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test_back_propagation.py
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test_back_propagation.py
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from unittest import TestCase
from back_propagation import *
class TestBackPropagation(TestCase):
def test_unit(self):
unit1 = Unit()
unit2 = Unit()
unit3 = Unit(unit1, unit2)
self.assertSequenceEqual(unit1.get_parents(), [])
self.assertSequenceEqual(unit1.get_children(), [(unit3, 0)])
self.assertSequenceEqual(unit2.get_parents(), [])
self.assertSequenceEqual(unit2.get_children(), [(unit3, 1)])
self.assertSequenceEqual(unit3.get_parents(), [unit1, unit2])
self.assertSequenceEqual(unit3.get_children(), [])
def test_variable(self):
self.assertEqual(Variable(2).evaluate(), 2)
np.testing.assert_almost_equal(Variable(np.array([1, 2])).evaluate(), np.array([1, 2]))
def test_add(self):
add = Add(Variable(2), Variable(3))
self.assertEqual(add.evaluate(), 5)
self.assertEqual(add.get_gradient(0).evaluate(), 1)
self.assertEqual(add.get_gradient(1).evaluate(), 1)
add = Add(Variable(np.array([1, 2])), Variable(np.array([3, 4])))
np.testing.assert_almost_equal(add.evaluate(), np.array([4, 6]))
np.testing.assert_almost_equal(add.get_gradient(0).evaluate(), np.ones(2))
np.testing.assert_almost_equal(add.get_gradient(1).evaluate(), np.ones(2))
add = Add(Variable(np.array([1, 2])), Variable(3))
np.testing.assert_almost_equal(add.evaluate(), np.array([4, 5]))
np.testing.assert_almost_equal(add.get_gradient(0).evaluate(), np.array([1, 1]))
np.testing.assert_almost_equal(add.get_gradient(1).evaluate(), np.array([1, 1]))
def test_subtract(self):
subtract = Subtract(Variable(2), Variable(3))
self.assertEqual(subtract.evaluate(), -1)
self.assertEqual(subtract.get_gradient(0).evaluate(), 1)
self.assertEqual(subtract.get_gradient(1).evaluate(), -1)
A = Variable(np.array([[5, 6], [7, 8]]))
B = Variable(np.array([[1, 2], [3, 4]]))
subtract = Subtract(A, B)
np.testing.assert_almost_equal(subtract.evaluate(), np.array([[4, 4], [4, 4]]))
np.testing.assert_almost_equal(subtract.get_gradient(0).evaluate(), np.ones(A.evaluate().shape))
np.testing.assert_almost_equal(subtract.get_gradient(1).evaluate(), -np.ones(B.evaluate().shape))
def test_multiply(self):
multiply = Multiply(Variable(2), Variable(3))
self.assertEqual(multiply.evaluate(), 6)
self.assertEqual(multiply.get_gradient(0).evaluate(), 3)
self.assertEqual(multiply.get_gradient(1).evaluate(), 2)
multiply = Multiply(Variable(2), Variable(3), Variable(4))
self.assertEqual(multiply.evaluate(), 24)
self.assertEqual(multiply.get_gradient(0).evaluate(), 12)
self.assertEqual(multiply.get_gradient(1).evaluate(), 8)
self.assertEqual(multiply.get_gradient(2).evaluate(), 6)
A = Variable(np.array([[1, 2], [3, 4]]))
B = Variable(np.array([[5, 6], [7, 8]]))
multiply = Multiply(A, B)
np.testing.assert_almost_equal(multiply.evaluate(), np.array([[5, 12], [21, 32]]))
np.testing.assert_almost_equal(multiply.get_gradient(0).evaluate(), B.evaluate())
np.testing.assert_almost_equal(multiply.get_gradient(1).evaluate(), A.evaluate())
A = Variable(np.array([1, 2]))
B = Variable(np.array([3, 4]))
C = Variable(np.array([5, 6]))
multiply = Multiply(A, B, C)
np.testing.assert_almost_equal(multiply.evaluate(), np.array([15, 48]))
np.testing.assert_almost_equal(multiply.get_gradient(0).evaluate(), np.array([15, 24]))
np.testing.assert_almost_equal(multiply.get_gradient(1).evaluate(), np.array([5, 12]))
