def test_mul_ndarray_variable_forward(self):
x0 = np.array([1, 2, 3])
x1 = Variable(np.array([1, 2, 3]))
y = x0 * x1
res = y.data
expected = np.array([1, 4, 9])
self.assertTrue(array_equal(res, expected))
def numerical_grad(f, x, *args, **kwargs):
"""Computes numerical gradient by finite differences.
Args:
f (callable): A function which gets `Variable`s and returns `Variable`s.
x (`ndarray` or `dezero.Variable`): A target `Variable` for computing
the gradient.
*args: If `f` needs variables except `x`, you can specify with this
argument.
**kwargs: If `f` needs keyword variables, you can specify with this
argument.
Returns:
`ndarray`: Gradient.
"""
eps = 1e-4
x0 = Variable(x.data - eps)
x1 = Variable(x.data + eps)
y0 = f(x0, *args, **kwargs)
y1 = f(x1, *args, **kwargs)
return (y1.data - y0.data) / (2 * eps)
def test_add_variable_ndarray_backward2(self):
x = Variable(np.random.randn(3, 3))
y = np.random.randn(3, 1)
f = lambda x, y: x + y
self.assertTrue(gradient_check(f, x, y))
def test_change_sign_of_numpy_when_backward(self):
x = Variable(np.random.randn(5, 5))
f = lambda x: -x
self.assertTrue(gradient_check(f, x))
def test_pow_variable_backward2(self):
x = Variable(np.random.randn(5, 5))
f = lambda x: x**3
self.assertTrue(gradient_check(f, x))
def test_pow_variable_forward(self):
x = Variable(np.array([4, 5, 6]))
result = (x**2).data
expected = np.array([16, 25, 36])
return self.assertTrue(array_equal(result, expected))
def test_div_variable_ndarray_backward(self):
x0 = Variable(np.random.randn(3, 3))
x1 = np.random.randn(3, 3)
f = lambda x, y: x / y
self.assertTrue(gradient_check(f, x0, x1))
def test_exp_variable_backward1(self):
x = Variable(np.random.randn(3, 3))
self.assertTrue(gradient_check(F.exp, x))
def test_change_sign_of_Variable_when_forward(self):
x = Variable(np.array([1, 2, 3]))
y = -x
res = y.data
expected = np.array([-1, -2, -3])
self.assertTrue(array_equal(res, expected))
def test_div_variable_ndarray_forward(self):
x0 = Variable(np.array([4, 5, 6]))
x1 = np.array([1, 2, 3])
result = (x0 / x1).data
expected = np.array([4 / 1, 5 / 2, 6 / 3])
return self.assertTrue(array_equal(result, expected))
def test_sub_ndarray_variable_backward(self):
x0 = np.random.randn(3, 3)
x1 = Variable(np.random.randn(3, 3))
f = lambda x, y: x - y
self.assertTrue(gradient_check(f, x0, x1))
'''
Need the dot binary from the graphviz package (www.graphviz.org).
'''
if '__file__' in globals():
import os, sys
sys.path.append(os.path.join(os.path.dirname(__file__), '..'))
import numpy as np
from dezerohit import Variable
from dezerohit.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))
y = Variable(np.array(1.0))
z = goldstein(x, y)
z.backward()
x.name = 'x'
y.name = 'y'
z.name = 'z'
plot_dot_graph(z, verbose=False, to_file='goldstein.png')
def test_square_variable_backward2(self):
x = Variable(np.random.randn(3))
self.assertTrue(gradient_check(F.square, x))
def test_square_variable_forward(self):
x = Variable(np.array([1, 2, 3]))
y = F.square(x)
expected = np.array([1, 4, 9])
self.assertTrue(array_equal(y.data, expected))
def test_sub_variable_ndarray_forward(self):
x0 = Variable(np.array([4, 5, 6]))
x1 = np.array([1, 2, 3])
result = (x0 - x1).data
expected = np.array([3, 3, 3])
return self.assertTrue(array_equal(expected, result))
def test_div_ndarray_variable_forward(self):
x0 = np.array([1, 2, 3])
x1 = Variable(np.array([4, 5, 6]))
result = (x0 / x1).data
expected = np.array([1 / 4, 2 / 5, 3 / 6])
return self.assertTrue(array_equal(result, expected))
def test_exp_variable_forward(self):
x = Variable(np.array([1, 2, 3]))
y = F.exp(x)
expected = np.exp(x.data)
self.assertTrue(array_equal(y.data, expected))