def generate_samples(self, eval_points, n, img_shape):
tiled_points = tf.tile(tf.expand_dims(eval_points, 0), [n, 1, 1, 1, 1])
noised_eval_im = tf.clip_by_value(
tiled_points +
tf.random_poisson(self.lamda, tf.shape(tiled_points)), 0, 1)
return noised_eval_im
def add_channel_noise(chan, a_sd, b_si, batchsize, im_h, im_w):
##
## determine sensor noise at each pixel using non-clipped poisson-gauss model from FOI et al
##
if a_sd == 0.0:
chi = 0
sigdep = chan
else:
chi = 1.0 / a_sd
rate = tf.maximum(chi * chan, 0)
sigdep = tf.random_poisson(rate, shape=[]) / chi
#
sigindep = tf.sqrt(b_si) * tf.random_normal(
shape=(batchsize, im_h, im_w, 1), mean=0.0, stddev=1.0)
# sum the two noise sources
chan_noise = sigdep + sigindep
#
#sigdep = tf.sqrt(a_sd*chan)*tf.random_normal(shape=(batchsize,im_h, im_w, 1), mean=0.0, stddev=1.0)
#sigindep = tf.sqrt(b_si)*tf.random_normal(shape=(batchsize,im_h, im_w, 1), mean=0.0, stddev=1.0)
#chan_noise = chan + sigdep + sigindep
#
#chan_noise = chan + tf.sqrt(a_sd*chan + b_si)*tf.random_normal(shape=(batchsize,im_h, im_w, 1), mean=0.0, stddev=1.0)
#
# clip the noise between 0 and 1 (baking in 0 and 255 limits)
clip_chan_noise = tf.clip_by_value(chan_noise, 0.0, 1.0)
#
return clip_chan_noise
def add_poisson_noise(input_tensor):
if not isinstance(input_tensor, tf.Tensor):
raise TypeError("Requre Tensor, got {}.".format(type(input_tensor)))
with tf.name_scope('add_poisson_noise'):
if input_tensor.dtype != tf.float32:
input_tensor = tf.cast(input_tensor, tf.float32)
return tf.random_poisson(input_tensor, [])
def Predict_image(self,src,noisy=False,max_noise_rms=0.1):
'''
Given an input for the source image (and a lens model),
return an output image corresponding to the lens model raytraced
image.
'''
self.src = src
xsrc , ysrc = self.raytrace()
xsrc = tf.reshape(xsrc,[-1])
ysrc = tf.reshape(ysrc,[-1])
img_pred = self._interpolate(self.src,xsrc,ysrc,[self.numpix_side,self.numpix_side],self.src_res)
img_pred = tf.reshape(img_pred,[-1,self.numpix_side,self.numpix_side,1])
if self.psf == True:
#img_pred = batch_conv(img_pred,self.psf_pl)
img_pred = tf.nn.conv2d(img_pred,self.psf_pl,strides=[1,1,1,1],padding='SAME')
if self.poisson:
counts = tf.random_uniform([1,1,1,1],minval=100,maxval=1000)
img_pred = tf.random_poisson(counts*img_pred,[1])[0]/counts
if noisy ==True:
noise_rms = tf.random_uniform(shape=[1],minval=max_noise_rms/100.,maxval=max_noise_rms)
noise = tf.random_normal(tf.shape(img_pred),mean=0.0,stddev = noise_rms)
img_pred = tf.add(img_pred,noise)
self.noise_rms = noise_rms
return img_pred
def _get_histogram_var_by_type(self,
histogram_type,
shape,
name=None,
**kwargs):
with tf.name_scope(name, "get_hist_{}".format(histogram_type)):
if histogram_type == "normal":
# Make a normal distribution, with a shifting mean
mean = tf.Variable(kwargs['mean'])
stddev = tf.Variable(kwargs['stddev'])
return tf.random_normal(
shape=shape, mean=mean, stddev=stddev), [mean, stddev]
elif histogram_type == "gamma":
# Add a gamma distribution
alpha = tf.Variable(kwargs['alpha'])
return tf.random_gamma(shape=shape, alpha=alpha), [alpha]
elif histogram_type == "poisson":
lam = tf.Variable(kwargs['lam'])
return tf.random_poisson(shape=shape, lam=lam), [lam]
elif histogram_type == "uniform":
# Add a uniform distribution
maxval = tf.Variable(kwargs['maxval'])
return tf.random_uniform(shape=shape, maxval=maxval), [maxval]
raise Exception('histogram type error %s' % histogram_type,
'builtin type', self._histogram_distribute_list)
def add_train_noise_tf(self, x: tf.Tensor) -> tf.Tensor:
"""Defines an operation to add poisson noise to a tensor of an image with a random chi-value
in the range from 0.001 to the specified max value."""
chi_rng = tf.random_uniform(shape=[1, 1, 1], minval=0.001, maxval=self.lam_max)
