import os
os.makedirs(os.path.join('..','data'),exist_ok=True)
datafile = os.path.join('..','data','house_tiny.csv')
with open(datafile,'w') as f:
f.write('NumRooms,Alley,Pricen')
f.write('NA,Pave,127500n')
f.write('2,NA,106000n')
f.write('4,NA,178100n')
f.write('NA,NA,140000n')
import pandas as pd
data =pd.read_csv(datafile)
data
| NumRooms | Alley | Price |
|---|
| 0 | NaN | Pave | 127500 |
|---|
| 1 | 2.0 | NaN | 106000 |
|---|
| 2 | 4.0 | NaN | 178100 |
|---|
| 3 | NaN | NaN | 140000 |
|---|
#取值
inputs,outputs = data.iloc[:,0:2],data.iloc[:,2]
inputs,outputs
( NumRooms Alley
0 NaN Pave
1 2.0 NaN
2 4.0 NaN
3 NaN NaN,
0 127500
1 106000
2 178100
3 140000
Name: Price, dtype: int64)
#均值填充缺失值
inputs = inputs.fillna(inputs.mean())
inputs
| NumRooms | Alley |
|---|
| 0 | 3.0 | Pave |
|---|
| 1 | 2.0 | NaN |
|---|
| 2 | 4.0 | NaN |
|---|
| 3 | 3.0 | NaN |
|---|
#one hot encode
inputs = pd.get_dummies(inputs,dummy_na=True)
inputs
| NumRooms | Alley_Pave | Alley_nan |
|---|
| 0 | 3.0 | 1 | 0 |
|---|
| 1 | 2.0 | 0 | 1 |
|---|
| 2 | 4.0 | 0 | 1 |
|---|
| 3 | 3.0 | 0 | 1 |
|---|
1.标量：运算
import torch
#DataFrame转为tensor
X,y =torch.tensor(inputs.values),torch.tensor(outputs.values)
X,y
(tensor([[3., 1., 0.],
[2., 0., 1.],
[4., 0., 1.],
[3., 0., 1.]], dtype=torch.float64),
tensor([127500, 106000, 178100, 140000]))
2.向量 维度
x = torch.tensor([3.0])
y = torch.tensor([2.0])
x+y,x*y,x/y,x**y
(tensor([5.]), tensor([6.]), tensor([1.5000]), tensor([9.]))
x = torch.arange(4)
x
tensor([0, 1, 2, 3])
len(x)
4
x.shape
torch.Size([4])
x.size()
torch.Size([4])
3.矩阵 矩阵取数、方阵、对称矩阵、转置
A=torch.arange(20).reshape(5,4)
A
tensor([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19]])
#转置
A.T
tensor([[ 0, 4, 8, 12, 16],
[ 1, 5, 9, 13, 17],
[ 2, 6, 10, 14, 18],
[ 3, 7, 11, 15, 19]])
x=torch.arange(24).reshape(2,3,4)
x
tensor([[[ 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=torch.arange(24).reshape(4,6)
X
tensor([[ 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*2
tensor([[ 0, 2, 4, 6, 8, 10],
[12, 14, 16, 18, 20, 22],
[24, 26, 28, 30, 32, 34],
[36, 38, 40, 42, 44, 46]])
4.降维：沿轴卷动，求和或平均，非降维求和
#所有元素求和
X.sum()
tensor(276)
#按0轴求和
X_sum_axis0 = X.sum(axis=0)
X_sum_axis0,X_sum_axis0.shape
(tensor([36, 40, 44, 48, 52, 56]), torch.Size([6]))
#按1轴求和
X_sum_axis1 = X.sum(axis=1)
X_sum_axis1,X_sum_axis1.shape
(tensor([ 15, 51, 87, 123]), torch.Size([4]))
#保持原始维度
X_sum_axis1 = X.sum(axis=1,keepdim=True)
X_sum_axis1
tensor([[ 15],
[ 51],
[ 87],
[123]])
#按0轴累加求和
X,X.cumsum(axis=0)
(tensor([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23]]),
tensor([[ 0, 1, 2, 3, 4, 5],
[ 6, 8, 10, 12, 14, 16],
[18, 21, 24, 27, 30, 33],
[36, 40, 44, 48, 52, 56]]))
5.点积
#全1
y = torch.ones(4,dtype=torch.float32)
y
tensor([1., 1., 1., 1.])
x = torch.arange(4,dtype=torch.float32)
x
tensor([0., 1., 2., 3.])
#它是向量(即只能是⼀维的张量)的对应位相乘再求和
torch.dot(x,y)
tensor(6.)
6.点积推广
#相当于dot
torch.sum(x*y)
tensor(6.)
7.矩阵乘法 ：注意维度
B= torch.ones(6,2,dtype=torch.long)
X.shape,B
(torch.Size([4, 6]),
tensor([[1, 1],
[1, 1],
[1, 1],
[1, 1],
[1, 1],
[1, 1]]))
#矩阵乘法
torch.mm(X,B)
tensor([[ 15, 15],
[ 51, 51],
[ 87, 87],
[123, 123]])
8.范数
# l2范数 sqrt(3**2+(-4)**2)
u = torch.tensor([3.0,-4.0])
torch.norm(u)
tensor(5.)
#l1范数
torch.abs(u).sum(),torch.norm(u,p=1)
(tensor(7.), tensor(7.))
