return f
def df(x): #fの勾配
const = -2 * (1 - pmas.ups(x))
df = const * pmas.dups(x)
# df = np.array(df)
# print(df)
return df
########
initial = np.array([5.0, -14.48, 8.6, 0.28, -280000.0, 34.9, 17.0]) #初期値
########
algo = gd.GradientDescent(f, df) # 勾配降下法のインスタンスを生成
algo.solve(initial) # 勾配降下法を計算
print(algo.x__) # 計算結果で得られた xx を出力
print(algo.opt__) # 最小化された目的関数 f を出力
plt.scatter(initial[0], initial[1])
plt.plot(algo.path__[:, 0], algo.path__[:, 1], linewidth=1.5)
xs = np.linspace(-2, 2, 300)
ys = np.linspace(-2, 2, 300)
xmesh, ymesh = np.meshgrid(xs, ys)
xx = np.r_[xmesh.reshape(1, -1), ymesh.reshape(1, -1)]
levels = [-3.0, -2.5, -2.0, 0, 1, 2]
# plt.contour(xs,ys,f(xx).reshape(xmesh,ymesh),levels = levels, colors = "k", linestyles = "dotted")
import gd
def f(xx):
x = xx[0]
y = xx[1]
return 5 * x**2 - 6 * x * y + 3 * y**2 + 6 * x - 6 * y
def df(xx):
x = xx[0]
y = xx[1]
return np.array([10 * x - 6 * y + 6, -6 * x + 6 * y - 6])
algo = gd.GradientDescent(f, df)
initial = np.array([1, 1])
algo.solve(initial)
print(algo.x_)
print(algo.opt_)
plt.scatter(initial[0], initial[1], color="k", marker="o")
plt.plot(algo.path_[:, 0], algo.path_[:, 1], color="k", linewidth=1.5)
xs = np.linspace(-2, 2, 300)
ys = np.linspace(-2, 2, 300)
xmesh, ymesh = np.meshgrid(xs, ys)
xx = np.r_[xmesh.reshape(1, -1), ymesh.reshape(1, -1)]
levels = [-3, -2.9, -2.8, -2.6, -2.4, -2.2, -2, -1, 0, 1, 2, 3, 4]
z = fxy(x_vec).reshape(xmesh.shape)
return xmesh, ymesh, z
if __name__ == '__main__':
# constant
alphas = [0.01, 0.05, 0.1, 0.2]
x_range, y_range = [-3, 3], [-3, 3]
levels = [-3, -2.9, -2.8, -2.6, -2.4, -2.2, -2, -1, 0, 1, 2, 3,
4] # contour levels
fig = plt.figure(figsize=(15, 5))
axes = fig.subplots(1, len(alphas))
# calculation
for i, alpha in enumerate(alphas):
# solve
algo = gd.GradientDescent(f, df, alpha=alpha)
initial = np.array([1, 1])
algo.solve(initial)
# plot
xmesh, ymesh, z = mesh(x_range, y_range, fxy=f)
axes[i].scatter(initial[0], initial[1], marker="o", s=20)
axes[i].plot(algo.path[:, 0], algo.path[:, 1], ls="-", color="k")
map_ax = axes[i].contour(xmesh,
ymesh,
z,
linestyles="dotted",
colors="b",
levels=levels) # cmap="jet"
# config