def stimulate(t, X, stimuli):
stimulated = np.zeros_like(X)
for stimulus in stimuli:
active = np.greater_equal(t, stimulus["start"])
active &= (np.mod(stimulus["start"] - t + 1, stimulus["period"]) < stimulus["duration"])
stimulated = np.where(stimulus["field"] * (active), stimulus["field"], stimulated)
return np.where(stimulated != 0, stimulated, X)
def update_periodically(steps: jnp.ndarray, target_update_period: int,
params: types.NestedArray,
target_params: types.NestedArray) -> types.NestedArray:
"""Checks whether to update the params and returns the correct params."""
return jax.lax.cond(
jnp.mod(steps, target_update_period) == 0, lambda _: params,
lambda _: target_params, None)
def test_sorted_piecewise_constant_pdf_sparse_delta(self):
"""Test sampling when given a large distribution with a big delta in it."""
num_samples = 100
num_bins = 100000
key = random.PRNGKey(0)
bins = jnp.arange(num_bins)
weights = np.ones(len(bins) - 1)
delta_idx = len(weights) // 2
weights[delta_idx] = len(weights) - 1
samples = math.sorted_piecewise_constant_pdf(
key,
bins[None],
weights[None],
num_samples,
True,
)[0]
# All samples should be within the range of the bins.
self.assertTrue(jnp.all(samples >= bins[0]))
self.assertTrue(jnp.all(samples <= bins[-1]))
# Samples modded by their bin index should resemble a uniform distribution.
samples_mod = jnp.mod(samples, 1)
self.assertLessEqual(
sp.stats.kstest(samples_mod, 'uniform', (0, 1)).statistic, 0.2)
# The delta function bin should contain ~half of the samples.
in_delta = (samples >= bins[delta_idx]) & (samples <=
bins[delta_idx + 1])
self.assertAllClose(jnp.mean(in_delta), 0.5, atol=0.05)
def test_sorted_piecewise_constant_pdf_large_flat(self):
"""Test sampling when given a large flat distribution."""
num_samples = 100
num_bins = 100000
key = random.PRNGKey(0)
bins = jnp.arange(num_bins)
weights = np.ones(len(bins) - 1)
samples = math.sorted_piecewise_constant_pdf(
key,
bins[None],
weights[None],
num_samples,
True,
)[0]
# All samples should be within the range of the bins.
self.assertTrue(jnp.all(samples >= bins[0]))
self.assertTrue(jnp.all(samples <= bins[-1]))
# Samples modded by their bin index should resemble a uniform distribution.
samples_mod = jnp.mod(samples, 1)
self.assertLessEqual(
sp.stats.kstest(samples_mod, 'uniform', (0, 1)).statistic, 0.2)
# All samples should collectively resemble a uniform distribution.
self.assertLessEqual(
sp.stats.kstest(samples, 'uniform', (bins[0], bins[-1])).statistic,
0.2)
def periodic_update(
new_tensors: base.Params,
old_tensors: base.Params,
steps: chex.Array,
update_period: int
) -> base.Params:
"""Periodically update all parameters with new values.
A slow copy of a model's parameters, updated every K actual updates, can be
used to implement forms of self-supervision (in supervised learning), or to
stabilise temporal difference learning updates (in reinforcement learning).
References:
[Grill et al., 2020](https://arxiv.org/abs/2006.07733)
[Mnih et al., 2015](https://arxiv.org/abs/1312.5602)
Args:
new_tensors: the latest value of the tensors.
old_tensors: a slow copy of the model's parameters.
steps: number of update steps on the "online" network.
update_period: every how many steps to update the "target" network.
Returns:
a slow copy of the model's parameters, updated every `update_period` steps.
