def test_exp(self):
self.assertEqual(imath.exp(0), interval[1])
self.assertEqual(imath.exp(1), interval[math.e,
helpers.nudge(math.e, +1)])
self.assertEqual(
imath.exp(interval([-fpu.infinity, 0], [1, fpu.infinity])),
interval([0, 1], [math.e, fpu.infinity]))
def test_cosh(self):
self.assertEqual(imath.cosh(0), interval[1])
assert imath.cosh(2) in (imath.exp(2) + imath.exp(-2))/2
assert imath.cosh(interval[1, 2]) == interval.hull((imath.cosh(1), imath.cosh(2)))
assert imath.cosh(interval[-2, -1]) == imath.cosh(interval[1, 2])
assert imath.cosh(interval[-2, 1]) == interval.hull((interval[1], imath.cosh(2)))
assert imath.cosh(interval[-1, 2]) == interval.hull((interval[1], imath.cosh(2)))
def test_exp(self):
z = interval[-100, 100].newton(lambda x: imath.exp(x) + x,
lambda x: imath.exp(x) + 1)
assert z == interval[-0.56714329040978395,
helpers.nudge(-0.56714329040978395, +1)]
w = interval[-100, 100].newton(lambda x: imath.exp(-x) * x + 1,
lambda x: imath.exp(-x) * (1 - x))
assert z == w
def test_cosh(self):
self.assertEqual(imath.cosh(0), interval[1])
assert imath.cosh(2) in (imath.exp(2) + imath.exp(-2)) / 2
assert imath.cosh(interval[1, 2]) == interval.hull(
(imath.cosh(1), imath.cosh(2)))
assert imath.cosh(interval[-2, -1]) == imath.cosh(interval[1, 2])
assert imath.cosh(interval[-2, 1]) == interval.hull(
(interval[1], imath.cosh(2)))
assert imath.cosh(interval[-1, 2]) == interval.hull(
(interval[1], imath.cosh(2)))
def test_log(self):
self.assertEqual(imath.log(1), interval[0])
self.assertEqual(imath.log(0), interval[-fpu.infinity])
self.assertEqual(imath.log(imath.exp(1)), interval[helpers.nudge(1, -1), helpers.nudge(1, +1)])
self.assertEqual(imath.log(0), interval[-fpu.infinity])
self.assertEqual(imath.log(interval[0, 1]), interval[-fpu.infinity, 0])
self.assertEqual(imath.log(interval[-1, 1]), interval[-fpu.infinity, 0])
self.assertEqual(imath.log(interval[-2, -1]), interval())
def test_log(self):
assert imath.log(1) == interval[0]
assert imath.log(0) == interval[-fpu.infinity]
assert imath.log(imath.exp(1)) == interval[helpers.nudge(1, -1), helpers.nudge(1, +1)]
assert imath.log(0) == interval[-fpu.infinity]
assert imath.log(interval[0, 1]) == interval[-fpu.infinity, 0]
assert imath.log(interval[-1, 1]) == interval[-fpu.infinity, 0]
assert imath.log(interval[-2, -1]) == interval()
def test_log(self):
assert imath.log(1) == interval[0]
assert imath.log(0) == interval[-fpu.infinity]
assert imath.log(imath.exp(1)) == interval[helpers.nudge(1, -1),
helpers.nudge(1, +1)]
assert imath.log(0) == interval[-fpu.infinity]
assert imath.log(interval[0, 1]) == interval[-fpu.infinity, 0]
assert imath.log(interval[-1, 1]) == interval[-fpu.infinity, 0]
assert imath.log(interval[-2, -1]) == interval()
def test_log(self):
self.assertEqual(imath.log(1), interval[0])
self.assertEqual(imath.log(0), interval[-fpu.infinity])
self.assertEqual(imath.log(imath.exp(1)),
interval[helpers.nudge(1, -1),
helpers.nudge(1, +1)])
self.assertEqual(imath.log(0), interval[-fpu.infinity])
self.assertEqual(imath.log(interval[0, 1]), interval[-fpu.infinity, 0])
self.assertEqual(imath.log(interval[-1, 1]), interval[-fpu.infinity,
0])
self.assertEqual(imath.log(interval[-2, -1]), interval())
def __fwd_eval(self, n_id, box):
n = self.dag[n_id]
fwd = self.__fwd
rec = self.__fwd_eval
if n[0] == '+':
rec(n[1], box)
rec(n[2], box)
fwd[n_id] = fwd[n[1]] + fwd[n[2]]
elif n[0] == '-':
rec(n[1], box)
rec(n[2], box)
fwd[n_id] = fwd[n[1]] - fwd[n[2]]
elif n[0] == '*':
rec(n[1], box)
rec(n[2], box)
fwd[n_id] = fwd[n[1]] * fwd[n[2]]
elif n[0] == '/':
rec(n[1], box)
rec(n[2], box)
fwd[n_id] = fwd[n[1]] / fwd[n[2]]
elif n[0] == '^':
rec(n[1], box)
i = self.dag[n[2]][1]
fwd[n_id] = fwd[n[1]]**i
