def model(X: DeviceArray) -> DeviceArray:
"""Gamma-Poisson hierarchical model for daily sales forecasting
Args:
X: input data
Returns:
output data
"""
n_stores, n_days, n_features = X.shape
n_features -= 1 # remove one dim for target
eps = 1e-12 # epsilon
plate_features = numpyro.plate(Plate.features, n_features, dim=-1)
plate_stores = numpyro.plate(Plate.stores, n_stores, dim=-2)
plate_days = numpyro.plate(Plate.days, n_days, dim=-1)
disp_param_mu = numpyro.sample(Site.disp_param_mu,
dist.Normal(loc=4., scale=1.))
disp_param_sigma = numpyro.sample(Site.disp_param_sigma,
dist.HalfNormal(scale=1.))
with plate_stores:
disp_param_offsets = numpyro.sample(
Site.disp_param_offsets,
dist.Normal(loc=jnp.zeros((n_stores, 1)), scale=0.1))
disp_params = disp_param_mu + disp_param_offsets * disp_param_sigma
disp_params = numpyro.sample(Site.disp_params,
dist.Delta(disp_params),
obs=disp_params)
with plate_features:
coef_mus = numpyro.sample(
Site.coef_mus,
dist.Normal(loc=jnp.zeros(n_features), scale=jnp.ones(n_features)))
coef_sigmas = numpyro.sample(
Site.coef_sigmas, dist.HalfNormal(scale=2. * jnp.ones(n_features)))
with plate_stores:
coef_offsets = numpyro.sample(
Site.coef_offsets,
dist.Normal(loc=jnp.zeros((n_stores, n_features)), scale=1.))
coefs = coef_mus + coef_offsets * coef_sigmas
coefs = numpyro.sample(Site.coefs, dist.Delta(coefs), obs=coefs)
with plate_days, plate_stores:
targets = X[..., -1]
features = jnp.nan_to_num(X[..., :-1]) # padded features to 0
is_observed = jnp.where(jnp.isnan(targets), jnp.zeros_like(targets),
jnp.ones_like(targets))
not_observed = 1 - is_observed
means = (is_observed * jnp.exp(
jnp.sum(jnp.expand_dims(coefs, axis=1) * features, axis=2)) +
not_observed * eps)
betas = is_observed * jnp.exp(-disp_params) + not_observed
alphas = means * betas
return numpyro.sample(Site.days,
dist.GammaPoisson(alphas, betas),
obs=jnp.nan_to_num(targets))
def main(cfg_path: Path, log_level: int):
logging.basicConfig(
stream=sys.stdout,
level=log_level,
datefmt='%Y-%m-%d %H:%M',
format='%(asctime)s - %(name)s - %(levelname)s - %(message)s')
with open(cfg_path) as f:
cfg = yaml.load(f, Loader=yaml.FullLoader)
nside = cfg['nside']
outpath = cfg['hdf5_path']
mask_file = 'data/n0512.fits'
mask_data = old_np.nan_to_num(
hp.read_map(mask_file, verbose=False, dtype=np.float32))
mask_apodized = nmt.mask_apodization(mask_data, 5., apotype="C2")
mask_binary = old_np.where(mask_data > 0.0, 1.0, 0.0)
with h5py.File(outpath, 'w') as f:
ns0512 = f.require_group('ns0512')
data_dset = ns0512.require_dataset('binary',
shape=(hp.nside2npix(nside), ),
dtype=np.float32)
data_dset[...] = np.nan_to_num(mask_binary)
apodized = ns0512.require_group('apodized')
data_dset2 = apodized.require_dataset('basic',
shape=(hp.nside2npix(nside), ),
dtype=np.float32)
data_dset2[...] = np.nan_to_num(mask_apodized)
def uniform_stochastic_quantize(v: jnp.ndarray,
num_levels: int,
rng: PRNGKey,
v_min: Optional[float] = None,
v_max: Optional[float] = None) -> jnp.ndarray:
"""Uniform stochastic algorithm in https://arxiv.org/pdf/1611.00429.pdf.
Args:
v: vector to be quantized.
num_levels: Number of levels of quantization.
rng: jax random key.
v_min: minimum threshold for quantization. If None, sets it to jnp.amin(v).
v_max: maximum threshold for quantization. If None, sets it to jnp.amax(v).