"""
return jax.lax.cond(
jnp.mod(steps, update_period) == 0,
lambda _: new_tensors,
lambda _: old_tensors,
None)
def value(self, count: JTensor) -> JTensor:
relative_step = jnp.mod(count, self._period)
output = self._schedules[0].value(count)
for boundary, schedule in zip(self._boundaries, self._schedules[1:]):
output = jnp.where(relative_step < boundary, output,
schedule.value(count))
return output
def stimulate(t, X, stimuli):
for stimulus in stimuli:
active = t > stimulus["start"]
active &= t < stimulus["start"] + stimulus["duration"]
# for some weird reason checks for cyclic stimuli does not work
active = (np.mod(t - stimulus["start"], stimulus["period"]) < stimulus["duration"]) # cyclic
X = np.where(stimulus["field"] * (active), stimulus["field"], X)
return X
def body_fun(i_acc):
i, acc = i_acc
return (i + 1,
(jnp.cos(acc) +
lax.cond(jnp.mod(i, 2) == 0,
lambda acc: jnp.sin(acc),
lambda acc: acc,
acc)))
def kepler(mean_anom, ecc):
# We're going to apply array broadcasting here since the logic of our op
# is much simpler if we require the inputs to all have the same shapes
mean_anom_, ecc_ = jnp.broadcast_arrays(mean_anom, ecc)
# Then we need to wrap into the range [0, 2*pi)
M_mod = jnp.mod(mean_anom_, 2 * np.pi)
return _kepler_prim.bind(M_mod, ecc_)
def current_stimulate(t, X, stimuli):
stimulated = np.zeros_like(X)
for stimulus in stimuli:
# active = np.greater_equal(t, stimulus["start"])
# active &= (np.mod(stimulus["start"] - t + 1, stimulus["period"]) < stimulus["duration"])
active = np.greater_equal(t ,stimulus["start"])
# active &= np.greater_equal(stimulus["start"] + stimulus["duration"],t)
active &= (np.mod(t - stimulus["start"], stimulus["period"]) < stimulus["duration"]) # this works for cyclics
stimulated = np.where(stimulus["field"] * (active), stimulus["field"], stimulated)
return np.where(stimulated != 0, stimulated, X)
def visualize_cmap(value,
weight,
colormap,
lo=None,
hi=None,
percentile=99.,
curve_fn=lambda x: x,
modulus=None,
matte_background=True):
"""Visualize a 1D image and a 1D weighting according to some colormap.
Args:
value: A 1D image.
weight: A weight map, in [0, 1].
colormap: A colormap function.
lo: The lower bound to use when rendering, if None then use a percentile.
hi: The upper bound to use when rendering, if None then use a percentile.
percentile: What percentile of the value map to crop to when automatically
generating `lo` and `hi`. Depends on `weight` as well as `value'.
curve_fn: A curve function that gets applied to `value`, `lo`, and `hi`
before the rest of visualization. Good choices: x, 1/(x+eps), log(x+eps).
modulus: If not None, mod the normalized value by `modulus`. Use (0, 1]. If
`modulus` is not None, `lo`, `hi` and `percentile` will have no effect.
matte_background: If True, matte the image over a checkerboard.
Returns:
A colormap rendering.
"""
# Identify the values that bound the middle of `value' according to `weight`.
lo_auto, hi_auto = math.weighted_percentile(
value, weight, [50 - percentile / 2, 50 + percentile / 2])
# If `lo` or `hi` are None, use the automatically-computed bounds above.
eps = jnp.finfo(jnp.float32).eps
lo = lo or (lo_auto - eps)
hi = hi or (hi_auto + eps)
# Curve all values.
value, lo, hi = [curve_fn(x) for x in [value, lo, hi]]
# Wrap the values around if requested.
if modulus:
value = jnp.mod(value, modulus) / modulus
else:
# Otherwise, just scale to [0, 1].
value = jnp.nan_to_num(
jnp.clip((value - jnp.minimum(lo, hi)) / jnp.abs(hi - lo), 0, 1))
if colormap:
colorized = colormap(value)[:, :, :3]
else:
assert len(value.shape) == 3 and value.shape[-1] == 3
colorized = value
return matte(colorized, weight) if matte_background else colorized
def getn(l):
"""
IN: l = n^2 - n / 2
OUT: n (positive integer solution)
"""
n = (1 + np.sqrt(1 + 8 * l)) / 2
assert np.equal(np.mod(n, 1), 0) # make sure n is an integer
n = int(n)
assert l == n**2 - n / 2
return n
def learning_rate_fn(step):
d_step = step - wait_steps
pfraction = jnp.mod(d_step, halfwavelength_steps) / halfwavelength_steps
scale_factor = min_value + (1.0 - min_value) * 0.5 * (
jnp.cos(jnp.pi * pfraction) + 1.0)
scale_factor = lax.cond(d_step < 0., d_step, lambda d_step: 1.0, d_step,
lambda d_step: scale_factor)
lr = base_learning_rate * scale_factor
if warmup_length > 0.0:
lr = lr * jnp.minimum(1., step / float(warmup_length) / steps_per_epoch)
return lr
def periodic_displacement(side, dR):
"""Wraps displacement vectors into a hypercube.
Args:
side: Specification of hypercube size. Either,
(a) float if all sides have equal length.
(b) ndarray(spatial_dim) if sides have different lengths.
dR: Matrix of displacements; ndarray(shape=[..., spatial_dim]).
Returns:
Matrix of wrapped displacements; ndarray(shape=[..., spatial_dim]).
