text_prompt
stringlengths 100
17.7k
⌀ | code_prompt
stringlengths 7
9.86k
⌀ |
|---|---|
<SYSTEM_TASK:>
Evaluate all spherical harmonics of degree at most `n` at angles `polar`,
<END_TASK>
<USER_TASK:>
Description:
def tree_sph(polar, azimuthal, n, standardization, symbolic=False):
"""Evaluate all spherical harmonics of degree at most `n` at angles `polar`,
`azimuthal`.
""" |
cos = numpy.vectorize(sympy.cos) if symbolic else numpy.cos
# Conventions from
# <https://en.wikipedia.org/wiki/Spherical_harmonics#Orthogonality_and_normalization>.
config = {
"acoustic": ("complex spherical", False),
"quantum mechanic": ("complex spherical", True),
"geodetic": ("complex spherical 1", False),
"schmidt": ("schmidt", False),
}
standard, cs_phase = config[standardization]
return tree_alp(
cos(polar),
n,
phi=azimuthal,
standardization=standard,
with_condon_shortley_phase=cs_phase,
symbolic=symbolic,
) |
<SYSTEM_TASK:>
Check if this file exist and if it's a directory
<END_TASK>
<USER_TASK:>
Description:
def check_if_this_file_exist(filename):
"""Check if this file exist and if it's a directory
This function will check if the given filename
actually exists and if it's not a Directory
Arguments:
filename {string} -- filename
Return:
True : if it's not a directory and if this file exist
False : If it's not a file and if it's a directory
""" |
#get the absolute path
filename = os.path.abspath(filename)
#Boolean
this_file_exist = os.path.exists(filename)
a_directory = os.path.isdir(filename)
result = this_file_exist and not a_directory
if result == False:
raise ValueError('The filename given was either non existent or was a directory')
else:
return result |
<SYSTEM_TASK:>
Handle the command line call
<END_TASK>
<USER_TASK:>
Description:
def command_line(cmd):
"""Handle the command line call
keyword arguments:
cmd = a list
return
0 if error
or a string for the command line output
""" |
try:
s = subprocess.Popen(cmd, stdout=subprocess.PIPE)
s = s.stdout.read()
return s.strip()
except subprocess.CalledProcessError:
return 0 |
<SYSTEM_TASK:>
Return a csv representation of the exif
<END_TASK>
<USER_TASK:>
Description:
def get_csv(filename):
""" Return a csv representation of the exif
get a filename and returns a unicode string with a CSV format
Arguments:
filename {string} -- your filename
Returns:
[unicode] -- unicode string
""" |
check_if_this_file_exist(filename)
#Process this function
filename = os.path.abspath(filename)
s = command_line(['exiftool', '-G', '-csv', '-sort', filename])
if s:
#convert bytes to string
s = s.decode('utf-8')
return s
else:
return 0 |
<SYSTEM_TASK:>
Render email with provided context
<END_TASK>
<USER_TASK:>
Description:
def render(self, context=None, clean=False):
"""
Render email with provided context
Arguments
---------
context : dict
|context| If not specified then the
:attr:`~mail_templated.EmailMessage.context` property is
used.
Keyword Arguments
-----------------
clean : bool
If ``True``, remove any template specific properties from the
message object. Default is ``False``.
""" |
# Load template if it is not loaded yet.
if not self.template:
self.load_template(self.template_name)
# The signature of the `render()` method was changed in Django 1.7.
# https://docs.djangoproject.com/en/1.8/ref/templates/upgrading/#get-template-and-select-template
if hasattr(self.template, 'template'):
context = (context or self.context).copy()
else:
context = Context(context or self.context)
# Add tag strings to the context.
context.update(self.extra_context)
result = self.template.render(context)
# Don't overwrite default value with empty one.
subject = self._get_block(result, 'subject')
if subject:
self.subject = self._get_block(result, 'subject')
body = self._get_block(result, 'body')
is_html_body = False
# The html block is optional, and it also may be set manually.
html = self._get_block(result, 'html')
if html:
if not body:
# This is an html message without plain text part.
body = html
is_html_body = True
else:
# Add alternative content.
self.attach_alternative(html, 'text/html')
# Don't overwrite default value with empty one.
if body:
self.body = body
if is_html_body:
self.content_subtype = 'html'
self._is_rendered = True
if clean:
self.clean() |
<SYSTEM_TASK:>
Send email message, render if it is not rendered yet.
<END_TASK>
<USER_TASK:>
Description:
def send(self, *args, **kwargs):
"""
Send email message, render if it is not rendered yet.
Note
----
Any extra arguments are passed to
:class:`EmailMultiAlternatives.send() <django.core.mail.EmailMessage>`.
Keyword Arguments
-----------------
clean : bool
If ``True``, remove any template specific properties from the
message object. Default is ``False``.
""" |
clean = kwargs.pop('clean', False)
if not self._is_rendered:
self.render()
if clean:
self.clean()
return super(EmailMessage, self).send(*args, **kwargs) |
<SYSTEM_TASK:>
Easy wrapper for sending a single email message to a recipient list using
<END_TASK>
<USER_TASK:>
Description:
def send_mail(template_name, context, from_email, recipient_list,
fail_silently=False, auth_user=None, auth_password=None,
connection=None, **kwargs):
"""
Easy wrapper for sending a single email message to a recipient list using
django template system.
It works almost the same way as the standard
:func:`send_mail()<django.core.mail.send_mail>` function.
.. |main_difference| replace:: The main
difference is that two first arguments ``subject`` and ``body`` are
replaced with ``template_name`` and ``context``. However you still can
pass subject or body as keyword arguments to provide static content if
needed.
|main_difference|
The ``template_name``, ``context``, ``from_email`` and ``recipient_list``
parameters are required.
Note
----
|args_note|
Arguments
---------
template_name : str
|template_name|
context : dict
|context|
from_email : str
|from_email|
recipient_list : list
|recipient_list|
Keyword Arguments
-----------------
fail_silently : bool
If it's False, send_mail will raise an :exc:`smtplib.SMTPException`.
See the :mod:`smtplib` docs for a list of possible exceptions, all of
which are subclasses of :exc:`smtplib.SMTPException`.
auth_user | str
The optional username to use to authenticate to the SMTP server. If
this isn't provided, Django will use the value of the
:django:setting:`EMAIL_HOST_USER` setting.
auth_password | str
The optional password to use to authenticate to the SMTP server. If
this isn't provided, Django will use the value of the
:django:setting:`EMAIL_HOST_PASSWORD` setting.
connection : EmailBackend
The optional email backend to use to send the mail. If unspecified,
an instance of the default backend will be used. See the documentation
on :ref:`Email backends<django:topic-email-backends>` for more details.
subject : str
|subject|
body : str
|body|
render : bool
|render|
Returns
-------
int
The number of successfully delivered messages (which can be 0 or 1
since it can only send one message).
See Also
--------
:func:`django.core.mail.send_mail`
Documentation for the standard ``send_mail()`` function.
""" |
connection = connection or mail.get_connection(username=auth_user,
password=auth_password,
fail_silently=fail_silently)
clean = kwargs.pop('clean', True)
return EmailMessage(
template_name, context, from_email, recipient_list,
connection=connection, **kwargs).send(clean=clean) |
<SYSTEM_TASK:>
Compute the mean Silhouette Coefficient of all samples.
<END_TASK>
<USER_TASK:>
Description:
def silhouette_score(X, labels, metric='euclidean', sample_size=None,
random_state=None, **kwds):
"""Compute the mean Silhouette Coefficient of all samples.
The Silhouette Coefficient is calculated using the mean intra-cluster
distance (``a``) and the mean nearest-cluster distance (``b``) for each
sample. The Silhouette Coefficient for a sample is ``(b - a) / max(a,
b)``. To clarify, ``b`` is the distance between a sample and the nearest
cluster that the sample is not a part of.
Note that Silhouette Coefficient is only defined if number of labels
is 2 <= n_labels <= n_samples - 1.
This function returns the mean Silhouette Coefficient over all samples.
To obtain the values for each sample, use :func:`silhouette_samples`.
The best value is 1 and the worst value is -1. Values near 0 indicate
overlapping clusters. Negative values generally indicate that a sample has
been assigned to the wrong cluster, as a different cluster is more similar.
Read more in the :ref:`User Guide <silhouette_coefficient>`.
Parameters
----------
X : array [n_samples_a, n_samples_a] if metric == "precomputed", or, \
[n_samples_a, n_features] otherwise
Array of pairwise distances between samples, or a feature array.
labels : array, shape = [n_samples]
Predicted labels for each sample.
metric : string, or callable
The metric to use when calculating distance between instances in a
feature array. If metric is a string, it must be one of the options
allowed by :func:`metrics.pairwise.pairwise_distances
<sklearn.metrics.pairwise.pairwise_distances>`. If X is the distance
array itself, use ``metric="precomputed"``.
sample_size : int or None
The size of the sample to use when computing the Silhouette Coefficient
on a random subset of the data.
If ``sample_size is None``, no sampling is used.
random_state : int, RandomState instance or None, optional (default=None)
The generator used to randomly select a subset of samples. If int,
random_state is the seed used by the random number generator; If
RandomState instance, random_state is the random number generator; If
None, the random number generator is the RandomState instance used by
`np.random`. Used when ``sample_size is not None``.
**kwds : optional keyword parameters
Any further parameters are passed directly to the distance function.
If using a scipy.spatial.distance metric, the parameters are still
metric dependent. See the scipy docs for usage examples.
Returns
-------
silhouette : float
Mean Silhouette Coefficient for all samples.
References
----------
.. [1] `Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
Interpretation and Validation of Cluster Analysis". Computational
and Applied Mathematics 20: 53-65.
<http://www.sciencedirect.com/science/article/pii/0377042787901257>`_
.. [2] `Wikipedia entry on the Silhouette Coefficient
<https://en.wikipedia.org/wiki/Silhouette_(clustering)>`_
""" |
if sample_size is not None:
X, labels = check_X_y(X, labels, accept_sparse=['csc', 'csr'])
random_state = check_random_state(random_state)
indices = random_state.permutation(X.shape[0])[:sample_size]
if metric == "precomputed":
X, labels = X[indices].T[indices].T, labels[indices]
else:
X, labels = X[indices], labels[indices]
return np.mean(silhouette_samples(X, labels, metric=metric, **kwds)) |
<SYSTEM_TASK:>
Compute the Silhouette Coefficient for each sample.
<END_TASK>
<USER_TASK:>
Description:
def silhouette_samples(X, labels, metric='euclidean', **kwds):
"""Compute the Silhouette Coefficient for each sample.
The Silhouette Coefficient is a measure of how well samples are clustered
with samples that are similar to themselves. Clustering models with a high
Silhouette Coefficient are said to be dense, where samples in the same
cluster are similar to each other, and well separated, where samples in
different clusters are not very similar to each other.
The Silhouette Coefficient is calculated using the mean intra-cluster
distance (``a``) and the mean nearest-cluster distance (``b``) for each
sample. The Silhouette Coefficient for a sample is ``(b - a) / max(a,
b)``.
Note that Silhouette Coefficient is only defined if number of labels
is 2 <= n_labels <= n_samples - 1.
This function returns the Silhouette Coefficient for each sample.
The best value is 1 and the worst value is -1. Values near 0 indicate
overlapping clusters.
Read more in the :ref:`User Guide <silhouette_coefficient>`.
Parameters
----------
X : array [n_samples_a, n_samples_a] if metric == "precomputed", or, \
[n_samples_a, n_features] otherwise
Array of pairwise distances between samples, or a feature array.
labels : array, shape = [n_samples]
label values for each sample
metric : string, or callable
The metric to use when calculating distance between instances in a
feature array. If metric is a string, it must be one of the options
allowed by :func:`sklearn.metrics.pairwise.pairwise_distances`. If X is
the distance array itself, use "precomputed" as the metric.
**kwds : optional keyword parameters
Any further parameters are passed directly to the distance function.
If using a ``scipy.spatial.distance`` metric, the parameters are still
metric dependent. See the scipy docs for usage examples.
Returns
-------
silhouette : array, shape = [n_samples]
Silhouette Coefficient for each samples.
References
----------
.. [1] `Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
Interpretation and Validation of Cluster Analysis". Computational
and Applied Mathematics 20: 53-65.
<http://www.sciencedirect.com/science/article/pii/0377042787901257>`_
.. [2] `Wikipedia entry on the Silhouette Coefficient
<https://en.wikipedia.org/wiki/Silhouette_(clustering)>`_
""" |
X, labels = check_X_y(X, labels, accept_sparse=['csc', 'csr'])
le = LabelEncoder()
labels = le.fit_transform(labels)
check_number_of_labels(len(le.classes_), X.shape[0])
distances = pairwise_distances(X, metric=metric, **kwds)
unique_labels = le.classes_
n_samples_per_label = np.bincount(labels, minlength=len(unique_labels))
# For sample i, store the mean distance of the cluster to which
# it belongs in intra_clust_dists[i]
intra_clust_dists = np.zeros(distances.shape[0], dtype=distances.dtype)
# For sample i, store the mean distance of the second closest
# cluster in inter_clust_dists[i]
inter_clust_dists = np.inf + intra_clust_dists
for curr_label in range(len(unique_labels)):
# Find inter_clust_dist for all samples belonging to the same
# label.
mask = labels == curr_label
current_distances = distances[mask]
# Leave out current sample.
n_samples_curr_lab = n_samples_per_label[curr_label] - 1
if n_samples_curr_lab != 0:
intra_clust_dists[mask] = np.sum(
current_distances[:, mask], axis=1) / n_samples_curr_lab
# Now iterate over all other labels, finding the mean
# cluster distance that is closest to every sample.
for other_label in range(len(unique_labels)):
if other_label != curr_label:
other_mask = labels == other_label
other_distances = np.mean(
current_distances[:, other_mask], axis=1)
inter_clust_dists[mask] = np.minimum(
inter_clust_dists[mask], other_distances)
sil_samples = inter_clust_dists - intra_clust_dists
sil_samples /= np.maximum(intra_clust_dists, inter_clust_dists)
# score 0 for clusters of size 1, according to the paper
sil_samples[n_samples_per_label.take(labels) == 1] = 0
return sil_samples |
<SYSTEM_TASK:>
Compute the Calinski and Harabaz score.
<END_TASK>
<USER_TASK:>
Description:
def calinski_harabaz_score(X, labels):
"""Compute the Calinski and Harabaz score.
The score is defined as ratio between the within-cluster dispersion and
the between-cluster dispersion.
Read more in the :ref:`User Guide <calinski_harabaz_index>`.
Parameters
----------
X : array-like, shape (``n_samples``, ``n_features``)
List of ``n_features``-dimensional data points. Each row corresponds
to a single data point.
labels : array-like, shape (``n_samples``,)
Predicted labels for each sample.
Returns
-------
score : float
The resulting Calinski-Harabaz score.
References
----------
.. [1] `T. Calinski and J. Harabasz, 1974. "A dendrite method for cluster
analysis". Communications in Statistics
<http://www.tandfonline.com/doi/abs/10.1080/03610927408827101>`_
""" |
X, labels = check_X_y(X, labels)
le = LabelEncoder()
labels = le.fit_transform(labels)
n_samples, _ = X.shape
n_labels = len(le.classes_)
check_number_of_labels(n_labels, n_samples)
extra_disp, intra_disp = 0., 0.
mean = np.mean(X, axis=0)
for k in range(n_labels):
cluster_k = X[labels == k]
mean_k = np.mean(cluster_k, axis=0)
extra_disp += len(cluster_k) * np.sum((mean_k - mean) ** 2)
intra_disp += np.sum((cluster_k - mean_k) ** 2)
return (1. if intra_disp == 0. else
extra_disp * (n_samples - n_labels) /
(intra_disp * (n_labels - 1.))) |
<SYSTEM_TASK:>
Compute joint probabilities p_ij from distances.
