# Variable¶

class paddle.static. Variable ( block, type=VarType.LOD_TENSOR, 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')


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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 ( )
Notes:

This API is ONLY available in Dygraph mode

Returns a new Variable, detached from the current graph.

Returns

The detached Variable.

Return type

( Variable | dtype is same as current Variable)

Examples

import paddle.fluid as fluid
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)
y = x.detach()

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
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 )
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

x = np.ones([2, 2], np.float32)
inputs = []
for _ in range(10):
# 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.
inputs.append(tmp)
loss.backward()

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.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)
inputs2.append(tmp)
ret2 = fluid.layers.sums(inputs2)
loss2 = fluid.layers.reduce_sum(ret2)
loss2.backward()

# example2: return tuple of ndarray
with fluid.dygraph.guard():
embedding = fluid.dygraph.Embedding(
size=[20, 32],
param_attr='emb.w',
is_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()

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.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)
inputs2.append(tmp)
ret2 = fluid.layers.sums(inputs2)
loss2 = fluid.layers.reduce_sum(ret2)
loss2.backward()

to_string ( throw_on_error, with_details=False )

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

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))


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)
out = fluid.layers.concat(input=[out1, out2, c], axis=1)
out.backward()


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))


Indicating name of the gradient Variable of current Variable.

**Notes: This is a read-only property. It simply returns name of

Inline strong start-string without end-string.

gradient Variable from a naming convention but doesn’t guarantee the gradient exists.**

Examples




x = fluid.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.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("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))

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

The cloned Variable.

Return type

Variable

Examples

import paddle

# 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 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

the value in given scope.

Return type

Tensor

Examples

import paddle
import numpy as np

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

y = static.nn.fc(x, 10, name='fc')
exe = static.Executor(place)
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()

for var in prog.list_vars():
if var.persistable:

set_value ( value, scope=None )

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 numpy as np

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

y = static.nn.fc(x, 10, name='fc')
exe = static.Executor(place)
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()

for var in prog.list_vars():
if var.persistable:

abs ( name=None )

Abs Operator.

This operator is used to perform elementwise abs for input $X$. $$out = |x|$$

Parameters
• x (Tensor) – (Tensor), The input tensor of abs op.

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

Returns

(Tensor), The output tensor of abs op.

Return type

out (Tensor)

Examples

import paddle

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

acos ( name=None )

Arccosine Operator.

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

Parameters
• x (Tensor) – Input of acos operator

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

Returns

Output of acos operator

Return type

out (Tensor)

Examples

import paddle

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


The equation is:

$$Out = X + Y$$

• $X$: a tensor of any dimension.

• $Y$: a tensor whose dimensions must be less than or equal to the dimensions of $X$.

There are two cases for this operator:

1. The shape of $Y$ is the same with $X$.

2. The shape of $Y$ is a continuous subsequence of $X$.

For case 2:

1. Broadcast $Y$ to match the shape of $X$, where $axis$ is the start dimension index for broadcasting $Y$ onto $X$.

2. If $axis$ is -1 (default), $axis = rank(X) - rank(Y)$.

3. The trailing dimensions of size 1 for $Y$ will be ignored for the consideration of subsequence, such as shape(Y) = (2, 1) => (2).

For example:

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) – (Variable), Tensor or LoDTensor of any dimensions. Its dtype should be int32, int64, float32, float64.

• y (Tensor) – (Variable), Tensor or LoDTensor of any dimensions. Its dtype should be int32, int64, float32, float64.

• name (string, optional) – Name of the output. Default is None. It’s used to print debug info for developers. Details: Name

Returns

N-dimension 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')
print(z)  # [3., 8., 6. ]

Return type

out (Tensor)

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

This OP is used to 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) – 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 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')
# [[8., 10., 12.],
#  [14., 16., 18.]]

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

This operator is used to 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) – Coefficient of $input$.

• alpha (float) – Coefficient of $x*y$.

• name (str, optional) – Name of the output. Normally there is no need for user to set this property. For more information, please refer to Name. Default is None.

Returns

The output Tensor of addmm op.

Return type

Tensor

Examples

import paddle

print(out)
# [[10.5 10.5]
# [10.5 10.5]]

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

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

Return type

Tensor

Raises
• ValueError – If the data type of x is not bool.

• TypeError – The type of axis must be int, list or tuple.

Examples

import paddle
import numpy as np

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

# out1 should be [False]
print(out1)

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

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

# keep_dim=True, out4 should be [[False], [True]], out.shape should be (2,1)
out4 = paddle.cast(out4, 'int32')  # [[False], [True]]
print(out4)

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

This operator checks 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 $$numpy.allclose$$, 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 float32, float64.

• y (Tensor) – The input tensor, it’s data type should be 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

Raises
• TypeError – The data type of x must be one of float32, float64.

• TypeError – The data type of y must be one of float32, float64.

• TypeError – The type of rtol must be float.

• TypeError – The type of atol must be float.

• TypeError – The type of equal_nan must be bool.

Examples

import paddle

result1 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
equal_nan=False, name="ignore_nan")
np_result1 = result1.numpy()
# [False]
result2 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
equal_nan=True, name="equal_nan")
np_result2 = result2.numpy()
# [False]

result1 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
equal_nan=False, name="ignore_nan")
np_result1 = result1.numpy()
# [False]
result2 = paddle.allclose(x, y, rtol=1e-05, atol=1e-08,
equal_nan=True, name="equal_nan")
np_result2 = result2.numpy()
# [True]

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

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

Return type

Tensor

Raises
• ValueError – If the data type of x is not bool.

• TypeError – The type of axis must be int, list or tuple.

Examples

import paddle
import numpy as np

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

# out1 should be [True]
print(out1)

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

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

# keep_dim=True, result should be [[True], [False]], out.shape should be (2,1)
out4 = paddle.cast(out4, 'int32')  # [[True], [False]]
print(out4)

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

This OP 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 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) – Keep the axis that selecting max. The defalut value 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) – 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, return the tensor of int32 if set dtype is int32, otherwise return the tensor of int64

Examples

import paddle

[0,0,1,7],
[6,9,2,4]])
print(out1) # 2
print(out2)
# [2 3 1]
print(out3)
# [2 3 1]

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

This OP 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 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) – Keep the axis that selecting min. The defalut value is False.

