def test_atan(self):
a = Leaf(0.6)
c = atan(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, 1 / (1 + 0.6 * 0.6))
del c
self.assertEqual(a.node.ref_count, 1)
def test_cos(self):
a = Leaf(2.0)
c = cos(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, -math.sin(2.0))
del c
self.assertEqual(a.node.ref_count, 1)
def test_acos(self):
a = Leaf(0.6)
c = acos(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, -(1 - 0.36)**-0.5)
del c
self.assertEqual(a.node.ref_count, 1)
def test_log(self):
a = Leaf(4.0)
c = log(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, 0.25)
del c
self.assertEqual(a.node.ref_count, 1)
def test_sqrt(self):
a = Leaf(9.0)
c = sqrt(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, 1.0 / 6.0)
del c
self.assertEqual(a.node.ref_count, 1)
def test_inv(self):
a = Leaf(2.0)
c = inv(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, -0.25)
del c
self.assertEqual(a.node.ref_count, 1)
def test_neg(self):
a = Leaf(13.0)
c = -a
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, -1.0)
del c
self.assertEqual(a.node.ref_count, 1)
def test_tanh(self):
a = Leaf(2.0)
c = tanh(a)
res = Derivative([c], [a])[0, 0].value
self.assertEqual(res, math.cosh(2.0)**-2)
del c
self.assertEqual(a.node.ref_count, 1)
def test_hook2(self):
a = Leaf(1.0)
b = exp(a)
b_plain = b.plain()
c = Derivative([b, b_plain], [a]).value
self.assertEqual(c[0][0], b.value)
self.assertEqual(c[1][0], 0.0)
def test_squ(self):
a = Leaf(13.0)
c = a * a
d = squ(a)
res = Derivative([c, d], [a]).value
self.assertListEqual(res, [[26.0], [26.0]])
del c, d
self.assertEqual(a.node.ref_count, 1)
def test_div(self):
a, b = Leaf(6.0), Leaf(4.0)
c = a / b
res = Derivative([c], [a, b])[0].value
self.assertListEqual(res, [0.25, -0.375])
del c
self.assertEqual(a.node.ref_count, 1)
self.assertEqual(b.node.ref_count, 1)
def test_mul(self):
a, b = Leaf(11.0), Leaf(7.0)
c = a * b
res = Derivative([c], [a, b])[0].value
self.assertListEqual(res, [7.0, 11.0])
del c
self.assertEqual(a.node.ref_count, 1)
self.assertEqual(b.node.ref_count, 1)
def test_pow(self):
a, b = Leaf(3.0), Leaf(4.0)
c = a**b
res = Derivative([c], [a, b])[0].value
self.assertListEqual(res, [108.0, 81 * math.log(3.0)])
del c
self.assertEqual(a.node.ref_count, 1)
self.assertEqual(b.node.ref_count, 1)
def test_sel(self):
a, b = Leaf(13.0), Leaf(4.0)
c = a.select(b)
d = Derivative([c], [a, b])
self.assertListEqual(d.value, [[1.0, 0.0]])
b.value = -1.0
d[0][0].invalidate()
self.assertListEqual(d.value, [[0.0, 0.0]])
del c, d
self.assertEqual(a.node.ref_count, 1)
self.assertEqual(b.node.ref_count, 1)
def test_empanadina(self):
def func(x):
y = x**6
J = 6 * x**5
return y, J
a = Leaf(2.0)
b = sqrt(a)
y = empanadina(func, b)
self.assertAlmostEqual(y.value, 8.0)
self.assertAlmostEqual(Derivative([y], [a])[0, 0].value, 12.0)
def test_multiple(self):
a, b, c, d, e = map(Leaf, range(5))
f = (a + b) * c
g = b * b
h = d * e
i = h + f
ref = [[2.0, 2.0, 1.0, 0.0], [0.0, 2.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 4.0], [2.0, 2.0, 1.0, 4.0]]
res = Derivative([f, g, h, i], [a, b, c, d]).value
self.assertListEqual(res, ref)
def test_empanada(self):
from math import sin as fsin, cos as fcos, exp as fexp, sqrt as fsqrt
def func(x):
a, b = x
c = fexp(a + b)
y = [a, a * fsin(b), c]
J = [[1.0, 0.0], [fsin(b), a * fcos(b)], [c, c]]
return y, J
x = Leaf(2.0)
z = [x * x, sqrt(x)]
y = empanada(func, z, dim_out=3)
dydx = Derivative(y, [x]).value
dydx = [entry[0] for entry in dydx]
ref = [
4.0, 4 * fsin(fsqrt(2)) + fsqrt(2) * fcos(fsqrt(2)),
(4 + 0.5 / fsqrt(2)) * fexp(4 + fsqrt(2))
]
for r1, r2 in zip(dydx, ref):
self.assertAlmostEqual(r1, r2)