TypeErrorエラーを修正することができません！

発生している問題・エラーメッセージ

<ipython-input-8-47a407e0b23b>:13: RuntimeWarning: overflow encountered in double_scalars
  return np.array([10 * x - 6 * y + 6,   -6 * x + 6 * y - 6])

TypeError                                 Traceback (most recent call last)
<ipython-input-8-47a407e0b23b> in <module>
     33     ax[ i ].set_xlim((xmin, xmax))
     34     ax[ i ].set_ylim((ymin, ymax))
---> 35     ax[ i ].set_title("alpha={}".format(alpha[ i ]))
     36     ax[ i ].scatter(initial[0], initial[1], color="k", marker="o")
     37     ax[ i ].plot(algos[ i ].path_[:, 0], algos[ i ].path_[:, 1], color="k", linewidth=1.5)

TypeError: 'float' object is not subscriptable

該当のソースコード

Pyhon3.8
1import numpy as np
2import matplotlib.pyplot as plt
3import gd
4
5def f(xx):
6    x = xx[0]
7    y = xx[1]
8    return 5 * x**2 - 6 * x * y + 3 * y**2 + 6 * x - 6 * y
9
10def df(xx):
11    x = xx[0]
12    y = xx[1]
13    return np.array([10 * x - 6 * y + 6,   -6 * x + 6 * y - 6])
14
15xmin, xmax, ymin, ymax = -3, 3, -3, 3
16
17algos = []
18initial = np.array([1, 1])
19alphas = [0.1, 0.2]
20for alpha in alphas :
21    algo = gd.GradientDescent(f, df, alpha)
22    algo.solve(np.array(initial))
23    algos.append(algo)
24
25xs = np.linspace(xmin, xmax, 300)
26ys = np.linspace(ymin, ymax, 300)
27xmesh, ymesh = np.meshgrid(xs, ys)
28xx = np.r_[xmesh.reshape(1, -1), ymesh.reshape(1, -1)]
29fig, ax = plt.subplots(1, 2)
30levels = [-3, -2.9, -2.8, -2.6, -2.4, -2.2, -2, -1, 0, 1, 2, 3, 4]
31
32for i in range(2) :
33    ax[ i ].set_xlim((xmin, xmax))
34    ax[ i ].set_ylim((ymin, ymax))
35    ax[ i ].set_title("alpha={}".format(alpha[ i ]))
36    ax[ i ].scatter(initial[0], initial[1], color="k", marker="o")
37    ax[ i ].plot(algos[ i ].path_[:, 0], algos[ i ].path_[:, 1], color="k", linewidth=1.5)
38    ax[ i ].contour(xs, ys, f(xx).reshape(xmesh.shape), levels=levels, colors="k", linestyles="dotted")
39plt.show()

gdファイル
import numpy as np

class GradientDescent :
    def __init__(self, f, df, alpha=0.01, eps=1e-6) :
        self.f = f
        self.df = df
        self.alpha = alpha
        self.eps = eps
        self.path = None
            
    def solve(self, init):
        x = init
        path = []
        grad = self.df(x)
        path.append(x)
        while (grad**2).sum() > self.eps**2:
            x = x - self.alpha * grad
            grad = self.df(x)
            path.append(x)
        self.path_ = np.array(path)
        self.x_ = x
        self.opt_ = self.f(x)