1. 数据类型

如何表示string?

• One-hot

  • [0, 1, 0, 0, ...]

• Embedding

  • Word2vec

  • glove

类型推断

import torch# type check
a = torch.randn(2, 3)
print(a.type())                            #torch.FloatTensor
print(type(a))                             #<class 'torch.Tensor'>  这种情况比较少
print(isinstance(a, torch.FloatTensor))    #True

标量

• 标量 dimension 0/rank 0(常用于loss)

# 标量 dimension 0/rank 0(常用于loss)
b = torch.tensor(1.3)
print(b)                 # tensor(1.3000)
print(b.shape)           # torch.Size([])  成员
print(len(b.shape))      # 0
print(b.size())          # torch.Size([])  成员函数

张量(tensor)

• 张量 dimension 1(常用于bias)

# 张量 dimension 1(常用于bias)
print(torch.tensor([1.1]))    # tensor([1.1000]) 指定具体数据，可以是 N 维print(torch.FloatTensor(1))   # tensor([9.6429e-39]) 指定第一维度的长度，随机初始化data = np.ones(2)             # 长度为2的numpy array
print(data)                   # array([1., 1.])
print(torch.from_numpy(data)) # tensor([1., 1.], dtype=torch.float64) 从numpy引入c = torch.ones(2)
print(c.shape)                # torch.Size([2]), 第一维的长度为2

• 张量 dimension 2(常用于batch等)

# 张量 dimension 2
d = torch.randn(2, 3)
print(d)
#tensor([[-1.8543, -0.7280,  0.6671],
#        [ 1.1492, -0.6379, -0.4835]])
print(d.shape)          # torch.Size([2, 3])，第一维长度为2，第二维长度为3(两行3列)
print(d.shape[0])       # 2
print(d.size(1))        # 或者d.shape[1]，3

• 张量 dimension 3(常用于RNN等)

# 张量 dimension 3
f = torch.rand(1,2,3)              # 理解：1个数据集，2个Tx，每个Tx有3个输出
print(f)
#tensor([[[0.3690, 0.5702, 0.2382],
#         [0.3130, 0.5591, 0.3829]]])print(f.shape)         # torch.Size([1, 2, 3])
print(f[0])            # 取第一个维度
#tensor([[0.4535, 0.4307, 0.6469],
#        [0.1591, 0.0778, 0.4489]])
print(f[0][1])         # tensor([0.1591, 0.0778, 0.4489])

• 张量 dimension 4(常用于表示图片类型)

eg：a = torch.rand(b,c,h,w) 表示b张 c通道、h*w的图片

a = torch.rand(2,3,28,28)   # 2张图片，每张图片3通道，大小为28x28
print(a)print(a.shape)
print(a.numel())   # 2x3x28x28=4704, 全部元素个数
print(a.dim())     # 4, 维度数量

tensor([[[[0.2607, 0.6929, 0.4447,  ..., 0.7346, 0.1117, 0.6536],...,[0.4591, 0.7439, 0.0944,  ..., 0.0986, 0.9818, 0.9580]],[[0.2049, 0.2220, 0.6390,  ..., 0.7402, 0.0301, 0.1057],...,[0.4375, 0.9904, 0.0813,  ..., 0.5896, 0.6167, 0.2628]],[[0.4288, 0.6137, 0.6558,  ..., 0.0282, 0.5398, 0.0905],...,[0.0021, 0.2103, 0.1029,  ..., 0.4861, 0.5915, 0.4245]]],[[[0.4978, 0.4922, 0.8510,  ..., 0.7856, 0.6859, 0.7466],...,[0.7721, 0.9057, 0.9594,  ..., 0.8764, 0.0646, 0.3901]],[[0.0570, 0.9745, 0.9952,  ..., 0.8184, 0.5966, 0.6161],...,[0.1213, 0.6930, 0.9880,  ..., 0.6633, 0.0317, 0.9526]],[[0.6238, 0.6210, 0.7574,  ..., 0.1725, 0.6625, 0.9828],...,[0.6864, 0.2697, 0.2041,  ..., 0.9683, 0.6482, 0.1793]]]])
torch.Size([2, 3, 28, 28])
4704
4

2. 创建Tensor

import torch
import numpy as np# 方法一：import from numpy
a = np.ones([2,3])
print(torch.from_numpy(a))#tensor([[1., 1., 1.],
#        [1., 1., 1.]], dtype=torch.float64)# 方法二：import from List
print(torch.tensor([[2.,3.2],[1.,22.3]]))# tensor([[ 2.0000,  3.2000],
#        [ 1.0000, 22.3000]])# 方法三：接受shape或者现成数据
print(torch.Tensor(2, 3))
print(torch.FloatTensor(2, 4))# tensor([[0., 0., 0.],
#         [0., 0., 0.]])
# tensor([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00],
#         [0.0000e+00, 1.8750e+00, 4.3485e-05, 1.6595e-07]], dtype=torch.float32)

