def test_rev_mul():
x = Rev_Var(0.5)
y = Rev_Var(4.2)
z = x * y
z.grad_value = 1.0
assert z.value == 2.1
assert x.grad() == pytest.approx(y.value)
def test_rev_rpow():
x = Rev_Var(0.5)
a = 3
z = 3**x
z.grad_value = 1
assert z.value == pytest.approx(1.7320508075688772)
assert x.grad() == pytest.approx(1.902852301792692)
def test_rev_add():
x = Rev_Var(0.5)
y = Rev_Var(4.2)
z = x + y
z.grad_value = 1.0
assert z.value == 4.7
assert y.grad() == 1
def test_rtruediv():
x = Rev_Var(0.5)
y = 5
z = x / y
z.grad_value = 1.0
assert z.value == 0.1
assert x.grad() == 0.2
def test_tahh():
x = Rev_Var(2.0)
z = Rev_Var.tanh(x)
z.grad_value = 1
z4 = Rev_Var.tanh(2)
assert z.value == pytest.approx(0.964027580075817)
assert z4 == (np.exp(2) - np.exp(-2)) / (np.exp(2) + np.exp(-2))
assert x.grad() == pytest.approx(0.07065082485316432)
def test_cosh():
x = Rev_Var(2.0)
z = Rev_Var.cosh(x)
z.grad_value = 1
z3 = Rev_Var.cosh(2)
assert z.value == pytest.approx(3.7621956910836314)
assert z3 == pytest.approx(3.7621956910836314)
assert x.grad() == pytest.approx(3.626860407847019)
def test_logistic():
x = Rev_Var(3.0)
z = Rev_Var.logistic(x)
z.grad_value = 1
z2 = Rev_Var.logistic(3.0)
assert z.value == pytest.approx(1 / (1 + np.exp(-3)))
assert x.grad() == pytest.approx(np.exp(3) / ((1 + np.exp(3))**2))
assert z2 == 1 / (1 + np.exp(-3.0))
def test_sqrt():
x = Rev_Var(2.0)
z1 = Rev_Var.sqrt(x)
z1.grad_value = 1
z2 = Rev_Var.sqrt(2)
assert z1.value == pytest.approx(1.4142135623730951)
assert x.grad() == pytest.approx(0.3535533905932738)
assert z2 == np.sqrt(2)
def test_logk():
x = Rev_Var(2.0)
z2 = Rev_Var.logk(x, 3.0)
z2.grad_value = 1
z3 = Rev_Var.logk(2.0, 3.0)
assert z2.value == np.log(2) / np.log(3)
assert x.grad() == pytest.approx(0.45511961331341866)
assert z3 == np.log(2) / np.log(3)
def test_cos():
x = Rev_Var(2.0)
y = 2
z = Rev_Var.cos(x)
z.grad_value = 1
assert z.value == pytest.approx(-0.4161468365471424)
assert x.grad() == pytest.approx(-0.9092974268256817)
assert Rev_Var.cos(y) == np.cos(y)
def test_arctan():
x = Rev_Var(0.5)
y = 0.25
z = Rev_Var.arctan(x)
z.grad_value = 1
assert z.value == pytest.approx(0.46364760900080615)
assert x.grad() == pytest.approx(0.8)
assert Rev_Var.arctan(y) == np.arctan(y)
def test_arccos():
x = Rev_Var(0.5)
y = 0.3
z = Rev_Var.arccos(x)
z.grad_value = 1
assert z.value == pytest.approx(1.0471975511965976)
assert x.grad() == pytest.approx(-1.1547005383792517)
assert Rev_Var.arccos(y) == np.arccos(y)
def test_arcsin():
x = Rev_Var(0.5)
y = 0.3
z = Rev_Var.arcsin(x)
z.grad_value = 1
assert z.value == pytest.approx(0.5235987755982988)
assert x.grad() == pytest.approx(1.1547005383792517)
assert Rev_Var.arcsin(y) == np.arcsin(y)
def test_tan():
x = Rev_Var(2.0)
y = 2
z = Rev_Var.tan(x)
z.grad_value = 1
assert z.value == pytest.approx(-2.185039863261519)
assert x.grad() == pytest.approx(5.774399204041917)
assert Rev_Var.tan(y) == np.tan(y)
def test_exp():
x = Rev_Var(2.0)
z1 = Rev_Var.exp(x)
y = 5
z1.grad_value = 1
z2 = Rev_Var.exp(y)
assert z1.value == pytest.approx(7.38905609893065)
assert z2 == pytest.approx(148.4131591025766)
assert x.grad() == pytest.approx(7.38905609893065)
def test_log():
x = Rev_Var(2.0)
z1 = Rev_Var.log(x)
z1.grad_value = 1
z2 = Rev_Var.log(2.0)
assert z1.value == pytest.approx(0.6931471805599453)
assert z1.value == np.log(2)
assert x.grad() == pytest.approx(0.5)
