def test_simpleFunc9():
func14_val = lambda x: np.sin(x) / (3 - 2 * np.cos(x))
func14_der = lambda x: (-2 + 3 * np.cos(x)) / (3 - 2 * np.cos(x))**2
a14 = np.pi / 4
x14 = ad.variable(a14)
f14 = ad.sin(x14) / (3 - 2 * ad.cos(x14))
assert np.isclose(f14.val, func14_val(a14))
assert np.isclose(f14.der, func14_der(a14))
def test_simpleFunc6():
func11_val = lambda x: ((x**3) + 4 * x) / np.sin(3)
func11_der = lambda x: ((3 * x**2) + 4) / np.sin(3)
a11 = 6
x11 = ad.variable(a11)
f11 = ((x11**3) + 4 * x11) / ad.sin(3)
assert f11.val == func11_val(a11)
assert f11.der == func11_der(a11)
def test_simpleFunc3():
def f1(x):
return np.sin(x) / 3 + np.cos(x) / x
def f1_dx(x):
return -np.sin(x) / x - np.cos(x) / x**2 + np.cos(x) / 3
x1 = ad.variable(83)
f = ad.sin(x1) / 3 + ad.cos(x1) / x1
assert f.val == f1(83)
assert f.der == f1_dx(83)
def test_sin():
# Sine of variable:
f1 = ad.sin(np.pi)
assert np.isclose(f1.val, 0.0)
assert np.isclose(f1.der, 0.0)
# Sine of variable:
x2 = ad.variable(np.pi)
f2 = ad.sin(x2)
assert np.isclose(f2.val, 0.0)
assert np.isclose(f2.der, -1.0)
# Sine of variable times constant:
x3 = ad.variable(0.0)
f3 = ad.sin(x3) * 5
assert np.isclose(f3.val, 0.0)
assert np.isclose(f3.der, 5.0)
# Sine of constant times variable:
x4 = ad.variable(np.pi)
f4 = ad.sin(x4 * 2)
assert np.isclose(f4.val, 0.0)
assert np.isclose(f4.der, 2.0)
def func1(x):
f1 = (ad.sin(x))**2
return f1
def func5(x, y):
f1 = x * y + ad.cos(x)
f2 = x * y + ad.sin(y)
return [f1, f2]
def root_finding(a):
return ad.sin(a)