• dtype (str) – 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) – 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, return the tensor of int32 if set dtype is int32, otherwise return the tensor of int64

Examples

import paddle

[0,0,1,7],
[6,9,2,4]])
print(out1) # 4
print(out2)
# [0 0 2]
print(out3)
# [0 0 2]

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

This OP 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 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 0.

• 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) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

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

Return type

Tensor

Examples

import paddle

[0,0,1,7],
[6,9,2,4]],
[[5,2,4,2],
[4,7,7,9],
[1,7,0,6]]],
dtype='float32')
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]]]

asin ( name=None )

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

Output of asin operator

Return type

out (Tensor)

Examples

import paddle

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

astype ( dtype )
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:

import paddle.fluid as fluid

startup_prog = fluid.Program()
main_prog = fluid.Program()
with fluid.program_guard(startup_prog, main_prog):
original_variable = fluid.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 )

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

Output of atan operator

Return type

out (Tensor)

Examples

import paddle

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

bmm ( y, name=None )

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

# In imperative mode: # size x: (2, 2, 3) and y: (2, 3, 2) x = paddle.to_tensor([[[1.0, 1.0, 1.0],

Unexpected indentation.

[2.0, 2.0, 2.0]],

Block quote ends without a blank line; unexpected unindent.

[[3.0, 3.0, 3.0],

[4.0, 4.0, 4.0]]])

Block quote ends without a blank line; unexpected unindent.

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]]])

Definition list ends without a blank line; unexpected unindent.

out = paddle.bmm(x, y) #output size: (2, 2, 2) #output value: #[[[6.0, 6.0],[12.0, 12.0]],[[45.0, 45.0],[60.0, 60.0]]] out_np = out.numpy()

The function returns the shape of doing operation with broadcasting on tensors of x_shape and y_shape, please refer to Broadcasting for more details.

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

# [2, 3, 3]

# ValueError (terminated with error message).


Broadcast the input tensor to a given shape.

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

Parameters
• x (Tensor) – The input tensor, its data type is bool, float32, float64, int32 or int64.

• shape (list|tuple|Tensor) – The result shape after broadcasting. The data type is int32. If shape is a list or tuple, all its elements should be integers or 1-D Tensors with the data type int32. If shape is a Tensor, it should be an 1-D Tensor with the data type int32. The value -1 in shape means keeping the corresponding dimension unchanged.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

A Tensor with the given shape. The data type is the same as x.

Return type

N-D Tensor

Examples

import paddle

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

cast ( dtype )

This OP takes in the Tensor x with x.dtype and casts 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|core.VarDesc.VarType|str) – Data type of the output: bool, float16, float32, float64, int8, int32, int64, uint8.

Returns

A Tensor with the same shape as input’s.

Return type

Tensor

Examples

import paddle

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

ceil ( name=None )

Ceil Operator. Computes ceil of x element-wise.

$$out = \\lceil x \\rceil$$

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

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

Return type

out (Tensor)

Examples

import paddle

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

ceil_ ( name=None )

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 )

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.

Returns

A Tensor with same shape and data type as x. It represents

triangular matrices generated by Cholesky decomposition.

Return type

Tensor

Examples

import paddle
import numpy as np

a = np.random.rand(3, 3)
a_t = np.transpose(a, [1, 0])
x_data = np.matmul(a, a_t) + 1e-03
print(out)
# [[1.190523   0.         0.        ]
#  [0.9906703  0.27676893 0.        ]
#  [1.25450498 0.05600871 0.06400121]]

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

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 scalar with type int or a Tensor with shape [1] and data type int32 or int64. If :math::axis < 0, the axis to split along is $$rank(x) + axis$$. 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

The list of segmented Tensors.

Return type

list(Tensor)

Example

import numpy as np

# x is a Tensor which shape is [3, 9, 5]
x_np = np.random.random([3, 9, 5]).astype("int32")

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 )

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 float32, float64, int32 or int64.

• min (float|int|Tensor) – The lower bound with type float , int or a Tensor with shape [1] and type int32, float32, float64.

• max (float|int|Tensor) – The upper bound with type float, int or a Tensor with shape [1] and type int32, float32, float64.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to 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')
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 )

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 )

This OP concatenates the input along the axis.

Parameters
• x (list|tuple) – x is a Tensor list or Tensor tuple which is with data type bool, float16, float32, float64, int32, int64, uint8. All the Tensors in x must have same data type.

• axis (int|Tensor, optional) – Specify the axis to operate on the input Tensors. It’s a scalar with data type int or a Tensor with shape [1] and data type int32 or int64. The effective range is [-R, R), where R is Rank(x). When axis < 0, it works the same way as axis+R. Default is 0.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

A Tensor with the same data type as x.

Return type

Tensor

Examples

import paddle

[4, 5, 6]])
[14, 15, 16]])
[23, 24]])
# 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)
# 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]]

conj ( name=None )

This function computes the conjugate of the Tensor elementwisely.

Parameters
• x (Tensor) – The input tensor which hold the complex numbers. Optional data types are: complex64, complex128, float32, float64, int32 or 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 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]])
#       [[(1+1j), (2+2j), (3+3j)],
#        [(4+4j), (5+5j), (6+6j)]])

#       [[(1-1j), (2-2j), (3-3j)],
#        [(4-4j), (5-5j), (6-6j)]])

cos ( name=None )

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

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

Return type

out (Tensor)

Examples

import paddle

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

cosh ( name=None )

Cosh Activation Operator.

$$out = cosh(x)$$

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

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

Return type

out (Tensor)

Examples

import paddle

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

cross ( y, axis=None, name=None )

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.

• y (Tensor) – The second input tensor.

• axis (int, optional) – The axis along which to compute the cross product. It defaults to 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

[2.0, 2.0, 2.0],
[3.0, 3.0, 3.0]])
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0]])

# [[-1. -1. -1.]
#  [ 2.  2.  2.]
#  [-1. -1. -1.]]

# [[0. 0. 0.]
#  [0. 0. 0.]
#  [0. 0. 0.]]

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

The cumulative sum of the elements along a given axis.

Note: The first element of the result is the same of the first element of the input.

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 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

# [ 0  1  3  6 10 15 21 28 36 45 55 66]

# [[ 0  1  2  3]
#  [ 4  6  8 10]
#  [12 15 18 21]]

# [[ 0  1  3  6]
#  [ 4  9 15 22]
#  [ 8 17 27 38]]

print(y.dtype)
# VarType.FP64

dist ( y, p=2 )

This OP 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 numpy’s broadcasting:

• 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 z.