"""
return np.mod(dR + side * f32(0.5), side) - f32(0.5) * side
def periodic_shift(L, x, dx):
"""
do a periodic shift
arguments
L : Array
length of dimension
x : Array
positions
dx : Array
position increment
"""
return jnp.mod(x + dx, L)
def stimulate(t, X, stimuli):
stimulated = jnp.zeros_like(X)
for stimulus in stimuli:
# check if stimulus is in the past
active = jnp.greater_equal(t, stimulus.protocol.start)
# check if stimulus is active at the current time
active &= (jnp.mod(stimulus.protocol.start - t + 1,
stimulus.protocol.period) <
stimulus.protocol.duration)
# build the stimulus field
stimulated = jnp.where(stimulus.field * (active), stimulus.field,
stimulated)
# set the field to the stimulus
return jnp.where(stimulated != 0, stimulated, X)
def split_top_k(split_queries: Array) -> Tuple[Array, Array, Array]:
# Find most similar clusters
prototype_scores = jnp.einsum('qd,pd->qp', split_queries,
prototypes)
top_indices = jax.lax.top_k(prototype_scores, self.n_search)[1]
# Perform approximate top-k similarity search over most similar clusters.
selected_data = table[top_indices]
split_scores = jnp.einsum('qd,qcrvd->qcrv', split_queries,
selected_data)
# Find highest scoring vector for each row.
top_id_by_row = jnp.argmax(split_scores, axis=-1)
top_score_by_row = jnp.max(split_scores, axis=-1)
top_id_by_row = top_id_by_row.reshape(
queries_per_split, self.n_search * rows_per_cluster)
top_score_by_row = top_score_by_row.reshape(
queries_per_split, self.n_search * rows_per_cluster)
# Take k highest scores among all rows.
top_row_idx = jnp.argsort(top_score_by_row,
axis=-1)[:, :-self.k_top - 1:-1]
# Sub-select best indices for k best rows.
ids_by_topk_row = jut.matmul_slice(top_id_by_row, top_row_idx)
# Gather highest scoring vectors for k best rows.
query_index = jnp.arange(queries_per_split).reshape(-1, 1).tile(
[1, self.k_top])
top_cluster_idx, top_cluster_row_idx = jnp.divmod(
top_row_idx, rows_per_cluster)
split_topk_values = selected_data[query_index, top_cluster_idx,
top_cluster_row_idx,
ids_by_topk_row]
row_offset = jnp.mod(
jnp.arange(0, self.n_search * values_per_cluster,
values_per_row), values_per_cluster)
cluster_offset = jnp.arange(0, table_size, values_per_cluster)
# Convert row indices to indices into flattened table.
top_table_id_by_row = top_id_by_row + row_offset.reshape(
1, -1) + cluster_offset[top_indices].repeat(rows_per_cluster,
axis=-1)
# Get best ids into flattened table.
split_topk_ids = jut.matmul_slice(top_table_id_by_row, top_row_idx)
split_topk_scores = jut.matmul_slice(top_score_by_row, top_row_idx)
return split_topk_values, split_topk_scores, split_topk_ids
def advect(f, vx, vy):
"""Move field f according to x and y velocities (u and v)
using an implicit Euler integrator."""
rows, cols = f.shape
cell_ys, cell_xs = np.meshgrid(np.arange(rows), np.arange(cols))
cell_xs = cell_xs.astype(dtype)
cell_ys = cell_ys.astype(dtype)
center_xs = (cell_xs - vx).ravel()
center_ys = (cell_ys - vy).ravel()
# Compute indices of source cells.
left_ix = np.floor(center_xs).astype(int)
top_ix = np.floor(center_ys).astype(int)
rw = center_xs - left_ix # Relative weight of right-hand cells.
bw = center_ys - top_ix # Relative weight of bottom cells.
left_ix = np.mod(left_ix, rows) # Wrap around edges of simulation.
right_ix = np.mod(left_ix + 1, rows)
top_ix = np.mod(top_ix, cols)
bot_ix = np.mod(top_ix + 1, cols)
# A linearly-weighted sum of the 4 surrounding cells.
flat_f = (1 - rw) * ((1 - bw)*f[left_ix, top_ix] + bw*f[left_ix, bot_ix]) \
+ rw * ((1 - bw)*f[right_ix, top_ix] + bw*f[right_ix, bot_ix])
return np.reshape(flat_f, (rows, cols))
def visualize_depth(depth,
acc=None,
near=None,
far=None,
curve_fn=lambda x: jnp.log(x + jnp.finfo(jnp.float32).eps),
modulus=0,
colormap=None):
"""Visualize a depth map.
Args:
depth: A depth map.
acc: An accumulation map, in [0, 1].
near: The depth of the near plane, if None then just use the min().
far: The depth of the far plane, if None then just use the max().
curve_fn: A curve function that gets applied to `depth`, `near`, and `far`
before the rest of visualization. Good choices: x, 1/(x+eps), log(x+eps).
modulus: If > 0, mod the normalized depth by `modulus`. Use (0, 1].
colormap: A colormap function. If None (default), will be set to
matplotlib's viridis if modulus==0, sinebow otherwise.
