张量操作

一、张量的拼接

1. torch.cat()

   功能：将张量按维度dim进行拼接,且[不会扩张张量的维度]

• tensors:张量序列

• dim:要拼接的维度

  torch.cat(tensors,
  dim=0,
  out=None)

  flag = True

  flag = False

  if flag:
  t1 = torch.full((4, 4), 10)
  t2 = torch.full((4, 4), 5)
  print(t1)
  print(t2)
  t3 = torch.cat([t1, t2], dim=0,out=None)
  print(t3)
  print("t1.shape:{}\nt2.shape:{}\nt3.shape:{}".format(t1.shape, t2.shape, t3.shape))

  tensor([[10, 10, 10, 10],
  [10, 10, 10, 10],
  [10, 10, 10, 10],
  [10, 10, 10, 10]])
  tensor([[5, 5, 5, 5],
  [5, 5, 5, 5],
  [5, 5, 5, 5],
  [5, 5, 5, 5]])
  tensor([[10, 10, 10, 10],
  [10, 10, 10, 10],
  [10, 10, 10, 10],
  [10, 10, 10, 10],
  [ 5, 5, 5, 5],
  [ 5, 5, 5, 5],
  [ 5, 5, 5, 5],
  [ 5, 5, 5, 5]])
  t1.shape:torch.Size([4, 4])
  t2.shape:torch.Size([4, 4])
  t3.shape:torch.Size([8, 4])

1. torch.stack()

   功能：在新创建的维度dim上进行拼接[会扩张张量的维度]

• tensors:张量序列

• dim:要拼接的维度

  torch.stack(
  tensors,
  dim=0,
  out=None)

  flag = True

  flag = False

  if flag:
  t1 = torch.full((2, 4), 10)
  t2 = torch.full((2, 4), 5)
  print(t1)
  print(t2)
  t3 = torch.stack([t1, t1, t2], dim=1,out=None)
  print(t3)
  print("t1.shape:{}\nt2.shape:{}\nt3.shape:{}".format(t1.shape, t2.shape, t3.shape))

  tensor([[10, 10, 10, 10],
  [10, 10, 10, 10]])
  tensor([[5, 5, 5, 5],
  [5, 5, 5, 5]])
  tensor([[[10, 10, 10, 10],
  [10, 10, 10, 10],
  [ 5, 5, 5, 5]],

      [[10, 10, 10, 10],
       [10, 10, 10, 10],
       [ 5,  5,  5,  5]]])

  t1.shape:torch.Size([2, 4])
  t2.shape:torch.Size([2, 4])
  t3.shape:torch.Size([2, 3, 4])

二、张量的切分

1. torch.chunk(input,chunks,dim=0)

   将tensor按照dim进行平均切分返回张量列表，若不能整除，最后一份tensor小于其他张量

• input:需要切分的张量

• chunks:要切分的份数

• dim:要切分的维度

  flag = True

  flag = False

  if flag:
  t1 = torch.full((6, 5), 10)
  t3 = torch.chunk(t1, chunks=3, dim=0)
  for num, t in enumerate(t3):
  print(num, t, t.shape)

  0 tensor([[10, 10, 10, 10, 10],
  [10, 10, 10, 10, 10]]) torch.Size([2, 5])
  1 tensor([[10, 10, 10, 10, 10],
  [10, 10, 10, 10, 10]]) torch.Size([2, 5])
  2 tensor([[10, 10, 10, 10, 10],
  [10, 10, 10, 10, 10]]) torch.Size([2, 5])

1. torch.split(tensor,split_size_or_sections,dim)

   将张量按照dim进行切分，返回张量列表

   split_size_or_sections：为int时表示每一份的长度，为list时表示按list元素切分

   flag = True

   flag = False

   if flag:
   t1 = torch.full((6, 5), 10)
   t3 = torch.split(t1, split_size_or_sections=2, dim=0)
   t4 = torch.split(t1, [2, 1, 1, 1, 1], dim=0)
   for num, t in enumerate(t4):
   print(num, t, t.shape)
   for num, t in enumerate(t3):
   print(num, t, t.shape)

   0 tensor([[10, 10, 10, 10, 10],
   [10, 10, 10, 10, 10]]) torch.Size([2, 5])
   1 tensor([[10, 10, 10, 10, 10]]) torch.Size([1, 5])
   2 tensor([[10, 10, 10, 10, 10]]) torch.Size([1, 5])
   3 tensor([[10, 10, 10, 10, 10]]) torch.Size([1, 5])
   4 tensor([[10, 10, 10, 10, 10]]) torch.Size([1, 5])
   0 tensor([[10, 10, 10, 10, 10],
   [10, 10, 10, 10, 10]]) torch.Size([2, 5])
   1 tensor([[10, 10, 10, 10, 10],
   [10, 10, 10, 10, 10]]) torch.Size([2, 5])
   2 tensor([[10, 10, 10, 10, 10],
   [10, 10, 10, 10, 10]]) torch.Size([2, 5])

