def test_unimplemented_interpreter_rules(self):
foo_p = Primitive('foo')
def foo(x):
return foo_p.bind(x)
jtu.check_raises(lambda: foo(1.0), NotImplementedError,
"Evaluation rule for 'foo' not implemented")
jtu.check_raises(lambda: jit(foo)(1.0), NotImplementedError,
"Abstract evaluation for 'foo' not implemented")
jtu.check_raises(
lambda: grad(foo)(1.0), NotImplementedError,
"Forward-mode differentiation rule for 'foo' not implemented")
foo_p.def_abstract_eval(lambda x: x)
jtu.check_raises(lambda: jit(foo)(1.0), NotImplementedError,
"XLA translation rule for 'foo' not implemented")
foo_p.def_impl(lambda x: x)
defjvp(foo_p, lambda g, x: foo(g))
jtu.check_raises(
lambda: grad(foo)(1.0), NotImplementedError,
"Reverse-mode differentiation rule for 'foo' not implemented")
def decorator(fenics_function: Callable) -> Callable:
@functools.wraps(fenics_function)
@custom_vjp
def jax_fem_eval(*args):
return jax_fem_eval_p.bind(*args)
jax_fem_eval_p = Primitive("jax_fem_eval")
jax_fem_eval_p.def_impl(
lambda *args: evaluate_primal(fenics_function, fenics_templates, *args)[0]
)
jax_fem_eval_p.def_abstract_eval(
lambda *args: jax.abstract_arrays.make_shaped_array(
evaluate_primal(fenics_function, fenics_templates, *args)[0]
)
)
def jax_fem_eval_batch(vector_arg_values, batch_axes):
assert len(set(batch_axes)) == 1 # assert that all batch axes are same
assert (
batch_axes[0] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
res = list(map(jax_fem_eval, *vector_arg_values))
res = np.asarray(res)
return res, batch_axes[0]
jax.interpreters.batching.primitive_batchers[
jax_fem_eval_p
] = jax_fem_eval_batch
def primal(*args):
numpy_output, fenics_output, fenics_inputs, tape = evaluate_primal(
fenics_function, fenics_templates, *args
)
return (
numpy_output,
(PyadjointMetadata(fenics_output, fenics_inputs, tape), args),
)
def pullback(aux_args, g):
pb_fn = get_pullback_function(fenics_function, fenics_templates)
# for some reason output of get_pullback_function is a list but we need tuple
return tuple(pb_fn(aux_args, g))
jax_fem_eval.defvjp(primal, pullback)
return jax_fem_eval
def decorator(fenics_function: Callable) -> Callable:
@functools.wraps(fenics_function)
def jax_solve_eval(*args):
return jax_solve_eval_p.bind(*args)
jax_solve_eval_p = Primitive("jax_solve_eval")
jax_solve_eval_p.def_impl(lambda *args: solve_eval(
fenics_function, fenics_templates, *args)[0])
jax_solve_eval_p.def_abstract_eval(
lambda *args: jax.abstract_arrays.make_shaped_array(
solve_eval(fenics_function, fenics_templates, *args)[0]))
def jax_solve_eval_batch(vector_arg_values, batch_axes):
assert len(
set(batch_axes)) == 1 # assert that all batch axes are same
assert (
batch_axes[0] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
# compute function row-by-row
res = np.asarray([
jax_solve_eval(*(vector_arg_values[j][i]
for j in range(len(batch_axes))))
for i in range(vector_arg_values[0].shape[0])
])
return res, batch_axes[0]
jax.batching.primitive_batchers[
jax_solve_eval_p] = jax_solve_eval_batch
# @trace("djax_solve_eval")
def djax_solve_eval(*args):
return djax_solve_eval_p.bind(*args)
djax_solve_eval_p = Primitive("djax_solve_eval")
# djax_solve_eval_p.multiple_results = True
djax_solve_eval_p.def_impl(lambda *args: vjp_solve_eval(
fenics_function, fenics_templates, *args))
defvjp_all(jax_solve_eval_p, djax_solve_eval)
return jax_solve_eval
def decorator(fenics_function: Callable) -> Callable:
def jax_assemble_eval(*args):
return jax_assemble_eval_p.bind(*args)
jax_assemble_eval_p = Primitive("jax_assemble_eval")
jax_assemble_eval_p.def_impl(
lambda *args: assemble_eval(fenics_function, fenics_templates, *args)[0]
)
jax_assemble_eval_p.def_abstract_eval(
lambda *args: jax.abstract_arrays.make_shaped_array(
assemble_eval(fenics_function, fenics_templates, *args)[0]
)
)
def jax_assemble_eval_batch(vector_arg_values, batch_axes):
