000000, 1.        ],
# [0.60000000, 0.50000000]]),
# >>> U
# Tensor(shape=[2, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
# [[5.        , 6.        ],
# [0.        , 0.80000000]]))

# one can verify : X = P @ L @ U ;

            

masked_select ( mask, name=None ) masked_select¶

Returns a new 1-D tensor which indexes the input tensor according to the mask which is a tensor with data type of bool.

Parameters

x (Tensor) – The input Tensor, the data type can be int32, int64, uint16, float16, float32, float64.
mask (Tensor) – The Tensor containing the binary mask to index with, it’s data type is bool.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

A 1-D Tensor which is the same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0, 3.0, 4.0],
                      [5.0, 6.0, 7.0, 8.0],
                      [9.0, 10.0, 11.0, 12.0]])
mask = paddle.to_tensor([[True, False, False, False],
                         [True, True, False, False],
                         [True, False, False, False]])
out = paddle.masked_select(x, mask)
#[1.0 5.0 6.0 9.0]

            

matmul ( y, transpose_x=False, transpose_y=False, name=None ) matmul¶

Applies matrix multiplication to two tensors. matmul follows the complete broadcast rules, and its behavior is consistent with np.matmul.

Currently, the input tensors’ number of dimensions can be any, matmul can be used to achieve the dot, matmul and batchmatmul.

The actual behavior depends on the shapes of $x$, $y$ and the flag values of transpose_x, transpose_y. Specifically:

If a transpose flag is specified, the last two dimensions of the tensor are transposed. If the tensor is ndim-1 of shape, the transpose is invalid. If the tensor is ndim-1 of shape $[D]$, then for $x$ it is treated as $[1, D]$, whereas for $y$ it is the opposite: It is treated as $[D, 1]$.

The multiplication behavior depends on the dimensions of x and y. Specifically:

If both tensors are 1-dimensional, the dot product result is obtained.
If both tensors are 2-dimensional, the matrix-matrix product is obtained.
If the x is 1-dimensional and the y is 2-dimensional, a 1 is prepended to its dimension in order to conduct the matrix multiply. After the matrix multiply, the prepended dimension is removed.
If the x is 2-dimensional and y is 1-dimensional, the matrix-vector product is obtained.
If both arguments are at least 1-dimensional and at least one argument is N-dimensional (where N > 2), then a batched matrix multiply is obtained. If the first argument is 1-dimensional, a 1 is prepended to its dimension in order to conduct the batched matrix multiply and removed after. If the second argument is 1-dimensional, a 1 is appended to its dimension for the purpose of the batched matrix multiple and removed after. The non-matrix (exclude the last two dimensions) dimensions are broadcasted according the broadcast rule. For example, if input is a (j, 1, n, m) tensor and the other is a (k, m, p) tensor, out will be a (j, k, n, p) tensor.

Parameters

x (Tensor) – The input tensor which is a Tensor.
y (Tensor) – The input tensor which is a Tensor.
transpose_x (bool, optional) – Whether to transpose $x$ before multiplication.
transpose_y (bool, optional) – Whether to transpose $y$ before multiplication.
name (str, optional) – A name for this layer(optional). If set None, the layer will be named automatically.

Returns

The output Tensor.

Return type

Tensor

Examples

             import paddle

# vector * vector
x = paddle.rand([10])
y = paddle.rand([10])
z = paddle.matmul(x, y)
print(z.shape)
# ()

# matrix * vector
x = paddle.rand([10, 5])
y = paddle.rand([5])
z = paddle.matmul(x, y)
print(z.shape)
# (10,)

# batched matrix * broadcasted vector
x = paddle.rand([10, 5, 2])
y = paddle.rand([2])
z = paddle.matmul(x, y)
print(z.shape)
# (10, 5)

# batched matrix * batched matrix
x = paddle.rand([10, 5, 2])
y = paddle.rand([10, 2, 5])
z = paddle.matmul(x, y)
print(z.shape)
# (10, 5, 5)

# batched matrix * broadcasted matrix
x = paddle.rand([10, 1, 5, 2])
y = paddle.rand([1, 3, 2, 5])
z = paddle.matmul(x, y)
print(z.shape)
# (10, 3, 5, 5)

            

matrix_power ( n, name=None ) matrix_power¶

Computes the n-th power of a square matrix or a batch of square matrices.

Let $X$ be a sqaure matrix or a batch of square matrices, $n$ be an exponent, the equation should be:

\[Out = X ^ {n}\]

Specifically,

If n > 0, it returns the matrix or a batch of matrices raised to the power of n.
If n = 0, it returns the identity matrix or a batch of identity matrices.
If n < 0, it returns the inverse of each matrix (if invertible) raised to the power of abs(n).

Parameters

x (Tensor) – A square matrix or a batch of square matrices to be raised to power n. Its shape should be [*, M, M], where * is zero or more batch dimensions. Its data type should be float32 or float64.
n (int) – The exponent. It can be any positive, negative integer or zero.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, The n-th power of the matrix (or the batch of matrices) x. Its data type should be the same as that of x.

Examples

             import paddle

x = paddle.to_tensor([[1, 2, 3],
                      [1, 4, 9],
                      [1, 8, 27]], dtype='float64')
print(paddle.linalg.matrix_power(x, 2))
# [[6.  , 34. , 102.],
#  [14. , 90. , 282.],
#  [36. , 250., 804.]]

print(paddle.linalg.matrix_power(x, 0))
# [[1., 0., 0.],
#  [0., 1., 0.],
#  [0., 0., 1.]]

print(paddle.linalg.matrix_power(x, -2))
# [[ 12.91666667, -12.75000000,  2.83333333 ],
#  [-7.66666667 ,  8.         , -1.83333333 ],
#  [ 1.80555556 , -1.91666667 ,  0.44444444 ]]

            

max ( axis=None, keepdim=False, name=None ) max¶

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.

Parameters

x (Tensor) – A tensor, the data type is float32, float64, int32, int64.
axis (int|list|tuple, optional) – The axis along which the maximum is computed. If None, compute the maximum over all elements of x and return a Tensor with a single element, otherwise must be in the range $[-x.ndim(x), x.ndim(x))$. If $axis[i] < 0$, the axis to reduce is $x.ndim + axis[i]$.
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 keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of maximum on the specified axis of input tensor, it’s data type is the same as x.

Examples

             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()
print(result1, x.grad)
# 0.9, [[0., 0., 0., 1.], [0., 0., 0., 0.]]

x.clear_grad()
result2 = paddle.max(x, axis=0)
result2.backward()
print(result2, x.grad)
#[0.2, 0.3, 0.6, 0.9], [[1., 1., 0., 1.], [0., 0., 1., 0.]]

x.clear_grad()
result3 = paddle.max(x, axis=-1)
result3.backward()
print(result3, x.grad)
#[0.9, 0.7], [[0., 0., 0., 1.], [0., 0., 0., 1.]]

x.clear_grad()
result4 = paddle.max(x, axis=1, keepdim=True)
result4.backward()
print(result4, x.grad)
#[[0.9], [0.7]], [[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()
print(result5, y.grad)
#[4., 8.], [[[0., 0.], [0., 1.]], [[0., 0.], [0., 1.]]]

y.clear_grad()
result6 = paddle.max(y, axis=[0, 1])
result6.backward()
print(result6, y.grad)
#[7., 8.], [[[0., 0.], [0., 0.]], [[0., 0.], [1., 1.]]]

            

maximum ( y, name=None ) maximum¶

Compare two tensors and returns a new tensor containing the element-wise maxima. The equation is:

\[out = max(x, y)\]

Note

paddle.maximum supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.maximum, line 10); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             import paddle

x = paddle.to_tensor([[1, 2], [7, 8]])
y = paddle.to_tensor([[3, 4], [5, 6]])
res = paddle.maximum(x, y)
print(res)
# 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.maximum(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.maximum(x, y)
print(res)
# Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [2. , nan, nan])

x = paddle.to_tensor([5, 3, float("inf")], dtype='float32')
y = paddle.to_tensor([1, -float("inf"), 5], dtype='float32')
res = paddle.maximum(x, y)
print(res)
# Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [5.  , 3.  , inf.])

            

mean ( axis=None, keepdim=False, name=None ) mean¶

Computes the mean of the input tensor’s elements along axis.

Parameters

x (Tensor) – The input Tensor with data type float32, float64.
axis (int|list|tuple, optional) – The axis along which to perform mean calculations. axis should be int, list(int) or tuple(int). If axis is a list/tuple of dimension(s), mean 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 $axis + D$ . If axis is None, mean 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of average along axis of x, with the same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[[1., 2., 3., 4.],
                       [5., 6., 7., 8.],
                       [9., 10., 11., 12.]],
                      [[13., 14., 15., 16.],
                       [17., 18., 19., 20.],
                       [21., 22., 23., 24.]]])
out1 = paddle.mean(x)
# 12.5
out2 = paddle.mean(x, axis=-1)
# [[ 2.5  6.5 10.5]
#  [14.5 18.5 22.5]]
out3 = paddle.mean(x, axis=-1, keepdim=True)
# [[[ 2.5]
#   [ 6.5]
#   [10.5]]
#  [[14.5]
#   [18.5]
#   [22.5]]]
out4 = paddle.mean(x, axis=[0, 2])
# [ 8.5 12.5 16.5]

            

median ( axis=None, keepdim=False, name=None ) median¶

Compute the median along the specified axis.

Parameters

x (Tensor) – The input Tensor, it’s data type can be bool, float16, float32, float64, int32, int64.
axis (int, optional) – The axis along which to perform median calculations axis should be int. axis should be in range [-D, D), where D is the dimensions of x . If axis is less than 0, it works the same way as $axis + D$. If axis is None, median 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of median along axis of x. If data type of x is float64, data type of results will be float64, otherwise data type will be float32.

Examples

             import paddle

x = paddle.arange(12).reshape([3, 4])
# Tensor(shape=[3, 4], dtype=int64, place=Place(cpu), stop_gradient=True,
#        [[0 , 1 , 2 , 3 ],
#         [4 , 5 , 6 , 7 ],
#         [8 , 9 , 10, 11]])

y1 = paddle.median(x)
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        5.50000000)

y2 = paddle.median(x, axis=0)
# Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [4., 5., 6., 7.])

y3 = paddle.median(x, axis=1)
# Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [1.50000000, 5.50000000, 9.50000000])

y4 = paddle.median(x, axis=0, keepdim=True)
# Tensor(shape=[1, 4], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[4., 5., 6., 7.]])

            

min ( axis=None, keepdim=False, name=None ) min¶

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.

Parameters

x (Tensor) – A tensor, the data type is float32, float64, int32, int64.
axis (int|list|tuple, optional) – The axis along which the minimum is computed. If None, compute the minimum over all elements of x and return a Tensor with a single element, otherwise must be in the range $[-x.ndim, x.ndim)$. If $axis[i] < 0$, the axis to reduce is $x.ndim + axis[i]$.
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 keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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()
print(result1, x.grad)
# 0.1, [[0., 0., 0., 0.], [1., 0., 0., 0.]]

x.clear_grad()
result2 = paddle.min(x, axis=0)
result2.backward()
print(result2, x.grad)
#[0.1, 0.2, 0.5, 0.7], [[0., 0., 1., 0.], [1., 1., 0., 1.]]

x.clear_grad()
result3 = paddle.min(x, axis=-1)
result3.backward()
print(result3, x.grad)
#[0.2, 0.1], [[1., 0., 0., 0.], [1., 0., 0., 0.]]

x.clear_grad()
result4 = paddle.min(x, axis=1, keepdim=True)
result4.backward()
print(result4, x.grad)
#[[0.2], [0.1]], [[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()
print(result5, y.grad)
#[1., 5.], [[[1., 0.], [0., 0.]], [[1., 0.], [0., 0.]]]

y.clear_grad()
result6 = paddle.min(y, axis=[0, 1])
result6.backward()
print(result6, y.grad)
#[1., 2.], [[[1., 1.], [0., 0.]], [[0., 0.], [0., 0.]]]

            

minimum ( y, name=None ) minimum¶

Compare two tensors and return a new tensor containing the element-wise minima. The equation is:

\[out = min(x, y)\]

Note

paddle.minimum supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.minimum, line 10); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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.