Tips：

• torch.tensor：接受现成的数据

• torch.Tensor/torch.FloatTensor：接受shape或者现成的数据

未初始化的方法(作为容器，要用其他类型把数据覆盖掉！)：

• torch.empty()

• torch.FloatTensor(d1, d2, d3)

• torch.IntTensor(d1,d2,d3)

print(torch.empty(1, 2))
print(torch.FloatTensor(1, 2))
print(torch.IntTensor(2, 3))# tensor([[ 0.0000e+00, 2.1220e-314]])
# tensor([[0., 0.]], dtype=torch.float32)
# tensor([[1664692530, 1630878054, 1681351009],
#         [ 842019426, 1664312883,  828728417]], dtype=torch.int32)

设置默认类型

• torch.set_default_tensor_type

# 设置默认类型
print(torch.tensor([1.2,3]).type())               # torch.FloatTensor(不设定的话，默认值)torch.set_default_tensor_type(torch.DoubleTensor)
print(torch.tensor([1.2,3]).type())               # torch.DoubleTensor

随机初始化

• rand/rand_like, randint

# rand [0,1]
a = torch.rand(2,2)
print(a)# tensor([[0.9422, 0.6025],
#         [0.1540, 0.6282]])print(torch.rand_like(a))         # 根据a的形状生成，也可用dtype指定新类型# tensor([[0.4822, 0.6752],
#         [0.3491, 0.8990]])# randint [min,max) 不包含max
print(torch.randint(1,10, [3,3]))  # 第1个参数是min，第二个参数是max，第三个参数是shape# tensor([[8, 9, 7],
#         [5, 7, 5],
#         [9, 6, 9]])

正态分布

print(torch.full([2, 3], 2.3))        # 2维3列，全部为2.3的tensor# tensor([[2.3000, 2.3000, 2.3000],
#         [2.3000, 2.3000, 2.3000]])

# 正态分布
print(torch.randn(3,3))         # N(0,1), 均值为0，方差为1
# tensor([[-1.6209,  0.0208, -0.8792],
#         [ 2.4513, -0.1906,  3.4904],
#         [ 0.5434,  0.8524,  0.6850]])print(torch.normal(mean=torch.full([10], 0),std = torch.arange(1,0,-0.1)))    # normal得到的维度为1，均值为0，方差为1
# tensor([ 0.1445, -0.5133, -0.5565,  0.0831,  0.1350,  0.1023, -0.6264, -0.1651, 0.2856,  0.0187])

其他

• torch.full

• torch.arange

• torch.linspace

• torch.logspace(0, 1, step=10)： \(10^0 \to 10^{1}\)

• torch.randperm

# ones全1，zeros全0，eye对角，ones_like
print(torch.full([2,3],7))             # 第一个参数是shape，第二个参数是value
# tensor([[7., 7., 7.],
#         [7., 7., 7.]])
print(torch.full([], 7))               # tensor(7.) 生成标量# 生成 [0, n-1]的等差数列
print(torch.arange(0,10,2))            # tensor([0, 2, 4, 6, 8])# [0,10]等间距切割成steps份
print(torch.linspace(0, 10, steps=6))  # tensor([ 0.,  2.,  4.,  6.,  8., 10.])
print(torch.logspace(0, 1, steps=5))   # tensor([ 1.0000,  1.7783,  3.1623,  5.6234, 10.0000])# randperm: [0, n-1]打乱出现，不重复
print(torch.randperm(10))             # tensor([8, 5, 2, 4, 7, 1, 3, 9, 6, 0])a = torch.rand(2, 3)
idx = torch.randperm(2)
print(idx)                            # tensor([1, 0])
print(a)
print(a[idx])# tensor([[0.7896, 0.0143, 0.7092],
#        [0.8881, 0.5194, 0.6708]])
# tensor([[0.8881, 0.5194, 0.6708],
#         [0.7896, 0.0143, 0.7092]])

3. 索引与切片

# 切片与索引
a = torch.rand(4, 3, 28, 28)    # 4张图片，每张图片有3个channel，每个通道图片大小：28x28
print(a[0].shape)               # torch.Size([3, 28, 28])
print(a[0,0].shape)             # torch.Size([28, 28])
print(a[0,0,2,4])               # tensor(0.5385)print(a[:2,:1].shape)           # torch.Size([2, 1, 28, 28])  等价于a[:2,:1,:,:].shape
print(a[:,:,::2,::2].shape)     # torch.Size([4, 3, 14, 14])