三、tensor索引

1. torch.index_select(input,dim,index,out=None)

   按照index索引数据返回依索引数据拼接的张量

   flag = True

   flag = False

   if flag:
   torch.manual_seed(1)
   t1 = torch.randint(1, 10, size=(6, 5))
   t_list = [0, 1]
   t2 = torch.tensor(t_list,dtype=torch.long)
   t4 = torch.index_select(t1, dim=0, index=t2, out=None)
   print(t1)
   print(t4)

   tensor([[5, 6, 1, 6, 8],
   [2, 3, 6, 9, 1],
   [3, 4, 2, 9, 5],
   [1, 4, 7, 3, 8],
   [7, 7, 9, 8, 7],
   [1, 8, 9, 9, 5]])
   tensor([[5, 6, 1, 6, 8],
   [2, 3, 6, 9, 1]])

2. torch.masked_select(input,mask,out=None)

   按mask中的True进行索引，并返回一维张量,其中mask代表与input同形状的布尔类型张量

   eq,ne,gt,ge,lt,le

   flag = True

   flag = False

   if flag:
   torch.manual_seed(1)
   t1 = torch.randint(1, 10, size=(6, 5))
   t1_mask = t1.ge(5)
   t4 = torch.masked_select(t1,t1_mask)
   print(t1)
   print(t1_mask)
   print(t4)

   tensor([[5, 6, 1, 6, 8],
   [2, 3, 6, 9, 1],
   [3, 4, 2, 9, 5],
   [1, 4, 7, 3, 8],
   [7, 7, 9, 8, 7],
   [1, 8, 9, 9, 5]])
   tensor([[ True, True, False, True, True],
   [False, False, True, True, False],
   [False, False, False, True, True],
   [False, False, True, False, True],
   [ True, True, True, True, True],
   [False, True, True, True, True]])
   tensor([5, 6, 6, 8, 6, 9, 9, 5, 7, 8, 7, 7, 9, 8, 7, 8, 9, 9, 5])

四、张量变换

3.1 torch.reshape(input,shape)

变换张量形状，当张量在内存中是连续时，新张量与input共享数据内存

flag = True
# flag = False
if flag:
    torch.manual_seed(1)
    t1 = torch.randint(1, 10, size=(6, 5))
    t2 = torch.reshape(t1, (-1,3,5))
    t1[0,0] = 33
    print(t1, id(t1.data))
    print(t2, id(t2.data))


tensor([[33,  6,  1,  6,  8],
        [ 2,  3,  6,  9,  1],
        [ 3,  4,  2,  9,  5],
        [ 1,  4,  7,  3,  8],
        [ 7,  7,  9,  8,  7],
        [ 1,  8,  9,  9,  5]]) 1778886266112
tensor([[[33,  6,  1,  6,  8],
         [ 2,  3,  6,  9,  1],
         [ 3,  4,  2,  9,  5]],

        [[ 1,  4,  7,  3,  8],
         [ 7,  7,  9,  8,  7],
         [ 1,  8,  9,  9,  5]]]) 1778886266112

3.2 torch.transpose(input,dim0,dim1)

交换两个维度，即转置.

在图像预处理部分会用到，比如我们的输入图像是 c*h*w，维数乘高乘宽，可以使用两次变换得到h*w*c

flag = True
# flag = False
if flag:
    torch.manual_seed(1)
    t1 = torch.randint(1, 10, size=(2, 6, 3))

    t2 = torch.transpose(t1,1,2)
    print(t1,t1.shape)
    print(t2,t2.shape)


tensor([[[5, 6, 1],
         [6, 8, 2],
         [3, 6, 9],
         [1, 3, 4],
         [2, 9, 5],
         [1, 4, 7]],

        [[3, 8, 7],
         [7, 9, 8],
         [7, 1, 8],
         [9, 9, 5],
         [6, 3, 7],
         [7, 8, 7]]]) torch.Size([2, 6, 3])
tensor([[[5, 6, 3, 1, 2, 1],
         [6, 8, 6, 3, 9, 4],
         [1, 2, 9, 4, 5, 7]],