Examples

             import paddle

x = paddle.to_tensor([[1, 2], [7, 8]])
y = paddle.to_tensor([[3, 4], [5, 6]])
res = paddle.minimum(x, y)
print(res)
# 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.minimum(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.minimum(x, y)
print(res)
# Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [1. , nan, nan])

x = paddle.to_tensor([5, 3, float("inf")], dtype='float64')
y = paddle.to_tensor([1, -float("inf"), 5], dtype='float64')
res = paddle.minimum(x, y)
print(res)
# Tensor(shape=[3], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [ 1.  , -inf.,  5.  ])

            

mm ( mat2, name=None ) mm¶

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 $x$ or $mat2$ is rank-1 and nontransposed, the prepended or appended dimension $1$ will be removed after matrix multiplication.

Parameters

input (Tensor) – The input tensor which is a Tensor.
mat2 (Tensor) – The input tensor which is a Tensor.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The product Tensor.

Return type

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

             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)
print(out)
#        [[11., 14., 17., 20.],
#         [23., 30., 37., 44.],
#         [35., 46., 57., 68.]])

            

mod ( y, name=None ) mod¶

Mod two tensors element-wise. The equation is:

\[out = x \% y\]

Note

paddle.remainder supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.remainder, line 11); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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)  # [0, 3, 2, 1]

            

mode ( axis=- 1, keepdim=False, name=None ) mode¶

Used to find values and indices of the modes at the optional axis.

Parameters

x (Tensor) – Tensor, an input N-D Tensor with type float32, float64, int32, int64.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is x.ndim. when axis < 0, it works the same way as axis + R. Default is -1.
keepdim (bool, optional) – Whether to keep the given axis in output. If it is True, the dimensions will be same as input x and with size one in the axis. Otherwise the output dimentions is one fewer than x since the axis is squeezed. Default is False.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

tuple (Tensor), return the values and indices. The value data type is the same as the input x. The indices data type is int64.

Examples

             import paddle

tensor = paddle.to_tensor([[[1,2,2],[2,3,3]],[[0,5,5],[9,9,0]]], dtype=paddle.float32)
res = paddle.mode(tensor, 2)
print(res)
# (Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#   [[2., 3.],
#    [5., 9.]]), Tensor(shape=[2, 2], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
#   [[2, 2],
#    [2, 1]]))

            

moveaxis ( source, destination, name=None ) moveaxis¶

Move the axis of tensor from source position to destination position.

Other axis that have not been moved remain their original order.

Parameters

x (Tensor) – The input Tensor. It is a N-D Tensor of data types bool, int32, int64, float32, float64, complex64, complex128.
source (int|tuple|list) – source position of axis that will be moved. Each element must be unique and integer.
destination (int|tuple|list(int)) – destination position of axis that has been moved. Each element must be unique and integer.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

Tensor, A new tensor whose axis have been moved.

Examples

             import paddle

x = paddle.ones([3, 2, 4])
paddle.moveaxis(x, [0, 1], [1, 2]).shape
# [4, 3, 2]

x = paddle.ones([2, 3])
paddle.moveaxis(x, 0, 1).shape # equivalent to paddle.t(x)
# [3, 2]

            

multi_dot ( name=None ) multi_dot¶

Multi_dot is an operator that calculates multiple matrix multiplications.

Supports inputs of float16(only GPU support), float32 and float64 dtypes. This function does not support batched inputs.

The input tensor in [x] must be 2-D except for the first and last can be 1-D. If the first tensor is a 1-D vector of shape(n, ) it is treated as row vector of shape(1, n), similarly if the last tensor is a 1D vector of shape(n, ), it is treated as a column vector of shape(n, 1).

If the first and last tensor are 2-D matrix, then the output is also 2-D matrix, otherwise the output is a 1-D vector.

Multi_dot will select the lowest cost multiplication order for calculation. The cost of multiplying two matrices with shapes (a, b) and (b, c) is a * b * c. Given matrices A, B, C with shapes (20, 5), (5, 100), (100, 10) respectively, we can calculate the cost of different multiplication orders as follows: - Cost((AB)C) = 20x5x100 + 20x100x10 = 30000 - Cost(A(BC)) = 5x100x10 + 20x5x10 = 6000

In this case, multiplying B and C first, then multiply A, which is 5 times faster than sequential calculation.

Parameters

x ([Tensor]) – The input tensors which is a list Tensor.
name (str|None) – A name for this layer(optional). If set None, the layer will be named automatically.

Returns

The output Tensor.

Return type

Tensor

Examples:

             import paddle

# A * B
A = paddle.rand([3, 4])
B = paddle.rand([4, 5])
out = paddle.linalg.multi_dot([A, B])
print(out.shape)
# [3, 5]

# A * B * C
A = paddle.rand([10, 5])
B = paddle.rand([5, 8])
C = paddle.rand([8, 7])
out = paddle.linalg.multi_dot([A, B, C])
print(out.shape)
# [10, 7]

            

multiplex ( index, name=None ) multiplex¶

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 $m$ Tensors, where $I_{i}$ means the i-th input Tensor, $i$ between $[0,m)$ .

And $O$ means the output, where $O[i]$ means the i-th row of the output, then the output satisfies that $O[i] = I_{index[i]}[i]$ .

For Example:

               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]

              

Parameters

inputs (list) – The input Tensor list. The list elements are N-D Tensors of data types float32, float64, int32, int64. 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Output of multiplex OP, with data type being float32, float64, int32, int64.

Return type

Tensor

Examples

             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([[5., 6.], [3., 4.]], dtype=float32)

            

multiply ( y, name=None ) multiply¶

multiply two tensors element-wise. The equation is:

\[out = x * y\]

Note

paddle.multiply supports broadcasting. If you would like to know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.multiply, line 10); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, its data type should be one of float32, float64, int32, int64, bool.
y (Tensor) – the input tensor, its data type should be one of float32, float64, int32, int64, bool.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             import paddle

x = paddle.to_tensor([[1, 2], [3, 4]])
y = paddle.to_tensor([[5, 6], [7, 8]])
res = paddle.multiply(x, y)
print(res) # [[5, 12], [21, 32]]

x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]])
y = paddle.to_tensor([2])
res = paddle.multiply(x, y)
print(res) # [[[2, 4, 6], [2, 4, 6]]]

            

multiply_ ( y, name=None ) multiply_¶: Inplace version of multiply API, the output Tensor will be inplaced with input x. Please refer to api_tensor_multiply.

mv ( vec, name=None ) mv¶

Performs a matrix-vector product of the matrix x and the vector vec.

Parameters

x (Tensor) – A tensor with shape $[M, N]$ , The data type of the input Tensor x should be one of float32, float64.
vec (Tensor) – A tensor with shape $[N]$ , The data type of the input Tensor x should be one of float32, float64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The tensor which is producted by x and vec.

Return type

Tensor

Examples

             # x: [M, N], vec: [N]
# paddle.mv(x, vec)  # out: [M]

import paddle

x = paddle.to_tensor([[2, 1, 3], [3, 0, 1]]).astype("float64")
vec = paddle.to_tensor([3, 5, 1]).astype("float64")
out = paddle.mv(x, vec)
print(out)
# Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [14., 10.])

            

nan_to_num ( nan=0.0, posinf=None, neginf=None, name=None ) nan_to_num¶

Replaces NaN, positive infinity, and negative infinity values in input tensor.

Parameters

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, 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, 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Results of nan_to_num operation input Tensor x.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([float('nan'), 0.3, float('+inf'), float('-inf')], dtype='float32')
out1 = paddle.nan_to_num(x)  # [0, 0.3, 3.4028235e+38, -3.4028235e+38]
out2 = paddle.nan_to_num(x, nan=1)  # [1, 0.3, 3.4028235e+38, -3.4028235e+38]
out3 = paddle.nan_to_num(x, posinf=5)  # [0, 0.3, 5, -3.4028235e+38]
out4 = paddle.nan_to_num(x, nan=10, neginf=-99)  # [10, 0.3, 3.4028235e+38, -99]

            

nanmean ( axis=None, keepdim=False, name=None ) nanmean¶

Compute the arithmetic mean along the specified axis, ignoring NaNs.

Parameters

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 $axis + D$ . 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of arithmetic mean along axis of x, with the same data type as x.

Examples

             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)
# 0.44999996
out2 = paddle.nanmean(x, axis=0)
# [0.1, 0.25, 0.5, 0.79999995]
out3 = paddle.nanmean(x, axis=0, keepdim=True)
# [[0.1, 0.25, 0.5, 0.79999995]]
out4 = paddle.nanmean(x, axis=1)
# [0.56666666 0.33333334]
out5 = paddle.nanmean(x, axis=1, keepdim=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])
# [2.66666675, 6.33333349]
out7 = paddle.nanmean(y, axis=[0, 1])
# [3., 6.]

            

nanmedian ( axis=None, keepdim=False, name=None ) nanmedian¶

Compute the median along the specified axis, while ignoring NaNs.

If the valid count of elements is a even number, the average value of both elements in the middle is calculated as the median.

Parameters

x (Tensor) – The input Tensor, it’s data type can be int32, int64, float16, float32, float64.
axis (None|int|list|tuple, optional) – The axis along which to perform median calculations axis should be int or list of int. axis should be in range [-D, D), where D is the dimensions of x . If axis is less than 0, it works the same way as $axis + D$. If axis is None, median 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of median along axis of x. The output dtype is the same as x.

Examples

             import paddle
x = paddle.to_tensor([[float('nan'), 2. , 3. ], [0. , 1. , 2. ]])

y1 = x.nanmedian()
# y1 is 2.

y2 = x.nanmedian(0)
# y2 is [0., 1.5, 2.5]

y3 = x.nanmedian(0, keepdim=True)
# y3 is [[0.,  1.5, 2.5]]

y4 = x.nanmedian((0, 1))
# y4 is 2.

            

nanquantile ( q, axis=None, keepdim=False ) nanquantile¶

Compute the quantile of the input as if NaN values in input did not exist. If all values in a reduced row are NaN, then the quantiles for that reduction will be NaN.

Parameters

x (Tensor) – The input Tensor, it’s data type can be float32, float64, int32, int64.
q (int|float|list) – The q for calculate quantile, which should be in range [0, 1]. If q is a list, each q will be calculated and the first dimension of output is same to the number of q .
axis (int|list, optional) – The axis along which to calculate quantile. axis should be int or list of int. axis should be in range [-D, D), where D is the dimensions of x . If axis is less than 0, it works the same way as $axis + D$. If axis is a list, quantile is calculated over all elements of given axises. If axis is None, quantile 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of quantile along axis of x. In order to obtain higher precision, data type of results will be float64.

Examples

             import paddle

x = paddle.to_tensor(
    [[0, 1, 2, 3, 4],
        [5, 6, 7, 8, 9]],
    dtype="float32")
x[0,0] = float("nan")

y1 = paddle.nanquantile(x, q=0.5, axis=[0, 1])
# Tensor(shape=[], dtype=float64, place=Place(cpu), stop_gradient=True,
#        5.)

y2 = paddle.nanquantile(x, q=0.5, axis=1)
# Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [2.50000000, 7.        ])

y3 = paddle.nanquantile(x, q=[0.3, 0.5], axis=0)
# Tensor(shape=[2, 5], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [[5.        , 2.50000000, 3.50000000, 4.50000000, 5.50000000],
#         [5.        , 3.50000000, 4.50000000, 5.50000000, 6.50000000]])

y4 = paddle.nanquantile(x, q=0.8, axis=1, keepdim=True)
# Tensor(shape=[2, 1], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [[3.40000000],
#         [8.20000000]])

nan = paddle.full(shape=[2, 3], fill_value=float("nan"))
y5 = paddle.nanquantile(nan, q=0.8, axis=1, keepdim=True)
# Tensor(shape=[2, 1], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [[nan],
#         [nan]])

            

nansum ( axis=None, dtype=None, keepdim=False, name=None ) nansum¶

Computes the sum of tensor elements over the given axis, treating Not a Numbers (NaNs) as zero.

Parameters

x (Tensor) – An N-D Tensor, the data type is float16, float32, float64, int32 or int64.
axis (int|list|tuple, optional) – The dimensions along which the nansum is performed. If None, nansum all elements of x and return a Tensor with a single element, otherwise must be in the range $[-rank(x), rank(x))$. If $axis[i] < 0$, the dimension to reduce is $rank + axis[i]$.
dtype (str, optional) – The dtype of output Tensor. The default value is None, the dtype of output is the same as input Tensor x.
keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result Tensor will have one fewer dimension than the x unless keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Results of summation operation on the specified axis of input Tensor x,

Return type

Tensor

Examples

             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)          # 2.7
out2 = paddle.nansum(x, axis=0)  # [0.1, 0.5, 0.5, 1.6]
out3 = paddle.nansum(x, axis=-1) # [1.7, 1.0]
out4 = paddle.nansum(x, axis=1, keepdim=True)  # [[1.7], [1.0]]

# 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]) # [8, 19]
out6 = paddle.nansum(y, axis=[0, 1]) # [9, 18]

            

property ndim

Returns the dimension of current Variable

Returns: the dimension

Examples

             import paddle

paddle.enable_static()

# create a static Variable
x = paddle.static.data(name='x', shape=[3, 2, 1])
# print the dimension of the Variable
print(x.ndim)

            

neg ( name=None ) neg¶

This function computes the negative of the Tensor elementwisely.

