def test11_hyp():
for i in range(-5, 5):
for j in range(-5, 5):
a = ek.sinh(C(i, j))
b = C(cmath.sinh(complex(i, j)))
assert ek.allclose(a, b)
a = ek.cosh(C(i, j))
b = C(cmath.cosh(complex(i, j)))
assert ek.allclose(a, b)
sa, ca = ek.sincosh(C(i, j))
sb = C(cmath.sinh(complex(i, j)))
cb = C(cmath.cosh(complex(i, j)))
assert ek.allclose(sa, sb)
assert ek.allclose(ca, cb)
# Python appears to handle the branch cuts
# differently from Enoki, C, and Mathematica..
a = ek.asinh(C(i + 0.1, j))
b = C(cmath.asinh(complex(i + 0.1, j)))
assert ek.allclose(a, b)
a = ek.acosh(C(i, j))
b = C(cmath.acosh(complex(i, j)))
assert ek.allclose(a, b, atol=1e-7)
if abs(i) != 1 or j != 0:
a = ek.atanh(C(i, j))
b = C(cmath.atanh(complex(i, j)))
assert ek.allclose(a, b, atol=1e-7)
def acosh_(a0):
if not a0.IsFloat:
raise Exception("acosh(): requires floating point operands!")
ar, sr = _check1(a0)
if not a0.IsSpecial:
for i in range(sr):
ar[i] = _ek.acosh(a0[i])
elif a0.IsComplex:
return 2 * _ek.log(_ek.sqrt(.5 * (a0 + 1)) + _ek.sqrt(.5 * (a0 - 1)))
else:
raise Exception("acosh(): unsupported array type!")
return ar
def test38_acosh(m):
x = ek.linspace(m.Float, 1.01, 2, 10)
ek.enable_grad(x)
y = ek.acosh(x)
ek.backward(y)
assert ek.allclose(
y,
m.Float(0.141304, 0.485127, 0.665864, 0.802882, 0.916291, 1.01426,
1.10111, 1.17944, 1.25098, 1.31696))
assert ek.allclose(
ek.grad(x),
m.Float(7.05346, 1.98263, 1.39632, 1.12112, 0.952381, 0.835191,
0.747665, 0.679095, 0.623528, 0.57735))