def test_higher_derivative_sin():
x = Variable(np.array(1))
y = sin(x)
y.backward(create_graph=True)
for i in range(3):
gx = x.grad
x.clear_grad()
gx.backward(create_graph=True)
LOGGER.debug('{} {}'.format(i, x.grad))
assert x.grad.data == pytest.approx(0.8414709)
def test_gradient_step14():
x = Variable(np.array(3.0))
y = x + x
y.backward()
assert y.data == 6
assert x.grad.data == 2
x.clear_grad() # teardown 1st tests
y = (x + x) + x
y.backward()
assert x.grad.data == 3
def test_newtons_method():
f = lambda t: t**4 - 2 * t**2
x = Variable(np.array(2.0))
iters = 10
for i in range(iters):
LOGGER.debug('{} {}'.format(i, x))
y = f(x)
x.clear_grad()
y.backward(create_graph=True)
gx = x.grad
x.clear_grad()
gx.backward()
gx2 = x.grad
x.data -= gx.data / gx2.data
assert x.data == 1
x, y = Variable(x), Variable(y)
W = Variable(np.zeros((1, 1)))
b = Variable(np.zeros(1))
def predict(x):
y = F.matmul(x, W) + b
return y
def mean_squared_error(x0, x1):
diff = x0 - x1
return F.sum(diff**2) / len(diff)
lr = 0.1
iters = 10000
for i in range(iters):
y_pred = predict(x)
loss = mean_squared_error(y, y_pred)
W.clear_grad()
b.clear_grad()
loss.backward()
W.data -= lr * W.grad.data
b.data -= lr * b.grad.data
if i % 1000 == 0:
print(W, b, loss)
import numpy as np
import matplotlib.pyplot as plt
from dezero import Variable
import dezero.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.clear_grad()
gx.backward(create_graph=True)
# draw graph
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 dezero import Variable
def rosenbrock(x0, x1):
y = 100 * (x1 - x0**2)**2 + (x0 - 1)**2
return y
x0 = Variable(np.array(0.0))
x1 = Variable(np.array(2.0))
lr = 0.001
iters = 1000
for i in range(iters):
print(x0, x1)
y = rosenbrock(x0, x1)
x0.clear_grad()
x1.clear_grad()
y.backward()
x0.data -= lr * x0.grad
x1.data -= lr * x1.grad
def predict(x):
y = F.linear(x, W1, b1)
y = F.sigmoid(y)
y = F.linear(y, W2, b2)
return y
lr = 0.2
iters = 10000
for i in range(iters):
y_pred = predict(x)
loss = F.mean_squared_error(y, y_pred)
W1.clear_grad()
b1.clear_grad()
W2.clear_grad()
b2.clear_grad()
loss.backward()
W1.data -= lr * W1.grad.data
b1.data -= lr * b1.grad.data
W2.data -= lr * W2.grad.data
b2.data -= lr * b2.grad.data
if i % 1000 == 0:
print(loss)
# Plot
plt.scatter(x.data, y.data, s=10)
plt.xlabel('x')