def power(x1, x2):
"""Calculate the exponential of the input x1 with base x2
Keyword arguments:
x1 -- a real number or a dual number
x2 -- a real number or a dual number
Return:
the exponential value x1 with base x2
"""
if (isinstance(x1,Dual)) and (isinstance(x2,Dual)):
# da^u/dx = ln(a) a^u du/dx
factor = x1.val ** (x2.val -1)
sum_1 = x2.val * x1.der
sum_2 = x1.val * np.log(x1.val) * x2.der
temp = factor * (sum_1 + sum_2)
return Dual(x1.val ** x2.val, temp)
elif (isinstance(x1,Dual)):
# du^n/dx = n * u^(n-1) * du/dx
temp = x2 * x1.val ** (x2-1) * x1.der
return Dual(x1.val ** x2, temp)
elif (isinstance(x2,Dual)):
# da^u/dx = ln(a) a^u du/dx
temp = np.log(x2.val) * x2.val ** x1 * x2.der
return Dual(x1 ** x2.val, temp)
else:
return np.power(x1,x2)
def sum(xs):
"""Calculate the sum of the input
Keyword arguments:
xs -- a real value list
Return:
the sum of the array
"""
cur_val = 0
cur_der = 0
is_dual = False
# print('xs')
for x in xs:
# print('val: ',x.val)
if (isinstance(x,Dual)):
is_dual = True
cur_der += x.der
cur_val += x.val
else:
cur_val += x
if is_dual:
return Dual(cur_val,cur_der)
else:
return cur_val
def test2__cos_fn__():
tests = np.linspace(-10, 100, 15)
for test in tests:
x = Dual(test)
f = admath.cos(x)
assert np.cos(test) == admath.cos(test)
assert np.cos(test) == f.val
assert -1 * np.sin(test) == f.der
def test_sqrt_fn__():
tests = np.linspace(1, 100, 15)
for test in tests:
x = Dual(test)
f = admath.sqrt(x)
assert np.sqrt(test) == admath.sqrt(test)
assert np.sqrt(test) == f.val
assert 1 / 2 * 1 / np.sqrt(test) == f.der
def test_logb__():
tests = np.linspace(1, 100, 15)
for test in tests:
x = Dual(test)
f = admath.logb(x, np.exp(1))
assert np.log(test) == admath.logb(test, np.exp(1))
assert np.log(test) == f.val
assert 1 / test == f.der
def test_exp_fn__():
tests = np.linspace(-100, 100, 15)
for test in tests:
x = Dual(test)
f = admath.exp(x)
assert np.exp(test) == admath.exp(test)
assert np.exp(test) == f.val
assert np.exp(test) == f.der
def test_log10_fn__():
tests = np.linspace(1, 100, 15)
for test in tests:
x = Dual(test)
f = admath.log10(x)
assert np.log10(test) == admath.log10(test)
assert np.log10(test) == f.val
assert 1 / (test * np.log(10)) == f.der
def test_log_fn__():
tests = np.linspace(1, 100, 15)
for test in tests:
x = Dual(test)
f = admath.log(x)
assert np.log(test) == admath.log(test)
assert np.log(test) == f.val
assert 1 / test == f.der
def test_power1():
x = Dual(2)
f = admath.power(x, x)
assert f.der == 2 * (2 + 2 * np.log(2))
assert f.val == 4.0
assert admath.power(2, 2) == 4.0
f = admath.power(x, 2)
assert f.val == 4
assert f.der == 4
f = admath.power(2, x)
assert f.val == 4.0
assert f.der == np.log(2) * 2**2
def test_arctan():
x = Dual(0)
f = admath.arctan(x)
assert 1 == f.der
assert 0 == f.val
assert 0 == admath.arctan(0)
def test1__sin_fn__():
x = Dual(0)
f = admath.sin(x)
assert f.val == 0
assert f.der == 1
def test1__tan_fn__():
x = Dual(0)
f = admath.tan(x)
assert f.val == 0
assert f.der == 1
assert admath.tan(0) == 0
def test1__cos_fn__():
x = Dual(0)
f = admath.cos(x)
assert f.val == np.cos(0)
assert f.der == -1 * np.sin(0)
def test_arccos():
x = Dual(0)
f = admath.arccos(x)
assert -1 == f.der
assert np.pi / 2 == f.val
assert np.pi / 2 == admath.arccos(0)
def test_abs():
x = Dual(-1)
f = admath.abs(x**3)
assert -1 == f.der
assert 1 == f.val
assert 1 == admath.abs(-1)
def test_sum():
x = Dual(1)
f = admath.sum([x**2, x**3])
assert 5 == f.der
assert 2 == f.val
assert 5 == admath.sum([2, 3])
def test_logistic():
x = Dual(1)
f = admath.logistic(x)
assert 0.25 == f.der
assert 0.50 == f.val
assert 0.50 == admath.logistic(1)
def test_tanh():
x = Dual(0)
f = admath.tanh(x)
assert 1 == f.der
assert 0 == f.val
assert 0 == admath.tanh(0)
def test_cosh():
x = Dual(0)
f = admath.cosh(x)
assert 0 == f.der
assert 1 == f.val
assert 1 == admath.cosh(0)