# Copyright 2023 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Tools to create numpy-style ufuncs."""
_AT_INPLACE_WARNING = """\
Because JAX arrays are immutable, jnp.ufunc.at() cannot operate inplace like
np.ufunc.at(). Instead, you can pass inplace=False and capture the result; e.g.
>>> arr = jnp.add.at(arr, ind, val, inplace=False)
"""
from functools import partial
import math
import operator
from typing import Any, Callable, Optional
import jax
from jax._src.typing import Array, ArrayLike, DTypeLike
from jax._src.lax import lax as lax_internal
from jax._src.numpy import reductions
from jax._src.numpy.lax_numpy import _eliminate_deprecated_list_indexing, append, take
from jax._src.numpy.reductions import _moveaxis
from jax._src.numpy.util import _wraps, check_arraylike, _broadcast_to, _where
from jax._src.numpy.vectorize import vectorize
from jax._src.util import canonicalize_axis, set_module
import numpy as np
def get_if_single_primitive(fun: Callable[..., Any], *args: Any) -> Optional[jax.core.Primitive]:
"""
If fun(*args) lowers to a single primitive with inputs and outputs matching
function inputs and outputs, return that primitive. Otherwise return None.
"""
try:
jaxpr = jax.make_jaxpr(fun)(*args)
except:
return None
while len(jaxpr.eqns) == 1:
eqn = jaxpr.eqns[0]
if (eqn.invars, eqn.outvars) != (jaxpr.jaxpr.invars, jaxpr.jaxpr.outvars):
return None
elif (eqn.primitive == jax._src.pjit.pjit_p and
all(jax._src.pjit.is_unspecified(sharding) for sharding in
(*eqn.params['in_shardings'], *eqn.params['out_shardings']))):
jaxpr = jaxpr.eqns[0].params['jaxpr']
else:
return jaxpr.eqns[0].primitive
return None
_primitive_reducers: dict[jax.core.Primitive, Callable[..., Any]] = {
lax_internal.add_p: reductions.sum,
lax_internal.mul_p: reductions.prod,
}
_primitive_accumulators: dict[jax.core.Primitive, Callable[..., Any]] = {
lax_internal.add_p: reductions.cumsum,
lax_internal.mul_p: reductions.cumprod,
}
@set_module('jax.numpy')
class ufunc:
"""Functions that operate element-by-element on whole arrays.
This is a class for LAX-backed implementations of numpy ufuncs.
"""
[docs]
def __init__(self, func: Callable[..., Any], /,
nin: int, nout: int, *,
name: Optional[str] = None,
nargs: Optional[int] = None,
identity: Any = None, update_doc=False):
# We want ufunc instances to work properly when marked as static,
# and for this reason it's important that their properties not be
# mutated. We prevent this by storing them in a dunder attribute,
# and accessing them via read-only properties.
if update_doc:
self.__doc__ = func.__doc__
self.__name__ = name or func.__name__
self.__static_props = {
'func': func,
'call': vectorize(func),
'nin': operator.index(nin),
'nout': operator.index(nout),
'nargs': operator.index(nargs or nin),
'identity': identity
}
_func = property(lambda self: self.__static_props['func'])
_call = property(lambda self: self.__static_props['call'])
nin = property(lambda self: self.__static_props['nin'])
nout = property(lambda self: self.__static_props['nout'])
nargs = property(lambda self: self.__static_props['nargs'])
identity = property(lambda self: self.__static_props['identity'])
def __hash__(self) -> int:
# Do not include _call, because it is computed from _func.
return hash((self._func, self.__name__, self.identity,
self.nin, self.nout, self.nargs))
def __eq__(self, other: Any) -> bool:
# Do not include _call, because it is computed from _func.
return isinstance(other, ufunc) and (
(self._func, self.__name__, self.identity, self.nin, self.nout, self.nargs) ==
(other._func, other.__name__, other.identity, other.nin, other.nout, other.nargs))
def __repr__(self) -> str:
return f"<jnp.ufunc '{self.__name__}'>"
def __call__(self, *args: ArrayLike,
out: None = None, where: None = None,
**kwargs: Any) -> Any:
if out is not None:
raise NotImplementedError(f"out argument of {self}")
if where is not None:
raise NotImplementedError(f"where argument of {self}")
return self._call(*args, **kwargs)
@_wraps(np.ufunc.reduce, module="numpy.ufunc")
@partial(jax.jit, static_argnames=['self', 'axis', 'dtype', 'out', 'keepdims'])
def reduce(self, a: ArrayLike, axis: int = 0, dtype: Optional[DTypeLike] = None,
out: None = None, keepdims: bool = False, initial: Optional[ArrayLike] = None,
where: Optional[ArrayLike] = None) -> Array:
check_arraylike(f"{self.__name__}.reduce", a)
if self.nin != 2:
raise ValueError("reduce only supported for binary ufuncs")
if self.nout != 1:
raise ValueError("reduce only supported for functions returning a single value")
if out is not None:
raise NotImplementedError(f"out argument of {self.__name__}.reduce()")
if initial is not None:
check_arraylike(f"{self.__name__}.reduce", initial)
if where is not None:
check_arraylike(f"{self.__name__}.reduce", where)
if self.identity is None and initial is None:
raise ValueError(f"reduction operation {self.__name__!r} does not have an identity, "
"so to use a where mask one has to specify 'initial'.")