使用特定索引 index_select

#select by specific index
print(a.index_select(2, torch.arange(8)).shape)  # torch.Size([4, 3, 8, 28])  第1个参数：选择的维度，第2个参数：索引号(Tensor类型)# ...表示任意多的维度
print(a[0, ...].shape)            # torch.Size([3, 28, 28])
print(a[:, 1, ...].shape)         # torch.Size([4, 28, 28])

使用掩码索引 masked_select

• torch.masked_select(x, mask)后变成一维

x = torch.randn(3,4)
print(x)mask = x.ge(0.5)                  # greater equal: >=
print(mask)# select by mask
torch.masked_select(x, mask)      # 维度为1# tensor([[ 0.2953, -2.4538, -0.0996,  1.6746],
#         [ 0.5318, -1.2000, -0.8475,  0.3967],
#         [-1.2162, -1.4913,  0.5404, -0.1377]])# tensor([[False, False, False,  True],
#         [ True, False, False, False],
#         [False, False,  True, False]])# tensor([1.6746, 0.5318, 0.5404])

take索引

• take: 在原来Tensor的shape基础上打平，然后在打平后的Tensor上进行索引)

# select by flatten index
src = torch.tensor([[4, 3, 5], [6, 7, 8]])print(torch.take(src, torch.tensor([0, 2, 5])))  # tensor([4, 5, 8])

4. 维度变换

reshape/view

• 可以调整Tensor的shape，返回一个新shape的Tensor

• 要记住维度展开的顺序，如果要还原维度，就得按原来顺序还原

a = torch.rand(4, 1, 28, 28)print(a.view(4, 28*28).shape)        # torch.Size([4, 784]), 语法没错，数据被破坏了
print(a.reshape(4*28, 28).shape)     # torch.Size([112, 28])

unsqueeze(index)增加维度

• index的范围: [-a.dim()-1, a.dim()+1)

  • 如：a.unsqueeze(2): 在二维处添加一维。若 a 的维度=4，index范围是[-5,5)

• 新增加的这一个维度，不会改变数据本身，只是为数据新增加了一个组别，这个组别是什么由我们自己定义。

a = torch.rand(4,1,28,28)
print(a.shape)                      # torch.Size([4, 1, 28, 28])
print(a.unsqueeze(0).shape)         # torch.Size([1, 4, 1, 28, 28]print('='*30)
b = torch.tensor([1.2, 2.3])        # torch.Size([2])
print(b)
print(b.unsqueeze(0))               # tensor([[1.2000, 2.3000]])   torch.Size([1, 2])
print(b.unsqueeze(-1))              # torch.Size([2, 1])
print(b.unsqueeze(1))               # torch.Size([2, 1])
# tensor([[1.2000],
#         [2.3000]])print('='*30)
x = torch.rand(32)
print(x.shape)                                  # torch.Size([32])
print(x.unsqueeze(1).shape)                     # torch.Size([32, 1])
print(x.unsqueeze(1).unsqueeze(2).shape)        # torch.Size([32, 1, 1])
x = x.unsqueeze(1).unsqueeze(2).unsqueeze(0)    # torch.Size([1, 32, 1, 1])
print(x.shape)                                  # torch.Size([1, 32, 1, 1])) 再进行扩展即可计算x+y

squeeze(index)删减维度

• 删除 size=1 的维度

• size不等于1，删减不了

a=torch.rand(1,32,1,1)print(a.squeeze().shape)             # torch.Size([32])  不指定维度就挤压全部
print(a.squeeze(0).shape)            # torch.Size([32, 1, 1])
print(a.squeeze(-1).shape)           # torch.Size([1, 32, 1])
print(a.squeeze(1).shape)            # torch.Size([1, 32, 1, 1])  size不等于1，删减不了

expand维度扩展：broadcasting(只是改变了理解方式，并没有增加数据)

