def _batch_compute(args):
"""
Internal function to compute a batch of the time series in parallel.
Parameters
----------
args : tuple
Various attributes used for computing the batch.
(
batch_start : int
The starting index for this batch.
batch_end : int
The ending index for this batch.
ts : array_like
The time series to compute the matrix profile for.
query : array_like
The query.
window_size : int
The size of the window to compute the profile over.
data_length : int
The number of elements in the time series.
profile_length : int
The number of elements that will be in the final matrix
profile.
exclusion_zone : int
Used to exclude trivial matches.
is_join : bool
Flag to indicate if an AB join or self join is occuring.
data_mu : array_like
The moving average over the time series for the given window
size.
data_sig : array_like
The moving standard deviation over the time series for the
given window size.
first_product : array_like
The first sliding dot product for the time series over index
0 to window_size.
skip_locs : array_like
Indices that should be skipped for distance profile calculation
due to a nan or inf.
)
Returns
-------
dict : profile
The matrix profile, left and right matrix profiles and their respective
profile indices.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> }
"""
batch_start, batch_end, ts, query, window_size, data_length, \
profile_length, exclusion_zone, is_join, data_mu, data_sig, \
first_product, skip_locs = args
# initialize matrices
matrix_profile = np.full(profile_length, np.inf)
profile_index = np.full(profile_length, 0)
left_matrix_profile = None
right_matrix_profile = None
left_profile_index = None
right_profile_index = None
if not is_join:
left_matrix_profile = np.copy(matrix_profile)
right_matrix_profile = np.copy(matrix_profile)
left_profile_index = np.copy(profile_index)
right_profile_index = np.copy(profile_index)
# with batch 0 we do not need to recompute the dot product
# however with other batch windows, we need the previous iterations sliding
# dot product
last_product = None
if batch_start is 0:
first_window = query[batch_start:batch_start + window_size]
last_product = np.copy(first_product)
else:
first_window = query[batch_start - 1:batch_start + window_size - 1]
last_product = core.fft_convolve(ts, first_window)
query_sum = np.sum(first_window)
query_2sum = np.sum(first_window**2)
query_mu, query_sig = core.moving_avg_std(first_window, window_size)
drop_value = first_window[0]
# only compute the distance profile for index 0 and update
if batch_start is 0:
distance_profile = core.distance_profile(last_product, window_size,
data_mu, data_sig, query_mu,
query_sig)
# apply exclusion zone
distance_profile = core.apply_exclusion_zone(exclusion_zone, is_join,
window_size, data_length,
0, distance_profile)
# update the matrix profile
indices = (distance_profile < matrix_profile)
matrix_profile[indices] = distance_profile[indices]
profile_index[indices] = 0
batch_start += 1
# make sure to compute inclusively from batch start to batch end
# otherwise there are gaps in the profile
if batch_end < profile_length:
batch_end += 1
# iteratively compute distance profile and update with element-wise mins
for i in range(batch_start, batch_end):
# check for nan or inf and skip
if skip_locs[i]:
continue
query_window = query[i:i + window_size]
query_sum = query_sum - drop_value + query_window[-1]
query_2sum = query_2sum - drop_value**2 + query_window[-1]**2
query_mu = query_sum / window_size
query_sig2 = query_2sum / window_size - query_mu**2
query_sig = np.sqrt(query_sig2)
last_product[1:] = last_product[0:data_length - window_size] \
- ts[0:data_length - window_size] * drop_value \
+ ts[window_size:] * query_window[-1]
last_product[0] = first_product[i]
drop_value = query_window[0]
distance_profile = core.distance_profile(last_product, window_size,
data_mu, data_sig, query_mu,
query_sig)
# apply the exclusion zone
distance_profile = core.apply_exclusion_zone(exclusion_zone, is_join,
window_size, data_length,
i, distance_profile)
# update the matrix profile
indices = (distance_profile < matrix_profile)
matrix_profile[indices] = distance_profile[indices]
profile_index[indices] = i
# update the left and right matrix profiles
if not is_join:
# find differences, shift left and update
indices = distance_profile[i:] < left_matrix_profile[i:]
falses = np.zeros(i).astype('bool')
indices = np.append(falses, indices)
left_matrix_profile[indices] = distance_profile[indices]
left_profile_index[np.argwhere(indices)] = i
# find differences, shift right and update
indices = distance_profile[0:i] < right_matrix_profile[0:i]
falses = np.zeros(profile_length - i).astype('bool')
indices = np.append(indices, falses)
right_matrix_profile[indices] = distance_profile[indices]
right_profile_index[np.argwhere(indices)] = i
return {
'mp': matrix_profile,
'pi': profile_index,
'rmp': right_matrix_profile,
'rpi': right_profile_index,
'lmp': left_matrix_profile,
'lpi': left_profile_index,
}
def _batch_compute(args):
"""
Internal function to compute a batch of the time series in parallel.
Parameters
----------
args : tuple
Various attributes used for computing the batch.
(
batch_start : int
The starting index for this batch.
batch_end : int
The ending index for this batch.
ts : array_like
The time series to compute the matrix profile for.
query : array_like
The query.
window_size : int
The size of the window to compute the profile over.
data_length : int
The number of elements in the time series.
profile_length : int
The number of elements that will be in the final matrix
profile.
exclusion_zone : int
Used to exclude trivial matches.
data_mu : array_like
The moving average over the time series for the given window
size.
data_sig : array_like
The moving standard deviation over the time series for the
given window size.
first_product : array_like
The first sliding dot product for the time series over index
0 to window_size.
skip_locs : array_like
Indices that should be skipped for distance profile calculation
due to a nan or inf.