<END_TASK>
<USER_TASK:>
Description:
def _joint_probabilities(distances, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances.
Parameters
----------
distances : array, shape (n_samples * (n_samples-1) / 2,)
Distances of samples are stored as condensed matrices, i.e.
we omit the diagonal and duplicate entries and store everything
in a one-dimensional array.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : array, shape (n_samples * (n_samples-1) / 2,)
Condensed joint probability matrix.
""" |
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances = distances.astype(np.float32, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances, None, desired_perplexity, verbose)
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON)
return P |
<SYSTEM_TASK:>
Compute joint probabilities p_ij from distances using just nearest
<END_TASK>
<USER_TASK:>
Description:
def _joint_probabilities_nn(distances, neighbors, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances using just nearest
neighbors.
This method is approximately equal to _joint_probabilities. The latter
is O(N), but limiting the joint probability to nearest neighbors improves
this substantially to O(uN).
Parameters
----------
distances : array, shape (n_samples, k)
Distances of samples to its k nearest neighbors.
neighbors : array, shape (n_samples, k)
Indices of the k nearest-neighbors for each samples.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : csr sparse matrix, shape (n_samples, n_samples)
Condensed joint probability matrix with only nearest neighbors.
""" |
t0 = time()
# Compute conditional probabilities such that they approximately match
# the desired perplexity
n_samples, k = neighbors.shape
distances = distances.astype(np.float32, copy=False)
neighbors = neighbors.astype(np.int64, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances, neighbors, desired_perplexity, verbose)
assert np.all(np.isfinite(conditional_P)), \
"All probabilities should be finite"
# Symmetrize the joint probability distribution using sparse operations
P = csr_matrix((conditional_P.ravel(), neighbors.ravel(),
range(0, n_samples * k + 1, k)),
shape=(n_samples, n_samples))
P = P + P.T
# Normalize the joint probability distribution
sum_P = np.maximum(P.sum(), MACHINE_EPSILON)
P /= sum_P
assert np.all(np.abs(P.data) <= 1.0)
if verbose >= 2:
duration = time() - t0
print("[t-SNE] Computed conditional probabilities in {:.3f}s"
.format(duration))
return P |
<SYSTEM_TASK:>
Batch gradient descent with momentum and individual gains.
<END_TASK>
<USER_TASK:>
Description:
def _gradient_descent(objective, p0, it, n_iter,
n_iter_check=1, n_iter_without_progress=300,
momentum=0.8, learning_rate=200.0, min_gain=0.01,
min_grad_norm=1e-7, verbose=0, args=None, kwargs=None):
"""Batch gradient descent with momentum and individual gains.
Parameters
----------
objective : function or callable
Should return a tuple of cost and gradient for a given parameter
vector. When expensive to compute, the cost can optionally
be None and can be computed every n_iter_check steps using
the objective_error function.
p0 : array-like, shape (n_params,)
Initial parameter vector.
it : int
Current number of iterations (this function will be called more than
once during the optimization).
n_iter : int
Maximum number of gradient descent iterations.
n_iter_check : int
Number of iterations before evaluating the global error. If the error
is sufficiently low, we abort the optimization.
n_iter_without_progress : int, optional (default: 300)
Maximum number of iterations without progress before we abort the
optimization.
momentum : float, within (0.0, 1.0), optional (default: 0.8)
The momentum generates a weight for previous gradients that decays
exponentially.
learning_rate : float, optional (default: 200.0)
The learning rate for t-SNE is usually in the range [10.0, 1000.0]. If
the learning rate is too high, the data may look like a 'ball' with any
point approximately equidistant from its nearest neighbours. If the
learning rate is too low, most points may look compressed in a dense
cloud with few outliers.
min_gain : float, optional (default: 0.01)
Minimum individual gain for each parameter.
min_grad_norm : float, optional (default: 1e-7)
If the gradient norm is below this threshold, the optimization will
be aborted.
verbose : int, optional (default: 0)
Verbosity level.
args : sequence
Arguments to pass to objective function.
kwargs : dict
Keyword arguments to pass to objective function.
Returns
-------
p : array, shape (n_params,)
Optimum parameters.
error : float
Optimum.
i : int
Last iteration.
""" |
if args is None:
args = []
if kwargs is None:
kwargs = {}
p = p0.copy().ravel()
update = np.zeros_like(p)
gains = np.ones_like(p)
error = np.finfo(np.float).max
best_error = np.finfo(np.float).max
best_iter = i = it
tic = time()
for i in range(it, n_iter):
error, grad = objective(p, *args, **kwargs)
grad_norm = linalg.norm(grad)
inc = update * grad < 0.0
dec = np.invert(inc)
gains[inc] += 0.2
gains[dec] *= 0.8
np.clip(gains, min_gain, np.inf, out=gains)
grad *= gains
update = momentum * update - learning_rate * grad
p += update
if (i + 1) % n_iter_check == 0:
toc = time()
duration = toc - tic
tic = toc
if verbose >= 2:
print("[t-SNE] Iteration %d: error = %.7f,"
" gradient norm = %.7f"
" (%s iterations in %0.3fs)"
% (i + 1, error, grad_norm, n_iter_check, duration))
if error < best_error:
best_error = error
best_iter = i
elif i - best_iter > n_iter_without_progress:
if verbose >= 2:
print("[t-SNE] Iteration %d: did not make any progress "
"during the last %d episodes. Finished."
% (i + 1, n_iter_without_progress))
break
if grad_norm <= min_grad_norm:
if verbose >= 2:
print("[t-SNE] Iteration %d: gradient norm %f. Finished."
% (i + 1, grad_norm))
break
return p, error, i |
<SYSTEM_TASK:>
Expresses to what extent the local structure is retained.
<END_TASK>
<USER_TASK:>
Description:
def trustworthiness(X, X_embedded, n_neighbors=5, precomputed=False):
"""Expresses to what extent the local structure is retained.
The trustworthiness is within [0, 1]. It is defined as
.. math::
T(k) = 1 - \frac{2}{nk (2n - 3k - 1)} \sum^n_{i=1}
\sum_{j \in U^{(k)}_i} (r(i, j) - k)
where :math:`r(i, j)` is the rank of the embedded datapoint j
according to the pairwise distances between the embedded datapoints,
:math:`U^{(k)}_i` is the set of points that are in the k nearest
neighbors in the embedded space but not in the original space.
* "Neighborhood Preservation in Nonlinear Projection Methods: An
Experimental Study"
J. Venna, S. Kaski
* "Learning a Parametric Embedding by Preserving Local Structure"
L.J.P. van der Maaten
Parameters
----------
X : array, shape (n_samples, n_features) or (n_samples, n_samples)
If the metric is 'precomputed' X must be a square distance
matrix. Otherwise it contains a sample per row.
X_embedded : array, shape (n_samples, n_components)
Embedding of the training data in low-dimensional space.
n_neighbors : int, optional (default: 5)
Number of neighbors k that will be considered.
precomputed : bool, optional (default: False)
Set this flag if X is a precomputed square distance matrix.
Returns
-------
trustworthiness : float
Trustworthiness of the low-dimensional embedding.
""" |
if precomputed:
dist_X = X
else:
dist_X = pairwise_distances(X, squared=True)
dist_X_embedded = pairwise_distances(X_embedded, squared=True)
ind_X = np.argsort(dist_X, axis=1)
ind_X_embedded = np.argsort(dist_X_embedded, axis=1)[:, 1:n_neighbors + 1]
n_samples = X.shape[0]
t = 0.0
ranks = np.zeros(n_neighbors)
for i in range(n_samples):
for j in range(n_neighbors):
ranks[j] = np.where(ind_X[i] == ind_X_embedded[i, j])[0][0]
ranks -= n_neighbors
t += np.sum(ranks[ranks > 0])
t = 1.0 - t * (2.0 / (n_samples * n_neighbors *
(2.0 * n_samples - 3.0 * n_neighbors - 1.0)))
return t |
<SYSTEM_TASK:>
Integrate and batch correct a list of data sets.
<END_TASK>
<USER_TASK:>
Description:
def correct(datasets_full, genes_list, return_dimred=False,
batch_size=BATCH_SIZE, verbose=VERBOSE, ds_names=None,
dimred=DIMRED, approx=APPROX, sigma=SIGMA, alpha=ALPHA, knn=KNN,
return_dense=False, hvg=None, union=False,
geosketch=False, geosketch_max=20000):
"""Integrate and batch correct a list of data sets.
Parameters
----------
datasets_full : `list` of `scipy.sparse.csr_matrix` or of `numpy.ndarray`
Data sets to integrate and correct.
genes_list: `list` of `list` of `string`
List of genes for each data set.
return_dimred: `bool`, optional (default: `False`)
In addition to returning batch corrected matrices, also returns
integrated low-dimesional embeddings.
batch_size: `int`, optional (default: `5000`)
The batch size used in the alignment vector computation. Useful when
correcting very large (>100k samples) data sets. Set to large value
that runs within available memory.
verbose: `bool` or `int`, optional (default: 2)
When `True` or not equal to 0, prints logging output.
ds_names: `list` of `string`, optional
When `verbose=True`, reports data set names in logging output.
dimred: `int`, optional (default: 100)
Dimensionality of integrated embedding.
approx: `bool`, optional (default: `True`)
Use approximate nearest neighbors, greatly speeds up matching runtime.
sigma: `float`, optional (default: 15)
Correction smoothing parameter on Gaussian kernel.
alpha: `float`, optional (default: 0.10)
Alignment score minimum cutoff.
knn: `int`, optional (default: 20)
Number of nearest neighbors to use for matching.
return_dense: `bool`, optional (default: `False`)
Return `numpy.ndarray` matrices instead of `scipy.sparse.csr_matrix`.
hvg: `int`, optional (default: None)
Use this number of top highly variable genes based on dispersion.
Returns
-------
corrected, genes
By default (`return_dimred=False`), returns a two-tuple containing a
list of `scipy.sparse.csr_matrix` each with batch corrected values,
and a single list of genes containing the intersection of inputted
genes.
integrated, corrected, genes
When `return_dimred=False`, returns a three-tuple containing a list
of `numpy.ndarray` with integrated low dimensional embeddings, a list
of `scipy.sparse.csr_matrix` each with batch corrected values, and a
a single list of genes containing the intersection of inputted genes.
""" |
datasets_full = check_datasets(datasets_full)
datasets, genes = merge_datasets(datasets_full, genes_list,
ds_names=ds_names, union=union)
datasets_dimred, genes = process_data(datasets, genes, hvg=hvg,
dimred=dimred)
datasets_dimred = assemble(
datasets_dimred, # Assemble in low dimensional space.
expr_datasets=datasets, # Modified in place.
verbose=verbose, knn=knn, sigma=sigma, approx=approx,
alpha=alpha, ds_names=ds_names, batch_size=batch_size,
geosketch=geosketch, geosketch_max=geosketch_max,
)
if return_dense:
datasets = [ ds.toarray() for ds in datasets ]
if return_dimred:
return datasets_dimred, datasets, genes
return datasets, genes |
<SYSTEM_TASK:>
Integrate a list of data sets.
<END_TASK>
<USER_TASK:>
Description:
def integrate(datasets_full, genes_list, batch_size=BATCH_SIZE,
verbose=VERBOSE, ds_names=None, dimred=DIMRED, approx=APPROX,
sigma=SIGMA, alpha=ALPHA, knn=KNN, geosketch=False,
geosketch_max=20000, n_iter=1, union=False, hvg=None):
"""Integrate a list of data sets.
Parameters
----------
datasets_full : `list` of `scipy.sparse.csr_matrix` or of `numpy.ndarray`
Data sets to integrate and correct.
genes_list: `list` of `list` of `string`
List of genes for each data set.
batch_size: `int`, optional (default: `5000`)
The batch size used in the alignment vector computation. Useful when
correcting very large (>100k samples) data sets. Set to large value
that runs within available memory.
verbose: `bool` or `int`, optional (default: 2)
When `True` or not equal to 0, prints logging output.
ds_names: `list` of `string`, optional
When `verbose=True`, reports data set names in logging output.
dimred: `int`, optional (default: 100)
Dimensionality of integrated embedding.
approx: `bool`, optional (default: `True`)
Use approximate nearest neighbors, greatly speeds up matching runtime.
sigma: `float`, optional (default: 15)
Correction smoothing parameter on Gaussian kernel.
alpha: `float`, optional (default: 0.10)
Alignment score minimum cutoff.
knn: `int`, optional (default: 20)
Number of nearest neighbors to use for matching.
hvg: `int`, optional (default: None)
Use this number of top highly variable genes based on dispersion.
Returns
-------
integrated, genes
Returns a two-tuple containing a list of `numpy.ndarray` with
integrated low dimensional embeddings and a single list of genes
containing the intersection of inputted genes.
""" |
datasets_full = check_datasets(datasets_full)
datasets, genes = merge_datasets(datasets_full, genes_list,
ds_names=ds_names, union=union)
datasets_dimred, genes = process_data(datasets, genes, hvg=hvg,
dimred=dimred)
for _ in range(n_iter):
datasets_dimred = assemble(
datasets_dimred, # Assemble in low dimensional space.
verbose=verbose, knn=knn, sigma=sigma, approx=approx,
alpha=alpha, ds_names=ds_names, batch_size=batch_size,
geosketch=geosketch, geosketch_max=geosketch_max,
)
return datasets_dimred, genes |
<SYSTEM_TASK:>
Batch correct a list of `scanpy.api.AnnData`.
<END_TASK>
<USER_TASK:>
Description:
def correct_scanpy(adatas, **kwargs):
"""Batch correct a list of `scanpy.api.AnnData`.
Parameters
----------
adatas : `list` of `scanpy.api.AnnData`
Data sets to integrate and/or correct.
kwargs : `dict`
See documentation for the `correct()` method for a full list of
parameters to use for batch correction.
Returns
-------
corrected
By default (`return_dimred=False`), returns a list of
`scanpy.api.AnnData` with batch corrected values in the `.X` field.
corrected, integrated
When `return_dimred=False`, returns a two-tuple containing a list of
`np.ndarray` with integrated low-dimensional embeddings and a list
of `scanpy.api.AnnData` with batch corrected values in the `.X`
field.
""" |
if 'return_dimred' in kwargs and kwargs['return_dimred']:
datasets_dimred, datasets, genes = correct(
[adata.X for adata in adatas],
[adata.var_names.values for adata in adatas],
**kwargs
)
else:
datasets, genes = correct(
[adata.X for adata in adatas],
[adata.var_names.values for adata in adatas],
**kwargs
)
new_adatas = []
for i, adata in enumerate(adatas):
adata.X = datasets[i]
new_adatas.append(adata)
if 'return_dimred' in kwargs and kwargs['return_dimred']:
return datasets_dimred, new_adatas
else:
return new_adatas |
<SYSTEM_TASK:>
Integrate a list of `scanpy.api.AnnData`.
<END_TASK>
<USER_TASK:>
Description:
def integrate_scanpy(adatas, **kwargs):
"""Integrate a list of `scanpy.api.AnnData`.
