一起读《动手学深度学习（PyTorch版）》- 数据操作及线性代数基础

LitchiCheng 发表于 2024-9-30 21:22

<div class='showpostmsg'><article data-content="[{"type":"block","id":"3060-1621846615933","name":"heading","data":{"level":"h2"},"nodes":[{"type":"text","id":"p5PQ-1621846617594","leaves":[{"text":"环境介绍","marks":[]}]}],"state":{}},{"type":"block","id":"6w4C-1726412717860","name":"paragraph","data":{"version":1},"nodes":[{"type":"text","id":"NOne-1726412717861","leaves":[{"text":"硬件：Jetson Orin Nano 8G","marks":[]}]}],"state":{}}]">
<p><span style="font-size:22px;">环境介绍</span></p>

<p>硬件：Jetson Orin Nano 8G</p>

<p> pytorch版本：2.1.0a0+41361538.nv23.06</p>

<article data-content="[{"type":"block","id":"byhV-1726412713656","name":"paragraph","data":{},"nodes":[{"type":"text","id":"7Nke-1726412713654","leaves":[{"text":"pytorch版本：2.1.0a0+41361538.nv23.06","marks":[]}]}],"state":{}},{"type":"block","id":"ykNs-1726413193012","name":"paragraph","data":{},"nodes":[{"type":"text","id":"O3LK-1726413193011","leaves":[{"text":"python版本：3.8.10","marks":[]}]}],"state":{}}]">
<p>python版本：3.8.10</p>

<p> </p>

<article data-content="[{"type":"block","id":"UQjA-1726413169775","name":"heading","data":{"level":"h2"},"nodes":[{"type":"text","id":"GfZ2-1726413169774","leaves":[{"text":"torch常用操作","marks":[{"type":"bold"},{"type":"fontSize","value":22}]}]}]}]">
<p>torch常用操作</p>

<pre>
<code>import torch

print("输出torch的版本")
print(torch.__version__)

print("创建行向量，由0开始，12个整数 ")
x = torch.arange(12)
print(x)

print("改变形状，变成3行4列的矩阵，不改变数量和值")
x1 = x.reshape(3,4)
print(x1)

print("创建3行4列的张量，元素从均值为0，标准差为1的标准高斯分布中随机采样")
x2 = torch.randn(3,4)
print(x2)

print("根据形状，遍历所有元素求和,直接使用求和函数")
sum1 = 0
dim0, dim1 = x2.shape
for i in range(dim0):
for j in range(dim1):
   element = x2
   sum1 = sum1 + element

sum2 = x2.sum()
print(sum1, sum2)

print("浮点数")
x3 = torch.arange(12, dtype=torch.float32).reshape(3,4)
print(x3)

print("索引, 最后一个；第一个到第二个；全部")
x4 = torch.tensor()
x5 = torch.tensor()
print(x4[-1], x4, x4[:])

print("节省内存, 变量不出现两次相同, id函数可以打印内存地址")
print(id(x4))
x4 += x5
print(id(x4))
print(x4)
</code></pre>

<article data-content="[{"type":"block","id":"vS9h-1726413227898","name":"paragraph","data":{},"nodes":[{"type":"text","id":"cne2-1726413227899","leaves":[{"text":"对应输出结果","marks":[]}]}],"state":{}}]">
<p>对应输出结果</p>

<pre>
<code>输出torch的版本
2.1.0a0+41361538.nv23.06
创建行向量，由0开始，12个整数
tensor([ 0,1,2,3,4,5,6,7,8,9, 10, 11])
改变形状，变成3行4列的矩阵，不改变数量和值
tensor([[ 0,1,2,3],
   [ 4,5,6,7],
   [ 8,9, 10, 11]])
创建3行4列的张量，元素从均值为0，标准差为1的标准高斯分布中随机采样
tensor([[-0.3059,1.4878,0.2026, -0.7363],
   [-1.2357,0.8356,1.3819, -1.3026],
   [ 1.4943, -0.8299,1.2947,1.3532]])
根据形状，遍历所有元素求和,直接使用求和函数
tensor(3.6397) tensor(3.6397)
浮点数
tensor([[ 0.,1.,2.,3.],
   [ 4.,5.,6.,7.],
   [ 8.,9., 10., 11.]])
矩阵点乘
tensor([ 2.,4.,8., 16.])
索引, 最后一个；第一个到第二个；全部
tensor(8.) tensor() tensor()
节省内存, 变量不出现两次相同, id函数可以打印内存地址
281470915534336
281470915534336
tensor([ 3.,4.,6., 10.])</code></pre>

<article data-content="[{"type":"block","id":"5xeJ-1726413227900","name":"heading","data":{"level":"h2"},"nodes":[{"type":"text","id":"C4EZ-1726413227901","leaves":[{"text":"数学基础","marks":[]}]}],"state":{}},{"type":"block","id":"2DpY-1726413357607","name":"heading","data":{"level":"h3"},"nodes":[{"type":"text","id":"6Z1A-1726413357608","leaves":[{"text":"线性代数","marks":[{"type":"bold"},{"type":"fontSize","value":20}]}]}]}]">
<p><span style="font-size:22px;">数学基础</span></p>