Returns:
Quantized array.
"""
# Rescale the vector to be between zero to one.
if v_min is None:
v_min = jnp.amin(v)
if v_max is None:
v_max = jnp.amax(v)
v = jnp.nan_to_num((v - v_min) / (v_max - v_min))
v = jnp.maximum(0., jnp.minimum(v, 1.))
# Compute the upper and lower boundary of each value.
v_ceil = jnp.ceil(v * (num_levels - 1)) / (num_levels - 1)
v_floor = jnp.floor(v * (num_levels - 1)) / (num_levels - 1)
# uniformly quantize between v_ceil and v_floor.
rand = jax.random.uniform(key=rng, shape=v.shape)
threshold = jnp.nan_to_num((v - v_floor) / (v_ceil - v_floor))
quantized = jnp.where(rand > threshold, v_floor, v_ceil)
# Rescale the values and return it.
return v_min + quantized * (v_max - v_min)
def _giou(boxes1: jnp.ndarray, boxes2: jnp.ndarray) -> jnp.ndarray:
b1_ymin, b1_xmin, b1_ymax, b1_xmax = jnp.hsplit(boxes1, 4)
b2_ymin, b2_xmin, b2_ymax, b2_xmax = jnp.hsplit(boxes2, 4)
b1_width = jnp.maximum(0, b1_xmax - b1_xmin)
b1_height = jnp.maximum(0, b1_ymax - b1_ymin)
b2_width = jnp.maximum(0, b2_xmax - b2_xmin)
b2_height = jnp.maximum(0, b2_ymax - b2_ymin)
b1_area = b1_width * b1_height
b2_area = b2_width * b2_height
intersect_ymin = jnp.maximum(b1_ymin, b2_ymin)
intersect_xmin = jnp.maximum(b1_xmin, b2_xmin)
intersect_ymax = jnp.minimum(b1_ymax, b2_ymax)
intersect_xmax = jnp.minimum(b1_xmax, b2_xmax)
intersect_width = jnp.maximum(0, intersect_xmax - intersect_xmin)
intersect_height = jnp.maximum(0, intersect_ymax - intersect_ymin)
intersect_area = intersect_width * intersect_height
union_area = b1_area + b2_area - intersect_area
iou = jnp.nan_to_num(intersect_area / union_area)
enclose_ymin = jnp.minimum(b1_ymin, b2_ymin)
enclose_xmin = jnp.minimum(b1_xmin, b2_xmin)
enclose_ymax = jnp.maximum(b1_ymax, b2_ymax)
enclose_xmax = jnp.maximum(b1_xmax, b2_xmax)
enclose_width = jnp.maximum(0, enclose_xmax - enclose_xmin)
enclose_height = jnp.maximum(0, enclose_ymax - enclose_ymin)
enclose_area = enclose_width * enclose_height
giou = iou - jnp.nan_to_num((enclose_area - union_area) / enclose_area)
return giou.squeeze()
def recursive_check(tuple_object, dict_object):
if isinstance(tuple_object, (List, Tuple)):
for tuple_iterable_value, dict_iterable_value in zip(tuple_object, dict_object):
recursive_check(tuple_iterable_value, dict_iterable_value)
elif tuple_object is None:
return
else:
self.assert_almost_equals(jnp.nan_to_num(tuple_object), jnp.nan_to_num(dict_object), 1e-5)
def mutual_information(net, samples):
probs = net.prob_factors(samples)
avgP = jnp.mean(probs, axis=2)
S = (avgP * jnp.nan_to_num(jnp.log(avgP)) +
(1. - avgP) * jnp.nan_to_num(jnp.log(1. - avgP))) / jnp.log(2.)
