Pytorch学习记录（二）：张量

1. 张量的创建

import torch
import numpy as np

# Import from numpy
a1 = np.array([2, 3.3])
b1 = torch.from_numpy(a1)
a2 = np.ones([2,3])
b2 = torch.from_numpy(a)

# Import from List
a3 = torch.tensor([2., 3.2])
a4 = torch.FloatTensor([2., 3.2])

# set default type
a5 = torch.tensor([1.2, 3]).type()
torch.set_default_tensor_type(torch.DoubleTensor)
a6 = tensor.tensor(1.2, 3).type()

# rand() 随机0-1初始化
torch.rand(2) # 向量
# tensor([0.2300, 0.7452])
torch.rand(2,3)  # 矩阵
# tensor([[0.0214, 0.4409, 0.3778],
# [0.8571, 0.4957, 0.7218]])
torch.rand(2,2,3)  # 三维
# tensor([[[0.7301, 0.0870, 0.0573],
# [0.4576, 0.5049, 0.9410]],
# [[0.7045, 0.6702, 0.3119],
# [0.1384, 0.9376, 0.9691]]])

# rand_like() 给定tensor的随机0-1初始化
# 创建一个向量
data = torch.tensor([1.1, 2.2, 3.3])  
# 随机0-1初始化一个shape和data相同的tensor
torch.rand_like(data)
# tensor([0.7710, 0.5399, 0.4941])

# randint() 在某一范围内随机整数采样
# 需要指定最小值, 最大值, shape，随机采样包含最小值，不包含最大值
torch.randint(1, 10, size=[2,3])
# tensor([[4, 3, 2],
# [5, 2, 2]])

# randn() 随机正态分布
torch.randn(3)  # 向量
# tensor([-0.8556, -1.3012, -0.1202])
 
torch.randn(size=[2,3])  # 矩阵
# tensor([[-0.5486, 1.0590, 2.7441],
# [ 0.4896, 0.0592, -0.5964]])

# 全为1的张量
#（1）ones() # 全为1的tensor
data = torch.ones(size=[2,3])
# tensor([[1., 1., 1.],
# [1., 1., 1.]])
 
# 和data的shape相同的全为1的tensor
torch.ones_like(data)
# tensor([[1., 1., 1.],
# [1., 1., 1.]])

# 全为0的张量
#（2）zeros() # 全为0的tensor
data = torch.zeros(size=[2,3])
# tensor([[0., 0., 0.],
# [0., 0., 0.]])
 
# 和data的shape相同的全为1的tensor
torch.zeros_like(data)
# tensor([[0., 0., 0.],
# [0., 0., 0.]])

# 全为某个值的张量
# 2行3列全为1的tensor
torch.full(size=[2,3], fill_value=7.0)
# tensor([[7., 7., 7.],
# [7., 7., 7.]])
 
# 初始化一个标量
torch.full(size=[], fill_value=7)
# tensor(7)
 
# 初始化一个向量
torch.full(size=[1], fill_value=7)
# tensor([7])

# 单位矩阵
# 三行三列，可略写(3,3)
torch.eye(3)
# tensor([[1., 0., 0.],
# [0., 1., 0.],
# [0., 0., 1.]])
 
torch.eye(3,4)
# tensor([[1., 0., 0., 0.],
# [0., 1., 0., 0.],
# [0., 0., 1., 0.]])

# arange() 递增张量
# 从0到10每次递增1，包含0不包含10
torch.arange(0,10)
# tensor([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
 
# 从0到10每次递增2，包含0不包含10
torch.arange(0, 10, 2)
# tensor([0, 2, 4, 6, 8])

# linspace 等分张量
# 从0到10，等分成4份的等差数列，包含0也包含10
torch.linspace(0, 10, 4)
# tensor([ 0.0000, 3.3333, 6.6667, 10.0000])
 
# 0到10等分7份
torch.linspace(0, 10, 7)
# tensor([ 0.0000, 1.6667, 3.3333, 5.0000, 6.6667, 8.3333, 10.0000])

# logspace 幂指数递增
# base代表对数的底数，0-10分成11步，计算10^(n)
torch.logspace(0, 10, steps=10, base=10)
# tensor([1.0000e+00, 1.0000e+01, 1.0000e+02, 1.0000e+03, 1.0000e+04, 1.0000e+05, 1.0000e+06, 1.0000e+07, 1.0000e+08, 1.0000e+09, 1.0000e+10])
 