Returns:
An RGB visualization of `depth`.
"""
# If `near` or `far` are None, identify the min/max non-NaN values.
eps = jnp.finfo(jnp.float32).eps
near = near or jnp.min(jnp.nan_to_num(depth, jnp.inf)) - eps
far = far or jnp.max(jnp.nan_to_num(depth, -jnp.inf)) + eps
# Curve all values.
depth, near, far = [curve_fn(x) for x in [depth, near, far]]
# Wrap the values around if requested.
if modulus > 0:
value = jnp.mod(depth, modulus) / modulus
colormap = colormap or sinebow
else:
# Scale to [0, 1].
value = jnp.nan_to_num(jnp.clip((depth - near) / (far - near), 0, 1))
colormap = colormap or cm.get_cmap('viridis')
vis = colormap(value)[:, :, :3]
# Set non-accumulated pixels to white.
if acc is not None:
vis = vis * acc[:, :, None] + (1 - acc)[:, :, None]
return vis
def circdist(x: jnp.ndarray, y: jnp.ndarray, circumference: float) -> jnp.ndarray:
"""Calculate the signed circular distance between two arrays.
Returns positive numbers if y is clockwise compared to x, negative if y is counter-
clockwise compared to x.
Args:
x: The first array.
y: The second array.
circumference: The circumference of the circle.
Returns:
An array of the same shape as x and y, containing the signed circular distances.
"""
assert y.shape == x.shape
return -jnp.mod(x - y - circumference / 2, circumference) + circumference / 2
def mobius_flow(theta: jnp.ndarray, w: jnp.ndarray) -> jnp.ndarray:
"""Following [1] the Mobius flow must have the property that the endpoints of
the interval [0, 2pi] are mapped to themselves. This transformation
enforces this property by appling a backwards rotation to bring the zero
angle back to itself.
Args:
theta: The angle parameterizing a point on the circle.
w: Center points of the Mobius transformation.
Returns:
out: The Mobius flow as a transformation on angles leaving the endpoints
of the interval invariant.
"""
theta = jnp.hstack((0., theta))
omega = mobius_angle(theta, w)
omega -= omega[..., [0]]
return jnp.squeeze(jnp.mod(omega[..., 1:], 2.*jnp.pi))
def mutate_population(key: jnp.ndarray,
population: Population,
mutation_rate: float = 0.15,
alphabet_size: int = 4) -> Population:
"""Mutate a polymer population.
Here we convert the total mutation rate into mutation rates for each
member of an alphabet and use this, combined with the non-mutation
rate, to sample mutations. These mutations are simply members of the
alphabet that are added to the existing values followed by a modulo
operation for the size of the alphabet.
Example:
alphabet_size = 4, pop = [[0,1,2,3]], mutation = [[0,0,1,2]],
new_population = [[0,1,3,1]]
Args:
key: A random number generator key e.g. produced via
jax.random.PRNGKey.
population: A polymer population.
mutation_rate: The combined rate of mutation over all forms
of mutation. E.g. 15% that it would be one of 1->2 or 2->3.
alphabet_size: The size of the alphabet from which polymer
elements are sampled.
Returns:
Population: A population of polymers.
"""
individual_p_mutation = mutation_rate / alphabet_size
# Lazily double-counts self-transitions as a type of mutation
# in the interest of prototyping
p_no_mutation = (1 - mutation_rate)
mutation_probs = [individual_p_mutation for _ in range(alphabet_size)]
mutation_probs = [p_no_mutation] + mutation_probs
mutation = random.choice(key,
a=jnp.array(range(alphabet_size + 1)),
shape=population.shape,
p=jnp.array(mutation_probs))
return jnp.mod(population + mutation, alphabet_size - 1)
def segment_max(data,
segment_ids,
num_segments=None,
indices_are_sorted=False,
unique_indices=False):
"""Computes the max within segments of an array.
Similar to TensorFlow's segment_max:
https://www.tensorflow.org/api_docs/python/tf/math/segment_max
Args:
data: an array with the values to be maxed over.
segment_ids: an array with integer dtype that indicates the segments of
`data` (along its leading axis) to be maxed over. Values can be repeated
and need not be sorted. Values outside of the range [0, num_segments) are
wrapped into that range by applying jnp.mod.
num_segments: optional, an int with positive value indicating the number of
segments. The default is ``jnp.maximum(jnp.max(segment_ids) + 1,
jnp.max(-segment_ids))`` but since `num_segments` determines the size of
the output, a static value must be provided to use ``segment_max`` in a
``jit``-compiled function.
indices_are_sorted: whether ``segment_ids`` is known to be sorted
unique_indices: whether ``segment_ids`` is known to be free of duplicates
Returns:
An array with shape ``(num_segments,) + data.shape[1:]`` representing
the segment maxs.