assert len(set(batch_axes)) == 1 # assert that all batch axes are same
assert (
batch_axes[0] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
res = list(map(jax_assemble_eval, *vector_arg_values))
res = np.asarray(res)
return res, batch_axes[0]
batching.primitive_batchers[jax_assemble_eval_p] = jax_assemble_eval_batch
# @trace("djax_assemble_eval")
def djax_assemble_eval(*args):
return djax_assemble_eval_p.bind(*args)
djax_assemble_eval_p = Primitive("djax_assemble_eval")
# djax_assemble_eval_p.multiple_results = True
djax_assemble_eval_p.def_impl(
lambda *args: vjp_assemble_eval(fenics_function, fenics_templates, *args)
)
defvjp_all(jax_assemble_eval_p, djax_assemble_eval)
return jax_assemble_eval
def decorator(fenics_function: Callable) -> Callable:
@functools.wraps(fenics_function)
def jax_solve_eval(*args):
return jax_solve_eval_p.bind(*args)
jax_solve_eval_p = Primitive("jax_solve_eval")
jax_solve_eval_p.def_impl(
lambda *args: solve_eval(fenics_function, fenics_templates, *args)[0]
)
jax_solve_eval_p.def_abstract_eval(
lambda *args: jax.abstract_arrays.make_shaped_array(
solve_eval(fenics_function, fenics_templates, *args)[0]
)
)
def jax_solve_eval_batch(vector_arg_values, batch_axes):
assert len(set(batch_axes)) == 1 # assert that all batch axes are same
assert (
batch_axes[0] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
res = list(map(jax_solve_eval, *vector_arg_values))
res = np.asarray(res)
return res, batch_axes[0]
jax.batching.primitive_batchers[jax_solve_eval_p] = jax_solve_eval_batch
# @trace("jvp_jax_solve_eval")
def jvp_jax_solve_eval(ps, ts):
return jvp_jax_solve_eval_p.bind(ps, ts)
jvp_jax_solve_eval_p = Primitive("jvp_jax_solve_eval")
jvp_jax_solve_eval_p.multiple_results = True
jvp_jax_solve_eval_p.def_impl(
lambda ps, ts: jvp_solve_eval(fenics_function, fenics_templates, ps, ts)
)
jax.interpreters.ad.primitive_jvps[jax_solve_eval_p] = jvp_jax_solve_eval
# TODO: JAX Tracer goes inside fenics wrappers and zero array is returned
# because fenics numpy conversion works only for concrete arrays
vjp_jax_solve_eval_p = Primitive("vjp_jax_solve_eval")
vjp_jax_solve_eval_p.def_impl(
lambda ct, *args: vjp_solve_eval(fenics_function, fenics_templates, *args)[
1
](ct)
)
jax.interpreters.ad.primitive_transposes[
jax_solve_eval_p
] = vjp_jax_solve_eval_p
return jax_solve_eval
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_scatter_abstract_eval(x, token, root, comm):
comm = unpack_hashable(comm)
rank = comm.Get_rank()
if rank == root:
out_shape = x.shape[1:]
else:
out_shape = x.shape
return (
abstract_arrays.ShapedArray(out_shape, x.dtype),
core.abstract_token,
)
mpi_scatter_p.multiple_results = True
mpi_scatter_p.def_impl(mpi_scatter_impl)
mpi_scatter_p.def_abstract_eval(mpi_scatter_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][
mpi_scatter_p] = mpi_scatter_xla_encode_cpu
xla.backend_specific_translations["gpu"][
mpi_scatter_p] = mpi_scatter_xla_encode_gpu
scale = 1 / prod(fft_lengths)
out = scale * mask * x
assert out.dtype == _complex_dtype(t.dtype), (out.dtype, t.dtype)
# Use JAX's convention for complex gradients
# https://github.com/google/jax/issues/6223#issuecomment-807740707
return lax.conj(out)
def fft_transpose_rule(t, operand, fft_type, fft_lengths):
if fft_type == xla_client.FftType.RFFT:
result = _rfft_transpose(t, fft_lengths)
elif fft_type == xla_client.FftType.IRFFT:
result = _irfft_transpose(t, fft_lengths)
else:
result = fft(t, fft_type, fft_lengths)
return result,
def fft_batching_rule(batched_args, batch_dims, fft_type, fft_lengths):
x, = batched_args
bd, = batch_dims
x = batching.moveaxis(x, bd, 0)
return fft(x, fft_type, fft_lengths), 0
fft_p = Primitive('fft')
fft_p.def_impl(fft_impl)
fft_p.def_abstract_eval(fft_abstract_eval)
xla.translations[fft_p] = fft_translation_rule
ad.deflinear2(fft_p, fft_transpose_rule)
batching.primitive_batchers[fft_p] = fft_batching_rule