$||z||_\infty=\max_i |z_i|$

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

Returns

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

Return type

Tensor

Examples

import paddle
import numpy as np

x = paddle.to_tensor(np.array([[3, 3],[3, 3]]), "float32")
y = paddle.to_tensor(np.array([[3, 3],[3, 1]]), "float32")
print(out) # out = [1.]

print(out) # out = [2.]

print(out) # out = [2.]

print(out) # out = [0.]

divide ( y, name=None )

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 Broadcasting .

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')
print(z)  # [2., 0.6, 2.]

dot ( y, name=None )

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
import numpy as np

x_data = np.random.uniform(0.1, 1, [10]).astype(np.float32)
y_data = np.random.uniform(1, 3, [10]).astype(np.float32)
print(z)

equal ( y, name=None )

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

NOTICE: The output of this OP 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, 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

print(result1)  # result1 = [True False False]

equal_all ( y, name=None )

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

NOTICE: The output of this OP 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

print(result1) # result1 = [True ]
print(result2) # result2 = [False ]

erf ( name=None )

Erf Operator For more details, see [Error function](https://en.wikipedia.org/wiki/Error_function).

Equation:
$\begin{split}out = \\frac{2}{\\sqrt{\\pi}} \\int_{0}^{x}e^{- \\eta^{2}}d\\eta\end{split}$
Parameters

x (Tensor) – The input tensor, it’s data type should be float32, float64.

Returns

The output of Erf op, 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])
print(out)
# [-0.42839236 -0.22270259  0.11246292  0.32862676]

exp ( name=None )

Exp Operator. 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

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

Return type

out (Tensor)

Examples

import paddle

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

exp_ ( name=None )

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 the input tensor to a given shape.

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

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 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

A Tensor with the given shape. The data type is the same as x.

Return type

N-D Tensor

Examples

import paddle

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

expand_as ( y, name=None )

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

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

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

A Tensor with the same shape as y. The data type is the same as x.

Return type

N-D Tensor

Examples

import paddle

data_x = paddle.to_tensor([1, 2, 3], 'int32')
data_y = paddle.to_tensor([[1, 2, 3], [4, 5, 6]], 'int32')
np_out = out.numpy()
# [[1, 2, 3], [1, 2, 3]]

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

Flatten op

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

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

For Example:

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 float32, float64, int8, int32, int64, uint8.

• start_axis (int) – the start axis to flatten

• stop_axis (int) – the stop axis to flatten

• name (str, Optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

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.

Return type

Tensor

Raises
• ValueError – If x is not a Tensor.

• ValueError – If start_axis or stop_axis is illegal.

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])

# 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 )

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

flip ( axis, name=None )

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) – The axis(axes) to flip on. Negative indices for indexing from the end are accepted.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

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

Return type

Tensor

Examples

import paddle
import numpy as np

image_shape=(3, 2, 2)
x = np.arange(image_shape[0] * image_shape[1] * image_shape[2]).reshape(image_shape)
x = x.astype('float32')

print(out) # [[[10,11][8, 9]],[[6, 7],[4, 5]] [[2, 3],[0, 1]]]

floor ( name=None )

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

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

Return type

out (Tensor)

Examples

import paddle

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

floor_ ( name=None )

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 two tensors element-wise. The equation is:

$out = x // y$

Note: paddle.floor_divide supports broadcasting. If you want know more about broadcasting, please refer to Broadcasting .

Parameters
• x (Tensor) – the input tensor, it’s data type should be int32, int64.

• y (Tensor) – the input tensor, it’s data type should be int32, int64.

• name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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])
print(z)  # [2, 0, 2, 2]

floor_mod ( y, name=None )

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 Broadcasting .

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, 8, 7])
y = paddle.to_tensor([1, 5, 3, 3])
print(z)  # [0, 3, 2, 1]

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

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=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

The output is a tensor with the same rank as x.

Return type

output (Tensor)

Examples

import paddle

# expected output: [[1,2],[3,4]]

gather_nd ( index, name=None )

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, float32, float64, int32, int64.

• index (Tensor) – The index input with rank > 1, index.shape[-1] <= input.rank. Its dtype should be int32, int64.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

A tensor with the shape index.shape[:-1] + input.shape[index.shape[-1]:]

Return type

output (Tensor)

Examples

import paddle

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

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

greater_equal ( y, name=None )

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

NOTICE: The output of this OP 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 tensor storing the output, the output shape is same as input x.

Return type

Tensor, the output data type is bool

Examples

import paddle

print(result1)  # result1 = [True False True]

greater_than ( y, name=None )

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

NOTICE: The output of this OP 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 tensor storing the output, the output shape is same as input x .

Return type

Tensor, the output data type is bool

Examples

import paddle

print(result1)  # result1 = [False False True]

histogram ( bins=100, min=0, max=0 )

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) – number of histogram bins

• min (int) – lower end of the range (inclusive)

• max (int) – upper end of the range (inclusive)

Returns

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

Return type

Tensor

Examples

import paddle

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

imag ( name=None )

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

[[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)]])

# 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 )

The OP 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

# [1.]

index_sample ( index )

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, 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')
[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')
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
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 )

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 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) – 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 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')
#[[1. 2. 3. 4.]
# [5. 6. 7. 8.]
# [5. 6. 7. 8.]]
#[[ 1.  2.  2.]
# [ 5.  6.  6.]
# [ 9. 10. 10.]]

inverse ( name=None )

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) – 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 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')
print(inv) # [[0.5, 0], [0, 0.5]]

is_empty ( name=None )

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')
print("res:", res)
# ('res:', Tensor: eager_tmp_1
#    - place: CPUPlace
#    - shape: [1]
#    - layout: NCHW
#    - dtype: bool
#    - data: [0])

is_tensor ( )

This function 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')
print(check)  #True

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

isfinite ( name=None )

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')])
print(out)  # [False  True  True False  True False False]

isinf ( name=None )

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')])
print(out)  # [ True False False  True False False False]

isnan ( name=None )

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')])
print(out)  # [False False False False False  True  True]

kron ( y, name=None )

Kron Operator.

This operator computes the Kronecker product of two tensors, a composite tensor made of blocks of the second tensor scaled by the first.

