Tensors ｜ 张量

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• Tensors 是类似 arrays 和 matrices 的数据结构 (在 Pytorch 中使用 tensors 来编码模型的输入和输出，以及模型的参数)
• Tensors 类似于 Numpy 的 ndarrays，但是可以在 GPU 或其他特殊硬件上使用来加速计算

import torch
import numpy as np

Tensor Initialization

• Tensor 可以通过多种方式进行初始化

Directly from data

• Tensor 可以直接从 data 中进行初始化 (数据类型会自动推断)

data = [[1, 2], [3, 4]]
x_data = torch.tensor(data)

From a NumPy array

• Tensor 可以从 NumPy array 中进行初始化，并且保留 NumPy array 的维度和数据类型 (反之亦然, see Bridge with NumPy

np_array = np.array(data)
x_np = torch.from_numpy(np_array)

From another tensor

• 新的 tensor 保留了原始 tensor 的属性 (shape, datatype)，除非被显式地重写

codeoutput

x_ones = torch.ones_like(x_data) # retains the properties of x_data
print(f"Ones Tensor: \n {x_ones} \n")

x_rand = torch.rand_like(x_data, dtype=torch.float) # overrides the datatype of x_data
print(f"Random Tensor: \n {x_rand} \n")

Ones Tensor: 
 tensor([[1, 1],
        [1, 1]])

Random Tensor:
 tensor([[0.7576, 0.2793],
        [0.4031, 0.7347]])

With random or constant values

• shape 是 tensor 维度的元组(tuple), 上面的函数中，它确定了输出张量的维度

codeoutput

shape = (2, 3,) # tuple of tensor dimensions
rand_tensor = torch.rand(shape)
ones_tensor = torch.ones(shape)
zeros_tensor = torch.zeros(shape)

print(f"Random Tensor: \n {rand_tensor} \n")
print(f"Ones Tensor: \n {ones_tensor} \n")
print(f"Zeros Tensor: \n {zeros_tensor}")

``` output
Random Tensor:
tensor([[0.3904, 0.6009, 0.2566],
[0.7936, 0.9408, 0.1332]])

Ones Tensor:
tensor([[1., 1., 1.],
[1., 1., 1.]])

Zeros Tensor:
tensor([[0., 0., 0.],
[0., 0., 0.]])

Tensor Attributes

• Tensor attributrs describe their shape, datatype, and the device on which they are stored

codeoutput

tensor = torch.rand(3, 4)

print(f"Shape of tensor: {tensor.shape}")
print(f"Datatype of tensor: {tensor.dtype}")
print(f"Device tensor is stored on: {tensor.device}")

Shape of tensor: torch.Size([3, 4])
Datatype of tensor: torch.float32
Device tensor is stored on: cpu

Tensor Operations

• Over 100 tensor operations, including transposing, indexing, slicing, mathematical operations, linear algebra, random sampling, and more are comprehensively described here.
• 这些操作都能在 GPU 上运行（通常比在 CPU 上运行速度更快）

codeoutput

# We move our tensor to the GPU if available
if torch.cuda.is_available():
    tensor = tensor.to('cuda')
    print(f"Device tensor is stored on: {tensor.device}")

Device tensor is stored on: cuda:0

Some operations

If you’re familiar with the NumPy API, you’ll find the Tensor API a breeze to use.

Standard numpy-like indexing and slicing

codeoutput

tensor = torch.ones(4, 4)
tensor[:,1] = 0
print(tensor)

tensor([[1., 0., 1., 1.],
        [1., 0., 1., 1.],
        [1., 0., 1., 1.],
        [1., 0., 1., 1.]])

Joining tensors

• We can use torch.cat to concatenate a sequence of tensors along a given dimension.

• See also torch.stack and torch.split
• another tensor joining op that is subtly different from torch.cat.

codeoutput

t1 = torch.cat([tensor, tensor, tensor], dim=1)
print(t1)

``` output
tensor([[1., 0., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1.],
[1., 0., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1.],
[1., 0., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1.],
[1., 0., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1.]])

Multiplying tensors

• Computing the element-wise product

  codeoutput

  # This computes the element-wise product
  print(f"tensor.mul(tensor) \n {tensor.mul(tensor)} \n")
  # Alternative syntax:
  print(f"tensor * tensor \n {tensor * tensor}")
  

  tensor.mul(tensor)
  tensor([[1., 0., 1., 1.],
          [1., 0., 1., 1.],
          [1., 0., 1., 1.],
          [1., 0., 1., 1.]])
  
  tensor * tensor
  tensor([[1., 0., 1., 1.],
          [1., 0., 1., 1.],
          [1., 0., 1., 1.],
          [1., 0., 1., 1.]])
  

• Computing the matrix multiplication between two tensors

  codeoutput

  print(f"tensor.matmul(tensor.T) \n {tensor.matmul(tensor.T)} \n")
  # Alternative syntax:
  print(f"tensor @ tensor.T \n {tensor @ tensor.T}")
  

  tensor.matmul(tensor.T)
  tensor([[3., 3., 3., 3.],
          [3., 3., 3., 3.],
          [3., 3., 3., 3.],
          [3., 3., 3., 3.]])
  
  tensor @ tensor.T
  tensor([[3., 3., 3., 3.],
          [3., 3., 3., 3.],
          [3., 3., 3., 3.],
          [3., 3., 3., 3.]])
  

In-place operations

• Operations that have a _ suffix are in-place
• 这种操作会改变被操作的张量本身，例如 x.copy_(y), x.t_(), 将会改变 x

Note

In-place operations 可以节省一些内存，但在计算导数时会丢失历史信息。因此，不鼓励使用它们。

codeoutput

# tensor.add_(5)
tensor.add_(5)
print(tensor)

tensor([[6., 5., 6., 6.],
        [6., 5., 6., 6.],
        [6., 5., 6., 6.],
        [6., 5., 6., 6.]])

Bridge with NumPy

Tensors on the CPU and NumPy arrays can share their underlying memory locations, and changing one will change the other.

Tensor to NumPy array

codeoutput

t = torch.ones(5)
print(f"t: {t}")
n = t.numpy()
print(f"n: {n}")

t: tensor([1., 1., 1., 1., 1.])
n: [1. 1. 1. 1. 1.]

• A change in the tensor reflects in the NumPy array.

codeoutput

t.add_(1)
print(f"t: {t}")
print(f"n: {n}")

t: tensor([2., 2., 2., 2., 2.])
n: [2. 2. 2. 2. 2.]

NumPy array to Tensor

np = np.ones(5)
t = torch.from_numpy(np)

• Changes in the NumPy array reflects in the tensor.

codeoutput

np.add(n, 1, out=n)
print(f"t: {t}")
print(f"np: {np}")

t: tensor([2., 2., 2., 2., 2.], dtype=torch.float64)
n: [2. 2. 2. 2. 2.]

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