        [[3, 7, 7, 9, 6, 7],
         [8, 9, 1, 9, 3, 8],
         [7, 8, 8, 5, 7, 7]]]) torch.Size([2, 3, 6])

3.3 torch.t(input)

二维张量转置，相当于对二维矩阵作torch.transpose(input,0,1)

flag = True
# flag = False
if flag:
    torch.manual_seed(1)
    t1 = torch.randint(1, 10, size=(6, 3))
    t2 = torch.t(t1)
    print(t1,t1.shape)
    print(t2,t2.shape)


tensor([[5, 6, 1],
        [6, 8, 2],
        [3, 6, 9],
        [1, 3, 4],
        [2, 9, 5],
        [1, 4, 7]]) torch.Size([6, 3])
tensor([[5, 6, 3, 1, 2, 1],
        [6, 8, 6, 3, 9, 4],
        [1, 2, 9, 4, 5, 7]]) torch.Size([3, 6])

3.4 torch.squeeze(input,dim=None,out=None)

压缩长度为1的维度（轴），若指定维度，当且仅当该轴长度为1时，可以被移除

flag = True
# flag = False
if flag:
    torch.manual_seed(1)
    t1 = torch.randint(1, 10, size=(6, 3, 1))
    t2 = torch.squeeze(t1)
    print(t1,t1.shape)
    print(t2,t2.shape)


tensor([[[5],
         [6],
         [1]],

        [[6],
         [8],
         [2]],

        [[3],
         [6],
         [9]],

        [[1],
         [3],
         [4]],

        [[2],
         [9],
         [5]],

        [[1],
         [4],
         [7]]]) torch.Size([6, 3, 1])
tensor([[5, 6, 1],
        [6, 8, 2],
        [3, 6, 9],
        [1, 3, 4],
        [2, 9, 5],
        [1, 4, 7]]) torch.Size([6, 3])

3.5 torch.usqueeze(input,dim,out=None)

依据dim扩展维度

flag = True
# flag = False
if flag:
    torch.manual_seed(1)
    t1 = torch.randint(1, 10, size=(6, 3))
    t2 = torch.unsqueeze(t1,dim=2)
    print(t1,t1.shape)
    print(t2,t2.shape)


tensor([[5, 6, 1],
        [6, 8, 2],
        [3, 6, 9],
        [1, 3, 4],
        [2, 9, 5],
        [1, 4, 7]]) torch.Size([6, 3])
tensor([[[5],
         [6],
         [1]],

        [[6],
         [8],
         [2]],

        [[3],
         [6],
         [9]],

        [[1],
         [3],
         [4]],

        [[2],
         [9],
         [5]],

        [[1],
         [4],
         [7]]]) torch.Size([6, 3, 1])

张量的数学运算

张量的加减乘除，对数指数幂函数，三角函数

1. torch.add(input,alpha=1,outher,out=None)

   实现逐元素计算input+alpha*other,input是第一个张量，alpha是乘项因子，other是第二个张量。

   torch.addcdiv()

\[out_i = input_i+value \times \frac{tensor1_i}{tensor2_i}
\]

torch.addcmul(input,value=1,tensor1,tensor2,out=None)

\[out_i = input_i + value \times tensor1_i \times tensor2_i
\]

flag = True
# flag = False
if flag:
    torch.manual_seed(1)
    t1 = torch.randint(1, 10, size=(6, 3))
    t2 = torch.ones_like(t1)
    t3 = torch.add(t1,t2,alpha=2)
    print(t1,t1.shape)
    print(t2,t2.shape)
    print(t3,t3.shape)


tensor([[5, 6, 1],
        [6, 8, 2],
        [3, 6, 9],
        [1, 3, 4],
        [2, 9, 5],
        [1, 4, 7]]) torch.Size([6, 3])
tensor([[1, 1, 1],
        [1, 1, 1],
        [1, 1, 1],
        [1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]]) torch.Size([6, 3])
tensor([[ 7,  8,  3],
        [ 8, 10,  4],
        [ 5,  8, 11],
        [ 3,  5,  6],
        [ 4, 11,  7],
        [ 3,  6,  9]]) torch.Size([6, 3])

线性回归

线性回归是分析一个变量与另外一个变量之间关系的方法

因变量：y 自变量：x 关系：线性

y = wx+b

分析：求解w,b

求解步骤:

1. 确定模型，Model:y = wx+b
2. 选择损失函数，MSE:

\[\frac{1}{m}\sum^{m}_{i=1}(y_i-\hat{y_i})
\]

1. 求解梯度并更新w,b

   w = w - LR* w.grad

   b = b -LR* b.grad