# 计算2^(n)，从0到-1分成11步
torch.logspace(0, -1, steps=10, base=2)
# tensor([1.0000, 0.9259, 0.8572, 0.7937, 0.7349, 0.6804, 0.6300, 0.5833, 0.5400, 0.5000])

# randperm() 随机打乱
# 生成0-10的随机索引[0,9]之间
torch.randperm(10)
# tensor([7, 8, 9, 6, 3, 1, 0, 4, 2, 5])
 
# 索引打乱后还能配对
index = torch.randperm(10)
# 创建两个张量
data1 = torch.arange(0,10)
data2 = torch.arange(0,10) * 10
# 索引配对打乱，不改变data1和data2各元素之间的对应关系
data1[index]*10 == data2[index] 
# tensor([True, True, True, True, True, True, True, True, True, True])

---

2. Tensor的索引和切片

2.1 直接索引

2.2 连续索引

2.3 索引+步长

2.4 任意的维度

2.5 获取指定维度上的指定索引

2.6 使用掩码的索引

2.7 使用展平的的索引

---

3. 维度变换

3.1 shape转换 view/reshape

import torch
a = torch.randn(4, 1, 28, 28) #假设为MINIST数据集
print(a.shape)
b = a.view(4 ,28,28)    
print(b.shape)
c = a.view(4,28*28) #将图像展平
print(c.shape)
d = a.view(4*28, 28) #关注所有图像所行
print(d.shape)  

''' torch.Size([4, 1, 28, 28]) torch.Size([4, 28, 28]) torch.Size([4, 784]) torch.Size([112, 28]) '''

3.2 增加维度 unsqueeze

import torch
a = torch.randn(4, 1, 28, 28) #假设为MINIST数据集
print('a',a.shape)
b = torch.unsqueeze(a, 0) #在0维度前面插入一个维度 没有增加数据
print('b', b.shape)
c = a.unsqueeze(4) #在4维度前面插入一个维度
print('c', c.shape)
d = a.unsqueeze(2) #在第2个维度前面插入一个维度
print('d', d.shape)
e = a.unsqueeze(-1) #在最后-1维度后面插入一个维度
print('e',e.shape)
f = a.unsqueeze(-3) #在-3维度后面之后插入一个维度
print('f',f.shape)

''' a torch.Size([4, 1, 28, 28]) b torch.Size([1, 4, 1, 28, 28]) c torch.Size([4, 1, 28, 28, 1]) d torch.Size([4, 1, 1, 28, 28]) e torch.Size([4, 1, 28, 28, 1]) f torch.Size([4, 1, 1, 28, 28]) '''

3.3 维度挤压 squeeze

import torch
bias = torch.randn(32)
f = torch.rand(4, 32, 14,14) #bias相当于每个通道上的偏置
# 将bias叠加在f上
b = bias.unsqueeze(0).unsqueeze(2).unsqueeze(3) #[1,32]->[1,32,1]->[1,32,1,1]
print('b', b.shape)
c = b.squeeze()  #挤压掉所有为1的维度
print('c', c.shape)
d = b.squeeze(0) #挤压掉0维数据
print('d', d.shape)
e = b.squeeze(1) #挤压掉第1维数据 如果第1维大小不为1,则挤压失败，返回原来的维度
print('e', e.shape)
f = b.squeeze(-4) #挤压第-4维维度
print('f', f.shape)

''' b torch.Size([1, 32, 1, 1]) c torch.Size([32]) d torch.Size([32, 1, 1]) e torch.Size([1, 32, 1, 1]) f torch.Size([32, 1, 1]) '''