<p>线性代数</p>

<pre>
<code>import torch

print("矩阵的转置(transpose)")
A = torch.arange(16).reshape(4,4)
print(A)
print(A.T)

print("对称矩阵（symmetric matrix）和其转置矩阵相等")
B = torch.tensor([,
            ,
            ])
print(B == B.T)

print("矩阵乘以一个标量，不会改变形状")
C = 3 * A
print(C, "\n", ((C / 3) == A))

print("哈达玛积，相同shape矩阵各元素相乘，输出仍为矩阵，用于信号、图像处理等")
D = A * C
print(D)

print("点积(矩阵乘法)，行列对应相同，表示相似度")
E = torch.matmul(A, C)
print(E)

print("叉积，用于确定法向量和确定平面")
tmp_v1 = torch.tensor()
tmp_v2 = torch.tensor()
F = torch.cross(tmp_v1, tmp_v2)
print(F)

print("降维，求和、平均都可以指定轴进行")
tmp_v1 = torch.tensor([,

               ])
print(tmp_v1.sum(axis=0),"\n", tmp_v1.sum(axis=1))
print(tmp_v1.mean(axis=0),"\n", tmp_v1.mean(axis=1))

print("范数，表示分量的大小，L₂范数表示向量元素平方和的平方根（欧几里得距离），L₁范数表示向量元素的绝对值之合")
tmp_v1 = torch.tensor()
print(torch.norm(tmp_v1), "\n", torch.abs(tmp_v1).sum())
</code></pre>

<article data-content="[{"type":"block","id":"Y6ja-1726413420957","name":"paragraph","data":{},"nodes":[{"type":"text","id":"XR5x-1726413420958","leaves":[{"text":"对应输出结果","marks":[]}]}],"state":{}}]">
<p>对应输出结果</p>

<pre>
<code>矩阵的转置(transpose)
tensor([[ 0,1,2,3],
   [ 4,5,6,7],
   [ 8,9, 10, 11],
   ])
tensor([[ 0,4,8, 12],
   [ 1,5,9, 13],
   [ 2,6, 10, 14],
   [ 3,7, 11, 15]])
对称矩阵（symmetric matrix）和其转置矩阵相等
tensor([,
   ,
   ])
矩阵乘以一个标量，不会改变形状
tensor([[ 0,3,6,9],
   ,
   ,
   ])
tensor([,
   ,
   ,
   ])
哈达玛积，相同shape矩阵各元素相乘，输出仍为矩阵，用于信号、图像处理等
tensor([,
   [ 48,75, 108, 147],
   ,
   ])
点积(矩阵乘法)，行列对应相同，表示相似度
tensor([[ 168,186,204,222],
   [ 456,522,588,654],
   [ 744,858,972, 1086],
   ])
叉积，用于确定法向量和确定平面
tensor([-2,4, -2])
降维，求和、平均都可以指定轴进行
tensor()
tensor([ 6., 15.])
tensor()
tensor()
范数，表示分量的大小，L₂范数表示向量元素平方和的平方根（欧几里得距离），L₁范数表示向量元素的绝对值之合
tensor(3.6056)
tensor(4.6000)</code></pre>

<article data-content="[{"type":"block","id":"OPLf-1726579179518","name":"heading","data":{"level":"h3"},"nodes":[{"type":"text","id":"UO1p-1726579179517","leaves":[{"text":"微积分","marks":[]}]}],"state":{}},{"type":"block","id":"4DDd-1726579848155","name":"paragraph","data":{"version":1},"nodes":[{"type":"text","id":"XkED-1726579848156","leaves":[{"text":"求导，切线函数","marks":[]}]}],"state":{}}]">
<p>微积分</p>

<p>求导，切线函数</p>

<pre>
<code>import numpy as np
import matplotlib.pyplot as plt

# 定义函数
def func(x):
return 0.01 * x**2 + 0.1 * x

# 数值求导函数
def numerical_diff(f, x):
h = 1e-4
return (f(x + h) - f(x - h)) / (2 * h)

# 切线函数
def tangent_line(f, x):
d = numerical_diff(f, x)
y = f(x) - d * x
return lambda t: d * t + y

# 定义x范围
x = np.arange(0.0, 20.0, 0.1)
y = func(x)

# 计算切线
x_tangent = 10
tangent = tangent_line(func, x_tangent)
y_tangent = tangent(x)

# 绘制图像
plt.plot(x, y, label='Function')
plt.plot(x, y_tangent, label='Tangent at x=10', linestyle='--')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()</code></pre>