# Add 0.5 to pixel to make it positive as arg for poisson distribution.
# Subtract 0.5 at the end to fit in range again.
return tf.random_poisson(chi_rng*(x+0.5), shape=[])/chi_rng - 0.5
def log_prob(self, z_L, w_L, batch):
weight_log_prob = tf.reduce_sum([tf.reduce_sum(gamma_log_prob(self.prior_W_alpha, self.prior_W_beta, w)) for w in w_L])
z_log_prob = gamma_log_prob(self.prior_Z_alpha, self.prior_Z_beta, z_L[0])
l_prob = weight_log_prob + tf.reduce_sum(z_log_prob)
layer_wise = [z_log_prob,]
z_count = 0
for (z, w) in zip(z_L[:-1], w_L[:-1]):
z_sum_w = tf.matmul(z, w)
g_alpha = self.layer_alpha
g_beta = g_alpha / z_sum_w
l_p = tf.reduce_sum(gamma_log_prob(g_alpha, g_beta, z_L[z_count + 1]))
layer_wise.append(l_p)
l_prob += l_p
z_count += 1
obs_sum_w = tf.matmul(z_L[-1], w_L[-1])
l_prob += tf.reduce_sum(poisson_log_prob(batch, obs_sum_w))
for i in range(len(layer_wise)):
tf.summary.scalar("l_p_%i" %(i), tf.reduce_mean(layer_wise[i]))
#tf.summary.image("batch", tf.transpose(tf.reshape(batch, [320, 64, 64, 1]), [0, 2, 1, 3]), max_outputs = 4)
#tf.summary.image("obs_sum_w", tf.transpose(tf.reshape(obs_sum_w, [320, 64, 64, 1]), [0, 2, 1, 3]), max_outputs=4)
if do_images:
tf.summary.image("sampled_reconstruction", tf.transpose(tf.reshape(tf.minimum(tf.random_poisson(obs_sum_w, [1]), 255.0), [320, 64, 64, 1]), [0, 2, 1, 3]), max_outputs = 4)
return tf.reduce_sum(l_prob)
def _add_noise(
x: typing.Union[np.ndarray, tf.Tensor],
random_state: typing.Optional[np.random.RandomState] = None
) -> typing.Union[np.ndarray, tf.Tensor]:
if random_state is None:
return tf.squeeze(tf.random_poisson(x, [1]), axis=0)
else:
return random_state.poisson(x)
def _sample_y(self):
# expand dims to account for time and mc dims when applying mapping
# now (1 x num_samples x num_time_pts x dim_latent)
z_samples_ex = tf.expand_dims(self.z_samples_prior, axis=0)
y_means_ls = [] # contribution from latent space
y_means_lp = [] # contribution from linear predictors
y_means = []
for pop, pop_dim in enumerate(self.dim_obs):
y_means_ls.append(
tf.squeeze(self.networks[pop].apply_network(
z_samples_ex[:, :, :, self.latent_indxs[pop][0]:self.
latent_indxs[pop][-1]]),
axis=0))
if self.num_clusters is not None:
F = tf.expand_dims(y_means_ls[-1], axis=2)
y_means_ls[-1] = tf.squeeze(tf.matmul(F, self.mark_probs))
if self.dim_predictors is not None:
# append new list for this population
y_means_lp.append([])
for pred, pred_dim in enumerate(self.dim_predictors):
if self.predictor_indx[pop][pred] is not None:
net_out = self.networks_linear[pop][pred]. \
apply_network(self.linear_predictors_phs[pred])
y_means_lp[-1].append(net_out)
# else:
# self.y_pred_lp[-1].append(0.0)
y_means.append(tf.add(y_means_ls[-1],
tf.add_n(y_means_lp[-1])))
else:
y_means.append(y_means_ls[-1])
# get random samples from observation space
if self.noise_dist is 'gaussian':
obs_rand_samples = []
for pop, pop_dim in enumerate(self.dim_obs):
obs_rand_samples.append(
tf.random_normal(shape=[
self.num_samples_ph, self.num_time_pts, pop_dim
],
mean=0.0,
stddev=1.0,
dtype=self.dtype,
name=str('obs_rand_samples_%02i' % pop)))
self.y_samples_prior.append(
y_means[pop] +
tf.multiply(obs_rand_samples[pop], self.R_sqrt[pop]))
elif self.noise_dist is 'poisson':
for pop, pop_dim in enumerate(self.dim_obs):
self.y_samples_prior.append(
tf.squeeze(tf.random_poisson(lam=y_means[pop],
shape=[1],
dtype=self.dtype),
axis=0))
def random_poisson(lam: Any,
shape: Any,
dtype: DType = ztypes.float,
seed: Any = None,
name: Any = None):
return tf.random_poisson(lam=lam,
shape=shape,
dtype=dtype,
seed=seed,
name=name)
def run_all(logdir, verbose=False):
"""Generate a bunch of histogram data, and write it to logdir."""
k = tf.placeholder(tf.float32)
# Make a normal distribution, with a shifting mean
mean_moving_normal = tf.random_normal(shape=[1000], mean=(5 * k), stddev=1)
# Record that distribution into a histogram summary
tf.summary.histogram("normal/moving_mean", mean_moving_normal)
# Make a normal distribution with shrinking variance
variance_shrinking_normal = tf.random_normal(shape=[1000],
mean=0,
stddev=1 - (k))
# Record that distribution too
tf.summary.histogram("normal/shrinking_variance",
variance_shrinking_normal)
# Let's combine both of those distributions into one dataset
normal_combined = tf.concat(
[mean_moving_normal, variance_shrinking_normal], 0)
# We add another histogram summary to record the combined distribution
tf.summary.histogram("normal/bimodal", normal_combined)
# Add a gamma distribution
gamma = tf.random_gamma(shape=[1000], alpha=k)
tf.summary.histogram("gamma", gamma)
# And a poisson distribution
poisson = tf.random_poisson(shape=[1000], lam=k)
tf.summary.histogram("poisson", poisson)
# And a uniform distribution
uniform = tf.random_uniform(shape=[1000], maxval=k * 10)
tf.summary.histogram("uniform", uniform)
# Finally, combine everything together!
all_distributions = [
mean_moving_normal, variance_shrinking_normal, gamma, poisson, uniform
]
all_combined = tf.concat(all_distributions, 0)
tf.summary.histogram("all_combined", all_combined)
summaries = tf.summary.merge_all()
# Setup a session and summary writer
sess = tf.Session()
writer = tf.summary.FileWriter(logdir)
# Setup a loop and write the summaries to disk
N = 400
for step in xrange(N):
k_val = step / float(N)
summ = sess.run(summaries, feed_dict={k: k_val})
writer.add_summary(summ, global_step=step)
def _get_sinogram_mice(self):
from ..raw.mice import Dataset
from dxpy.learn.model.normalizer import FixWhite
from ..super_resolution import SuperResolutionDataset
with tf.name_scope('mice_sinogram_dataset'):
dataset = Dataset(self.name / 'mice_sinogram')
self.register_node('id', dataset['id'])
bs = dataset.param('batch_size')
stat = {'mean': dataset.MEAN, 'std': dataset.STD}
dataset = dataset['sinogram']
if self.param('with_poission_noise'):
with tf.name_scope('add_with_poission_noise'):
if self.param('low_dose'):
ratio = self.param('low_dose_ratio')
ratio_norm = 4e6 * bs / ratio
dataset = dataset / tf.reduce_sum(dataset) * ratio_norm
stat['mean'] = stat['mean'] / ratio
stat['std'] = stat['std'] / ratio
else:
dataset = dataset / tf.reduce_sum(dataset) * 4e6 * bs
noise = tf.random_poisson(dataset, shape=[])
dataset = tf.concat([noise, dataset], axis=0)
if self.param('with_white_normalization'):
dataset = FixWhite(name=self.name / 'fix_white',
inputs=dataset,
mean=stat['mean'],
std=stat['std']).as_tensor()
dataset = tf.random_crop(dataset, [shape_as_list(dataset)[0]] +
list(self.param('target_shape')) + [1])
dataset = SuperResolutionDataset(
self.name / 'super_resolution',
lambda: {'image': dataset},
input_key='image',
nb_down_sample=self.param('nb_down_sample'))
keys = [
'image{}x'.format(2**i)
for i in range(dataset.param('nb_down_sample') + 1)
]
result = dict()
if self.param('with_poission_noise'):
result.update({
'noise/' + k:
dataset[k][:shape_as_list(dataset[k])[0] // 2, ...]