This operator assumes that the rank of the two tensors, $X$ and $Y$ are the same, if necessary prepending the smallest with ones. If the shape of $X$ is [$r_0$, $r_1$, …, $r_N$] and the shape of $Y$ is [$s_0$, $s_1$, …, $s_N$], then the shape of the output tensor is [$r_{0}s_{0}$, $r_{1}s_{1}$, …, $r_{N}s_{N}$]. The elements are products of elements from $X$ and $Y$.

The equation is: $$output[k_{0}, k_{1}, …, k_{N}] = X[i_{0}, i_{1}, …, i_{N}] * Y[j_{0}, j_{1}, …, j_{N}]$$

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

Args:
x (Tensor): the fist operand of kron op, data type: 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): The default value is None. Normally there is no

Returns:

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

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')
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]])

less_equal ( y, name=None )

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

NOTICE: The output of this OP 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 tensor storing the output, the output shape is same as input x.

Return type

Tensor, the output data type is bool

Examples

import paddle

print(result1)  # result1 = [True True False]

less_than ( y, name=None )

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

NOTICE: The output of this OP 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 tensor storing the output, the output shape is same as input x.

Return type

Tensor, the output data type is bool

Examples

import paddle

print(result1)  # result1 = [False True False]

log ( name=None )

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

$\begin{split}Out = \\ln(x)\end{split}$
Parameters
• x (Tensor) – Input Tensor. Must be one of the following types: float32, float64.

• name (str|None) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to 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]]
# [[0.693147, 1.09861, 1.38629], [1.94591, 2.07944, 2.19722]]

log10 ( name=None )

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

$\begin{split}Out = \\log_10_x\end{split}$
Parameters
• x (Tensor) – Input tensor must be one of the following types: float32, float64.

• name (str|None) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to 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
res = paddle.log10(x_i) # [[0.], [1.0]]

# example 2: x is float32
print(res) # [1.0]

# example 3: x is float64
print(res) # [1.0]

log1p ( name=None )

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

$\begin{split}Out = \\ln(x+1)\end{split}$
Parameters
• x (Tensor) – Input Tensor. Must be one of the following types: 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

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

Examples

import paddle

# [[0.], [0.6931472]]

log2 ( name=None )

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

$\begin{split}Out = \\log_2x\end{split}$
Parameters
• x (Tensor) – Input tensor must be one of the following types: float32, float64.

• name (str|None) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to 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
res = paddle.log2(x_i) # [[0.], [1.0]]

# example 2: x is float32
print(res) # [1.0]

# example 3: x is float64
print(res) # [1.0]

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

logical_and operator computes element-wise logical AND on x and y, and returns out. x, y and out are 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 Broadcasting.

Parameters
• x (Tensor) – the input tensor, it’s data type should be bool.

• y (Tensor) – the input tensor, it’s data type should be bool.

• 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

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

logical_not ( out=None, name=None )

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

$out = !x$
Parameters
• x (Tensor) – Operand of logical_not operator. Must be a Tensor of type bool.

• 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-dim bool LoDTensor or Tensor

Return type

Tensor

Examples

import paddle

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

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

logical_or operator computes element-wise logical OR on x and y, and returns out. x, y and out are 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 Broadcasting.

Parameters
• x (Tensor) – the input tensor, it’s data type should be bool.

• y (Tensor) – the input tensor, it’s data type should be bool.

• 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
import numpy as np

x_data = np.array([True, False], dtype=np.bool).reshape(2, 1)
y_data = np.array([True, False, True, False], dtype=np.bool).reshape(2, 2)
print(res) # [[ True  True] [ True False]]

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

logical_xor operator computes element-wise logical XOR on x and y, and returns out. x, y and out are 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 Broadcasting.

Parameters
• x (Tensor) – the input tensor, it’s data type should be bool.

• y (Tensor) – the input tensor, it’s data type should be bool.

• 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
import numpy as np

x_data = np.array([True, False], dtype=np.bool).reshape([2, 1])
y_data = np.array([True, False, True, False], dtype=np.bool).reshape([2, 2])
print(res) # [[False,  True], [ True, False]]

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

This OP calculates the log of the sum of exponentials of x along axis .

$\begin{split}logsumexp(x) = \\log\\sum exp(x)\end{split}$
Parameters
• x (Tensor) – The input Tensor with data type float32, float64.

• axis (int|list|tuple, optional) – The axis along which to perform logsumexp calculations. axis should be int, list(int) or tuple(int). If axis is a list/tuple of dimension(s), logsumexp is calculated along all element(s) of axis . axis or element(s) of axis should be in range [-D, D), where D is the dimensions of x . If axis or element(s) of axis is less than 0, it works the same way as $$axis + D$$ . 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]])
out2 = paddle.logsumexp(x, 1) # [2.15317821, 3.15684602]


This OP 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, float32, float64.

• mask (Tensor) – The Tensor containing the binary mask to index with, it’s data type is bool.

• 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 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]])
[True, True, False, False],
[True, False, False, False]])
#[1.0 5.0 6.0 9.0]

matmul ( y, transpose_x=False, transpose_y=False, name=None )

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) – Whether to transpose $$x$$ before multiplication.

• transpose_y (bool) – Whether to transpose $$y$$ before multiplication.

• 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
import numpy as np

# vector * vector
x_data = np.random.random([10]).astype(np.float32)
y_data = np.random.random([10]).astype(np.float32)
print(z.numpy().shape)
# [1]

# matrix * vector
x_data = np.random.random([10, 5]).astype(np.float32)
y_data = np.random.random([5]).astype(np.float32)
print(z.numpy().shape)
# [10]

# batched matrix * broadcasted vector
x_data = np.random.random([10, 5, 2]).astype(np.float32)
y_data = np.random.random([2]).astype(np.float32)
print(z.numpy().shape)
# [10, 5]

# batched matrix * batched matrix
x_data = np.random.random([10, 5, 2]).astype(np.float32)
y_data = np.random.random([10, 2, 5]).astype(np.float32)
print(z.numpy().shape)
# [10, 5, 5]

# batched matrix * broadcasted matrix
x_data = np.random.random([10, 1, 5, 2]).astype(np.float32)
y_data = np.random.random([1, 3, 2, 5]).astype(np.float32)
print(z.numpy().shape)
# [10, 3, 5, 5]

max ( axis=None, keepdim=False, name=None )

Computes the maximum of tensor elements over the given axis.