if pocketfft:
xla.backend_specific_translations['cpu'][fft_p] = pocketfft.pocketfft
operands=(
sendbuf,
token,
),
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_allgather_abstract_eval(x, token, comm):
comm = unpack_hashable(comm)
size = comm.Get_size()
out_shape = (size, *x.shape)
return (
abstract_arrays.ShapedArray(out_shape, x.dtype),
abstract_arrays.abstract_token,
)
mpi_allgather_p.multiple_results = True
mpi_allgather_p.def_impl(mpi_allgather_impl)
mpi_allgather_p.def_abstract_eval(mpi_allgather_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][
mpi_allgather_p] = mpi_allgather_xla_encode_cpu
xla.backend_specific_translations["gpu"][
mpi_allgather_p] = mpi_allgather_xla_encode_gpu
# Use JAX's convention for complex gradients
# https://github.com/google/jax/issues/6223#issuecomment-807740707
return lax.conj(out)
def _fft_transpose_rule(t, operand, fft_type, fft_lengths):
if fft_type == xla_client.FftType.RFFT:
result = _rfft_transpose(t, fft_lengths)
elif fft_type == xla_client.FftType.IRFFT:
result = _irfft_transpose(t, fft_lengths)
else:
result = fft(t, fft_type, fft_lengths)
return result,
def _fft_batching_rule(batched_args, batch_dims, fft_type, fft_lengths):
x, = batched_args
bd, = batch_dims
x = batching.moveaxis(x, bd, 0)
return fft(x, fft_type, fft_lengths), 0
fft_p = Primitive('fft')
fft_p.def_impl(_fft_impl)
fft_p.def_abstract_eval(fft_abstract_eval)
mlir.register_lowering(fft_p, _fft_lowering)
ad.deflinear2(fft_p, _fft_transpose_rule)
batching.primitive_batchers[fft_p] = _fft_batching_rule
if pocketfft:
mlir.register_lowering(fft_p, _fft_lowering_cpu, platform='cpu')
import numpy as np
from jax.util import safe_map, safe_zip
from jax.core import Primitive
from jax.interpreters import ad, xla, batching, numpy_eval
from jax.lax import dynamic_update_slice_p
map = safe_map
zip = safe_zip
inplace_dynamic_update_slice_p = Primitive('inplace_dynamic_update_slice')
inplace_dynamic_update_slice_p.def_impl(dynamic_update_slice_p.impl)
inplace_dynamic_update_slice_p.def_abstract_eval(dynamic_update_slice_p.abstract_eval)
for rules in [xla.translations, ad.primitive_jvps, ad.primitive_transposes,
batching.primitive_batchers]:
rules[inplace_dynamic_update_slice_p] = rules[dynamic_update_slice_p]
def _numpy_inplace_dynamic_update_slice(operand, update, *start_indices):
slices = tuple(map(slice, start_indices, np.add(start_indices, update.shape)))
operand[slices] = update
return operand
numpy_eval.np_impl[inplace_dynamic_update_slice_p] = \
_numpy_inplace_dynamic_update_slice
def inplace_dynamic_update_slice(operand, update, start_indices):
return inplace_dynamic_update_slice_p.bind(operand, update, *start_indices)
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_gather_abstract_eval(x, token, root, comm):
comm = unpack_hashable(comm)
rank = comm.Get_rank()
size = comm.Get_size()
if rank == root:
out_shape = (size, *x.shape)
else:
out_shape = x.shape
return (
abstract_arrays.ShapedArray(out_shape, x.dtype),
core.abstract_token,
)
mpi_gather_p.multiple_results = True
mpi_gather_p.def_impl(mpi_gather_impl)
mpi_gather_p.def_abstract_eval(mpi_gather_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][mpi_gather_p] = mpi_gather_xla_encode_cpu
xla.backend_specific_translations["gpu"][mpi_gather_p] = mpi_gather_xla_encode_gpu
def get_pullback_function(
fenics_function: Callable, fenics_templates: Collection[BackendVariable]
) -> Callable:
"""Computes the gradients of the output with respect to the input
Input:
fenics_function (callable): FEniCS function to be executed during the forward pass
Output:
A Python callable representing the VJP map from output cotangents to input cotangents.
The returned VJP function must accept a value with the same shape as the value of fun applied
to the arguments and must return a tuple with length equal to the number of positional arguments to fun.
