def backward(self):
grad_pos, grad_vel = self.grad_out()
# Run for 100 iterations
it = m.UInt32(100)
loop = m.Loop(it, grad_pos, grad_vel)
n = ek.width(grad_pos)
while loop.cond(it > 0):
# Retrieve loop variables, reverse chronological order
it -= 1
index = it * n + ek.arange(m.UInt32, n)
pos = ek.gather(m.Array2f, self.temp_pos, index)
vel = ek.gather(m.Array2f, self.temp_vel, index)
# Differentiate loop body in reverse mode
ek.enable_grad(pos, vel)
pos_out, vel_out = self.timestep(pos, vel)
ek.set_grad(pos_out, grad_pos)
ek.set_grad(vel_out, grad_vel)
ek.enqueue(pos_out, vel_out)
ek.traverse(m.Float, reverse=True)
# Update loop variables
grad_pos.assign(ek.grad(pos))
grad_vel.assign(ek.grad(vel))
self.set_grad_in('pos', grad_pos)
self.set_grad_in('vel', grad_vel)
def backward(self):
grad_pos, grad_vel = self.grad_out()
pos, vel = self.pos, self.vel
# Run for 100 iterations
it = m.UInt32(0)
loop = m.Loop(it, pos, vel, grad_pos, grad_vel)
while loop.cond(it < 100):
# Take reverse step in time
pos_rev, vel_rev = self.timestep(pos, vel, dt=-0.02)
pos.assign(pos_rev)
vel.assign(vel_rev)
# Take a forward step in time, keep track of derivatives
ek.enable_grad(pos_rev, vel_rev)
pos_fwd, vel_fwd = self.timestep(pos_rev, vel_rev, dt=0.02)
ek.set_grad(pos_fwd, grad_pos)
ek.set_grad(vel_fwd, grad_vel)
ek.enqueue(pos_fwd, vel_fwd)
ek.traverse(m.Float, reverse=True)
grad_pos.assign(ek.grad(pos_rev))
grad_vel.assign(ek.grad(vel_rev))
it += 1
self.set_grad_in('pos', grad_pos)
self.set_grad_in('vel', grad_vel)
def backward(self):
grad_pos, grad_vel = self.grad_out()
pos, vel = self.pos, self.vel
# Run for 100 iterations
it = m.UInt32(0)
loop = m.Loop("backward", lambda:
(it, pos, vel, grad_pos, grad_vel))
while loop(it < 100):
# Take reverse step in time
pos, vel = self.timestep(pos, vel, dt=-0.02)
# Take a forward step in time, keep track of derivatives
pos_rev, vel_rev = m.Array2f(pos), m.Array2f(vel)
ek.enable_grad(pos_rev, vel_rev)
pos_fwd, vel_fwd = self.timestep(pos_rev, vel_rev, dt=0.02)
ek.set_grad(pos_fwd, grad_pos)
ek.set_grad(vel_fwd, grad_vel)
ek.enqueue(pos_fwd, vel_fwd)
ek.traverse(m.Float, reverse=True)
grad_pos = ek.grad(pos_rev)
grad_vel = ek.grad(vel_rev)
it += 1
self.set_grad_in('pos', grad_pos)
self.set_grad_in('vel', grad_vel)
def test52_scatter_fwd_eager(m):
with EagerMode():
x = m.Float(4.0)
ek.enable_grad(x)
ek.set_grad(x, 1)
values = x * x * ek.linspace(m.Float, 1, 4, 4)
idx = 2 * ek.arange(m.UInt32, 4)
buf = ek.zero(m.Float, 10)
ek.scatter(buf, values, idx)
assert ek.grad_enabled(buf)
ref = [16.0, 0.0, 32.0, 0.0, 48.0, 0.0, 64.0, 0.0, 0.0, 0.0]