condS = jnp.mean(
(probs * jnp.nan_to_num(jnp.log(probs)) +
(1. - probs) * jnp.nan_to_num(jnp.log(1. - probs))) / jnp.log(2.),
axis=2)
return condS - S
def calc_delta_correlated_error_jax(areas_a, ematrix_a, areas_b, errors_b):
diffs_a, diffs_b = delta_differential_jax(areas_a, areas_b)
# need to do nan_to_num since the differential can return nan...
# not sure how to fix "properly" though
diffs_a = jnp.nan_to_num(diffs_a)
diffs_b = jnp.nan_to_num(diffs_b)
# for the total, we need to do
# diffs_a * ematrix_a * diffs_a + diffs_b*errors_b*diffs_b,
# since the errors on a and b have no connections, we can get away with this.
# err_a_sq = diffs_a.T @ ematrix_a @ diffs_a
err_a_sq = jnp.matmul(diffs_a.T, jnp.matmul(ematrix_a, diffs_a))
err_b_sq = jnp.sum(jnp.square((diffs_b * errors_b)))
return jnp.sqrt(err_a_sq + err_b_sq)
def update(delta_x, delta_gx, Us, VTs, n_step):
# Add column/row to Us/VTs with updated approximation
# Calculate J_i
vT = rmatvec(Us, VTs, delta_x)
u = (delta_x - matvec(Us, VTs, delta_gx)) / _einsum(
'bij, bij -> b', vT, delta_gx)[:, None, None]
vT = jnp.nan_to_num(vT)
u = jnp.nan_to_num(u)
# Store in UTs and VTs for calculating J
VTs = jax.ops.index_update(VTs, jax.ops.index[:, n_step - 1], vT)
Us = jax.ops.index_update(Us, jax.ops.index[:, :, :, n_step - 1], u)
return Us, VTs
def ps_ir(*, draws, proposal_densities, target_densities, num_resampled, key):
logits = target_densities - proposal_densities
logits = jnp.nan_to_num(logits, nan=-jnp.inf, neginf=-jnp.inf)
idxs = jax.random.categorical(key=key,
logits=logits,
shape=(num_resampled, ))
return draws[idxs]
def reweighted_stddev(f_n: Array, target_logpdf_n: Array,
source_logpdf_n: Array) -> Float:
"""Compute reweighted estimate of
stddev(f(x)) under x ~ p_target
based on samples x ~ p_source
where
p_target(x) = exp(target_logpdf(x)) / Z_target
using samples from a different source
x_n ~ p_source
where
p_source(x) = exp(source_logpdf(x)) / Z_source
The inputs are arrays "{fxn_name}_n" containing the result of
calling each fxn on a fixed array of samples:
* f_n = [f(x_n) for x_n in samples]
* target_logpdf_n = [target_logpdf(x_n) for x_n in samples]
* source_logpdf_n = [source_logpdf(x_n) for x_n in samples]
"""
log_weights_n = target_logpdf_n - source_logpdf_n
weights = np.exp(log_weights_n - logsumexp(log_weights_n)).flatten()
f_mean = np.sum(weights * f_n)
squared_deviations = (f_n - f_mean)**2
# sanitize 0 * inf -> 0 (instead of nan)
weighted_squared_deviations = weights * squared_deviations
sanitized = np.nan_to_num(weighted_squared_deviations, nan=0)
stddev = np.sqrt(np.sum(sanitized))
return stddev
def precision(
y_true: jnp.ndarray,
y_pred: jnp.ndarray,
threshold: jnp.ndarray,
class_id: jnp.ndarray,
sample_weight: jnp.ndarray,
true_positives: ReduceConfusionMatrix,
false_positives: ReduceConfusionMatrix,
) -> jnp.ndarray:
# TODO: class_id behavior
y_pred = (y_pred > threshold).astype(jnp.float32)
if y_true.dtype != y_pred.dtype:
y_pred = y_pred.astype(y_true.dtype)
true_positives = true_positives(y_true=y_true,
y_pred=y_pred,
sample_weight=sample_weight)
false_positives = false_positives(y_true=y_true,
y_pred=y_pred,
sample_weight=sample_weight)
return jnp.nan_to_num(
jnp.divide(true_positives, true_positives + false_positives))
def rnn_cell(carry, x):
newCarry, logits = jax.vmap(eval_cell)(carry[0], carry[1])
sampleOut = jax.random.categorical(x, logits)
sample = jax.nn.one_hot(sampleOut, inputDim)
logProb = jnp.sum(nn.log_softmax(logits) * sample, axis=1)
return (newCarry, sample), (jnp.nan_to_num(logProb,
nan=-35), sampleOut)
def loss(self, params, batch):
"""Cross-entropy loss"""
inputs, targets = batch
preds = self.predict(params, inputs)
return jnp.mean(
jnp.nan_to_num(-targets * jnp.log(preds) -
(1 - targets) * jnp.log(1 - preds)))
def syn2post_softmax(syn_values,
post_ids,
post_num: int,
indices_are_sorted=True):
"""The syn-to-post softmax computation.