"""
# @trace("vjp_fun1")
def vjp_fun1(aux_args, g):
return vjp_fun1_p.bind(aux_args, g)
def vjp_fun1_p_impl(aux_args, g):
fe_aux, args = aux_args
fenics_output, fenics_inputs, tape = (
fe_aux.fenics_output,
fe_aux.fenics_inputs,
fe_aux.tape,
)
return tuple(
vjp if vjp is not None else jax.ad_util.zeros_like_jaxval(args[i])
for i, vjp in enumerate(
evaluate_pullback(fenics_output, fenics_inputs, tape, g)
)
)
vjp_fun1_p = Primitive("vjp_fun1")
vjp_fun1_p.multiple_results = True
vjp_fun1_p.def_impl(vjp_fun1_p_impl)
# @trace("vjp_fun1_abstract_eval")
def vjp_fun1_abstract_eval(aux_args, g):
_, args = aux_args
if len(args) > 1:
return tuple(
(jax.abstract_arrays.ShapedArray(arg.shape, arg.dtype) for arg in args)
)
else:
return (
jax.abstract_arrays.ShapedArray((1, *args[0].shape), args[0].dtype),
)
vjp_fun1_p.def_abstract_eval(vjp_fun1_abstract_eval)
# @trace("vjp_fun1_batch")
def vjp_fun1_batch(vector_arg_values, batch_axes):
"""Computes the batched version of the primitive.
This must be a JAX-traceable function.
Args:
vector_arg_values: a tuple of arguments, each being a tensor of matching
shape.
batch_axes: the axes that are being batched. See vmap documentation.
Returns:
a tuple of the result, and the result axis that was batched.
"""
# _trace("Using vjp_fun1 to compute the batch:")
_, args = vector_arg_values[0]
assert (
batch_axes[0] is None
) # assert that batch axis is None, need to rewrite for a general case?
assert (
batch_axes[1] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
# apply function row-by-row
vjp_fun1_partial = functools.partial(vjp_fun1, vector_arg_values[0])
res = list(map(vjp_fun1_partial, *(vector_arg_values[1],)))
# transpose resulting list
res_T = list(itertools.zip_longest(*res))
return tuple(map(np.vstack, res_T)), (batch_axes[1],) * len(args)
jax.interpreters.batching.primitive_batchers[vjp_fun1_p] = vjp_fun1_batch
return vjp_fun1
def decorator(fenics_function: Callable) -> Callable:
@functools.wraps(fenics_function)
def jax_fem_eval(*args):
return jax_fem_eval_p.bind(*args)
jax_fem_eval_p = Primitive("jax_fem_eval")
def jax_fem_eval_p_impl(*args):
args = (
jax_to_fenics_numpy(arg, ft) for arg, ft in zip(args, fenics_templates)
)
return evaluate_primal(fenics_function, fenics_templates, *args)[0]
jax_fem_eval_p.def_impl(jax_fem_eval_p_impl)
def jax_fem_eval_p_abstract_eval(*args):
args = (
jax_to_fenics_numpy(arg, ft) for arg, ft in zip(args, fenics_templates)
)
return jax.abstract_arrays.make_shaped_array(
evaluate_primal(fenics_function, fenics_templates, *args)[0]
)
jax_fem_eval_p.def_abstract_eval(jax_fem_eval_p_abstract_eval)
def jax_fem_eval_batch(vector_arg_values, batch_axes):
assert len(set(batch_axes)) == 1 # assert that all batch axes are same
assert (
batch_axes[0] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
res = list(map(jax_fem_eval, *vector_arg_values))
res = np.asarray(res)
return res, batch_axes[0]
jax.interpreters.batching.primitive_batchers[
jax_fem_eval_p
] = jax_fem_eval_batch
# @trace("jvp_jax_fem_eval")
def jvp_jax_fem_eval(ps, ts):
return jvp_jax_fem_eval_p.bind(ps, ts)
jvp_jax_fem_eval_p = Primitive("jvp_jax_fem_eval")
jvp_jax_fem_eval_p.multiple_results = True
def jvp_jax_fem_eval_impl(primals, tangents):
primals = (
jax_to_fenics_numpy(p, ft) for p, ft in zip(primals, fenics_templates)
)
numpy_output, fenics_output, fenics_inputs, tape = evaluate_primal(