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) – 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, 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]])
print(result1)
#[0.9]
print(result2)
#[0.2 0.3 0.6 0.9]
print(result3)
#[0.9 0.7]
print(result4)
#[[0.9]
# [0.7]]

# 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]]])
print(result5)
#[4. 8.]
print(result6)
#[7. 8.]

maximum ( y, name=None )

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 Broadcasting .

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 numpy as np

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

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

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

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

mean ( axis=None, keepdim=False, name=None )

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.]]])
# [12.5]
# [[ 2.5  6.5 10.5]
#  [14.5 18.5 22.5]]
# [[[ 2.5]
#   [ 6.5]
#   [10.5]]
#  [[14.5]
#   [18.5]
#   [22.5]]]
# [ 8.5 12.5 16.5]

median ( axis=None, keepdim=False, name=None )

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 is [[0 , 1 , 2 , 3 ],
#       [4 , 5 , 6 , 7 ],
#       [8 , 9 , 10, 11]]

# y1 is [5.5]

# y2 is [4., 5., 6., 7.]

# y3 is [1.5, 5.5, 9.5]

# y4 is [[4., 5., 6., 7.]]

min ( axis=None, keepdim=False, name=None )

Computes the minimum of tensor elements over the given axis

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) – 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, results of minimum on the specified axis of input tensor, it’s data type is the same as input’s Tensor.

Examples

import paddle

# 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]])
print(result1)
#[0.1]
print(result2)
#[0.1 0.2 0.5 0.7]
print(result3)
#[0.2 0.1]
print(result4)
#[[0.2]
# [0.1]]

# 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]]])
print(result5)
#[1. 5.]
print(result6)
#[1. 2.]

minimum ( y, name=None )

Compare two tensors and returns 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 Broadcasting .

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 numpy as np

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

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

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

x = paddle.to_tensor([5, 3, np.inf], dtype='float64')
y = paddle.to_tensor([1, -np.inf, 5], dtype='float64')
print(res)
#       [   1., -inf.,    5.]

mm ( mat2, name=None )

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) – 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 product Tensor.

Return type

Tensor

Examples

import paddle
print(out)
#        [[11., 14., 17., 20.],
#         [23., 30., 37., 44.],
#         [35., 46., 57., 68.]])

mod ( y, name=None )

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 Broadcasting .

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, 8, 7])
y = paddle.to_tensor([1, 5, 3, 3])
print(z)  # [0, 3, 2, 1]

multiplex ( index, name=None )

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) – 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 of multiplex OP, with data type being float32, float64, int32, int64.

Return type

Tensor

Examples

import paddle
import numpy as np
img1 = np.array([[1, 2], [3, 4]]).astype(np.float32)
img2 = np.array([[5, 6], [7, 8]]).astype(np.float32)
print(res) # [array([[5., 6.], [3., 4.]], dtype=float32)]

multiply ( y, name=None )

Elementwise Mul Operator.

Multiply two tensors element-wise

The equation is:

$$Out = X \\odot Y$$

• $X$: a tensor of any dimension.

• $Y$: a tensor whose dimensions must be less than or equal to the dimensions of $X$.

There are two cases for this operator:

1. The shape of $Y$ is the same with $X$.

2. The shape of $Y$ is a continuous subsequence of $X$.

For case 2:

1. Broadcast $Y$ to match the shape of $X$, where $axis$ is the start dimension index for broadcasting $Y$ onto $X$.

2. If $axis$ is -1 (default), $axis = rank(X) - rank(Y)$.

3. The trailing dimensions of size 1 for $Y$ will be ignored for the consideration of subsequence, such as shape(Y) = (2, 1) => (2).

For example:

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) – (Variable), Tensor or LoDTensor of any dimensions. Its dtype should be int32, int64, float32, float64.

• y (Tensor) – (Variable), Tensor or LoDTensor of any dimensions. Its dtype should be int32, int64, float32, float64.

• name (string, optional) – Name of the output. Default is None. It’s used to print debug info for developers. Details: Name

Returns

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

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 Broadcasting .

param x

the input tensor, its data type should be float32, float64, int32, int64.

type x

Tensor

param y

the input tensor, its data type should be float32, float64, int32, int64.

type y

Tensor

param name

type name

str, optional

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]])
print(res) # [[5, 12], [21, 32]]

x = paddle.to_tensor([[[1, 2, 3], [1, 2, 3]]])
print(res) # [[[2, 4, 6], [2, 4, 6]]]

Return type

out (Tensor)

mv ( vec, name=None )

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 numpy as np

x_data = np.array([[2, 1, 3], [3, 0, 1]]).astype("float64")
vec_data = np.array([3, 5, 1])

nonzero ( as_tuple=False )

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) – Return type, Tensor or tuple of Tensor.

Returns

Tensor. The data type is int64.

Examples

import paddle

[0.0, 2.0, 0.0],
[0.0, 0.0, 3.0]])
x2 = paddle.to_tensor([0.0, 1.0, 0.0, 3.0])
print(out_z1)
#[[0 0]
# [1 1]
# [2 2]]
for out in out_z1_tuple:
print(out)
#[[0]
# [1]
# [2]]
#[[0]
# [1]
# [2]]
print(out_z2)
#[[1]
# [3]]
for out in out_z2_tuple:
print(out)
#[[1]
# [3]]

norm ( p='fro', axis=None, keepdim=False, name=None )

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. Defalut 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
import numpy as np
shape=[2, 3, 4]
np_input = np.arange(24).astype('float32') - 12
np_input = np_input.reshape(shape)
#[[[-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.numpy() [17.435596 16.911535 16.7332   16.911535]

# compute 2-order vector norm along last dimension.
#out_pnorm.numpy(): [[21.118711  13.190906   5.477226]
#                    [ 3.7416575 11.224972  19.131126]]

# compute 2-order  norm along [0,1] dimension.
#out_pnorm.numpy(): [17.435596 16.911535 16.7332   16.911535]

# compute inf-order  norm
#out_pnorm.numpy()  = [12.]
#out_pnorm.numpy(): [[12. 11. 10. 9.] [8. 7. 6. 7.] [8. 9. 10. 11.]]

