def mass2(ts, query):
"""
Compute the distance profile for the given query over the given time
series. Optionally, the correlation coefficient can be returned.
Parameters
----------
ts : array_like
The array to create a rolling window on.
query : array_like
The query.
Returns
-------
An array of distances.
Raises
------
ValueError
If ts is not a list or np.array.
If query is not a list or np.array.
If ts or query is not one dimensional.
"""
ts, query = mtscore.precheck_series_and_query(ts, query)
n = len(ts)
m = len(query)
x = ts
y = query
meany = np.mean(y)
sigmay = np.std(y)
meanx = mtscore.moving_average(x, m)
meanx = np.append(np.ones([1, len(x) - len(meanx)]), meanx)
sigmax = mtscore.moving_std(x, m)
sigmax = np.append(np.zeros([1, len(x) - len(sigmax)]), sigmax)
y = np.append(np.flip(y), np.zeros([1, n - m]))
X = np.fft.fft(x)
Y = np.fft.fft(y)
Y.resize(X.shape)
Z = X * Y
z = np.fft.ifft(Z)
dist = 2 * (m - (z[m - 1:n] - m * meanx[m - 1:n] * meany) /
(sigmax[m - 1:n] * sigmay))
dist = np.sqrt(dist)
return dist
def mass3(ts, query, pieces):
"""
Compute the distance profile for the given query over the given time
series. This version of MASS is hardware efficient given the right number
of pieces.
Parameters
----------
ts : array_like
The array to create a rolling window on.
query : array_like
The query.
pieces : int
Number of pieces to process. This is best as a power of 2.
Returns
-------
An array of distances.
Raises
------
ValueError
If ts is not a list or np.array.
If query is not a list or np.array.
If ts or query is not one dimensional.
If pieces is less than the length of the query.
"""
ts, query = mtscore.precheck_series_and_query(ts, query)
m = len(query)
if pieces < m:
raise ValueError('pieces should be larger than the query length.')
n = len(ts)
k = pieces
x = ts
dist = np.array([])
# compute stats in O(n)
meany = np.mean(query)
sigmay = np.std(query)
meanx = mtscore.moving_average(x, m)
meanx = np.append(np.ones([1, len(x) - len(meanx)]), meanx)
sigmax = mtscore.moving_std(x, m)
sigmax = np.append(np.zeros([1, len(x) - len(sigmax)]), sigmax)
# reverse the query and append zeros
y = np.append(np.flip(query), np.zeros(pieces - m))
step_size = k - m + 1
stop = n - k + 1
for j in range(0, stop, step_size):
# The main trick of getting dot products in O(n log n) time
X = np.fft.fft(x[j:j + k])
Y = np.fft.fft(y)
Z = X * Y
z = np.fft.ifft(Z)
d = 2 * (m - (z[m - 1:k] - m * meanx[m + j - 1:j + k] * meany) /
(sigmax[m + j - 1:j + k] * sigmay))
d = np.sqrt(d)
dist = np.append(dist, d)
j = j + k - m
k = n - j - 1
if k >= m:
X = np.fft.fft(x[j:n - 1])
y = y[0:k]
Y = np.fft.fft(y)
Z = X * Y
z = np.fft.ifft(Z)
d = 2 * (m - (z[m - 1:k] - m * meanx[j + m - 1:n - 1] * meany) /
(sigmax[j + m - 1:n - 1] * sigmay))
d = np.sqrt(d)
dist = np.append(dist, d)
return np.array(dist)
def test_moving_std():
a = np.array([1, 2, 3, 4, 5, 6])
actual = mtscore.moving_std(a, 3)
desired = np.array([0.81649658, 0.81649658, 0.81649658, 0.81649658])
np.testing.assert_almost_equal(actual, desired)