def test_sin_backward_twice(self):
x = Variable(np.array(1.0))
y = F.sin(x)
y.backward(create_graph=True)
gx = x.grad
x.cleargrad()
gx.backward(create_graph=False)
result = x.grad.data
assert np.allclose(result, -0.84147098)
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_sin(self):
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)
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.savefig('test.png')
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()
def test_backward(self):
x = Variable(np.array(np.pi / 4))
y = sin(x)
y.backward()
self.assertAlmostEqual(x.grad.data, 1 / np.sqrt(2))
def test_forward(self):
x = Variable(np.array(np.pi / 4))
y = sin(x)
self.assertAlmostEqual(y.data, 1/np.sqrt(2))
def test_sin_backward_once(self):
x = Variable(np.array(np.pi / 4))
y = F.sin(x)
y.backward()
result = x.grad.data
assert np.allclose(result, 0.70710678)
def test_sin_forward(self):
x = Variable(np.array(np.pi / 4))
y = F.sin(x)
assert np.allclose(y.data, 0.7071)
def test_sin(self):
x = Variable(np.array(2.0))
y = sin(x)
y.backward()
self.assertEqual(y.data, np.sin(x.data))
self.assertEqual(x.grad.data, np.cos(x.data))
import numpy as np
import matplotlib.pyplot as plt
from dezero import Variable
import dezero.functions as f
if __name__ == '__main__':
x = Variable(np.linspace(-7, 7, 200))
y = f.sin(x)
y.backward(create_graph=True)
logs = [y.data.flatten()]
for i in range(3):
logs.append(x.grad.data.flatten())
gx = x.grad
x.clear_grad()
gx.backward(create_graph=True)
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()
