def lu_pivots_to_permutation(swaps, m):
"""Converts the pivots (row swaps) returned by LU to a permutation.
We build a permutation rather than applying `swaps` directly to the rows
of a matrix because lax loops aren't differentiable.
Args:
swaps: an array of shape (..., k) of row swaps to perform
m: the size of the output permutation. m should be >= k.
Returns:
An int32 array of shape (..., m).
"""
assert len(swaps.shape) >= 1
batch_dims = swaps.shape[:-1]
k = swaps.shape[-1]
def body_fn(i, permutation):
j = swaps[..., i]
iotas = np.ix_(*(lax.iota(np.int32, b) for b in batch_dims))
x = permutation[..., i]
y = permutation[iotas + (j, )]
permutation = ops.index_update(permutation, ops.index[..., i], y)
return ops.index_update(permutation, ops.index[iotas + (j, )], x)
permutation = lax.broadcasted_iota(np.int32, batch_dims + (m, ),
len(batch_dims))
return lax.fori_loop(onp.array(0, onp.int32), onp.array(k, onp.int32),
body_fn, permutation)
def _approx_top_k_jvp(primals, tangents, *, k, reduction_dimension,
recall_target, is_max_k, reduction_input_size_override,
aggregate_to_topk):
operand, = primals
tangent, = tangents
if is_max_k:
val_out, arg_out = approx_max_k(operand, k, reduction_dimension,
recall_target,
reduction_input_size_override,
aggregate_to_topk)
else:
val_out, arg_out = approx_min_k(operand, k, reduction_dimension,
recall_target,
reduction_input_size_override,
aggregate_to_topk)
if type(tangent) is ad_util.Zero:
tangent_out = ad_util.Zero.from_value(val_out)
else:
arg_shape = arg_out.shape
rank = len(arg_shape)
if reduction_dimension < 0:
reduction_dimension += rank
iotas = [
lax.broadcasted_iota(arg_out.dtype, arg_shape, i)
for i in range(rank)
]
idx = tuple(arg_out if i == reduction_dimension else iotas[i]
for i in range(rank))
tangent_out = tangent[idx]
return (val_out, arg_out), (tangent_out, ad_util.Zero.from_value(arg_out))
def svd(a,
full_matrices: bool = True,
compute_uv: bool = True,
hermitian: bool = False):
a, = _promote_dtypes_inexact(jnp.asarray(a))
if hermitian:
w, v = lax_linalg.eigh(a)
s = lax.abs(v)
if compute_uv:
sign = lax.sign(v)
idxs = lax.broadcasted_iota(np.int64,
s.shape,
dimension=s.ndim - 1)
s, idxs, sign = lax.sort((s, idxs, sign), dimension=-1, num_keys=1)
s = lax.rev(s, dimensions=[s.ndim - 1])
idxs = lax.rev(idxs, dimensions=[s.ndim - 1])
sign = lax.rev(sign, dimensions=[s.ndim - 1])
u = jnp.take_along_axis(w, idxs[..., None, :], axis=-1)
vh = _H(u * sign[..., None, :])
return u, s, vh
else:
return lax.rev(lax.sort(s, dimension=-1), dimensions=[s.ndim - 1])
return lax_linalg.svd(a,
full_matrices=full_matrices,
compute_uv=compute_uv)
def threefry_random_bits(key: jnp.ndarray, bit_width, shape):
"""Sample uniform random bits of given width and shape using PRNG key."""
if not _is_threefry_prng_key(key):
raise TypeError("_random_bits got invalid prng key.")
if bit_width not in (8, 16, 32, 64):
raise TypeError("requires 8-, 16-, 32- or 64-bit field width.")
