def test_power():
"""Boolean condition asserts that value and derivative of a power function using the AutoDiff class are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = [1, 2]
def myfunc(x, y):
f1 = 3**x**y**1
return f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {
'diff': [
math.log(3) * 3**(c[0]**c[1]) * c[1] * c[0]**(c[1] - 1),
math.log(3) * 3**(c[0]**c[1]) * math.log(c[0]) * c[0]**c[1]
],
'value':
3**1**2
}
assert res == expectAns
def test_arccos():
"""Boolean condition asserts that value and derivative of the inverse of cosine of the AutoDiff instance are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = 0.5
def myfunc(x):
f1 = EF.arccos(x)
return f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {'diff': -1 / math.sqrt(1 - c**2), 'value': math.acos(c)}
assert res == expectAns
def test_neg_sub():
"""Boolean condition asserts that value and derivative of a subtraction using the AutoDiff class are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = [1, 2]
def myfunc(x, y):
f1 = 1 - x - y - 2
return -f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {'diff': [1, 1], 'value': 4}
assert res == expectAns
def test_log():
"""Boolean condition asserts that value and derivative of the natural logarithm of the AutoDiff instance are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = 14
def myfunc(x):
f1 = EF.log(x)
return f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {'diff': 1 / c, 'value': math.log(c)}
assert res == expectAns
def test_cot():
"""Boolean condition asserts that value and derivative of the cotangent of the AutoDiff instance are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = 0.5
def myfunc(x):
f1 = EF.cot(x)
return f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {
'diff': 2 / (math.cos(c * 2) - 1),
'value': math.cos(c) / math.sin(c)
}
assert res == expectAns
def test_cosh():
"""Boolean condition asserts that value and derivative of the cosecant of the AutoDiff instance are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = 2
def myfunc(x):
f1 = EF.cosh(x)
return f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {
'diff': 3.626860407847019,
'value': math.cosh(c)
} #sinh(x) differ in last digits
assert res == expectAns
def test_tanh():
"""Boolean condition asserts that value and derivative of the cosecant of the AutoDiff instance are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
c = 14
def myfunc(x):
f1 = EF.tanh(x)
return f1
f_obj = ADiff(myfunc)
res = f_obj.Jac(c)
expectAns = {
'diff': (1 / ((math.exp(c) + math.exp(-c)) / 2) *
((math.exp(c) + math.exp(-c)) / 2)),
'value':
((math.exp(c) - math.exp(-c)) / 2) / ((math.exp(c) + math.exp(-c)) / 2)
}
assert res == expectAns
def test_vec_func1():
"""Boolean condition asserts that value and derivative of a function of the Autodiff class comprising several elementary operations are equal to the expected value and derivative as calculated in the function.
RETURNS
========
If the boolean condition returns True nothing is returned. If it is computed to be false, then an AssertionError is raised.
"""
def myfunc(x, y):
f1 = x * y
f2 = EF.sin(x)
f3 = 10
f4 = x + y + EF.sin(x * y) + 10
return [f1 + f2, -(f3 - f4)]
f_obj = ADiff(myfunc)
res = f_obj.Jac([1, 2])
expectAns = {
'diff': [[2.5403023058681398, 1.0],
[0.1677063269057152, 0.5838531634528576]],
'value': [2.8414709848078967, 3.909297426825681]
}
assert res == expectAns
