def test1(self):
"""truncated bins"""
u = self.data
cdf = percentile(u)
#open('./data/cdftest1','wb').write(str(cdf))
r = open('./data/cdftest1').read()
self.assertEqual(str(cdf), r)
def test0(self):
u = self.data
cdf = percentile(u, numbins=100)
cdf2 = eval(repr(cdf))
assert_array_almost_equal(cdf.percentiles, cdf2.percentiles)
assert_array_almost_equal(cdf.bin_edges, cdf2.bin_edges)
def test1(self):
"""truncated bins"""
u = self.data
cdf = percentile(u)
#open('./data/cdftest1','wb').write(str(cdf))
r = open('./data/cdftest1').read()
self.assertEqual(str(cdf), r)
def test0(self):
u = self.data
cdf = percentile(u, numbins=100)
cdf2 = eval(repr(cdf))
assert_array_almost_equal(cdf.percentiles, cdf2.percentiles)
assert_array_almost_equal(cdf.bin_edges, cdf2.bin_edges)
def test0(self):
u = self.data
cdf = percentile(u)
import matplotlib.pyplot as plt
fig = cdf.plot()
fig.savefig('./output/cdf.png')
plt.close('all')
def test0(self):
u = self.data
cdf = percentile(u)
import matplotlib.pyplot as plt
fig = cdf.plot()
fig.savefig('./output/cdf.png')
plt.close('all')
def test0(self):
r_bins = \
np.array([ -1050.231 , -1043.33599147, -1036.44098295, -1029.54597442,
-1022.6509659 , -1015.75595737, -1008.86094885, -1001.96594033,
-995.0709318 , -988.17592327, -981.28091475, -974.38590622,
-967.4908977 , -960.59588918, -953.70088065, -946.80587212,
-939.9108636 , -933.01585507, -926.12084655, -919.22583803,
-912.3308295 , -905.43582097, -898.54081245, -891.64580392,
-884.7507954 , -877.85578687, -870.96077835, -864.06576982,
-857.1707613 , -850.27575278, -843.38074425, -836.48573573,
-829.5907272 , -822.69571867, -815.80071015, -808.90570163,
-802.0106931 , -795.11568457, -788.22067605, -781.32566752,
-774.430659 , -767.53565048, -760.64064195, -753.74563343,
-746.8506249 , -739.95561637, -733.06060785, -726.16559932,
-719.2705908 , -712.37558227, -705.48057375, -698.58556522,
-691.6905567 , -684.79554818, -677.90053965, -671.00553112,
-664.1105226 , -657.21551407, -650.32050555, -643.42549702,
-636.5304885 , -629.63547997, -622.74047145, -615.84546292,
-608.9504544 , -602.05544588, -595.16043735, -588.26542882,
-581.3704203 , -574.47541177, -567.58040325, -560.68539472,
-553.7903862 , -546.89537767, -540.00036915, -533.10536063,
-526.2103521 , -519.31534357, -512.42033505, -505.52532652,
-498.630318 , -491.73530947, -484.84030095, -477.94529242,
-471.0502839 , -464.15527537, -457.26026685, -450.36525832,
-443.4702498 , -436.57524127, -429.68023275, -422.78522422,
-415.8902157 , -408.99520717, -402.10019865, -395.20519012,
-388.3101816 , -381.41517307, -374.52016455, -367.62515602,
-360.7301475 , -353.83513897, -346.94013045, -340.04512192,
-333.1501134 , -326.25510487, -319.36009635, -312.46508782,
-305.5700793 , -298.67507077, -291.78006225, -284.88505372,
-277.9900452 , -271.09503667, -264.20002815, -257.30501962,
-250.4100111 , -243.51500257, -236.61999405, -229.72498552,
-222.829977 , -215.93496847, -209.03995995, -202.14495142,
-195.2499429 , -188.35493437, -181.45992585, -174.56491732,
-167.6699088 , -160.77490027, -153.87989175, -146.98488322,
-140.0898747 , -133.19486617, -126.29985765, -119.40484912,