fenics_function, fenics_templates, *primals
)
tangents = (
jax_to_fenics_numpy(t, ft) for t, ft in zip(tangents, fenics_templates)
)
dnumpy_output = evaluate_pushforward(
fenics_output, fenics_inputs, tape, tangents
)
return numpy_output, dnumpy_output
jvp_jax_fem_eval_p.def_impl(jvp_jax_fem_eval_impl)
jax.interpreters.ad.primitive_jvps[jax_fem_eval_p] = jvp_jax_fem_eval
# TODO: JAX Tracer goes inside fenics wrappers and zero array is returned
# because fenics numpy conversion works only for concrete arrays
# vjp_jax_fem_eval_p = Primitive("vjp_jax_fem_eval")
# vjp_jax_fem_eval_p.def_impl(
# lambda ct, *args: vjp_fem_eval(fenics_function, fenics_templates, *args)[1](
# ct
# )
# )
# jax.interpreters.ad.primitive_transposes[jax_fem_eval_p] = vjp_jax_fem_eval_p
return jax_fem_eval
def PmapPrimitive(name):
prim = Primitive(name)
prim.def_impl(partial(_unbound_name_error, name))
prim.def_abstract_eval(lambda x, *args, **kwargs: x)
return prim
)
return xla_client.ops.CustomCall(
c,
b"mpi_scan",
operands=(
x,
token,
),
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_scan_abstract_eval(xs, token, op, comm):
return (
abstract_arrays.ShapedArray(xs.shape, xs.dtype),
core.abstract_token,
)
mpi_scan_p.multiple_results = True
mpi_scan_p.def_impl(mpi_scan_impl)
mpi_scan_p.def_abstract_eval(mpi_scan_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][mpi_scan_p] = mpi_scan_xla_encode_cpu
xla.backend_specific_translations["gpu"][mpi_scan_p] = mpi_scan_xla_encode_gpu
operands=(a, b, c, d),
shape_with_layout=shape,
operand_shapes_with_layout=(shape, ) * 4,
opaque=opaque)
def tridiag(a, b, c, d):
if not a.shape == b.shape == c.shape == d.shape:
raise ValueError('all inputs must have identical shape')
if not a.dtype == b.dtype == c.dtype == d.dtype:
raise ValueError('all inputs must have the same dtype')
return tridiag_p.bind(a, b, c, d) #transpose(res, (0,2,1))
def tridiag_impl(*args, **kwargs):
return xla.apply_primitive(tridiag_p, *args, **kwargs)
def _tridiag_gpu_translation_rule(computation_builder, a, b, c, d):
return _tridiag(computation_builder, a, b, c, d)
def tridiag_abstract_eval(a, b, c, d):
return abstract_arrays.ShapedArray(a.shape, a.dtype)
tridiag_p = Primitive('tridiag')
tridiag_p.def_impl(tridiag_impl)
tridiag_p.def_abstract_eval(tridiag_abstract_eval)
xla.backend_specific_translations['gpu'][
tridiag_p] = _tridiag_gpu_translation_rule
return grads.reshape(alpha.shape)
def _standard_gamma_abstract_eval(key, alpha, jaxpr, aval, consts):
return lax.maybe_tracer_tuple_to_abstract_tuple(aval)
def _standard_gamma_translate(c, key, alpha, jaxpr, aval, consts):
xla_computation = xla.jaxpr_computation(jaxpr, consts, (), c.GetShape(key),
c.GetShape(alpha))
return c.Call(xla_computation, (key, alpha))
# define primitive
standard_gamma_p = Primitive('standard_gamma')
standard_gamma_p.def_impl(partial(xla.apply_primitive, standard_gamma_p))
standard_gamma_p.def_abstract_eval(_standard_gamma_abstract_eval)
xla.translations[standard_gamma_p] = _standard_gamma_translate
ad.defjvp2(
standard_gamma_p, None, lambda tangent, sample, key, alpha, **kwargs:
tangent * _standard_gamma_grad(sample, alpha))
@partial(jit, static_argnums=(2, 3))
def standard_gamma(key, alpha, shape=(), dtype=np.float32):
shape = shape or np.shape(alpha)
alpha = lax.convert_element_type(alpha, dtype)
if np.shape(alpha) != shape:
alpha = np.broadcast_to(alpha, shape)
