-
Notifications
You must be signed in to change notification settings - Fork 1.3k
/
_peak_finder.py
181 lines (152 loc) · 6.15 KB
/
_peak_finder.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
import numpy as np
from .. utils import logger, verbose, _pl
@verbose
def peak_finder(x0, thresh=None, extrema=1, verbose=None):
"""Noise-tolerant fast peak-finding algorithm.
Parameters
----------
x0 : 1d array
A real vector from the maxima will be found (required).
thresh : float | None
The amount above surrounding data for a peak to be
identified. Larger values mean the algorithm is more selective in
finding peaks. If ``None``, use the default of
``(max(x0) - min(x0)) / 4``.
extrema : {-1, 1}
1 if maxima are desired, -1 if minima are desired
(default = maxima, 1).
%(verbose)s
Returns
-------
peak_loc : array
The indices of the identified peaks in x0.
peak_mag : array
The magnitude of the identified peaks.
Notes
-----
If repeated values are found the first is identified as the peak.
Conversion from initial Matlab code from:
Nathanael C. Yoder (ncyoder@purdue.edu)
Examples
--------
>>> import numpy as np
>>> from mne.preprocessing import peak_finder
>>> t = np.arange(0, 3, 0.01)
>>> x = np.sin(np.pi*t) - np.sin(0.5*np.pi*t)
>>> peak_locs, peak_mags = peak_finder(x) # doctest: +SKIP
>>> peak_locs # doctest: +SKIP
array([36, 260]) # doctest: +SKIP
>>> peak_mags # doctest: +SKIP
array([0.36900026, 1.76007351]) # doctest: +SKIP
"""
x0 = np.asanyarray(x0)
s = x0.size
if x0.ndim >= 2 or s == 0:
raise ValueError('The input data must be a non empty 1D vector')
if thresh is None:
thresh = (np.max(x0) - np.min(x0)) / 4
logger.debug('Peak finder automatic threshold: %0.2g' % (thresh,))
assert extrema in [-1, 1]
if extrema == -1:
x0 = extrema * x0 # Make it so we are finding maxima regardless
dx0 = np.diff(x0) # Find derivative
# This is so we find the first of repeated values
dx0[dx0 == 0] = -np.finfo(float).eps
# Find where the derivative changes sign
ind = np.where(dx0[:-1:] * dx0[1::] < 0)[0] + 1
# Include endpoints in potential peaks and valleys
x = np.concatenate((x0[:1], x0[ind], x0[-1:]))
ind = np.concatenate(([0], ind, [s - 1]))
del x0
# x only has the peaks, valleys, and endpoints
length = x.size
min_mag = np.min(x)
if length > 2: # Function with peaks and valleys
# Set initial parameters for loop
temp_mag = min_mag
found_peak = False
left_min = min_mag
# Deal with first point a little differently since tacked it on
# Calculate the sign of the derivative since we taked the first point
# on it does not necessarily alternate like the rest.
signDx = np.sign(np.diff(x[:3]))
if signDx[0] <= 0: # The first point is larger or equal to the second
ii = -1
if signDx[0] == signDx[1]: # Want alternating signs
x = np.concatenate((x[:1], x[2:]))
ind = np.concatenate((ind[:1], ind[2:]))
length -= 1
else: # First point is smaller than the second
ii = 0
if signDx[0] == signDx[1]: # Want alternating signs
x = x[1:]
ind = ind[1:]
length -= 1
# Preallocate max number of maxima
maxPeaks = int(np.ceil(length / 2.0))
peak_loc = np.zeros(maxPeaks, dtype=np.int64)
peak_mag = np.zeros(maxPeaks)
c_ind = 0
# Loop through extrema which should be peaks and then valleys
while ii < (length - 1):
ii += 1 # This is a peak
# Reset peak finding if we had a peak and the next peak is bigger
# than the last or the left min was small enough to reset.
if found_peak and ((x[ii] > peak_mag[-1]) or
(left_min < peak_mag[-1] - thresh)):
temp_mag = min_mag
found_peak = False
# Make sure we don't iterate past the length of our vector
if ii == length - 1:
break # We assign the last point differently out of the loop
# Found new peak that was lager than temp mag and threshold larger
# than the minimum to its left.
if (x[ii] > temp_mag) and (x[ii] > left_min + thresh):
temp_loc = ii
temp_mag = x[ii]
ii += 1 # Move onto the valley
# Come down at least thresh from peak
if not found_peak and (temp_mag > (thresh + x[ii])):
found_peak = True # We have found a peak
left_min = x[ii]
peak_loc[c_ind] = temp_loc # Add peak to index
peak_mag[c_ind] = temp_mag
c_ind += 1
elif x[ii] < left_min: # New left minima
left_min = x[ii]
# Check end point
if (x[-1] > temp_mag) and (x[-1] > (left_min + thresh)):
peak_loc[c_ind] = length - 1
peak_mag[c_ind] = x[-1]
c_ind += 1
elif not found_peak and temp_mag > min_mag:
# Check if we still need to add the last point
peak_loc[c_ind] = temp_loc
peak_mag[c_ind] = temp_mag
c_ind += 1
# Create output
peak_inds = ind[peak_loc[:c_ind]]
peak_mags = peak_mag[:c_ind]
else: # This is a monotone function where an endpoint is the only peak
x_ind = np.argmax(x)
peak_mags = x[x_ind]
if peak_mags > (min_mag + thresh):
peak_inds = ind[x_ind]
else:
peak_mags = []
peak_inds = []
# Change sign of data if was finding minima
if extrema < 0:
peak_mags *= -1.0
# ensure output type array
if not isinstance(peak_inds, np.ndarray):
peak_inds = np.atleast_1d(peak_inds).astype('int64')
if not isinstance(peak_mags, np.ndarray):
peak_mags = np.atleast_1d(peak_mags).astype('float64')
# Plot if no output desired
if len(peak_inds) == 0:
logger.info('No significant peaks found')
else:
logger.info('Found %d significant peak%s'
% (len(peak_inds), _pl(peak_inds)))
return peak_inds, peak_mags