-112.5098406 , -105.61483207, -98.71982355, -91.82481502,
-84.9298065 , -78.03479797, -71.13978945, -64.24478092,
-57.3497724 , -50.45476387, -43.55975535, -36.66474682,
-29.7697383 , -22.87472977, -15.97972125, -9.08471272,
-2.1897042 , 4.70530433, 11.60031285, 18.49532138,
25.3903299 , 32.28533843, 39.18034695, 46.07535548,
52.970364 , 59.86537253, 66.76038105, 73.65538958,
80.5503981 , 87.44540663, 94.34041515, 101.23542368,
108.1304322 , 115.02544073, 121.92044925, 128.81545778,
135.7104663 , 142.60547483, 149.50048335, 156.39549188,
163.2905004 , 170.18550893, 177.08051745, 183.97552598,
190.8705345 , 197.76554303, 204.66055155, 211.55556008,
218.4505686 , 225.34557713, 232.24058565, 239.13559418,
246.0306027 , 252.92561123, 259.82061975, 266.71562828,
273.6106368 , 280.50564533, 287.40065385, 294.29566238,
301.1906709 , 308.08567943, 314.98068795, 321.87569648,
328.770705 ])
r_percentiles = \
np.array([ 0.00788452, 0.00860721, 0.00932989, 0.01005257, 0.01077526,
0.01149794, 0.01222062, 0.01294331, 0.01366599, 0.01438868,
0.01511136, 0.01949853, 0.02447029, 0.02685264, 0.029235 ,
0.03816535, 0.03870205, 0.03923875, 0.03977545, 0.04031214,
0.04084884, 0.04138554, 0.04192224, 0.04245893, 0.04299563,
0.04353233, 0.04406903, 0.04460572, 0.04514242, 0.04587917,
0.04666457, 0.04744996, 0.04823536, 0.04902075, 0.04980615,
0.05059154, 0.05137694, 0.05216234, 0.05515276, 0.05817619,
0.06144373, 0.06480917, 0.07465794, 0.08016102, 0.0870895 ,
0.08841823, 0.08974696, 0.09107569, 0.09240443, 0.09606674,
0.10644608, 0.11426144, 0.11800995, 0.12511504, 0.13906042,
0.14134499, 0.14362955, 0.1500741 , 0.15956579, 0.17179116,
0.18368956, 0.18592559, 0.18816161, 0.19211337, 0.19841317,
0.2029537 , 0.20541953, 0.20788537, 0.21266664, 0.22193011,
0.22927148, 0.23452336, 0.23801757, 0.24402634, 0.24829478,
0.2593486 , 0.26444222, 0.26710829, 0.2786814 , 0.28588673,
0.29055915, 0.30362949, 0.30988025, 0.31149286, 0.31310547,
0.31486499, 0.31998583, 0.33378933, 0.34527317, 0.36329378,
0.36957257, 0.37964864, 0.38529406, 0.38825826, 0.39021331,
0.39216836, 0.41376866, 0.42376066, 0.43533998, 0.460219 ,
0.47645825, 0.49932141, 0.51131487, 0.5139218 , 0.52057234,
0.52577312, 0.53170762, 0.54289616, 0.5514161 , 0.55749038,
0.56657762, 0.57084495, 0.5756384 , 0.58497631, 0.59406697,
0.60124967, 0.61191264, 0.61861008, 0.63526535, 0.64147876,
0.64424147, 0.64812518, 0.65628559, 0.6611236 , 0.66513402,
0.67247715, 0.6865401 , 0.69855775, 0.70405424, 0.70993554,
0.71712121, 0.74659026, 0.75933937, 0.76285267, 0.77698097,
0.77843327, 0.77988556, 0.78203854, 0.79001124, 0.79668959,
0.80160361, 0.81324827, 0.81889569, 0.83359027, 0.8376273 ,
0.84045596, 0.84676012, 0.85137567, 0.86174448, 0.86334239,
0.86940656, 0.88236389, 0.88443058, 0.88731063, 0.89183958,
0.89734229, 0.90254643, 0.90947058, 0.91505731, 0.92255361,
0.93161672, 0.93531119, 0.93928433, 0.94184878, 0.94358849,
0.9453282 , 0.94657215, 0.94779349, 0.94905589, 0.95096511,
0.95565876, 0.9591155 , 0.96179936, 0.96485932, 0.96873016,
0.97047112, 0.9715957 , 0.97272028, 0.97393729, 0.97516837,
0.97661306, 0.97872525, 0.97977577, 0.98043513, 0.98109449,
