def test_rtruediv():
x = Var(3, np.array([1, 0]))
y = 2
assert y / x == Var(
pytest.approx(0.6666666666666666),
np.array([pytest.approx(-0.22222222),
pytest.approx(-0.)]))
def test_real_pow():
x = Var(3, np.array([1, 0]))
y = 2
assert x**y == Var(9, np.array([6, 0]))
assert y**x == Var(
8, np.array([pytest.approx(5.54517744),
pytest.approx(0.)]))
def test_two_variables():
ad = AD(np.array([2, 2]), np.array([1, 1]))
f1 = lambda x, y: Var.log(x)**Var.sin(y)
assert AD.auto_diff(self=ad, func=f1) == Var(
pytest.approx(0.7165772257590739),
np.array([pytest.approx(0.47001694),
pytest.approx(0.10929465)]))
def __init__(self, vals, ders, mode=AD_Mode.FORWARD):
"""
init the AD class
INPUT
=======
self: an AD class
vals: a list of initial value for a list of variables
ders: a list of initial derivative for a list of variables
mode: the mode for auto-diff, ie, FORWARD or REVERSE
RETURNS
=======
the output of automatic differentiation for the given vals and ders
EXAMPLES
=======
>>> ad = AD(np.array([2, 2]), np.array([1, 1]), AD_Mode.FORWARD)
>>> print(vars(ad.vars[0]), vars(ad.vars[1]))
{'val': 2, 'der': array([1, 0])} {'val': 2, 'der': array([0, 1])}
>>> ad = AD(np.array([2, 2]), np.array([1, 1]), AD_Mode.REVERSE)
>>> print(vars(ad.vars[0]), vars(ad.vars[1]))
{'value': 2, 'children': [], 'grad_value': None} {'value': 2, 'children': [], 'grad_value': None}
"""
self.mode = mode
if self.mode == AD_Mode.FORWARD:
assert (len(vals) == len(ders))
self.vars = []
dimen = len(vals)
cnt = 0
for val, der in zip(vals, ders):
der_list = np.array([0 for i in range(dimen)])
der_list[cnt] = der
self.vars.append(Var(val, der_list))
cnt += 1
else:
self.vals = vals
self.vars = []
for val in self.vals:
self.vars.append(Rev_Var(val))
def auto_diff(self, func):
"""
Passing a function to a AD object, and return the final Var object with val and der.
INPUT
=======
a function
RETURNS
=======
returns the final Var object with val and der
EXAMPLES
=======
>>> f1 = lambda x, y: Var.log(x) ** Var.sin(y)
>>> ad = AD(np.array([2, 2]), np.array([1, 1]), AD_Mode.FORWARD)
>>> print("Var.log(x) ** Var.sin(y): {}".format(vars(ad.auto_diff(f1))))
Var.log(x) ** Var.sin(y): {'val': 0.7165772257590739, 'der': array([0.47001694, 0.10929465])}
>>> f1 = lambda x: Var.log(x) ** 2
>>> ad = AD(np.array([2]), np.array([1]), AD_Mode.FORWARD)
>>> print("Var.log(x) ** 2: {}".format(vars(ad.auto_diff(f1))))
Var.log(x) ** 2: {'val': 0.4804530139182014, 'der': array([0.69314718])}
>>> f1 = lambda x, y: Rev_Var.log(x) ** Rev_Var.sin(y)
>>> ad = AD(np.array([2, 2]), np.array([1, 1]), AD_Mode.REVERSE)
>>> print("Rev_Var.log(x) ** Rev_Var.sin(y): {}".format(vars(ad.auto_diff(f1))))
Rev_Var.log(x) ** Rev_Var.sin(y): {'val': 0.7165772257590739, 'der': array([0.47001694, 0.10929465])}
>>> f1 = lambda x: Rev_Var.log(x) ** 2
>>> ad = AD(np.array([2]), np.array([1]), AD_Mode.REVERSE)
>>> print("Rev_Var.log(x) ** 2: {}".format(vars(ad.auto_diff(f1))))
Rev_Var.log(x) ** 2: {'val': 0.4804530139182014, 'der': array([0.69314718])}
"""
if self.mode == AD_Mode.FORWARD:
return func(*self.vars)
else:
self.clear()
z = func(*self.vars)
z.grad_value = 1.0
res = list(map(lambda x: x.grad(), self.vars))
return Var(z.value, np.array(res)) # provide a unify interface
def test_real_mul():
x = 3
y = Var(2, np.array([0, 1]))
assert x * y == Var(6, np.array([0, 3]))
def test_arctan():
x = Var(0.5, np.array([1]))
y = 0.5
assert Var.arctan(x) == Var(pytest.approx(0.46364760900080615),
np.array([pytest.approx(0.8)]))
assert Var.arctan(y) == np.arctan(y)
def test_equal():
