def test_eq():
a = Ad_Var(1, -1)
b = Ad_Var(1, -1)
print(a)
assert a == b
x = Ad_Var(1, np.array([1, 0]))
y = Ad_Var(1, np.array([1, 0]))
print(x)
assert (x == y).all()
def test_pow():
## scalar
a = Ad_Var(1, -3)
b = a**2
assert b.get_val() == 1
assert b.get_ders() == -6
## scalar (rpow)
c = Ad_Var(2)
try:
_ = 'not a number'**c
except TypeError:
print("TypeError successfully caught - rpow")
d = 2**c
assert d.get_val() == 4
assert d.get_ders() == np.log(2) * 4
## sqrt
e = Ad_Var(4)
assert e.sqrt().get_val() == 2.0
assert e.sqrt().get_ders() == 0.25
## gradient
x1 = Ad_Var(1, np.array([1, 0]))
x2 = Ad_Var(2, np.array([0, 1]))
f = x1**2 + x2**(-3)
assert f.get_val() == 1.125
assert (f.get_ders() == [2, -3 / 16]).all()
try:
a = Ad_Var(1, 3)
b = a**'s'
except TypeError:
print("TypeError sucessfully catched - pow")
## gradient (rpow)
f2 = 2**x1 + 2**x2
assert f2.get_val() == 6.0
assert (f.get_ders() == [2., -3 / 16]).all()
def test_neg():
## scaler
a = Ad_Var(1, -3)
b = -a
assert b.get_val() == -1
assert b.get_ders() == 3
## gradient
x1 = Ad_Var(1, np.array([1, 0]))
x2 = -x1
assert x2.get_val() == -1
assert (x2.get_ders() == [-1, 0]).all()
def test_exp():
## scaler
a = Ad_Var(1, -3)
b = Ad_Var.exp(a)
assert b.get_val() == np.exp(1)
assert b.get_ders() == -3 * np.exp(1)
## gradient
x1 = Ad_Var(1, np.array([1, 0]))
x2 = Ad_Var(1, np.array([0, 1]))
f = Ad_Var.exp(x1 + x2)
assert f.get_val() == np.exp(1 + 1)
assert (f.get_ders() == [np.exp(1 + 1), np.exp(1 + 1)]).all()
def test_log():
## scaler
a = Ad_Var(1, -3)
b = Ad_Var.log(a)
assert b.get_val() == np.log(1)
assert b.get_ders() == -3
## gradient
x1 = Ad_Var(1, np.array([1, 0]))
x2 = Ad_Var(1, np.array([0, 1]))
f = Ad_Var.log(x1 + x2)
assert f.get_val() == np.log(1 + 1)
assert (f.get_ders() == [1 / 2, 1 / 2]).all()
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()
def test_eq_input():
x = Ad_Var(1, np.array([1, 0, 0]))
y = Ad_Var(2, 1)
try:
x == y
except TypeError:
print("TypeERror successfully caught - Equality operator test 1")
try:
x != y
except TypeError:
print("TypeERror successfully caught - Equality operator test 2")
try:
y != x
except TypeError:
print("TypeERror successfully caught - Equality operator test 3")
def test_hyperbolic():
## scalar
a = Ad_Var(0.1, -3)
b = Ad_Var.sinh(a)
c = Ad_Var.cosh(a)
d = Ad_Var.tanh(a)
assert b.get_val() == np.sinh(0.1)
assert b.get_ders() == -3 * np.cosh(0.1)
assert c.get_val() == np.cosh(0.1)
assert c.get_ders() == -3 * np.sinh(0.1)
assert d.get_val() == np.tanh(0.1)
assert d.get_ders() == -3 * (1 - np.tanh(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.sinh(x1) + Ad_Var.cosh(x2) - Ad_Var.tanh(x3)
assert f.get_val() == np.sinh(0.1) + np.cosh(0.2) - np.tanh(0.3)
assert (f.get_ders() == [np.cosh(0.1),
np.sinh(0.2), -1 + np.tanh(0.3)**2]).all()
def test_trig():
## scaler
a = Ad_Var(np.pi / 4, -3)
b = Ad_Var.sin(a)
c = Ad_Var.cos(a)
d = Ad_Var.tan(a)
assert b.get_val() == np.sin(np.pi / 4)
assert b.get_ders() == -3 * np.cos(np.pi / 4)
assert c.get_val() == np.cos(np.pi / 4)
