def test_inverse_trig():
## scalar
a = Ad_Var(0.1, -3)
b = Ad_Var.arcsin(a)
c = Ad_Var.arccos(a)
d = Ad_Var.arctan(a)
assert b.get_val() == np.arcsin(0.1)
assert b.get_ders() == -3 / np.sqrt(1 - 0.1**2)
assert c.get_val() == np.arccos(0.1)
assert c.get_ders() == 3 / np.sqrt(1 - 0.1**2)
assert d.get_val() == np.arctan(0.1)
assert d.get_ders() == -3 / (1 + 0.1**2)
## gradient
x1 = Ad_Var(0.1, np.array([1, 0, 0]))
x2 = Ad_Var(0.2, np.array([0, 1, 0]))
x3 = Ad_Var(0.3, np.array([0, 0, 1]))
f = Ad_Var.arcsin(x1) + Ad_Var.arccos(x2) + Ad_Var.arctan(x3)
assert f.get_val() == 1.7610626216439926
assert (f.get_ders() == [
1.005037815259212, -1.0206207261596576, 0.9174311926605504
]).all()
e = Ad_Var(-3, 2)
try:
f = Ad_Var.arcsin(e)
except ValueError:
print("ValueError successfully caught - inversetsin")
try:
f = Ad_Var.arccos(e)
except ValueError:
print("ValueError successfully caught - inversecos")
try:
f = Ad_Var.arctan(e)
except ValueError:
print("ValueError successfully caught - inversetan")
def test_func():
x = Ad_Var(1, np.array([1, 0, 0]))
y = Ad_Var(2, np.array([0, 1, 0]))
z = 's'
try:
f = np.array([
Ad_Var.cos(x) * (y + 2), 1 + y**2 / (x * y * 3),
3 * Ad_Var.log(x * 2) + Ad_Var.exp(x / y),
Ad_Var.arctan(Ad_Var.arcsin(y / 4))
])
Ad_Var.get_values(f, z)
except TypeError:
print("TypeError sucessfully catched - get_values1")
try:
Ad_Var.get_values([3, 2, 1])
except TypeError:
print("TypeError sucessfully catched - get_values2")
try:
f = np.array([
Ad_Var.cos(x) * (y + 2), 1 + y**2 / (x * y * 3),
3 * Ad_Var.log(x * 2) + Ad_Var.exp(x / y),
Ad_Var.arctan(Ad_Var.arcsin(y / 4))
])
Ad_Var.get_jacobian(f, z)
except TypeError:
print("TypeError sucessfully catched - get_jacobian1")
try:
f = np.array([
Ad_Var.cos(x) * (y + 2), 1 + y**2 / (x * y * 3),
3 * Ad_Var.log(x * 2) + Ad_Var.exp(x / y),
Ad_Var.arctan(Ad_Var.arcsin(y / 4))
])
Ad_Var.get_jacobian([1, 2, 3], 3, 2)
except TypeError:
print("TypeError sucessfully catched - get_jacobian2")
try:
f = np.array([
Ad_Var.cos(x) * (y + 2), 1 + x**2 / (x * y * 3),
3 * Ad_Var.log(x * 2) + Ad_Var.exp(x / y),
Ad_Var.arctan(Ad_Var.arcsin(y / 4))
])
Ad_Var.get_jacobian(f, 5, 4)
except ValueError:
print("ValueError sucessfully catched - get_jacobian3")
def test_multiple():
x = Ad_Var(1, np.array([1, 0, 0]))
y = Ad_Var(2, np.array([0, 1, 0]))
z = Ad_Var(3, np.array([0, 0, 1]))
f = np.array([
Ad_Var.cos(x) * (y + 2), 1 + z**2 / (x * y * 3),
3 * Ad_Var.log(x * 2) + Ad_Var.exp(x / z),
Ad_Var.arctan(Ad_Var.arcsin(y / 4))
])
assert (Ad_Var.get_values(f) == [
np.cos(1) * 4, 1 + 3**2 / 6, 3 * np.log(2) + np.exp(1 / 3),
np.arctan(np.arcsin(1 / 2))
]).all()
assert (Ad_Var.get_jacobian(f, 4, 3) == [
[-4 * np.sin(1), np.cos(1), 0], [-1.5, -0.75, 1],
[3 + np.exp(1 / 3) / 3, 0, -np.exp(1 / 3) / 9],
[0, 1 / (4 * (np.sqrt(3 / 4)) * (np.arcsin(1 / 2)**2 + 1)), 0]
]).all()