for k in keys
})
result.update({
'clean/' + k:
dataset[k][shape_as_list(dataset[k])[0] // 2:, ...]
for k in keys
})
else:
result.update({'clean/' + k: dataset[k] for k in keys})
result.update({'noise/' + k: dataset[k] for k in keys})
return result
def estimate_elbo(self, batch):
elbo_z_L = [z.elbo_sample() for z in self.latent_layers]
elbo_w_L = [w.elbo_sample() for w in self.weight_layers]
the_prob = self.log_prob(elbo_z_L, elbo_w_L, batch)
new_sample = tf.matmul(elbo_z_L[-1], elbo_w_L[-1])
if do_images:
tf.summary.image("unconditional_sample", tf.transpose(tf.reshape(tf.minimum(tf.random_poisson(new_sample, [1]), 255.0), [320, 64, 64, 1]), [0, 2, 1, 3]), max_outputs = 4)
return the_prob + tf.reduce_sum([z.entropy() for z in self.latent_layers]) + tf.reduce_sum([w.entropy() for w in self.weight_layers])
def _get_sinogram_aps(self):
from ..raw.analytical_phantom_sinogram import Dataset
from dxpy.learn.model.normalizer import FixWhite
from ..super_resolution import SuperResolutionDataset
fields = ['sinogram', 'id', 'phantom']
with tf.name_scope('aps_sinogram_dataset'):
dataset = Dataset(self.name / 'analytical_phantom_sinogram',
fields=fields)
self.register_node('id', dataset['id'])
self.register_node('phantom', dataset['phantom'])
if self.param('log_scale'):
stat = dataset.LOG_SINO_STAT
else:
stat = dataset.SINO_STAT
dataset = dataset['sinogram']
if self.param('with_poission_noise'):
with tf.name_scope('add_with_poission_noise'):
noise = tf.random_poisson(dataset, shape=[])
dataset = tf.concat([noise, dataset], axis=0)
if self.param('log_scale'):
dataset = tf.log(dataset + 0.4)
if self.param('with_white_normalization'):
dataset = FixWhite(name=self.name / 'fix_white',
inputs=dataset,
mean=stat['mean'],
std=stat['std']).as_tensor()
dataset = tf.random_crop(dataset, [shape_as_list(dataset)[0]] +
list(self.param('target_shape')) + [1])
dataset = SuperResolutionDataset(
self.name / 'super_resolution',
lambda: {'image': dataset},
input_key='image',
nb_down_sample=self.param('nb_down_sample'))
keys = [
'image{}x'.format(2**i)
for i in range(dataset.param('nb_down_sample') + 1)
]
result = dict()
if self.param('with_poission_noise'):
result.update({
'noise/' + k:
dataset[k][:shape_as_list(dataset[k])[0] // 2, ...]
for k in keys
})
result.update({
'clean/' + k:
dataset[k][shape_as_list(dataset[k])[0] // 2:, ...]
for k in keys
})
else:
result.update({'clean/' + k: dataset[k] for k in keys})
result.update({'noise/' + k: dataset[k] for k in keys})
return result
def build_denoising_unet(ggg, rgb, p=0.7, is_realnoisy=False):
_, h, w, c = np.shape(ggg)
ggg_tensor = tf.identity(ggg)
rgb_tensor = tf.identity(rgb)
# stain_tensor = tf.identity(stain)
# stain_tensor = tf.transpose(stain_tensor, [0, 3, 1, 2])
is_flip_lr = tf.placeholder(tf.int16)
is_flip_ud = tf.placeholder(tf.int16)
ggg_tensor = data_arg(ggg_tensor, is_flip_lr, is_flip_ud)
rgb_tensor = data_arg(rgb_tensor, is_flip_lr, is_flip_ud)
response = tf.transpose(ggg_tensor, [0, 3, 1, 2])
mask_tensor = tf.ones_like(response)
mask_tensor = tf.nn.dropout(mask_tensor, p) * p
# mask_tensor = tf.multiply(mask_tensor,stain_tensor)
response = tf.multiply(mask_tensor, response)
slice_avg = tf.get_variable('slice_avg',
shape=[_, h, w, c],
initializer=tf.initializers.zeros())
if is_realnoisy:
response = tf.squeeze(tf.random_poisson(25 * response, [1]) / 25, 0)
response = autoencoder(response,
mask_tensor,
channel=c,
width=w,
height=h,
p=p)
response = tf.transpose(response, [0, 2, 3, 1])
mask_tensor = tf.transpose(mask_tensor, [0, 2, 3, 1])
data_loss = mask_loss(response, rgb_tensor, 1. - mask_tensor)
response = data_arg(response, is_flip_lr, is_flip_ud)
avg_op = slice_avg.assign(slice_avg * 0.99 + response * 0.01)
our_image = response
training_error = data_loss
tf.summary.scalar('data loss', data_loss)
merged = tf.summary.merge_all()
saver = tf.train.Saver(max_to_keep=3)
model = {
'training_error': training_error,
'data_loss': data_loss,
'saver': saver,
'summary': merged,
'our_image': our_image,
'is_flip_lr': is_flip_lr,
'is_flip_ud': is_flip_ud,
'avg_op': avg_op,
'slice_avg': slice_avg,
}
return model
def _sample_n(self, n, seed=None):