if lax_internal._dtype(where) != bool:
raise ValueError(f"where argument must have dtype=bool; got dtype={lax_internal._dtype(where)}")
primitive = get_if_single_primitive(self._call, *(self.nin * [lax_internal._one(a)]))
if primitive is None:
reducer = self._reduce_via_scan
else:
reducer = _primitive_reducers.get(primitive, self._reduce_via_scan)
return reducer(a, axis=axis, dtype=dtype, keepdims=keepdims, initial=initial, where=where)
def _reduce_via_scan(self, arr: ArrayLike, axis: int = 0, dtype: Optional[DTypeLike] = None,
keepdims: bool = False, initial: Optional[ArrayLike] = None,
where: Optional[ArrayLike] = None) -> Array:
assert self.nin == 2 and self.nout == 1
arr = lax_internal.asarray(arr)
if initial is None:
initial = self.identity
if dtype is None:
dtype = jax.eval_shape(self._func, lax_internal._one(arr), lax_internal._one(arr)).dtype
if where is not None:
where = _broadcast_to(where, arr.shape)
if isinstance(axis, tuple):
axis = tuple(canonicalize_axis(a, arr.ndim) for a in axis)
raise NotImplementedError("tuple of axes")
elif axis is None:
if keepdims:
final_shape = (1,) * arr.ndim
else:
final_shape = ()
arr = arr.ravel()
if where is not None:
where = where.ravel()
axis = 0
else:
axis = canonicalize_axis(axis, arr.ndim)
if keepdims:
final_shape = (*arr.shape[:axis], 1, *arr.shape[axis + 1:])
else:
final_shape = (*arr.shape[:axis], *arr.shape[axis + 1:])
# TODO: handle without transpose?
if axis != 0:
arr = _moveaxis(arr, axis, 0)
if where is not None:
where = _moveaxis(where, axis, 0)
if initial is None and arr.shape[0] == 0:
raise ValueError("zero-size array to reduction operation {self.__name__} which has no ideneity")
def body_fun(i, val):
if where is None:
return self._call(val, arr[i].astype(dtype))
else:
return _where(where[i], self._call(val, arr[i].astype(dtype)), val)
start_value: ArrayLike
if initial is None:
start_index = 1
start_value = arr[0]
else:
start_index = 0
start_value = initial
start_value = _broadcast_to(lax_internal.asarray(start_value).astype(dtype), arr.shape[1:])
result = jax.lax.fori_loop(start_index, arr.shape[0], body_fun, start_value)
if keepdims:
result = result.reshape(final_shape)
return result
@_wraps(np.ufunc.accumulate, module="numpy.ufunc")
@partial(jax.jit, static_argnames=['self', 'axis', 'dtype'])
def accumulate(self, a: ArrayLike, axis: int = 0, dtype: Optional[DTypeLike] = None,
out: None = None) -> Array:
if self.nin != 2:
raise ValueError("accumulate only supported for binary ufuncs")
if self.nout != 1:
raise ValueError("accumulate only supported for functions returning a single value")
if out is not None:
raise NotImplementedError(f"out argument of {self.__name__}.accumulate()")
primitive = get_if_single_primitive(self._call, *(self.nin * [lax_internal._one(a)]))
if primitive is None:
accumulator = self._accumulate_via_scan
else:
accumulator = _primitive_accumulators.get(primitive, self._accumulate_via_scan)
return accumulator(a, axis=axis, dtype=dtype)
def _accumulate_via_scan(self, arr: ArrayLike, axis: int = 0,
dtype: Optional[DTypeLike] = None) -> Array:
assert self.nin == 2 and self.nout == 1
check_arraylike(f"{self.__name__}.accumulate", arr)
arr = lax_internal.asarray(arr)
if dtype is None:
dtype = jax.eval_shape(self._func, lax_internal._one(arr), lax_internal._one(arr)).dtype
if axis is None or isinstance(axis, tuple):
raise ValueError("accumulate does not allow multiple axes")
axis = canonicalize_axis(axis, np.ndim(arr))
arr = _moveaxis(arr, axis, 0)
def scan_fun(carry, _):
i, x = carry
y = _where(i == 0, arr[0].astype(dtype), self._call(x.astype(dtype), arr[i].astype(dtype)))
return (i + 1, y), y
_, result = jax.lax.scan(scan_fun, (0, arr[0].astype(dtype)), None, length=arr.shape[0])
return _moveaxis(result, 0, axis)
@_wraps(np.ufunc.accumulate, module="numpy.ufunc")
@partial(jax.jit, static_argnums=[0], static_argnames=['inplace'])
def at(self, a: ArrayLike, indices: Any, b: Optional[ArrayLike] = None, /, *,
inplace: bool = True) -> Array:
if inplace:
raise NotImplementedError(_AT_INPLACE_WARNING)
if b is None:
return self._at_via_scan(a, indices)
else:
return self._at_via_scan(a, indices, b)
def _at_via_scan(self, a: ArrayLike, indices: Any, *args: Any) -> Array:
assert len(args) in {0, 1}
check_arraylike(f"{self.__name__}.at", a, *args)
dtype = jax.eval_shape(self._func, lax_internal._one(a), *(lax_internal._one(arg) for arg in args)).dtype
a = lax_internal.asarray(a).astype(dtype)
args = tuple(lax_internal.asarray(arg).astype(dtype) for arg in args)
indices = _eliminate_deprecated_list_indexing(indices)
if not indices:
return a
shapes = [np.shape(i) for i in indices if not isinstance(i, slice)]
shape = shapes and jax.lax.broadcast_shapes(*shapes)
if not shape:
return a.at[indices].set(self._call(a.at[indices].get(), *args))
if args:
arg = _broadcast_to(args[0], (*shape, *args[0].shape[len(shape):]))
args = (arg.reshape(math.prod(shape), *args[0].shape[len(shape):]),)
indices = [idx if isinstance(idx, slice) else _broadcast_to(idx, shape).ravel() for idx in indices]
def scan_fun(carry, x):
i, a = carry
idx = tuple(ind if isinstance(ind, slice) else ind[i] for ind in indices)
a = a.at[idx].set(self._call(a.at[idx].get(), *(arg[i] for arg in args)))
return (i + 1, a), x
carry, _ = jax.lax.scan(scan_fun, (0, a), None, len(indices[0]))
return carry[1]
@_wraps(np.ufunc.reduceat, module="numpy.ufunc")
@partial(jax.jit, static_argnames=['self', 'axis', 'dtype'])
def reduceat(self, a: ArrayLike, indices: Any, axis: int = 0,
dtype: Optional[DTypeLike] = None, out: None = None) -> Array:
if self.nin != 2:
raise ValueError("reduceat only supported for binary ufuncs")
if self.nout != 1:
raise ValueError("reduceat only supported for functions returning a single value")
if out is not None:
raise NotImplementedError(f"out argument of {self.__name__}.reduceat()")
return self._reduceat_via_scan(a, indices, axis=axis, dtype=dtype)
def _reduceat_via_scan(self, a: ArrayLike, indices: Any, axis: int = 0,
dtype: Optional[DTypeLike] = None) -> Array:
check_arraylike(f"{self.__name__}.reduceat", a, indices)
a = lax_internal.asarray(a)
idx_tuple = _eliminate_deprecated_list_indexing(indices)
assert len(idx_tuple) == 1
indices = idx_tuple[0]
if a.ndim == 0:
raise ValueError(f"reduceat: a must have 1 or more dimension, got {a.shape=}")
if indices.ndim != 1:
raise ValueError(f"reduceat: indices must be one-dimensional, got {indices.shape=}")
if dtype is None:
dtype = a.dtype
if axis is None or isinstance(axis, (tuple, list)):
raise ValueError("reduceat requires a single integer axis.")
axis = canonicalize_axis(axis, a.ndim)
out = take(a, indices, axis=axis)
ind = jax.lax.expand_dims(append(indices, a.shape[axis]),
list(np.delete(np.arange(out.ndim), axis)))
ind_start = jax.lax.slice_in_dim(ind, 0, ind.shape[axis] - 1, axis=axis)
ind_end = jax.lax.slice_in_dim(ind, 1, ind.shape[axis], axis=axis)
def loop_body(i, out):
return _where((i > ind_start) & (i < ind_end),
self._call(out, take(a, i.reshape(1), axis=axis)),
out)
return jax.lax.fori_loop(0, a.shape[axis], loop_body, out)
@_wraps(np.ufunc.outer, module="numpy.ufunc")
@partial(jax.jit, static_argnums=[0])
def outer(self, A: ArrayLike, B: ArrayLike, /, **kwargs) -> Array:
if self.nin != 2:
raise ValueError("outer only supported for binary ufuncs")
if self.nout != 1:
raise ValueError("outer only supported for functions returning a single value")
check_arraylike(f"{self.__name__}.outer", A, B)
_ravel = lambda A: jax.lax.reshape(A, (np.size(A),))
result = jax.vmap(jax.vmap(partial(self._call, **kwargs), (None, 0)), (0, None))(_ravel(A), _ravel(B))
return result.reshape(*np.shape(A), *np.shape(B))
[docs]
def frompyfunc(func: Callable[..., Any], /, nin: int, nout: int,
*, identity: Any = None) -> ufunc:
"""Create a JAX ufunc from an arbitrary JAX-compatible scalar function.
Args:
func : a callable that takes `nin` scalar arguments and return `nout` outputs.
nin: integer specifying the number of scalar inputs
nout: integer specifying the number of scalar outputs
identity: (optional) a scalar specifying the identity of the operation, if any.
Returns:
wrapped : jax.numpy.ufunc wrapper of func.
"""
return ufunc(func, nin, nout, identity=identity, update_doc=True)