)
Returns
-------
dict : profile
The matrix profile, left and right matrix profiles and their respective
profile indices.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> }
"""
num_dim, batch_start, batch_end, ts, query, window_size, data_length, \
profile_length, exclusion_zone, data_mu, data_sig, \
first_product, skip_locs, profile_dimension, return_dimension = args
# initialize matrices
matrix_profile = np.full((num_dim, profile_length), np.inf)
profile_index = np.full((num_dim, profile_length), 0)
left_matrix_profile = None
right_matrix_profile = None
left_profile_index = None
right_profile_index = None
left_matrix_profile = np.copy(matrix_profile)
right_matrix_profile = np.copy(matrix_profile)
left_profile_index = np.copy(profile_index)
right_profile_index = np.copy(profile_index)
# with batch 0 we do not need to recompute the dot product
# however with other batch windows, we need the previous iterations sliding
# dot product
last_product = np.copy(first_product)
if batch_start is 0:
first_window = query[:, batch_start:batch_start + window_size]
else:
first_window = query[:, batch_start - 1:batch_start + window_size - 1]
for i in range(num_dim):
last_product[i, :] = core.fft_convolve(ts[i, :], first_window[i, :])
query_sum = np.sum(first_window, axis=1)
query_2sum = np.sum(first_window**2, axis=1)
query_mu, query_sig = np.empty(num_dim), np.empty(num_dim)
for i in range(num_dim):
query_mu[i], query_sig[i] = core.moving_avg_std(first_window[i, :], window_size)
drop_value = np.empty(num_dim)
for i in range(num_dim):
drop_value[i] = first_window[i, 0]
distance_profile = np.empty((num_dim, profile_length))
# make sure to compute inclusively from batch start to batch end
# otherwise there are gaps in the profile
if batch_end < profile_length:
batch_end += 1
# iteratively compute distance profile and update with element-wise mins
for i in range(batch_start, batch_end):
# check for nan or inf and skip
if skip_locs[i]:
continue
for j in range(num_dim):
if i == 0:
query_window = query[j, i:i + window_size]
distance_profile[j, :] = core.distance_profile(last_product[j, :], window_size, data_mu[j, :],
data_sig[j, :], query_mu[j], query_sig[j])
# apply exclusion zone
distance_profile[j, :] = core.apply_exclusion_zone(exclusion_zone, 0, window_size, data_length, 0,
distance_profile[j, :])
else:
query_window = query[j, i:i + window_size]
query_sum[j] = query_sum[j] - drop_value[j] + query_window[-1]
query_2sum[j] = query_2sum[j] - drop_value[j]**2 + query_window[-1]**2
query_mu[j] = query_sum[j] / window_size
query_sig2 = query_2sum[j] / window_size - query_mu[j]**2
if query_sig2 < _EPS:
query_sig2 = _EPS
query_sig[j] = np.sqrt(query_sig2)
last_product[j, 1:] = last_product[j, 0:data_length - window_size] \
- ts[j, 0:data_length - window_size] * drop_value[j] \
+ ts[j, window_size:] * query_window[-1]
last_product[j, 0] = first_product[j, i]
distance_profile[j, :] = core.distance_profile(last_product[j, :], window_size, data_mu[j, :],
data_sig[j, :], query_mu[j], query_sig[j])
# apply the exclusion zone
distance_profile[j, :] = core.apply_exclusion_zone(exclusion_zone, 0, window_size, data_length, i,
distance_profile[j, :])
distance_profile[j, distance_profile[j, :] < _EPS] = 0
drop_value[j] = query_window[0]
if np.any(query_sig < _EPS):
continue
distance_profile[:, skip_locs] = np.inf
distance_profile[data_sig < np.sqrt(_EPS)] = np.inf
distance_profile_dim = np.argsort(distance_profile, axis=0)
distance_profile_sort = np.sort(distance_profile, axis=0)
distance_profile_cumsum = np.zeros(profile_length)
for j in range(num_dim):
distance_profile_cumsum += distance_profile_sort[j, :]
distance_profile_mean = distance_profile_cumsum / (j + 1)
# update the matrix profile
indices = (distance_profile_mean < matrix_profile[j, :])
matrix_profile[j, indices] = distance_profile_mean[indices]
profile_index[j, indices] = i
if return_dimension:
profile_dimension[j][:, indices] = distance_profile_dim[:j + 1, indices]
# update the left and right matrix profiles
# find differences, shift left and update
indices = distance_profile_mean[i:] < left_matrix_profile[j, i:]
falses = np.zeros(i).astype('bool')
indices = np.append(falses, indices)
left_matrix_profile[j, indices] = distance_profile_mean[indices]
left_profile_index[j, np.argwhere(indices)] = i
# find differences, shift right and update
indices = distance_profile_mean[0:i] < right_matrix_profile[j, 0:i]
falses = np.zeros(profile_length - i).astype('bool')
indices = np.append(indices, falses)
right_matrix_profile[j, indices] = distance_profile_mean[indices]
right_profile_index[j, np.argwhere(indices)] = i
return {
'mp': matrix_profile,
'pi': profile_index,
'pd': profile_dimension,
'rmp': right_matrix_profile,
'rpi': right_profile_index,
'lmp': left_matrix_profile,
'lpi': left_profile_index,
}