# Here we use the fact that if:
# lam ~ Gamma(concentration=total_count, rate=(1-probs)/probs)
# then X ~ Poisson(lam) is Negative Binomially distributed.
rate = tf.random_gamma(shape=[n],
alpha=self.total_count,
beta=tf.exp(-self.logits),
dtype=self.dtype,
seed=seed)
return tf.random_poisson(rate,
shape=[],
dtype=self.dtype,
seed=distribution_util.gen_new_seed(
seed, "negative_binom"))
def _sample_n(self, n, seed=None):
# Here we use the fact that if:
# lam ~ Gamma(concentration=total_count, rate=(1-probs)/probs)
# then X ~ Poisson(lam) is Negative Binomially distributed.
stream = seed_stream.SeedStream(seed, salt="NegativeBinomial")
rate = tf.random_gamma(shape=[n],
alpha=self.total_count,
beta=tf.exp(-self.logits),
dtype=self.dtype,
seed=stream())
return tf.random_poisson(rate,
shape=[],
dtype=self.dtype,
seed=stream())
def _sample_n(self, n, seed=None):
# Here we use the fact that if:
# lam ~ Gamma(concentration=total_count, rate=(1-probs)/probs)
# then X ~ Poisson(lam) is Negative Binomially distributed.
rate = tf.random_gamma(
shape=[n],
alpha=self.total_count,
beta=tf.exp(-self.logits),
dtype=self.dtype,
seed=seed)
return tf.random_poisson(
rate,
shape=[],
dtype=self.dtype,
seed=distribution_util.gen_new_seed(seed, "negative_binom"))
def _sample_n(self, n, seed=None):
# Here we use the fact that if:
# lam ~ Gamma(concentration=total_count, rate=(1-probs)/probs)
# then X ~ Poisson(lam) is Negative Binomially distributed.
stream = seed_stream.SeedStream(seed, salt="NegativeBinomial")
rate = tf.random_gamma(
shape=[n],
alpha=self.total_count,
beta=tf.exp(-self.logits),
dtype=self.dtype,
seed=stream())
return tf.random_poisson(
rate,
shape=[],
dtype=self.dtype,
seed=stream())
def analytical_super_resolution_dataset(image_type: str,
poission_noise: bool,
batch_size: int,
nb_down_sample: int,
target_shape: typing.List[int],
idxs: typing.List[int],
*,
name: str = 'dataset',
path_dataset: "str|None" = None):
"""
Args:
- image_type: 'sinogram' or 'image'
- batch_size
Returns:
a `Graph` object, which has several nodes:
Raises:
"""
from ...model.normalizer.normalizer import FixWhite, ReduceSum
from ..super_resolution import SuperResolutionDataset
from ...model.tensor import ShapeEnsurer
from ...config import config
normalizer_configs = {'analytical_phantoms': {'mean': 4.88, 'std': 4.68}}
config_origin = {}
config_normalizer = normalizer_configs[dataset_name]
config['dataset'] = {
'origin': config_origin,
'fix_white': config_normalizer
}
with tf.name_scope('{img_type}_dataset'.format(img_type=image_type)):
if image_type == 'sinogram':
dataset_origin = AnalyticalPhantomSinogramDataset(
name=name, batch_size=batch_size, fields=['sinogram'], idxs)
dataset_summed = ReduceSum('dataset/reduce_sum',
dataset_origin[image_type],
fixed_summation_value=1e6).as_tensor()
dataset = FixWhite(name='dataset/fix_white', inputs=dataset_summed)()
if poission_noise:
with tf.name_scope('add_poission_noise'):
dataset = tf.random_poisson(dataset, shape=[])
dataset = tf.random_crop(dataset,
[batch_size] + list(target_shape) + [1])
dataset = SuperResolutionDataset('dataset/super_resolution',
lambda: {'image': dataset},
input_key='image',
nb_down_sample=3)
return dataset
def _get_sinogram_external(self):
from dxpy.learn.model.normalizer import FixWhite
from ..super_resolution import SuperResolutionDataset
with tf.name_scope('external_dataset'):
dataset = self._make_input_place_holder()
self.register_node('external_place_holder', dataset)
if self.param('with_poission_noise'):
with tf.name_scope('add_with_poission_noise'):
noise = tf.random_poisson(dataset, shape=[])
dataset = tf.concat([noise, dataset], axis=0)
if self.param('with_white_normalization'):
dataset = FixWhite(name=self.name / 'fix_white',
inputs=dataset,
mean=self.param('mean'),
std=self.param('std')).as_tensor()
if self.param('with_random_crop'):
dataset = tf.random_crop(dataset, self._target_shape(dataset))
dataset = SuperResolutionDataset(
self.name / 'super_resolution',
lambda: {'image': dataset},
input_key='image',
nb_down_sample=self.param('nb_down_sample'))
keys = [
'image{}x'.format(2**i)
for i in range(dataset.param('nb_down_sample') + 1)
]
result = dict()
if self.param('with_poission_noise'):
result.update({
'noise/' + k:
dataset[k][:shape_as_list(dataset[k])[0] // 2, ...]
for k in keys
})
result.update({
'clean/' + k:
dataset[k][shape_as_list(dataset[k])[0] // 2:, ...]
for k in keys
})
else:
result.update({'clean/' + k: dataset[k] for k in keys})
result.update({'noise/' + k: dataset[k] for k in keys})
return result
def _sample_n(self, n, seed=None):
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
batch_size = self.batch_shape.num_elements()
if batch_size is None:
batch_size = tf.reduce_prod(self.batch_shape_tensor())
# We need to "sample extra" from the mixture distribution if it doesn't
# already specify a probs vector for each batch coordinate.
# We only support this kind of reduced broadcasting, i.e., there is exactly
# one probs vector for all batch dims or one for each.
stream = seed_stream.SeedStream(
seed, salt="PoissonLogNormalQuadratureCompound")
ids = self._mixture_distribution.sample(
sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(
self.mixture_distribution.is_scalar_batch(),
[batch_size],
np.int32([]))),
seed=stream())
# We need to flatten batch dims in case mixture_distribution has its own
# batch dims.
ids = tf.reshape(
ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(), np.int32([]),
np.int32([-1]))))
# Stride `quadrature_size` for `batch_size` number of times.
offset = tf.range(
start=0,
limit=batch_size * self._quadrature_size,
delta=self._quadrature_size,
dtype=ids.dtype)
ids += offset
rate = tf.gather(tf.reshape(self.distribution.rate, shape=[-1]), ids)
rate = tf.reshape(
rate, shape=concat_vectors([n], self.batch_shape_tensor()))
return tf.random_poisson(lam=rate, shape=[], dtype=self.dtype, seed=seed)
def _sample_n(self, n, seed=None):
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
batch_size = self.batch_shape.num_elements()
if batch_size is None:
batch_size = tf.reduce_prod(self.batch_shape_tensor())
