def test_rmul():
t1 = 3 * AD(val=3, der=1)
assert t1.val == 9
assert t1.der == 3
t3 = (-4) * AD(val=-3, der=[1, 2])
assert t3.val == 12
assert t3.der.tolist() == [-4, -8]
def test_rsub():
t1 = 3 - AD(val=3, der=1)
assert t1.val == 0
assert t1.der == -1
t3 = -4 - AD(val=3, der=[1, 2])
assert t3.val == -7
assert t3.der.tolist() == [-1, -2]
def test_radd():
t1 = 3 + AD(val=3, der=1)
assert t1.val == 6
assert t1.der == 1
t3 = -4 + AD(val=3, der=[1, 2])
assert t3.val == -1
assert t3.der.tolist() == [1, 2]
def test_rtruediv():
t1 = 3 / AD(val=3, der=1)
assert t1.val == 1
assert t1.der == pytest.approx(-0.3333333333333333)
t3 = -8 / AD(val=-4, der=[1, 2])
assert t3.val == 2
assert t3.der.tolist() == [pytest.approx(0.5), pytest.approx(1)]
def test_gt():
t1 = AD(val=3, der=1)
assert t1 > 2
t2 = AD(val=2, der=1)
assert t1 > t2
t3 = AD(val=3, der=[1, 2])
assert t3 > 2
t4 = AD(val=4, der=[1, 2])
assert t4 > t3
def test_le():
t1 = AD(val=3, der=1)
assert t1 <= 3
t2 = AD(val=4, der=1)
assert t1 <= t2
t3 = AD(val=3, der=[1, 2])
assert t3 <= 3
t4 = AD(val=3, der=[1, 2])
assert t4 <= t3
def test_lt():
t1 = AD(val=3, der=1)
assert t1 < 4
t2 = AD(val=4, der=1)
assert t1 < t2
t3 = AD(val=3, der=[1, 2])
assert t3 < 4
t4 = AD(val=2, der=[1, 2])
assert t4 < t3
def test_ge():
t1 = AD(val=3, der=1)
assert t1 >= 2
t2 = AD(val=3, der=1)
assert t1 >= t2
t3 = AD(val=3, der=[1, 2])
assert t3 >= 2
t4 = AD(val=3, der=[1, 2])
assert t4 >= t3
def test_eq():
t1 = AD(val=3, der=1)
assert t1 == 3
t2 = AD(val=3, der=1)
assert t1 == t2
t3 = AD(val=3, der=[1, 2])
assert t3 == 3
t4 = AD(val=3, der=[1, 2])
assert t4 == t3
def test_pos():
t1 = +AD(val=3, der=1)
assert t1.val == 3
assert t1.der == 1
t2 = +AD(val=-3, der=1)
assert t2.val == -3
assert t2.der == 1
t3 = +AD(val=-3, der=[1, 2])
assert t3.val == -3
assert t3.der.tolist() == [1, 2]
def test_neg():
t1 = -AD(val=3, der=1)
assert t1.val == -3
assert t1.der == -1
t2 = -AD(val=-3, der=1)
assert t2.val == 3
assert t2.der == -1
t3 = -AD(val=-3, der=[1, 2])
assert t3.val == 3
assert t3.der.tolist() == [-1, -2]
def test_rpow():
t1 = 2**AD(val=3, der=1)
assert t1.val == 8
assert t1.der == pytest.approx(5.54517744)
t2 = 0**AD(val=3, der=1)
assert t2.val == 0
assert t2.der == 0
t2 = 1**AD(val=0, der=1)
assert t2.val == 1
assert t2.der == 0
def test_multi_var():
fn = expressioncc('log(x,2) + sin(y)', ['x', 'y']).get_fn()
x = AD(4, der=[1, 0])
y = AD(3, der=[0, 1])
t1 = fn(x, y)
assert t1.val == pytest.approx(2.1411200080598674)
assert t1.der.tolist() == [
pytest.approx(0.36067376),
pytest.approx(-0.9899925)
]
def test_missing_der_missing_nvars_idx():
# test missing n_vars
with pytest.raises(KeyError):
t1 = AD(val=3, idx=1)
# test missing idx
with pytest.raises(KeyError):
t2 = AD(val=3, n_vars=2)
# test declaring with only n_vars
t3 = AD(val=3, n_vars=1)
def test_tanh():
t1 = tanh(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(0.29131261)
assert t1.der == pytest.approx(0.91513696)
t2 = tanh(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(0.29131261)
assert t2.der.tolist() == [
pytest.approx(0.91513696),
pytest.approx(1.8302739236532586)
]
t3 = tanh(0.3)
assert t3 == pytest.approx(0.29131261)
def test_cosh():
t1 = cosh(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(1.04533851)
assert t1.der == pytest.approx(0.30452029)
t2 = cosh(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(1.04533851)
assert t2.der.tolist() == [
pytest.approx(0.30452029),
pytest.approx(0.6090405868942852)
]
t3 = cosh(0.3)
assert t3 == pytest.approx(1.0453385141288605)
def test_sin():
