def test_basic_multiplication_v():
x = FD(3, 1)
y = FD(2, 0)
derivative = x * y
assert ((float(derivative.val) == 6.0) &
(float(derivative.der)
== 2.0)), Exception(f'test_basic_multiplication_v() has error.')
def test_basic_addition_v():
x = FD(3, 1)
y = FD(2, 0)
derivative = x + y
assert (float(derivative.get_value()) == 5.0) & (float(
derivative.get_derivative()) == 1.0), Exception(
f'test_basic_addition_c() has error.')
def test_basic_power_v1():
x = FD(3, 1)
y = FD(2, 0)
derivative = x**y
assert ((float(derivative.val) == 9.0) &
(float(derivative.der)
== 6.0)), Exception(f'test_basic_power_v1() has error.')
def test_basic_subtraction_v():
x = FD(3, 1)
y = FD(2, 0)
derivative = x - y
assert ((float(derivative.val)) == 1.0) & (float(
derivative.der) == 1.0), Exception(
f'test_basic_subtraction_v() has error.')
def test_basic_logarithm_v():
x = FD(3, 1)
y = FD(2, 2)
derivative = FD.logarithm(x, np.e)
assert (float(derivative.val) == np.log(3)) & (float(
derivative.der) == 1 / 3), Exception(
f'test_basic_logarithm_v() has error.')
derivative2 = FD.logarithm([x, y], base=np.e)
assert (float(derivative2[1].val) == np.log(2)) & (float(
derivative2[1].der) == 1), Exception(
f'test_basic_logarithm_v() has error.')
def test_basic_logistic_v():
x = FD(3, 1)
y = FD(2, 2)
derivative = FD.logistic(x)
assert (float(derivative.val) == 1 / (1 + np.e**(-3))) & (
float(derivative.der) == (np.e**(3)) /
(1 + np.e**(3))**2), Exception(f'test_basic_logistic_v() has error.')
derivative2 = FD.logistic([x, y])
assert (float(derivative2[1].val) == 1 / (1 + np.e**(-2))) & (
float(derivative2[1].der) == 2 * (np.e**(2)) /
(1 + np.e**(2))**2), Exception(f'test_basic_logistic_v() has error.')
def Jacobian(arr):
# initialize with input value
num_var = len(arr)
output = [[] for x in range(num_var)]
for i in range(num_var):
for j in range(num_var):
if i == j:
output[i].append(FD(arr[i], 1))
else:
output[i].append(FD(arr[i], 0))
return np.array(output)
def test_function_jacobian():
x = Jacobian([1, 3, 4])
fun = np.sin(3 * x[0] + 2 * x[1] - x[2])
assert isinstance(fun[0], FD), AssertionError('Not an instance of AD.')
assert isinstance(fun[0].val, int) or isinstance(
fun[0].val, float), AssertionError('Value is not a number.')
assert isinstance(fun[0].der, int) or isinstance(
fun[0].der, float), AssertionError('Derivative is not a number.')
jacob = FD.get_derivatives(fun)
values = FD.get_values(fun)
assert isinstance(jacob[0], np.ndarray), AssertionError(
"get_derivatives method doesn't return numpy ndarray")
assert isinstance(values[0], np.ndarray), AssertionError(
"get_values method doesn't return numpy ndarray")
def test_multiple_functions_jacobian():
x = Jacobian([1, 3, 4])
fun = [np.sin(3 * x[0] + 2 * x[1] - x[2]), x[0]**x[1] - x[2]]
assert len(fun) == 2, AssertionError(
"Didn't return correct number of functions.")
assert len(fun[0]) == 3, AssertionError(
"Didn't return correct number of variables.")
assert isinstance(fun[0][0], FD), AssertionError('Not an instance of AD.')
assert isinstance(fun[0][0].val, int) or isinstance(
fun[0][0].val, float), AssertionError('Value is not a number.')
assert isinstance(fun[0][0].der, int) or isinstance(
fun[0][0].der, float), AssertionError('Derivative is not a number.')
jacob = FD.get_derivatives(fun)
values = FD.get_values(fun)
assert jacob.shape == (
2,
3), AssertionError("Jacobian Matrix doesn't have correct dimensions")
assert values.shape == (
2, 3), AssertionError("Values Matrix doesn't have correct dimensions")
assert isinstance(jacob[0], np.ndarray), AssertionError(
"get_derivatives method doesn't return numpy ndarray")
assert isinstance(values[0], np.ndarray), AssertionError(
"get_values method doesn't return numpy ndarray")
def test_basic_rmul_c():
x = FD(3, 1)
derivative = 2 * x
assert ((float(derivative.val) == 6.0) & (float(
derivative.der) == 2.0)), Exception(f'test_basic_rmul_c() has error.')