0.98175384, 0.98267924, 0.9861103 , 0.9879409 , 0.99216572,
0.99465729, 0.99529709, 0.99593689, 0.99657669, 0.99721649,
0.99777873, 0.99833404, 0.99888936, 0.99944468, 1. ])
u = self.data
cdf = percentile(u[:200])
np.testing.assert_array_almost_equal(r_bins, cdf.bin_edges)
np.testing.assert_array_almost_equal(r_percentiles, cdf.percentiles)
def test0(self):
u = self.data
cdf = percentile(u)
self.assertAlmostEqual(cdf.find(.5), -315.27959365994514)
def test_find_out_of_bounds2(self):
u = self.data
cdf = percentile(u)
with self.assertRaises(ValueError):
cdf.find(1.1)
def test_find_at_upper_bound(self):
u = self.data
cdf = percentile(u)
self.assertAlmostEqual(cdf.find(1.0), 806.14998224278111)
def test_find_at_lower_bound(self):
u = self.data
cdf = percentile(u)
self.assertAlmostEqual(cdf.find(0.0), -1265.052)
def fit_baseline(self, x, fs=60., _tsplot=False):
"""
fit_baseline(self, x[, fs=60.][, _tsplot=False])
Finds AR coefficients to build prediction errors and estimates baseline
prediction errors distribution. Returns the baseline entropy.
Parameters
----------
x : array_like
Input data. Should specify steering wheel angle over at least 120 s.
x[:N/2] is used to find the AR coefficients.
x[N/2:] is used to build the baseline prediciton error distribution.
fs : float
sampling rate of x in Hz. Default is 60 Hz. Be sure to specify fs if
x was not sampled at 60 Hz.
Returns
-------
hbas : float
baseline entropy
"""
# unpack relevant parameters
N = len(x)
M = self.M
alpha = self.alpha
resample_fs = self.resample_fs
# apply LP and downsample signal
_x = self._resample(x, fs)
Nx = len(_x)
if len(_x) < resample_fs * 60:
raise Exception('Need at least 60 seconds of steering '
'data to calculate baseline\n(ideally '
'need ~ 120 seconds of data).')
# use first half of x to find coefficients of AR model
# using Burg's method
#
# sign on coeffs returned by arburg is reversed
b_pe = arburg(_x[:Nx/2], 3)
# use second half of x to calculate baseline entropy
# use AR coefficents to build prediction errors
PE = lfilter(b_pe, 1, _x[Nx/2:])
# need to build bins to approximate the PE distribution
cdf = percentile(PE) # cdf is a CDF object
pe_alpha = 0.5*(abs(cdf.find(alpha)) + abs(cdf.find(1.-alpha)))
bin_edges = [-10e12]+list(np.linspace(-M, M, 2*M+1)*pe_alpha)+[10e12]
# now we can calculate the baseline entropy
# np.histogram returns a tuple of histogram counts and bin_edges
Pk = np.histogram(PE, bins=bin_edges)[0]/float(len(PE))
# replace small values to avoid excessively high entropy
Pk[Pk < 1e-3] = 1e-3
# and the baseline entropy is
hbas = np.sum(np.multiply(-Pk, np.log2(Pk)))
# store the relevant information
self.bin_edges = bin_edges
self.b_pe = b_pe
self.cdf = cdf
self.pkbas = Pk
self.hbas = hbas
if _tsplot:
return hbas, self._baseline_tsplot(x[N/2:], _x[Nx/2:], PE, fs)
return hbas
def test0(self):
u = self.data
cdf = percentile(u, numbins=100)
#open('./data/cdftest0','wb').write(str(cdf))
r = open('./data/cdftest0').read()
self.assertEqual(str(cdf), r)
def test0(self):
u = self.data
cdf = percentile(u, numbins=100)
#open('./data/cdftest0','wb').write(str(cdf))
r = open('./data/cdftest0').read()
self.assertEqual(str(cdf), r)
def test0(self):