jaxpr, out, consts = partial_eval.trace_unwrapped_to_jaxpr(
_standard_gamma_impl, tuple(lax._abstractify(o) for o in (key, alpha)))
out = _ops.CustomCall(
c,
b"mpi_send",
operands=(
_nitems,
x,
_constant_s32_scalar(c, dest),
_constant_s32_scalar(c, tag),
_constant_u64_scalar(c, to_mpi_ptr(comm)),
_constant_u64_scalar(c, _dtype_ptr),
token,
),
shape=sh,
has_side_effect=True,
)
return xla_client.ops.GetTupleElement(out, 0)
# This function evaluates only the shapes during AST construction
def mpi_send_abstract_eval(xs, token, dest, tag, comm):
return abstract_arrays.abstract_token
# mpi_send_p.multiple_results = True
mpi_send_p.def_impl(mpi_send_impl)
mpi_send_p.def_abstract_eval(mpi_send_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][mpi_send_p] = mpi_send_xla_encode
return xla_client.ops.CustomCall(
c,
b"mpi_alltoall",
operands=(
x,
token,
),
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_alltoall_abstract_eval(xs, token, comm):
return (
abstract_arrays.ShapedArray(xs.shape, xs.dtype),
core.abstract_token,
)
mpi_alltoall_p.multiple_results = True
mpi_alltoall_p.def_impl(mpi_alltoall_impl)
mpi_alltoall_p.def_abstract_eval(mpi_alltoall_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][
mpi_alltoall_p] = mpi_alltoall_xla_encode_cpu
xla.backend_specific_translations["gpu"][
mpi_alltoall_p] = mpi_alltoall_xla_encode_gpu
def vjp_solve_eval(fenics_function: Callable, fenics_templates: FenicsVariable,
*args: np.array) -> Tuple[np.array, Callable]:
"""Computes the gradients of the output with respect to the input
Input:
fenics_function (callable): FEniCS function to be executed during the forward pass
args (tuple): jax array representation of the input to fenics_function
Output:
A pair where the first element is the value of fun applied to the arguments and the second element
is a Python callable representing the VJP map from output cotangents to input cotangents.
The returned VJP function must accept a value with the same shape as the value of fun applied
to the arguments and must return a tuple with length equal to the number of positional arguments to fun.
"""
numpy_output, fenics_solution, residual_form, fenics_inputs, bcs = solve_eval(
fenics_function, fenics_templates, *args)
# @trace("vjp_fun1")
def vjp_fun1(g):
return vjp_fun1_p.bind(g)
vjp_fun1_p = Primitive("vjp_fun1")
vjp_fun1_p.multiple_results = True
vjp_fun1_p.def_impl(lambda g: tuple(
vjp if vjp is not None else jax.ad_util.zeros_like_jaxval(args[i])
for i, vjp in enumerate(
vjp_solve_eval_impl(g, fenics_solution, residual_form,
fenics_inputs, bcs))))
# @trace("vjp_fun1_abstract_eval")
def vjp_fun1_abstract_eval(g):
if len(args) > 1:
return tuple(
(jax.abstract_arrays.ShapedArray(arg.shape, arg.dtype)
for arg in args))
else:
return (jax.abstract_arrays.ShapedArray((1, *args[0].shape),
args[0].dtype), )
vjp_fun1_p.def_abstract_eval(vjp_fun1_abstract_eval)
# @trace("vjp_fun1_batch")
def vjp_fun1_batch(vector_arg_values, batch_axes):
"""Computes the batched version of the primitive.
This must be a JAX-traceable function.
Args:
vector_arg_values: a tuple of arguments, each being a tensor of matching
shape.
batch_axes: the axes that are being batched. See vmap documentation.
Returns:
a tuple of the result, and the result axis that was batched.
"""
# _trace("Using vjp_fun1 to compute the batch:")
assert (
batch_axes[0] == 0
) # assert that batch axis is zero, need to rewrite for a general case?