"""
if num_segments is None:
num_segments = jnp.maximum(
jnp.max(segment_ids) + 1, jnp.max(-segment_ids))
num_segments = int(num_segments)
min_value = dtype_min_value(data.dtype)
out = jnp.full((num_segments, ) + data.shape[1:],
min_value,
dtype=data.dtype)
segment_ids = jnp.mod(segment_ids, num_segments)
return jax.ops.index_max(out, segment_ids, data, indices_are_sorted,
unique_indices)
def __call__(self, inputs, prev_state):
"""Writes a new memory into the episodic memory.
Args:
inputs: A Tensor of shape ``[batch_size, memory_size]``.
prev_state: The previous state of the episodic memory, which is a tuple
with a (i) counter of shape ``[batch_size, 1]`` indicating how many
memories have been written so far, and (ii) a tensor of shape
``[batch_size, capacity, memory_size]`` with the full content of the
episodic memory.
Returns:
A tuple with (i) a tensor of shape ``[batch_size, capacity, memory_size]``
with the full content of the episodic memory, including the newly
written memory, and (ii) the new state of the episodic memory.
"""
inputs = jax.lax.stop_gradient(inputs)
counter, memories = prev_state
counter_mod = jnp.mod(counter, self._capacity)
slot_selector = jnp.expand_dims(
jax.nn.one_hot(counter_mod, self._capacity), axis=2)
memories = memories * (1 - slot_selector) + (
slot_selector * jnp.expand_dims(inputs, 1))
counter = counter + 1
return memories, (counter, memories)
def onnx_mod(a, b, fmod=0):
if fmod:
return jnp.fmod(a, b)
else:
return jnp.mod(a, b)
def cell_list_fn(position: Array,
capacity_overflow_update: Optional[Tuple[
int, bool, Callable[..., CellList]]] = None,
extra_capacity: int = 0,
**kwargs) -> CellList:
N = position.shape[0]
dim = position.shape[1]
if dim != 2 and dim != 3:
# NOTE(schsam): Do we want to check this in compute_fn as well?
raise ValueError(
f'Cell list spatial dimension must be 2 or 3. Found {dim}.')
_, cell_size, cells_per_side, cell_count = \
_cell_dimensions(dim, box_size, minimum_cell_size)
if capacity_overflow_update is None:
cell_capacity = _estimate_cell_capacity(position, box_size,
cell_size,
buffer_size_multiplier)
cell_capacity += extra_capacity
overflow = False
update_fn = cell_list_fn
else:
cell_capacity, overflow, update_fn = capacity_overflow_update
hash_multipliers = _compute_hash_constants(dim, cells_per_side)
# Create cell list data.
particle_id = lax.iota(i32, N)
# NOTE(schsam): We use the convention that particles that are successfully,
# copied have their true id whereas particles empty slots have id = N.
# Then when we copy data back from the grid, copy it to an array of shape
# [N + 1, output_dimension] and then truncate it to an array of shape
# [N, output_dimension] which ignores the empty slots.
cell_position = jnp.zeros((cell_count * cell_capacity, dim),
dtype=position.dtype)
cell_id = N * jnp.ones((cell_count * cell_capacity, 1), dtype=i32)
# It might be worth adding an occupied mask. However, that will involve
# more compute since often we will do a mask for species that will include
# an occupancy test. It seems easier to design around this empty_data_value
# for now and revisit the issue if it comes up later.
empty_kwarg_value = 10**5
cell_kwargs = {}
# pytype: disable=attribute-error
for k, v in kwargs.items():
if not util.is_array(v):
raise ValueError(
(f'Data must be specified as an ndarray. Found "{k}" '
f'with type {type(v)}.'))
if v.shape[0] != position.shape[0]:
raise ValueError(
('Data must be specified per-particle (an ndarray '
f'with shape ({N}, ...)). Found "{k}" with '
f'shape {v.shape}.'))
kwarg_shape = v.shape[1:] if v.ndim > 1 else (1, )
cell_kwargs[k] = empty_kwarg_value * jnp.ones(
(cell_count * cell_capacity, ) + kwarg_shape, v.dtype)
# pytype: enable=attribute-error
indices = jnp.array(position / cell_size, dtype=i32)
hashes = jnp.sum(indices * hash_multipliers, axis=1)