assert c.get_ders() == 3 * np.sin(np.pi / 4)
assert d.get_val() == np.tan(np.pi / 4)
assert d.get_ders() == -3 / np.cos(np.pi / 4)**2
## gradient
x1 = Ad_Var(np.pi / 4, np.array([1, 0, 0]))
x2 = Ad_Var(np.pi / 4, np.array([0, 1, 0]))
x3 = Ad_Var(np.pi / 4, np.array([0, 0, 1]))
f = Ad_Var.sin(x1) + Ad_Var.cos(x2) + Ad_Var.tan(x3)
assert f.get_val() == 2**0.5 + 1
assert (f.get_ders() == [
np.cos(np.pi / 4), -np.sin(np.pi / 4), 1 / np.cos(np.pi / 4)**2
]).all()
def test_comparison():
## scaler
a = Ad_Var(1, -3)
b = Ad_Var(1, -3)
c = Ad_Var(2, 4)
assert a == b
assert a != c
## gradient
x1 = Ad_Var(1, np.array([1, 0]))
x2 = Ad_Var(1, np.array([1, 0]))
x3 = Ad_Var(1, np.array([2, 0]))
assert x1 == x2
assert x1 != x3
try:
a == x1
except TypeError:
print("TypeError successfully caught - comparison")
try:
x1 == a
except TypeError:
print("TypeError successfully caught - comparison")
try:
a != x1
except TypeError:
print("TypeError successfully caught - comparison")
try:
x1 != a
except TypeError:
print("TypeError successfully caught - comparison")
def test_input():
try:
f = Ad_Var('s', 2)
except TypeError:
print("TypeError sucessfully catched - value1")
try:
f = Ad_Var([2, 3, 4], 2)
except TypeError:
print("TypeError sucessfully catched - value2")
try:
f = Ad_Var(2, 's')
except TypeError:
print("TypeError sucessfully catched - der1")
try:
f = Ad_Var(2, np.array([1, 2, 'dog']))
except TypeError:
print("TypeError sucessfully catched - der2")
try:
a = Ad_Var(20)
b = rAd_Var(5)
f = a + b
except TypeError:
print("TypeError successfully catched - _typecheck_other")
def test_input():
try:
print(rAd_Var('NaN'))
except TypeError:
print("Input test 1 passed.")
try:
print(rAd_Var(None))
except TypeError:
print("Input test 2 passed.")
try:
_ = rAd_Var(5) + Ad_Var(5)
except TypeError:
print("rAd_Var and Ad_Var incompatibility check passed.")
a = rAd_Var(np.array([42]))
a.set_val(5)
assert (a.get_val() == 5)
print("Testing for __str__ method:\n", a)
repr(a)
def test_logistic():
def sigmoid(x):
return 1.0 / (1 + np.exp(-x))
def sigmoid_derivative(x):
der = (1 - sigmoid(x)) * sigmoid(x)
return der
a = Ad_Var(1, 2)
b = Ad_Var.logistic(a)
assert b.get_val() == sigmoid(1)
assert b.get_ders() == 2 * sigmoid_derivative(1)
x1 = Ad_Var(0.1, np.array([1, 0]))
x2 = Ad_Var(0.2, np.array([0, 1]))
f = Ad_Var.logistic(x1) - Ad_Var.logistic(x2)
assert f.get_val() == sigmoid(0.1) - sigmoid(0.2)
assert (f.get_ders() == [
sigmoid_derivative(0.1), -sigmoid_derivative(0.2)
]).all()
def test_mul1():
x1 = Ad_Var(1, np.array([1, 0]))
x2 = Ad_Var(2, np.array([0, 1]))
f = (x1 + 1) * x2
assert f.get_val() == 4
assert (f.get_ders() == [2, 2]).all()
def test_set_ders():
x1 = Ad_Var(1)
x1.set_ders(2)
def test_sub2():
x1 = Ad_Var(1)
x2 = 2
f = x2 - x1
assert f.get_val() == 1
assert f.get_ders() == -1
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_grid_eval():
#scalar function - one variable
x = Ad_Var()
f_str = "x**2 + 2*x"
dict = Ad_Var.grid_eval(f_str, ['x'], [x], [[2, 5]])
assert dict[(2, )] == (8, 6)
assert dict[(5, )] == (35, 12)
#scalar function - two variables
