def show_trace(res):
# 设置绘制框的大小
n = max(abs(min(res)), abs(max(res)), 10)
# 画线时的尺度
f_line = np.arange(-n, n, 0.1)
plot.set_figsize()
# 绘制x**2的线
plot.plt.plot(f_line, [x * x for x in f_line])
# 绘制结果线
plot.plt.plot(res, [x * x for x in res], '-o')
plot.plt.xlabel('x')
plot.plt.ylabel('f(x)')
plot.plt.show()
import torch
import math
import numpy as np
from PIL import Image
import sys
sys.path.append(r".")
from d2lzh_pytorch import plot, detection
"""
这一节介绍如何利用锚框来进行目标检测
"""
# 首先先尝试生成多个锚框,要注意的一点是下面的每个像素是对应了多个锚框的
# 修改numpy的打印精度为2位
np.set_printoptions(2)
plot.set_figsize()
# 直接用PIL来读取图片并输出尺寸测试
img = Image.open(r"./Datasets"+'/Img/catdog.jpg')
w, h = img.size
print("w=%d, h=%d" % (w, h))
# 这里保存函数MultiBoxPrior来生成锚框
# 构造输⼊数据，这里先构造出图片尺寸X
X = torch.Tensor(1, 3, h, w)
# 然后输入希望的锚框的大小和宽高比，配合图片尺寸X，会自动返回所有生成的锚框
# 下面出现了三个尺寸指的是有三种可能的尺寸，三个宽高比是三种形状，是(3+3-1)种锚框(见书)
# 这里的尺寸和宽高比都是先验的式子而已，一个锚框的真正宽为ws*sqrt(r)，高为hs/sqrt(r)
# 返回的尺寸为(批量大小，锚框个数，4)，4表示描述锚框左上角和右下角的两个坐标，坐标以对
# 应图像宽高的比例来表示
def train_pytorch_ch7(optimizer_fn,
optimizer_hyperparams,
features,
labels,
batch_size=10,
num_epochs=2):
"""
The training function of chapter7, but this is the pytorch library version
Parameters
----------
optimizer_fn : [function]
the optimizer function that wants to use
optimizer_hyperparams : [pair]
hyperparams delivered to optimizer
features : [tensor]
batch of features
labels : [tensor]
batch of labels
batch_size : [int], optional
size of a batch, by default 10
num_epochs : [int], optional
summary of number of epochs, by default 2
"""
# init the net, using one linear layer to simulate the linear regression
net = nn.Sequential(nn.Linear(features.shape[-1], 1))
loss = nn.MSELoss()
optimizer = optimizer_fn(net.parameters(), **optimizer_hyperparams)
# get loss
def eval_loss():
return loss(net(features).view(-1), labels).item() / 2
# prepare data and strutures
ls = [eval_loss()]
data_iter = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(
features, labels),
batch_size,
shuffle=True)
# for each epochs
for _ in range(num_epochs):
start = time.time()
# for each batches
for batch_i, (X, y) in enumerate(data_iter):
# divided by 2 is used to make sure the loss is equal to train_ch7's
l = loss(net(X).view(-1), y) / 2
optimizer.zero_grad()
l.backward()
optimizer.step()
# save current loss
if (batch_i + 1) * batch_size % 100 == 0:
ls.append(eval_loss())
# output results
print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))
plot.set_figsize()
plot.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
plot.plt.xlabel('epoch')
plot.plt.ylabel('loss')
plot.plt.show()
def train_ch7(optimizer_fn,
states,
hyperparams,
features,
labels,
batch_size=10,
num_epochs=2):
"""
The training function of chapter7, it is a more useful function.
In Chapter7, it is used with some different optimizer functions.
Parameters
----------
optimizer_fn : [function]
the optimizer function that wants to use
states : [int]
states delivered to optimizer
hyperparams : [pair]
hyperparams delivered to optimizer
features : [tensor]
batch of features
labels : [tensor]
batch of labels
batch_size : [int], optional
size of a batch, by default 10
num_epochs : [int], optional
summary of number of epochs, by default 2
"""
# using linear regression and squared loss for training
net, loss = linear_reg.linreg, linear_reg.squared_loss
# init params
w = torch.nn.Parameter(torch.tensor(np.random.normal(
0, 0.01, size=(features.shape[1], 1)),
dtype=torch.float32),
requires_grad=True)
b = torch.nn.Parameter(torch.zeros(1, dtype=torch.float32),
requires_grad=True)
# get loss
def eval_loss():
return loss(net(features, w, b), labels).mean().item()
# prepare data and strutures
ls = [eval_loss()]
data_iter = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(
features, labels),
batch_size,
shuffle=True)
# for each epochs
for _ in range(num_epochs):
start = time.time()
for batch_i, (X, y) in enumerate(data_iter):
# using avg loss
l = loss(net(X, w, b), y).mean()
# clean gradients
if w.grad is not None:
w.grad.data.zero_()
b.grad.data.zero_()
l.backward()
optimizer_fn([w, b], states, hyperparams)
# save current loss
if (batch_i + 1) * batch_size % 100 == 0:
ls.append(eval_loss())
# output results
print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))
plot.set_figsize()
plot.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
plot.plt.xlabel('epoch')
plot.plt.ylabel('loss')
plot.plt.show()
import numpy as np
"""
这一节介绍了一些关于深度学习中优化目标函数的知识
"""
# 首先是由于很多问题在优化途中没有解析解，所以需要用机器学习方法得到数值解
# 而对于数值解，求解过程中容易掉入鞍点或局部最小值，这里是局部最小值的示例
# 函数在x的值比邻近区域都要小就称为局部最小值，此时优化算法可能会被困住
def f(x):
# 示例函数，f(x) = x*cos(pi*x)
return x*np.cos(np.pi*x)
plot.set_figsize((4.5, 2.5))
# 列出一组输入用的x
x = np.arange(-1.0, 2.0, 0.1)
# 将输入代入得到一组输出然后绘制到fig上
fig, = plot.plt.plot(x, f(x))
# 绘制两条指示线，指向的点是提前看出来的
fig.axes.annotate('local minium', xy=(-0.3, -0.25),
xytext=(-0.77, -1.0), arrowprops=dict(arrowstyle='->'))
fig.axes.annotate('global minium', xy=(1.1, -0.95),
xytext=(0.6, 0.8), arrowprops=dict(arrowstyle='->'))
plot.plt.xlabel('x')
plot.plt.ylabel('f(x)')
# plot.plt.show()
print('————————————————————————————')
# 除了局部最小值由于周边梯度为0会卡住外，鞍点的周边梯度也是0，同样会困住优化器