# compute -inf-order  norm
#out_pnorm.numpy(): [0.]
#out_pnorm.numpy(): [[0. 1. 2. 3.] [4. 5. 6. 5.] [4. 3. 2. 1.]]

not_equal ( y, name=None )

This OP returns the truth value of $$x != y$$ elementwise, which is equivalent function to the overloaded operator !=.

NOTICE: The output of this OP 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 tensor storing the output, the output shape is same as input x.

Return type

Tensor, the output data type is bool

Examples

import paddle

print(result1)  # result1 = [False True True]

numel ( name=None )

Returns the number of elements for a tensor, which is a int64 Tensor with shape [1] in static mode or a scalar value in imperative mode

Parameters

x (Tensor) – The input Tensor, it’s data type can be bool, float16, float32, float64, int32, int64.

Returns

The number of elements for the input Tensor.

Return type

Tensor

Examples

import paddle

x = paddle.full(shape=[4, 5, 7], fill_value=0, dtype='int32')

pow ( y, name=None )

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 Broadcasting .

Parameters
• x (Tensor) – An N-D Tensor, the data type is 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
print(res)
#        [1., 4., 9.])
print(res)
#        [1.         , 5.65685415 , 15.58845711])

# example 2: y is a Tensor
print(res)
#        [1., 4., 9.])

prod ( axis=None, keepdim=False, dtype=None, name=None )

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.

• dtype (str|np.dtype, optional) – The desired date type of returned tensor, can be float32, float64, int32, int64. If specified, the input tensor is casted to dtype before operator performed. This is very useful for avoiding data type overflows. The default value is None, the dtype of output is the same as input Tensor x.

• keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result tensor will have one fewer dimension than the input unless keepdim is true. Default is False.

• 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 .

Returns

Tensor, result of product on the specified dim of input tensor.

Raises
• ValueError – The dtype must be float32, float64, int32 or int64.

• TypeError – The type of axis must be int, list or tuple.

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]])
# [0.0002268]

# [0.027  0.0084]

# [0.02 0.06 0.3  0.63]

# [[0.02 0.06 0.3  0.63]]

# [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]]])
# [105. 384.]

# [  24. 1680.]

rank ( )

The OP returns the number of dimensions for a tensor, which is a 0-D int32 Tensor.

Parameters

input (Tensor) – The input N-D 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

print(rank)
# 3

real ( name=None )

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

[[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)]])

# 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 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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
print(out)
# [-2.5        -5.         10.          3.33333333]

reciprocal_ ( name=None )

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 )

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 Broadcasting .

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, 8, 7])
y = paddle.to_tensor([1, 5, 3, 3])
print(z)  # [0, 3, 2, 1]

reshape ( shape, name=None )

This operator changes the shape of x without changing its data.

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

Some tricks exist when specifying the target shape.

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

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

Here are some examples to explain it.

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

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

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

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, the elements of it should be integers or Tensors with shape [1]. If shape is an Tensor, it should be an 1-D Tensor .

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

A reshaped Tensor with the same data type as x.

Return type

Tensor

Examples

import numpy as np

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

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

print(out)
# the shape of out_2 is [4, 12].

print(out)
# the shape is [8, 6].
# out shares data with x in dygraph mode
x[0, 0, 0] = 10.
print(out[0, 0])
# the value is [10.]

reshape_ ( shape, name=None )

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 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) – The axis(axes) to flip on. Negative indices for indexing from the end are accepted.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

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

Return type

Tensor

Examples

import paddle
import numpy as np

image_shape=(3, 2, 2)
x = np.arange(image_shape[0] * image_shape[1] * image_shape[2]).reshape(image_shape)
x = x.astype('float32')

print(out) # [[[10,11][8, 9]],[[6, 7],[4, 5]] [[2, 3],[0, 1]]]

roll ( shifts, axis=None, name=None )

Roll the x tensor along the given axis(axes). With specific ‘shifts’, Elements that roll beyond the last position are re-introduced at the first according to ‘shifts’. If a axis is not specified, the tensor will be flattened before rolling and then restored to the original shape.

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|None) – axis(axes) along which to roll.

Returns

A Tensor with same data type as x.

Return type

Tensor

Examples

import paddle

[4.0, 5.0, 6.0],
[7.0, 8.0, 9.0]])
print(out_z1)
#[[9. 1. 2.]
# [3. 4. 5.]
# [6. 7. 8.]]
print(out_z2)
#[[7. 8. 9.]
# [1. 2. 3.]
# [4. 5. 6.]]

round ( name=None )

The OP rounds 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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([-0.5, -0.2, 0.6, 1.5])
print(out)
# [-1. -0.  1.  2.]

round_ ( name=None )

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 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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([0.1, 0.2, 0.3, 0.4])
print(out)
# [3.16227766 2.23606798 1.82574186 1.58113883]

rsqrt_ ( name=None )

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 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 Tensor with shape [1] 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) – 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 of scale operator, with shape and data type same as input.

Return type

Tensor

Examples

# scale as a float32 number


# scale with parameter scale as a Tensor


scale_ ( scale=1.0, bias=0.0, bias_after_scale=True, act=None, name=None )

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 Layer Output is obtained by updating the input on selected indices based on updates.

import numpy as np
#input:
x = np.array([[1, 1], [2, 2], [3, 3]])
index = np.array([2, 1, 0, 1])
# shape of updates should be the same as x
# shape of updates with dim > 1 should be the same as input
updates = np.array([[1, 1], [2, 2], [3, 3], [4, 4]])
overwrite = False
# calculation:
if not overwrite:
for i in range(len(index)):
x[index[i]] = np.zeros((2))
for i in range(len(index)):
if (overwrite):
else:
# output:
out = np.array([[3, 3], [6, 6], [1, 1]])
out.shape # [3, 2]


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

Parameters
• x (Tensor) – The input N-D Tensor with ndim>=1. Data type can be float32, float64.

• index (Tensor) – The index 1-D Tensor. Data type can be int32, int64. The length of index cannot exceed updates’s length, and the value in index cannot exceed input’s length.

• updates (Tensor) – update input with updates parameter based on index. shape should be the same as input, and dim value with dim > 1 should be the same as input.

• overwrite (bool) –

The mode that updating the output when there are same indices. If True, use the overwrite mode to update the output of the same index,

Unexpected indentation.

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

The output is a Tensor with the same shape as x.

Return type

Tensor

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')

# [[3., 3.],
#  [6., 6.],
#  [1., 1.]]

# 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 )

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 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

The output is a tensor with the same type as updates .