Parameters
----------
syn_values: jax.numpy.ndarray, JaxArray, Variable
The synaptic values.
post_ids: jax.numpy.ndarray, JaxArray
The post-synaptic neuron ids. If ``post_ids`` is generated by
``brainpy.conn.TwoEndConnector``, then it has sorted indices.
Otherwise, this function cannot guarantee indices are sorted.
You's better set ``indices_are_sorted=False``.
post_num: int
The number of the post-synaptic neurons.
indices_are_sorted: whether ``post_ids`` is known to be sorted.
Returns
-------
post_val: jax.numpy.ndarray, JaxArray
The post-synaptic value.
"""
post_ids = as_device_array(post_ids)
syn_values = as_device_array(syn_values)
if syn_values.dtype == jnp.bool_:
syn_values = jnp.asarray(syn_values, dtype=jnp.int32)
syn_maxs = _jit_seg_max(syn_values, post_ids, post_num, indices_are_sorted)
syn_values = syn_values - syn_maxs[post_ids]
syn_values = jnp.exp(syn_values)
normalizers = _jit_seg_sum(syn_values, post_ids, post_num,
indices_are_sorted)
softmax = syn_values / normalizers[post_ids]
return jnp.nan_to_num(softmax)
def top_k_error_rate_metric(logits: jnp.ndarray,
one_hot_labels: jnp.ndarray,
k: int = 5,
mask: Optional[jnp.ndarray] = None) -> jnp.ndarray:
"""Returns the top-K error rate between some predictions and some labels.
Args:
logits: Output of the model.
one_hot_labels: One-hot encoded labels. Dimensions should match the logits.
k: Number of class the model is allowed to predict for each example.
mask: Mask to apply to the loss to ignore some samples (usually, the padding
of the batch). Array of ones and zeros.
Returns:
The error rate (1 - accuracy), averaged over the first dimension (samples).
"""
if mask is None:
mask = jnp.ones([logits.shape[0]])
mask = mask.reshape([logits.shape[0]])
true_labels = jnp.argmax(one_hot_labels, -1).reshape([-1, 1])
top_k_preds = jnp.argsort(logits, axis=-1)[:, -k:]
hit = jax.vmap(jnp.isin)(true_labels, top_k_preds)
error_rate = 1 - ((hit * mask).sum() / mask.sum())
# Set to zero if there is no non-masked samples.
return jnp.nan_to_num(error_rate)
def biot_savart_oncoil(r_eval, dl, ll, I_arr):
"""
Calculate the Biot-Savart integral over the coils (also ON) a segment of the
coil.
specified by l and dl.
Arguments:
*r_eval*: (lenght 3 array) the point wherer the field is to be evaluated in cartesian
coordinates. Has to be on a coil.
*dl*: ( n_coils, nsegments, 3)-array of the distance vector to every
other coil line segment
*l* ( n_coils, nsegments, 3)-array of the position of each coil segment
Note on algoritnm: the None allows one to add new axes to in-line
cast the array into the proper shape.
The biot-savart integral is calculated as a sum over all segments.
returns:
*B*: magnetic field at position r_eval
"""
top = np.cross(dl, r_eval[None, None, :] - ll) * I_arr[:, None,
None] #unchecked
bottom = np.linalg.norm(r_eval[None, None, :] - ll, axis=-1)**3
# sum over all infinitesimal line segments, replacing the NaN with zero
B = np.sum(np.nan_to_num(top / bottom[:, :, None]), axis=(0, 1))
return B
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 piecewise_constant_pdf(key, bins, weights, num_samples, randomized):
"""Piecewise-Constant PDF sampling.
Args:
key: jnp.ndarray(float32), [2,], random number generator.
bins: jnp.ndarray(float32), [batch_size, num_bins + 1].
weights: jnp.ndarray(float32), [batch_size, num_bins].
num_samples: int, the number of samples.
randomized: bool, use randomized samples.