u = self.data
cdf = percentile(u)
self.assertAlmostEqual(cdf.find(.5), -315.27959365994514)
def test0(self):
r_bins = \
np.array([ -1050.231 , -1043.33599147, -1036.44098295, -1029.54597442,
-1022.6509659 , -1015.75595737, -1008.86094885, -1001.96594033,
-995.0709318 , -988.17592327, -981.28091475, -974.38590622,
-967.4908977 , -960.59588918, -953.70088065, -946.80587212,
-939.9108636 , -933.01585507, -926.12084655, -919.22583803,
-912.3308295 , -905.43582097, -898.54081245, -891.64580392,
-884.7507954 , -877.85578687, -870.96077835, -864.06576982,
-857.1707613 , -850.27575278, -843.38074425, -836.48573573,
-829.5907272 , -822.69571867, -815.80071015, -808.90570163,
-802.0106931 , -795.11568457, -788.22067605, -781.32566752,
-774.430659 , -767.53565048, -760.64064195, -753.74563343,
-746.8506249 , -739.95561637, -733.06060785, -726.16559932,
-719.2705908 , -712.37558227, -705.48057375, -698.58556522,
-691.6905567 , -684.79554818, -677.90053965, -671.00553112,
-664.1105226 , -657.21551407, -650.32050555, -643.42549702,
-636.5304885 , -629.63547997, -622.74047145, -615.84546292,
-608.9504544 , -602.05544588, -595.16043735, -588.26542882,
-581.3704203 , -574.47541177, -567.58040325, -560.68539472,
-553.7903862 , -546.89537767, -540.00036915, -533.10536063,
-526.2103521 , -519.31534357, -512.42033505, -505.52532652,
-498.630318 , -491.73530947, -484.84030095, -477.94529242,
-471.0502839 , -464.15527537, -457.26026685, -450.36525832,
-443.4702498 , -436.57524127, -429.68023275, -422.78522422,
-415.8902157 , -408.99520717, -402.10019865, -395.20519012,
-388.3101816 , -381.41517307, -374.52016455, -367.62515602,
-360.7301475 , -353.83513897, -346.94013045, -340.04512192,
-333.1501134 , -326.25510487, -319.36009635, -312.46508782,
-305.5700793 , -298.67507077, -291.78006225, -284.88505372,
-277.9900452 , -271.09503667, -264.20002815, -257.30501962,
-250.4100111 , -243.51500257, -236.61999405, -229.72498552,
-222.829977 , -215.93496847, -209.03995995, -202.14495142,
-195.2499429 , -188.35493437, -181.45992585, -174.56491732,
-167.6699088 , -160.77490027, -153.87989175, -146.98488322,
-140.0898747 , -133.19486617, -126.29985765, -119.40484912,
-112.5098406 , -105.61483207, -98.71982355, -91.82481502,
-84.9298065 , -78.03479797, -71.13978945, -64.24478092,
-57.3497724 , -50.45476387, -43.55975535, -36.66474682,
-29.7697383 , -22.87472977, -15.97972125, -9.08471272,
-2.1897042 , 4.70530433, 11.60031285, 18.49532138,
25.3903299 , 32.28533843, 39.18034695, 46.07535548,
52.970364 , 59.86537253, 66.76038105, 73.65538958,
80.5503981 , 87.44540663, 94.34041515, 101.23542368,
108.1304322 , 115.02544073, 121.92044925, 128.81545778,
135.7104663 , 142.60547483, 149.50048335, 156.39549188,
163.2905004 , 170.18550893, 177.08051745, 183.97552598,
190.8705345 , 197.76554303, 204.66055155, 211.55556008,
218.4505686 , 225.34557713, 232.24058565, 239.13559418,
246.0306027 , 252.92561123, 259.82061975, 266.71562828,
273.6106368 , 280.50564533, 287.40065385, 294.29566238,
301.1906709 , 308.08567943, 314.98068795, 321.87569648,
328.770705 ])
r_percentiles = \
np.array([ 0.00788452, 0.00860721, 0.00932989, 0.01005257, 0.01077526,