Return type

output (Tensor)

Examples

import paddle
import numpy as np

index_data = np.array([[1, 1],
[0, 1],
[1, 3]]).astype(np.int64)
shape = [3, 5, 9, 10]



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)

we get:

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

Parameters
• x (Tensor) – The x input. Its dtype should be 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

The output is a tensor with the same shape and dtype as x.

Return type

output (Tensor)

Examples

import paddle
import numpy as np

x = paddle.rand(shape=[3, 5, 9, 10], dtype='float32')
index_data = np.array([[1, 1],
[0, 1],
[1, 3]]).astype(np.int64)

shard_index ( index_num, nshards, shard_id, ignore_value=- 1 )

Recompute the input indices according to the offset of the shard. The length of the indices is evenly divided into N shards, and if the shard_id matches the shard with the input index inside, the index is recomputed on the basis of the shard offset, elsewise it is set to ignore_value. The detail is as follows:

shard_size = (index_num + nshards - 1) // nshards
y = x % shard_size if x // shard_size == shard_id else ignore_value


NOTE: If the length of indices cannot be evely divided by the shard number, the size of the last shard will be less than the calculated shard_size

Args:

input (Tensor): Input indices with data type int64. It’s last dimension must be 1. index_num (int): An integer defining the range of the index. nshards (int): The number of shards. shard_id (int): The index of the current shard. ignore_value (int): An integer value out of sharded index range.

Returns:

Tensor: The sharded index of input.

Examples:
import paddle
index_num=20,
nshards=2,
shard_id=0)
print(shard_label)
# [[-1], [1]]

sign ( name=None )

This OP 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) – 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 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')
print(out)  # [1.0, 0.0, -1.0, 1.0]

sin ( name=None )

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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
print(out)
# [-0.38941834 -0.19866933  0.09983342  0.29552021]

sinh ( name=None )

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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
print(out)
# [-0.41075233 -0.201336    0.10016675  0.30452029]

slice ( axes, starts, ends )

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, the elements of it should be integers or Tensors with shape [1]. If starts is an Tensor, it should be an 1-D Tensor. It represents starting indices of corresponding axis in axes.

• ends (list|tuple|Tensor) – The data type is int32 . If ends is a list or tuple, the elements of it should be integers or Tensors with shape [1]. If ends is an Tensor, it should be an 1-D Tensor . It represents ending indices of corresponding axis in axes.

Returns

A Tensor. The data type is same as input.

Return type

Tensor

Raises
• TypeError – The type of starts must be list, tuple or Tensor.

• TypeError – The type of ends must be list, tuple or Tensor.

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[0:3, 0:2, 2:4].

# example 2:
# attr starts is a list which contain tensor.
sliced_2 = paddle.slice(input, axes=axes, starts=[minus_3, 0, 2], ends=ends)
# sliced_2 is input[0:3, 0:2, 2:4].

sort ( axis=- 1, descending=False, name=None )

This OP 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 0.

• 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) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name.

Returns

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

Return type

Tensor

Examples

import paddle

[0,0,1,7],
[6,9,2,4]],
[[5,2,4,2],
[4,7,7,9],
[1,7,0,6]]],
dtype='float32')
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 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.

• num_or_sections (int|list|tuple) – If num_or_sections is an int, then num_or_sections indicates the number of equal sized sub-Tensors that the x will be divided into. If num_or_sections is a list or tuple, the length of it indicates the number of sub-Tensors and the elements in it indicate the sizes of sub-Tensors’ dimension orderly. The length of the list must not be larger than the x ‘s size of specified axis.

• axis (int|Tensor, optional) – The axis along which to split, it can be a scalar with type int or a Tensor with shape [1] and data type int32 or int64. If :math::axis < 0, the axis to split along is $$rank(x) + axis$$. 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

The list of segmented Tensors.

Return type

list(Tensor)

Example

import paddle

# x is a Tensor of shape [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 Activation Operator.

$$out=\\sqrt{x}=x^{1/2}$$

Note:

input value must be greater than or equal to zero.

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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([0.1, 0.2, 0.3, 0.4])
print(out)
# [0.31622777 0.4472136  0.54772256 0.63245553]

sqrt_ ( name=None )

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

square ( name=None )

The OP 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

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

Return type

out (Tensor)

Examples

import paddle

x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3])
print(out)
# [0.16 0.04 0.01 0.09]

squeeze ( axis=None, name=None )

This OP will squeeze the dimension(s) of size 1 of input tensor x’s shape.

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

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

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

Squeezed Tensor with the same data type as input Tensor.

Return type

Tensor

Examples

import paddle

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 )

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 )

This OP stacks all the input tensors x along axis dimemsion. All tensors must be of the same shape and same dtype.

For example, given N tensors of shape [A, B], if axis == 0, the shape of stacked tensor is [N, A, B]; if axis == 1, the shape of stacked tensor is [A, N, B], etc.

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) – Please refer to Name, Default None.

Returns

The stacked tensor with same data type as input.

Return type

Tensor

Example

import paddle

out = paddle.stack([x1, x2, x3], axis=0)
print(out.shape)  # [3, 1, 2]
print(out)
# [[[1., 2.]],
#  [[3., 4.]],
#  [[5., 6.]]]

stanh ( scale_a=0.67, scale_b=1.7159, name=None )

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 )

Computes the standard-deviation of x along axis .

Parameters
• x (Tensor) – The input Tensor with data type 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]])
# [1.63299316]
# [1.       2.081666]

strided_slice ( axes, starts, ends, strides, name=None )

This operator produces a slice of x along multiple axes. Similar to numpy: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html Slice uses axes, starts and ends attributes to specify the start and end dimension for each axis in the list of axes and Slice uses this information to slice the input data tensor. If a negative value is passed to starts or ends such as $$-i$$, 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 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 [1]. If starts is an Tensor, it should be an 1-D Tensor. It represents starting indices of corresponding axis in axes.

• ends (list|tuple|Tensor) – The data type is int32 . If ends is a list or tuple, the elements of it should be integers or Tensors with shape [1]. If ends is an Tensor, it should be an 1-D Tensor . It represents ending indices of corresponding axis in axes.