Parameters

x (Tensor) – Input of neg operator, an N-D Tensor, with data type float32, float64, int8, int16, int32, or int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The negative of input Tensor. The shape and data type are the same with input Tensor.

Return type

out (Tensor)

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.neg(x)
print(out)
# [0.4 0.2 -0.1 -0.3]

            

nextafter ( y, name=None ) nextafter¶

Return the next floating-point value after input towards other, elementwise. The shapes of input and other must be broadcastable.

Parameters

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 Name.

Returns

An N-D Tensor, the shape and data type is the same with input.

Return type

out (Tensor)

Examples

             import paddle
out = paddle.nextafter(paddle.to_tensor([1.0,2.0]),paddle.to_tensor([2.0,1.0]))
print(out)
#Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
#       [1.00000012, 1.99999988])

            

nonzero ( as_tuple=False ) nonzero¶

Return a tensor containing the indices of all non-zero elements of the input tensor. If as_tuple is True, return a tuple of 1-D tensors, one for each dimension in input, each containing the indices (in that dimension) of all non-zero elements of input. Given a n-Dimensional input tensor with shape [x_1, x_2, …, x_n], If as_tuple is False, we can get a output tensor with shape [z, n], where z is the number of all non-zero elements in the input tensor. If as_tuple is True, we can get a 1-D tensor tuple of length n, and the shape of each 1-D tensor is [z, 1].

Parameters

x (Tensor) – The input tensor variable.
as_tuple (bool, optional) – Return type, Tensor or tuple of Tensor.

Returns

Tensor. The data type is int64.

Examples

             import paddle

x1 = paddle.to_tensor([[1.0, 0.0, 0.0],
                       [0.0, 2.0, 0.0],
                       [0.0, 0.0, 3.0]])
x2 = paddle.to_tensor([0.0, 1.0, 0.0, 3.0])
out_z1 = paddle.nonzero(x1)
print(out_z1)
#[[0 0]
# [1 1]
# [2 2]]
out_z1_tuple = paddle.nonzero(x1, as_tuple=True)
for out in out_z1_tuple:
    print(out)
#[[0]
# [1]
# [2]]
#[[0]
# [1]
# [2]]
out_z2 = paddle.nonzero(x2)
print(out_z2)
#[[1]
# [3]]
out_z2_tuple = paddle.nonzero(x2, as_tuple=True)
for out in out_z2_tuple:
    print(out)
#[[1]
# [3]]

            

norm ( p='fro', axis=None, keepdim=False, name=None ) norm¶

Returns the matrix norm (Frobenius) or vector norm (the 1-norm, the Euclidean or 2-norm, and in general the p-norm for p > 0) of a given tensor.

Note

This norm API is different from numpy.linalg.norm. This api supports high-order input tensors (rank >= 3), and certain axis need to be pointed out to calculate the norm. But numpy.linalg.norm only supports 1-D vector or 2-D matrix as input tensor. For p-order matrix norm, this api actually treats matrix as a flattened vector to calculate the vector norm, NOT REAL MATRIX NORM.

Parameters

x (Tensor) – The input tensor could be N-D tensor, and the input data type could be float32 or float64.
p (float|string, optional) – Order of the norm. Supported values are fro, 0, 1, 2, inf, -inf and any positive real number yielding the corresponding p-norm. Not supported: ord < 0 and nuclear norm. Default value is fro.
axis (int|list|tuple, optional) – The axis on which to apply norm operation. If axis is int or list(int)/tuple(int) with only one element, the vector norm is computed over the axis. If axis < 0, the dimension to norm operation is rank(input) + axis. If axis is a list(int)/tuple(int) with two elements, the matrix norm is computed over the axis. Default value is None.
keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result tensor will have fewer dimension than the input unless keepdim is true, default value is False.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

results of norm operation on the specified axis of input tensor, it’s data type is the same as input’s Tensor.

Return type

Tensor

Examples

             import paddle
x = paddle.arange(24, dtype="float32").reshape([2, 3, 4]) - 12
# x: Tensor(shape=[2, 3, 4], dtype=float32, place=Place(cpu), stop_gradient=True,
#          [[[-12., -11., -10., -9. ],
#            [-8. , -7. , -6. , -5. ],
#            [-4. , -3. , -2. , -1. ]],

#           [[ 0. ,  1. ,  2. ,  3. ],
#            [ 4. ,  5. ,  6. ,  7. ],
#            [ 8. ,  9. ,  10.,  11.]]])

# compute frobenius norm along last two dimensions.
out_fro = paddle.linalg.norm(x, p='fro', axis=[0,1])
# out_fro: Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True,
#                 [17.43559647, 16.91153526, 16.73320007, 16.91153526])

# compute 2-order vector norm along last dimension.
out_pnorm = paddle.linalg.norm(x, p=2, axis=-1)
# out_pnorm: Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True,
#                [[21.11871147, 13.19090557, 5.47722578 ],
#                 [3.74165750 , 11.22497177, 19.13112640]])

# compute 2-order  norm along [0,1] dimension.
out_pnorm = paddle.linalg.norm(x, p=2, axis=[0,1])
# out_pnorm: Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True,
#                  [17.43559647, 16.91153526, 16.73320007, 16.91153526])

# compute inf-order  norm
out_pnorm = paddle.linalg.norm(x, p=float("inf"))
# out_pnorm  = Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#                    12.)

out_pnorm = paddle.linalg.norm(x, p=float("inf"), axis=0)
# out_pnorm: Tensor(shape=[3, 4], dtype=float32, place=Place(cpu), stop_gradient=True,
#                 [[12., 11., 10., 9. ],
#                  [8. , 7. , 6. , 7. ],
#                  [8. , 9. , 10., 11.]])

# compute -inf-order  norm
out_pnorm = paddle.linalg.norm(x, p=-float("inf"))
# out_pnorm: Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#                  0.)

out_pnorm = paddle.linalg.norm(x, p=-float("inf"), axis=0)
# out_pnorm: Tensor(shape=[3, 4], dtype=float32, place=Place(cpu), stop_gradient=True,
#                  [[0., 1., 2., 3.],
#                  [4., 5., 6., 5.],
#                  [4., 3., 2., 1.]])

            

not_equal ( y, name=None ) not_equal¶

Returns the truth value of $x != y$ elementwise, which is equivalent function to the overloaded operator !=.

Note

The output has no gradient.

Parameters

x (Tensor) – First input to compare which is N-D tensor. The input data type should be bool, float32, float64, int32, int64.
y (Tensor) – Second input to compare which is N-D tensor. The input data type should be bool, float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The output shape is same as input x. The output data type is bool.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([1, 2, 3])
y = paddle.to_tensor([1, 3, 2])
result1 = paddle.not_equal(x, y)
print(result1)  # result1 = [False True True]

            

numel ( name=None ) numel¶

Returns the number of elements for a tensor, which is a 0-D int64 Tensor with shape [].

Parameters

x (Tensor) – The input Tensor, it’s data type can be bool, float16, float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The number of elements for the input Tensor, whose shape is [].

Return type

Tensor

Examples

             import paddle

x = paddle.full(shape=[4, 5, 7], fill_value=0, dtype='int32')
numel = paddle.numel(x) # 140

outer ( y, name=None ) outer¶

Outer product of two Tensors.

Input is flattened if not already 1-dimensional.

Parameters

x (Tensor) – An N-D Tensor or a Scalar Tensor.
y (Tensor) – An N-D Tensor or a Scalar Tensor.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The outer-product Tensor.

Return type

Tensor

Examples

             import paddle
x = paddle.arange(1, 4).astype('float32')
y = paddle.arange(1, 6).astype('float32')
out = paddle.outer(x, y)
print(out)
#        ([[1, 2, 3, 4, 5],
#         [2, 4, 6, 8, 10],
#         [3, 6, 9, 12, 15]])

            

place ( ) place¶: Variable don’t have ‘place’ interface in static graph mode But this interface can greatly facilitate dy2static. So we give a warnning here and return None.

polar ( angle, name=None ) polar¶

Return a Cartesian coordinates corresponding to the polar coordinates compelx tensor given the abs and angle component.

Parameters

abs (Tensor) – The abs component. The data type should be ‘float32’ or ‘float64’.
angle (Tensor) – The anglee component. The data type should be the same as abs.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

The output tensor. The data type is ‘complex64’ or ‘complex128’, with the same precision as abs and angle.

Return type

Tensor

Note

paddle.polar supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.creation.polar, line 17); backlink

Duplicate explicit target name: “introduction to tensor”.

Examples

             import paddle
import numpy as np

abs = paddle.to_tensor([1, 2], dtype=paddle.float64)
angle = paddle.to_tensor([np.pi / 2, 5 * np.pi / 4], dtype=paddle.float64)
out = paddle.polar(abs, angle)
print(out)
# Tensor(shape=[2], dtype=complex128, place=Place(cpu), stop_gradient=True,
#       [ (6.123233995736766e-17+1j) ,
#       (-1.4142135623730954-1.414213562373095j)])

            

polygamma ( n, name=None ) polygamma¶

Calculates the polygamma of the given input tensor, element-wise.

The equation is:

\[\Phi^n(x) = \frac{d^n}{dx^n} [\ln(\Gamma(x))]\]

Parameters

x (Tensor) – Input Tensor. Must be one of the following types: float32, float64.
n (int) – Order of the derivative. Must be integral.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

out (Tensor), A Tensor. the polygamma of the input Tensor, the shape and data type is the same with input.

Examples

             import paddle

data = paddle.to_tensor([2, 3, 25.5], dtype='float32')
res = paddle.polygamma(data, 1)
print(res)
# Tensor(shape=[2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#       [0.64493407,  0.39493407,  0.03999467])

            

pop ( *args ) pop¶

The type variable must be LoD Tensor Array. When self is LoDTensorArray, calling pop is similar to Python’s pop on list. This interface is used to simplify dygraph to static graph operations.

Parameters

self (Variable) – The source variable, which must be LOD_TENSOR_ARRAY
*args – optional, a int means index.

Returns

self[index]

Return type

Variable

pow ( y, name=None ) pow¶

Compute the power of Tensor elements. The equation is:

\[out = x^{y}\]

Note

paddle.pow supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.pow, line 10); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – An N-D Tensor, the data type is float16, float32, float64, int32 or int64.
y (float|int|Tensor) – If it is an N-D Tensor, its data type should be the same as x.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

N-D Tensor. A location into which the result is stored. Its dimension and data type are the same as x.

Examples

             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=CUDAPlace(0), stop_gradient=True,
#        [1., 4., 9.])
res = paddle.pow(x, 2.5)
print(res)
# Tensor(shape=[3], dtype=float32, place=CUDAPlace(0), 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=CUDAPlace(0), stop_gradient=True,
#        [1., 4., 9.])

            

prod ( axis=None, keepdim=False, dtype=None, name=None ) prod¶

Compute the product of tensor elements over the given axis.

Parameters

x (Tensor) – The input tensor, its data type should be float32, float64, int32, int64.
axis (int|list|tuple, optional) – The axis along which the product is computed. If None, multiply all elements of x and return a Tensor with a single element, otherwise must be in the range $[-x.ndim, x.ndim)$. If $axis[i]<0$, the axis to reduce is $x.ndim + axis[i]$. Default is None.
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|np.dtype, optional) – The desired date type of returned tensor, can be float32, float64, int32, int64. If specified, the input tensor is casted to dtype before operator performed. This is very useful for avoiding data type overflows. The default value is None, the dtype of output is the same as input Tensor x.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, result of product on the specified dim of input tensor.

Examples

             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)
# 0.0002268

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

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

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

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

# the axis is list
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])
# [105. 384.]

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

            

put_along_axis ( indices, values, axis, reduce='assign' ) put_along_axis¶

Put values into the destination array by given indices matrix along the designated axis.

Parameters

arr (Tensor) – The Destination Tensor. Supported data types are float32 and float64.
indices (Tensor) – Indices to put along each 1d slice of arr. This must match the dimension of arr, and need to broadcast against arr. Supported data type are int and int64.
axis (int) – The axis to put 1d slices along.
reduce (str, optional) – The reduce operation, default is ‘assign’, support ‘add’, ‘assign’, ‘mul’ and ‘multiply’.