x = Ad_Var(ders=np.array([1, 0]))
y = Ad_Var(ders=np.array([0, 1]))
f_str = "x**2 * 3*y"
dict = Ad_Var.grid_eval(f_str, ['x', 'y'], [x, y], [[1], [2, 3]])
#assert first point of the grid
assert dict[(1, 2)][0] == 6 #assert value
assert (dict[(1, 2)][1] == [12, 3]).all() #assert gradient
#assert second point of grid
assert dict[(1, 3)][0] == 9
assert (dict[(1, 3)][1] == [18, 3]).all()
#vector function - two functions of two variables
f_str = "[x**2 * 3*y, Ad_Var.exp(x)]"
dict = Ad_Var.grid_eval(f_str, ['x', 'y'], [x, y], [[1], [2, 3]])
assert (dict[(1, 2)][0] == np.array(
[6, np.exp(1)])).all() #assert the value of the vector valued function
assert (dict[(1, 2)][1] == np.array([[12, 3],
[np.exp(1),
0]])).all() #assert the jacobian
assert (dict[(1, 3)][0] == np.array(
[9,
np.exp(1)])).all() # assert the value of the vector valued function
assert (dict[(1, 3)][1] == np.array([[18, 3],
[np.exp(1),
0]])).all() # assert the jacobian
try:
f_str = "[x**2 * 3*y, ad.exp(x)]"
dict = Ad_Var.grid_eval(f_str, ['x', 'y'], [x, y], [[1], [2, 3]])
except NameError:
print(
"NameError successfully catched - ad is not the scope of grid_eval, Ad_Var should be used in func_string."
)
try:
f_str = "[x**2 * 3*y, Ad_Var.exp(x)]"
dict = Ad_Var.grid_eval(f_str, ['x', 'y'], [x, y], [[2, 3]])
except ValueError:
print(
"ValueError successfully catched - a list of values for each variable should be passed to create the grid."
)
try:
f_str = "[x**2 * 3*y, Ad_Var.exp(x)]"
dict = Ad_Var.grid_eval(f_str, ['x'], [x, y], [[2, 3]])
except ValueError:
print(
"ValueError successfully catched - list of strings should have equal length to list of Ad_Var objects."
)
try:
f_str = "[x**2 * 3*y, Ad_Var.exp(x)]"
dict = Ad_Var.grid_eval(f_str, ['x', 'a'], [x, y], [[2, 3]])
except NameError:
print("NameError successfully catched - test_grid_eval")
try:
f_str = "import os"
dict = Ad_Var.grid_eval(f_str, ['x', 'y'], [x, y], [[2, 3]])
except ValueError:
print("ValueError successfully catched - test_grid_eval")
try:
f_str = "a*5 + x*y"
dict = Ad_Var.grid_eval(f_str, ['x', 'y'], [x, y], [[2, 3]])
except NameError:
print(
"NameError successfully catched - function string contains a which is not in the variables passed."
)
def test_sub3():
x1 = Ad_Var(1, np.array([1, 0]))
x2 = 2
f = x2 - x1
assert f.get_val() == 1
assert (f.get_ders() == [-1, 0]).all()
def test_sub4():
x1 = Ad_Var(5)
x2 = 3
f = x1 - x2
assert f.get_val() == 2
assert f.get_ders() == 1
def test_div1():
x1 = Ad_Var(1, np.array([1, 0]))
x2 = Ad_Var(2, np.array([0, 1]))
f = (x1 + 1) / x2
assert f.get_val() == 1
assert (f.get_ders() == [1 / 2, -1 / 2]).all()
def test_div2():
x1 = Ad_Var(1)
x2 = 2
f = (x1 + 1) / x2 + x2 / (x1 + 1)
assert f.get_val() == 2
assert f.get_ders() == 0 #1/2 - 1/2
def test_setters():
a = Ad_Var(1, -3)
a.set_val(2)
a.set_ders(2)
assert a.get_val() == 2
assert a.get_ders() == 2
def test_mul2():
x1 = Ad_Var(1)
x2 = 2
f = (x1 + 1) * x2 + x2 * (x1 + 1)
assert f.get_val() == 8
assert f.get_ders() == 4
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")