def test_repr():
x = AD(1.5)
assert x.__repr__() == '====== Function Value(s) ======\n1.5\n===== Derivative Value(s) =====\n1.0\n'
x = AD(2, [1,0])
y = AD(3, [0,1])
f = AD([x + y, x*y])
assert f.__repr__() == '====== Function Value(s) ======\n[5 6]\n===== Derivative Value(s) =====\n[[1 1]\n [3 2]]\n'
def test_log():
x = AD(-1)
with np.testing.assert_raises(ValueError):
f = np.log(x)
x = AD(1)
f = np.log(x)
assert f == AD(0,1)
def test_r2_to_r2():
# f(x,y) = (x + y, x * y)
x = AD(2, [1,0])
y = AD(3, [0,1])
f = AD([x + y, x*y])
assert len(f.val) == 2
assert (f.val == np.array([5,6])).all()
assert (f.der == np.array([[1,1],[3,2]])).all()
def test_add():
x = AD(2, 1)
f = x + 4
assert f == AD(6, 1)
y = AD(4, 2)
assert x + y == AD(6, 3)
f2 = x + 2 + x + 4
assert f2 == AD(10, 2)
def test_tan():
x = AD(np.pi / 4)
f = 3 * np.tan(x)
assert np.round(f.val, 2) == 3.0
assert np.round(f.der, 2) == 6.0
with np.testing.assert_raises(ValueError):
x = AD(np.pi / 2)
f = np.tan(x)
def test_mul():
x = AD(5, 1)
f1 = x * 3
assert f1 == AD(15, 3)
y = AD(10, 2)
f2 = x * y
assert f2 == AD(50, 20) # 1 * 10 + 5 * 2 = 20
f3 = x * x
assert f3 == AD(25, 10)
def test_r2_to_r1():
# f(x,y) = cos(x) + exp(y)
x = AD(np.pi/2, [1,0])
y = AD(1, [0,1])
f = np.cos(x) + np.exp(y)
assert np.round(f.val,2) == 2.72
assert len(f.der) == 2
assert np.round(f.der[0],2) == -1.0
assert np.round(f.der[1],2) == 2.72
def test_r1_to_r2():
# f(x) = (x^2, sin(x))
x = AD(np.pi/2, 1)
f = AD([x**2, np.sin(x)])
assert len(f.val) == 2
assert np.round(f.val[0], 2) == 2.47
assert np.round(f.val[1], 2) == 1.00
assert len(f.der) == 2
assert np.round(f.der[0], 2) == 3.14
assert np.round(f.der[1], 2) == 0
def test_arccos():
with np.testing.assert_raises(ValueError):
x = AD(-2)
f = np.arccos(x)
with np.testing.assert_raises(ZeroDivisionError):
x = AD(-1)
f = np.arccos(x)
x = AD(0)
f = np.arccos(x)
assert np.round(f.val, 2) == 1.57
assert np.round(f.der, 2) == -1.00
def test_rtruediv():
x = AD(2)
f = 1 / x
assert np.round(f.val, 2) == 0.5
assert np.round(f.der, 2) == -0.25
f3 = 2 / x / x
assert f3 == AD(0.50, -0.50)
with np.testing.assert_raises(ZeroDivisionError):
z = AD(0, 3)
f4 = 10/z
def test_truediv():
x = AD(3)
f = x / 2
assert np.round(f.val, 2) == 1.5
assert np.round(f.der, 2) == 0.5
y = AD(3)
f2 = x / y
assert f2 == AD(1.0, 0.0)
with np.testing.assert_raises(ZeroDivisionError):
f3 = x/0
with np.testing.assert_raises(ZeroDivisionError):
z = AD(0, 3)
f4 = x/z
def test_logistic():
a = 0.5
loga = 0.5 + 0.5 * np.tanh(a/2)
x = AD(a)
f = x.logistic()
assert np.round(f.val,2) == np.round(loga,2)
assert np.round(f.der, 2) == np.round(np.exp(a) / (np.exp(a)+1)**2, 2)
def test_rpow():
x = AD(3)
f = 2 ** x# 2**x * log(2)
assert f.val == 8
assert np.round(f.der,2) == 5.55 # 2**3 * ln(2)
f2 = 0 ** x
assert f2.val == 0
assert f2.der == 0
x = AD(0)
f3 = 0 ** x
assert f3 == AD(1,0)
with np.testing.assert_raises(ZeroDivisionError):
x = AD(-1,1)
f4 = 0 ** x
with np.testing.assert_raises(ValueError):
f3 = (-1) ** x
def test_sub():
x = AD(5)
f = x - 6
assert f == AD(-1, 1)
y = AD(4, 2)
assert x - y == AD(1, -1)
f2 = x - x - x - 1
assert f2 == AD(-6, -1)
assert x == AD(5, 1)
def test_gt():
x = AD(2)
y = AD(3)
assert x > 0
assert y > 0
assert y > x
def test_le():
x = AD(2)
y = AD(3)
assert x <= 2
assert x <= y
assert y <= 3
def test_lt():
x = AD(2)
y = AD(3)
assert x < y
assert x < 10 and y < 10
def test_eq():
x = AD(1.5,1)
assert x == 1.5
x = AD(2, [3,2])
y = AD(2, [3,2])
assert x == y
def test_arctan():
x = AD(1)
f = np.arctan(x)
assert np.round(f.val, 2) == 0.79
assert np.round(f.der, 2) == 0.50
def test_sinh():
x = AD(0.5)
f = np.sinh(x)
assert np.round(f.val, 2) == 0.52
assert np.round(f.der, 2) == 1.13
def test_sin():
x = AD(np.pi / 2)
f = 2 * np.sin(x)
assert np.round(f.val, 2) == 2.0
assert np.round(f.der, 2) == 0.0
def test_cosh():
x = AD(0.5)
f = np.cosh(x)
assert np.round(f.val, 2) == 1.13
assert np.round(f.der, 2) == 0.52
def test_ge():
x = AD(2)
y = AD(3)
assert x>=2
assert y>=2
assert y>=x
def test_tanh():
x = AD(0.5)
f = np.tanh(x)
assert np.round(f.val, 2) == np.round(np.tanh(0.5),2)
assert np.round(f.der, 2) == np.round(1/(np.cosh(0.5) ** 2), 2)
def test_negative():
x = AD(10)
f = -x
assert f == AD(-10, -1)
def test_ne():
x = AD(1.5,1)
y = AD(1.5,2)
assert x != y
assert x != 2
def test_radd():
x = AD(2)
f = 4 + x
assert f == AD(6, 1)
assert x == AD(2, 1)
def test_cos():
x = AD(np.pi / 2)
f = 2 * np.cos(x)
assert np.round(f.val, 2) == 0.0
assert np.round(f.der, 2) == -2.0
def test_rsub():
x = AD(5)
f = 6 - x
assert f == AD(1, -1)
assert x == AD(5)
def test_exp():
x = AD(5)
f = np.exp(x)
assert np.round(f.val,2) == 148.41
assert np.round(f.der,2) == 148.41