Returns

Tensor, The indexed element, same dtype with arr

Examples

             import paddle

x = paddle.to_tensor([[10, 30, 20], [60, 40, 50]])
index = paddle.to_tensor([[0]])
value = 99
axis = 0
result = paddle.put_along_axis(x, index, value, axis)
print(result)
# [[99, 99, 99],
# [60, 40, 50]]

            

put_along_axis_ ( indices, values, axis, reduce='assign' ) put_along_axis_¶: Inplace version of put_along_axis API, the output Tensor will be inplaced with input arr. Please refer to api_tensor_put_along_axis.

qr ( mode='reduced', name=None ) qr¶

Computes the QR decomposition of one matrix or batches of matrice (backward is unsupported now).

Parameters

x (Tensor) – The input tensor. Its shape should be […, M, N], where … is zero or more batch dimensions. M and N can be arbitrary positive number. The data type of x should be float32 or float64.
mode (str, optional) – A flag to control the behavior of qr, the default is “reduced”. Suppose x’s shape is […, M, N] and denoting K = min(M, N): If mode = “reduced”, qr op will return reduced Q and R matrices, which means Q’s shape is […, M, K] and R’s shape is […, K, N]. If mode = “complete”, qr op will return complete Q and R matrices, which means Q’s shape is […, M, M] and R’s shape is […, M, N]. If mode = “r”, qr op will only return reduced R matrix, which means R’s shape is […, K, N].
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

If mode = “reduced” or mode = “complete”, qr will return a two tensor-tuple, which represents Q and R. If mode = “r”, qr will return a tensor which represents R.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]).astype('float64')
q, r = paddle.linalg.qr(x)
print (q)
print (r)

# Q = [[-0.16903085,  0.89708523],
#      [-0.50709255,  0.27602622],
#      [-0.84515425, -0.34503278]])

# R = [[-5.91607978, -7.43735744],
#      [ 0.        ,  0.82807867]])

# one can verify : X = Q * R ;

            

quantile ( q, axis=None, keepdim=False ) quantile¶

Compute the quantile of the input along the specified axis. If any values in a reduced row are NaN, then the quantiles for that reduction will be NaN.

Parameters

x (Tensor) – The input Tensor, it’s data type can be float32, float64, int32, int64.
q (int|float|list) – The q for calculate quantile, which should be in range [0, 1]. If q is a list, each q will be calculated and the first dimension of output is same to the number of q .
axis (int|list, optional) – The axis along which to calculate quantile. axis should be int or list of int. axis should be in range [-D, D), where D is the dimensions of x . If axis is less than 0, it works the same way as $axis + D$. If axis is a list, quantile is calculated over all elements of given axises. If axis is None, quantile 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of quantile along axis of x. In order to obtain higher precision, data type of results will be float64.

Examples

             import paddle

y = paddle.arange(0, 8 ,dtype="float32").reshape([4, 2])
# Tensor(shape=[4, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[0., 1.],
#         [2., 3.],
#         [4., 5.],
#         [6., 7.]])

y1 = paddle.quantile(y, q=0.5, axis=[0, 1])
# Tensor(shape=[], dtype=float64, place=Place(cpu), stop_gradient=True,
#        3.50000000)

y2 = paddle.quantile(y, q=0.5, axis=1)
# Tensor(shape=[4], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [0.50000000, 2.50000000, 4.50000000, 6.50000000])

y3 = paddle.quantile(y, q=[0.3, 0.5], axis=0)
# Tensor(shape=[2, 2], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [[1.80000000, 2.80000000],
#         [3.        , 4.        ]])

y[0,0] = float("nan")
y4 = paddle.quantile(y, q=0.8, axis=1, keepdim=True)
# Tensor(shape=[4, 1], dtype=float64, place=Place(cpu), stop_gradient=True,
#        [[nan       ],
#         [2.80000000],
#         [4.80000000],
#         [6.80000000]])

            

rad2deg ( name=None ) rad2deg¶

Convert each of the elements of input x from angles in radians to degrees.

Equation:: \[rad2deg(x)=180/ \pi * x\]

Parameters

x (Tensor) – An N-D Tensor, the data type is float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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).

Return type

out (Tensor)

Examples

             import paddle
import math

x1 = paddle.to_tensor([3.142, -3.142, 6.283, -6.283, 1.570, -1.570])
result1 = paddle.rad2deg(x1)
print(result1)
# Tensor(shape=[6], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#         [180.02334595, -180.02334595,  359.98937988, -359.98937988,
#           9.95437622 , -89.95437622])

x2 = paddle.to_tensor(math.pi/2)
result2 = paddle.rad2deg(x2)
print(result2)
# Tensor(shape=[], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#         90.)

x3 = paddle.to_tensor(1)
result3 = paddle.rad2deg(x3)
print(result3)
# Tensor(shape=[], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        57.29578018)

            

rank ( ) rank¶

Returns the number of dimensions for a tensor, which is a 0-D int32 Tensor.

Parameters: input (Tensor) – The input Tensor with shape of $[N_1, N_2, ..., N_k]$, the data type is arbitrary.
Returns: The 0-D tensor with the dimensions of the input Tensor.
Return type: Tensor, the output data type is int32.

Examples

             import paddle

input = paddle.rand((3, 100, 100))
rank = paddle.rank(input)
print(rank)
# 3

            

real ( name=None ) real¶

Returns a new Tensor containing real values of the input Tensor.

Parameters

x (Tensor) – the input Tensor, its data type could be complex64 or complex128.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

a Tensor containing real values of the input Tensor.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor(
    [[1 + 6j, 2 + 5j, 3 + 4j], [4 + 3j, 5 + 2j, 6 + 1j]])
# Tensor(shape=[2, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
#        [[(1+6j), (2+5j), (3+4j)],
#         [(4+3j), (5+2j), (6+1j)]])

real_res = paddle.real(x)
# Tensor(shape=[2, 3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        [[1., 2., 3.],
#         [4., 5., 6.]])

real_t = x.real()
# Tensor(shape=[2, 3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#        [[1., 2., 3.],
#         [4., 5., 6.]])

            

reciprocal ( name=None ) reciprocal¶

Reciprocal Activation Operator.

\[out = \frac{1}{x}\]

Parameters

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

Returns

Tensor. Output of Reciprocal operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.reciprocal(x)
print(out)
# [-2.5        -5.         10.          3.33333333]

            

reciprocal_ ( name=None ) reciprocal_¶: Inplace version of reciprocal API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_reciprocal.

remainder ( y, name=None ) remainder¶

Mod two tensors element-wise. The equation is:

\[out = x \% y\]

Note

paddle.remainder supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.remainder, line 11); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float16, float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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)  # [0, 3, 2, 1]

            

remainder_ ( y, name=None ) remainder_¶: Inplace version of remainder API, the output Tensor will be inplaced with input x. Please refer to api_tensor_remainder.

repeat_interleave ( repeats, axis=None, name=None ) repeat_interleave¶

Returns a new tensor which repeats the x tensor along dimension axis using the entries in repeats which is a int or a Tensor.

Parameters

x (Tensor) – The input Tensor to be operated. The data of x can be one of float32, float64, int32, int64.
repeats (Tensor or int) – The number of repetitions for each element. repeats is broadcasted to fit the shape of the given axis.
axis (int, optional) – The dimension in which we manipulate. Default: None, the output tensor is flatten.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

Tensor, A Tensor with same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[1, 2, 3], [4, 5, 6]])
repeats  = paddle.to_tensor([3, 2, 1], dtype='int32')

paddle.repeat_interleave(x, repeats, 1)
# [[1, 1, 1, 2, 2, 3],
#  [4, 4, 4, 5, 5, 6]]

paddle.repeat_interleave(x, 2, 0)
# [[1, 2, 3], [1, 2, 3], [4, 5, 6], [4, 5, 6]]

paddle.repeat_interleave(x, 2, None)
# [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6]

            

reshape ( shape, name=None ) reshape¶

Changes the shape of x without changing its data.

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

Some tricks exist when specifying the target shape.

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

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

Here are some examples to explain it.

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

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

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

Parameters

x (Tensor) – An N-D Tensor. The data type is float32, float64, int32, int64 or bool
shape (list|tuple|Tensor) – Define the target shape. At most one dimension of the target shape can be -1. The data type is int32 . If shape is a list or tuple, each element of it should be integer or Tensor with shape []. If shape is an Tensor, it should be an 1-D Tensor .
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, A reshaped Tensor with the same data type as x.

Examples

             import paddle

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

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

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

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

            

reshape_ ( shape, name=None ) reshape_¶: Inplace version of reshape API, the output Tensor will be inplaced with input x. Please refer to api_paddle_tensor_reshape.

reverse ( axis, name=None ) reverse¶

Reverse the order of a n-D tensor along given axis in axis.

Parameters

x (Tensor) – A Tensor(or LoDTensor) with shape $[N_1, N_2,..., N_k]$ . The data type of the input Tensor x should be float32, float64, int32, int64, bool.
axis (list|tuple|int) – The axis(axes) to flip on. Negative indices for indexing from the end are accepted.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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

Examples

             import paddle

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

out = paddle.flip(tmp,-1)
print(out) # [[[11,10],[9, 8]], [[7, 6],[5, 4]], [[3, 2],[1, 0]]]

            

roll ( shifts, axis=None, name=None ) roll¶

Roll the x tensor along the given axis(axes). With specific ‘shifts’, Elements that roll beyond the last position are re-introduced at the first according to ‘shifts’. If a axis is not specified, the tensor will be flattened before rolling and then restored to the original shape.

Parameters

x (Tensor) – The x tensor as input.
shifts (int|list|tuple) – The number of places by which the elements of the x tensor are shifted.
axis (int|list|tuple, optional) – axis(axes) along which to roll. Default: None
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

Tensor, A Tensor with same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0, 3.0],
                      [4.0, 5.0, 6.0],
                      [7.0, 8.0, 9.0]])
out_z1 = paddle.roll(x, shifts=1)
print(out_z1)
#[[9. 1. 2.]
# [3. 4. 5.]
# [6. 7. 8.]]
out_z2 = paddle.roll(x, shifts=1, axis=0)
print(out_z2)
#[[7. 8. 9.]
# [1. 2. 3.]
# [4. 5. 6.]]
out_z3 = paddle.roll(x, shifts=1, axis=1)
print(out_z3)
#[[3. 1. 2.]
# [6. 4. 5.]
# [9. 7. 8.]]

            

rot90 ( k=1, axes=[0, 1], name=None ) rot90¶

Rotate a n-D tensor by 90 degrees. The rotation direction and times are specified by axes and the absolute value of k. Rotation direction is from axes[0] towards axes[1] if k > 0, and from axes[1] towards axes[0] for k < 0.

Parameters

x (Tensor) – The input Tensor(or LoDTensor). The data type of the input Tensor x should be float16, float32, float64, int32, int64, bool. float16 is only supported on gpu.
k (int, optional) – Direction and number of times to rotate, default value: 1.
axes (list|tuple, optional) – Axes to rotate, dimension must be 2. default value: [0, 1].
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

Tensor, Tensor or LoDTensor calculated by rot90 layer. The data type is same with input x.

Examples

             import paddle

data = paddle.arange(4)
data = paddle.reshape(data, (2, 2))
print(data)
#[[0, 1],
# [2, 3]]

y = paddle.rot90(data, 1, [0, 1])
print(y)
#[[1, 3],
# [0, 2]]

y= paddle.rot90(data, -1, [0, 1])
print(y)
#[[2, 0],
# [3, 1]]

data2 = paddle.arange(8)
data2 = paddle.reshape(data2, (2,2,2))
print(data2)
#[[[0, 1],
#  [2, 3]],
# [[4, 5],
#  [6, 7]]]

y = paddle.rot90(data2, 1, [1, 2])
print(y)
#[[[1, 3],
#  [0, 2]],
# [[5, 7],
#  [4, 6]]]

            

round ( name=None ) round¶

Round the values in the input to the nearest integer value.

             input:
  x.shape = [4]
  x.data = [1.2, -0.9, 3.4, 0.9]

output:
  out.shape = [4]
  out.data = [1., -1., 3., 1.]

            

Parameters

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

Returns

Tensor. Output of Round operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.5, -0.2, 0.6, 1.5])
out = paddle.round(x)
print(out)
# [-1. -0.  1.  2.]

            

round_ ( name=None ) round_¶: Inplace version of round API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_round.

rsqrt ( name=None ) rsqrt¶

Rsqrt Activation Operator.