Parameters
----------
adatas : `list` of `scanpy.api.AnnData`
Data sets to integrate.
kwargs : `dict`
See documentation for the `integrate()` method for a full list of
parameters to use for batch correction.
Returns
-------
integrated
Returns a list of `np.ndarray` with integrated low-dimensional
embeddings.
""" |
datasets_dimred, genes = integrate(
[adata.X for adata in adatas],
[adata.var_names.values for adata in adatas],
**kwargs
)
return datasets_dimred |
<SYSTEM_TASK:>
Augment a knot vector.
<END_TASK>
<USER_TASK:>
Description:
def augknt(knots, order):
"""Augment a knot vector.
Parameters:
knots:
Python list or rank-1 array, the original knot vector (without endpoint repeats)
order:
int, >= 0, order of spline
Returns:
list_of_knots:
rank-1 array that has (`order` + 1) copies of ``knots[0]``, then ``knots[1:-1]``, and finally (`order` + 1) copies of ``knots[-1]``.
Caveats:
`order` is the spline order `p`, not `p` + 1, and existing knots are never deleted.
The knot vector always becomes longer by calling this function.
""" |
if isinstance(knots, np.ndarray) and knots.ndim > 1:
raise ValueError("knots must be a list or a rank-1 array")
knots = list(knots) # ensure Python list
# One copy of knots[0] and knots[-1] will come from "knots" itself,
# so we only need to prepend/append "order" copies.
#
return np.array( [knots[0]] * order + knots + [knots[-1]] * order ) |
<SYSTEM_TASK:>
Compute the running average of `k` successive elements of `t`. Return the averaged array.
<END_TASK>
<USER_TASK:>
Description:
def aveknt(t, k):
"""Compute the running average of `k` successive elements of `t`. Return the averaged array.
Parameters:
t:
Python list or rank-1 array
k:
int, >= 2, how many successive elements to average
Returns:
rank-1 array, averaged data. If k > len(t), returns a zero-length array.
Caveat:
This is slightly different from MATLAB's aveknt, which returns the running average
of `k`-1 successive elements of ``t[1:-1]`` (and the empty vector if ``len(t) - 2 < k - 1``).
""" |
t = np.atleast_1d(t)
if t.ndim > 1:
raise ValueError("t must be a list or a rank-1 array")
n = t.shape[0]
u = max(0, n - (k-1)) # number of elements in the output array
out = np.empty( (u,), dtype=t.dtype )
for j in range(u):
out[j] = sum( t[j:(j+k)] ) / k
return out |
<SYSTEM_TASK:>
Create an acceptable knot vector.
<END_TASK>
<USER_TASK:>
Description:
def aptknt(tau, order):
"""Create an acceptable knot vector.
Minimal emulation of MATLAB's ``aptknt``.
The returned knot vector can be used to generate splines of desired `order`
that are suitable for interpolation to the collocation sites `tau`.
Note that this is only possible when ``len(tau)`` >= `order` + 1.
When this condition does not hold, a valid knot vector is returned,
but using it to generate a spline basis will not have the desired effect
(the spline will return a length-zero array upon evaluation).
Parameters:
tau:
Python list or rank-1 array, collocation sites
order:
int, >= 0, order of spline
Returns:
rank-1 array, `k` copies of ``tau[0]``, then ``aveknt(tau[1:-1], k-1)``,
and finally `k` copies of ``tau[-1]``, where ``k = min(order+1, len(tau))``.
""" |
tau = np.atleast_1d(tau)
k = order + 1
if tau.ndim > 1:
raise ValueError("tau must be a list or a rank-1 array")
# emulate MATLAB behavior for the "k" parameter
#
# See
# https://se.mathworks.com/help/curvefit/aptknt.html
#
if len(tau) < k:
k = len(tau)
if not (tau == sorted(tau)).all():
raise ValueError("tau must be nondecreasing")
# last processed element needs to be:
# i + k - 1 = len(tau)- 1
# => i + k = len(tau)
# => i = len(tau) - k
#
u = len(tau) - k
for i in range(u):
if tau[i+k-1] == tau[i]:
raise ValueError("k-fold (or higher) repeated sites not allowed, but tau[i+k-1] == tau[i] for i = %d, k = %d" % (i,k))
# form the output sequence
#
prefix = [ tau[0] ] * k
suffix = [ tau[-1] ] * k
# https://se.mathworks.com/help/curvefit/aveknt.html
# MATLAB's aveknt():
# - averages successive k-1 entries, but ours averages k
# - seems to ignore the endpoints
#
tmp = aveknt(tau[1:-1], k-1)
middle = tmp.tolist()
return np.array( prefix + middle + suffix, dtype=tmp.dtype ) |
<SYSTEM_TASK:>
Count multiplicities of elements in a sorted list or rank-1 array.
<END_TASK>
<USER_TASK:>
Description:
def knt2mlt(t):
"""Count multiplicities of elements in a sorted list or rank-1 array.
Minimal emulation of MATLAB's ``knt2mlt``.
Parameters:
t:
Python list or rank-1 array. Must be sorted!
Returns:
out
rank-1 array such that
out[k] = #{ t[i] == t[k] for i < k }
Example:
If ``t = [1, 1, 2, 3, 3, 3]``, then ``out = [0, 1, 0, 0, 1, 2]``.
Caveat:
Requires input to be already sorted (this is not checked).
""" |
t = np.atleast_1d(t)
if t.ndim > 1:
raise ValueError("t must be a list or a rank-1 array")
out = []
e = None
for k in range(t.shape[0]):
if t[k] != e:
e = t[k]
count = 0
else:
count += 1
out.append(count)
return np.array( out ) |
<SYSTEM_TASK:>
Return collocation matrix.
<END_TASK>
<USER_TASK:>
Description:
def spcol(knots, order, tau):
"""Return collocation matrix.
Minimal emulation of MATLAB's ``spcol``.
Parameters:
knots:
rank-1 array, knot vector (with appropriately repeated endpoints; see `augknt`, `aptknt`)
order:
int, >= 0, order of spline
tau:
rank-1 array, collocation sites
Returns:
rank-2 array A such that
A[i,j] = D**{m(i)} B_j(tau[i])
where
m(i) = multiplicity of site tau[i]
D**k = kth derivative (0 for function value itself)
""" |
m = knt2mlt(tau)
B = bspline.Bspline(knots, order)
dummy = B(0.)
nbasis = len(dummy) # perform dummy evaluation to get number of basis functions
A = np.empty( (tau.shape[0], nbasis), dtype=dummy.dtype )
for i,item in enumerate(zip(tau,m)):
taui,mi = item
f = B.diff(order=mi)
A[i,:] = f(taui)
return A |
<SYSTEM_TASK:>
Convenience function to compute first derivative of basis functions. 'Memoized' for speed.
<END_TASK>
<USER_TASK:>
Description:
def d(self, xi):
"""Convenience function to compute first derivative of basis functions. 'Memoized' for speed.""" |
return self.__basis(xi, self.p, compute_derivatives=True) |
<SYSTEM_TASK:>
Plot basis functions over full range of knots.
<END_TASK>
<USER_TASK:>
Description:
def plot(self):
"""Plot basis functions over full range of knots.
Convenience function. Requires matplotlib.
""" |
try:
import matplotlib.pyplot as plt
except ImportError:
from sys import stderr
print("ERROR: matplotlib.pyplot not found, matplotlib must be installed to use this function", file=stderr)
raise
x_min = np.min(self.knot_vector)
x_max = np.max(self.knot_vector)
x = np.linspace(x_min, x_max, num=1000)
N = np.array([self(i) for i in x]).T
for n in N:
plt.plot(x,n)
return plt.show() |
<SYSTEM_TASK:>
Differentiate a B-spline once, and return the resulting coefficients and Bspline objects.
<END_TASK>
<USER_TASK:>
Description:
def __diff_internal(self):
"""Differentiate a B-spline once, and return the resulting coefficients and Bspline objects.
This preserves the Bspline object nature of the data, enabling recursive implementation
of higher-order differentiation (see `diff`).
The value of the first derivative of `B` at a point `x` can be obtained as::
def diff1(B, x):
terms = B.__diff_internal()
return sum( ci*Bi(x) for ci,Bi in terms )
Returns:
tuple of tuples, where each item is (coefficient, Bspline object).
See:
`diff`: differentiation of any order >= 0
""" |
assert self.p > 0, "order of Bspline must be > 0" # we already handle the other case in diff()
# https://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-derv.html
#
t = self.knot_vector
p = self.p
Bi = Bspline( t[:-1], p-1 )
Bip1 = Bspline( t[1:], p-1 )
numer1 = +p
numer2 = -p
denom1 = t[p:-1] - t[:-(p+1)]
denom2 = t[(p+1):] - t[1:-p]
with np.errstate(divide='ignore', invalid='ignore'):
ci = np.where(denom1 != 0., (numer1 / denom1), 0.)
cip1 = np.where(denom2 != 0., (numer2 / denom2), 0.)
return ( (ci,Bi), (cip1,Bip1) ) |
<SYSTEM_TASK:>
Differentiate a B-spline `order` number of times.
<END_TASK>
<USER_TASK:>
Description:
def diff(self, order=1):
"""Differentiate a B-spline `order` number of times.
Parameters:
order:
int, >= 0
Returns:
**lambda** `x`: ... that evaluates the `order`-th derivative of `B` at the point `x`.
The returned function internally uses __call__, which is 'memoized' for speed.
""" |
order = int(order)
if order < 0:
raise ValueError("order must be >= 0, got %d" % (order))
if order == 0:
return self.__call__
if order > self.p: # identically zero, but force the same output format as in the general case
dummy = self.__call__(0.) # get number of basis functions and output dtype
nbasis = dummy.shape[0]
return lambda x: np.zeros( (nbasis,), dtype=dummy.dtype ) # accept but ignore input x
# At each differentiation, each term maps into two new terms.
# The number of terms in the result will be 2**order.
#
# This will cause an exponential explosion in the number of terms for high derivative orders,
# but for the first few orders (practical usage; >3 is rarely needed) the approach works.
#
terms = [ (1.,self) ]
for k in range(order):
tmp = []
for Ci,Bi in terms:
tmp.extend( (Ci*cn, Bn) for cn,Bn in Bi.__diff_internal() ) # NOTE: also propagate Ci
terms = tmp
# perform final summation at call time
return lambda x: sum( ci*Bi(x) for ci,Bi in terms ) |
<SYSTEM_TASK:>
Compute collocation matrix.
<END_TASK>
<USER_TASK:>
Description:
def collmat(self, tau, deriv_order=0):
"""Compute collocation matrix.
Parameters:
tau:
Python list or rank-1 array, collocation sites
deriv_order:
int, >=0, order of derivative for which to compute the collocation matrix.
The default is 0, which means the function value itself.
Returns:
A:
if len(tau) > 1, rank-2 array such that
A[i,j] = D**deriv_order B_j(tau[i])
where
D**k = kth derivative (0 for function value itself)
if len(tau) == 1, rank-1 array such that
A[j] = D**deriv_order B_j(tau)
Example:
If the coefficients of a spline function are given in the vector c, then::
np.sum( A*c, axis=-1 )
will give a rank-1 array of function values at the sites tau[i] that were supplied
to `collmat`.
Similarly for derivatives (if the supplied `deriv_order`> 0).
""" |
# get number of basis functions and output dtype
dummy = self.__call__(0.)
nbasis = dummy.shape[0]
tau = np.atleast_1d(tau)
if tau.ndim > 1:
raise ValueError("tau must be a list or a rank-1 array")
A = np.empty( (tau.shape[0], nbasis), dtype=dummy.dtype )
f = self.diff(order=deriv_order)
for i,taui in enumerate(tau):
A[i,:] = f(taui)
return np.squeeze(A) |
<SYSTEM_TASK:>
Returns a normalized request string as described iN OAuth2 MAC spec.
<END_TASK>
<USER_TASK:>
Description:
def get_normalized_request_string(method, url, nonce, params, ext='', body_hash=None):
"""
Returns a normalized request string as described iN OAuth2 MAC spec.
http://tools.ietf.org/html/draft-ietf-oauth-v2-http-mac-00#section-3.3.1
""" |
urlparts = urlparse.urlparse(url)
if urlparts.query:
norm_url = '%s?%s' % (urlparts.path, urlparts.query)
elif params:
norm_url = '%s?%s' % (urlparts.path, get_normalized_params(params))
else:
norm_url = urlparts.path
if not body_hash:
body_hash = get_body_hash(params)
port = urlparts.port
if not port:
assert urlparts.scheme in ('http', 'https')
if urlparts.scheme == 'http':
port = 80
elif urlparts.scheme == 'https':
port = 443
output = [nonce, method.upper(), norm_url, urlparts.hostname, port, body_hash, ext, '']
return '\n'.join(map(str, output)) |
<SYSTEM_TASK:>
Computes the viterbi paths using the current HMM model
<END_TASK>
<USER_TASK:>
Description:
def compute_viterbi_paths(self):
"""
Computes the viterbi paths using the current HMM model
""" |
# get parameters
K = len(self._observations)
A = self._hmm.transition_matrix
pi = self._hmm.initial_distribution
# compute viterbi path for each trajectory
paths = np.empty(K, dtype=object)
for itraj in range(K):
obs = self._observations[itraj]
# compute output probability matrix
pobs = self._hmm.output_model.p_obs(obs)
# hidden path
paths[itraj] = hidden.viterbi(A, pobs, pi)
# done
return paths |
<SYSTEM_TASK:>
Generate random samples from a Gaussian distribution.
<END_TASK>
<USER_TASK:>
Description:
def sample_gaussian(mean, covar, covariance_type='diag', n_samples=1,
random_state=None):
"""Generate random samples from a Gaussian distribution.
Parameters
----------
mean : array_like, shape (n_features,)
Mean of the distribution.
covar : array_like, optional
Covariance of the distribution. The shape depends on `covariance_type`:
scalar if 'spherical',
(n_features) if 'diag',
(n_features, n_features) if 'tied', or 'full'
covariance_type : string, optional
Type of the covariance parameters. Must be one of
'spherical', 'tied', 'diag', 'full'. Defaults to 'diag'.
n_samples : int, optional
Number of samples to generate. Defaults to 1.
Returns
-------
X : array, shape (n_features, n_samples)
Randomly generated sample
""" |
rng = check_random_state(random_state)
n_dim = len(mean)
rand = rng.randn(n_dim, n_samples)
if n_samples == 1:
rand.shape = (n_dim,)
if covariance_type == 'spherical':
rand *= np.sqrt(covar)
elif covariance_type == 'diag':
rand = np.dot(np.diag(np.sqrt(covar)), rand)
else:
s, U = linalg.eigh(covar)
s.clip(0, out=s) # get rid of tiny negatives
np.sqrt(s, out=s)
U *= s
rand = np.dot(U, rand)
return (rand.T + mean).T |
<SYSTEM_TASK:>
Performing the covariance M step for diagonal cases
<END_TASK>
<USER_TASK:>
Description:
def _covar_mstep_diag(gmm, X, responsibilities, weighted_X_sum, norm,
min_covar):
"""Performing the covariance M step for diagonal cases""" |
avg_X2 = np.dot(responsibilities.T, X * X) * norm
avg_means2 = gmm.means_ ** 2
avg_X_means = gmm.means_ * weighted_X_sum * norm
return avg_X2 - 2 * avg_X_means + avg_means2 + min_covar |
<SYSTEM_TASK:>
Performing the covariance M step for spherical cases
<END_TASK>
<USER_TASK:>
Description:
def _covar_mstep_spherical(*args):
"""Performing the covariance M step for spherical cases""" |
cv = _covar_mstep_diag(*args)
return np.tile(cv.mean(axis=1)[:, np.newaxis], (1, cv.shape[1])) |
<SYSTEM_TASK:>
Performing the covariance M step for full cases
<END_TASK>
<USER_TASK:>
Description:
def _covar_mstep_full(gmm, X, responsibilities, weighted_X_sum, norm,
min_covar):
"""Performing the covariance M step for full cases""" |
# Eq. 12 from K. Murphy, "Fitting a Conditional Linear Gaussian
# Distribution"
n_features = X.shape[1]
cv = np.empty((gmm.n_components, n_features, n_features))
for c in range(gmm.n_components):
post = responsibilities[:, c]
mu = gmm.means_[c]
diff = X - mu
with np.errstate(under='ignore'):
# Underflow Errors in doing post * X.T are not important
avg_cv = np.dot(post * diff.T, diff) / (post.sum() + 10 * EPS)
cv[c] = avg_cv + min_covar * np.eye(n_features)
return cv |
<SYSTEM_TASK:>
Return the per-sample likelihood of the data under the model.