3.4 维度扩展 Expand/repeat

• expend

import torch
bias = torch.randn(32)
f = torch.rand(4, 32, 14,14) #bias相当于每个通道上的偏置
# 将bias叠加在f上
b = bias.unsqueeze(0).unsqueeze(2).unsqueeze(3) #[1,32]->[1,32,1]->[1,32,1,1]
print('b', b.shape)

# c = b.expand(4,10,1,1) #扩展第0个维度 第1个维度不为1，所以该扩展失败（报错），其余维度不变
d = b.expand(4,32,14,14) #扩展所有维度
print(d.shape)
e = b.expand(100,32,1,1)
print(e.shape)

''' b torch.Size([1, 32, 1, 1]) torch.Size([4, 32, 14, 14]) torch.Size([100, 32, 1, 1]) '''

• repeat

import torch
bias = torch.randn(32)
f = torch.rand(4, 32, 14,14) #bias相当于每个通道上的偏置
# 将bias叠加在f上
b = bias.unsqueeze(0).unsqueeze(2).unsqueeze(3) #[1,32]->[1,32,1]->[1,32,1,1]
print('b', b.shape)

c = b.repeat(4,1,14,14)  #[1,32,1,1] -> [14,32,14,14] 拷贝
print('after repeat all dim:', b.shape)

d = b.repeat(10,32,1,1) #[1,32,1,1]->[1*10,32*32,1,1]拷贝第一个维度10次，第二个维度拷贝32次， 其余的拷贝一次 
print('repeat dim 0,1:', d.shape)

''' b torch.Size([1, 32, 1, 1]) after repeat all dim: torch.Size([1, 32, 1, 1]) repeat dim 0,1: torch.Size([10, 1024, 1, 1]) '''

3.5 tensor转置

• .t

import torch
b = torch.randn(3,4)
print('b', b.shape)
c = b.t()
print('b.t()', c.shape)

''' b torch.Size([3, 4]) b.t() torch.Size([4, 3]) '''

• transpose()

import torch
a = torch.randn(4,3,32,32)
b = a.transpose(1,3).contiguous().view(4,3*32*32).view(4,3,32,32)  #数据污染了
c = a.transpose(1,3).contiguous().view(4,3*32*32).view(4,32,32,3).transpose(1,3)
d = a.transpose(1,3).contiguous().view(-1)  #使用a.transpose(1,3).view(-1)会报错， 必须要加一个contiguous()函数

• permute转置

#将tensor图像数据转换为numpy图像数据
import torch
a = torch.randn(4,3,32,32)
print(a.shape)
b = a.transpose(1,3).transpose(1,2)  #[b,c,h,w]->[b,w,h,c]->[b,h,w,c]
print(b.shape)
c = a.permute(0,2,3,1)
print(c.shape)

''' torch.Size([4, 3, 32, 32]) torch.Size([4, 32, 32, 3]) torch.Size([4, 32, 32, 3]) '''

---

4. 合并与分割

4.1 cat操作

#tensor拼接
import torch
a = torch.rand(4,32,8)
b = torch.rand(5,32,8)
c = torch.cat((a,b),dim=0)
print(c.shape)

''' torch.Size([9, 32, 8]) '''

4.2 stack操作

#tensor堆叠
import torch
a = torch.rand(4,32,8)
b = torch.rand(4,32,8)
c = torch.stack((a,b),dim=0)
print(c.shape)

''' torch.Size([2, 4, 32, 8]) '''

4.3 split操作

#tensor拆分
import torch
a = torch.rand(4,3,3)  
aa,bb = torch.split(a,[1,3], dim=0)  
print(aa.shape)
print(bb.shape)
cc,dd = torch.split(a, 2, dim = 0) #在0维度上按照单元长度为2进行拆分
print(cc.shape)
print(dd.shape)

''' torch.Size([1, 3, 3]) torch.Size([3, 3, 3]) torch.Size([2, 3, 3]) torch.Size([2, 3, 3]) '''

4.4 chunk操作

#tensor拆分
import torch
a = torch.rand(4,3,3)  
bb,cc,dd,ee = torch.chunk(a,4,dim=0) #将零维度拆分为4个块 
print(bb.shape)
print(cc.shape)
print(dd.shape)
print(ee.shape)