Returns:
z_samples: jnp.ndarray(float32), [batch_size, num_samples].
"""
# Pad each weight vector (only if necessary) to bring its sum to `eps`. This
# avoids NaNs when the input is zeros or small, but has no effect otherwise.
eps = 1e-5
weight_sum = jnp.sum(weights, axis=-1, keepdims=True)
padding = jnp.maximum(0, eps - weight_sum)
weights += padding / weights.shape[-1]
weight_sum += padding
# Compute the PDF and CDF for each weight vector, while ensuring that the CDF
# starts with exactly 0 and ends with exactly 1.
pdf = weights / weight_sum
cdf = jnp.minimum(1, jnp.cumsum(pdf[Ellipsis, :-1], axis=-1))
cdf = jnp.concatenate([
jnp.zeros(list(cdf.shape[:-1]) + [1]), cdf,
jnp.ones(list(cdf.shape[:-1]) + [1])
],
axis=-1)
# Draw uniform samples.
if randomized:
# Note that `u` is in [0, 1) --- it can be zero, but it can never be 1.
u = random.uniform(key, list(cdf.shape[:-1]) + [num_samples])
else:
# Match the behavior of random.uniform() by spanning [0, 1-eps].
u = jnp.linspace(0., 1. - jnp.finfo('float32').eps, num_samples)
u = jnp.broadcast_to(u, list(cdf.shape[:-1]) + [num_samples])
# Identify the location in `cdf` that corresponds to a random sample.
# The final `True` index in `mask` will be the start of the sampled interval.
mask = u[Ellipsis, None, :] >= cdf[Ellipsis, :, None]
def find_interval(x):
# Grab the value where `mask` switches from True to False, and vice versa.
# This approach takes advantage of the fact that `x` is sorted.
x0 = jnp.max(jnp.where(mask, x[Ellipsis, None], x[Ellipsis, :1, None]), -2)
x1 = jnp.min(jnp.where(~mask, x[Ellipsis, None], x[Ellipsis, -1:, None]), -2)
return x0, x1
bins_g0, bins_g1 = find_interval(bins)
cdf_g0, cdf_g1 = find_interval(cdf)
t = jnp.clip(jnp.nan_to_num((u - cdf_g0) / (cdf_g1 - cdf_g0), 0), 0, 1)
samples = bins_g0 + t * (bins_g1 - bins_g0)
# Prevent gradient from backprop-ing through `samples`.
return lax.stop_gradient(samples)
def arithmetic_encoding_num_bits(v: jnp.ndarray) -> int: """Computes number of bits needed to store v via arithmetic coding.""" v = jnp.nan_to_num(v) v = v.flatten() uniq = jnp.unique(v) entropy = _entropy(v, uniq) hist_bits = _hist_bits(v, uniq) return hist_bits + (v.size * entropy) + (2 * 32) + 2
def replace_inf_with_zero(x):
return jnp.nan_to_num(
x,
copy=False,
nan=0.0,
posinf=0.0,
neginf=0.0,
)
def _log_prob(self, inputs: np.ndarray) -> np.ndarray:
"""Log prob for arrays."""
# calculate log_prob
u, log_det = self._inverse(self._params, inputs)
log_prob = self.prior.log_prob(u) + log_det
# set NaN's to negative infinity (i.e. zero probability)
log_prob = np.nan_to_num(log_prob, nan=np.NINF)
return log_prob
def calc_delta_jax(areas_a, areas_b):