<END_TASK>
<USER_TASK:>
Description:
def score_samples(self, X):
"""Return the per-sample likelihood of the data under the model.
Compute the log probability of X under the model and
return the posterior distribution (responsibilities) of each
mixture component for each element of X.
Parameters
----------
X: array_like, shape (n_samples, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
logprob : array_like, shape (n_samples,)
Log probabilities of each data point in X.
responsibilities : array_like, shape (n_samples, n_components)
Posterior probabilities of each mixture component for each
observation
""" |
check_is_fitted(self, 'means_')
X = check_array(X)
if X.ndim == 1:
X = X[:, np.newaxis]
if X.size == 0:
return np.array([]), np.empty((0, self.n_components))
if X.shape[1] != self.means_.shape[1]:
raise ValueError('The shape of X is not compatible with self')
lpr = (log_multivariate_normal_density(X, self.means_, self.covars_,
self.covariance_type)
+ np.log(self.weights_))
logprob = logsumexp(lpr, axis=1)
responsibilities = np.exp(lpr - logprob[:, np.newaxis])
return logprob, responsibilities |
<SYSTEM_TASK:>
Predict label for data.
<END_TASK>
<USER_TASK:>
Description:
def predict(self, X):
"""Predict label for data.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
Returns
-------
C : array, shape = (n_samples,)
""" |
logprob, responsibilities = self.score_samples(X)
return responsibilities.argmax(axis=1) |
<SYSTEM_TASK:>
Estimate model parameters with the expectation-maximization
<END_TASK>
<USER_TASK:>
Description:
def fit(self, X, y=None):
"""Estimate model parameters with the expectation-maximization
algorithm.
A initialization step is performed before entering the em
algorithm. If you want to avoid this step, set the keyword
argument init_params to the empty string '' when creating the
GMM object. Likewise, if you would like just to do an
initialization, set n_iter=0.
Parameters
----------
X : array_like, shape (n, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
""" |
# initialization step
X = check_array(X, dtype=np.float64)
if X.shape[0] < self.n_components:
raise ValueError(
'GMM estimation with %s components, but got only %s samples' %
(self.n_components, X.shape[0]))
max_log_prob = -np.infty
for _ in range(self.n_init):
if 'm' in self.init_params or not hasattr(self, 'means_'):
if np.issubdtype(X.dtype, np.float32):
from bhmm._external.clustering.kmeans_clustering_32 import init_centers
elif np.issubdtype(X.dtype, np.float64):
from bhmm._external.clustering.kmeans_clustering_64 import init_centers
else:
raise ValueError("Could not handle dtype %s for clustering!" % X.dtype)
centers = init_centers(X, 'euclidean', self.n_components)
self.means_ = centers
if 'w' in self.init_params or not hasattr(self, 'weights_'):
self.weights_ = np.tile(1.0 / self.n_components,
self.n_components)
if 'c' in self.init_params or not hasattr(self, 'covars_'):
cv = np.cov(X.T) + self.min_covar * np.eye(X.shape[1])
if not cv.shape:
cv.shape = (1, 1)
self.covars_ = \
distribute_covar_matrix_to_match_covariance_type(
cv, self.covariance_type, self.n_components)
# EM algorithms
current_log_likelihood = None
# reset self.converged_ to False
self.converged_ = False
# this line should be removed when 'thresh' is removed in v0.18
tol = (self.tol if self.thresh is None
else self.thresh / float(X.shape[0]))
for i in range(self.n_iter):
prev_log_likelihood = current_log_likelihood
# Expectation step
log_likelihoods, responsibilities = self.score_samples(X)
current_log_likelihood = log_likelihoods.mean()
# Check for convergence.
# (should compare to self.tol when dreprecated 'thresh' is
# removed in v0.18)
if prev_log_likelihood is not None:
change = abs(current_log_likelihood - prev_log_likelihood)
if change < tol:
self.converged_ = True
break
# Maximization step
self._do_mstep(X, responsibilities, self.params,
self.min_covar)
# if the results are better, keep it
if self.n_iter:
if current_log_likelihood > max_log_prob:
max_log_prob = current_log_likelihood
best_params = {'weights': self.weights_,
'means': self.means_,
'covars': self.covars_}
# check the existence of an init param that was not subject to
# likelihood computation issue.
if np.isneginf(max_log_prob) and self.n_iter:
raise RuntimeError(
"EM algorithm was never able to compute a valid likelihood " +
"given initial parameters. Try different init parameters " +
"(or increasing n_init) or check for degenerate data.")
# self.n_iter == 0 occurs when using GMM within HMM
if self.n_iter:
self.covars_ = best_params['covars']
self.means_ = best_params['means']
self.weights_ = best_params['weights']
return self |
<SYSTEM_TASK:>
Perform the Mstep of the EM algorithm and return the class weihgts.
<END_TASK>
<USER_TASK:>
Description:
def _do_mstep(self, X, responsibilities, params, min_covar=0):
""" Perform the Mstep of the EM algorithm and return the class weihgts.
""" |
weights = responsibilities.sum(axis=0)
weighted_X_sum = np.dot(responsibilities.T, X)
inverse_weights = 1.0 / (weights[:, np.newaxis] + 10 * EPS)
if 'w' in params:
self.weights_ = (weights / (weights.sum() + 10 * EPS) + EPS)
if 'm' in params:
self.means_ = weighted_X_sum * inverse_weights
if 'c' in params:
covar_mstep_func = _covar_mstep_funcs[self.covariance_type]
self.covars_ = covar_mstep_func(
self, X, responsibilities, weighted_X_sum, inverse_weights,
min_covar)
return weights |
<SYSTEM_TASK:>
Return the number of free parameters in the model.
<END_TASK>
<USER_TASK:>
Description:
def _n_parameters(self):
"""Return the number of free parameters in the model.""" |
ndim = self.means_.shape[1]
if self.covariance_type == 'full':
cov_params = self.n_components * ndim * (ndim + 1) / 2.
elif self.covariance_type == 'diag':
cov_params = self.n_components * ndim
elif self.covariance_type == 'tied':
cov_params = ndim * (ndim + 1) / 2.
elif self.covariance_type == 'spherical':
cov_params = self.n_components
mean_params = ndim * self.n_components
return int(cov_params + mean_params + self.n_components - 1) |
<SYSTEM_TASK:>
Bayesian information criterion for the current model fit
<END_TASK>
<USER_TASK:>
Description:
def bic(self, X):
"""Bayesian information criterion for the current model fit
and the proposed data
Parameters
----------
X : array of shape(n_samples, n_dimensions)
Returns
-------
bic: float (the lower the better)
""" |
return (-2 * self.score(X).sum() +
self._n_parameters() * np.log(X.shape[0])) |
<SYSTEM_TASK:>
Generate an initial model with 1D-Gaussian output densities
<END_TASK>
<USER_TASK:>
Description:
def init_model_gaussian1d(observations, nstates, reversible=True):
"""Generate an initial model with 1D-Gaussian output densities
Parameters
----------
observations : list of ndarray((T_i), dtype=float)
list of arrays of length T_i with observation data
nstates : int
The number of states.
Examples
--------
Generate initial model for a gaussian output model.
>>> from bhmm import testsystems
>>> [model, observations, states] = testsystems.generate_synthetic_observations(output='gaussian')
>>> initial_model = init_model_gaussian1d(observations, model.nstates)
""" |
ntrajectories = len(observations)
# Concatenate all observations.
collected_observations = np.array([], dtype=config.dtype)
for o_t in observations:
collected_observations = np.append(collected_observations, o_t)
# Fit a Gaussian mixture model to obtain emission distributions and state stationary probabilities.
from bhmm._external.sklearn import mixture
gmm = mixture.GMM(n_components=nstates)
gmm.fit(collected_observations[:,None])
from bhmm import GaussianOutputModel
output_model = GaussianOutputModel(nstates, means=gmm.means_[:,0], sigmas=np.sqrt(gmm.covars_[:,0]))
logger().info("Gaussian output model:\n"+str(output_model))
# Extract stationary distributions.
Pi = np.zeros([nstates], np.float64)
Pi[:] = gmm.weights_[:]
logger().info("GMM weights: %s" % str(gmm.weights_))
# Compute fractional state memberships.
Nij = np.zeros([nstates, nstates], np.float64)
for o_t in observations:
# length of trajectory
T = o_t.shape[0]
# output probability
pobs = output_model.p_obs(o_t)
# normalize
pobs /= pobs.sum(axis=1)[:,None]
# Accumulate fractional transition counts from this trajectory.
for t in range(T-1):
Nij[:,:] = Nij[:,:] + np.outer(pobs[t,:], pobs[t+1,:])
logger().info("Nij\n"+str(Nij))
# Compute transition matrix maximum likelihood estimate.
import msmtools.estimation as msmest
import msmtools.analysis as msmana
Tij = msmest.transition_matrix(Nij, reversible=reversible)
pi = msmana.stationary_distribution(Tij)
# Update model.
model = HMM(pi, Tij, output_model)
return model |
<SYSTEM_TASK:>
Returns the output probability for symbol o from all hidden states
<END_TASK>
<USER_TASK:>
Description:
def _p_o(self, o):
"""
Returns the output probability for symbol o from all hidden states
Parameters
----------
o : float
A single observation.
Return
------
p_o : ndarray (N)
p_o[i] is the probability density of the observation o from state i emission distribution
Examples
--------
Create an observation model.
>>> output_model = GaussianOutputModel(nstates=3, means=[-1, 0, 1], sigmas=[0.5, 1, 2])
Compute the output probability of a single observation from all hidden states.
>>> observation = 0
>>> p_o = output_model._p_o(observation)
""" |
if self.__impl__ == self.__IMPL_C__:
return gc.p_o(o, self.means, self.sigmas, out=None, dtype=type(o))
elif self.__impl__ == self.__IMPL_PYTHON__:
if np.any(self.sigmas < np.finfo(self.sigmas.dtype).eps):
raise RuntimeError('at least one sigma is too small to continue.')
C = 1.0 / (np.sqrt(2.0 * np.pi) * self.sigmas)
Pobs = C * np.exp(-0.5 * ((o-self.means)/self.sigmas)**2)
return Pobs
else:
raise RuntimeError('Implementation '+str(self.__impl__)+' not available') |
<SYSTEM_TASK:>
Fits the output model given the observations and weights
<END_TASK>
<USER_TASK:>
Description:
def estimate(self, observations, weights):
"""
Fits the output model given the observations and weights
Parameters
----------
observations : [ ndarray(T_k,) ] with K elements
A list of K observation trajectories, each having length T_k and d dimensions
weights : [ ndarray(T_k,nstates) ] with K elements
A list of K weight matrices, each having length T_k
weights[k][t,n] is the weight assignment from observations[k][t] to state index n
Examples
--------
Generate an observation model and samples from each state.
>>> ntrajectories = 3
>>> nobs = 1000
>>> output_model = GaussianOutputModel(nstates=3, means=[-1, 0, +1], sigmas=[0.5, 1, 2])
>>> observations = [ np.random.randn(nobs) for _ in range(ntrajectories) ] # random observations
>>> weights = [ np.random.dirichlet([2, 3, 4], size=nobs) for _ in range(ntrajectories) ] # random weights
Update the observation model parameters my a maximum-likelihood fit.
>>> output_model.estimate(observations, weights)
""" |
# sizes
N = self.nstates
K = len(observations)
# fit means
self._means = np.zeros(N)
w_sum = np.zeros(N)
for k in range(K):
# update nominator
for i in range(N):
self.means[i] += np.dot(weights[k][:, i], observations[k])
# update denominator
w_sum += np.sum(weights[k], axis=0)
# normalize
self._means /= w_sum
# fit variances
self._sigmas = np.zeros(N)
w_sum = np.zeros(N)
for k in range(K):
# update nominator
for i in range(N):
Y = (observations[k] - self.means[i])**2
self.sigmas[i] += np.dot(weights[k][:, i], Y)
# update denominator
w_sum += np.sum(weights[k], axis=0)
# normalize
self._sigmas /= w_sum
self._sigmas = np.sqrt(self.sigmas)
if np.any(self._sigmas < np.finfo(self._sigmas.dtype).eps):
raise RuntimeError('at least one sigma is too small to continue.') |
<SYSTEM_TASK:>
r""" Samples of the initial distribution
<END_TASK>
<USER_TASK:>
Description:
def initial_distribution_samples(self):
r""" Samples of the initial distribution """ |
res = np.empty((self.nsamples, self.nstates), dtype=config.dtype)
for i in range(self.nsamples):
res[i, :] = self._sampled_hmms[i].stationary_distribution
return res |
<SYSTEM_TASK:>
r""" Samples of the transition matrix
<END_TASK>
<USER_TASK:>
Description:
def transition_matrix_samples(self):
r""" Samples of the transition matrix """ |
res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype)
for i in range(self.nsamples):
res[i, :, :] = self._sampled_hmms[i].transition_matrix
return res |
<SYSTEM_TASK:>
r""" Samples of the eigenvalues
<END_TASK>
<USER_TASK:>
Description:
def eigenvalues_samples(self):
r""" Samples of the eigenvalues """ |
res = np.empty((self.nsamples, self.nstates), dtype=config.dtype)
for i in range(self.nsamples):
res[i, :] = self._sampled_hmms[i].eigenvalues
return res |
<SYSTEM_TASK:>
r""" Samples of the left eigenvectors of the hidden transition matrix
<END_TASK>
<USER_TASK:>
Description:
def eigenvectors_left_samples(self):
r""" Samples of the left eigenvectors of the hidden transition matrix """ |
res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype)
for i in range(self.nsamples):
res[i, :, :] = self._sampled_hmms[i].eigenvectors_left
return res |
<SYSTEM_TASK:>
r""" Samples of the right eigenvectors of the hidden transition matrix
<END_TASK>
<USER_TASK:>
Description:
def eigenvectors_right_samples(self):
r""" Samples of the right eigenvectors of the hidden transition matrix """ |
res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype)
for i in range(self.nsamples):
res[i, :, :] = self._sampled_hmms[i].eigenvectors_right
return res |
<SYSTEM_TASK:>
Returns the element-wise logarithm of the output probabilities for an entire trajectory and all hidden states
<END_TASK>
<USER_TASK:>
Description:
def log_p_obs(self, obs, out=None, dtype=np.float32):
"""
Returns the element-wise logarithm of the output probabilities for an entire trajectory and all hidden states
This is a default implementation that will take the log of p_obs(obs) and should only be used if p_obs(obs)
is numerically stable. If there is any danger of running into numerical problems *during* the calculation of
p_obs, this function should be overwritten in order to compute the log-probabilities directly.