Please make sure input is legal in case of numeric errors.

\[out = \frac{1}{\sqrt{x}}\]

Parameters

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

Returns

Tensor. Output of Rsqrt operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([0.1, 0.2, 0.3, 0.4])
out = paddle.rsqrt(x)
print(out)
# [3.16227766 2.23606798 1.82574186 1.58113883]

            

rsqrt_ ( name=None ) rsqrt_¶: Inplace version of rsqrt API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_rsqrt.

scale ( scale=1.0, bias=0.0, bias_after_scale=True, act=None, name=None ) scale¶

Scale operator.

Putting scale and bias to the input Tensor as following:

bias_after_scale is True:

\[Out=scale*X+bias\]

bias_after_scale is False:

\[Out=scale*(X+bias)\]

Parameters

x (Tensor) – Input N-D Tensor of scale operator. Data type can be float32, float64, int8, int16, int32, int64, uint8.
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, optional) – Activation applied to the output such as tanh, softmax, sigmoid, relu.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Output Tensor of scale operator, with shape and data type same as input.

Return type

Tensor

Examples

             # scale as a float32 number
import paddle

data = paddle.randn(shape=[2,3], dtype='float32')
res = paddle.scale(data, scale=2.0, bias=1.0)

             # scale with parameter scale as a Tensor
import paddle

data = paddle.randn(shape=[2, 3], dtype='float32')
factor = paddle.to_tensor([2], dtype='float32')
res = paddle.scale(data, scale=factor, bias=1.0)

            

scale_ ( scale=1.0, bias=0.0, bias_after_scale=True, act=None, name=None ) scale_¶: Inplace version of scale API, the output Tensor will be inplaced with input x. Please refer to api_tensor_scale.

scatter ( index, updates, overwrite=True, name=None ) scatter¶

Scatter Layer Output is obtained by updating the input on selected indices based on updates.

             import paddle
#input:
x = paddle.to_tensor([[1, 1], [2, 2], [3, 3]], dtype='float32')
index = paddle.to_tensor([2, 1, 0, 1], dtype='int64')
# shape of updates should be the same as x
# shape of updates with dim > 1 should be the same as input
updates = paddle.to_tensor([[1, 1], [2, 2], [3, 3], [4, 4]], dtype='float32')
overwrite = False
# calculation:
if not overwrite:
    for i in range(len(index)):
        x[index[i]] = paddle.zeros([2])
for i in range(len(index)):
    if (overwrite):
        x[index[i]] = updates[i]
    else:
        x[index[i]] += updates[i]
# output:
out = paddle.to_tensor([[3, 3], [6, 6], [1, 1]])
out.shape # [3, 2]

            

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

Parameters

x (Tensor) – The input N-D Tensor with ndim>=1. Data type can be float32, float64.
index (Tensor) – The index is a 1-D or 0-D Tensor. Data type can be int32, int64. The length of index cannot exceed updates’s length, and the value in index cannot exceed input’s length.
updates (Tensor) – Update input with updates parameter based on index. When the index is a 1-D tensor, the updates shape should be the same as input, and dim value with dim > 1 should be the same as input. When the index is a 0-D tensor, the updates should be a (N-1)-D tensor, the ith dim of the updates should be queal with the (i+1)th dim of the input.
overwrite (bool, optional) –
The mode that updating the output when there are same indices.

If True, use the overwrite mode to update the output of the same index, if False, use the accumulate mode to update the output of the same index. Default value is True.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

Tensor, The output is a Tensor with the same shape as x.

Examples

             import paddle

x = paddle.to_tensor([[1, 1], [2, 2], [3, 3]], dtype='float32')
index = paddle.to_tensor([2, 1, 0, 1], dtype='int64')
updates = paddle.to_tensor([[1, 1], [2, 2], [3, 3], [4, 4]], dtype='float32')

output1 = paddle.scatter(x, index, updates, overwrite=False)
# [[3., 3.],
#  [6., 6.],
#  [1., 1.]]

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

            

scatter_ ( index, updates, overwrite=True, name=None ) scatter_¶: Inplace version of scatter API, the output Tensor will be inplaced with input x. Please refer to api_paddle_tensor_scatter.

scatter_nd ( updates, shape, name=None ) scatter_nd¶

Scatter_nd Layer

Output is obtained by scattering the updates in a new tensor according to index . This op is similar to scatter_nd_add, except the tensor of shape is zero-initialized. Correspondingly, scatter_nd(index, updates, shape) is equal to scatter_nd_add(paddle.zeros(shape, updates.dtype), index, updates) . If index has repeated elements, then the corresponding updates are accumulated. Because of the numerical approximation issues, the different order of repeated elements in index may cause different results. The specific calculation method can be seen scatter_nd_add . This op is the inverse of the gather_nd op.

Parameters

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

Returns

output (Tensor), The output is a tensor with the same type as updates .

Examples

             import paddle

index = paddle.to_tensor([[1, 1],
                        [0, 1],
                        [1, 3]], dtype="int64")
updates = paddle.rand(shape=[3, 9, 10], dtype='float32')
shape = [3, 5, 9, 10]

output = paddle.scatter_nd(index, updates, shape)

            

scatter_nd_add ( index, updates, name=None ) scatter_nd_add¶

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

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

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

             Given:

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

  we get:

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

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

  we get:

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

            

Parameters

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

Returns

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

Examples

             import paddle

x = paddle.rand(shape=[3, 5, 9, 10], dtype='float32')
updates = paddle.rand(shape=[3, 9, 10], dtype='float32')
index = paddle.to_tensor([[1, 1],
                        [0, 1],
                        [1, 3]], dtype='int64')

output = paddle.scatter_nd_add(x, index, updates)
print(output.shape)
# [3, 5, 9, 10]

            

sgn ( name=None ) sgn¶

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.

Parameters

x (Tensor) – The input tensor, which data type should be float16, float32, float64, complex64, complex128.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

A sign Tensor for real input, or normalized Tensor for complex input, shape and data type are same as input.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[3 + 4j, 7 - 24j, 0, 1 + 2j], [6 + 8j, 3, 0, -2]])
print(paddle.sgn(x))
#[[0.6+0.8j       0.28-0.96j      0.+0.j      0.4472136+0.8944272j]
# [0.6+0.8j       1.+0.j          0.+0.j      -1.+0.j]]

            

shard_index ( index_num, nshards, shard_id, ignore_value=- 1 ) shard_index¶

Reset the values of input according to the shard it beloning to. Every value in input must be a non-negative integer, and the parameter index_num represents the integer above the maximum value of input. Thus, all values in input must be in the range [0, index_num) and each value can be regarded as the offset to the beginning of the range. The range is further split into multiple shards. Specifically, we first compute the shard_size according to the following formula, which represents the number of integers each shard can hold. So for the i’th shard, it can hold values in the range [i*shard_size, (i+1)*shard_size).

             shard_size = (index_num + nshards - 1) // nshards

            

For each value v in input, we reset it to a new value according to the following formula:

             v = v - shard_id * shard_size if shard_id * shard_size <= v < (shard_id+1) * shard_size else ignore_value

            

That is, the value v is set to the new offset within the range represented by the shard shard_id if it in the range. Otherwise, we reset it to be ignore_value.

Parameters

input (Tensor) – Input tensor with data type int64 or int32. It’s last dimension must be 1.
index_num (int) – An integer represents the integer above the maximum value of input.
nshards (int) – The number of shards.
shard_id (int) – The index of the current shard.
ignore_value (int, optional) – An integer value out of sharded index range. The default value is -1.

Returns

Tensor.

Examples

             import paddle
label = paddle.to_tensor([[16], [1]], "int64")
shard_label = paddle.shard_index(input=label,
                                 index_num=20,
                                 nshards=2,
                                 shard_id=0)
print(shard_label)
# [[-1], [1]]

            

sigmoid ( name=None ) sigmoid¶

Sigmoid Activation.

\[out = \frac{1}{1 + e^{-x}}\]

Parameters

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

Returns

Tensor. Output of Sigmoid operator, a Tensor with shape same as input.

Examples

             import paddle
import paddle.nn.functional as F

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = F.sigmoid(x)
print(out)
# [0.40131234 0.450166   0.52497919 0.57444252]

            

sigmoid_ ( name=None ) sigmoid_¶: Inplace version of sigmoid API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_sigmoid.

sign ( name=None ) sign¶

Returns sign of every element in x: 1 for positive, -1 for negative and 0 for zero.

Parameters

x (Tensor) – The input tensor. The data type can be float16, float32 or float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output sign tensor with identical shape and data type to the input x.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([3.0, 0.0, -2.0, 1.7], dtype='float32')
out = paddle.sign(x=x)
print(out)  # [1.0, 0.0, -1.0, 1.0]

sin ( name=None ) sin¶

Sine Activation Operator.

\[out = sin(x)\]

Parameters

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

Returns

Tensor. Output of Sin operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.sin(x)
print(out)
# [-0.38941834 -0.19866933  0.09983342  0.29552021]

            

sinh ( name=None ) sinh¶

Sinh Activation Operator.

\[out = sinh(x)\]

Parameters

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

Returns

Tensor. Output of Sinh operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.sinh(x)
print(out)
# [-0.41075233 -0.201336    0.10016675  0.30452029]

            

slice ( axes, starts, ends ) slice¶

This operator produces a slice of input along multiple axes. Similar to numpy: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html Slice uses axes, starts and ends attributes to specify the start and end dimension for each axis in the list of axes and Slice uses this information to slice the input data tensor. If a negative value is passed to starts or ends such as $-i$, it represents the reverse position of the axis $i-1$ (here 0 is the initial position). If the value passed to starts or ends is greater than n (the number of elements in this dimension), it represents n. For slicing to the end of a dimension with unknown size, it is recommended to pass in INT_MAX. The size of axes must be equal to starts and ends. Following examples will explain how slice works:

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

Case2:
    Given:
        data = [ [1, 2, 3, 4], [5, 6, 7, 8], ]
        axes = [0, 1]
        starts = [0, 1]
        ends = [-1, 1000]       # -1 denotes the reverse 0th position of dimension 0.
    Then:
        result = [ [2, 3, 4], ] # result = data[0:1, 1:4]

            

Parameters

input (Tensor) – A Tensor . The data type is float16, float32, float64, int32 or int64.
axes (list|tuple) – The data type is int32 . Axes that starts and ends apply to .
starts (list|tuple|Tensor) – The data type is int32 . If starts is a list or tuple, each element of it should be integer or 0-D int Tensor with shape []. If starts is an Tensor, it should be an 1-D Tensor. It represents starting indices of corresponding axis in axes.
ends (list|tuple|Tensor) – The data type is int32 . If ends is a list or tuple, each element of it should be integer or 0-D int Tensor with shape []. If ends is an Tensor, it should be an 1-D Tensor . It represents ending indices of corresponding axis in axes.

Returns

Tensor, A Tensor. The data type is same as input.

Examples

             import paddle

input = paddle.rand(shape=[4, 5, 6], dtype='float32')
# example 1:
# attr starts is a list which doesn't contain tensor.
axes = [0, 1, 2]
starts = [-3, 0, 2]
ends = [3, 2, 4]
sliced_1 = paddle.slice(input, axes=axes, starts=starts, ends=ends)
# sliced_1 is input[1:3, 0:2, 2:4].

# example 2:
# attr starts is a list which contain tensor.
minus_3 = paddle.full([1], -3, "int32")
sliced_2 = paddle.slice(input, axes=axes, starts=[minus_3, 0, 2], ends=ends)
# sliced_2 is input[1:3, 0:2, 2:4].

            

solve ( y, name=None ) solve¶

Computes the solution of a square system of linear equations with a unique solution for input ‘X’ and ‘Y’. Let $X$ be a sqaure matrix or a batch of square matrices, $Y$ be a vector/matrix or a batch of vectors/matrices, the equation should be:

\[Out = X^-1 * Y\]

Specifically, this system of linear equations has one solution if and only if input ‘X’ is invertible.

Parameters

x (Tensor) – A square matrix or a batch of square matrices. Its shape should be [*, M, M], where * is zero or more batch dimensions. Its data type should be float32 or float64.
y (Tensor) – A vector/matrix or a batch of vectors/matrices. Its shape should be [*, M, K], where * is zero or more batch dimensions. Its data type should be float32 or float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The solution of a square system of linear equations with a unique solution for input ‘x’ and ‘y’. Its data type should be the same as that of x.

Return type

Tensor

Examples

             # a square system of linear equations:
# 2*X0 + X1 = 9
# X0 + 2*X1 = 8

import paddle

x = paddle.to_tensor([[3, 1],[1, 2]], dtype="float64")
y = paddle.to_tensor([9, 8], dtype="float64")
out = paddle.linalg.solve(x, y)

print(out)
# [2., 3.])

