def newton_method():
x = Variable(np.array(2.0))
iters = 10
for i in range(iters):
print(i, x)
y = f(x)
x.cleargrad()
y.backward()
x.data -= x.grad / gx2(x.data)
def accuracy(y, t):
y, t = as_variable(y), as_variable(t)
pred = y.data.argmax(axis=1).reshape(t.shape)
result = (pred == t.data)
acc = result.mean()
return Variable(as_array(acc))
def gradient_descent():
x0 = Variable(np.array(0.0))
x1 = Variable(np.array(2.0))
lr = 0.001 # Learning rate
iters = 1000 # iterations
for i in range(iters):
print(i, x0, x1)
y = rosenbrock(x0, x1)
x0.cleargrad()
x1.cleargrad()
y.backward()
x0.data -= lr * x0.grad
x1.data -= lr * x1.grad
def secondorder_method():
x = Variable(np.array(2.0))
iters = 10
for i in range(iters):
print(i, x)
y = f(x)
x.cleargrad()
y.backward(create_graph=True)
gx = x.grad
x.cleargrad()
gx.backward(create_graph=True)
gx2 = x.grad
x.data -= gx.data / gx2.data
import numpy as np
from myke import Variable
from myke.utils import plot_dot_graph
def goldstein(x, y):
z = (1 + (x + y + 1)**2 * (19 - 14*x + 3*x**2 - 14*y + 6*x*y + 3*y**2)) * \
(30 + (2*x - 3*y)**2 * (18 - 32*x + 12*x**2 + 48*y - 36*x*y + 27*y**2))
return z
x = Variable(np.array(1.0), 'x')
y = Variable(np.array(1.0), 'y')
z = goldstein(x, y)
z.name = 'z'
plot_dot_graph(z, verbose=False)
import numpy as np
from myke import Variable
import myke.functions as F
# 토이 데이터셋
np.random.seed(0) # 시드값 고정
x = np.random.rand(100, 1)
y = 5 + 2 * x + np.random.rand(100, 1) # y에 무작위 노이즈 추가
x, y = Variable(x), Variable(y) # 생략 가능
W = Variable(np.zeros((1, 1)))
b = Variable(np.zeros(1))
def predict(x):
y = F.matmul(x, W) + b
return y
lr = 0.1
iters = 100
for i in range(iters):
y_pred = predict(x)
loss = F.mean_squared_error(y, y_pred)
W.cleargrad()
b.cleargrad()
loss.backward()
W.data -= lr * W.grad.data
#%%
import numpy as np
import matplotlib.pyplot as plt
from myke import Variable
import myke.functions as F
x = Variable(np.linspace(-7, 7, 200))
y = F.sin(x)
y.backward(create_graph=True)
logs = [y.data]
for i in range(3):
logs.append(x.grad.data)
gx = x.grad
x.cleargrad()
gx.backward(create_graph=True)
# 그래프 그리기
labels = ["y=sin(x)", "y'", "y''", "y'''"]
for i, v in enumerate(logs):
plt.plot(x.data, logs[i], label=labels[i])
plt.legend(loc='lower right')
plt.show()
# %%
import numpy as np
from myke import Variable
import myke.functions as F
def f(x):
y = x**4 - 2 * x**2
return y
x = Variable(np.array(2.0))
y = f(x)
y.backward(create_graph=True)
print(x.grad)
gx = x.grad
x.cleargrad()
gx.backward(create_graph=True)
print(x.grad)
x = Variable(np.array(1.0))
y = F.sin(x)
y.backward(create_graph=True)
for i in range(3):
gx = x.grad
x.cleargrad()
gx.backward(create_graph=True)
print(x.grad)
import numpy as np from myke import Variable import myke.functions as F x0 = Variable(np.array([1, 2, 3])) x1 = Variable(np.array([10])) y = x0 + x1 print(y) y.backward() print(x1.grad)
import numpy as np
import math
from myke import Variable
from myke.utils import plot_dot_graph
def sphere(x, y):
z = x**2 + y**2
return z
x = Variable(np.array(1.0))
y = Variable(np.array(1.0))
z = sphere(x, y)
z.backward()
print("sphere", z)
print(x.grad, y.grad)
def matyas(x, y):
z = 0.26 * (x**2 + y**2) - 0.48 * x * y
return z
x = Variable(np.array(1.0))
y = Variable(np.array(1.0))
z = matyas(x, y)
z.backward()