Parameters
----------
obs : ndarray((T), dtype=int)
a discrete trajectory of length T
Return
------
p_o : ndarray (T,N)
the log probability of generating the symbol at time point t from any of the N hidden states
""" |
if out is None:
return np.log(self.p_obs(obs))
else:
self.p_obs(obs, out=out, dtype=dtype)
np.log(out, out=out)
return out |
<SYSTEM_TASK:>
Coarse grain transition matrix P using memberships M
<END_TASK>
<USER_TASK:>
Description:
def coarse_grain_transition_matrix(P, M):
""" Coarse grain transition matrix P using memberships M
Computes
.. math:
Pc = (M' M)^-1 M' P M
Parameters
----------
P : ndarray(n, n)
microstate transition matrix
M : ndarray(n, m)
membership matrix. Membership to macrostate m for each microstate.
Returns
-------
Pc : ndarray(m, m)
coarse-grained transition matrix.
""" |
# coarse-grain matrix: Pc = (M' M)^-1 M' P M
W = np.linalg.inv(np.dot(M.T, M))
A = np.dot(np.dot(M.T, P), M)
P_coarse = np.dot(W, A)
# this coarse-graining can lead to negative elements. Setting them to zero here.
P_coarse = np.maximum(P_coarse, 0)
# and renormalize
P_coarse /= P_coarse.sum(axis=1)[:, None]
return P_coarse |
<SYSTEM_TASK:>
Regularizes the hidden initial distribution and transition matrix.
<END_TASK>
<USER_TASK:>
Description:
def regularize_hidden(p0, P, reversible=True, stationary=False, C=None, eps=None):
""" Regularizes the hidden initial distribution and transition matrix.
Makes sure that the hidden initial distribution and transition matrix have
nonzero probabilities by setting them to eps and then renormalizing.
Avoids zeros that would cause estimation algorithms to crash or get stuck
in suboptimal states.
Parameters
----------
p0 : ndarray(n)
Initial hidden distribution of the HMM
P : ndarray(n, n)
Hidden transition matrix
reversible : bool
HMM is reversible. Will make sure it is still reversible after modification.
stationary : bool
p0 is the stationary distribution of P. In this case, will not regularize
p0 separately. If stationary=False, the regularization will be applied to p0.
C : ndarray(n, n)
Hidden count matrix. Only needed for stationary=True and P disconnected.
epsilon : float or None
minimum value of the resulting transition matrix. Default: evaluates
to 0.01 / n. The coarse-graining equation can lead to negative elements
and thus epsilon should be set to at least 0. Positive settings of epsilon
are similar to a prior and enforce minimum positive values for all
transition probabilities.
Return
------
p0 : ndarray(n)
regularized initial distribution
P : ndarray(n, n)
regularized transition matrix
""" |
# input
n = P.shape[0]
if eps is None: # default output probability, in order to avoid zero columns
eps = 0.01 / n
# REGULARIZE P
P = np.maximum(P, eps)
# and renormalize
P /= P.sum(axis=1)[:, None]
# ensure reversibility
if reversible:
P = _tmatrix_disconnected.enforce_reversible_on_closed(P)
# REGULARIZE p0
if stationary:
_tmatrix_disconnected.stationary_distribution(P, C=C)
else:
p0 = np.maximum(p0, eps)
p0 /= p0.sum()
return p0, P |
<SYSTEM_TASK:>
Regularizes the output probabilities.
<END_TASK>
<USER_TASK:>
Description:
def regularize_pobs(B, nonempty=None, separate=None, eps=None):
""" Regularizes the output probabilities.
Makes sure that the output probability distributions has
nonzero probabilities by setting them to eps and then renormalizing.
Avoids zeros that would cause estimation algorithms to crash or get stuck
in suboptimal states.
Parameters
----------
B : ndarray(n, m)
HMM output probabilities
nonempty : None or iterable of int
Nonempty set. Only regularize on this subset.
separate : None or iterable of int
Force the given set of observed states to stay in a separate hidden state.
The remaining nstates-1 states will be assigned by a metastable decomposition.
reversible : bool
HMM is reversible. Will make sure it is still reversible after modification.
Returns
-------
B : ndarray(n, m)
Regularized output probabilities
""" |
# input
B = B.copy() # modify copy
n, m = B.shape # number of hidden / observable states
if eps is None: # default output probability, in order to avoid zero columns
eps = 0.01 / m
# observable sets
if nonempty is None:
nonempty = np.arange(m)
if separate is None:
B[:, nonempty] = np.maximum(B[:, nonempty], eps)
else:
nonempty_nonseparate = np.array(list(set(nonempty) - set(separate)), dtype=int)
nonempty_separate = np.array(list(set(nonempty).intersection(set(separate))), dtype=int)
B[:n-1, nonempty_nonseparate] = np.maximum(B[:n-1, nonempty_nonseparate], eps)
B[n-1, nonempty_separate] = np.maximum(B[n-1, nonempty_separate], eps)
# renormalize and return copy
B /= B.sum(axis=1)[:, None]
return B |
<SYSTEM_TASK:>
Initializes discrete HMM using maximum likelihood of observation counts
<END_TASK>
<USER_TASK:>
Description:
def init_discrete_hmm_ml(C_full, nstates, reversible=True, stationary=True, active_set=None, P=None,
eps_A=None, eps_B=None, separate=None):
"""Initializes discrete HMM using maximum likelihood of observation counts""" |
raise NotImplementedError('ML-initialization not yet implemented') |
<SYSTEM_TASK:>
r""" Updates the transition matrix and recomputes all derived quantities
<END_TASK>
<USER_TASK:>
Description:
def update(self, Pi, Tij):
r""" Updates the transition matrix and recomputes all derived quantities """ |
from msmtools import analysis as msmana
# update transition matrix by copy
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[0] == self._nstates, 'Given transition matrix has unexpected number of states '
# reset spectral decomposition
self._spectral_decomp_available = False
# check initial distribution
assert np.all(Pi >= 0), 'Given initial distribution contains negative elements.'
assert np.any(Pi > 0), 'Given initial distribution is zero'
self._Pi = np.array(Pi) / np.sum(Pi) |
<SYSTEM_TASK:>
r""" Whether the MSM is stationary, i.e. whether the initial distribution is the stationary distribution
<END_TASK>
<USER_TASK:>
Description:
def is_stationary(self):
r""" Whether the MSM is stationary, i.e. whether the initial distribution is the stationary distribution
of the hidden transition matrix. """ |
# for disconnected matrices, the stationary distribution depends on the estimator, so we can't compute
# it directly. Therefore we test whether the initial distribution is stationary.
return np.allclose(np.dot(self._Pi, self._Tij), self._Pi) |
<SYSTEM_TASK:>
r""" Compute stationary distribution of hidden states if possible.
<END_TASK>
<USER_TASK:>
Description:
def stationary_distribution(self):
r""" Compute stationary distribution of hidden states if possible.
Raises
------
ValueError if the HMM is not stationary
""" |
assert _tmatrix_disconnected.is_connected(self._Tij, strong=False), \
'No unique stationary distribution because transition matrix is not connected'
import msmtools.analysis as msmana
return msmana.stationary_distribution(self._Tij) |
<SYSTEM_TASK:>
r""" Relaxation timescales of the hidden transition matrix
<END_TASK>
<USER_TASK:>
Description:
def timescales(self):
r""" Relaxation timescales of the hidden transition matrix
Returns
-------
ts : ndarray(m)
relaxation timescales in units of the input trajectory time step,
defined by :math:`-tau / ln | \lambda_i |, i = 2,...,nstates`, where
:math:`\lambda_i` are the hidden transition matrix eigenvalues.
""" |
from msmtools.analysis.dense.decomposition import timescales_from_eigenvalues as _timescales
self._ensure_spectral_decomposition()
ts = _timescales(self._eigenvalues, tau=self._lag)
return ts[1:] |
<SYSTEM_TASK:>
r""" Lifetimes of states of the hidden transition matrix
<END_TASK>
<USER_TASK:>
Description:
def lifetimes(self):
r""" Lifetimes of states of the hidden transition matrix
Returns
-------
l : ndarray(nstates)
state lifetimes in units of the input trajectory time step,
defined by :math:`-tau / ln | p_{ii} |, i = 1,...,nstates`, where
:math:`p_{ii}` are the diagonal entries of the hidden transition matrix.
""" |
return -self._lag / np.log(np.diag(self.transition_matrix)) |
<SYSTEM_TASK:>
r""" Returns HMM on a subset of states
<END_TASK>
<USER_TASK:>
Description:
def sub_hmm(self, states):
r""" Returns HMM on a subset of states
Returns the HMM restricted to the selected subset of states.
Will raise exception if the hidden transition matrix cannot be normalized on this subset
""" |
# restrict initial distribution
pi_sub = self._Pi[states]
pi_sub /= pi_sub.sum()
# restrict transition matrix
P_sub = self._Tij[states, :][:, states]
# checks if this selection is possible
assert np.all(P_sub.sum(axis=1) > 0), \
'Illegal sub_hmm request: transition matrix cannot be normalized on ' + str(states)
P_sub /= P_sub.sum(axis=1)[:, None]
# restrict output model
out_sub = self.output_model.sub_output_model(states)
return HMM(pi_sub, P_sub, out_sub, lag=self.lag) |
<SYSTEM_TASK:>
Compute the transition count matrix from hidden state trajectory.
<END_TASK>
<USER_TASK:>
Description:
def count_matrix(self):
# TODO: does this belong here or to the BHMM sampler, or in a subclass containing HMM with data?
"""Compute the transition count matrix from hidden state trajectory.
Returns
-------
C : numpy.array with shape (nstates,nstates)
C[i,j] is the number of transitions observed from state i to state j
Raises
------
RuntimeError
A RuntimeError is raised if the HMM model does not yet have a hidden state trajectory associated with it.
Examples
--------
""" |
if self.hidden_state_trajectories is None:
raise RuntimeError('HMM model does not have a hidden state trajectory.')
C = msmest.count_matrix(self.hidden_state_trajectories, 1, nstates=self._nstates)
return C.toarray() |
<SYSTEM_TASK:>
Compute the counts at the first time step
<END_TASK>
<USER_TASK:>
Description:
def count_init(self):
"""Compute the counts at the first time step
Returns
-------
n : ndarray(nstates)
n[i] is the number of trajectories starting in state i
""" |
if self.hidden_state_trajectories is None:
raise RuntimeError('HMM model does not have a hidden state trajectory.')
n = [traj[0] for traj in self.hidden_state_trajectories]
return np.bincount(n, minlength=self.nstates) |
<SYSTEM_TASK:>
Collect a vector of all observations belonging to a specified hidden state.
<END_TASK>
<USER_TASK:>
Description:
def collect_observations_in_state(self, observations, state_index):
# TODO: this would work well in a subclass with data
"""Collect a vector of all observations belonging to a specified hidden state.
Parameters
----------
observations : list of numpy.array
List of observed trajectories.
state_index : int
The index of the hidden state for which corresponding observations are to be retrieved.
dtype : numpy.dtype, optional, default=numpy.float64
The numpy dtype to use to store the collected observations.
Returns
-------
collected_observations : numpy.array with shape (nsamples,)
The collected vector of observations belonging to the specified hidden state.
Raises
------
RuntimeError
A RuntimeError is raised if the HMM model does not yet have a hidden state trajectory associated with it.
""" |
if not self.hidden_state_trajectories:
raise RuntimeError('HMM model does not have a hidden state trajectory.')
dtype = observations[0].dtype
collected_observations = np.array([], dtype=dtype)
for (s_t, o_t) in zip(self.hidden_state_trajectories, observations):
indices = np.where(s_t == state_index)[0]
collected_observations = np.append(collected_observations, o_t[indices])
return collected_observations |
<SYSTEM_TASK:>
Generate a synthetic state trajectory.
<END_TASK>
<USER_TASK:>
Description:
def generate_synthetic_state_trajectory(self, nsteps, initial_Pi=None, start=None, stop=None, dtype=np.int32):
"""Generate a synthetic state trajectory.
Parameters
----------
nsteps : int
Number of steps in the synthetic state trajectory to be generated.
initial_Pi : np.array of shape (nstates,), optional, default=None
The initial probability distribution, if samples are not to be taken from the intrinsic
initial distribution.
start : int
starting state. Exclusive with initial_Pi
stop : int
stopping state. Trajectory will terminate when reaching the stopping state before length number of steps.
dtype : numpy.dtype, optional, default=numpy.int32
The numpy dtype to use to store the synthetic trajectory.
Returns
-------
states : np.array of shape (nstates,) of dtype=np.int32
The trajectory of hidden states, with each element in range(0,nstates).
Examples
--------
Generate a synthetic state trajectory of a specified length.
>>> from bhmm import testsystems
>>> model = testsystems.dalton_model()
>>> states = model.generate_synthetic_state_trajectory(nsteps=100)
""" |
# consistency check
if initial_Pi is not None and start is not None:
raise ValueError('Arguments initial_Pi and start are exclusive. Only set one of them.')
# Generate first state sample.
if start is None:
if initial_Pi is not None:
start = np.random.choice(range(self._nstates), size=1, p=initial_Pi)
else:
start = np.random.choice(range(self._nstates), size=1, p=self._Pi)
# Generate and return trajectory
from msmtools import generation as msmgen
traj = msmgen.generate_traj(self.transition_matrix, nsteps, start=start, stop=stop, dt=1)
return traj.astype(dtype) |
<SYSTEM_TASK:>
Generate a synthetic realization of observables.
<END_TASK>
<USER_TASK:>
Description:
def generate_synthetic_observation_trajectory(self, length, initial_Pi=None):
"""Generate a synthetic realization of observables.
Parameters
----------
length : int
Length of synthetic state trajectory to be generated.
initial_Pi : np.array of shape (nstates,), optional, default=None
The initial probability distribution, if samples are not to be taken from equilibrium.
Returns
-------
o_t : np.array of shape (nstates,) of dtype=np.float32
The trajectory of observations.
s_t : np.array of shape (nstates,) of dtype=np.int32
The trajectory of hidden states, with each element in range(0,nstates).
Examples
--------
Generate a synthetic observation trajectory for an equilibrium realization.
>>> from bhmm import testsystems
>>> model = testsystems.dalton_model()
>>> [o_t, s_t] = model.generate_synthetic_observation_trajectory(length=100)
Use an initial nonequilibrium distribution.
>>> from bhmm import testsystems
>>> model = testsystems.dalton_model()
>>> [o_t, s_t] = model.generate_synthetic_observation_trajectory(length=100, initial_Pi=np.array([1,0,0]))
""" |
# First, generate synthetic state trajetory.
s_t = self.generate_synthetic_state_trajectory(length, initial_Pi=initial_Pi)
# Next, generate observations from these states.
o_t = self.output_model.generate_observation_trajectory(s_t)
return [o_t, s_t] |
<SYSTEM_TASK:>
Generate a number of synthetic realization of observables from this model.
<END_TASK>
<USER_TASK:>
Description:
def generate_synthetic_observation_trajectories(self, ntrajectories, length, initial_Pi=None):
"""Generate a number of synthetic realization of observables from this model.