# Copy the particle data into the grid. Here we use a trick to allow us to
# copy into all cells simultaneously using a single lax.scatter call. To do
# this we first sort particles by their cell hash. We then assign each
# particle to have a cell id = hash * cell_capacity + grid_id where
# grid_id is a flat list that repeats 0, .., cell_capacity. So long as
# there are fewer than cell_capacity particles per cell, each particle is
# guarenteed to get a cell id that is unique.
sort_map = jnp.argsort(hashes)
sorted_position = position[sort_map]
sorted_hash = hashes[sort_map]
sorted_id = particle_id[sort_map]
sorted_kwargs = {}
for k, v in kwargs.items():
sorted_kwargs[k] = v[sort_map]
sorted_cell_id = jnp.mod(lax.iota(i32, N), cell_capacity)
sorted_cell_id = sorted_hash * cell_capacity + sorted_cell_id
cell_position = cell_position.at[sorted_cell_id].set(sorted_position)
sorted_id = jnp.reshape(sorted_id, (N, 1))
cell_id = cell_id.at[sorted_cell_id].set(sorted_id)
cell_position = _unflatten_cell_buffer(cell_position, cells_per_side,
dim)
cell_id = _unflatten_cell_buffer(cell_id, cells_per_side, dim)
for k, v in sorted_kwargs.items():
if v.ndim == 1:
v = jnp.reshape(v, v.shape + (1, ))
cell_kwargs[k] = cell_kwargs[k].at[sorted_cell_id].set(v)
cell_kwargs[k] = _unflatten_cell_buffer(cell_kwargs[k],
cells_per_side, dim)
occupancy = ops.segment_sum(jnp.ones_like(hashes), hashes, cell_count)
max_occupancy = jnp.max(occupancy)
overflow = overflow | (max_occupancy >= cell_capacity)
return CellList(cell_position, cell_id, cell_kwargs, overflow,
cell_capacity, update_fn) # pytype: disable=wrong-arg-count
def _sample_next(sampler, machine, parameters: PyTree,
state: MetropolisPtSamplerState):
new_rng, rng = jax.random.split(state.rng)
# def cbr(data):
# new_rng, rng = data
# print("sample_next newrng:\n", new_rng, "\nand rng:\n", rng)
# return new_rng
# new_rng = hcb.call(
# cbr,
# (new_rng, rng),
# result_shape=jax.ShapeDtypeStruct(new_rng.shape, new_rng.dtype),
# )
with loops.Scope() as s:
s.key = rng
s.σ = state.σ
s.log_prob = sampler.machine_pow * machine(parameters,
state.σ).real
s.beta = state.beta
# for logging
s.beta_0_index = state.beta_0_index
s.n_accepted_per_beta = state.n_accepted_per_beta
s.beta_position = state.beta_position
s.beta_diffusion = state.beta_diffusion
for i in s.range(sampler.n_sweeps):
# 1 to propagate for next iteration, 1 for uniform rng and n_chains for transition kernel
s.key, key1, key2, key3, key4 = jax.random.split(s.key, 5)
# def cbi(data):
# i, beta = data
# print("sweep #", i, " for beta=\n", beta)
# return beta
# beta = hcb.call(
# cbi,
# (i, s.beta),
# result_shape=jax.ShapeDtypeStruct(s.beta.shape, s.beta.dtype),
# )
beta = s.beta
σp, log_prob_correction = sampler.rule.transition(
sampler, machine, parameters, state, key1, s.σ)
proposal_log_prob = sampler.machine_pow * machine(
parameters, σp).real
uniform = jax.random.uniform(key2, shape=(sampler.n_batches, ))
if log_prob_correction is not None:
do_accept = uniform < jnp.exp(
beta.reshape((-1, )) *
(proposal_log_prob - s.log_prob + log_prob_correction))
else:
do_accept = uniform < jnp.exp(
beta.reshape(
(-1, )) * (proposal_log_prob - s.log_prob))
# do_accept must match ndim of proposal and state (which is 2)
s.σ = jnp.where(do_accept.reshape(-1, 1), σp, s.σ)
n_accepted_per_beta = s.n_accepted_per_beta + do_accept.reshape(
(sampler.n_chains, sampler.n_replicas))
s.log_prob = jax.numpy.where(do_accept.reshape(-1),
proposal_log_prob, s.log_prob)
# exchange betas
# randomly decide if every set of replicas should be swapped in even or odd order
swap_order = jax.random.randint(
key3,
minval=0,
maxval=2,
shape=(sampler.n_chains, ),
) # 0 or 1
iswap_order = jnp.mod(swap_order + 1, 2) # 1 or 0
# indices of even swapped elements (per-row)
idxs = jnp.arange(0, sampler.n_replicas, 2).reshape(
(1, -1)) + swap_order.reshape((-1, 1))
# indices off odd swapped elements (per-row)
inn = (idxs + 1) % sampler.n_replicas
# for every rows of the input, swap elements at idxs with elements at inn
@partial(jax.vmap, in_axes=(0, 0, 0), out_axes=0)