np.testing.assert_almost_equal(multiply.get_gradient(2).evaluate(), np.array([3, 8]))
def test_power(self):
power = Power(Variable(2), 3)
self.assertEqual(power.evaluate(), 8)
self.assertEqual(power.get_gradient(0).evaluate(), 12)
power = Power(Variable(3), 2)
self.assertEqual(power.evaluate(), 9)
self.assertEqual(power.get_gradient(0).evaluate(), 6)
power = Power(Variable(np.array([1, 2])), 3)
np.testing.assert_almost_equal(power.evaluate(), np.array([1, 8]))
np.testing.assert_almost_equal(power.get_gradient(0).evaluate(), np.array([3, 12]))
power = Power(Variable(np.array([2, 3])), 2)
np.testing.assert_almost_equal(power.evaluate(), np.array([4, 9]))
np.testing.assert_almost_equal(power.get_gradient(0).evaluate(), np.array([4, 6]))
def test_sum(self):
sum = Sum(Variable(np.array([1, 2])))
self.assertEqual(sum.evaluate(), 3)
np.testing.assert_almost_equal(sum.get_gradient(0).evaluate(), np.ones(2))
def test_matrix_mutiply(self):
# vector-vector
matrix_multiply = MatrixMultiply(Variable(np.array([1, 2])), Variable(np.array([3, 4])))
self.assertEqual(matrix_multiply.evaluate(), 11)
np.testing.assert_almost_equal(matrix_multiply.get_gradient(0).evaluate(), np.array([3, 4]))
np.testing.assert_almost_equal(matrix_multiply.get_gradient(1).evaluate(), np.array([1, 2]))
# vector-matrix
matrix_multiply = MatrixMultiply(Variable(np.array([1, 2])), Variable(np.array([[3, 4], [5, 6]])))
np.testing.assert_almost_equal(matrix_multiply.evaluate(), np.array([13, 16]))
np.testing.assert_almost_equal(matrix_multiply.get_gradient(0).evaluate(), np.array([[3, 4], [5, 6]]))
# matrix-vector
matrix_multiply = MatrixMultiply(Variable(np.array([[1, 2], [3, 4]])), Variable(np.array([5, 6])))
np.testing.assert_almost_equal(matrix_multiply.evaluate(), np.array([17, 39]))
np.testing.assert_almost_equal(matrix_multiply.get_gradient(1).evaluate(), np.array([[1, 3], [2, 4]]))
def test_repeat(self):
repeat = Repeat(Variable(2), 3)
np.testing.assert_almost_equal(repeat.evaluate(), np.array([2, 2, 2]))
np.testing.assert_almost_equal(repeat.get_gradient(0).evaluate(), np.array([1, 0, 0]))
def test_relu(self):
relu = Relu(Variable(3))
self.assertEqual(relu.evaluate(), 3)
self.assertEqual(relu.get_gradient(0).evaluate(), 1)
relu = Relu(Variable(-3))
self.assertEqual(relu.evaluate(), 0)
self.assertEqual(relu.get_gradient(0).evaluate(), 0)
relu = Relu(Variable(np.array([1, -2])))
np.testing.assert_almost_equal(relu.evaluate(), np.array([1, 0]))
np.testing.assert_almost_equal(relu.get_gradient(0).evaluate(), np.array([[1, 0], [0, 0]]))
relu = Relu(Variable(np.array([[1, -2], [-3, 4]])))
np.testing.assert_almost_equal(relu.evaluate(), np.array([[1, 0], [0, 4]]))
np.testing.assert_almost_equal(relu.get_gradient(0).evaluate(), [[[[1, 0], [0, 0]], [[0, -2], [0, 0]]], [[[0, 0], [-3, 0]], [[0, 0], [0, 4]]]])
def test_differentiate(self):
x = Variable(3)
y = Variable(2)
self.assertEqual(differentiate(y, x).evaluate(), 0)
x = Variable(3)
y = Variable(4) * x
self.assertEqual(differentiate(y, x).evaluate(), 4)
x = Variable(3)
y = x * x
self.assertEqual(differentiate(y, x).evaluate(), 6)
x = Variable(3)
y = x + x * x
self.assertEqual(differentiate(y, x).evaluate(), 7)
x = Variable(3)
y = x * x * x
derivative = differentiate(y, x)
self.assertEqual(derivative.evaluate(), 27)
second_derivative = differentiate(derivative, x)
self.assertEqual(second_derivative.evaluate(), 18)
x = Variable(np.array([1, 2]))