t1 = sin(AD(val=3, der=1))
assert t1.val == pytest.approx(0.1411200080598672, 0.1)
assert t1.der == pytest.approx(-0.9899924966004454)
t2 = sin(AD(val=3, der=[1, 2]))
assert t2.val == pytest.approx(0.1411200080598672, 0.1)
assert t2.der.tolist() == [
pytest.approx(-0.9899924966004454),
pytest.approx(-1.9799849932008908)
]
t3 = sin(3)
assert t3 == pytest.approx(0.1411200080598672, 0.1)
def test_sinh():
t1 = sinh(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(0.30452029)
assert t1.der == pytest.approx(1.04533851)
t2 = sinh(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(0.30452029)
assert t2.der.tolist() == [
pytest.approx(1.0453385141),
pytest.approx(2.090677028257721)
]
t3 = sinh(0.3)
assert t3 == pytest.approx(0.30452029)
def test_tan():
t1 = tan(AD(val=3, der=1))
assert t1.val == pytest.approx(-0.1425465430742778)
assert t1.der == pytest.approx(1.020319516942427)
t2 = tan(AD(val=3, der=[1, 2]))
assert t2.val == pytest.approx(-0.1425465430742778)
assert t2.der.tolist() == [
pytest.approx(1.020319516942427),
pytest.approx(2.040639033884854)
]
t3 = tan(3)
assert t3 == pytest.approx(-0.1425465430742778)
def test_logistic():
t1 = logistic(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(0.57444252)
assert t1.der == pytest.approx(0.24445831)
t2 = logistic(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(0.57444252)
assert t2.der.tolist() == [
pytest.approx(0.24445831),
pytest.approx(0.4889166233814918)
]
t3 = logistic(0.3)
assert t3 == pytest.approx(0.57444252)
def test_exp():
t1 = exp(AD(val=3, der=1))
assert t1.val == pytest.approx(20.085536923187668)
assert t1.der == pytest.approx(20.085536923187668)
t2 = exp(AD(val=3, der=[1, 2]))
assert t2.val == pytest.approx(20.085536923187668)
assert t2.der.tolist() == [
pytest.approx(20.08553692),
pytest.approx(40.17107385)
]
t3 = exp(3)
assert t3 == pytest.approx(20.085536923187668)
def test_cos():
t1 = cos(AD(val=3, der=1))
assert t1.val == pytest.approx(-0.9899924966004454)
assert t1.der == pytest.approx(-0.1411200080598672)
t2 = cos(AD(val=3, der=[1, 2]))
assert t2.val == pytest.approx(-0.9899924966004454)
assert t2.der.tolist() == [
pytest.approx(-0.1411200080598672),
pytest.approx(-0.2822400161197344)
]
t3 = cos(3)
assert t3 == pytest.approx(-0.9899924966004454)
def test_arctan():
t1 = arctan(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(0.29145679)
assert t1.der == pytest.approx(0.91743119)
t2 = arctan(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(0.29145679)
assert t2.der.tolist() == [
pytest.approx(0.9174311926605504),
pytest.approx(1.8348623853211008)
]
t3 = arctan(0.3)
assert t3 == pytest.approx(0.2914567944778671)
def test_log():
t1 = log(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(-1.2039728)
assert t1.der == pytest.approx(3.33333333)
t2 = log(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(-1.2039728)
assert t2.der.tolist() == [
pytest.approx(3.33333333),
pytest.approx(6.666666666666667)
]
t3 = log(0.3)
assert t3 == pytest.approx(-1.2039728)
with pytest.raises(ValueError):
t4 = log(-1)
with pytest.raises(ValueError):
t4 = log(AD(val=-1, der=[1, 2]))
def arccos(obj):
"""Returns the arccos of a scalar or an AD object
INPUTS
=======
obj: AD object, scalar, or vector
RETURNS
========
Returns the arccos of obj
EXAMPLES
=========
>>> x = AD(val=0.5, der=1)
>>> print(arccos(x))
(array(1.04719755), array(-1.15470054))
"""
if isinstance(obj, AD):
values = obj.val
if (values < (-1) or values > (1)).any():
raise ValueError('Values are not in the domain of arcsin [-1, 1].')