def swap_rows(beta_row, idxs, inn):
proposed_beta = jax.ops.index_update(
beta_row,
idxs,
beta_row[inn],
unique_indices=True,
indices_are_sorted=True,
)
proposed_beta = jax.ops.index_update(
proposed_beta,
inn,
beta_row[idxs],
unique_indices=True,
indices_are_sorted=False,
)
return proposed_beta
proposed_beta = swap_rows(beta, idxs, inn)
@partial(jax.vmap, in_axes=(0, 0, 0), out_axes=0)
def compute_proposed_prob(prob, idxs, inn):
prob_rescaled = prob[idxs] + prob[inn]
return prob_rescaled
# compute the probability of the swaps
log_prob = (proposed_beta - state.beta) * s.log_prob.reshape(
(sampler.n_chains, sampler.n_replicas))
prob_rescaled = jnp.exp(
compute_proposed_prob(log_prob, idxs, inn))
prob_rescaled = jnp.exp(
compute_proposed_prob(log_prob, idxs, inn))
uniform = jax.random.uniform(key4,
shape=(sampler.n_chains,
sampler.n_replicas // 2))
do_swap = uniform < prob_rescaled
do_swap = jnp.dstack((do_swap, do_swap)).reshape(
(-1, sampler.n_replicas)) # concat along last dimension
# roll if swap_ordeer is odd
@partial(jax.vmap, in_axes=(0, 0), out_axes=0)
def fix_swap(do_swap, swap_order):
return jax.lax.cond(swap_order == 0, lambda x: x,
lambda x: jnp.roll(x, 1), do_swap)
do_swap = fix_swap(do_swap, swap_order)
# jax.experimental.host_callback.id_print(state.beta)
# jax.experimental.host_callback.id_print(proposed_beta)
new_beta = jax.numpy.where(do_swap, proposed_beta, beta)
def cb(data):
_bt, _pbt, new_beta, so, do_swap, log_prob, prob = data
print("--------.---------.---------.--------")
print(" cur beta:\n", _bt)
print("proposed beta:\n", _pbt)
print(" new beta:\n", new_beta)
print("swaporder :", so)
print("do_swap :\n", do_swap)
print("log_prob;\n", log_prob)
print("prob_rescaled;\n", prob)
return new_beta
# new_beta = hcb.call(
# cb,
# (
# beta,
# proposed_beta,
# new_beta,
# swap_order,
# do_swap,
# log_prob,
# prob_rescaled,
# ),
# result_shape=jax.ShapeDtypeStruct(new_beta.shape, new_beta.dtype),
# )
# s.beta = new_beta
swap_order = swap_order.reshape(-1)
beta_0_moved = jax.vmap(lambda do_swap, i: do_swap[i],
in_axes=(0, 0),
out_axes=0)(do_swap,
state.beta_0_index)
proposed_beta_0_index = jnp.mod(
state.beta_0_index + (-jnp.mod(swap_order, 2) * 2 + 1) *
(-jnp.mod(state.beta_0_index, 2) * 2 + 1),
sampler.n_replicas,
)
s.beta_0_index = jnp.where(beta_0_moved, proposed_beta_0_index,
s.beta_0_index)
# swap acceptances
swapped_n_accepted_per_beta = swap_rows(
n_accepted_per_beta, idxs, inn)
s.n_accepted_per_beta = jax.numpy.where(
do_swap,
swapped_n_accepted_per_beta,
n_accepted_per_beta,
)
# Update statistics to compute diffusion coefficient of replicas
# Total exchange steps performed
delta = s.beta_0_index - s.beta_position
s.beta_position = s.beta_position + delta / (
state.exchange_steps + i)
delta2 = s.beta_0_index - s.beta_position
s.beta_diffusion = s.beta_diffusion + delta * delta2
new_state = state.replace(
rng=new_rng,
σ=s.σ,
# n_accepted=s.accepted,
n_samples=state.n_samples +
sampler.n_sweeps * sampler.n_chains,
beta=s.beta,
beta_0_index=s.beta_0_index,
beta_position=s.beta_position,
beta_diffusion=s.beta_diffusion,
exchange_steps=state.exchange_steps + sampler.n_sweeps,
n_accepted_per_beta=s.n_accepted_per_beta,
)
offsets = jnp.arange(0, sampler.n_chains * sampler.n_replicas,
sampler.n_replicas)
return new_state, new_state.σ[new_state.beta_0_index + offsets, :]
tree_util.tree_map(count,
tree_util.tree_flatten(bij_params)[0])).sum()
print('number of parameters: {}'.format(num_params))
bij_params = tree_util.tree_map(lambda x: x / 2., bij_params)
# Direct estimation on the torus.
bij_params, trace = train(rng_train, bij_params, bij_fns, args.num_steps,
args.lr, 100)
# Sample from the learned distribution.
num_samples = 100000
num_dims = 2
xamb = random.normal(rng_xamb, [num_samples, num_dims])
xamb = forward(bij_params, bij_fns, xamb)
xtor = jnp.mod(xamb, 2.0 * jnp.pi)
lp = induced_torus_log_density(bij_params, bij_fns, xtor)
xobs = rejection_sampling(rng_xobs, len(xtor), torus_density, args.beta)