# We need to "sample extra" from the mixture distribution if it doesn't
# already specify a probs vector for each batch coordinate.
# We only support this kind of reduced broadcasting, i.e., there is exactly
# one probs vector for all batch dims or one for each.
stream = seed_stream.SeedStream(
seed, salt="PoissonLogNormalQuadratureCompound")
ids = self._mixture_distribution.sample(sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(
self.mixture_distribution.is_scalar_batch(), [batch_size],
np.int32([]))),
seed=stream())
# We need to flatten batch dims in case mixture_distribution has its own
# batch dims.
ids = tf.reshape(ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(),
np.int32([]),
np.int32([-1]))))
# Stride `quadrature_size` for `batch_size` number of times.
offset = tf.range(start=0,
limit=batch_size * self._quadrature_size,
delta=self._quadrature_size,
dtype=ids.dtype)
ids += offset
rate = tf.gather(tf.reshape(self.distribution.rate, shape=[-1]), ids)
rate = tf.reshape(rate,
shape=concat_vectors([n], self.batch_shape_tensor()))
return tf.random_poisson(lam=rate,
shape=[],
dtype=self.dtype,
seed=seed)
def fixed_row_histogram():
k = tf.placeholder(tf.float32)
shape_s = 20
t = tf.random_uniform([shape_s, 40], maxval=k * 1)
# t = tf.Variable([])
i = 0
hist = tf.constant(0, shape=[0, shape_s], dtype=tf.int32)
cond = lambda i, _: i < shape_s
def loop_body(i, hist):
h = tf.histogram_fixed_width(t[i, :], [0.0, 10.0], nbins=shape_s)
return i + 1, tf.concat([hist, tf.expand_dims(h, 0)], axis=0)
i, hist = tf.while_loop(
cond,
loop_body, [i, hist],
shape_invariants=[tf.TensorShape([]),
tf.TensorShape([None, shape_s])])
tf.summary.histogram("hist", hist)
poisson = tf.random_poisson(shape=[1000], lam=k)
tf.summary.histogram("poisson", poisson)
# sess = tf.InteractiveSession()
# print(hist.eval())
summaries = tf.summary.merge_all()
# Setup a session and summary writer
sess = tf.Session()
writer = tf.summary.FileWriter(LOGDIR)
cols = np.arange(0., 100., 10)
# Setup a loop and write the summaries to disk
N = 20
for step in range(N):
k_val = step / float(N)
summ = sess.run(summaries, feed_dict={k: k_val})
writer.add_summary(summ, global_step=step)
def predict_f(self, mu, sigma, phi_h_decoder, n_sampling):
f_predicted = 0
for i in range(n_sampling):
epsilon_sampling = tf.random_normal(tf.shape(mu), mean=0.0, stddev=1.0, dtype=tf.float32)
z_sampling = tf.multiply(epsilon_sampling, sigma) + mu
with tf.variable_scope("Decoder"):
with tf.variable_scope("Phi_z"):
phi_z_decoder_sampling = tf.layers.dense(z_sampling,
self.n_phi_z_decoder,
name='layer1',
activation=tf.nn.relu,
reuse=True)
with tf.variable_scope("Lambda_f"):
lmbda_sampling = tf.layers.dense(tf.concat([phi_h_decoder, phi_z_decoder_sampling], axis=1),
1,
name='layer1',
activation=tf.nn.softplus,
reuse=True)
with tf.variable_scope("F"):
f_predicted += tf.random_poisson(lmbda_sampling, dtype=tf.float32, shape=[])
f_predicted = f_predicted / n_sampling
return f_predicted
def poisson_gauss_tf(img_batch, a, gauss_var, clip=(0., 1.)):
# Apply poissonian-gaussian noise model following A.Foi et al.
# Foi, A., "Practical denoising of clipped or overexposed noisy images",
# Proc. 16th European Signal Process. Conf., EUSIPCO 2008, Lausanne, Switzerland, August 2008.
batch_shape = tf.shape(img_batch)
a_p = a[:, None, None, None]
out = tf.random_poisson(
shape=[], lam=tf.maximum(img_batch / a_p, 0.0), dtype=tf.float32) * a_p
#out = tf.Print(out, [tf.reduce_max(out), tf.reduce_min(out)])
gauss_var = tf.maximum(gauss_var, 0.0)
gauss_noise = tf.sqrt(gauss_var[:, None, None, None]) * tf.random_normal(
shape=batch_shape, dtype=tf.float32) #Gaussian component
out += gauss_noise
# Clipping
if clip is not None:
out = tf.clip_by_value(out, clip[0], clip[1])
# Return the simulated image
return out
def make_batch_hqjitter(patches, burst_length, batch_size, repeats, height, width,
to_shift, upscale, jitter, smalljitter):
# patches is [burst_length, h_up, w_up, 1]
j_up = jitter * upscale
h_up = height * upscale # + 2 * j_up
w_up = width * upscale # + 2 * j_up
bigj_patches = patches
# print ('bigj_patches: ', bigj_patches.shape)
delta_up = (jitter - smalljitter) * upscale
smallj_patches = patches[:, delta_up:-delta_up, delta_up:-delta_up, ...]
unique = batch_size//repeats
batch = []
for i in range(unique):
for j in range(repeats):
curr = [patches[i, j_up:-j_up, j_up:-j_up, :]]
prob = tf.minimum(tf.cast(tf.random_poisson(
1.5, []), tf.float32)/burst_length, 1.)
for k in range(burst_length - 1):
flip = tf.random_uniform([])
p2use = tf.cond(flip < prob, lambda: bigj_patches,
lambda: smallj_patches)
curr.append(tf.random_crop(p2use[i, ...], [h_up, w_up, 1]))
# new added see comment below
curr = [tf.random_crop(item, [height, width, 1]) for item in curr]
curr = tf.stack(curr, axis=0)
# original implementation
# curr = tf.image.resize_images(
# curr, [height, width], method=tf.image.ResizeMethod.AREA)
# use crop inside instead for raw
curr = tf.transpose(curr, [1, 2, 3, 0])
batch.append(curr)
batch = tf.stack(batch, axis=0)
# print ('batch_inside_make_batch_hqjitter shape: ', batch.shape)
return batch
def run_all(logdir, verbose=False):
"""Generate a bunch of histogram data, and write it to logdir."""
del verbose
tf.set_random_seed(0)
k = tf.placeholder(tf.float32)
# Make a normal distribution, with a shifting mean
mean_moving_normal = tf.random_normal(shape=[1000], mean=(5*k), stddev=1)
# Record that distribution into a histogram summary
histogram_summary.op("normal/moving_mean",
mean_moving_normal,
description="A normal distribution whose mean changes "
"over time.")