''' torch.Size([1, 3, 3]) torch.Size([1, 3, 3]) torch.Size([1, 3, 3]) torch.Size([1, 3, 3]) '''

---

5. 统计属性

5.1 范数 norm

import torch
a = torch.full([8],1, dtype = torch.float)
b = a.view(2,4)
c = a.view(2,2,2)
print(a.norm(1), b.norm(1), c.norm(1))
print(a.norm(2), b.norm(2), c.norm(2))
print(b.norm(1, dim = 1))
print(c.norm(2, dim = 0))

''' tensor(8.) tensor(8.) tensor(8.) tensor(2.8284) tensor(2.8284) tensor(2.8284) tensor([4., 4.]) tensor([[1.4142, 1.4142], [1.4142, 1.4142]]) '''

5.2 mean,sum,min,max,prod

import torch
a = torch.arange(8).view(2,4).float()

# mean,max,min等如果没有指定维度，则会将tensor展平，然后再统计
print(a.min(), a.max())
print(a.sum(), a.mean())
print(a.prod())
print(a.argmax(), a.argmin())

''' tensor(0.) tensor(7.) tensor(28.) tensor(3.5000) tensor(0.) tensor(7) tensor(0) '''

import torch

t = torch.arange(8).reshape(2,4).float()
print('**Caculate after flatten..')
print(t.max())
print(t.min())
print(t.sum())
print(t.mean())
print(t.prod())

print('**Get the position of the max/min elements on all dim..')
print(t.argmax())
print(t.argmin())

# dim指定维度
print('**Gaculate on special dim..')
print(t.mean(1))
print(t.max(1))
print(t.min(0))
print(t.sum(0))
print(t.prod(1))

''' **Caculate after flatten.. tensor(7.) tensor(0.) tensor(28.) tensor(3.5000) tensor(0.) **Get the position of the max/min elements on all dim.. tensor(7) tensor(0) **Gaculate on special dim.. tensor([1.5000, 5.5000]) torch.return_types.max( values=tensor([3., 7.]), indices=tensor([3, 3])) torch.return_types.min( values=tensor([0., 1., 2., 3.]), indices=tensor([0, 0, 0, 0])) tensor([ 4., 6., 8., 10.]) tensor([ 0., 840.]) '''

import torch
t = torch.arange(8).reshape(2,4).float()
print('**Gaculate on special dim..')
print(t.max(1, keepdim=True))
print(t.min(0, keepdim=True))
print(t.sum(0, keepdim=True))

''' **Gaculate on special dim.. torch.return_types.max( values=tensor([[3.], [7.]]), indices=tensor([[3], [3]])) torch.return_types.min( values=tensor([[0., 1., 2., 3.]]), indices=tensor([[0, 0, 0, 0]])) tensor([[ 4., 6., 8., 10.]]) '''

5.3 top-k k-th

import torch
t = torch.arange(8).reshape(2,4).float()  #K大值
t2 = t.topk(3, dim=1)
print(t2)
t3 = t.topk(3, dim=1, largest=False)  #K小值
print(t3)

print('*'*20)

t4 = t.kthvalue(2, dim=1)
print(t4)

''' torch.return_types.topk( values=tensor([[3., 2., 1.], [7., 6., 5.]]), indices=tensor([[3, 2, 1], [3, 2, 1]])) torch.return_types.topk( values=tensor([[0., 1., 2.], [4., 5., 6.]]), indices=tensor([[0, 1, 2], [0, 1, 2]])) ******************** torch.return_types.kthvalue( values=tensor([1., 5.]), indices=tensor([1, 1])) '''

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6. Tensor的高阶操作

6.1 where

import torch

cond = torch.tensor([[0.6,0.7],[0.8,0.4]])
a = torch.ones(2,2)
b = torch.zeros(2,2)
c = torch.where(cond>0.6, a,b)
print(c)

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

6.2 gather

import torch

table = torch.arange(4,8)
index = torch.tensor([0,2,1,0,3,0])
t = torch.gather(table,dim=0,index=index)
print(t)

''' tensor([4, 6, 5, 4, 7, 4]) '''