assert ek.allclose(buf, ref)
grad = ek.grad(buf)
ref_grad = [8.0, 0.0, 16.0, 0.0, 24.0, 0.0, 32.0, 0.0, 0.0, 0.0]
assert ek.allclose(grad, ref_grad)
# Overwrite first value with non-diff value, resulting gradient entry should be 0
y = m.Float(3)
idx = m.UInt32(0)
ek.scatter(buf, y, idx)
ref = [3.0, 0.0, 32.0, 0.0, 48.0, 0.0, 64.0, 0.0, 0.0, 0.0]
assert ek.allclose(buf, ref)
ek.forward(x)
grad = ek.grad(buf)
ref_grad = [0.0, 0.0, 16.0, 0.0, 24.0, 0.0, 32.0, 0.0, 0.0, 0.0]
assert ek.allclose(grad, ref_grad)
def test49_eager_fwd(m):
with EagerMode():
x = m.Float(1)
ek.enable_grad(x)
ek.set_grad(x, 10)
y = x * x * x
assert ek.grad(y) == 30
def test43_custom_reverse(m):
d = m.Array3f(1, 2, 3)
ek.enable_grad(d)
d2 = ek.custom(Normalize, d)
ek.set_grad(d2, m.Array3f(5, 6, 7))
ek.enqueue(d2)
ek.traverse(m.Float, reverse=True)
assert ek.allclose(ek.grad(d), m.Array3f(0.610883, 0.152721, -0.305441))
def test50_gather_fwd_eager(m):
with EagerMode():
x = ek.linspace(m.Float, -1, 1, 10)
ek.enable_grad(x)
ek.set_grad(x, 1)
y = ek.gather(m.Float, x * x, m.UInt(1, 1, 2, 3))
ref = [-1.55556, -1.55556, -1.11111, -0.666667]
assert ek.allclose(ek.grad(y), ref)
def test44_custom_forward(m):
d = m.Array3f(1, 2, 3)
ek.enable_grad(d)
d2 = ek.custom(Normalize, d)
ek.set_grad(d, m.Array3f(5, 6, 7))
ek.enqueue(d)
ek.traverse(m.Float, reverse=False, retain_graph=True)
assert ek.grad(d) == 0
ek.set_grad(d, m.Array3f(5, 6, 7))
assert ek.allclose(ek.grad(d2), m.Array3f(0.610883, 0.152721, -0.305441))
ek.enqueue(d)
ek.traverse(m.Float, reverse=False, retain_graph=False)
assert ek.allclose(ek.grad(d2),
m.Array3f(0.610883, 0.152721, -0.305441) * 2)
def test_ad_operations(package):
Float, Array3f = package.Float, package.Array3f
prepare(package)
class MyStruct:
ENOKI_STRUCT = {'a': Array3f, 'b': Float}
def __init__(self):
self.a = Array3f()
self.b = Float()
foo = ek.zero(MyStruct, 4)
assert not ek.grad_enabled(foo.a)
assert not ek.grad_enabled(foo.b)
assert not ek.grad_enabled(foo)
ek.enable_grad(foo)
assert ek.grad_enabled(foo.a)
assert ek.grad_enabled(foo.b)
assert ek.grad_enabled(foo)
foo_detached = ek.detach(foo)
assert not ek.grad_enabled(foo_detached.a)
assert not ek.grad_enabled(foo_detached.b)
assert not ek.grad_enabled(foo_detached)
x = Float(4.0)
ek.enable_grad(x)
foo.a += x
foo.b += x * x
ek.forward(x)
foo_grad = ek.grad(foo)
assert foo_grad.a == 1
assert foo_grad.b == 8
ek.set_grad(foo, 5.0)
foo_grad = ek.grad(foo)
assert foo_grad.a == 5.0
assert foo_grad.b == 5.0
ek.accum_grad(foo, 5.0)
foo_grad = ek.grad(foo)
assert foo_grad.a == 10.0
assert foo_grad.b == 10.0
def test51_scatter_reduce_fwd_eager(m):