val = np.arccos(obj.val)
# this is the negative of the derivative of the arcsin
der = -1 * (1 / np.sqrt(1 - (obj.val ** 2) * obj.der))
return AD(val=val, der=der)
if (np.array(obj) < -1 or np.array(obj) > 1).any():
raise ValueError('Values are not in the domain of arcsin [-1, 1].')
return np.arccos(obj)
def test_arccos():
t1 = arccos(AD(val=0.3, der=[1]))
assert t1.val == pytest.approx(1.26610367)
assert t1.der == pytest.approx(-1.04828484)
t2 = arccos(AD(val=0.3, der=[1, 2]))
assert t2.val == pytest.approx(1.26610367)
assert t2.der.tolist() == [
pytest.approx(-1.04828484),
pytest.approx(-1.1043152607484654)
]
t3 = arccos(0.3)
assert t3 == pytest.approx(1.26610367)
with pytest.raises(ValueError):
t4 = arccos(-10)
with pytest.raises(ValueError):
t5 = arccos(AD(val=-10, der=[1, 2]))
def log(obj, base=None):
"""Returns the log of a scalar, vector, or an AD object with any base
INPUTS
=======
obj: AD object, scalar, or vector
base: the base of the log, if None defaults to natural log
RETURNS
========
Returns the log of obj
EXAMPLES
=========
>>> x = AD(val = 3, der = 1)
>>> log(x)
(array(0.47712125), array(0.14476483))
"""
if not base:
base = np.exp(1)
if isinstance(obj, AD):
if obj <= 0:
raise ValueError('Log accepts only positive numbers')
val = np.log(obj.val) / np.log(base)
der = (1 / (obj.val * np.log(base))) * obj.der
return AD(val=val, der=der)
if obj <= 0:
raise ValueError('Log accepts only positive numbers')
return np.log(obj) / np.log(base)
def test_sqrt():
t1 = sqrt(AD(val=3, der=[1]))
assert t1.val == pytest.approx(1.7320508075688772)
assert t1.der == pytest.approx(0.28867513459481287)
t2 = sqrt(AD(val=3, der=[1, 2]))
assert t2.val == pytest.approx(1.7320508075688772)
assert t2.der.tolist() == [
pytest.approx(0.28867513459481287),
pytest.approx(0.57735027)
]
t3 = sqrt(3)
assert t3 == pytest.approx(1.7320508075688772)
with pytest.raises(TypeError,
match=r"Sqrt has a positive domain, input negative"):
t4 = sqrt(-1)
with pytest.raises(TypeError,
match=r"Sqrt has a positive domain, input negative"):
t5 = sqrt(AD(val=-1, der=[1, 2]))
def test_pow():
t1 = AD(val=3, der=1)**2
assert t1.val == 9
assert t1.der == 6
t2 = AD(val=3, der=1)**AD(val=5, der=1)
assert t2.val == 243
assert t2.der == pytest.approx(671.96278615)
t3 = AD(val=0, der=1)**AD(val=5, der=1)
assert t3.val == 0
assert t3.der == pytest.approx(0.)
t4 = AD(val=0, der=1)**2
assert t4.val.tolist() == 0
assert t4.der.tolist() == 0
t5 = AD(val=-1, der=1)**2
assert t5.val.tolist() == 1
assert t5.der.tolist() == -2
def test_sub():
t1 = AD(val=3, der=1) - 3
assert t1.val == 0
assert t1.der == 1
t2 = AD(val=3, der=1) - AD(val=4, der=1)
assert t2.val == -1
assert t2.der == 0
t3 = AD(val=3, der=[1, 2]) - 4
assert t3.val == -1
assert t3.der.tolist() == [1, 2]
t4 = AD(val=3, der=[1, 2]) - AD(val=-8, der=[3, 1])
assert t4 == 11
assert t4.der.tolist() == [-2, 1]