深度学习笔记之微积分及绘图

学习资料来源：微积分

%matplotlib inline
from matplotlib_inline import backend_inline
from mxnet import np, npx
from d2l import mxnet as d2lnpx.set_np()def f(x):return 3 * x ** 2 - 4 * xdef 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

def use_svg_display():"""使用svg格式在Jupyter中显示绘图"""backend_inline.set_matplotlib_formats('svg')def set_figsize(figsize=(3.5, 2.5)):"""设置matplotlib的图表大小"""use_svg_display()d2l.plt.rcParams['figure.figsize'] = figsize# set_axes函数用于设置matplotlib生成图表的轴的属性
def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):"""这是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()

通过use_svg_display()、set_figsize()、set_axes()用于图形配置的函数，定义plot函数来绘制曲线

def plot(X, Y=None, xlabel=None, ylabel=None, legend=None, xlim=None,ylim=None, xscale='linear', yscale='linear',fmts=('-', 'm--', 'g-.', 'r:'), figsize=(3.5, 2.5), axes=None):"""绘制数据点"""if legend is None:legend = []set_figsize(figsize)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)

# 绘制函数u=f(x)及其在x=1处的切线y=2x-3，其中系数2是切线的斜率
x = np.arange(0, 3, 0.1)
plot(x, [f(x), 2 * x - 3], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])

练习：