with EagerMode():
for i in range(3):
idx1 = ek.arange(m.UInt, 5)
idx2 = ek.arange(m.UInt, 4) + 3
x = ek.linspace(m.Float, 0, 1, 5)
y = ek.linspace(m.Float, 1, 2, 4)
buf = ek.zero(m.Float, 10)
if i % 2 == 0:
ek.enable_grad(buf)
ek.set_grad(buf, 1)
if i // 2 == 0:
ek.enable_grad(x, y)
ek.set_grad(x, 1)
ek.set_grad(y, 1)
x.label = "x"
y.label = "y"
buf.label = "buf"
buf2 = m.Float(buf)
ek.scatter_reduce(ek.ReduceOp.Add, buf2, x, idx1)
ek.scatter_reduce(ek.ReduceOp.Add, buf2, y, idx2)
s = ek.dot_async(buf2, buf2)
# Verified against Mathematica
assert ek.allclose(ek.detach(s), 15.5972)
assert ek.allclose(ek.grad(s), (25.1667 if i // 2 == 0 else 0) +
(17 if i % 2 == 0 else 0))
def test53_scatter_fwd_permute_eager(m):
with EagerMode():
x = m.Float(4.0)
ek.enable_grad(x)
ek.set_grad(x, 1)
values_0 = x * ek.linspace(m.Float, 1, 9, 5)
values_1 = x * ek.linspace(m.Float, 11, 19, 5)
buf = ek.zero(m.Float, 10)
idx_0 = ek.arange(m.UInt32, 5)
idx_1 = ek.arange(m.UInt32, 5) + 5
ek.scatter(buf, values_0, idx_0, permute=False)
ek.scatter(buf, values_1, idx_1, permute=False)
ref = [4.0, 12.0, 20.0, 28.0, 36.0, 44.0, 52.0, 60.0, 68.0, 76.0]
assert ek.allclose(buf, ref)
grad = ek.grad(buf)
ref_grad = [1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 13.0, 15.0, 17.0, 19.0]
assert ek.allclose(grad, ref_grad)
def test21_scatter_add_fwd(m):
for i in range(3):
idx1 = ek.arange(m.UInt, 5)
idx2 = ek.arange(m.UInt, 4) + 3
x = ek.linspace(m.Float, 0, 1, 5)
y = ek.linspace(m.Float, 1, 2, 4)
buf = ek.zero(m.Float, 10)
if i % 2 == 0:
ek.enable_grad(buf)
ek.set_grad(buf, 1)
if i // 2 == 0:
ek.enable_grad(x, y)
ek.set_grad(x, 1)
ek.set_grad(y, 1)
x.label = "x"
y.label = "y"
buf.label = "buf"
buf2 = m.Float(buf)
ek.scatter_add(buf2, x, idx1)
ek.scatter_add(buf2, y, idx2)
s = ek.dot_async(buf2, buf2)
if i % 2 == 0:
ek.enqueue(buf)
if i // 2 == 0:
ek.enqueue(x, y)
ek.traverse(m.Float, reverse=False)
# Verified against Mathematica
assert ek.allclose(ek.detach(s), 15.5972)
assert ek.allclose(ek.grad(s), (25.1667 if i // 2 == 0 else 0) +
(17 if i % 2 == 0 else 0))
def test02_add_fwd(m):
if True:
a, b = m.Float(1), m.Float(2)
ek.enable_grad(a, b)
c = 2 * a + b
ek.forward(a, retain_graph=True)
assert ek.grad(c) == 2
ek.set_grad(c, 101)
ek.forward(b)
assert ek.grad(c) == 102
if True:
a, b = m.Float(1), m.Float(2)
ek.enable_grad(a, b)
c = 2 * a + b
ek.set_grad(a, 1.0)
ek.enqueue(a)
ek.traverse(m.Float, retain_graph=True, reverse=False)
assert ek.grad(c) == 2
assert ek.grad(a) == 0
ek.set_grad(a, 1.0)
ek.enqueue(a)
ek.traverse(m.Float, retain_graph=False, reverse=False)
assert ek.grad(c) == 4