# compute function row-by-row
res = [
vjp_fun1(vector_arg_values[0][i])
for i in range(vector_arg_values[0].shape[0])
]
# transpose resulting list
res_T = list(itertools.zip_longest(*res))
return tuple(map(np.vstack, res_T)), (batch_axes[0], ) * len(args)
jax.interpreters.batching.primitive_batchers[vjp_fun1_p] = vjp_fun1_batch
return numpy_output, vjp_fun1
elif x.shape[i_old] > 1 and new_sizes[i_new] <= 1:
i_new += 1
else:
assert x.shape[i_old] == new_sizes[i_new]
i_old += 1
i_new += 1
return out_indices,
op2ind[lax.reshape_p] = reshape2ind
# Custom Primitive
tex_var_p = Primitive('tex_var')
tex_var_p.def_impl(lambda x, *depends_on, **kwargs: x)
tex_var_p.def_abstract_eval(lambda x, *depends_on, **kwargs: x)
def tex_var_jvp(primals, tangents, name, is_alias):
primal_out = tex_var(primals[0], name, is_alias, primals[1:])
tangent_out = tex_var(tangents[0], 'd' + name, False, primals[1:])
return primal_out, tangent_out
ad.primitive_jvps[tex_var_p] = tex_var_jvp
def tex_var_transpose(ct, x, *depends_on, **params):
del x
ct = tex_var(ct, '\\delta ' + params['name'][1:], False, depends_on)
return (ct,) + (ad.Zero,) * len(depends_on)
ad.primitive_transposes[tex_var_p] = tex_var_transpose
return xla_client.ops.CustomCall(
c,
b"mpi_reduce",
operands=(
x,
token,
),
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_reduce_abstract_eval(xs, token, op, root, comm):
return (
abstract_arrays.ShapedArray(xs.shape, xs.dtype),
abstract_arrays.abstract_token,
)
mpi_reduce_p.multiple_results = True
mpi_reduce_p.def_impl(mpi_reduce_impl)
mpi_reduce_p.def_abstract_eval(mpi_reduce_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][
mpi_reduce_p] = mpi_reduce_xla_encode_cpu
xla.backend_specific_translations["gpu"][
mpi_reduce_p] = mpi_reduce_xla_encode_gpu
== cosu.dtype == dt_tracer.dtype:
raise ValueError('all inputs must have the same dtype')
return superbee_p.bind(var, u_wgrid, v_wgrid, w_wgrid, maskW, dxt, dyt,
dzw, cost, cosu, dt_tracer)
def superbee_impl(*args, **kwargs):
return xla.apply_primitive(superbee_p, *args, **kwargs)
def _superbee_gpu_translation_rule(computation_builder, var, u_wgrid, v_wgrid,
w_wgrid, maskW, dxt, dyt, dzw, cost, cosu,
dt_tracer):
return _superbee(computation_builder, var, u_wgrid, v_wgrid, w_wgrid,
maskW, dxt, dyt, dzw, cost, cosu, dt_tracer)
def superbee_abstract_eval(var, u_wgrid, v_wgrid, w_wgrid, maskW, dxt, dyt,
dzw, cost, cosu, dt_tracer):
aarr = abstract_arrays.ShapedArray(var.shape, var.dtype)
return (aarr, ) * 3
superbee_p = Primitive('superbee')
superbee_p.multiple_results = True
superbee_p.def_impl(superbee_impl)
superbee_p.def_abstract_eval(superbee_abstract_eval)
xla.backend_specific_translations['gpu'][
superbee_p] = _superbee_gpu_translation_rule
compute_right_eigenvectors):
if compute_left_eigenvectors or compute_right_eigenvectors:
raise NotImplementedError(
'The derivatives of eigenvectors are not implemented, only '
'eigenvalues. See '
'https://github.com/google/jax/issues/2748 for discussion.')
# Formula for derivative of eigenvalues w.r.t. a is eqn 4.60 in
# https://arxiv.org/abs/1701.00392
a, = primals
da, = tangents
l, v = eig(a, compute_left_eigenvectors=False)
return [l], [jnp.sum(_solve(v, da.astype(v.dtype)) * _T(v), -1)]
eig_p = Primitive('eig')
eig_p.multiple_results = True
eig_p.def_impl(eig_impl)
eig_p.def_abstract_eval(eig_abstract_eval)
xla.translations[eig_p] = eig_translation_rule
xla.backend_specific_translations['cpu'][eig_p] = eig_cpu_translation_rule
batching.primitive_batchers[eig_p] = eig_batching_rule
ad.primitive_jvps[eig_p] = eig_jvp_rule
# Symmetric/Hermitian eigendecomposition
def eigh_impl(operand, lower):
v, w = xla.apply_primitive(eigh_p, operand, lower=lower)
return v, w
def eigh_translation_rule(c, operand, lower):
shape = c.get_shape(operand)
def qr_translation_rule(c, operand, full_matrices):
return c.QR(operand, full_matrices=full_matrices)
def qr_abstract_eval(operand, full_matrices):
if isinstance(operand, ShapedArray):
if operand.ndim < 2:
raise ValueError(
"Argument to QR decomposition must have ndims >= 2")
batch_dims = operand.shape[:-2]
m = operand.shape[-2]
n = operand.shape[-1]
k = m if full_matrices else min(m, n)
q = ShapedArray(batch_dims + (m, k), operand.dtype)