y = Variable(3) * x
np.testing.assert_almost_equal(differentiate(y, x).evaluate(), np.array([3, 3]))
x = Variable(np.array([1, 2]))
y = x + x * x
np.testing.assert_almost_equal(differentiate(y, x).evaluate(), np.array([3, 5]))
def test_linear_regression(self):
x = [Variable(0), Variable(1)]
y = [Variable(0), Variable(1)]
w = Variable(0)
f = [w * x[0], w * x[1]]
J = (y[0] - f[0]) ** 2 + (y[1] - f[1]) ** 2
dw = differentiate(J, w)
for i in range(10):
w_new = w.evaluate() - 0.5 * dw.evaluate()
w.set_value(w_new)
self.assertAlmostEqual(w.evaluate(), 1)
self.assertAlmostEqual(J.evaluate(), 0)
x = Variable(np.array([0, 1]))
y = Variable(np.array([0, 1]))
w = Variable(0)
f = w * x
J = Sum((y - f) ** 2)
dw = differentiate(J, w)
for i in range(10):
w_new = w.evaluate() - 0.5 * dw.evaluate()
w.set_value(w_new)
self.assertAlmostEqual(w.evaluate(), 1)
self.assertAlmostEqual(J.evaluate(), 0)
def test_multiple_regression_analysis(self):
X = Variable(np.array([[0, 0], [1, 0], [0, 1]]))
y = Variable(np.array([0, 1, 1]))
w = Variable(np.array([0, 0]))
p = X @ w
J = Sum((p - y) ** 2)
dw = differentiate(J, w)
for i in range(10):
w_new = w.evaluate() - 0.5 * dw.evaluate()
w.set_value(w_new)
np.testing.assert_almost_equal(w.evaluate(), [1, 1])
self.assertAlmostEqual(J.evaluate(), 0)
def test_bias(self):
x = Variable(np.array([0, 1]))
y = Variable(np.array([1, 2]))
w = Variable(0)
b = Variable(0)
f = w * x + Repeat(b, 2)
J = Sum((y - f) ** 2)
dw = differentiate(J, w)
db = differentiate(J, b)
for i in range(10):
w_new = w.evaluate() - 0.5 * dw.evaluate()
w.set_value(w_new)
b_new = b.evaluate() - 0.5 * db.evaluate()
b.set_value(b_new)
self.assertAlmostEqual(w.evaluate(), 1)
self.assertAlmostEqual(b.evaluate(), 1)
self.assertAlmostEqual(J.evaluate(), 0)
def test_multi_regression_bias(self):
X = Variable(np.array([[0, 0], [1, 0], [0, 1]]))
y = Variable(np.array([1, 2, 2]))
w = Variable(np.array([0, 0]))
b = Variable(0)
p = X @ w + Repeat(b, 3)
J = Sum((p - y) ** 2)
dw = differentiate(J, w)
db = differentiate(J, b)
for i in range(10):
w_new = w.evaluate() - 0.5 * dw.evaluate()
w.set_value(w_new)
b_new = b.evaluate() - 0.5 * db.evaluate()
b.set_value(b_new)
np.testing.assert_almost_equal(w.evaluate(), [1, 1])
self.assertAlmostEqual(b.evaluate(), 1)
self.assertAlmostEqual(J.evaluate(), 0)
def test_xor(self):
X = Variable(np.array([[0, 0], [1, 0], [0, 1], [1, 1]]))
W1 = Variable(np.array([[1, 1], [1, 1]]))
c = Variable(np.array([0, -1]))
w2 = Variable(np.array([1, -2]))
np.testing.assert_almost_equal((X @ W1).evaluate(), np.array([[0, 0], [1, 1], [1, 1], [2, 2]]))
np.testing.assert_almost_equal((X @ W1 + c).evaluate(), np.array([[0, -1], [1, 0], [1, 0], [2, 1]]))
np.testing.assert_almost_equal(Relu(X @ W1 + c).evaluate(), np.array([[0, 0], [1, 0], [1, 0], [2, 1]]))
np.testing.assert_almost_equal((Relu(X @ W1 + c) @ w2).evaluate(), np.array([0, 1, 1, 0]))
def test_relu_regression(self):
X = Variable(np.array([[0, 0], [1, 0], [0, 1], [-10, -10]]))
y = Variable(np.array([1, 2, 2, 0]))
w = Variable(np.array([1, 1]))
b = Variable(2)
p = Relu(X @ w + Repeat(b, 4))
J = Sum((p - y) ** 2)
dw = differentiate(J, w)
db = differentiate(J, b)
for i in range(100):
w_new = w.evaluate() - 0.4 * dw.evaluate()
w.set_value(w_new)
b_new = b.evaluate() - 0.4 * db.evaluate()
b.set_value(b_new)
self.assertAlmostEqual(J.evaluate(), 0)
np.testing.assert_almost_equal(w.evaluate(), [1, 1])
self.assertAlmostEqual(b.evaluate(), 1)