x = Var(3, np.array([1, 0]))
z = Var(3, np.array([1, 0]))
y = 2
assert x == z
assert (x == y) == False
def test_neg():
x = Var(3, np.array([1, 0]))
assert -x == Var(-3, np.array([-1, 0]))
def test_expk():
x = Var(3, np.array([1]))
y = 3
assert Var.expk(x, 4) == Var(64, np.array([pytest.approx(88.72283911)]))
assert Var.expk(y, 4) == 4**3
def test_var_pow():
x = Var(3, np.array([1, 0]))
y = Var(2, np.array([0, 1]))
assert x**y == Var(
9, np.array([pytest.approx(6.0),
pytest.approx(9.8875106)]))
def test_var_mul():
x = Var(3, np.array([1, 0]))
y = Var(2, np.array([0, 1]))
assert x * y == Var(6, np.array([2, 3]))
def test_cosh():
x = Var(0.5, np.array([1]))
y = 0.5
assert Var.cosh(x) == Var(pytest.approx(1.1276259652063807),
np.array([pytest.approx(0.52109531)]))
assert Var.cosh(y) == (np.exp(y) + np.exp(-y)) / 2
def test_sinh():
x = Var(0.5, np.array([1]))
y = 0.5
assert Var.sinh(x) == Var(pytest.approx(0.5210953054937474),
np.array([pytest.approx(1.12762597)]))
assert Var.sinh(y) == (np.exp(y) - np.exp(-y)) / 2
def test_sin():
x = Var(3, np.array([1]))
y = 2
assert Var.sin(x) == Var(pytest.approx(0.1411200080598672),
np.array([pytest.approx(-0.9899925)]))
assert Var.sin(y) == np.sin(y)
def test_sqrt():
x = Var(3, np.array([1]))
y = 2
assert Var.sqrt(x) == Var(pytest.approx(1.7320508075688772),
np.array([pytest.approx(0.28867513)]))
assert Var.sqrt(y) == np.sqrt(y)
def test_logistic():
x = Var(3, np.array([1]))
y = 3
assert Var.logistic(x) == Var(pytest.approx(0.9525741268224334),
np.array([pytest.approx(0.04517666)]))
assert Var.logistic(y) == pytest.approx(0.9525741268224334)
def test_var_sub():
x = Var(3, np.array([1, 0]))
y = Var(2, np.array([0, 1]))
assert x - y == Var(1, np.array([1, -1]))
def test_real_sub():
x = 3
y = Var(2, np.array([0, 1]))
assert x - y == Var(1, np.array([0, -1]))
def test_var_add():
x = Var(3, np.array([1, 0]))
y = Var(2, np.array([0, 1]))
assert x + y == Var(5, np.array([1, 1]))
def test_tanh():
x = Var(0.5, np.array([1]))
y = 0.5
assert Var.tanh(x) == Var(pytest.approx(0.46211715726000985),
np.array([pytest.approx(0.78644773)]))
assert Var.tanh(y) == (np.exp(y) - np.exp(-y)) / (np.exp(y) + np.exp(-y))
def test_exp():
x = Var(3, np.array([1]))
y = 2
assert Var.exp(x) == Var(pytest.approx(20.085536923187668),
np.array([pytest.approx(20.08553692)]))
assert Var.exp(y) == np.exp(y)
def test_truediv():
x = Var(3, np.array([1, 0]))
y = Var(2, np.array([0, 1]))
assert x / y == Var(1.5, np.array([0.5, -0.75]))
def test_cos():
x = Var(3, np.array([1]))
y = 2
assert Var.cos(x) == Var(pytest.approx(-0.9899924966004454),
np.array([pytest.approx(-0.14112001)]))
assert Var.cos(y) == np.cos(y)
def test_div():
x = Var(3, np.array([1, 0]))
y = 2
assert x / y == Var(1.5, np.array([0.5, 0.]))
def test_tan():
x = Var(3, np.array([1]))
y = 2
assert Var.tan(x) == Var(pytest.approx(-0.1425465430742778),
np.array([pytest.approx(1.02031952)]))
assert Var.tan(y) == np.tan(y)
def test_pos():
x = Var(3, np.array([1, 0]))
assert +x == Var(3, np.array([1, 0]))
def test_arcsin():
x = Var(0.5, np.array([1]))
y = 0.5
assert Var.arcsin(x) == Var(pytest.approx(0.5235987755982988),
np.array([pytest.approx(1.15470054)]))
assert Var.arcsin(y) == np.arcsin(y)
def test_notequal():
x = Var(3, np.array([1, 0]))
y = 2
z = Var(2, np.array([0, 1]))
assert x != z
assert (x != y) == True
def test_arccos():
x = Var(0.5, np.array([1]))
y = 0.5
assert Var.arccos(x) == Var(pytest.approx(1.0471975511965976),
np.array([pytest.approx(-1.15470054)]))
assert Var.arccos(y) == np.arccos(y)
