def test_problematic():
a = Variable(val=2, name='a')
with pytest.raises(ZeroDivisionError):
t1 = Diff().auto_diff(function=div_zero, eval_point=[a])
with pytest.raises(NotImplementedError):
t1 = Diff().hessian(functions=[add_function], eval_points=[a])
with pytest.raises(NotImplementedError):
print(bm.arcsinh(1))
with pytest.raises(NotImplementedError):
print(bm.arccosh(1))
with pytest.raises(NotImplementedError):
print(bm.arctanh(1))
def test_non_alphabetical_22():
x = Variable(val=3, name='z')
y = Variable(val=5, name='a')
t1 = Diff().jacobian([f1,f2], [x,y])
assert(t1.shape == (2,2))
assert(t1[0][0] == 30)
assert(t1[0][1] == 9)
assert(t1[1][0] == 5)
assert(t1[1][1] == bm.cos(5))
def test_jacobian_22():
x = Variable(val=3, name='x')
y = Variable(val=5, name='y')
t1 = Diff().jacobian([f1,f2], [x,y])
assert(t1.shape == (2,2))
assert(t1[0][0] == 30)
assert(t1[0][1] == 9)
assert(t1[1][0] == 5)
assert(t1[1][1] == bm.cos(5))
def test_jacobian_32():
x = Variable(val=3, name='c')
y = Variable(val=5, name='a')
z = Variable(val=5, name='t')
t1 = Diff().jacobian([f1,f2,f3], [x,y])
assert(t1.shape == (3,2))
assert(t1[0][0] == 30)
assert(t1[0][1] == 9)
assert(t1[1][0] == 5)
assert(t1[1][1] == bm.cos(5))
assert(t1[2][0] == 5)
assert(t1[2][1] == 4)
def test_jacobian_23():
x = Variable(val=3, name='x')
y = Variable(val=5, name='y')
z = Variable(val=2, name='z')
t1 = Diff().jacobian([f1,f2], [x,y,z])
assert(t1.shape == (2,3))
assert(t1[0][0] == 30)
assert(t1[0][1] == 9)
assert(t1[0][2] == 1)
assert(t1[1][0] == 5)
assert(t1[1][1] == bm.cos(5))
assert(t1[0][2] == 1)
def test_more_operators():
a = Variable(val=4, name='a')
# Power
t1 = Diff().auto_diff(function=power_scalar, eval_point=[a])
assert (t1.val == 26)
assert (t1.der['a'] == 8)
# Square root
t2 = Diff().auto_diff(function=sqrt_scalar, eval_point=[a])
assert (t2.val == 13)
assert (t2.der['a'] == 1 / 3)
# Power function
t3 = Diff().auto_diff(function=power_function, eval_point=[a])
assert (t3.val == 16)
assert (t3.der['a'] == bm.log(2) * 16)
assert (t3.der['a'] == np.log(2) * 16)
# Power function general
t4 = Diff().auto_diff(function=power_function_general, eval_point=[a])
assert (t4.val == 256)
assert (t4.der['a'] == 256 * (bm.log(4) + 1))
assert (t4.der['a'] == 256 * (np.log(4) + 1))
def test_sanity_checks():
assert (bm.log(4.1) == np.log(4.1))
assert (bm.exp(-10.1) == np.exp(-10.1))
assert (bm.sqrt(112.3) == np.sqrt(112.3))
assert (bm.sin(4.1) == np.sin(4.1))
assert (bm.cos(2.2) == np.cos(2.2))
assert (bm.tan(2) == np.tan(2.0))
assert (bm.arcsin(0) == np.arcsin(0))
assert (bm.arccos(0.2) == np.arccos(0.2))
assert (bm.arctan(2) == np.arctan(2))
assert (bm.sinh(2) == np.sinh(2))
assert (bm.cosh(2) == np.cosh(2))
assert (bm.tanh(2) == np.tanh(2))
assert (bm.logk(2, np.exp(1)) == np.log(2))
def logk_e(x):
return bm.logk(x, bm.exp(1))
def cosh_fn(x, y):
return -x * y * bm.cosh(x * y)
def sinh_cosh(x, y):
return bm.sinh(x) + bm.cosh(y)
def logk_test(x):
return bm.logk(x * x, base=10)
def sqrt_function(x, y):
return bm.sqrt(x) + bm.sqrt(y)
def tan_function(x, y):
return bm.tan(2 * x * y)
def arctan_fn(x, y):
return -y * bm.arctan(x * y)
def sinh_fn(x, y):
return -x * y * bm.sinh(x * y)
def arcsin_fn(x, y):
return -y * bm.arcsin(x * y)
def arccos_fn(x, y):
return -y * bm.arccos(x * y)
def tan_fn(x, y):
return y * bm.tan(x * y)
def sin_cos(x, y):
return y * bm.sin(x * x * x) + x * bm.cos(y)
def sqrt_fn(x, y):
return x * bm.sqrt(x * y) + x * x * x
def sqrt_scalar(x):
return 10 + bm.sqrt(2 * x + 1)
def tanh_fn(x, y):
return -x * y * bm.tanh(x * y)
def log_exp_function(x, y):
return bm.log(x) + bm.exp(y)
def tan_function(x):
return bm.tan(2 * x)
def sin_cos(x, y):
return bm.sin(x) + bm.cos(y)
def inverse_trig(x):
# arcsin, arccos, arctan
return bm.arcsin(x) - bm.arccos(x) + bm.arctan(x)
def inverse_trig(x, y, z):
return bm.arcsin(x) - bm.arccos(y) + bm.arctan(z)
def logk_none(x):
return bm.logk(x) + 40 - 40
def tanh(x, y):
return bm.tanh(x * y)
def log_exp(x, y):
return bm.log(x * x) + x * bm.exp(y)