0.01149794, 0.01222062, 0.01294331, 0.01366599, 0.01438868,
0.01511136, 0.01949853, 0.02447029, 0.02685264, 0.029235 ,
0.03816535, 0.03870205, 0.03923875, 0.03977545, 0.04031214,
0.04084884, 0.04138554, 0.04192224, 0.04245893, 0.04299563,
0.04353233, 0.04406903, 0.04460572, 0.04514242, 0.04587917,
0.04666457, 0.04744996, 0.04823536, 0.04902075, 0.04980615,
0.05059154, 0.05137694, 0.05216234, 0.05515276, 0.05817619,
0.06144373, 0.06480917, 0.07465794, 0.08016102, 0.0870895 ,
0.08841823, 0.08974696, 0.09107569, 0.09240443, 0.09606674,
0.10644608, 0.11426144, 0.11800995, 0.12511504, 0.13906042,
0.14134499, 0.14362955, 0.1500741 , 0.15956579, 0.17179116,
0.18368956, 0.18592559, 0.18816161, 0.19211337, 0.19841317,
0.2029537 , 0.20541953, 0.20788537, 0.21266664, 0.22193011,
0.22927148, 0.23452336, 0.23801757, 0.24402634, 0.24829478,
0.2593486 , 0.26444222, 0.26710829, 0.2786814 , 0.28588673,
0.29055915, 0.30362949, 0.30988025, 0.31149286, 0.31310547,
0.31486499, 0.31998583, 0.33378933, 0.34527317, 0.36329378,
0.36957257, 0.37964864, 0.38529406, 0.38825826, 0.39021331,
0.39216836, 0.41376866, 0.42376066, 0.43533998, 0.460219 ,
0.47645825, 0.49932141, 0.51131487, 0.5139218 , 0.52057234,
0.52577312, 0.53170762, 0.54289616, 0.5514161 , 0.55749038,
0.56657762, 0.57084495, 0.5756384 , 0.58497631, 0.59406697,
0.60124967, 0.61191264, 0.61861008, 0.63526535, 0.64147876,
0.64424147, 0.64812518, 0.65628559, 0.6611236 , 0.66513402,
0.67247715, 0.6865401 , 0.69855775, 0.70405424, 0.70993554,
0.71712121, 0.74659026, 0.75933937, 0.76285267, 0.77698097,
0.77843327, 0.77988556, 0.78203854, 0.79001124, 0.79668959,
0.80160361, 0.81324827, 0.81889569, 0.83359027, 0.8376273 ,
0.84045596, 0.84676012, 0.85137567, 0.86174448, 0.86334239,
0.86940656, 0.88236389, 0.88443058, 0.88731063, 0.89183958,
0.89734229, 0.90254643, 0.90947058, 0.91505731, 0.92255361,
0.93161672, 0.93531119, 0.93928433, 0.94184878, 0.94358849,
0.9453282 , 0.94657215, 0.94779349, 0.94905589, 0.95096511,
0.95565876, 0.9591155 , 0.96179936, 0.96485932, 0.96873016,
0.97047112, 0.9715957 , 0.97272028, 0.97393729, 0.97516837,
0.97661306, 0.97872525, 0.97977577, 0.98043513, 0.98109449,
0.98175384, 0.98267924, 0.9861103 , 0.9879409 , 0.99216572,
0.99465729, 0.99529709, 0.99593689, 0.99657669, 0.99721649,
0.99777873, 0.99833404, 0.99888936, 0.99944468, 1. ])
u = self.data
cdf = percentile(u[:200])
np.testing.assert_array_almost_equal(r_bins, cdf.bin_edges)
np.testing.assert_array_almost_equal(r_percentiles, cdf.percentiles)
def test_find_out_of_bounds2(self):
u = self.data
cdf = percentile(u)
with self.assertRaises(ValueError):
cdf.find(1.1)
def test_find_at_upper_bound(self):
u = self.data
cdf = percentile(u)
self.assertAlmostEqual(cdf.find(1.0), 806.14998224278111)
def test1_spec_numbins(self):
r_bins = \
np.array([ -1265.052 , -1244.1328598, -1223.2137196, -1202.2945794,
-1181.3754392, -1160.456299 , -1139.5371588, -1118.6180186,
-1097.6988784, -1076.7797382, -1055.860598 , -1034.9414578,
-1014.0223176, -993.1031774, -972.1840372, -951.264897 ,
-930.3457568, -909.4266166, -888.5074764, -867.5883362,
-846.669196 , -825.7500558, -804.8309156, -783.9117754,