# Make a normal distribution with shrinking variance
shrinking_normal = tf.random_normal(shape=[1000], mean=0, stddev=1-(k))
# Record that distribution too
histogram_summary.op("normal/shrinking_variance", shrinking_normal,
description="A normal distribution whose variance "
"shrinks over time.")
# Let's combine both of those distributions into one dataset
normal_combined = tf.concat([mean_moving_normal, shrinking_normal], 0)
# We add another histogram summary to record the combined distribution
histogram_summary.op("normal/bimodal", normal_combined,
description="A combination of two normal distributions, "
"one with a moving mean and one with "
"shrinking variance. The result is a "
"distribution that starts as unimodal and "
"becomes more and more bimodal over time.")
# Add a gamma distribution
gamma = tf.random_gamma(shape=[1000], alpha=k)
histogram_summary.op("gamma", gamma,
description="A gamma distribution whose shape "
"parameter, α, changes over time.")
# And a poisson distribution
poisson = tf.random_poisson(shape=[1000], lam=k)
histogram_summary.op("poisson", poisson,
description="A Poisson distribution, which only "
"takes on integer values.")
# And a uniform distribution
uniform = tf.random_uniform(shape=[1000], maxval=k*10)
histogram_summary.op("uniform", uniform,
description="A simple uniform distribution.")
# Finally, combine everything together!
all_distributions = [mean_moving_normal, shrinking_normal,
gamma, poisson, uniform]
all_combined = tf.concat(all_distributions, 0)
histogram_summary.op("all_combined", all_combined,
description="An amalgamation of five distributions: a "
"uniform distribution, a gamma "
"distribution, a Poisson distribution, and "
"two normal distributions.")
summaries = tf.summary.merge_all()
# Setup a session and summary writer
sess = tf.Session()
writer = tf.summary.FileWriter(logdir)
# Setup a loop and write the summaries to disk
N = 400
for step in xrange(N):
k_val = step/float(N)
summ = sess.run(summaries, feed_dict={k: k_val})
writer.add_summary(summ, global_step=step)
def _process_sinogram(self, dataset):
from ...model.normalizer.normalizer import ReduceSum, FixWhite
from dxpy.learn.model.normalizer import FixWhite
from ..super_resolution import SuperResolutionDataset
from ...utils.tensor import shape_as_list
if self.param('log_scale'):
stat = dataset.LOG_SINO_STAT
else:
stat = dataset.SINO_STAT
# dataset = ReduceSum(self.name / 'reduce_sum', dataset['sinogram'],
# fixed_summation_value=1e6).as_tensor()
if 'phantom' in dataset:
phan = dataset['phantom']
else:
phan = None
dataset = dataset['sinogram']
if self.param('with_poission_noise'):
with tf.name_scope('add_with_poission_noise'):
noise = tf.random_poisson(dataset, shape=[])
dataset = tf.concat([noise, dataset], axis=0)
if self.param('log_scale'):
dataset = tf.log(dataset + 0.4)
if self.param('with_white_normalization'):
dataset = FixWhite(name=self.name / 'fix_white',
inputs=dataset,
mean=stat['mean'],
std=stat['std']).as_tensor()
# random phase shift
# if self.param('with_phase_shift'):
# phase_view = tf.random_uniform(
# [], 0, shape_as_list(dataset)[1], dtype=tf.int64)
# dataset_l = dataset[:, phase_view:, :, :]
# dataset_r = dataset[:, :phase_view, :, :]
# dataset = tf.concat([dataset_l, dataset_r], axis=1)
dataset = tf.random_crop(dataset, [shape_as_list(dataset)[0]] +
list(self.param('target_shape')) + [1])
dataset = SuperResolutionDataset(
self.name / 'super_resolution',
lambda: {'image': dataset},
input_key='image',
nb_down_sample=self.param('nb_down_sample'))
keys = [
'image{}x'.format(2**i)
for i in range(dataset.param('nb_down_sample') + 1)
]
if self.param('with_poission_noise'):
result = {
'input/' + k: dataset[k][:shape_as_list(dataset[k])[0] // 2,
...]
for k in keys
}
result.update({
'label/' + k: dataset[k][shape_as_list(dataset[k])[0] // 2:,
...]
for k in keys
})
else:
result = {'input/' + k: dataset[k] for k in keys}
result.update({'label/' + k: dataset[k] for k in keys})
result.update({
'noise/' + k: dataset[k][:shape_as_list(dataset[k])[0] // 2, ...]
for k in keys
})
result.update({
'clean/' + k: dataset[k][shape_as_list(dataset[k])[0] // 2:, ...]
for k in keys
})
if phan is not None:
result.update({'phantom': phan})
return result
def _sample_n(self, n, seed=None): return tf.random_poisson(self.rate, [n], dtype=self.dtype, seed=seed)
# YOUR CODE ############################################################################### # 1e: Create a diagnoal 2-d tensor of size 6 x 6 with the diagonal values of 1, # 2, ..., 6 # Hint: Use tf.range() and tf.diag(). ############################################################################### x = tf.diag(tf.range(start=1, limit=6)) # YOUR CODE ############################################################################### # 1f: Create a random 2-d tensor of size 10 x 10 from any distribution. # Calculate its determinant. # Hint: Look at tf.matrix_determinant(). ############################################################################### x = tf.random_poisson([10, 10]) # YOUR CODE ############################################################################### # 1g: Create tensor x with value [5, 2, 3, 5, 10, 6, 2, 3, 4, 2, 1, 1, 0, 9]. # Return the unique elements in x # Hint: use tf.unique(). Keep in mind that tf.unique() returns a tuple. ############################################################################### x = tf.constant([5, 2, 3, 5, 10, 6, 2, 3, 4, 2, 1, 1, 0, 9]) out, indexes = tf.unique(x) # YOUR CODE ############################################################################### # 1h: Create two tensors x and y of shape 300 from any normal distribution, # as long as they are from the same distribution.