            

sort ( axis=- 1, descending=False, name=None ) sort¶

Sorts the input along the given axis, and returns the sorted output tensor. The default sort algorithm is ascending, if you want the sort algorithm to be descending, you must set the descending as True.

Parameters

x (Tensor) – An input N-D Tensor with type float32, float64, int16, int32, int64, uint8.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is Rank(x). when axis<0, it works the same way as axis+R. Default is -1.
descending (bool, optional) – Descending is a flag, if set to true, algorithm will sort by descending order, else sort by ascending order. Default is false.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

sorted tensor(with the same shape and data type as x).

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([[[5,8,9,5],
                       [0,0,1,7],
                       [6,9,2,4]],
                      [[5,2,4,2],
                       [4,7,7,9],
                       [1,7,0,6]]],
                     dtype='float32')
out1 = paddle.sort(x=x, axis=-1)
out2 = paddle.sort(x=x, axis=0)
out3 = paddle.sort(x=x, axis=1)
print(out1)
#[[[5. 5. 8. 9.]
#  [0. 0. 1. 7.]
#  [2. 4. 6. 9.]]
# [[2. 2. 4. 5.]
#  [4. 7. 7. 9.]
#  [0. 1. 6. 7.]]]
print(out2)
#[[[5. 2. 4. 2.]
#  [0. 0. 1. 7.]
#  [1. 7. 0. 4.]]
# [[5. 8. 9. 5.]
#  [4. 7. 7. 9.]
#  [6. 9. 2. 6.]]]
print(out3)
#[[[0. 0. 1. 4.]
#  [5. 8. 2. 5.]
#  [6. 9. 9. 7.]]
# [[1. 2. 0. 2.]
#  [4. 7. 4. 6.]
#  [5. 7. 7. 9.]]]

            

split ( num_or_sections, axis=0, name=None ) split¶

Split the input tensor into multiple sub-Tensors.

Parameters

x (Tensor) – A N-D Tensor. The data type is bool, bfloat16, float16, float32, float64, uint8, int8, int32 or int64.
num_or_sections (int|list|tuple) – If num_or_sections is an int, then num_or_sections indicates the number of equal sized sub-Tensors that the x will be divided into. If num_or_sections is a list or tuple, the length of it indicates the number of sub-Tensors and the elements in it indicate the sizes of sub-Tensors’ dimension orderly. The length of the list must not be larger than the x ‘s size of specified axis.
axis (int|Tensor, optional) – The axis along which to split, it can be a integer or a 0-D Tensor with shape [] and data type int32 or int64. If :math::axis < 0, the axis to split along is $rank(x) + axis$. Default is 0.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

list(Tensor), The list of segmented Tensors.

Example

             import paddle

# x is a Tensor of shape [3, 9, 5]
x = paddle.rand([3, 9, 5])

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

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

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

# axis is negative, the real axis is (rank(x) + axis)=1
out0, out1, out2 = paddle.split(x, num_or_sections=3, axis=-2)
print(out0.shape)  # [3, 3, 5]
print(out1.shape)  # [3, 3, 5]
print(out2.shape)  # [3, 3, 5]

            

sqrt ( name=None ) sqrt¶

Sqrt Activation Operator.

\[out=\sqrt{x}=x^{1/2}\]

Parameters

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

Returns

Tensor. Output of Sqrt operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([0.1, 0.2, 0.3, 0.4])
out = paddle.sqrt(x)
print(out)
# [0.31622777 0.4472136  0.54772256 0.63245553]

            

sqrt_ ( name=None ) sqrt_¶: Inplace version of sqrt API, the output Tensor will be inplaced with input x. Please refer to api_fluid_layers_sqrt.

square ( name=None ) square¶

Square each elements of the inputs.

\[out = x^2\]

Parameters

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

Returns

Tensor. Output of Square operator, a Tensor with shape same as input.

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.square(x)
print(out)
# [0.16 0.04 0.01 0.09]

            

squeeze ( axis=None, name=None ) squeeze¶

Squeeze the dimension(s) of size 1 of input tensor x’s shape.

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

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

             Case1:

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

Case2:

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

Case4:

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

Case4:

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

            

Parameters

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

Returns

Tensor, Squeezed Tensor with the same data type as input Tensor.

Examples

             import paddle

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

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

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

            

squeeze_ ( axis=None, name=None ) squeeze_¶: Inplace version of squeeze API, the output Tensor will be inplaced with input x. Please refer to api_paddle_tensor_squeeze.

stack ( axis=0, name=None ) stack¶

Stacks all the input tensors x along axis dimemsion. All tensors must be of the same shape and same dtype.

For example, given N tensors of shape [A, B], if axis == 0, the shape of stacked tensor is [N, A, B]; if axis == 1, the shape of stacked tensor is [A, N, B], etc.

             Case 1:

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

  Attrs:
    axis = 0

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


Case 2:

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


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

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

            

Parameters

x (list[Tensor]|tuple[Tensor]) – Input x can be a list or tuple of tensors, the Tensors in x must be of the same shape and dtype. Supported data types: float32, float64, int32, int64.
axis (int, optional) – The axis along which all inputs are stacked. axis range is [-(R+1), R+1), where R is the number of dimensions of the first input tensor x[0]. If axis < 0, axis = axis+R+1. The default value of axis is 0.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, The stacked tensor with same data type as input.

Example

             import paddle

x1 = paddle.to_tensor([[1.0, 2.0]])
x2 = paddle.to_tensor([[3.0, 4.0]])
x3 = paddle.to_tensor([[5.0, 6.0]])

out = paddle.stack([x1, x2, x3], axis=0)
print(out.shape)  # [3, 1, 2]
print(out)
# [[[1., 2.]],
#  [[3., 4.]],
#  [[5., 6.]]]

            

out = paddle.stack([x1, x2, x3], axis=-2) print(out.shape) # [1, 3, 2] print(out) # [[[1., 2.], # [3., 4.], # [5., 6.]]]

stanh ( scale_a=0.67, scale_b=1.7159, name=None ) stanh¶

stanh activation.

\[out = b * \frac{e^{a * x} - e^{-a * x}}{e^{a * x} + e^{-a * x}}\]

Parameters

x (Tensor) – The input Tensor with data type float32, float64.
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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

A Tensor with the same data type and shape as x .

Examples

             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) # [1.00616539, 1.49927628, 1.65933108, 1.70390463]

std ( axis=None, unbiased=True, keepdim=False, name=None ) std¶

Computes the standard-deviation of x along axis .

Parameters

x (Tensor) – The input Tensor with data type float16, float32, float64.
axis (int|list|tuple, optional) – The axis along which to perform standard-deviation calculations. axis should be int, list(int) or tuple(int). If axis is a list/tuple of dimension(s), standard-deviation 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 $axis + D$ . If axis is None, standard-deviation is calculated over all elements of x. Default is None.
unbiased (bool, optional) – Whether to use the unbiased estimation. If unbiased is True, the standard-deviation is calculated via the unbiased estimator. If unbiased is True, the divisor used in the computation is $N - 1$, where $N$ represents the number of elements along axis , otherwise the divisor is $N$. Default is True.
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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of standard-deviation along axis of x, with the same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0, 3.0], [1.0, 4.0, 5.0]])
out1 = paddle.std(x)
# 1.63299316
out2 = paddle.std(x, unbiased=False)
# 1.49071205
out3 = paddle.std(x, axis=1)
# [1.       2.081666]

            

strided_slice ( axes, starts, ends, strides, name=None ) strided_slice¶

This operator produces a slice of x along multiple axes. Similar to numpy: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html Slice uses axes, starts and ends attributes to specify the start and end dimension for each axis in the list of axes and Slice uses this information to slice the input data tensor. If a negative value is passed to starts or ends such as $-i$, it represents the reverse position of the axis $i-1$ th(here 0 is the initial position). The strides represents steps of slicing and if the strides is negative, slice operation is in the opposite direction. If the value passed to starts or ends is greater than n (the number of elements in this dimension), it represents n. For slicing to the end of a dimension with unknown size, it is recommended to pass in INT_MAX. The size of axes must be equal to starts , ends and strides. Following examples will explain how strided_slice works:

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

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

            

Parameters

x (Tensor) – An N-D Tensor. The data type is bool, float16, float32, float64, int32 or int64.
axes (list|tuple) – The data type is int32 . Axes that starts and ends apply to. It’s optional. If it is not provides, it will be treated as $[0,1,...,len(starts)-1]$.
starts (list|tuple|Tensor) – The data type is int32 . If starts is a list or tuple, the elements of it should be integers or Tensors with shape []. If starts is an Tensor, it should be an 1-D Tensor. It represents starting indices of corresponding axis in axes.
ends (list|tuple|Tensor) – The data type is int32 . If ends is a list or tuple, the elements of it should be integers or Tensors with shape []. If ends is an Tensor, it should be an 1-D Tensor. It represents ending indices of corresponding axis in axes.
strides (list|tuple|Tensor) – The data type is int32 . If strides is a list or tuple, the elements of it should be integers or Tensors with shape []. If strides is an Tensor, it should be an 1-D Tensor. It represents slice step of corresponding axis in axes.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

Tensor, A Tensor with the same dimension as x. The data type is same as x.

Examples

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

            

subtract ( y, name=None ) subtract¶

Substract two tensors element-wise. The equation is:

\[out = x - y\]

Note

paddle.subtract supports broadcasting. If you want know more about broadcasting, please refer to `Introduction to Tensor`_ .

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/fluid/framework.py:docstring of paddle.tensor.math.subtract, line 10); backlink

Duplicate explicit target name: “introduction to tensor”.

Parameters

x (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
y (Tensor) – the input tensor, it’s data type should be float32, float64, int32, int64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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

             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.])

            

subtract_ ( y, name=None ) subtract_¶: Inplace version of subtract API, the output Tensor will be inplaced with input x. Please refer to api_tensor_subtract.

sum ( axis=None, dtype=None, keepdim=False, name=None ) sum¶

Computes the sum of tensor elements over the given dimension.

Parameters

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 None, sum all elements of x and return a Tensor with a single element, otherwise must be in the range $[-rank(x), rank(x))$. If $axis[i] < 0$, the dimension to reduce is $rank + axis[i]$.
dtype (str, optional) – The dtype of output Tensor. The default value is None, the dtype of output is the same as input Tensor x.
keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result Tensor will have one fewer dimension than the x unless keepdim is true, default value is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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.

Return type

Tensor

Examples

             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)          # 3.5
out2 = paddle.sum(x, axis=0)  # [0.3, 0.5, 1.1, 1.6]
out3 = paddle.sum(x, axis=-1) # [1.9, 1.6]
out4 = paddle.sum(x, axis=1, keepdim=True)  # [[1.9], [1.6]]

# 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]) # [10, 26]
out6 = paddle.sum(y, axis=[0, 1]) # [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)          # 4
out8 = paddle.sum(x, axis=0)  # [1, 1, 1, 1]
out9 = paddle.sum(x, axis=1)  # [4, 0]

            

t ( name=None ) t¶

Transpose <=2-D tensor. 0-D and 1-D tensors are returned as it is and 2-D tensor is equal to the paddle.transpose function which perm dimensions set 0 and 1.

Parameters

input (Tensor) – The input Tensor. It is a N-D (N<=2) Tensor of data types float32, float64, int32, int64.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name

Returns

A transposed n-D Tensor, with data type being float16, float32, float64, int32, int64.

Return type

Tensor

Examples

               # Example 1 (0-D tensor)
  x = paddle.to_tensor([0.79])
  paddle.t(x) # [0.79]

  # Example 2 (1-D tensor)
  x = paddle.to_tensor([0.79, 0.84, 0.32])
  paddle.t(x) # [0.79000002, 0.83999997, 0.31999999]
  paddle.t(x).shape # [3]

  # Example 3 (2-D tensor)
  x = paddle.to_tensor([[0.79, 0.84, 0.32],
                       [0.64, 0.14, 0.57]])
  x.shape # [2, 3]
  paddle.t(x)
  # [[0.79000002, 0.63999999],
  #  [0.83999997, 0.14000000],
  #  [0.31999999, 0.56999999]]
  paddle.t(x).shape # [3, 2]

            

take ( index, mode='raise', name=None ) take¶

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.

Parameters

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 candicates 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, Tensor with the same shape as index, the data type is the same with input.