# do I need bin areas or densities?
# I guess since by definition sum(area_a) = 1, areas are needed?!
integrand = jnp.true_divide(jnp.square(areas_a - areas_b),
areas_a + areas_b)
# nan_to_num important as divide gives nans if both 0
delta = 0.5 * jnp.sum(jnp.nan_to_num(integrand))
return delta
def find_minimum_theta_scalar(fc_new, r_fil, theta_i): f = partial(objective_scalar, fc_new, r_fil) f_prime = grad(f) f_primeprime = grad(f_prime) for n in range(n_iter): new_ep = epsilon * np.exp(-n / 15) theta_i = theta_i - alpha * np.nan_to_num(f_prime(theta_i) / (f_primeprime(theta_i) + new_ep)) return theta_i
def apply(self, x, L=10, units=[10], inputDim=2, actFun=nn.elu, initScale=1.0):
initFunctionCell = jax.nn.initializers.variance_scaling(scale=1.0, mode="fan_avg", distribution="uniform")
initFunctionOut = jax.nn.initializers.variance_scaling(scale=initScale, mode="fan_in", distribution="uniform")
#initFunction = jax.nn.initializers.lecun_uniform()
cellInV = nn.Dense.shared(features=units[0],
name='rnn_cell_in_v',
bias=False)
cellInH = nn.Dense.shared(features=units[0],
name='rnn_cell_in_h',
bias=False)
cellCarryV = nn.Dense.shared(features=units[0],
name='rnn_cell_carry_v',
bias=False,
kernel_init=initFunctionCell)
cellCarryH = nn.Dense.shared(features=units[0],
name='rnn_cell_carry_h',
bias=True,
kernel_init=initFunctionCell)
outputDense = nn.Dense.shared(features=inputDim,
name='rnn_output_dense',
kernel_init=initFunctionOut)
batchSize = x.shape[0]
outputs = jnp.asarray(np.zeros((batchSize,L,L)))
states = jnp.asarray(np.zeros((L,batchSize,units[0])))
inputs = jnp.asarray(np.zeros((L+1,L+2,batchSize,inputDim)))
# Scan directions for zigzag path
direction = np.ones(L,dtype=np.int32)
direction[1::2] = -1
direction = jnp.asarray(direction)
x = jnp.transpose(x,axes=[1,2,0])
inputs = jax.ops.index_update(inputs,jax.ops.index[1:,1:-1],jax.nn.one_hot(x,inputDim))
def rnn_dim2(carry,x):
newCarry = actFun( cellInH(x[0]) + cellInV(x[1]) + cellCarryH(carry) + cellCarryV(x[2]) )
out = jnp.concatenate((newCarry, nn.softmax(outputDense(newCarry))), axis=1)
return newCarry, out
def rnn_dim1(carry,x):
_, out = jax.lax.scan(rnn_dim2,jnp.zeros((batchSize,units[0]),dtype=np.float32),
(self.reverse_line(x[0],x[2])[:-2],
self.reverse_line(x[1],x[2])[1:-1],
self.reverse_line(carry,x[2]))
)
carry = jax.ops.index_update(carry,jax.ops.index[:,:],out[:,:,:units[0]])
outputs = jnp.log( jnp.sum( out[:,:,units[0]:] * self.reverse_line(x[0],x[2])[1:-1,:], axis=2 ) )
return self.reverse_line(carry,x[2]), jnp.sum(outputs,axis=0)
_, prob = jax.lax.scan(rnn_dim1,states,(inputs[1:],inputs[:-1],direction))
return jnp.nan_to_num(jnp.sum(prob,axis=0))
def maximize_saturation(rgb):
"""Rescale the maximum saturation in `rgb` to be 1."""
hsv = pix.rgb_to_hsv(rgb)
scaling = jnp.maximum(1,
jnp.nan_to_num(1 / jnp.max(hsv[Ellipsis, 1]), nan=1))
rgb_scaled = pix.hsv_to_rgb(
jnp.stack(
[hsv[Ellipsis, 0], scaling * hsv[Ellipsis, 1], hsv[Ellipsis, 2]],
axis=-1))
return rgb_scaled
def update(i, g, state):
x, s, v = state
v = (1 - b2) * np.square(g) + b2 * v # Update 2nd moment.
vhat = v / (1 - b2**(i + 1)) # Bias correction.
g_norm = np.nan_to_num(g / np.sqrt(vhat)) # Normalise gradient.
g_norm = np.clip(g_norm, -g_bound, g_bound) # Bound g.
x *= np.exp(-step_size(i) * g_norm *
np.sign(x)) # Multiplicative update.
x = np.clip(x, -s, s) # Bound parameters.
return x, s, v
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 piecewise_constant_pdf(key, bins, weights, num_samples, randomized):
"""Piecewise-Constant PDF sampling.