# Compute comparison statistics.
mean_mse = jnp.square(jnp.linalg.norm(xtor.mean(0) - xobs.mean(0)))
cov_mse = jnp.square(jnp.linalg.norm(jnp.cov(xtor.T) - jnp.cov(xobs.T)))
approx = jnp.exp(lp)
target = torus_density(xtor)
w = target / approx
Z = jnp.nanmean(w)
log_approx = jnp.log(approx)
log_target = jnp.log(target)
klqp = jnp.nanmean(log_approx - log_target) + jnp.log(Z)
ess = jnp.square(jnp.nansum(w)) / jnp.nansum(jnp.square(w))
ress = 100 * ess / len(w)
def periodic_shift(side, R, dR): """Shifts positions, wrapping them back within a periodic hypercube.""" return np.mod(R + dR, side)
def build_cells(R, **kwargs):
N = R.shape[0]
dim = R.shape[1]
if dim != 2 and dim != 3:
# NOTE(schsam): Do we want to check this in compute_fn as well?
raise ValueError(
'Cell list spatial dimension must be 2 or 3. Found {}'.format(dim))
neighborhood_tile_count = 3 ** dim
_, cell_size, cells_per_side, cell_count = \
_cell_dimensions(dim, box_size, minimum_cell_size)
hash_multipliers = _compute_hash_constants(dim, cells_per_side)
# Create cell list data.
particle_id = lax.iota(np.int64, N)
# NOTE(schsam): We use the convention that particles that are successfully,
# copied have their true id whereas particles empty slots have id = N.
# Then when we copy data back from the grid, copy it to an array of shape
# [N + 1, output_dimension] and then truncate it to an array of shape
# [N, output_dimension] which ignores the empty slots.
mask_id = np.ones((N,), np.int64) * N
cell_R = np.zeros((cell_count * cell_capacity, dim), dtype=R.dtype)
cell_id = N * np.ones((cell_count * cell_capacity, 1), dtype=i32)
# It might be worth adding an occupied mask. However, that will involve
# more compute since often we will do a mask for species that will include
# an occupancy test. It seems easier to design around this empty_data_value
# for now and revisit the issue if it comes up later.
empty_kwarg_value = 10 ** 5
cell_kwargs = {}
for k, v in kwargs.items():
if not isinstance(v, np.ndarray):
raise ValueError((
'Data must be specified as an ndarry. Found "{}" with '
'type {}'.format(k, type(v))))
if v.shape[0] != R.shape[0]:
raise ValueError(
('Data must be specified per-particle (an ndarray with shape '
'(R.shape[0], ...)). Found "{}" with shape {}'.format(k, v.shape)))
kwarg_shape = v.shape[1:] if v.ndim > 1 else (1,)
cell_kwargs[k] = empty_kwarg_value * np.ones(
(cell_count * cell_capacity,) + kwarg_shape, v.dtype)
indices = np.array(R / cell_size, dtype=i32)
hashes = np.sum(indices * hash_multipliers, axis=1)
# Copy the particle data into the grid. Here we use a trick to allow us to
# copy into all cells simultaneously using a single lax.scatter call. To do
# this we first sort particles by their cell hash. We then assign each
# particle to have a cell id = hash * cell_capacity + grid_id where grid_id
# is a flat list that repeats 0, .., cell_capacity. So long as there are
# fewer than cell_capacity particles per cell, each particle is guarenteed
# to get a cell id that is unique.
sort_map = np.argsort(hashes)
sorted_R = R[sort_map]
sorted_hash = hashes[sort_map]
sorted_id = particle_id[sort_map]
sorted_kwargs = {}
for k, v in kwargs.items():
sorted_kwargs[k] = v[sort_map]
sorted_cell_id = np.mod(lax.iota(np.int64, N), cell_capacity)
sorted_cell_id = sorted_hash * cell_capacity + sorted_cell_id
cell_R = ops.index_update(cell_R, sorted_cell_id, sorted_R)
sorted_id = np.reshape(sorted_id, (N, 1))
cell_id = ops.index_update(
cell_id, sorted_cell_id, sorted_id)
cell_R = _unflatten_cell_buffer(cell_R, cells_per_side, dim)
cell_id = _unflatten_cell_buffer(cell_id, cells_per_side, dim)
for k, v in sorted_kwargs.items():
if v.ndim == 1:
v = np.reshape(v, v.shape + (1,))
cell_kwargs[k] = ops.index_update(cell_kwargs[k], sorted_cell_id, v)
cell_kwargs[k] = _unflatten_cell_buffer(
cell_kwargs[k], cells_per_side, dim)
return CellList(cell_R, cell_id, cell_kwargs)