Parameters
----------
ntrajectories : int
The number of trajectories to be generated.
length : int
Length of synthetic state trajectory to be generated.
initial_Pi : np.array of shape (nstates,), optional, default=None
The initial probability distribution, if samples are not to be taken from equilibrium.
Returns
-------
O : list of np.array of shape (nstates,) of dtype=np.float32
The trajectories of observations
S : list of np.array of shape (nstates,) of dtype=np.int32
The trajectories of hidden states
Examples
--------
Generate a number of synthetic trajectories.
>>> from bhmm import testsystems
>>> model = testsystems.dalton_model()
>>> O, S = model.generate_synthetic_observation_trajectories(ntrajectories=10, length=100)
Use an initial nonequilibrium distribution.
>>> from bhmm import testsystems
>>> model = testsystems.dalton_model(nstates=3)
>>> O, S = model.generate_synthetic_observation_trajectories(ntrajectories=10, length=100, initial_Pi=np.array([1,0,0]))
""" |
O = list() # observations
S = list() # state trajectories
for trajectory_index in range(ntrajectories):
o_t, s_t = self.generate_synthetic_observation_trajectory(length=length, initial_Pi=initial_Pi)
O.append(o_t)
S.append(s_t)
return O, S |
<SYSTEM_TASK:>
Maximum likelihood estimation of output model given the observations and weights
<END_TASK>
<USER_TASK:>
Description:
def estimate(self, observations, weights):
"""
Maximum likelihood estimation of output model given the observations and weights
Parameters
----------
observations : [ ndarray(T_k) ] with K elements
A list of K observation trajectories, each having length T_k
weights : [ ndarray(T_k, N) ] with K elements
A list of K weight matrices, each having length T_k and containing the probability of any of the states in
the given time step
Examples
--------
Generate an observation model and samples from each state.
>>> import numpy as np
>>> ntrajectories = 3
>>> nobs = 1000
>>> B = np.array([[0.5,0.5],[0.1,0.9]])
>>> output_model = DiscreteOutputModel(B)
>>> from scipy import stats
>>> nobs = 1000
>>> obs = np.empty(nobs, dtype = object)
>>> weights = np.empty(nobs, dtype = object)
>>> gens = [stats.rv_discrete(values=(range(len(B[i])), B[i])) for i in range(B.shape[0])]
>>> obs = [gens[i].rvs(size=nobs) for i in range(B.shape[0])]
>>> weights = [np.zeros((nobs, B.shape[1])) for i in range(B.shape[0])]
>>> for i in range(B.shape[0]): weights[i][:, i] = 1.0
Update the observation model parameters my a maximum-likelihood fit.
>>> output_model.estimate(obs, weights)
""" |
# sizes
N, M = self._output_probabilities.shape
K = len(observations)
# initialize output probability matrix
self._output_probabilities = np.zeros((N, M))
# update output probability matrix (numerator)
if self.__impl__ == self.__IMPL_C__:
for k in range(K):
dc.update_pout(observations[k], weights[k], self._output_probabilities, dtype=config.dtype)
elif self.__impl__ == self.__IMPL_PYTHON__:
for k in range(K):
for o in range(M):
times = np.where(observations[k] == o)[0]
self._output_probabilities[:, o] += np.sum(weights[k][times, :], axis=0)
else:
raise RuntimeError('Implementation '+str(self.__impl__)+' not available')
# normalize
self._output_probabilities /= np.sum(self._output_probabilities, axis=1)[:, None] |
<SYSTEM_TASK:>
Sum the probabilities of being in state i to time t
<END_TASK>
<USER_TASK:>
Description:
def state_counts(gamma, T, out=None):
""" Sum the probabilities of being in state i to time t
Parameters
----------
gamma : ndarray((T,N), dtype = float), optional, default = None
gamma[t,i] is the probabilty at time t to be in state i !
T : int
number of time steps
Returns
-------
count : numpy.array shape (N)
count[i] is the summed probabilty to be in state i !
See Also
--------
state_probabilities : to calculate `gamma`
""" |
return np.sum(gamma[0:T], axis=0, out=out) |
<SYSTEM_TASK:>
Retrieves the logger instance associated to the given name.
<END_TASK>
<USER_TASK:>
Description:
def logger(name='BHMM', pattern='%(asctime)s %(levelname)s %(name)s: %(message)s',
date_format='%H:%M:%S', handler=logging.StreamHandler(sys.stdout)):
"""
Retrieves the logger instance associated to the given name.
:param name: The name of the logger instance.
:type name: str
:param pattern: The associated pattern.
:type pattern: str
:param date_format: The date format to be used in the pattern.
:type date_format: str
:param handler: The logging handler, by default console output.
:type handler: FileHandler or StreamHandler or NullHandler
:return: The logger.
:rtype: Logger
""" |
_logger = logging.getLogger(name)
_logger.setLevel(config.log_level())
if not _logger.handlers:
formatter = logging.Formatter(pattern, date_format)
handler.setFormatter(formatter)
handler.setLevel(config.log_level())
_logger.addHandler(handler)
_logger.propagate = False
return _logger |
<SYSTEM_TASK:>
Sample from the BHMM posterior.
<END_TASK>
<USER_TASK:>
Description:
def sample(self, nsamples, nburn=0, nthin=1, save_hidden_state_trajectory=False,
call_back=None):
"""Sample from the BHMM posterior.
Parameters
----------
nsamples : int
The number of samples to generate.
nburn : int, optional, default=0
The number of samples to discard to burn-in, following which `nsamples` will be generated.
nthin : int, optional, default=1
The number of Gibbs sampling updates used to generate each returned sample.
save_hidden_state_trajectory : bool, optional, default=False
If True, the hidden state trajectory for each sample will be saved as well.
call_back : function, optional, default=None
a call back function with no arguments, which if given is being called
after each computed sample. This is useful for implementing progress bars.
Returns
-------
models : list of bhmm.HMM
The sampled HMM models from the Bayesian posterior.
Examples
--------
>>> from bhmm import testsystems
>>> [model, observations, states, sampled_model] = testsystems.generate_random_bhmm(ntrajectories=5, length=1000)
>>> nburn = 5 # run the sampler a bit before recording samples
>>> nsamples = 10 # generate 10 samples
>>> nthin = 2 # discard one sample in between each recorded sample
>>> samples = sampled_model.sample(nsamples, nburn=nburn, nthin=nthin)
""" |
# Run burn-in.
for iteration in range(nburn):
logger().info("Burn-in %8d / %8d" % (iteration, nburn))
self._update()
# Collect data.
models = list()
for iteration in range(nsamples):
logger().info("Iteration %8d / %8d" % (iteration, nsamples))
# Run a number of Gibbs sampling updates to generate each sample.
for thin in range(nthin):
self._update()
# Save a copy of the current model.
model_copy = copy.deepcopy(self.model)
# print "Sampled: \n",repr(model_copy)
if not save_hidden_state_trajectory:
model_copy.hidden_state_trajectory = None
models.append(model_copy)
if call_back is not None:
call_back()
# Return the list of models saved.
return models |
<SYSTEM_TASK:>
Update the current model using one round of Gibbs sampling.
<END_TASK>
<USER_TASK:>
Description:
def _update(self):
"""Update the current model using one round of Gibbs sampling.
""" |
initial_time = time.time()
self._updateHiddenStateTrajectories()
self._updateEmissionProbabilities()
self._updateTransitionMatrix()
final_time = time.time()
elapsed_time = final_time - initial_time
logger().info("BHMM update iteration took %.3f s" % elapsed_time) |
<SYSTEM_TASK:>
Updates the hidden-state transition matrix and the initial distribution
<END_TASK>
<USER_TASK:>
Description:
def _updateTransitionMatrix(self):
"""
Updates the hidden-state transition matrix and the initial distribution
""" |
# TRANSITION MATRIX
C = self.model.count_matrix() + self.prior_C # posterior count matrix
# check if we work with these options
if self.reversible and not _tmatrix_disconnected.is_connected(C, strong=True):
raise NotImplementedError('Encountered disconnected count matrix with sampling option reversible:\n '
+ str(C) + '\nUse prior to ensure connectivity or use reversible=False.')
# ensure consistent sparsity pattern (P0 might have additional zeros because of underflows)
# TODO: these steps work around a bug in msmtools. Should be fixed there
P0 = msmest.transition_matrix(C, reversible=self.reversible, maxiter=10000, warn_not_converged=False)
zeros = np.where(P0 + P0.T == 0)
C[zeros] = 0
# run sampler
Tij = msmest.sample_tmatrix(C, nsample=1, nsteps=self.transition_matrix_sampling_steps,
reversible=self.reversible)
# INITIAL DISTRIBUTION
if self.stationary: # p0 is consistent with P
p0 = _tmatrix_disconnected.stationary_distribution(Tij, C=C)
else:
n0 = self.model.count_init().astype(float)
first_timestep_counts_with_prior = n0 + self.prior_n0
positive = first_timestep_counts_with_prior > 0
p0 = np.zeros_like(n0)
p0[positive] = np.random.dirichlet(first_timestep_counts_with_prior[positive]) # sample p0 from posterior
# update HMM with new sample
self.model.update(p0, Tij) |
<SYSTEM_TASK:>
Computes the connected sets of C.
<END_TASK>
<USER_TASK:>
Description:
def connected_sets(C, mincount_connectivity=0, strong=True):
""" Computes the connected sets of C.
C : count matrix
mincount_connectivity : float
Minimum count which counts as a connection.
strong : boolean
True: Seek strongly connected sets. False: Seek weakly connected sets.
""" |
import msmtools.estimation as msmest
Cconn = C.copy()
Cconn[np.where(C <= mincount_connectivity)] = 0
# treat each connected set separately
S = msmest.connected_sets(Cconn, directed=strong)
return S |
<SYSTEM_TASK:>
Computes the strongly connected closed sets of C
<END_TASK>
<USER_TASK:>
Description:
def closed_sets(C, mincount_connectivity=0):
""" Computes the strongly connected closed sets of C """ |
n = np.shape(C)[0]
S = connected_sets(C, mincount_connectivity=mincount_connectivity, strong=True)
closed = []
for s in S:
mask = np.zeros(n, dtype=bool)
mask[s] = True
if C[np.ix_(mask, ~mask)].sum() == 0: # closed set, take it
closed.append(s)
return closed |
<SYSTEM_TASK:>
Returns the set of states that have at least one incoming or outgoing count
<END_TASK>
<USER_TASK:>
Description:
def nonempty_set(C, mincount_connectivity=0):
""" Returns the set of states that have at least one incoming or outgoing count """ |
# truncate to states with at least one observed incoming or outgoing count.
if mincount_connectivity > 0:
C = C.copy()
C[np.where(C < mincount_connectivity)] = 0
return np.where(C.sum(axis=0) + C.sum(axis=1) > 0)[0] |
<SYSTEM_TASK:>
Estimates full transition matrix for general connectivity structure
<END_TASK>
<USER_TASK:>
Description:
def estimate_P(C, reversible=True, fixed_statdist=None, maxiter=1000000, maxerr=1e-8, mincount_connectivity=0):
""" Estimates full transition matrix for general connectivity structure
Parameters
----------
C : ndarray
count matrix
reversible : bool
estimate reversible?
fixed_statdist : ndarray or None
estimate with given stationary distribution
maxiter : int
Maximum number of reversible iterations.
maxerr : float
Stopping criterion for reversible iteration: Will stop when infinity
norm of difference vector of two subsequent equilibrium distributions
is below maxerr.
mincount_connectivity : float
Minimum count which counts as a connection.
""" |
import msmtools.estimation as msmest
n = np.shape(C)[0]
# output matrix. Set initially to Identity matrix in order to handle empty states
P = np.eye(n, dtype=np.float64)
# decide if we need to proceed by weakly or strongly connected sets
if reversible and fixed_statdist is None: # reversible to unknown eq. dist. - use strongly connected sets.
S = connected_sets(C, mincount_connectivity=mincount_connectivity, strong=True)
for s in S:
mask = np.zeros(n, dtype=bool)
mask[s] = True
if C[np.ix_(mask, ~mask)].sum() > np.finfo(C.dtype).eps: # outgoing transitions - use partial rev algo.
transition_matrix_partial_rev(C, P, mask, maxiter=maxiter, maxerr=maxerr)
else: # closed set - use standard estimator
I = np.ix_(mask, mask)
if s.size > 1: # leave diagonal 1 if single closed state.
P[I] = msmest.transition_matrix(C[I], reversible=True, warn_not_converged=False,
maxiter=maxiter, maxerr=maxerr)
else: # nonreversible or given equilibrium distribution - weakly connected sets
S = connected_sets(C, mincount_connectivity=mincount_connectivity, strong=False)
for s in S:
I = np.ix_(s, s)
if not reversible:
Csub = C[I]
# any zero rows? must set Cii = 1 to avoid dividing by zero
zero_rows = np.where(Csub.sum(axis=1) == 0)[0]
Csub[zero_rows, zero_rows] = 1.0
P[I] = msmest.transition_matrix(Csub, reversible=False)
elif reversible and fixed_statdist is not None:
P[I] = msmest.transition_matrix(C[I], reversible=True, fixed_statdist=fixed_statdist,
maxiter=maxiter, maxerr=maxerr)
else: # unknown case
raise NotImplementedError('Transition estimation for the case reversible=' + str(reversible) +
' fixed_statdist=' + str(fixed_statdist is not None) + ' not implemented.')
# done
return P |
<SYSTEM_TASK:>
Maximum likelihood estimation of transition matrix which is reversible on parts
<END_TASK>
<USER_TASK:>
Description:
def transition_matrix_partial_rev(C, P, S, maxiter=1000000, maxerr=1e-8):
"""Maximum likelihood estimation of transition matrix which is reversible on parts
Partially-reversible estimation of transition matrix. Maximizes the likelihood:
.. math:
P_S &=& arg max prod_{S, :} (p_ij)^c_ij \\
\Pi_S P_{S,S} &=& \Pi_S P_{S,S}
where the product runs over all elements of the rows S, and detailed balance only
acts on the block with rows and columns S. :math:`\Pi_S` is the diagonal matrix of
equilibrium probabilities restricted to set S.
Note that this formulation
Parameters
----------
C : ndarray
full count matrix
P : ndarray
full transition matrix to write to. Will overwrite P[S]
S : ndarray, bool
boolean selection of reversible set with outgoing transitions
maxerr : float
maximum difference in matrix sums between iterations (infinity norm) in order to stop.
""" |
# test input
assert np.array_equal(C.shape, P.shape)
# constants
A = C[S][:, S]
B = C[S][:, ~S]
ATA = A + A.T
countsums = C[S].sum(axis=1)
# initialize
X = 0.5 * ATA
Y = C[S][:, ~S]
# normalize X, Y
totalsum = X.sum() + Y.sum()
X /= totalsum
Y /= totalsum
# rowsums
rowsums = X.sum(axis=1) + Y.sum(axis=1)
err = 1.0
it = 0
while err > maxerr and it < maxiter:
# update
d = countsums / rowsums
X = ATA / (d[:, None] + d)
Y = B / d[:, None]
# normalize X, Y
totalsum = X.sum() + Y.sum()
X /= totalsum
Y /= totalsum
# update sums
rowsums_new = X.sum(axis=1) + Y.sum(axis=1)
# compute error
err = np.max(np.abs(rowsums_new - rowsums))
# update
rowsums = rowsums_new
it += 1
# write to P
P[np.ix_(S, S)] = X
P[np.ix_(S, ~S)] = Y
P[S] /= P[S].sum(axis=1)[:, None] |
<SYSTEM_TASK:>
Enforces transition matrix P to be reversible on its closed sets.
