# STUMPY
# Copyright 2019 TD Ameritrade. Released under the terms of the 3-Clause BSD license.
# STUMPY is a trademark of TD Ameritrade IP Company, Inc. All rights reserved.
import logging
import numpy as np
from . import core, config
from .stump import _stump
from .aamped import aamped
logger = logging.getLogger(__name__)
[docs]@core.non_normalized(aamped)
def stumped(dask_client, T_A, m, T_B=None, ignore_trivial=True, normalize=True):
"""
Compute the z-normalized matrix profile with a distributed dask cluster
This is a highly distributed implementation around the Numba JIT-compiled
parallelized `_stump` function which computes the matrix profile according
to STOMPopt with Pearson correlations.
Parameters
----------
dask_client : client
A Dask Distributed client that is connected to a Dask scheduler and
Dask workers. Setting up a Dask distributed cluster is beyond the
scope of this library. Please refer to the Dask Distributed
documentation.
T_A : ndarray
The time series or sequence for which to compute the matrix profile
m : int
Window size
T_B : ndarray, default None
The time series or sequence that will be used to annotate T_A. For every
subsequence in T_A, its nearest neighbor in T_B will be recorded. Default is
`None` which corresponds to a self-join.
ignore_trivial : bool, default True
Set to `True` if this is a self-join. Otherwise, for AB-join, set this
to `False`. Default is `True`.
normalize : bool, default True
When set to `True`, this z-normalizes subsequences prior to computing distances.
Otherwise, this function gets re-routed to its complementary non-normalized
equivalent set in the `@core.non_normalized` function decorator.
Returns
-------
out : ndarray
The first column consists of the matrix profile, the second column
consists of the matrix profile indices, the third column consists of
the left matrix profile indices, and the fourth column consists of
the right matrix profile indices.
Notes
-----
`DOI: 10.1007/s10115-017-1138-x \
<https://www.cs.ucr.edu/~eamonn/ten_quadrillion.pdf>`__
See Section 4.5
The above reference outlines a general approach for traversing the distance
matrix in a diagonal fashion rather than in a row-wise fashion.
`DOI: 10.1145/3357223.3362721 \
<https://www.cs.ucr.edu/~eamonn/public/GPU_Matrix_profile_VLDB_30DraftOnly.pdf>`__
See Section 3.1 and Section 3.3
The above reference outlines the use of the Pearson correlation via Welford's
centered sum-of-products along each diagonal of the distance matrix in place of the
sliding window dot product found in the original STOMP method.
`DOI: 10.1109/ICDM.2016.0085 \
<https://www.cs.ucr.edu/~eamonn/STOMP_GPU_final_submission_camera_ready.pdf>`__
See Table II
This is a Dask distributed implementation of stump that scales
across multiple servers and is a convenience wrapper around the
parallelized `stump._stump` function
Timeseries, T_A, will be annotated with the distance location
(or index) of all its subsequences in another times series, T_B.
Return: For every subsequence, Q, in T_A, you will get a distance
and index for the closest subsequence in T_B. Thus, the array
returned will have length T_A.shape[0]-m+1. Additionally, the
left and right matrix profiles are also returned.
Note: Unlike in the Table II where T_A.shape is expected to be equal
to T_B.shape, this implementation is generalized so that the shapes of
T_A and T_B can be different. In the case where T_A.shape == T_B.shape,
then our algorithm reduces down to the same algorithm found in Table II.
Additionally, unlike STAMP where the exclusion zone is m/2, the default
exclusion zone for STOMP is m/4 (See Definition 3 and Figure 3).
For self-joins, set `ignore_trivial = True` in order to avoid the
trivial match.
Note that left and right matrix profiles are only available for self-joins.
"""
if T_B is None:
T_B = T_A
ignore_trivial = True
(
T_A,
μ_Q,
σ_Q_inverse,
μ_Q_m_1,
T_A_subseq_isfinite,
T_A_subseq_isconstant,
) = core.preprocess_diagonal(T_A, m)
(
T_B,
M_T,
Σ_T_inverse,
M_T_m_1,
T_B_subseq_isfinite,
T_B_subseq_isconstant,
) = core.preprocess_diagonal(T_B, m)
if T_A.ndim != 1: # pragma: no cover
raise ValueError(
f"T_A is {T_A.ndim}-dimensional and must be 1-dimensional. "
"For multidimensional STUMP use `stumpy.mstump` or `stumpy.mstumped`"
)
if T_B.ndim != 1: # pragma: no cover
raise ValueError(
f"T_B is {T_B.ndim}-dimensional and must be 1-dimensional. "
"For multidimensional STUMP use `stumpy.mstump` or `stumpy.mstumped`"
)
core.check_window_size(m, max_size=min(T_A.shape[0], T_B.shape[0]))
if ignore_trivial is False and core.are_arrays_equal(T_A, T_B): # pragma: no cover
logger.warning("Arrays T_A, T_B are equal, which implies a self-join.")