shape = core.as_named_shape(shape)
for name, size in shape.named_items:
real_size = lax.psum(1, name)
if real_size != size:
raise ValueError(
f"The shape of axis {name} was specified as {size}, "
f"but it really is {real_size}")
axis_index = lax.axis_index(name)
key = threefry_fold_in(key, axis_index)
size = prod(shape.positional)
# Compute ceil(bit_width * size / 32) in a way that is friendly to shape
# polymorphism
max_count, r = divmod(bit_width * size, 32)
if r > 0:
max_count += 1
if core.is_constant_dim(max_count):
nblocks, rem = divmod(max_count, jnp.iinfo(np.uint32).max)
else:
nblocks, rem = 0, max_count
if not nblocks:
bits = threefry_2x32(key, lax.iota(np.uint32, rem))
else:
keys = threefry_split(key, nblocks + 1)
subkeys, last_key = keys[:-1], keys[-1]
blocks = vmap(threefry_2x32,
in_axes=(0, None))(subkeys,
lax.iota(np.uint32,
jnp.iinfo(np.uint32).max))
last = threefry_2x32(last_key, lax.iota(np.uint32, rem))
bits = lax.concatenate([blocks.ravel(), last], 0)
dtype = UINT_DTYPES[bit_width]
if bit_width == 64:
bits = [lax.convert_element_type(x, dtype) for x in jnp.split(bits, 2)]
bits = lax.shift_left(bits[0], dtype(32)) | bits[1]
elif bit_width in [8, 16]:
# this is essentially bits.view(dtype)[:size]
bits = lax.bitwise_and(
np.uint32(np.iinfo(dtype).max),
lax.shift_right_logical(
lax.broadcast(bits, (1, )),
lax.mul(
np.uint32(bit_width),
lax.broadcasted_iota(np.uint32, (32 // bit_width, 1), 0))))
bits = lax.reshape(bits, (np.uint32(max_count * 32 // bit_width), ),
(1, 0))
bits = lax.convert_element_type(bits, dtype)[:size]
return lax.reshape(bits, shape)
def _mask(x, dims, alternative=0):
"""Masks `x` up to the dynamic shape `dims`.
Replaces values outside those dimensions with `alternative`. `alternative` is
broadcast with `x`.
"""
assert jnp.ndim(x) == len(dims)
mask = None
for i, d in enumerate(dims):
if d is not None:
mask_dim_i = lax.broadcasted_iota(jnp.int32, x.shape, i) < d
mask = mask_dim_i if mask is None else (mask & mask_dim_i)
return x if mask is None else jnp.where(mask, x, alternative)
def _intersect1d_sorted_mask(ar1, ar2, return_indices=False):
"""
Helper function for intersect1d which is jit-able
"""
ar = concatenate((ar1, ar2))
if return_indices:
iota = lax.broadcasted_iota(np.int64, np.shape(ar), dimension=0)
aux, indices = lax.sort_key_val(ar, iota)
else:
aux = sort(ar)
mask = aux[1:] == aux[:-1]
if return_indices:
return aux, mask, indices
else:
return aux, mask
def lu_pivots_to_permutation(swaps, m):
"""Converts the pivots (row swaps) returned by LU to a permutation.
We build a permutation rather than applying `swaps` directly to the rows
of a matrix because lax loops aren't differentiable.
Args:
swaps: an array of shape (..., k) of row swaps to perform
m: the size of the output permutation. m should be >= k.
Returns:
An int32 array of shape (..., m).
"""
assert len(swaps.shape) >= 1
batch_dims = swaps.shape[:-1]
k = swaps.shape[-1]
permutation = lax.broadcasted_iota(np.int32, batch_dims + (m, ),
len(batch_dims))
result, _ = lax.fori_loop(onp.array(0, onp.int32), onp.array(k, onp.int32),
_lu_pivots_body_fn, (permutation, swaps))
return result
def _one_hot(x: Array, num_classes: int, *, dtype: Any,
axis: Union[int, AxisName]) -> Array:
num_classes = core.concrete_or_error(
int, num_classes,
"The error arose in jax.nn.one_hot argument `num_classes`.")
dtype = dtypes.canonicalize_dtype(dtype)
x = jnp.asarray(x)
try:
output_pos_axis = util.canonicalize_axis(axis, x.ndim + 1)
except TypeError:
axis_size = lax.psum(1, axis)
if num_classes != axis_size:
raise ValueError(
f"Expected num_classes to match the size of axis {axis}, "
f"but {num_classes} != {axis_size}") from None
axis_idx = lax.axis_index(axis)
return jnp.asarray(x == axis_idx, dtype=dtype)
axis = operator.index(axis) # type: ignore[arg-type]
lhs = lax.expand_dims(x, (axis, ))
rhs_shape = [1] * x.ndim
rhs_shape.insert(output_pos_axis, num_classes)
rhs = lax.broadcasted_iota(x.dtype, rhs_shape, output_pos_axis)
return jnp.asarray(lhs == rhs, dtype=dtype)