• 某个 size=1 的维度上扩展到size, 缺失处填补该维度的数

• -1 指该维度不变

x = torch.rand(3)
x = x.unsqueeze(1).unsqueeze(2).unsqueeze(0)    # [3]->[3,1]->[3,1,1]->[1,3,1,1]
print(x.shape)                                  # torch.Size([1, 3, 1, 1])
print(x)# tensor([[[[0.5826]],#          [[0.6370]],#          [[0.6199]]]])print(x.expand(-1, 3, 3, 2))# tensor([[[[0.3054, 0.3054],
#           [0.3054, 0.3054],
#           [0.3054, 0.3054]],#          [[0.4798, 0.4798],
#           [0.4798, 0.4798],
#           [0.4798, 0.4798]],#          [[0.7628, 0.7628],
#           [0.7628, 0.7628],
#           [0.7628, 0.7628]]]])y = torch.rand(4, 3, 14, 14)print(x.expand(4,3,14,14).shape)               # torch.Size([4, 3, 14, 14])
print(x.expand(-1,3,3,-1).shape)               # torch.Size([1, 3, 3, 1])  -1：指该维度不变print((x.expand(4, 3, 14, 14) + y).shape)      # torch.Size([4, 3, 14, 14])

repeat维度重复：memory copied(增加了数据)

• repeat会重新申请内存空间，repeat()参数表示各个维度指定的重复次数。

a = torch.rand(1,32,1,1)print(a.repeat(4,32,1,1).shape)                 # torch.Size([1x4, 32x32, 1x1, 1x1])->torch.Size([4, 1024, 1, 1])
print(a.repeat(4,1,1,1).shape)                  # torch.Size([4, 32, 1, 1])y = torch.rand(5)
print(y.shape)                                  # torch.Size([5])
y_unsqueeze = y.unsqueeze(1)
print(y_unsqueeze.shape)                        # torch.Size([5, 1])
print(y_unsqueeze)# tensor([[0.3372],
#         [0.1044],
#         [0.8305],
#         [0.1960],
#         [0.7674]])print(y_unsqueeze.repeat(2, 2))# tensor([[0.3372, 0.3372],
#         [0.1044, 0.1044],
#         [0.8305, 0.8305],
#         [0.1960, 0.1960],
#         [0.7674, 0.7674],
#         [0.3372, 0.3372],
#         [0.1044, 0.1044],
#         [0.8305, 0.8305],
#         [0.1960, 0.1960],
#         [0.7674, 0.7674]])

转置操作

• .t 操作指适用于矩阵

a = torch.rand(3, 4)
print(a.t().shape)                             #torch.Size([4, 3])

transpose维度交换

a = torch.rand(4,3,32,32)
print(a.transpose(1, 3).shape)                                 # torch.Size([4, 32, 32, 3])
print(a.transpose(1, 3).contiguous().view(4, 3*32*32).shape)   # torch.Size([4, 3072]), 如果不加contiguous就需要把view改成reshape，contiguous是把数据重新变成连续
print(a.transpose(1, 3).contiguous().view(4, 3*32*32).reshape(4, 32, 32, 3).shape) # torch.Size([4, 32, 32, 3])a1 = a.transpose(1, 3).contiguous().view(4, 3*32*32).view(4, 3, 32, 32)
b = a.transpose(1, 3).contiguous().view(4, 3*32*32).view(4,32,32,3).transpose(1, 3)         # view(4,3*32*32).view(4,3,32,32)这样写就错了
# [b,c,h,w]->[b,w,h,c]->[b,whc]->[b,w,h,c]->[b,c,h,w]  展开时按原来的顺序展开whc对应32,32,3print(a.shape, b.shape)print(torch.all(torch.eq(a, b)))                       # tensor(True)
print(torch.all(torch.eq(a, a1)))                      # tensor(False)

t = torch.IntTensor([[[1,2,3],[4,5,6]], [[6,7,8],[9,10,11]]])
print(t, t.shape)
print(t.transpose(0, 2).contiguous().view(3, 4).view(2, 2, 3))  # 并没有恢复成原来的数据# tensor([[[ 1,  6,  4],
#          [ 9,  2,  7]],#         [[ 5, 10,  3],
#          [ 8,  6, 11]]], dtype=torch.int32)# 正确写法
print(t.transpose(0, 2).contiguous().view(3, 4).view(3, 2, 2).transpose(0, 2))# tensor([[[ 1,  2,  3],
#          [ 4,  5,  6]],#         [[ 6,  7,  8],
#          [ 9, 10, 11]]], dtype=torch.int32)

permute(区别 transpose)

• 四个维度表示的[batch,channel,h,w]，如果想把channel放到最后去，形成[batch,h,w,channel]

• 那么如果使用前面的维度交换，至少要交换两次(先13交换再12交换)

• 而使用permute 可以 直接指定维度新的所处位置，更加方便。

b = torch.rand(4,3,28,32)print(b.transpose(1, 3).shape)                      #torch.Size([4, 32, 28, 3])
print(b.transpose(1, 3).transpose(1, 2).shape)      #torch.Size([4, 28, 32, 3])print(b.permute(0,2,3,1).shape)                     #torch.Size([4, 28, 32, 3]