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jonyrock/step_detect.py

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step_detect.py
"""
Thomas Kahn
thomas.b.kahn@gmail.com
"""
from __future__ import absolute_import
from math import sqrt
import multiprocessing as mp
import numpy as np
from six.moves import range
from six.moves import zip
def t_scan(L, window = 1e3, num_workers = -1):
"""
Computes t statistic for i to i+window points versus i-window to i
points for each point i in input array. Uses multiple processes to
do this calculation asynchronously. Array is decomposed into window
number of frames, each consisting of points spaced at window
intervals. This optimizes the calculation, as the drone function
need only compute the mean and variance for each set once.
Parameters
----------
L : numpy array
1 dimensional array that represents time series of datapoints
window : int / float
Number of points that comprise the windows of data that are
compared
num_workers : int
Number of worker processes for multithreaded t_stat computation
Defult value uses num_cpu - 1 workers
Returns
-------
t_stat : numpy array
Array which holds t statistic values for each point. The first
and last (window) points are replaced with zero, since the t
statistic calculation cannot be performed in that case.
"""
size = L.size
window = int(window)
frames = list(range(window))
n_cols = (size // window) - 1
t_stat = np.zeros((window, n_cols))
if num_workers == 1:
results = [_t_scan_drone(L, n_cols, frame, window) for frame in frames]
else:
if num_workers == -1:
num_workers = mp.cpu_count() - 1
pool = mp.Pool(processes = num_workers)
results = [pool.apply_async(_t_scan_drone, args=(L, n_cols, frame, window)) for frame in frames]
results = [r.get() for r in results]
pool.close()
for index, row in results:
t_stat[index] = row
t_stat = np.concatenate((
np.zeros(window),
t_stat.transpose().ravel(order='C'),
np.zeros(size % window)
))
return t_stat
def _t_scan_drone(L, n_cols, frame, window=1e3):
"""
Drone function for t_scan. Not Intended to be called manually.
Computes t_scan for the designated frame, and returns result as
array along with an integer tag for proper placement in the
aggregate array
"""
size = L.size
window = int(window)
root_n = sqrt(window)
output = np.zeros(n_cols)
b = L[frame:window+frame]
b_mean = b.mean()
b_var = b.var()
for i in range(window+frame, size-window, window):
a = L[i:i+window]
a_mean = a.mean()
a_var = a.var()
output[i // window - 1] = root_n * (a_mean - b_mean) / sqrt(a_var + b_var)
b_mean, b_var = a_mean, a_var
return frame, output
def mz_fwt(x, n=2):
"""
Computes the multiscale product of the Mallat-Zhong discrete forward
wavelet transform up to and including scale n for the input data x.
If n is even, the spikes in the signal will be positive. If n is odd
the spikes will match the polarity of the step (positive for steps
up, negative for steps down).
This function is essentially a direct translation of the MATLAB code
provided by Sadler and Swami in section A.4 of the following:
http://www.dtic.mil/dtic/tr/fulltext/u2/a351960.pdf
Parameters
----------
x : numpy array
1 dimensional array that represents time series of data points
n : int
Highest scale to multiply to
Returns
-------
prod : numpy array
The multiscale product for x
"""
N_pnts = x.size
lambda_j = [1.5, 1.12, 1.03, 1.01][0:n]
if n > 4:
lambda_j += [1.0]*(n-4)
H = np.array([0.125, 0.375, 0.375, 0.125])
G = np.array([2.0, -2.0])
Gn = [2]
Hn = [3]
for j in range(1,n):
q = 2**(j-1)
Gn.append(q+1)
Hn.append(3*q+1)
S = np.concatenate((x[::-1], x))
S = np.concatenate((S, x[::-1]))
prod = np.ones(N_pnts)
for j in range(n):
n_zeros = 2**j - 1
Gz = _insert_zeros(G, n_zeros)
Hz = _insert_zeros(H, n_zeros)
current = (1.0/lambda_j[j])*np.convolve(S,Gz)
current = current[N_pnts+Gn[j]:2*N_pnts+Gn[j]]
prod *= current
if j == n-1:
break
S_new = np.convolve(S, Hz)
S_new = S_new[N_pnts+Hn[j]:2*N_pnts+Hn[j]]
S = np.concatenate((S_new[::-1], S_new))
S = np.concatenate((S, S_new[::-1]))
return prod
def _insert_zeros(x, n):
"""
Helper function for mz_fwt. Splits input array and adds n zeros
between values.
"""
newlen = (n+1)*x.size
out = np.zeros(newlen)
indices = list(range(0, newlen-n, n+1))
out[indices] = x
return out
def find_steps(array, threshold):
"""
Finds local maxima by segmenting array based on positions at which
the threshold value is crossed. Note that this thresholding is
applied after the absolute value of the array is taken. Thus,
the distinction between upward and downward steps is lost. However,
get_step_sizes can be used to determine directionality after the
fact.
Parameters
----------
array : numpy array
1 dimensional array that represents time series of data points
threshold : int / float
Threshold value that defines a step
Returns
-------
steps : list
List of indices of the detected steps
"""
steps = []
array = np.abs(array)
above_points = np.where(array > threshold, 1, 0)
ap_dif = np.diff(above_points)
cross_ups = np.where(ap_dif == 1)[0]
cross_dns = np.where(ap_dif == -1)[0]
for upi, dni in zip(cross_ups,cross_dns):
steps.append(np.argmax(array[upi:dni]) + upi)
return steps
def get_step_sizes(array, indices, window=1000):
"""
Calculates step size for each index within the supplied list. Step
size is determined by averaging over a range of points (specified
by the window parameter) before and after the index of step
occurrence. The directionality of the step is reflected by the sign
of the step size (i.e. a positive value indicates an upward step,
and a negative value indicates a downward step). The combined
standard deviation of both measurements (as a measure of uncertainty
in step calculation) is also provided.
Parameters
----------
array : numpy array
1 dimensional array that represents time series of data points
indices : list
List of indices of the detected steps (as provided by
find_steps, for example)
window : int, optional
Number of points to average over to determine baseline levels
before and after step.
Returns
-------
step_sizes : list
List of the calculated sizes of each step
step_error : list
"""
step_sizes = []
step_error = []
indices = sorted(indices)
last = len(indices) - 1
for i, index in enumerate(indices):
if i == 0:
q = min(window, indices[i+1]-index)
elif i == last:
q = min(window, index - indices[i-1])
else:
q = min(window, index-indices[i-1], indices[i+1]-index)
a = array[index:index+q]
b = array[index-q:index]
step_sizes.append(a.mean() - b.mean())
step_error.append(sqrt(a.var()+b.var()))
return step_sizes, step_error
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