<END_TASK>
<USER_TASK:>
Description:
def enforce_reversible_on_closed(P):
""" Enforces transition matrix P to be reversible on its closed sets. """ |
import msmtools.analysis as msmana
n = np.shape(P)[0]
Prev = P.copy()
# treat each weakly connected set separately
sets = closed_sets(P)
for s in sets:
I = np.ix_(s, s)
# compute stationary probability
pi_s = msmana.stationary_distribution(P[I])
# symmetrize
X_s = pi_s[:, None] * P[I]
X_s = 0.5 * (X_s + X_s.T)
# normalize
Prev[I] = X_s / X_s.sum(axis=1)[:, None]
return Prev |
<SYSTEM_TASK:>
Returns if P is reversible on its weakly connected sets
<END_TASK>
<USER_TASK:>
Description:
def is_reversible(P):
""" Returns if P is reversible on its weakly connected sets """ |
import msmtools.analysis as msmana
# treat each weakly connected set separately
sets = connected_sets(P, strong=False)
for s in sets:
Ps = P[s, :][:, s]
if not msmana.is_transition_matrix(Ps):
return False # isn't even a transition matrix!
pi = msmana.stationary_distribution(Ps)
X = pi[:, None] * Ps
if not np.allclose(X, X.T):
return False
# survived.
return True |
<SYSTEM_TASK:>
Simple estimator for stationary distribution for multiple strongly connected sets
<END_TASK>
<USER_TASK:>
Description:
def stationary_distribution(P, C=None, mincount_connectivity=0):
""" Simple estimator for stationary distribution for multiple strongly connected sets """ |
# can be replaced by msmtools.analysis.stationary_distribution in next msmtools release
from msmtools.analysis.dense.stationary_vector import stationary_distribution as msmstatdist
if C is None:
if is_connected(P, strong=True):
return msmstatdist(P)
else:
raise ValueError('Computing stationary distribution for disconnected matrix. Need count matrix.')
# disconnected sets
n = np.shape(C)[0]
ctot = np.sum(C)
pi = np.zeros(n)
# treat each weakly connected set separately
sets = connected_sets(C, mincount_connectivity=mincount_connectivity, strong=False)
for s in sets:
# compute weight
w = np.sum(C[s, :]) / ctot
pi[s] = w * msmstatdist(P[s, :][:, s])
# reinforce normalization
pi /= np.sum(pi)
return pi |
<SYSTEM_TASK:>
r""" Samples of the Gaussian distribution means
<END_TASK>
<USER_TASK:>
Description:
def means_samples(self):
r""" Samples of the Gaussian distribution means """ |
res = np.empty((self.nsamples, self.nstates, self.dimension), dtype=config.dtype)
for i in range(self.nsamples):
for j in range(self.nstates):
res[i, j, :] = self._sampled_hmms[i].means[j]
return res |
<SYSTEM_TASK:>
r""" Samples of the Gaussian distribution standard deviations
<END_TASK>
<USER_TASK:>
Description:
def sigmas_samples(self):
r""" Samples of the Gaussian distribution standard deviations """ |
res = np.empty((self.nsamples, self.nstates, self.dimension), dtype=config.dtype)
for i in range(self.nsamples):
for j in range(self.nstates):
res[i, j, :] = self._sampled_hmms[i].sigmas[j]
return res |
<SYSTEM_TASK:>
Suggests a HMM model type based on the observation data
<END_TASK>
<USER_TASK:>
Description:
def _guess_output_type(observations):
""" Suggests a HMM model type based on the observation data
Uses simple rules in order to decide which HMM model type makes sense based on observation data.
If observations consist of arrays/lists of integer numbers (irrespective of whether the python type is
int or float), our guess is 'discrete'.
If observations consist of arrays/lists of 1D-floats, our guess is 'discrete'.
In any other case, a TypeError is raised because we are not supporting that data type yet.
Parameters
----------
observations : list of lists or arrays
observation trajectories
Returns
-------
output_type : str
One of {'discrete', 'gaussian'}
""" |
from bhmm.util import types as _types
o1 = _np.array(observations[0])
# CASE: vector of int? Then we want a discrete HMM
if _types.is_int_vector(o1):
return 'discrete'
# CASE: not int type, but everything is an integral number. Then we also go for discrete
if _np.allclose(o1, _np.round(o1)):
isintegral = True
for i in range(1, len(observations)):
if not _np.allclose(observations[i], _np.round(observations[i])):
isintegral = False
break
if isintegral:
return 'discrete'
# CASE: vector of double? Then we want a gaussian
if _types.is_float_vector(o1):
return 'gaussian'
# None of the above? Then we currently do not support this format!
raise TypeError('Observations is neither sequences of integers nor 1D-sequences of floats. The current version'
'does not support your input.') |
<SYSTEM_TASK:>
r""" Create new trajectories that are subsampled at lag but shifted
<END_TASK>
<USER_TASK:>
Description:
def lag_observations(observations, lag, stride=1):
r""" Create new trajectories that are subsampled at lag but shifted
Given a trajectory (s0, s1, s2, s3, s4, ...) and lag 3, this function will generate 3 trajectories
(s0, s3, s6, ...), (s1, s4, s7, ...) and (s2, s5, s8, ...). Use this function in order to parametrize a MLE
at lag times larger than 1 without discarding data. Do not use this function for Bayesian estimators, where
data must be given such that subsequent transitions are uncorrelated.
Parameters
----------
observations : list of int arrays
observation trajectories
lag : int
lag time
stride : int, default=1
will return only one trajectory for every stride. Use this for Bayesian analysis.
""" |
obsnew = []
for obs in observations:
for shift in range(0, lag, stride):
obs_lagged = (obs[shift:][::lag])
if len(obs_lagged) > 1:
obsnew.append(obs_lagged)
return obsnew |
<SYSTEM_TASK:>
Initializes a 1D-Gaussian HMM
<END_TASK>
<USER_TASK:>
Description:
def gaussian_hmm(pi, P, means, sigmas):
""" Initializes a 1D-Gaussian HMM
Parameters
----------
pi : ndarray(nstates, )
Initial distribution.
P : ndarray(nstates,nstates)
Hidden transition matrix
means : ndarray(nstates, )
Means of Gaussian output distributions
sigmas : ndarray(nstates, )
Standard deviations of Gaussian output distributions
stationary : bool, optional, default=True
If True: initial distribution is equal to stationary distribution of transition matrix
reversible : bool, optional, default=True
If True: transition matrix will fulfill detailed balance constraints.
""" |
from bhmm.hmm.gaussian_hmm import GaussianHMM
from bhmm.output_models.gaussian import GaussianOutputModel
# count states
nstates = _np.array(P).shape[0]
# initialize output model
output_model = GaussianOutputModel(nstates, means, sigmas)
# initialize general HMM
from bhmm.hmm.generic_hmm import HMM as _HMM
ghmm = _HMM(pi, P, output_model)
# turn it into a Gaussian HMM
ghmm = GaussianHMM(ghmm)
return ghmm |
<SYSTEM_TASK:>
Initializes a discrete HMM
<END_TASK>
<USER_TASK:>
Description:
def discrete_hmm(pi, P, pout):
""" Initializes a discrete HMM
Parameters
----------
pi : ndarray(nstates, )
Initial distribution.
P : ndarray(nstates,nstates)
Hidden transition matrix
pout : ndarray(nstates,nsymbols)
Output matrix from hidden states to observable symbols
pi : ndarray(nstates, )
Fixed initial (if stationary=False) or fixed stationary distribution (if stationary=True).
stationary : bool, optional, default=True
If True: initial distribution is equal to stationary distribution of transition matrix
reversible : bool, optional, default=True
If True: transition matrix will fulfill detailed balance constraints.
""" |
from bhmm.hmm.discrete_hmm import DiscreteHMM
from bhmm.output_models.discrete import DiscreteOutputModel
# initialize output model
output_model = DiscreteOutputModel(pout)
# initialize general HMM
from bhmm.hmm.generic_hmm import HMM as _HMM
dhmm = _HMM(pi, P, output_model)
# turn it into a Gaussian HMM
dhmm = DiscreteHMM(dhmm)
return dhmm |
<SYSTEM_TASK:>
r""" Estimate maximum-likelihood HMM
<END_TASK>
<USER_TASK:>
Description:
def estimate_hmm(observations, nstates, lag=1, initial_model=None, output=None,
reversible=True, stationary=False, p=None, accuracy=1e-3, maxit=1000, maxit_P=100000,
mincount_connectivity=1e-2):
r""" Estimate maximum-likelihood HMM
Generic maximum-likelihood estimation of HMMs
Parameters
----------
observations : list of numpy arrays representing temporal data
`observations[i]` is a 1d numpy array corresponding to the observed trajectory index `i`
nstates : int
The number of states in the model.
lag : int
the lag time at which observations should be read
initial_model : HMM, optional, default=None
If specified, the given initial model will be used to initialize the BHMM.
Otherwise, a heuristic scheme is used to generate an initial guess.
output : str, optional, default=None
Output model type from [None, 'gaussian', 'discrete']. If None, will automatically select an output
model type based on the format of observations.
reversible : bool, optional, default=True
If True, a prior that enforces reversible transition matrices (detailed balance) is used;
otherwise, a standard non-reversible prior is used.
stationary : bool, optional, default=False
If True, the initial distribution of hidden states is self-consistently computed as the stationary
distribution of the transition matrix. If False, it will be estimated from the starting states.
Only set this to true if you're sure that the observation trajectories are initiated from a global
equilibrium distribution.
p : ndarray (nstates), optional, default=None
Initial or fixed stationary distribution. If given and stationary=True, transition matrices will be
estimated with the constraint that they have p as their stationary distribution. If given and
stationary=False, p is the fixed initial distribution of hidden states.
accuracy : float
convergence threshold for EM iteration. When two the likelihood does not increase by more than accuracy, the
iteration is stopped successfully.
maxit : int
stopping criterion for EM iteration. When so many iterations are performed without reaching the requested
accuracy, the iteration is stopped without convergence (a warning is given)
Return
------
hmm : :class:`HMM <bhmm.hmm.generic_hmm.HMM>`
""" |
# select output model type
if output is None:
output = _guess_output_type(observations)
if lag > 1:
observations = lag_observations(observations, lag)
# construct estimator
from bhmm.estimators.maximum_likelihood import MaximumLikelihoodEstimator as _MaximumLikelihoodEstimator
est = _MaximumLikelihoodEstimator(observations, nstates, initial_model=initial_model, output=output,
reversible=reversible, stationary=stationary, p=p, accuracy=accuracy,
maxit=maxit, maxit_P=maxit_P)
# run
est.fit()
# set lag time
est.hmm._lag = lag
# return model
# TODO: package into specific class (DiscreteHMM, GaussianHMM)
return est.hmm |
<SYSTEM_TASK:>
r""" Bayesian HMM based on sampling the posterior
<END_TASK>
<USER_TASK:>
Description:
def bayesian_hmm(observations, estimated_hmm, nsample=100, reversible=True, stationary=False,
p0_prior='mixed', transition_matrix_prior='mixed', store_hidden=False, call_back=None):
r""" Bayesian HMM based on sampling the posterior
Generic maximum-likelihood estimation of HMMs
Parameters
----------
observations : list of numpy arrays representing temporal data
`observations[i]` is a 1d numpy array corresponding to the observed trajectory index `i`
estimated_hmm : HMM
HMM estimated from estimate_hmm or initialize_hmm
reversible : bool, optional, default=True
If True, a prior that enforces reversible transition matrices (detailed balance) is used;
otherwise, a standard non-reversible prior is used.
stationary : bool, optional, default=False
If True, the stationary distribution of the transition matrix will be used as initial distribution.
Only use True if you are confident that the observation trajectories are started from a global
equilibrium. If False, the initial distribution will be estimated as usual from the first step
of the hidden trajectories.
nsample : int, optional, default=100
number of Gibbs sampling steps
p0_prior : None, str, float or ndarray(n)
Prior for the initial distribution of the HMM. Will only be active
if stationary=False (stationary=True means that p0 is identical to
the stationary distribution of the transition matrix).
Currently implements different versions of the Dirichlet prior that
is conjugate to the Dirichlet distribution of p0. p0 is sampled from:
.. math:
p0 \sim \prod_i (p0)_i^{a_i + n_i - 1}
where :math:`n_i` are the number of times a hidden trajectory was in
state :math:`i` at time step 0 and :math:`a_i` is the prior count.
Following options are available:
| 'mixed' (default), :math:`a_i = p_{0,init}`, where :math:`p_{0,init}`
is the initial distribution of initial_model.
| 'uniform', :math:`a_i = 1`
| ndarray(n) or float,
the given array will be used as A.
| None, :math:`a_i = 0`. This option ensures coincidence between
sample mean an MLE. Will sooner or later lead to sampling problems,
because as soon as zero trajectories are drawn from a given state,
the sampler cannot recover and that state will never serve as a starting
state subsequently. Only recommended in the large data regime and
when the probability to sample zero trajectories from any state
is negligible.
transition_matrix_prior : str or ndarray(n, n)
Prior for the HMM transition matrix.
Currently implements Dirichlet priors if reversible=False and reversible
transition matrix priors as described in [1]_ if reversible=True. For the
nonreversible case the posterior of transition matrix :math:`P` is:
.. math:
P \sim \prod_{i,j} p_{ij}^{b_{ij} + c_{ij} - 1}
where :math:`c_{ij}` are the number of transitions found for hidden
trajectories and :math:`b_{ij}` are prior counts.
| 'mixed' (default), :math:`b_{ij} = p_{ij,init}`, where :math:`p_{ij,init}`
is the transition matrix of initial_model. That means one prior
count will be used per row.
| 'uniform', :math:`b_{ij} = 1`
| ndarray(n, n) or broadcastable,
the given array will be used as B.
| None, :math:`b_ij = 0`. This option ensures coincidence between
sample mean an MLE. Will sooner or later lead to sampling problems,
because as soon as a transition :math:`ij` will not occur in a
sample, the sampler cannot recover and that transition will never
be sampled again. This option is not recommended unless you have
a small HMM and a lot of data.
store_hidden : bool, optional, default=False
store hidden trajectories in sampled HMMs
call_back : function, optional, default=None
a call back function with no arguments, which if given is being called
after each computed sample. This is useful for implementing progress bars.
Return
------
hmm : :class:`SampledHMM <bhmm.hmm.generic_sampled_hmm.SampledHMM>`
References
----------
.. [1] Trendelkamp-Schroer, B., H. Wu, F. Paul and F. Noe:
Estimation and uncertainty of reversible Markov models.
J. Chem. Phys. 143, 174101 (2015).
""" |
# construct estimator
from bhmm.estimators.bayesian_sampling import BayesianHMMSampler as _BHMM
sampler = _BHMM(observations, estimated_hmm.nstates, initial_model=estimated_hmm,
reversible=reversible, stationary=stationary, transition_matrix_sampling_steps=1000,
p0_prior=p0_prior, transition_matrix_prior=transition_matrix_prior,
output=estimated_hmm.output_model.model_type)
# Sample models.
sampled_hmms = sampler.sample(nsamples=nsample, save_hidden_state_trajectory=store_hidden,
call_back=call_back)
# return model
from bhmm.hmm.generic_sampled_hmm import SampledHMM
return SampledHMM(estimated_hmm, sampled_hmms) |
<SYSTEM_TASK:>
Computes the sum of arr assuming arr is in the log domain.
