def tan(x):
try:
return Dual(np.tan(x.val),
x.der * (1 / np.cos(x.val))**2, (1 / np.cos(x.val)**2) *
(x.der2 + 2 * x.der**2 * np.tan(x.val)))
except:
return np.tan(x)
def relu(x):
try:
u = np.maximum(0, x.val)
v = np.where(u > 0, 1, 0)
return Dual(u, x.der * v, 0)
except:
return np.maximum(0, x)
def test_sin():
assert (el.sin(3) == pytest.approx(0.1411, 0.001))
x = Dual(3, 3, 1)
sinx = el.sin(x)
assert (sinx.val == pytest.approx(0.1411, 0.001))
assert (sinx.der == pytest.approx(-2.9699, 0.001))
assert (sinx.der2 == pytest.approx(-2.260, 0.001))
def test_arctanh():
assert (el.arctanh(0.6) == pytest.approx(0.6931, 0.001))
x = Dual(0.5, 2, 3)
arctanhx = el.arctanh(x)
assert (arctanhx.val == pytest.approx(0.5493, 0.001))
assert (arctanhx.der == pytest.approx(1.333 * 2, 0.001))
assert (arctanhx.der2 == pytest.approx(11.11111, 0.001))
def test_exp2():
assert (el.exp2(0) == pytest.approx(1))
assert (el.exp2(4) == pytest.approx(16))
x = Dual(4, 4, 1)
x2 = el.exp2(x)
assert (x2.val == pytest.approx(16))
assert (x2.der == pytest.approx(44.361, 0.001))
def arctanh(x):
try:
return Dual(np.arctanh(x.val), -1 * x.der * 1 / (x.val**2 - 1),
(-1 * x.val**2 * x.der2 + x.der2 + 2 * x.val * x.der**2) /
(1 - x.val**2)**2)
except:
return np.arctanh(x)
def test_neg():
x = Dual(10, [1, 0], [1, 0])
z = -x
assert(z.val == -10)
assert(all(z.der == [-1, 0]))
assert(all(z.der2 == [-1, 0]))
def test_log():
assert (el.log(27) == pytest.approx(3.2958, 0.001))
x = Dual(3, 5, 2)
lnx = el.log(x)
assert (lnx.val == pytest.approx(1.098, 0.001))
assert (lnx.der == pytest.approx(1.6666, 0.001))
assert (lnx.der2 == pytest.approx(-2.11111, 0.001))
def test_arccosh():
assert (el.arccosh(2) == pytest.approx(1.3169, 0.001))
x = Dual(3, 2, 1)
arccoshx = el.arccosh(x)
assert (arccoshx.val == pytest.approx(1.7627, 0.001))
assert (arccoshx.der == pytest.approx(0.3535 * 2, 0.001))
assert (arccoshx.der2 == pytest.approx(-0.17677, 0.001))
def test_log2():
assert (el.log2(8) == pytest.approx(3))
x = Dual(4, 8, 3)
log2x = el.log2(x)
assert (log2x.val == pytest.approx(2))
assert (log2x.der == pytest.approx(2.8853, 0.001))
assert (log2x.der2 == pytest.approx(-4.68875, 0.001))
def arcsinh(x):
try:
return Dual(np.arcsinh(x.val), x.der * 1 / np.sqrt(x.val**2 + 1),
(x.val**2 * x.der2 + x.der2 - x.val * x.der**2) /
(x.val**2 + 1)**(3 / 2))
except:
return np.arcsinh(x)
def tanh(x):
try:
return Dual(np.tanh(x.val), x.der * 1 / (np.cosh(x.val)**2),
(1 / np.cosh(x.val))**2 *
(x.der2 - 2 * x.der**2 * np.tanh(x.val)))
except:
return np.tanh(x)
def arctan(x):
try:
return Dual(np.arctan(x.val), x.der * 1 / (x.val**2 + 1),
((x.val**2 + 1) * x.der2 - 2 * x.val * x.der**2) /
(x.val**2 + 1)**2)
except:
return np.arctan(x)
def arcsin(x):
try:
return Dual(np.arcsin(x.val), x.der * 1 / (np.sqrt(1 - x.val**2)),
(x.val * x.der**2 -
(x.val**2 - 1) * x.der2) / (1 - x.val**2)**(3 / 2))
except:
return np.arcsin(x)
def test_rmul():
x = 2
y = Dual(3, [0, 1], [0, 1])
z = x * y
assert(z.val == 6)
assert(all(z.der == [0, 2]))
assert(all(z.der2 == [0, 2]))
def test_rsub():
x = 2
y = Dual(3, [0, 1], [0, 1])
z = x - y
assert(z == -1)
assert(all(z.der == [0, 1]))
assert(all(z.der2 == [0, 1]))
def exp2(x):
try:
return Dual(
np.exp2(x.val),
np.exp2(x.val) * (x.der * np.log(2)),
np.log(2) * np.exp2(x.val) * (x.der2 + np.log(2) * x.der**2))
except:
return np.exp2(x)
def test_radd():
x = 2
y = Dual(3, [0, 1], [0, 1])
z = x + y
assert(z.val == 5)
assert(all(z.der == [0, 1]))
assert(all(z.der2 == [0, 1]))
def arccos(x):
try:
return Dual(
np.arccos(x.val), -1 * x.der * 1 / (np.sqrt(1 - x.val**2)),
-1 * (x.val**2 * -1 * (x.der2) + x.der2 + x.val * x.der**2) /
(1 - x.val**2)**(3 / 2))
except:
return np.arccos(x)
def _eval(self, pos, wrt_variables = False):
if isinstance(pos, collections.Iterable):
if wrt_variables:
params = []
for cursor, pos_i in enumerate(pos):
der_partials = np.zeros(self.num_params)
der_partials[cursor] = 1
params.append(Dual(pos_i, der_partials, np.zeros(self.num_params)))
else:
params = [Dual(pos_i,1,0) for pos_i in pos]
return self.func(*params)
else:
if wrt_variables:
params = Dual(pos,[1],[0])
else:
params = Dual(pos,1,0)
return self.func(params)
def test_exp():
assert (el.exp(0) == pytest.approx(1))
assert (el.exp(5)) == pytest.approx(148.413159, 0.0001)
x = Dual(3, 4, 5)
ex = el.exp(x)
assert (ex.val == pytest.approx(20.0855369, 0.0001))
assert (ex.der == pytest.approx(80.3421476, 0.0001))
assert (ex.der2 == pytest.approx(421.7962, 0.001))
def arccosh(x):
try:
return Dual(
np.arccosh(x.val),
x.der * (1 / np.sqrt(x.val - 1) * 1 / (np.sqrt(x.val + 1))),
(x.val**2 * x.der2 - x.der2 - x.val * x.der**2) /
((x.val - 1)**(3 / 2) * (x.val + 1)**(3 / 2)))
except:
return np.arccosh(x)
def _eval_func(func, args, der_attr):
if isinstance(args, collections.Iterable):
params = []
for cursor, arg in enumerate(args):
der_partials = np.zeros(len(args))
der_partials[cursor] = 1
params.append(Dual(arg, der_partials, np.zeros(len(args))))
res = func(*params)
if isinstance(res, collections.Iterable):
return [getattr(i, der_attr) for i in res]
else:
return getattr(res, der_attr)
else:
args = Dual(args,[1],[0])
res = func(args)
if isinstance(res, collections.Iterable):
return [getattr(i, der_attr) for i in res]
else:
return getattr(res, der_attr)
def test_rpow():
x = 2
y = Dual(3, [0, 1], [0, 1])
z = x**y
assert(z.val == 8)
assert(z.der[0] == 0)
assert(z.der[1] == pytest.approx(5.54517744))
assert(z.der2[0] == 0)
assert(z.der2[1] == pytest.approx(9.38880156))
def test_rtruediv():
x = 6
y = Dual(3, [0, 1], [0, 1])
z = x / y
assert(z.val == 2)
assert(z.der[0] == 0)
assert(z.der[1] == pytest.approx(-0.66666667))
assert(z.der2[0] == 0)
assert(z.der2[1] == pytest.approx(-0.2222222))
def test_pow():
x = Dual(2, [1, 0], [1, 0])
y = Dual(3, [0, 1], [0, 1])
z1 = x**y
assert(z1.val == 8)
assert(z1.der[0] == 12)
assert(z1.der[1] == pytest.approx(5.54517744))
assert(z1.der2[0] == 24)
assert(z1.der2[1] == pytest.approx(9.38880156))
z2 = x**x
assert(z2.val == 4)
assert(z2.der[0] == pytest.approx(6.77258872))
assert(z2.der[1] == 0)
assert(z2.der2[0] == pytest.approx(20.23957822))
assert(z2.der2[1] == 0)
def test_neq():
x = Dual(10, [1, 0], [1,0])
y = Dual(10, [0, 1], [1,0])
result = (x != y)
assert(result == True)
def test_sigmoid():
assert (el.sigmoid(5) == pytest.approx(0.9933, 0.001))
x = Dual(2, 3, 1)
sigmoidx = el.sigmoid(x)
assert (sigmoidx.val == pytest.approx(0.8807, 0.001))
assert (sigmoidx.der == pytest.approx(0.10499 * 3, 0.001))
def test_repr():
x = Dual(10, [1, 0], [1, 0])
assert(repr(x) == '[10, [1 0], [1 0]]')
def test_eq():
x = Dual(10, [1, 0], [1,0])
y = Dual(10, [1, 0], [1,0])
result = (x == y)
assert(result == True)