1. 导数和微分

import numpy as np
from IPython import display
from d2l import torch as d2ldef f(x):return 3 * x ** 2 - 4 * x

def numerical_lim(f, x, h):return (f(x + h) - f(x)) / hh = 0.1
for i in range(5):print(f'h={h:.5f}, numerical limit={numerical_lim(f, 1, h):.5f}')h *= 0.1

 

绘制函数u=f(x)u=f(x)及其在x=1x=1处的切线y=2x−3y=2x−3，其中系数2是切线的斜率。

由于原来程序是在jupyter中运行，程序跟李沐老师的稍有不同

#import numpy as np
#from IPython import display
from d2l import torch as d2l
import matplotlib.pyplot as plt
import numpy as npdef f(x):return 3 * x ** 2 - 4 * x
def numerical_lim(f, x, h):return (f(x + h) - f(x)) / hh = 0.1
for i in range(5):print(f'h={h:.5f}, numerical limit={numerical_lim(f, 1, h):.5f}')h *= 0.1plt.figure(figsize=(3.5,2.5))  #图片尺寸大小
def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):"""设置matplotlib的轴。"""axes.set_xlabel(xlabel)axes.set_ylabel(ylabel)axes.set_xscale(xscale)axes.set_yscale(yscale)axes.set_xlim(xlim)axes.set_ylim(ylim)if legend:axes.legend(legend)axes.grid()
def plot(X, Y=None, xlabel=None, ylabel=None, legend=None, xlim=None,ylim=None, xscale='linear', yscale='linear',fmts=('-', 'm--', 'g-.', 'r:'), axes=None):"""绘制数据点。"""if legend is None:legend = []axes = axes if axes else d2l.plt.gca()# 如果 `X` 有一个轴，输出Truedef has_one_axis(X):return (hasattr(X, "ndim") and X.ndim == 1 or isinstance(X, list)and not hasattr(X[0], "__len__"))if has_one_axis(X):X = [X]if Y is None:X, Y = [[]] * len(X), Xelif has_one_axis(Y):Y = [Y]if len(X) != len(Y):X = X * len(Y)axes.cla()for x, y, fmt in zip(X, Y, fmts):if len(x):axes.plot(x, y, fmt)else:axes.plot(y, fmt)set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend)x = np.arange(0, 3, 0.1)
y = 2*x-3
plot(x, [f(x), 2 * x - 3], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])
plt.show()

 2. 偏导数

3.梯度

 4.链式法则