r = ShapedArray(batch_dims + (k, n), operand.dtype)
else:
q = operand
r = operand
return core.AbstractTuple((q, r))
def qr_dtype_rule(operand, full_matrices=True):
return operand.dtype
qr_p = Primitive('qr')
qr_p.def_impl(qr_impl)
qr_p.def_abstract_eval(qr_abstract_eval)
xla.translations[qr_p] = qr_translation_rule
c,
b"mpi_sendrecv",
operands=(
sendbuf,
token,
),
shape=sh,
opaque=descriptor,
has_side_effect=True,
)
# This function evaluates only the shapes during AST construction
def mpi_sendrecv_abstract_eval(sendbuf, recvbuf, token, source, dest, sendtag,
recvtag, comm, status):
return (
abstract_arrays.ShapedArray(recvbuf.shape, recvbuf.dtype),
abstract_arrays.abstract_token,
)
mpi_sendrecv_p.multiple_results = True
mpi_sendrecv_p.def_impl(mpi_sendrecv_impl)
mpi_sendrecv_p.def_abstract_eval(mpi_sendrecv_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][
mpi_sendrecv_p] = mpi_sendrecv_xla_encode_cpu
xla.backend_specific_translations["gpu"][
mpi_sendrecv_p] = mpi_sendrecv_xla_encode_gpu
abstract_arrays.abstract_token,
)
def mpi_allreduce_value_and_jvp(in_args, tan_args, op, comm):
x, token = in_args
x_tan, token_tan = tan_args
res = Allreduce(x, token=token, op=op, comm=comm)
# Identify the correct adjoint
if op == _MPI.SUM:
jvp = (x_tan, token_tan)
else:
raise NotImplementedError(
"The adjoint of allreduce for {} operation is not defined".format(
op))
return (res, jvp)
mpi_allreduce_p.multiple_results = True
mpi_allreduce_p.def_impl(mpi_allreduce_impl)
mpi_allreduce_p.def_abstract_eval(mpi_allreduce_abstract_eval)
ad.primitive_jvps[mpi_allreduce_p] = mpi_allreduce_value_and_jvp
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][
mpi_allreduce_p] = mpi_allreduce_xla_encode
assert len(params) == 0
return ShapedArray((2,), 'uint32')
def _random_key_impl(*args, **params):
assert len(args) == 0
assert len(params) == 0
raise ValueError("This parametrized function is randomized and therefore requires "
"a random key when applied, i. e. `apply(*inputs, key=PRNGKey(0))`.")
random_key_p = Primitive("random_key")
random_key_p.def_custom_bind(bind(random_key_p))
random_key_p.def_impl(_random_key_impl)
random_key_p.def_abstract_eval(_random_key_abstract_eval)
def random_key():
"""When called inside a parametrized function, this will return a unique random key derived from
the `key` argument of `apply` or `init_parameters`."""
return random_key_p.bind()
class parametrized(Primitive):
"""Represents a parametrized function, providing an
`init_parameters` function for bundled initialization of all parameters,
and an `apply` function to evaluate the function given these bundled parameters.
For example, if a dense neural network layer is defined via:
_nan_like(c, vl))
vr = _broadcasting_select(c, xops.Reshape(ok, batch_dims + (1, 1)), vr,
_nan_like(c, vr))
return xops.Tuple(c, [w, vl, vr])
def eig_batching_rule(batched_args, batch_dims):
x, = batched_args
bd, = batch_dims
x = batching.moveaxis(x, bd, 0)
return eig_p.bind(x), (0, 0, 0)
eig_p = Primitive('eig')
eig_p.multiple_results = True
eig_p.def_impl(eig_impl)
eig_p.def_abstract_eval(eig_abstract_eval)
xla.translations[eig_p] = eig_translation_rule
xla.backend_specific_translations['cpu'][eig_p] = eig_cpu_translation_rule
batching.primitive_batchers[eig_p] = eig_batching_rule
# Symmetric/Hermitian eigendecomposition
def eigh_impl(operand, lower):
v, w = xla.apply_primitive(eigh_p, operand, lower=lower)
return v, w
def eigh_translation_rule(c, operand, lower):
shape = c.GetShape(operand)
_nitems,
_constant_s32_scalar(c, source),
_constant_s32_scalar(c, tag),
_constant_u64_scalar(c, to_mpi_ptr(comm)),
_constant_u64_scalar(c, _dtype_ptr),
_constant_u64_scalar(c, _status),
token,
)
out = _ops.CustomCall(
c, b"mpi_recv", operands=operands, shape=sh, has_side_effect=True,
)
return out
# This function evaluates only the shapes during AST construction
def mpi_recv_abstract_eval(xs, token, source, tag, comm, status):
return (
abstract_arrays.ShapedArray(xs.shape, xs.dtype),
abstract_arrays.abstract_token,
)
mpi_recv_p.multiple_results = True
mpi_recv_p.def_impl(mpi_recv_impl)
mpi_recv_p.def_abstract_eval(mpi_recv_abstract_eval)
# assign to the primitive the correct encoder
xla.backend_specific_translations["cpu"][mpi_recv_p] = mpi_recv_xla_encode