-762.9926352, -742.073495 , -721.1543548, -700.2352146,
-679.3160744, -658.3969342, -637.477794 , -616.5586538,
-595.6395136, -574.7203734, -553.8012332, -532.882093 ,
-511.9629528, -491.0438126, -470.1246724, -449.2055322,
-428.286392 , -407.3672518, -386.4481116, -365.5289714,
-344.6098312, -323.690691 , -302.7715508, -281.8524106,
-260.9332704, -240.0141302, -219.09499 , -198.1758498,
-177.2567096, -156.3375694, -135.4184292, -114.499289 ,
-93.5801488, -72.6610086, -51.7418684, -30.8227282,
-9.903588 , 11.0155522, 31.9346924, 52.8538326,
73.7729728, 94.692113 , 115.6112532, 136.5303934,
157.4495336, 178.3686738, 199.287814 , 220.2069542,
241.1260944, 262.0452346, 282.9643748, 303.883515 ,
324.8026552, 345.7217954, 366.6409356, 387.5600758,
408.479216 , 429.3983562, 450.3174964, 471.2366366,
492.1557768, 513.074917 , 533.9940572, 554.9131974,
575.8323376, 596.7514778, 617.670618 , 638.5897582,
659.5088984, 680.4280386, 701.3471788, 722.266319 ,
743.1854592, 764.1045994, 785.0237396, 805.9428798,
826.86202 ])
r_percentiles = \
np.array([ 1.52682325e-04, 2.94558006e-04, 6.16047975e-04,
7.02918092e-04, 7.73474112e-04, 8.21793025e-04,
8.70111939e-04, 1.10401110e-03, 1.34481409e-03,
1.83295542e-03, 2.47881609e-03, 3.68607187e-03,
5.15865394e-03, 6.73055980e-03, 8.61060936e-03,
1.04788857e-02, 1.23147839e-02, 1.56306574e-02,
1.87118249e-02, 2.12461678e-02, 2.56479572e-02,
3.05641053e-02, 3.62309399e-02, 4.08826236e-02,
4.93068431e-02, 5.73786087e-02, 6.70094435e-02,
7.80975453e-02, 8.85867316e-02, 9.97965662e-02,
1.13123710e-01, 1.25876664e-01, 1.42376196e-01,
1.62244613e-01, 1.83208974e-01, 2.05366050e-01,
2.29556330e-01, 2.53282959e-01, 2.77540635e-01,
3.05427136e-01, 3.36100492e-01, 3.63831154e-01,
3.94043118e-01, 4.25583501e-01, 4.55163960e-01,
4.86837208e-01, 5.20599620e-01, 5.48129193e-01,
5.78151849e-01, 6.08547876e-01, 6.40669188e-01,
6.70746937e-01, 7.01026286e-01, 7.25971707e-01,
7.51021605e-01, 7.77398045e-01, 8.00059380e-01,
8.22450308e-01, 8.40847440e-01, 8.57498407e-01,
8.75729509e-01, 8.91310252e-01, 9.05933655e-01,
9.18565943e-01, 9.29274795e-01, 9.40657581e-01,
9.48881056e-01, 9.57538817e-01, 9.63601434e-01,
9.70164957e-01, 9.75166523e-01, 9.79733128e-01,
9.83692163e-01, 9.86929642e-01, 9.89432271e-01,
9.91544580e-01, 9.93344271e-01, 9.94115203e-01,
9.95269177e-01, 9.96206415e-01, 9.97047263e-01,
9.97575959e-01, 9.98237416e-01, 9.98678170e-01,
9.98903131e-01, 9.99062383e-01, 9.99389219e-01,
9.99710548e-01, 9.99739859e-01, 9.99802006e-01,
9.99820441e-01, 9.99861218e-01, 9.99912599e-01,
9.99946445e-01, 9.99963921e-01, 9.99975528e-01,
9.99981646e-01, 9.99987764e-01, 9.99993882e-01,
1.00000000e+00])
u = self.data
cdf = percentile(u, numbins=100)
np.testing.assert_array_almost_equal(r_bins, cdf.bin_edges)
np.testing.assert_array_almost_equal(r_percentiles, cdf.percentiles)
def test_find_at_lower_bound(self):
u = self.data
cdf = percentile(u)
self.assertAlmostEqual(cdf.find(0.0), -1265.052)
def fit_baseline(self, x, fs=60., _tsplot=False):
"""
fit_baseline(self, x[, fs=60.][, _tsplot=False])
Finds AR coefficients to build prediction errors and estimates baseline
prediction errors distribution. Returns the baseline entropy.