<END_TASK>
<USER_TASK:>
Description:
def logsumexp(arr, axis=0):
"""Computes the sum of arr assuming arr is in the log domain.
Returns log(sum(exp(arr))) while minimizing the possibility of
over/underflow.
Examples
--------
>>> import numpy as np
>>> from sklearn.utils.extmath import logsumexp
>>> a = np.arange(10)
>>> np.log(np.sum(np.exp(a)))
9.4586297444267107
>>> logsumexp(a)
9.4586297444267107
""" |
arr = np.rollaxis(arr, axis)
# Use the max to normalize, as with the log this is what accumulates
# the less errors
vmax = arr.max(axis=0)
out = np.log(np.sum(np.exp(arr - vmax), axis=0))
out += vmax
return out |
<SYSTEM_TASK:>
Convert a sparse matrix to a given format.
<END_TASK>
<USER_TASK:>
Description:
def _ensure_sparse_format(spmatrix, accept_sparse, dtype, order, copy,
force_all_finite):
"""Convert a sparse matrix to a given format.
Checks the sparse format of spmatrix and converts if necessary.
Parameters
----------
spmatrix : scipy sparse matrix
Input to validate and convert.
accept_sparse : string, list of string or None (default=None)
String[s] representing allowed sparse matrix formats ('csc',
'csr', 'coo', 'dok', 'bsr', 'lil', 'dia'). None means that sparse
matrix input will raise an error. If the input is sparse but not in
the allowed format, it will be converted to the first listed format.
dtype : string, type or None (default=none)
Data type of result. If None, the dtype of the input is preserved.
order : 'F', 'C' or None (default=None)
Whether an array will be forced to be fortran or c-style.
copy : boolean (default=False)
Whether a forced copy will be triggered. If copy=False, a copy might
be triggered by a conversion.
force_all_finite : boolean (default=True)
Whether to raise an error on np.inf and np.nan in X.
Returns
-------
spmatrix_converted : scipy sparse matrix.
Matrix that is ensured to have an allowed type.
""" |
if accept_sparse is None:
raise TypeError('A sparse matrix was passed, but dense '
'data is required. Use X.toarray() to '
'convert to a dense numpy array.')
sparse_type = spmatrix.format
if dtype is None:
dtype = spmatrix.dtype
if sparse_type in accept_sparse:
# correct type
if dtype == spmatrix.dtype:
# correct dtype
if copy:
spmatrix = spmatrix.copy()
else:
# convert dtype
spmatrix = spmatrix.astype(dtype)
else:
# create new
spmatrix = spmatrix.asformat(accept_sparse[0]).astype(dtype)
if force_all_finite:
if not hasattr(spmatrix, "data"):
warnings.warn("Can't check %s sparse matrix for nan or inf."
% spmatrix.format)
else:
_assert_all_finite(spmatrix.data)
if hasattr(spmatrix, "data"):
spmatrix.data = np.array(spmatrix.data, copy=False, order=order)
return spmatrix |
<SYSTEM_TASK:>
Input validation on an array, list, sparse matrix or similar.
<END_TASK>
<USER_TASK:>
Description:
def check_array(array, accept_sparse=None, dtype="numeric", order=None,
copy=False, force_all_finite=True, ensure_2d=True,
allow_nd=False, ensure_min_samples=1, ensure_min_features=1):
"""Input validation on an array, list, sparse matrix or similar.
By default, the input is converted to an at least 2nd numpy array.
If the dtype of the array is object, attempt converting to float,
raising on failure.
Parameters
----------
array : object
Input object to check / convert.
accept_sparse : string, list of string or None (default=None)
String[s] representing allowed sparse matrix formats, such as 'csc',
'csr', etc. None means that sparse matrix input will raise an error.
If the input is sparse but not in the allowed format, it will be
converted to the first listed format.
dtype : string, type or None (default="numeric")
Data type of result. If None, the dtype of the input is preserved.
If "numeric", dtype is preserved unless array.dtype is object.
order : 'F', 'C' or None (default=None)
Whether an array will be forced to be fortran or c-style.
copy : boolean (default=False)
Whether a forced copy will be triggered. If copy=False, a copy might
be triggered by a conversion.
force_all_finite : boolean (default=True)
Whether to raise an error on np.inf and np.nan in X.
ensure_2d : boolean (default=True)
Whether to make X at least 2d.
allow_nd : boolean (default=False)
Whether to allow X.ndim > 2.
ensure_min_samples : int (default=1)
Make sure that the array has a minimum number of samples in its first
axis (rows for a 2D array). Setting to 0 disables this check.
ensure_min_features : int (default=1)
Make sure that the 2D array has some minimum number of features
(columns). The default value of 1 rejects empty datasets.
This check is only enforced when the input data has effectively 2
dimensions or is originally 1D and ``ensure_2d`` is True. Setting to 0
disables this check.
Returns
-------
X_converted : object
The converted and validated X.
""" |
if isinstance(accept_sparse, str):
accept_sparse = [accept_sparse]
# store whether originally we wanted numeric dtype
dtype_numeric = dtype == "numeric"
if sp.issparse(array):
if dtype_numeric:
dtype = None
array = _ensure_sparse_format(array, accept_sparse, dtype, order,
copy, force_all_finite)
else:
if ensure_2d:
array = np.atleast_2d(array)
if dtype_numeric:
if hasattr(array, "dtype") and getattr(array.dtype, "kind", None) == "O":
# if input is object, convert to float.
dtype = np.float64
else:
dtype = None
array = np.array(array, dtype=dtype, order=order, copy=copy)
# make sure we actually converted to numeric:
if dtype_numeric and array.dtype.kind == "O":
array = array.astype(np.float64)
if not allow_nd and array.ndim >= 3:
raise ValueError("Found array with dim %d. Expected <= 2" %
array.ndim)
if force_all_finite:
_assert_all_finite(array)
shape_repr = _shape_repr(array.shape)
if ensure_min_samples > 0:
n_samples = _num_samples(array)
if n_samples < ensure_min_samples:
raise ValueError("Found array with %d sample(s) (shape=%s) while a"
" minimum of %d is required."
% (n_samples, shape_repr, ensure_min_samples))
if ensure_min_features > 0 and array.ndim == 2:
n_features = array.shape[1]
if n_features < ensure_min_features:
raise ValueError("Found array with %d feature(s) (shape=%s) while"
" a minimum of %d is required."
% (n_features, shape_repr, ensure_min_features))
return array |
<SYSTEM_TASK:>
Compute confidence intervals of beta distributions.
<END_TASK>
<USER_TASK:>
Description:
def beta_confidence_intervals(ci_X, ntrials, ci=0.95):
"""
Compute confidence intervals of beta distributions.
Parameters
----------
ci_X : numpy.array
Computed confidence interval estimate from `ntrials` experiments
ntrials : int
The number of trials that were run.
ci : float, optional, default=0.95
Confidence interval to report (e.g. 0.95 for 95% confidence interval)
Returns
-------
Plow : float
The lower bound of the symmetric confidence interval.
Phigh : float
The upper bound of the symmetric confidence interval.
Examples
--------
>>> ci_X = np.random.rand(10,10)
>>> ntrials = 100
>>> [Plow, Phigh] = beta_confidence_intervals(ci_X, ntrials)
""" |
# Compute low and high confidence interval for symmetric CI about mean.
ci_low = 0.5 - ci/2;
ci_high = 0.5 + ci/2;
# Compute for every element of ci_X.
from scipy.stats import beta
Plow = ci_X * 0.0;
Phigh = ci_X * 0.0;
for i in range(ci_X.shape[0]):
for j in range(ci_X.shape[1]):
Plow[i,j] = beta.ppf(ci_low, a = ci_X[i,j] * ntrials, b = (1-ci_X[i,j]) * ntrials);
Phigh[i,j] = beta.ppf(ci_high, a = ci_X[i,j] * ntrials, b = (1-ci_X[i,j]) * ntrials);
return [Plow, Phigh] |
<SYSTEM_TASK:>
Compute specified symmetric confidence interval for empirical sample.
<END_TASK>
<USER_TASK:>
Description:
def empirical_confidence_interval(sample, interval=0.95):
"""
Compute specified symmetric confidence interval for empirical sample.
Parameters
----------
sample : numpy.array
The empirical samples.
interval : float, optional, default=0.95
Size of desired symmetric confidence interval (0 < interval < 1)
e.g. 0.68 for 68% confidence interval, 0.95 for 95% confidence interval
Returns
-------
low : float
The lower bound of the symmetric confidence interval.
high : float
The upper bound of the symmetric confidence interval.
Examples
--------
>>> sample = np.random.randn(1000)
>>> [low, high] = empirical_confidence_interval(sample)
>>> [low, high] = empirical_confidence_interval(sample, interval=0.65)
>>> [low, high] = empirical_confidence_interval(sample, interval=0.99)
""" |
# Sort sample in increasing order.
sample = np.sort(sample)
# Determine sample size.
N = len(sample)
# Compute low and high indices.
low_index = int(np.round((N-1) * (0.5 - interval/2))) + 1
high_index = int(np.round((N-1) * (0.5 + interval/2))) + 1
# Compute low and high.
low = sample[low_index]
high = sample[high_index]
return [low, high] |
<SYSTEM_TASK:>
Computes the mean and alpha-confidence interval of the given sample set
<END_TASK>
<USER_TASK:>
Description:
def confidence_interval(data, alpha):
"""
Computes the mean and alpha-confidence interval of the given sample set
Parameters
----------
data : ndarray
a 1D-array of samples
alpha : float in [0,1]
the confidence level, i.e. percentage of data included in the interval
Returns
-------
[m,l,r] where m is the mean of the data, and (l,r) are the m-alpha/2 and m+alpha/2
confidence interval boundaries.
""" |
if alpha < 0 or alpha > 1:
raise ValueError('Not a meaningful confidence level: '+str(alpha))
# compute mean
m = np.mean(data)
# sort data
sdata = np.sort(data)
# index of the mean
im = np.searchsorted(sdata, m)
if im == 0 or im == len(sdata):
pm = im
else:
pm = (im-1) + (m-sdata[im-1]) / (sdata[im]-sdata[im-1])
# left interval boundary
pl = pm - alpha * pm
il1 = max(0, int(math.floor(pl)))
il2 = min(len(sdata)-1, int(math.ceil(pl)))
l = sdata[il1] + (pl - il1)*(sdata[il2] - sdata[il1])
# right interval boundary
pr = pm + alpha * (len(data)-im)
ir1 = max(0, int(math.floor(pr)))
ir2 = min(len(sdata)-1, int(math.ceil(pr)))
r = sdata[ir1] + (pr - ir1)*(sdata[ir2] - sdata[ir1])
# return
return m, l, r |
<SYSTEM_TASK:>
Return the connection status, both locally and remotely.
<END_TASK>
<USER_TASK:>
Description:
def status(self, remote=False):
"""
Return the connection status, both locally and remotely.
The local connection status is a dictionary that gives:
* the count of multiple queries sent to the server.
* the count of single queries sent to the server.
* the count of actions sent to the server.
* the count of actions executed successfully by the server.
* the count of actions queued to go to the server.
The remote connection status includes whether the server is live,
as well as data about version and build. The server data is
cached, unless the remote flag is specified.
:param remote: whether to query the server for its latest status
:return: tuple of status dicts: (local, server).
""" |
if remote:
components = urlparse.urlparse(self.endpoint)
try:
result = self.session.get(components[0] + "://" + components[1] + "/status", timeout=self.timeout)
except Exception as e:
if self.logger: self.logger.debug("Failed to connect to server for status: %s", e)
result = None
if result and result.status_code == 200:
self.server_status = result.json()
self.server_status["endpoint"] = self.endpoint
elif result:
if self.logger: self.logger.debug("Server status response not understandable: Status: %d, Body: %s",
result.status_code, result.text)
self.server_status = {"endpoint": self.endpoint,
"status": ("Unexpected HTTP status " + str(result.status_code) + " at: " +
strftime("%d %b %Y %H:%M:%S +0000", gmtime()))}
else:
self.server_status = {"endpoint": self.endpoint,
"status": "Unreachable at: " + strftime("%d %b %Y %H:%M:%S +0000", gmtime())}
return self.local_status, self.server_status |
<SYSTEM_TASK:>
Add commands at the end of the sequence.
<END_TASK>
<USER_TASK:>
Description:
def append(self, **kwargs):
"""
Add commands at the end of the sequence.
Be careful: because this runs in Python 2.x, the order of the kwargs dict may not match
the order in which the args were specified. Thus, if you care about specific ordering,
you must make multiple calls to append in that order. Luckily, append returns
the Action so you can compose easily: Action(...).append(...).append(...).
See also insert, below.
:param kwargs: the key/value pairs to add
:return: the action
""" |
for k, v in six.iteritems(kwargs):
self.commands.append({k: v})
return self |
<SYSTEM_TASK:>
Insert commands at the beginning of the sequence.
<END_TASK>
<USER_TASK:>
Description:
def insert(self, **kwargs):
"""
Insert commands at the beginning of the sequence.
This is provided because certain commands
have to come first (such as user creation), but may be need to beadded
after other commands have already been specified.
Later calls to insert put their commands before those in the earlier calls.
Also, since the order of iterated kwargs is not guaranteed (in Python 2.x),
you should really only call insert with one keyword at a time. See the doc of append
for more details.
:param kwargs: the key/value pair to append first
:return: the action, so you can append Action(...).insert(...).append(...)
""" |
for k, v in six.iteritems(kwargs):
self.commands.insert(0, {k: v})
return self |
<SYSTEM_TASK:>
Report a server error executing a command.
<END_TASK>
<USER_TASK:>
Description:
def report_command_error(self, error_dict):
"""
Report a server error executing a command.
We keep track of the command's position in the command list,
and we add annotation of what the command was, to the error.
:param error_dict: The server's error dict for the error encountered
""" |
error = dict(error_dict)
error["command"] = self.commands[error_dict["step"]]
error["target"] = self.frame
del error["index"] # throttling can change which action this was in the batch
del error["step"] # throttling can change which step this was in the action
self.errors.append(error) |
<SYSTEM_TASK:>
Return a list of commands that encountered execution errors, with the error.
<END_TASK>
<USER_TASK:>
Description:
def execution_errors(self):
"""
Return a list of commands that encountered execution errors, with the error.
Each dictionary entry gives the command dictionary and the error dictionary
:return: list of commands that gave errors, with their error information
""" |
if self.split_actions:
# throttling split this action, get errors from the split
return [dict(e) for s in self.split_actions for e in s.errors]
else:
return [dict(e) for e in self.errors] |
<SYSTEM_TASK:>
Fetch the next page of the query.
<END_TASK>
<USER_TASK:>
Description:
def _next_page(self):
"""
Fetch the next page of the query.
""" |
if self._last_page_seen:
raise StopIteration
new, self._last_page_seen = self.conn.query_multiple(self.object_type, self._next_page_index,
self.url_params, self.query_params)
self._next_page_index += 1
if len(new) == 0:
self._last_page_seen = True # don't bother with next page if nothing was returned
else:
self._results += new |
<SYSTEM_TASK:>
Fetch the queried object.
<END_TASK>
<USER_TASK:>
Description:
def _fetch_result(self):
"""
Fetch the queried object.
""" |
self._result = self.conn.query_single(self.object_type, self.url_params, self.query_params) |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.