logger.warning("Try setting `ignore_trivial = True`.")
if ignore_trivial and core.are_arrays_equal(T_A, T_B) is False: # pragma: no cover
logger.warning("Arrays T_A, T_B are not equal, which implies an AB-join.")
logger.warning("Try setting `ignore_trivial = False`.")
n_A = T_A.shape[0]
n_B = T_B.shape[0]
l = n_A - m + 1
excl_zone = int(np.ceil(m / config.STUMPY_EXCL_ZONE_DENOM))
out = np.empty((l, 4), dtype=object)
hosts = list(dask_client.ncores().keys())
nworkers = len(hosts)
if ignore_trivial:
diags = np.arange(excl_zone + 1, n_A - m + 1)
else:
diags = np.arange(-(n_A - m + 1) + 1, n_B - m + 1)
ndist_counts = core._count_diagonal_ndist(diags, m, n_A, n_B)
diags_ranges = core._get_array_ranges(ndist_counts, nworkers)
diags_ranges += diags[0]
# Scatter data to Dask cluster
T_A_future = dask_client.scatter(T_A, broadcast=True, hash=False)
T_B_future = dask_client.scatter(T_B, broadcast=True, hash=False)
M_T_future = dask_client.scatter(M_T, broadcast=True, hash=False)
μ_Q_future = dask_client.scatter(μ_Q, broadcast=True, hash=False)
Σ_T_inverse_future = dask_client.scatter(Σ_T_inverse, broadcast=True, hash=False)
σ_Q_inverse_future = dask_client.scatter(σ_Q_inverse, broadcast=True, hash=False)
M_T_m_1_future = dask_client.scatter(M_T_m_1, broadcast=True, hash=False)
μ_Q_m_1_future = dask_client.scatter(μ_Q_m_1, broadcast=True, hash=False)
T_A_subseq_isfinite_future = dask_client.scatter(
T_A_subseq_isfinite, broadcast=True, hash=False
)
T_B_subseq_isfinite_future = dask_client.scatter(
T_B_subseq_isfinite, broadcast=True, hash=False
)
T_A_subseq_isconstant_future = dask_client.scatter(
T_A_subseq_isconstant, broadcast=True, hash=False
)
T_B_subseq_isconstant_future = dask_client.scatter(
T_B_subseq_isconstant, broadcast=True, hash=False
)
diags_futures = []
for i, host in enumerate(hosts):
diags_future = dask_client.scatter(
np.arange(diags_ranges[i, 0], diags_ranges[i, 1]),
workers=[host],
hash=False,
)
diags_futures.append(diags_future)
futures = []
for i in range(len(hosts)):
futures.append(
dask_client.submit(
_stump,
T_A_future,
T_B_future,
m,
M_T_future,
μ_Q_future,
Σ_T_inverse_future,
σ_Q_inverse_future,
M_T_m_1_future,
μ_Q_m_1_future,
T_A_subseq_isfinite_future,
T_B_subseq_isfinite_future,
T_A_subseq_isconstant_future,
T_B_subseq_isconstant_future,
diags_futures[i],
ignore_trivial,
)
)
results = dask_client.gather(futures)
profile, indices = results[0]
for i in range(1, len(hosts)):
P, I = results[i]
for col in range(P.shape[1]): # pragma: no cover
cond = P[:, col] < profile[:, col]
profile[:, col] = np.where(cond, P[:, col], profile[:, col])
indices[:, col] = np.where(cond, I[:, col], indices[:, col])
out[:, 0] = profile[:, 0]
out[:, 1:4] = indices
# Delete data from Dask cluster
dask_client.cancel(T_A_future)
dask_client.cancel(T_B_future)
dask_client.cancel(M_T_future)
dask_client.cancel(μ_Q_future)
dask_client.cancel(Σ_T_inverse_future)
dask_client.cancel(σ_Q_inverse_future)
dask_client.cancel(M_T_m_1_future)
dask_client.cancel(μ_Q_m_1_future)
dask_client.cancel(T_A_subseq_isfinite_future)
dask_client.cancel(T_B_subseq_isfinite_future)
dask_client.cancel(T_A_subseq_isconstant_future)
dask_client.cancel(T_B_subseq_isconstant_future)
for diags_future in diags_futures:
dask_client.cancel(diags_future)
for future in futures:
dask_client.cancel(future)
threshold = 10e-6
if core.are_distances_too_small(out[:, 0], threshold=threshold): # pragma: no cover
logger.warning(f"A large number of values are smaller than {threshold}.")
logger.warning("For a self-join, try setting `ignore_trivial = True`.")
return out