elif n[0] == 'exp':
rec(n[1], box)
fwd[n_id] = imath.exp(fwd[n[1]])
elif n[0] == 'sqrt':
rec(n[1], box)
fwd[n_id] = imath.sqrt(fwd[n[1]])
elif n[0] == 'sin':
rec(n[1], box)
fwd[n_id] = imath.sin(fwd[n[1]])
elif n[0] == 'cos':
rec(n[1], box)
fwd[n_id] = imath.cos(fwd[n[1]])
elif n[0] == 'C':
fwd[n_id] = interval[n[1]]
elif n[0] == 'V':
fwd[n_id] = box[n[1]]
else:
print('unsupported node: ' + n)
assert (False)
def test_exp(self):
self.assertEqual(imath.exp(0), interval[1])
self.assertEqual(imath.exp(1), interval[math.e, helpers.nudge(math.e, +1)])
self.assertEqual(imath.exp(interval([-fpu.infinity, 0], [1, fpu.infinity])),
interval([0, 1], [math.e, fpu.infinity]))
def test_exp(self):
z = interval[-100, 100].newton(lambda x: imath.exp(x) + x, lambda x: imath.exp(x) + 1)
assert z == interval[-0.56714329040978395, helpers.nudge(-0.56714329040978395, +1)]
w = interval[-100, 100].newton(lambda x: imath.exp(-x)*x + 1, lambda x: imath.exp(-x)*(1-x))
assert z == w
def test_sinh(self):
self.assertEqual(imath.sinh(0), interval[0])
assert imath.sinh(1) in ((imath.exp(1) - imath.exp(-1))/2)
def test_exp(self):
assert imath.exp(0) == interval[1]
assert imath.exp(1) == interval[math.e, helpers.nudge(math.e, +1)]
assert (
imath.exp(interval([-fpu.infinity, 0], [1, fpu.infinity])) ==
interval([0, 1], [math.e, fpu.infinity]))
def test_sinh(self):
assert imath.sinh(0) == interval[0]
assert imath.sinh(1) in ((imath.exp(1) - imath.exp(-1)) / 2)
def test_expm1(self):
assert imath.expm1(0) == interval[0]
assert imath.expm1(1) in (imath.exp(1) - 1)
def test_expm1(self):
assert imath.expm1(0) == interval[0]
assert imath.expm1(1) in (imath.exp(1) - 1)
def test_expm1(self):
self.assertEqual(imath.expm1(0), interval[0])
assert imath.expm1(1) in (imath.exp(1) - 1)
def test_sinh(self):
assert imath.sinh(0) == interval[0]
assert imath.sinh(1) in ((imath.exp(1) - imath.exp(-1)) / 2)
def test_sinh(self):
self.assertEqual(imath.sinh(0), interval[0])
assert imath.sinh(1) in ((imath.exp(1) - imath.exp(-1)) / 2)
def test_expm1(self):
self.assertEqual(imath.expm1(0), interval[0])
assert imath.expm1(1) in (imath.exp(1) - 1)
def __eval(self, n_id, box):
n = self.__dag[n_id]
rec = self.__eval
if n[0] == '+':
v1 = rec(n[1], box)
v2 = rec(n[2], box)
return v1 + v2
elif n[0] == '-':
v1 = rec(n[1], box)
v2 = rec(n[2], box)
return v1 - v2
elif n[0] == '*':
v1 = rec(n[1], box)
v2 = rec(n[2], box)
return v1 * v2
elif n[0] == '/':
v1 = rec(n[1], box)
v2 = rec(n[2], box)
return v1 / v2
elif n[0] == '^':
v = rec(n[1], box)
i = self.__dag[n[2]][1]
return v**i
elif n[0] == 'exp':
v = rec(n[1], box)
return imath.exp(v)
elif n[0] == 'log':
v = rec(n[1], box)
return imath.log(v)
elif n[0] == 'sqrt':
v = rec(n[1], box)
return imath.sqrt(v)
elif n[0] == 'sin':
v = rec(n[1], box)
return imath.sin(v)
elif n[0] == 'cos':
v = rec(n[1], box)
return imath.cos(v)
elif n[0] == 'tan':
v = rec(n[1], box)
return imath.tan(v)
elif n[0] == 'asin':
v = rec(n[1], box)
return imath.asin(v)
elif n[0] == 'acos':
v = rec(n[1], box)
return imath.acos(v)
elif n[0] == 'atan':
v = rec(n[1], box)
return imath.atan(v)
elif n[0] == 'sinh':
v = rec(n[1], box)
return imath.sinh(v)
elif n[0] == 'cosh':
v = rec(n[1], box)
return imath.cosh(v)
elif n[0] == 'tanh':
v = rec(n[1], box)
return imath.tanh(v)
elif n[0] == 'C':
return interval[n[1]]
elif n[0] == 'V':
return box[n[1]]
else:
print('unsupported node: ' + str(n))
assert (False)
def pow(x, n):
return imath.exp(n * imath.log(x))
def test_exp(self):
assert imath.exp(0) == interval[1]
assert imath.exp(1) == interval[math.e, helpers.nudge(math.e, +1)]
assert (imath.exp(interval([-fpu.infinity, 0],
[1, fpu.infinity])) == interval(
[0, 1], [math.e, fpu.infinity]))