def test_basic_div_c():
x = FD(3, 1)
derivative = x / 2
assert ((float(derivative.val) == 1.50) & (float(
derivative.der) == 0.5)), Exception(f'test_basic_div_c() has error.')
def test_basic_addition_c():
x = FD(3, 1)
derivative = x + 2
assert (float(derivative.val) == 5.0) & (float(
derivative.der) == 1.0), Exception(
f'test_basic_addition_c() has error.')
def test_basic_rsub_v():
x = FD(3, 1)
y = FD(2, 0)
derivative = y - x
assert ((float(derivative.val) == -1.0) & (float(
derivative.der) == -1.0)), Exception(f'test_basic_rsub_v() has error.')
def test_basic_str():
x = FD(3, 1)
assert str(x) == 'FD(3, 1)'
def test_basic_arccos_v():
x = FD(0.5, 1)
derivative = FD.arccos(x)
assert (float(derivative.val) == np.arccos(0.5)) & (float(
derivative.der) == -1 / np.sqrt(1 - 0.5**2)), Exception(
f'test_basic_arccos_v() has error.')
def test_basic_ne_v():
x = FD(3, 1)
y = FD(2, 0)
assert x != y, Exception(f'test_basic_ne_v() has error.')
def test_basic_rpow_c():
x = FD(3, 1)
derivative = 2**x
assert (float(derivative.val)
== 8.0) & (float(derivative.der) == 8 *
np.log(2)), Exception(f'test_basic_rpow_c() has error.')
def test_basic_sqrt_v():
x = FD(3, 1)
derivative = FD.sqrt(x)
assert (float(derivative.val) == np.sqrt(3)) & (float(
derivative.der) == 0.5 * 3**(-0.5)), Exception(
f'test_basic_sqrt_v() has error.')
def test_basic_radd_c():
x = FD(3, 1)
derivative = 2 + x
assert ((float(derivative.val)) == 5.0) & (float(
derivative.der) == 1.0), Exception(f'test_basic_radd_c() has error.')
def test_basic_tanh_v():
x = FD(3, 1)
derivative = FD.tanh(x)
assert (float(derivative.val) == np.tanh(3)) & (float(
derivative.der) == 1 / np.cosh(3)**2), Exception(
f'test_basic_tanh_v() has error.')
def test_basic_arctan_v():
x = FD(3, 1)
derivative = FD.arctan(x)
assert (float(derivative.val) == np.arctan(3)) & (
float(derivative.der) == 1 /
(1 + 3**2)), Exception(f'test_basic_arctan_v() has error.')
def test_basic_neg_v():
x = FD(3, 1)
derivative = -x
assert (float(derivative.val) == -3.0) & (float(
derivative.der) == -1.0), Exception(f'test_basic_neg_v() has error.')
def test_basic_power_v2():
x = FD(-1, 1)
y = FD(2, 1)
derivative = x**y
assert ((float(derivative.val) == 1) & (float(
derivative.der) == -2)), Exception(f'test_basic_power_v2() has error.')
def test_basic_rdiv_c(): # Account for when the divisor is 0
x = FD(3, 1)
derivative = 2 / x
assert (float(derivative.val) == (2 / 3)) & (float(
derivative.der) == -(2 / 9)), Exception(
f'test_basic_rdiv_c() has error.')
def test_basic_exponential_v():
x = FD(3, 1)
derivative = np.exp(x)
assert ((float(derivative.val) == np.exp(3)) &
(float(derivative.der) == np.exp(3))
), Exception(f'test_basic_exponential_v() has error.')
def test_basic_repr():
x = FD(3, 1)
assert repr(x) == 'FD(3, 1)'
def test_basic_eq_v():
x = FD(3, 1)
v = FD(3, 1)
assert x == v, Exception(f'test_basic_eq_v() has error.')
def test_basic_cos_v():
x = FD(3, 1)
derivative = FD.cos(x)
assert (float(derivative.val) == np.cos(3)) & (float(
derivative.der) == -np.sin(3)), Exception(
f'test_basic_cos_v() has error.')