<p>  </p>

<article data-content="[{"type":"block","id":"voss-1726579261509","name":"paragraph","data":{},"nodes":[{"type":"text","id":"PoNY-1726579261508","leaves":[{"text":"偏导数，多元函数（mulivaritae function）、梯度","marks":[]}]}],"state":{}},{"type":"block","id":"2vKJ-1726580627285","name":"paragraph","data":{"style":{"textIndent":28}},"nodes":[{"type":"text","id":"APzd-1726580627284","leaves":[{"text":"->  y关于每一个参数（元）都有偏导数，梯度就是所有偏导数组成的向量","marks":[]}]}],"state":{}},{"type":"block","id":"elSL-1726580700476","name":"paragraph","data":{"style":{"textIndent":0}},"nodes":[{"type":"text","id":"Vevf-1726580700475","leaves":[{"text":"链式法则","marks":[]}]}],"state":{}},{"type":"block","id":"w1LZ-1726580705625","name":"paragraph","data":{"style":{"textIndent":28}},"nodes":[{"type":"text","id":"MRUX-1726580705623","leaves":[{"text":"-> 复杂的多元函数，可以使用链式法则进行求d，将符合函数拆分成单变量函数，对于每一个函数都是可d的","marks":[]}]}],"state":{}},{"type":"block","id":"p08u-1726580881534","name":"paragraph","data":{"style":{"textIndent":0}},"nodes":[{"type":"text","id":"sjgm-1726580881533","leaves":[{"text":"自动微分","marks":[]}]}],"state":{}},{"type":"block","id":"EQYH-1726580886317","name":"paragraph","data":{"style":{"textIndent":28}},"nodes":[{"type":"text","id":"DQ5q-1726580886316","leaves":[{"text":"-> 深度学习框架帮你做这件事，根据模型构建一个计算图（跟踪计算哪些数据通过哪些组合产生的输出），然后通过反向传播（backpropagate）来填充每个参数的偏导数","marks":[]}]}],"state":{}}]">
<p>偏导数，多元函数（mulivaritae function）、梯度</p>

<p>-> y关于每一个参数（元）都有偏导数，梯度就是所有偏导数组成的向量</p>

<p>链式法则</p>

<p>-> 复杂的多元函数，可以使用链式法则进行求d，将符合函数拆分成单变量函数，对于每一个函数都是可d的</p>

<p>自动微分</p>

<p>-> 深度学习框架帮你做这件事，根据模型构建一个计算图（跟踪计算哪些数据通过哪些组合产生的输出），然后通过反向传播（backpropagate）来填充每个参数的偏导数</p>

<pre>
<code>import torch
x = torch.arange(8.0)
# 表示是否记录该变量的操作以便自动微分
x.requires_grad_(True)
# 进行一些操作
y = x * 2
z = y.mean()
# 反向传播
z.backward()
# 查看梯度
print(x.grad)</code></pre>

<article data-content="[{"type":"block","id":"Su4n-1726580601075","name":"paragraph","data":{"style":{"textIndent":28}},"nodes":[{"type":"text","id":"Twyb-1726580601074","leaves":[{"text":"->  tensor()","marks":[]}]}],"state":{}},{"type":"block","id":"2pGd-1726581930978","name":"paragraph","data":{"style":{"textIndent":28}},"nodes":[{"type":"text","id":"MAq5-1726581930977","leaves":[{"text":"->  这里可以看到z函数反向传播，实际上关于x的导数即z = (1/8)* (x*2) = (1/4)x，这个导数就是1/4，和上面的梯度张量相同","marks":[]}]}],"state":{}},{"type":"block","id":"yjaU-1726581855326","name":"paragraph","data":{"style":{"textIndent":28}},"nodes":[{"type":"text","id":"AePD-1726581855325","leaves":[{"text":"-> 如果requires_grad设置为False，则会报错：RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn","marks":[]}]}],"state":{}}]">
<p>-> tensor()</p>

<p>-> 这里可以看到z函数反向传播，实际上关于x的导数即z = (1/8)* (x*2) = (1/4)x，这个导数就是1/4，和上面的梯度张量相同</p>

<p>-> 如果requires_grad设置为False，则会报错：RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn</p>
</article>
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chejm 发表于 2024-10-1 07:24

<p>非常基础的技术知识，对刚入门的初学者很有帮助，希望楼主后续分享更多技术知识</p>

zhoullma 发表于 2024-10-1 19:25

LitchiCheng 发表于 2024-10-8 11:25

chejm 发表于 2024-10-1 07:24
非常基础的技术知识，对刚入门的初学者很有帮助，希望楼主后续分享更多技术知识

<p>共同进步</p>

LitchiCheng 发表于 2024-10-8 11:25

zhoullma 发表于 2024-10-1 19:25
加油，学习进步

<p>基础支持要扎牢</p>

nmg 发表于 2024-10-12 18:21

<p><img height="48" src="https://bbs.eeworld.com.cn/static/editor/plugins/hkemoji/sticker/facebook/lol.gif" width="48" />线性代数，当年学的时候，好像一直好奇它有啥实际用途</p>

LitchiCheng 发表于 2024-10-26 09:43

nmg 发表于 2024-10-12 18:21
线性代数，当年学的时候，好像一直好奇它有啥实际用途

<p>算法基本离不开</p>

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一起读《动手学深度学习（PyTorch版）》- 数据操作及线性代数基础