def test_sqrt(self):
a = Leaf(9.0)
c = sqrt(a)
res = sparse_derivative([c], [a])[0][0].value
self.assertEqual(res, 1.0 / 6.0)
del c
self.assertEqual(a.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 _do_calcs(self, a, b):
av, bv = a.value, b.value
self.assertEqual((a * b).value, av * bv)
self.assertEqual((a / b).value, av / bv)
self.assertEqual((a - b).value, av - bv)
self.assertEqual((-a).value, -av)
self.assertEqual((a ** b).value, av ** bv)
self.assertEqual(sin(a).value, math.sin(av))
self.assertEqual(cos(a).value, math.cos(av))
self.assertEqual(tan(a).value, math.tan(av))
a.value = av = 0.6
self.assertEqual(asin(a).value, math.asin(av))
self.assertEqual(acos(a).value, math.acos(av))
self.assertEqual(atan(a).value, math.atan(av))
self.assertEqual(sinh(a).value, math.sinh(av))
self.assertEqual(cosh(a).value, math.cosh(av))
self.assertEqual(tanh(a).value, math.tanh(av))
self.assertEqual(sqrt(a).value, math.sqrt(av))
self.assertEqual(log(a).value, math.log(av))
self.assertEqual(exp(a).value, math.exp(av))
self.assertEqual(squ(a).value, av*av)
self.assertEqual(inv(a).value, 1.0 / av)
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)