Examples

             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=int32, 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=int32, place=Place(cpu), stop_gradient=True,
#        [[0 , 0 , 0 , 1 , 2 ],
#         [3 , 4 , 5 , 6 , 7 ],
#         [8 , 9 , 10, 11, 11]])

            

take_along_axis ( indices, axis ) take_along_axis¶

Take values from the input array by given indices matrix along the designated axis.

Parameters

arr (Tensor) – The input Tensor. Supported data types are float32 and float64.
indices (Tensor) – Indices to take along each 1d slice of arr. This must match the dimension of arr, and need to broadcast against arr. Supported data type are int and int64.
axis (int) – The axis to take 1d slices along.

Returns

Tensor, The indexed element, same dtype with arr

Examples

             import paddle

x = paddle.to_tensor([[1, 2, 3], [4, 5, 6], [7,8,9]])
index = paddle.to_tensor([[0]])
axis = 0
result = paddle.take_along_axis(x, index, axis)
print(result)
# [[1, 2, 3]]

            

tanh ( name=None ) tanh¶

Tanh Activation Operator.

\[out = \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

Parameters

x (Tensor) – Input of Tanh operator, an N-D Tensor, with data type bfloat16, float32, float64 or float16.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

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

Examples

             import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
out = paddle.tanh(x)
print(out)
# [-0.37994896 -0.19737532  0.09966799  0.29131261]

            

tanh_ ( name=None ) tanh_¶: Inplace version of tanh API, the output Tensor will be inplaced with input x. Please refer to api_tensor_tanh.

tensordot ( y, axes=2, name=None ) tensordot¶

This function computes a contraction, which sum the product of elements from two tensors along the given axes.

Parameters

x (Tensor) – The left tensor for contraction with data type float16 or float32 or float64.
y (Tensor) – The right tensor for contraction with the same data type as x.
axes (int|tuple|list|Tensor, optional) –
The axes to contract for x and y, defaulted to integer 2.
1. It could be a non-negative integer n, in which the function will sum over the last n axes of x and the first n axes of y in order.
2. It could be a 1-d tuple or list with data type int, in which x and y will be contracted along the same given axes. For example, axes =[0, 1] applies contraction along the first two axes for x and the first two axes for y.
3. It could be a tuple or list containing one or two 1-d tuple|list|Tensor with data type int. When containing one tuple|list|Tensor, the data in tuple|list|Tensor specified the same axes for x and y to contract. When containing two tuple|list|Tensor, the first will be applied to x and the second to y. When containing more than two tuple|list|Tensor, only the first two axis sequences will be used while the others will be ignored.
4. It could be a tensor, in which the axes tensor will be translated to a python list and applied the same rules described above to determine the contraction axes. Note that the axes with Tensor type is ONLY available in Dygraph mode.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

Output (Tensor), The contraction result with the same data type as x and y. In general, $output.ndim = x.ndim + y.ndim - 2 \times n_{axes}$, where $n_{axes}$ denotes the number of axes to be contracted.

Notes

This function supports tensor broadcast, the size in the corresponding dimensions of x and y should be equal, or applies to the broadcast rules.
This function also supports axes expansion, when the two given axis sequences for x and y are of different lengths, the shorter sequence will expand the same axes as the longer one at the end. For example, if axes =[[0, 1, 2, 3], [1, 0]], the axis sequence for x is [0, 1, 2, 3], while the corresponding axis sequences for y will be expanded from [1, 0] to [1, 0, 2, 3].

Examples

             import paddle

data_type = 'float64'

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


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


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


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


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


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

            

tile ( repeat_times, name=None ) tile¶

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

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

Parameters

x (Tensor) – The input tensor, its data type should be bool, float16, float32, float64, int32 or int64.
repeat_times (list|tuple|Tensor) – The number of repeating times. If repeat_times is a list or tuple, all its elements should be integers or 1-D Tensors with the data type int32. If repeat_times is a Tensor, it should be an 1-D Tensor with the data type int32.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

N-D Tensor. The data type is the same as x. The size of the i-th dimension is equal to x[i] * repeat_times[i].

Examples

             import paddle

data = paddle.to_tensor([1, 2, 3], dtype='int32')
out = paddle.tile(data, repeat_times=[2, 1])
print(out)
# Tensor(shape=[2, 3], dtype=int32, place=Place(gpu:0), stop_gradient=True,
#        [[1, 2, 3],
#         [1, 2, 3]])

out = paddle.tile(data, repeat_times=(2, 2))
print(out)
# Tensor(shape=[2, 6], dtype=int32, place=Place(gpu:0), stop_gradient=True,
#        [[1, 2, 3, 1, 2, 3],
#         [1, 2, 3, 1, 2, 3]])

repeat_times = paddle.to_tensor([1, 2], dtype='int32')
out = paddle.tile(data, repeat_times=repeat_times)
print(out)
# Tensor(shape=[1, 6], dtype=int32, place=Place(gpu:0), stop_gradient=True,
#        [[1, 2, 3, 1, 2, 3]])

            

topk ( k, axis=None, largest=True, sorted=True, name=None ) topk¶

Return values and indices of the k largest or smallest at the optional axis. If the input is a 1-D Tensor, finds the k largest or smallest values and indices. If the input is a Tensor with higher rank, this operator computes the top k values and indices along the axis.

Parameters

x (Tensor) – Tensor, an input N-D Tensor with type float32, float64, int32, int64.
k (int, Tensor) – The number of top elements to look for along the axis.
axis (int, optional) – Axis to compute indices along. The effective range is [-R, R), where R is x.ndim. when axis < 0, it works the same way as axis + R. Default is -1.
largest (bool, optional) – largest is a flag, if set to true, algorithm will sort by descending order, otherwise sort by ascending order. Default is True.
sorted (bool, optional) – controls whether to return the elements in sorted order, default value is True. In gpu device, it always return the sorted value.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

tuple(Tensor), return the values and indices. The value data type is the same as the input x. The indices data type is int64.

Examples

             import paddle

data_1 = paddle.to_tensor([1, 4, 5, 7])
value_1, indices_1 = paddle.topk(data_1, k=1)
print(value_1) # [7]
print(indices_1) # [3]

data_2 = paddle.to_tensor([[1, 4, 5, 7], [2, 6, 2, 5]])
value_2, indices_2 = paddle.topk(data_2, k=1)
print(value_2) # [[7], [6]]
print(indices_2) # [[3], [1]]

value_3, indices_3 = paddle.topk(data_2, k=1, axis=-1)
print(value_3) # [[7], [6]]
print(indices_3) # [[3], [1]]

value_4, indices_4 = paddle.topk(data_2, k=1, axis=0)
print(value_4) # [[2, 6, 5, 7]]
print(indices_4) # [[1, 1, 0, 0]]

            

trace ( offset=0, axis1=0, axis2=1, name=None ) trace¶

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.

Parameters

x (Tensor) – The input tensor x. Must be at least 2-dimensional. The input data type should be 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, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

the output data type is the same as input data type.

Return type

Tensor

Examples

             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) # data2.shape = [3, 5]

            

transpose ( perm, name=None ) transpose¶

Permute the data dimensions of input according to perm.

The i-th dimension of the returned tensor will correspond to the perm[i]-th dimension of input.

Parameters

x (Tensor) – The input Tensor. It is a N-D Tensor of data types bool, float32, float64, int32.
perm (list|tuple) – Permute the input according to the data of perm.
name (str) – The name of this layer. It is optional.

Returns

A transposed n-D Tensor, with data type being bool, float32, float64, int32, int64.

Return type

Tensor

For Example:

               x = [[[ 1  2  3  4] [ 5  6  7  8] [ 9 10 11 12]]
    [[13 14 15 16] [17 18 19 20] [21 22 23 24]]]
shape(x) =  [2,3,4]

# Example 1
perm0 = [1,0,2]
y_perm0 = [[[ 1  2  3  4] [13 14 15 16]]
          [[ 5  6  7  8]  [17 18 19 20]]
          [[ 9 10 11 12]  [21 22 23 24]]]
shape(y_perm0) = [3,2,4]

# Example 2
perm1 = [2,1,0]
y_perm1 = [[[ 1 13] [ 5 17] [ 9 21]]
          [[ 2 14] [ 6 18] [10 22]]
          [[ 3 15]  [ 7 19]  [11 23]]
          [[ 4 16]  [ 8 20]  [12 24]]]
shape(y_perm1) = [4,3,2]

              

Examples

             import paddle

x = paddle.randn([2, 3, 4])
x_transposed = paddle.transpose(x, perm=[1, 0, 2])
print(x_transposed.shape)
# [3L, 2L, 4L]

            

trapezoid ( x=None, dx=None, axis=- 1, name=None ) trapezoid¶

Integrate along the given axis using the composite trapezoidal rule. Use the sum method.

Parameters

y (Tensor) – Input tensor to integrate. It’s data type should be float16, float32, float64.
x (Tensor, optional) – The sample points corresponding to the y values, the same type as y. It is known that the size of y is [d_1, d_2, … , d_n] and $axis=k$, then the size of x can only be [d_k] or [d_1, d_2, … , d_n ]. If x is None, the sample points are assumed to be evenly spaced dx apart. The default is None.
dx (float, optional) – The spacing between sample points when x is None. If neither x nor dx is provided then the default is $dx = 1$.
axis (int, optional) – The axis along which to integrate. The default is -1.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, Definite integral of y is N-D tensor as approximated along a single axis by the trapezoidal rule. If 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

             import paddle

y = paddle.to_tensor([4, 5, 6], dtype='float32')

print(paddle.trapezoid(y))
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        10.)

print(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')

print(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')

print(paddle.trapezoid(y, x))
# Tensor(shape=[], dtype=float64, place=Place(cpu), stop_gradient=True,
#        -8.)
y = paddle.arange(6).reshape((2, 3)).astype('float32')

print(paddle.trapezoid(y, axis=0))
# Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [1.50000000, 2.50000000, 3.50000000])
print(paddle.trapezoid(y, axis=1))
# Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [2., 8.])

            

trunc ( name=None ) trunc¶

This API is used to returns a new tensor with the truncated integer values of input.

Parameters

input (Tensor) – The input tensor, it’s data type should be int32, int64, float32, float64.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

The output Tensor of trunc.

Return type

Tensor

Examples

             import paddle

input = paddle.rand([2,2],'float32')
print(input)
# Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#         [[0.02331470, 0.42374918],
#         [0.79647720, 0.74970269]])

output = paddle.trunc(input)
print(output)
# Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
#         [[0., 0.],
#         [0., 0.]]))

            

unbind ( axis=0 ) unbind¶

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

Parameters

input (Tensor) – The input variable which is an N-D Tensor, data type being bool, float16, float32, float64, int32 or int64.
axis (int32|int64, optional) – A scalar with type int32|int64 shape [1]. The dimension along which to unbind. If $axis < 0$, the dimension to unbind along is $rank(input) + axis$. Default is 0.

Returns

list(Tensor), The list of segmented Tensor variables.

Example

             import paddle

# input is a Tensor which shape is [3, 4, 5]
input = paddle.rand([3, 4, 5])

[x0, x1, x2] = paddle.unbind(input, axis=0)
# x0.shape [4, 5]
# x1.shape [4, 5]
# x2.shape [4, 5]

[x0, x1, x2, x3] = paddle.unbind(input, axis=1)
# x0.shape [3, 5]
# x1.shape [3, 5]
# x2.shape [3, 5]
# x3.shape [3, 5]

            

unflatten ( axis, shape, name=None ) unflatten¶

Expand a certain dimension of the input x Tensor into a desired shape.

Parameters

x (Tensor) – An N-D Tensor. The data type is float16, float32, float64, int16, int32, int64, bool, uint16.
axis (int) – axis to be unflattened, specified as an index into x.shape.
shape (list|tuple|Tensor) – Unflatten shape on the specified axis. At most one dimension of the target shape can be -1. If the input shape does not contain -1 , the product of all elements in shape should be equal to x.shape[axis]. The data type is int . If shape is a list or tuple, the elements of it should be integers or Tensors with shape []. If shape is an Tensor, it should be an 1-D Tensor.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, return the unflatten tensor of x.

Examples

             import paddle

x = paddle.randn(shape=[4, 6, 8])
shape = [2, 3]
axis = 1
res = paddle.unflatten(x, axis, shape)
print(res.shape)
# [4, 2, 3, 8]

x = paddle.randn(shape=[4, 6, 8])
shape = (-1, 2)
axis = -1
res = paddle.unflatten(x, axis, shape)
print(res.shape)
# [4, 6, 4, 2]

x = paddle.randn(shape=[4, 6, 8])
shape = paddle.to_tensor([2, 2])
axis = 0
res = paddle.unflatten(x, axis, shape)
print(res.shape)
# [2, 2, 6, 8]

            

uniform_ ( min=- 1.0, max=1.0, seed=0, name=None ) uniform_¶

This is the inplace version of OP uniform, which returns a Tensor filled with random values sampled from a uniform distribution. The output Tensor will be inplaced with input x. Please refer to api_tensor_uniform.