def __init__(self, is_training=True):
self.graph = tf.Graph()
with self.graph.as_default():
if is_training:
self.x, self.y, self.xloc, self.yloc, self.m, self.num_batch = get_batch_data(
) # (N, T)
else: # inference
self.x = tf.placeholder(tf.int32, shape=(None, hp.x_maxlen))
self.y = tf.placeholder(tf.int32, shape=(None, hp.y_maxlen))
self.xloc = tf.placeholder(tf.int32, shape=(None, hp.x_maxlen))
self.yloc = tf.placeholder(tf.int32, shape=(None, hp.y_maxlen))
self.m = tf.placeholder(tf.int32, shape=(None, hp.x_maxlen))
# define decoder inputs
self.decoder_inputs = tf.concat(
(tf.ones_like(self.y[:, :1]) * 2, self.y[:, :-1]), -1) # 2:<S>
# Load vocabulary
src2idx, idx2src = load_src_vocab()
des2idx, idx2des = load_des_vocab()
self.hidden_units = hp.hidden_units
# Encoder
with tf.variable_scope("encoder"):
## Embedding
self.enc = embedding(self.x,
vocab_size=len(src2idx),
num_units=self.hidden_units,
scale=True,
scope="enc_embed")
clue_level = tf.random_poisson(shape=[1],
lam=1,
dtype=tf.int32)
#clue_level = tf.Print(clue_level, [clue_level])
#self.enc_mask = tf.expand_dims(tf.cast(tf.equal(self.m, 1), tf.float32), 2)
self.enc_mask = tf.expand_dims(
tf.cast(
tf.logical_and(tf.greater_equal(self.m, 1),
tf.less_equal(self.m, clue_level)),
tf.float32), 2)
self.enc = tf.concat([self.enc, self.enc_mask], axis=2)
self.hidden_units += 1
## Positional Encoding
if hp.sinusoid:
self.enc += positional_encoding(
self.x,
num_units=self.hidden_units,
zero_pad=False,
scale=False,
scope="enc_pe")
else:
self.enc += embedding(tf.tile(
tf.expand_dims(tf.range(tf.shape(self.x)[1]), 0),
[tf.shape(self.x)[0], 1]),
vocab_size=hp.x_maxlen,
num_units=self.hidden_units,
zero_pad=False,
scale=False,
scope="enc_pe")
tf.add_to_collection('explain_input', self.enc)
## Dropout
self.enc = tf.layers.dropout(
self.enc,
rate=hp.dropout_rate,
training=tf.convert_to_tensor(is_training))
## Blocks
for i in range(hp.num_blocks):
with tf.variable_scope("num_blocks_{}".format(i)):
### Multihead Attention
self.enc = multihead_attention(
queries=self.enc,
keys=self.enc,
num_units=self.hidden_units,
num_heads=hp.num_heads,
dropout_rate=hp.dropout_rate,
is_training=is_training,
causality=False)
### Feed Forward
self.enc = feedforward(self.enc,
num_units=[
4 * self.hidden_units,
self.hidden_units
])
# Decoder
with tf.variable_scope("decoder"):
## Embedding
self.dec = embedding(self.decoder_inputs,
vocab_size=len(des2idx),
num_units=self.hidden_units,
scale=True,
scope="dec_embed")
## Positional Encoding
if hp.sinusoid:
self.dec += positional_encoding(
self.decoder_inputs,
vocab_size=hp.y_maxlen,
num_units=self.hidden_units,
zero_pad=False,
scale=False,
scope="dec_pe")
else:
self.dec += embedding(tf.tile(
tf.expand_dims(
tf.range(tf.shape(self.decoder_inputs)[1]), 0),
[tf.shape(self.decoder_inputs)[0], 1]),
vocab_size=hp.y_maxlen,
num_units=self.hidden_units,
zero_pad=False,
scale=False,
scope="dec_pe")
tf.add_to_collection('explain_input', self.dec)
## Dropout
self.dec = tf.layers.dropout(
self.dec,
rate=hp.dropout_rate,
training=tf.convert_to_tensor(is_training))
## Blocks
for i in range(hp.num_blocks):
with tf.variable_scope("num_blocks_{}".format(i)):
## Multihead Attention ( self-attention)
self.dec = multihead_attention(
queries=self.dec,
keys=self.dec,
num_units=self.hidden_units,
num_heads=hp.num_heads,
dropout_rate=hp.dropout_rate,
is_training=is_training,
causality=True,
scope="self_attention")
## Multihead Attention ( vanilla attention)
self.dec = multihead_attention(
queries=self.dec,
keys=self.enc,
num_units=self.hidden_units,
num_heads=hp.num_heads,
dropout_rate=hp.dropout_rate,
is_training=is_training,
causality=False,
scope="vanilla_attention")
## Feed Forward
with tf.variable_scope(
"num_blocks_fc_dec_{}".format(i)):
self.dec = feedforward(self.dec,
num_units=[
4 * self.hidden_units,
self.hidden_units
])
self.loc_enc = self.enc
self.loc_logits = attention_matrix(queries=self.loc_enc,
keys=self.dec,
num_units=self.hidden_units,
dropout_rate=hp.dropout_rate,
is_training=is_training,
causality=False,
scope="copy_matrix")
xloc_vec = tf.one_hot(self.xloc,
depth=hp.y_maxlen,
dtype=tf.float32)
yloc_vec = tf.one_hot(self.yloc,
depth=hp.y_maxlen,
dtype=tf.float32)
loc_label = tf.matmul(yloc_vec, tf.transpose(xloc_vec, [0, 2, 1]))
self.loc_label_history = tf.cumsum(loc_label,
axis=1,
exclusive=True)
# Final linear projection
self.loc_logits = tf.transpose(self.loc_logits, [0, 2, 1])
self.loc_logits = tf.stack(
[self.loc_logits, self.loc_label_history], axis=3)
self.loc_logits = tf.squeeze(tf.layers.dense(self.loc_logits, 1),
axis=[3])
x_masks = tf.tile(tf.expand_dims(tf.equal(self.x, 0), 1),
[1, hp.y_maxlen, 1])
#y_masks = tf.tile(tf.expand_dims(tf.equal(self.y, 0), -1), [1, 1, hp.x_maxlen])
paddings = tf.ones_like(self.loc_logits) * (-1e6)