assert z2 == np.log(2)
def test_rev_pow():
x1 = Rev_Var(0.5)
x2 = Rev_Var(0.5)
y = Rev_Var(4.2)
a = 3
z1 = x1**y
z1.grad_value = 1
z2 = x2**3
z2.grad_value = 1
assert z1.value == pytest.approx(0.05440941020600775)
assert x1.grad() == pytest.approx(0.4570390457304651)
assert y.grad() == pytest.approx(-0.03771372928022378)
assert z2.value == pytest.approx(0.125)
assert x2.grad() == pytest.approx(0.75)
def test_rev_grad():
x = Rev_Var(0.5)
y = Rev_Var(4.2)
z = x * y + Rev_Var.sin(x)
z.grad_value = 1.0
assert z.value == pytest.approx(2.579425538604203)
assert x.grad() == pytest.approx(4.2 + np.cos(x.value))
assert y.grad() == pytest.approx(0.5)
def test_truediv():
x = Rev_Var(0.5)
y = Rev_Var(4.2)
z = x / y
z.grad_value = 1.0
assert z.value == pytest.approx(0.11904761904761904)
assert x.grad() == pytest.approx(0.23809523809523808)
assert y.grad() == pytest.approx(-0.028344671201814057)
def test_rev_sub():
x = Rev_Var(0.5)
y = Rev_Var(4.2)
a = 3
z1 = y - x
z1.grad_value = 1.0
assert z1.value == 3.7
assert x.grad() == -1
assert y.grad() == 1
z2 = y - 3
assert z2.value == pytest.approx(1.2)
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 test_jac_matrix(): f1 = lambda x, y: Rev_Var.log(x) ** Rev_Var.sin(y) f2 = lambda x, y: Rev_Var.sqrt(x) / y ad = AD(np.array([4.12, 5.13]), np.array([1, 1]), AD_Mode.REVERSE) assert np.array_equal(ad.jac_matrix([f1, f2]), np.array([[pytest.approx(-0.11403015), pytest.approx(0.10263124)], [pytest.approx(0.048018), pytest.approx(-0.07712832)]]))
def test_rev_rsub():
x = Rev_Var(0.5)
a = 3
z = a - x
assert z.value == pytest.approx(2.5)
def test_two_variables(): ad = AD(np.array([2, 2]), np.array([1, 1]), AD_Mode.REVERSE) f1 = lambda x, y: Rev_Var.log(x) ** Rev_Var.sin(y) assert ad.vars[0].value == 2 assert ad.vars[1].value == 2 assert AD.auto_diff(self=ad,func=f1) == Var(pytest.approx(0.7165772257590739),np.array([pytest.approx(0.47001694),pytest.approx(0.10929465)]))
def test_single_variable(): ad = AD(np.array([2]), np.array([1]),AD_Mode.REVERSE) f1 = lambda x: Rev_Var.log(x) ** 2 assert AD.auto_diff(self=ad,func=f1) == Var(pytest.approx(0.4804530139182014),np.array([pytest.approx(0.69314718)]))
def test_expk():
x = Rev_Var(2.0)
z = Rev_Var.expk(3.0, x)
z.grad_value = 1
assert z.value == pytest.approx(8)
assert x.grad() == pytest.approx(12)
def test_rev_rmul():
x = 3
y = Rev_Var(4.2)
z = x * y
assert z.value == pytest.approx(12.6)
def clear(self):
if self.mode == AD_Mode.REVERSE:
self.vars = []
for val in self.vals:
self.vars.append(Rev_Var(val))
from EasyDiff.ad import AD
from EasyDiff.var import Var
from EasyDiff.rev_var import Rev_Var
from EasyDiff.ad import AD_Mode
import numpy as np
# test forward mode.
# give it a function of your choice
func = lambda x, y: Var.log(x)**Var.sin(y)
# give the initial values to take the derivatives at
ad = AD(vals=np.array([2, 2]), ders=np.array([1, 1]), mode=AD_Mode.FORWARD)
# calculate and print the derivatives
print("Var.log(x) ** Var.sin(y): {}".format(vars(ad.auto_diff(func))))
# test reverse mode.
func = lambda x, y: Rev_Var.log(x)**Rev_Var.sin(y)
ad = AD(vals=np.array([2, 2]), ders=np.array([1, 1]), mode=AD_Mode.REVERSE)
print("Rev_Var.log(x) ** Rev_Var.sin(y): {}".format(vars(ad.auto_diff(func))))
def test_rev_real_add():
x = Rev_Var(0.5)
y = 4.2
z = x + y
assert z.value == x.value + y