Args:
key: jnp.ndarray(float32), [2,], random number generator.
bins: jnp.ndarray(float32), [batch_size, num_bins + 1].
weights: jnp.ndarray(float32), [batch_size, num_bins].
num_samples: int, the number of samples.
randomized: bool, use randomized samples.
Returns:
z_samples: jnp.ndarray(float32), [batch_size, num_samples].
"""
# Pad each weight vector (only if necessary) to bring its sum to `eps`. This
# avoids NaNs when the input is zeros or small, but has no effect otherwise.
eps = 1e-5
weight_sum = jnp.sum(weights, axis=-1, keepdims=True)
padding = jnp.maximum(0, eps - weight_sum)
weights += padding / weights.shape[-1]
weight_sum += padding
# Compute the PDF and CDF for each weight vector.
pdf = weights / weight_sum
cdf = jnp.cumsum(pdf, axis=-1)
cdf = jnp.concatenate([jnp.zeros(list(cdf.shape[:-1]) + [1]), cdf],
axis=-1)
# Take uniform samples
if randomized:
u = random.uniform(key, list(cdf.shape[:-1]) + [num_samples])
else:
u = jnp.linspace(0., 1., num_samples)
u = jnp.broadcast_to(u, list(cdf.shape[:-1]) + [num_samples])
# Invert CDF. This takes advantage of the fact that `bins` is sorted.
mask = (u[Ellipsis, None, :] >= cdf[Ellipsis, :, None])
def minmax(x):
x0 = jnp.max(jnp.where(mask, x[Ellipsis, None], x[Ellipsis, :1, None]),
-2)
x1 = jnp.min(
jnp.where(~mask, x[Ellipsis, None], x[Ellipsis, -1:, None]), -2)
x0 = jnp.minimum(x0, x[Ellipsis, -2:-1])
x1 = jnp.maximum(x1, x[Ellipsis, 1:2])
return x0, x1
bins_g0, bins_g1 = minmax(bins)
cdf_g0, cdf_g1 = minmax(cdf)
t = jnp.clip(jnp.nan_to_num((u - cdf_g0) / (cdf_g1 - cdf_g0), 0), 0, 1)
samples = bins_g0 + t * (bins_g1 - bins_g0)
# Prevent gradient from backprop-ing through `samples`.
return lax.stop_gradient(samples)
def excute(fn, grad_in=None):
if fn is not None:
if isinstance(fn, AccumulateGrad):
if fn.variable.requires_grad and grad_in is not None:
if fn.variable.grad is None:
fn.variable.grad = jnp.zeros(fn.variable.data.shape)
grad_in = jnp.where(grad_in == jnp.inf, 0, grad_in)
grad_in = jnp.nan_to_num(grad_in, copy=False)
if len(grad_in.shape) != 4:
if len(fn.variable.grad.shape) == 4:
gamma = gammapops(grad_in, fn.variable.data.shape[2],
fn.variable.data.shape[3])
grad_in = jnp.matmul(gamma, grad_in.T)
grad_in = grad_in.reshape(fn.variable.grad.shape)
else:
if grad_in.shape != fn.variable.grad.shape:
gamma = linearpops(fn.variable.grad.shape[1])
grad_in = jnp.transpose(
jnp.matmul(gamma.T, grad_in))
grad_in = jnp.where(grad_in == jnp.inf, 0, grad_in)
grad_in = jnp.nan_to_num(grad_in, copy=False)
fn.variable.grad = index_add(fn.variable.grad, index[:],
grad_in)
return
grad_outs, gamma = fn.apply(grad_in)
if gamma is not None:
gamma_stack.append(gamma)
if type(grad_outs) is not tuple:
grad_outs = (grad_outs, )
for i, next_func in enumerate(fn.next_functions):
excute(next_func, grad_outs[i])
def segment_mean(data, segment_ids, num_segments):
"""Returns mean for each segment.
Args:
data: the values which are averaged segment-wise.
segment_ids: indices for the segments.
num_segments: total number of segments.
"""
nominator = jax.ops.segment_sum(data, segment_ids, num_segments)
denominator = jax.ops.segment_sum(jnp.ones_like(data), segment_ids,
num_segments)
return jnp.nan_to_num(nominator / denominator)