self.loc_logits = tf.where(x_masks, paddings,
self.loc_logits) # (N, T_q, T_k)
#self.loc_logits = tf.where(y_masks, paddings, self.loc_logits) # (N, T_q, T_k)
self.logits = tf.layers.dense(self.dec, len(des2idx))
self.final_logits = tf.concat([self.logits, self.loc_logits],
axis=2)
tf.add_to_collection('explain_output', self.final_logits)
#self.final_logits = tf.Print(self.final_logits, [self.final_logits[0][0][-3:]], message="final_logits_last")
#self.final_logits = tf.Print(self.final_logits, [self.final_logits[0][0][:3]], message="final_logits_first")
self.preds = tf.to_int32(tf.argmax(self.final_logits, axis=-1))
self.istarget = tf.to_float(tf.not_equal(self.y, 0))
if is_training:
label = tf.one_hot(self.y,
depth=len(des2idx),
dtype=tf.float32)
# A special case, when copy is open, we should not need unk label
unk_pos = label[:, :, 1]
copy_pos = tf.sign(tf.reduce_sum(loc_label, axis=2))
fix_pos = unk_pos * copy_pos
#fix_pos = tf.Print(fix_pos, [tf.reduce_sum(unk_pos, axis=-1), tf.shape(unk_pos)], message="\nunk_pos", summarize=16)
#fix_pos = tf.Print(fix_pos, [tf.reduce_sum(fix_pos, axis=-1), tf.shape(fix_pos)], message="\nfix_pos", summarize=16)
fix_label = tf.expand_dims(label[:, :, 1] - fix_pos, axis=2)
label = tf.concat(
[label[:, :, :1], fix_label, label[:, :, 2:]], axis=-1)
self.final_label = tf.concat([label, loc_label], axis=2)
#self.final_label = tf.Print(self.final_label, [self.final_label[0][0][-3:]], message="final_label")
# Loss
self.min_logit_loc = min_logit_loc = tf.argmax(
self.final_logits + (-1e6) * (1.0 - self.final_label),
axis=-1)
#min_logit_loc = tf.Print(min_logit_loc, [min_logit_loc[0]], message="min_logit_loc")
self.min_label = tf.one_hot(min_logit_loc,
depth=len(des2idx) + hp.x_maxlen,
dtype=tf.float32)
vocab_count = len(des2idx) + hp.x_maxlen - tf.reduce_sum(
tf.cast(tf.equal(self.x, 0), dtype=tf.int32), axis=-1)
#vocab_count = tf.Print(vocab_count, [vocab_count[0]], message="vocab_count")
self.y_smoothed = label_smoothing_mask(self.min_label,
vocab_count)
#self.final_logits = tf.Print(self.final_logits, [self.final_logits[0][1][min_logit_loc[0][1]]], message="final_logits")
#self.y_smoothed = tf.Print(self.y_smoothed, [self.y_smoothed[0][1][min_logit_loc[0][1]]], message="y_smoothed")
self.loss = tf.nn.softmax_cross_entropy_with_logits_v2(
logits=self.final_logits, labels=self.y_smoothed)
#self.loss = tf.Print(self.loss, [self.final_label[0][1][min_logit_loc[0][1]]], message="final_label")
#self.loss = tf.Print(self.loss, [self.loss[0][-3:]], message="loss_last")
#self.loss = tf.Print(self.loss, [self.loss[0][:3]], message="loss_first")
self.mean_loss = tf.reduce_sum(
self.loss * self.istarget) / (tf.reduce_sum(self.istarget))
# Training Scheme
self.global_step = tf.Variable(0,
name='global_step',
trainable=False)
self.optimizer = tf.train.AdamOptimizer(learning_rate=hp.lr,
beta1=0.9,
beta2=0.98,
epsilon=1e-8)
self.train_op = self.optimizer.minimize(
self.mean_loss, global_step=self.global_step)
# Summary
tf.summary.scalar('mean_loss', self.mean_loss)
self.merged = tf.summary.merge_all()
mean_moving_normal = tf.random_normal(shape=[1000], mean=(5 * k), stddev=1)
tf.summary.histogram('normal/moving_mean', mean_moving_normal)
variance_shrinking_normal = tf.random_normal(shape=[1000],
mean=0,
stddev=1 - k)
tf.summary.histogram('normal/shrinking_variance', variance_shrinking_normal)
normal_combined = tf.concat([mean_moving_normal, variance_shrinking_normal], 0)
tf.summary.histogram('normal/bimodal', normal_combined)
gamma = tf.random_gamma(shape=[1000], alpha=k)
tf.summary.histogram('gamma', gamma)
poisson = tf.random_poisson(shape=[1000], lam=k)
tf.summary.histogram('poisson', poisson)
uniform = tf.random_uniform(shape=[1000], maxval=k * 10)
tf.summary.histogram('uniform', uniform)
all_distributions = [
mean_moving_normal, variance_shrinking_normal, normal_combined, gamma,
poisson, uniform
]
all_combined = tf.concat(all_distributions, 0)
tf.summary.histogram('all_combined', all_combined)
sess = tf.Session()
if tf.gfile.Exists('/tmp/histogram_example'):
def add_train_noise_tf(self, x):
chi_rng = tf.random_uniform(shape=[1, 1, 1],
minval=0.001,
maxval=self.lam_max)
return tf.random_poisson(chi_rng * (x + 0.5), shape=[]) / chi_rng - 0.5
from typing import Dict, Any, Union
import matplotlib.pyplot as plt
import tensorflow as tf
a = tf.add(2, 5)
b = tf.multiply(a, 3)
sess = tf.Session()
replace_dict: Dict[Union[object, Any], int] = {a: 15}
print(sess.run(b, feed_dict=replace_dict))
plt.subplot(211)
num_list = tf.random_normal([2, 20])
out = sess.run(num_list)
x, y = out
plt.scatter(x, y)
#plt.show()
num_list_1 = tf.random_poisson([6, 20], [2, 20])
out1 = sess.run(num_list_1)
x1, y1 = out1
plt.subplot(212)
plt.scatter(x1, y1, c='red', label='red', alpha=0.35, edgecolors='black')
plt.show()