y = f(x) - d * x
return lambda t: d * t + y
if __name__ == '__main__':
x0 = l.np.arange(-2, 2.5, 0.25)
x1 = l.np.arange(-2, 2.5, 0.25)
X, Y = l.np.meshgrid(x0, x1)
X = X.flatten()
Y = Y.flatten()
grad = numerical_gradient(function_2, l.np.array([X, Y]))
l.plt.figure()
l.plt.quiver(X,
Y,
-grad[0],
-grad[1],
angles="xy",
color="#666666",
label="something") #,headwidth=10,scale=40,color="#444444")
l.plt.xlim([-2, 2])
l.plt.ylim([-2, 2])
l.plt.xlabel('x0')
l.plt.ylabel('x1')
l.plt.grid()
l.plt.legend()
l.plt.draw()
l.plt_show_alt(l.plt)
y = f(x) - d * x
return lambda t: d * t + y
if __name__ == '__main__':
x0 = l.np.arange(-2, 2.5, 0.25)
x1 = l.np.arange(-2, 2.5, 0.25)
X, Y = l.np.meshgrid(x0, x1)
X = X.flatten()
Y = Y.flatten()
grad = numerical_gradient(function_2, l.np.array([X, Y]))
l.plt.figure()
l.plt.quiver(X,
Y,
-grad[0],
-grad[1],
angles="xy",
color="#666666",
label="...") #,headwidth=10,scale=40,color="#444444")
l.plt.xlim([-2, 2])
l.plt.ylim([-2, 2])
l.plt.xlabel('x0')
l.plt.ylabel('x1')
l.plt.grid()
l.plt.legend()
l.plt.draw()
l.plt_show_alt(l.plt, "4.4")
from mpl_toolkits.mplot3d import Axes3D
import sys, os
from common import lib as l
from common import mnist as m
def function_2(x):
return x[0]**2 + x[1]**2
x1 = l.np.arange(-3.0, 3.0, 0.1)
x2 = l.np.arange(-3.0, 3.0, 0.1)
X1, X2 = l.np.meshgrid(x1, x2)
y = function_2(l.np.array([X1, X2]))
l.plt.xlabel("x1")
l.plt.xlabel("x2")
l.plt.ylabel("f(x)")
fig = l.plt.figure()
ax = Axes3D(fig)
ax.plot_wireframe(X1, X2, y)
l.plt_show_alt(l.plt, "4.3.3")
d = numerical_diff(f, x)
print(d)
y = f(x) - d*x
return lambda t: d*t + y
x = l.np.arange(0.0, 20.0, 0.1)
y = function_1(x)
l.plt.xlabel("x")
l.plt.ylabel("f(x)")
tf = tangent_line(function_1, 5)
y2 = tf(x)
tf = tangent_line(function_1, 10)
y3 = tf(x)
l.plt.xlim(0, 20)
l.plt.ylim(0, 6)
l.plt.plot(x, y)
l.plt.plot(x, y2)
l.plt.plot(x, y3)
l.plt.plot([0, 5], [function_1(5), function_1(5)], ':', lw=1)
l.plt.plot([5, 5], [function_1(5), 0], ':', lw=1)
l.plt.plot([0, 10], [function_1(10), function_1(10)], ':', lw=1)
l.plt.plot([10, 10], [function_1(10), 0], ':', lw=1)
l.plt_show_alt(l.plt, "4.3.2")