def test14_rsqrt(m):
x = m.Float(1, .25, 0.0625)
ek.enable_grad(x)
y = ek.rsqrt(x)
ek.backward(y)
assert ek.allclose(ek.detach(y), [1, 2, 4])
assert ek.allclose(ek.grad(x), [-.5, -4, -32])
def test15_test_avx512_approx():
Float = get_class('enoki.llvm.Float')
x = ek.linspace(Float, 0, 10, 1000)
o = ek.full(Float, 1, 1000)
assert ek.allclose(ek.rsqrt(x), o / ek.sqrt(x), rtol=2e-7, atol=0)
assert ek.allclose(ek.rcp(x), o / x, rtol=2e-7, atol=0)
def matrix_to_quat(m):
if not _ek.is_matrix_v(m):
raise Exception('Unsupported type!')
name = _ek.detail.array_name('Quaternion', m.Type, [4], m.IsScalar)
module = _modules.get(m.__module__)
Quat4f = getattr(module, name)
o = 1.0
t0 = o + m[0, 0] - m[1, 1] - m[2, 2]
q0 = Quat4f(t0, m[1, 0] + m[0, 1], m[0, 2] + m[2, 0], m[2, 1] - m[1, 2])
t1 = o - m[0, 0] + m[1, 1] - m[2, 2]
q1 = Quat4f(m[1, 0] + m[0, 1], t1, m[2, 1] + m[1, 2], m[0, 2] - m[2, 0])
t2 = o - m[0, 0] - m[1, 1] + m[2, 2]
q2 = Quat4f(m[0, 2] + m[2, 0], m[2, 1] + m[1, 2], t2, m[1, 0] - m[0, 1])
t3 = o + m[0, 0] + m[1, 1] + m[2, 2]
q3 = Quat4f(m[2, 1] - m[1, 2], m[0, 2] - m[2, 0], m[1, 0] - m[0, 1], t3)
mask0 = m[0, 0] > m[1, 1]
t01 = _ek.select(mask0, t0, t1)
q01 = _ek.select(mask0, q0, q1)
mask1 = m[0, 0] < -m[1, 1]
t23 = _ek.select(mask1, t2, t3)
q23 = _ek.select(mask1, q2, q3)
mask2 = m[2, 2] < 0.0
t0123 = _ek.select(mask2, t01, t23)
q0123 = _ek.select(mask2, q01, q23)
return q0123 * (_ek.rsqrt(t0123) * 0.5)
def rsqrt_(a0):
if not a0.IsFloat:
raise Exception("rsqrt(): requires floating point operands!")
if not a0.IsSpecial:
ar, sr = _check1(a0)
for i in range(sr):
ar[i] = _ek.rsqrt(a0[i])
return ar
else:
return _ek.rcp(_ek.sqrt(a0))
def test08_misc():
for i in range(-5, 5):
for j in range(-5, 5):
a = ek.sqrt(C(i, j))
b = cmath.sqrt(complex(i, j))
assert ek.allclose(a, C(b))
assert ek.allclose(ek.conj(a), C(b.conjugate()))
assert ek.allclose(ek.abs(a), C(abs(b)))
if i != 0 and j != 0:
a = ek.rsqrt(C(i, j))
b = C(1 / cmath.sqrt(complex(i, j)))
assert ek.allclose(a, b)
def K(self, x, m_):
return ek.rsqrt(1 - m_ * ek.sqr(ek.sin(x)))