• strides (list|tuple|Tensor) – The data type is int32 . If strides is a list or tuple, the elements of it should be integers or Tensors with shape [1]. If strides is an Tensor, it should be an 1-D Tensor . It represents slice step of corresponding axis in axes.

• name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name .

Returns

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

Return type

Tensor

Examples

import paddle
# 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.
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 )

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 Broadcasting .

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 numpy as np

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

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

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

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

subtract_ ( y, name=None )

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 )

Computes the sum of tensor elements over the given dimension.

Parameters
• x (Tensor) – An N-D Tensor, the data type is float32, float64, int32 or int64.

• axis (int|list|tuple, optional) – The dimensions along which the sum is performed. If 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) – 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 summation operation on the specified axis of input Tensor x, it’s data type is the same as x.

Return type

Tensor

Raises
• ValueError – If the data type of x is float64, dtype can not be float32 or int32.

• ValueError – If the data type of x is int64, dtype can not be int32.

• TypeError – The type of axis must be int, list or tuple.

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]])
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]

t ( name=None )

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 float16, float32, float64, int32.

• 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

For Example:

# Example 1 (0-D tensor)
x = tensor([0.79])

# Example 2 (1-D tensor)
x = tensor([0.79, 0.84, 0.32])

# Example 3 (2-D tensor)
x = tensor([0.79, 0.84, 0.32],
[0.64, 0.14, 0.57])
[0.84, 0.14],
[0.32, 0.57])


Examples:

import paddle
print(x_transposed.shape)
# [3, 2]

tanh ( name=None )

Tanh Activation Operator.

$\begin{split}out = \\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\end{split}$
Parameters
• x (Tensor) – Input of Tanh operator, an N-D Tensor, with data type float32, float64 or float16.

• name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to 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])
print(out)
# [-0.37994896 -0.19737532  0.09966799  0.29131261]

tanh_ ( name=None )

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

tile ( repeat_times, name=None )

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

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

Parameters
• x (Tensor) – The input tensor, its data type should be bool, float32, float64, int32 or int64.

• repeat_times (Tensor|tuple|list) – The number of repeating times. If repeat_times is a list or tuple, all its elements should be integers or 1-D Tensors with the data type int32. If repeat_times is a Tensor, it should be an 1-D Tensor with the data type int32.

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

Returns

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

Examples

import paddle

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

np_out = out.numpy()
# [[1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 2, 3]]

np_out = out.numpy()
# [[1, 2, 3], [1, 2, 3]]

topk ( k, axis=None, largest=True, sorted=True, name=None )

This OP is used to find 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

tensor_1 = paddle.to_tensor([1, 4, 5, 7])
print(value_1)
# [7]
print(indices_1)
# [3]
tensor_2 = paddle.to_tensor([[1, 4, 5, 7], [2, 6, 2, 5]])
print(value_2)
# [[7]
#  [6]]
print(indices_2)
# [[3]
#  [1]]
value_3, indices_3 = paddle.topk(tensor_2, k=1, axis=-1)
print(value_3)
# [[7]
#  [6]]
print(indices_3)
# [[3]
#  [1]]
value_4, indices_4 = paddle.topk(tensor_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

This OP 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) – Normally there is no need for user to set this property. For more information, please refer to Name. Default: None.

Returns

the output data type is the same as input data type.

Return type

Tensor

Examples

import paddle

case3 = paddle.randn([3, 10, 5, 10])
data1 = paddle.trace(case1) # data1.shape = [1]
data2 = paddle.trace(case2, offset=1, axis1=1, axis2=2) # data2.shape = [3]
data3 = paddle.trace(case3, offset=-3, axis1=1, axis2=-1) # data2.shape = [3, 5]

transpose ( perm, name=None )

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 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 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_transposed = paddle.transpose(x, perm=[1, 0, 2])
print(x_transposed.shape)
# [3L, 2L, 4L]

unbind ( axis=0 )

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 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

The list of segmented Tensor variables.

Return type

list(Tensor)

Example

import paddle
import numpy as np
# input is a variable which shape is [3, 4, 5]
np_input = np.random.rand(3, 4, 5).astype('float32')
[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]

unique ( return_index=False, return_inverse=False, return_counts=False, axis=None, dtype='int64', name=None )

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

(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.

Return type

tuple

Examples

import paddle

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

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

np_unique = unique.numpy()
# [[2 1 3]
#  [3 0 1]]

unsqueeze ( axis, name=None )

Insert single-dimensional entries to the shape of input Tensor x. Takes one required argument axis, a dimension or list of dimensions that will be inserted. Dimension indices in axis are as seen in the output tensor.

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

Parameters
• x (Tensor) – The input Tensor to be unsqueezed. Supported data type: float32, float64, bool, int8, int32, int64.

• axis (int|list|tuple|Tensor) – Indicates the dimensions to be inserted. The data type is int32 . If axis is a list or tuple, the elements of it should be integers or Tensors with shape [1]. If axis is a Tensor, it should be an 1-D Tensor . If axis is negative, axis = axis + ndim(x) + 1.

• name (str|None) – Name for this layer. Please refer to Name, Default None.

Returns

Unsqueezed Tensor with the same data type as input Tensor.

Return type

Tensor

Examples

import paddle

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

print(out1.shape)  # [1, 5, 10]

print(out2.shape)  # [1, 5, 1, 10]

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 )

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 )
Alias_main

UnStack Layer

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

The unstacked Tensors list. The list elements are N-D Tensors of data types float32, float64, int32, int64.

Return type

list(Tensor)

Raises

ValueError – If x.shape[axis] <= 0 or axis is not in range [-D, D).

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]

var ( axis=None, unbiased=True, keepdim=False, name=None )

Computes the variance of x along axis .

Parameters
• x (Tensor) – The input Tensor with data type 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.

• 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 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]])
# [2.66666667]
# [1.         4.33333333]

where ( x, y, name=None )

Return a tensor of elements selected from either $x$ or $y$, depending on $condition$.

$\begin{split}out_i = \\begin{cases} x_i, \quad \\text{if} \\ condition_i \\ is \\ True \\\\ y_i, \quad \\text{if} \\ condition_i \\ is \\ False \\\\ \\end{cases}\end{split}$
Parameters
• condition (Tensor) – The condition to choose x or y.

• x (Tensor) – x is a Tensor with data type float32, float64, int32, int64.

• y (Tensor) – y is a Tensor with data type 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 Tensor with the same data dype as x.

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])
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