Parameters

x (Tensor) – The input tensor to be filled with random values.
min (float|int, optional) – The lower bound on the range of random values to generate, min is included in the range. Default is -1.0.
max (float|int, optional) – The upper bound on the range of random values to generate, max is excluded in the range. Default is 1.0.
seed (int, optional) – Random seed used for generating samples. If seed is 0, it will use the seed of the global default generator (which can be set by paddle.seed). Note that if seed is not 0, this operator will always generate the same random numbers every time. Default is 0.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

The input tensor x filled with random values sampled from a uniform distribution in the range [min, max).

Return type

Tensor

Examples

             import paddle
# example:
x = paddle.ones(shape=[3, 4])
x.uniform_()
print(x)
# [[ 0.84524226,  0.6921872,   0.56528175,  0.71690357], # random
#  [-0.34646994, -0.45116323, -0.09902662, -0.11397249], # random
#  [ 0.433519,    0.39483607, -0.8660099,   0.83664286]] # random

            

unique ( return_index=False, return_inverse=False, return_counts=False, axis=None, dtype='int64', name=None ) unique¶

Returns the unique elements of x in ascending order.

Parameters

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

Returns

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

Examples

             import paddle

x = paddle.to_tensor([2, 3, 3, 1, 5, 3])
unique = paddle.unique(x)
print(unique)
# Tensor(shape=[4], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [1, 2, 3, 5])

_, indices, inverse, counts = paddle.unique(x, return_index=True, return_inverse=True, return_counts=True)
print(indices)
# Tensor(shape=[4], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [3, 0, 1, 4])
print(inverse)
# Tensor(shape=[6], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [1, 2, 2, 0, 3, 2])
print(counts)
# Tensor(shape=[4], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [1, 1, 3, 1])

x = paddle.to_tensor([[2, 1, 3], [3, 0, 1], [2, 1, 3]])
unique = paddle.unique(x)
print(unique)
# Tensor(shape=[4], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [0, 1, 2, 3])

unique = paddle.unique(x, axis=0)
print(unique)
# Tensor(shape=[2, 3], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [[2, 1, 3],
#         [3, 0, 1]])

            

unique_consecutive ( return_inverse=False, return_counts=False, axis=None, dtype='int64', name=None ) unique_consecutive¶

Eliminates all but the first element from every consecutive group of equivalent elements.

Note

This function is different from unique in the sense that this function only eliminates consecutive duplicate values. This semantics is similar to unique in C++.

Parameters

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

Returns

out (Tensor), the unique consecutive tensor for x.
inverse (Tensor), the element of the input tensor corresponds to

the index of the elements in the unique consecutive tensor for x. inverse is provided only if return_inverse is True.
counts (Tensor), the counts of the every unique consecutive element in the input tensor.

counts is provided only if return_counts is True.

Example

             import paddle

x = paddle.to_tensor([1, 1, 2, 2, 3, 1, 1, 2])
output = paddle.unique_consecutive(x) #
print(output)
# Tensor(shape=[5], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [1, 2, 3, 1, 2])

_, inverse, counts = paddle.unique_consecutive(x, return_inverse=True, return_counts=True)
print(inverse)
# Tensor(shape=[8], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [0, 0, 1, 1, 2, 3, 3, 4])
print(counts)
# Tensor(shape=[5], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [2, 2, 1, 2, 1])

x = paddle.to_tensor([[2, 1, 3], [3, 0, 1], [2, 1, 3], [2, 1, 3]])
output = paddle.unique_consecutive(x, axis=0) #
print(output)
# Tensor(shape=[3, 3], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [[2, 1, 3],
#         [3, 0, 1],
#         [2, 1, 3]])

x = paddle.to_tensor([[2, 1, 3], [3, 0, 1], [2, 1, 3], [2, 1, 3]])
output = paddle.unique_consecutive(x, axis=0) #
print(output)
# Tensor(shape=[3, 3], dtype=int64, place=Place(gpu:0), stop_gradient=True,
#        [[2, 1, 3],
#         [3, 0, 1],
#         [2, 1, 3]])

            

unsqueeze ( axis, name=None ) unsqueeze¶

Insert single-dimensional entries to the shape of input Tensor x. Takes one required argument axis, a dimension or list of dimensions that will be inserted. Dimension indices in axis are as seen in the output tensor.

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

Parameters

x (Tensor) – The input Tensor to be unsqueezed. Supported data type: bfloat16, float16, float32, float64, bool, int8, int32, int64.
axis (int|list|tuple|Tensor) – Indicates the dimensions to be inserted. The data type is int32 . If axis is a list or tuple, each element of it should be integer or 0-D Tensor with shape []. If axis is a Tensor, it should be an 1-D Tensor . If axis is negative, axis = axis + ndim(x) + 1.
name (str|None) – Name for this layer. Please refer to Name, Default None.

Returns

Tensor, Unsqueezed Tensor with the same data type as input Tensor.

Examples

             import paddle

x = paddle.rand([5, 10])
print(x.shape)  # [5, 10]

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

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

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

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

            

unsqueeze_ ( axis, name=None ) unsqueeze_¶: Inplace version of unsqueeze API, the output Tensor will be inplaced with input x. Please refer to api_paddle_tensor_unsqueeze.

unstack ( axis=0, num=None ) unstack¶

This layer unstacks input Tensor x into several Tensors along axis.

If axis < 0, it would be replaced with axis+rank(x). If num is None, it would be inferred from x.shape[axis], and if x.shape[axis] <= 0 or is unknown, ValueError is raised.

Parameters

x (Tensor) – Input Tensor. It is a N-D Tensors of data types float32, float64, int32, int64.
axis (int) – The axis along which the input is unstacked.
num (int|None) – The number of output variables.

Returns

list(Tensor), The unstacked Tensors list. The list elements are N-D Tensors of data types float32, float64, int32, int64.

Examples

             import paddle
x = paddle.ones(name='x', shape=[2, 3, 5], dtype='float32')  # create a tensor with shape=[2, 3, 5]
y = paddle.unstack(x, axis=1)  # unstack with second axis, which results 3 tensors with shape=[2, 5]

            

vander ( n=None, increasing=False, name=None ) vander¶

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.

Parameters

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) – 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, optional) – For details, please refer to 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 $x^{(N-1)}$, the second $x^{(N-2)}$ and so forth. If increasing is True, the columns are $x^0$, $x^1$, …, $x^{(N-1)}$.

Examples

             import paddle
x = paddle.to_tensor([1., 2., 3.], dtype="float32")
out = paddle.vander(x)
print(out.numpy())
# [[1., 1., 1.],
#  [4., 2., 1.],
#  [9., 3., 1.]]
out1 = paddle.vander(x,2)
print(out1.numpy())
# [[1., 1.],
#  [2., 1.],
#  [3., 1.]]
out2 = paddle.vander(x, increasing = True)
print(out2.numpy())
# [[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)
print(out3.numpy())
# [[2.+1.j, 1.+0.j],
#  [4.+3.j, 1.+0.j]]

            

var ( axis=None, unbiased=True, keepdim=False, name=None ) var¶

Computes the variance of x along axis .

Parameters

x (Tensor) – The input Tensor with data type float16, float32, float64.
axis (int|list|tuple, optional) –
The axis along which to perform variance calculations. axis should be int, list(int) or tuple(int).
- If axis is a list/tuple of dimension(s), variance 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 $axis + D$ .
- If axis is None, variance is calculated over all elements of x. Default is None.
unbiased (bool, optional) – Whether to use the unbiased estimation. If unbiased is True, the divisor used in the computation is $N - 1$, where $N$ represents the number of elements along axis , otherwise the divisor is $N$. Default is True.
keep_dim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result tensor will have one fewer dimension than the input unless keep_dim is true. Default is False.
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, results of variance along axis of x, with the same data type as x.

Examples

             import paddle

x = paddle.to_tensor([[1.0, 2.0, 3.0], [1.0, 4.0, 5.0]])
out1 = paddle.var(x)
# 2.66666667
out2 = paddle.var(x, axis=1)
# [1.         4.33333333]

            

vsplit ( num_or_sections, name=None ) vsplit¶

Split the input tensor into multiple sub-Tensors along the vertical axis, which is equivalent to paddle.split with axis=0.

Parameters

x (Tensor) – A Tensor whose dimension must be greater than 1. The data type is bool, float16, float32, float64, uint8, int8, int32 or int64.
num_or_sections (int|list|tuple) – If num_or_sections is an int, then num_or_sections indicates the number of equal sized sub-Tensors that the x will be divided into. If num_or_sections is a list or tuple, the length of it indicates the number of sub-Tensors and the elements in it indicate the sizes of sub-Tensors’ dimension orderly. The length of the list must not be larger than the x ‘s size of axis 0.
name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

list[Tensor], The list of segmented Tensors.

Example

             import paddle

# x is a Tensor of shape [8, 6, 7]
x = paddle.rand([8, 6, 7])
out0, out1 = paddle.vsplit(x, num_or_sections=2)
print(out0.shape)  # [4, 6, 7]
print(out1.shape)  # [4, 6, 7]
out0, out1, out2 = paddle.vsplit(x, num_or_sections=[1, 3, 4])
print(out0.shape)  # [1, 6, 7]
print(out1.shape)  # [3, 6, 7]
print(out2.shape)  # [4, 6, 7]
out0, out1, out2 = paddle.vsplit(x, num_or_sections=[2, 3, -1])
print(out0.shape)  # [2, 6, 7]
print(out1.shape)  # [3, 6, 7]
print(out2.shape)  # [3, 6, 7]

            

where ( x=None, y=None, name=None ) where¶

Return a Tensor of elements selected from either x or y according to corresponding elements of condition. Concretely,

\[\begin{split}out_i = \begin{cases} x_i, & \text{if} \ condition_i \ \text{is} \ True \\ y_i, & \text{if} \ condition_i \ \text{is} \ False \\ \end{cases}.\end{split}\]

Notes

numpy.where(condition) is identical to paddle.nonzero(condition, as_tuple=True), please refer to nonzero.

Parameters

condition (Tensor) – The condition to choose x or y. When True (nonzero), yield x, otherwise yield y.
x (Tensor|scalar, optional) – A Tensor or scalar to choose when the condition is True with data type of bfloat16, float16, float32, float64, int32 or int64. Either both or neither of x and y should be given.
y (Tensor|scalar, optional) – A Tensor or scalar to choose when the condition is False with data type of bfloat16, float16, float32, float64, int32 or int64. Either both or neither of x and y should be given.
name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

A Tensor with the same shape as condition and same data type as x and y.

Return type

Tensor

Examples

             import paddle

x = paddle.to_tensor([0.9383, 0.1983, 3.2, 1.2])
y = paddle.to_tensor([1.0, 1.0, 1.0, 1.0])

out = paddle.where(x>1, x, y)
print(out)
#out: [1.0, 1.0, 3.2, 1.2]

out = paddle.where(x>1)
print(out)
#out: (Tensor(shape=[2, 1], dtype=int64, place=CPUPlace, stop_gradient=True,
#            [[2],
#             [3]]),)

            

Variable¶

detach¶

numpy¶

backward¶

gradient¶

clear_gradient¶

to_string¶

element_size¶

clone¶

get_value¶

set_value¶

size¶

attr¶

abs¶

acos¶

acosh¶

add¶

add_¶

add_n¶

addmm¶

all¶

allclose¶

amax¶

amin¶

angle¶

any¶

append¶

argmax¶

argmin¶

argsort¶

as_complex¶

as_real¶

asin¶

asinh¶

astype¶

atan¶

atanh¶

bincount¶

bitwise_and¶

bitwise_not¶

bitwise_or¶

bitwise_xor¶

bmm¶

broadcast_shape¶

broadcast_tensors¶

broadcast_to¶

bucketize¶

cast¶

cdist¶

ceil¶

ceil_¶

cholesky¶

cholesky_solve¶

chunk¶

clip¶

clip_¶

concat¶

cond¶

conj¶

corrcoef¶

cos¶

cosh¶

count_nonzero¶

cov¶

cpu¶

create_parameter¶

create_tensor¶

cross¶

cuda¶

cumprod¶

cumsum¶

cumulative_trapezoid¶

deg2rad¶

diagonal¶

diff¶

digamma¶

dist¶

divide¶

dot¶

eig¶