Parameters
----------
x : array_like
Input data. Should specify steering wheel angle over at least 120 s.
x[:N/2] is used to find the AR coefficients.
x[N/2:] is used to build the baseline prediciton error distribution.
fs : float
sampling rate of x in Hz. Default is 60 Hz. Be sure to specify fs if
x was not sampled at 60 Hz.
Returns
-------
hbas : float
baseline entropy
"""
# unpack relevant parameters
N = len(x)
M = self.M
alpha = self.alpha
resample_fs = self.resample_fs
# apply LP and downsample signal
_x = self._resample(x, fs)
Nx = len(_x)
if len(_x) < resample_fs * 60:
raise Exception('Need at least 60 seconds of steering '
'data to calculate baseline\n(ideally '
'need ~ 120 seconds of data).')
# use first half of x to find coefficients of AR model
# using Burg's method
#
# sign on coeffs returned by arburg is reversed
b_pe = arburg(_x[:Nx / 2], 3)
# use second half of x to calculate baseline entropy
# use AR coefficents to build prediction errors
PE = lfilter(b_pe, 1, _x[Nx / 2:])
# need to build bins to approximate the PE distribution
cdf = percentile(PE) # cdf is a CDF object
pe_alpha = 0.5 * (abs(cdf.find(alpha)) + abs(cdf.find(1. - alpha)))
bin_edges = [-10e12] + list(
np.linspace(-M, M, 2 * M + 1) * pe_alpha) + [10e12]
# now we can calculate the baseline entropy
# np.histogram returns a tuple of histogram counts and bin_edges
Pk = np.histogram(PE, bins=bin_edges)[0] / float(len(PE))
# replace small values to avoid excessively high entropy
Pk[Pk < 1e-3] = 1e-3
# and the baseline entropy is
hbas = np.sum(np.multiply(-Pk, np.log2(Pk)))
# store the relevant information
self.bin_edges = bin_edges
self.b_pe = b_pe
self.cdf = cdf
self.pkbas = Pk
self.hbas = hbas
if _tsplot:
return hbas, self._baseline_tsplot(x[N / 2:], _x[Nx / 2:], PE, fs)
return hbas
def test1_spec_numbins(self):
r_bins = \
np.array([ -1265.052 , -1244.1328598, -1223.2137196, -1202.2945794,
-1181.3754392, -1160.456299 , -1139.5371588, -1118.6180186,
-1097.6988784, -1076.7797382, -1055.860598 , -1034.9414578,
-1014.0223176, -993.1031774, -972.1840372, -951.264897 ,
-930.3457568, -909.4266166, -888.5074764, -867.5883362,
-846.669196 , -825.7500558, -804.8309156, -783.9117754,
-762.9926352, -742.073495 , -721.1543548, -700.2352146,
-679.3160744, -658.3969342, -637.477794 , -616.5586538,
-595.6395136, -574.7203734, -553.8012332, -532.882093 ,
-511.9629528, -491.0438126, -470.1246724, -449.2055322,
-428.286392 , -407.3672518, -386.4481116, -365.5289714,
-344.6098312, -323.690691 , -302.7715508, -281.8524106,
-260.9332704, -240.0141302, -219.09499 , -198.1758498,
-177.2567096, -156.3375694, -135.4184292, -114.499289 ,
-93.5801488, -72.6610086, -51.7418684, -30.8227282,
-9.903588 , 11.0155522, 31.9346924, 52.8538326,
73.7729728, 94.692113 , 115.6112532, 136.5303934,
157.4495336, 178.3686738, 199.287814 , 220.2069542,
241.1260944, 262.0452346, 282.9643748, 303.883515 ,
324.8026552, 345.7217954, 366.6409356, 387.5600758,
408.479216 , 429.3983562, 450.3174964, 471.2366366,
492.1557768, 513.074917 , 533.9940572, 554.9131974,
575.8323376, 596.7514778, 617.670618 , 638.5897582,
659.5088984, 680.4280386, 701.3471788, 722.266319 ,
743.1854592, 764.1045994, 785.0237396, 805.9428798,
826.86202 ])
r_percentiles = \
np.array([ 1.52682325e-04, 2.94558006e-04, 6.16047975e-04,
7.02918092e-04, 7.73474112e-04, 8.21793025e-04,
8.70111939e-04, 1.10401110e-03, 1.34481409e-03,
1.83295542e-03, 2.47881609e-03, 3.68607187e-03,
5.15865394e-03, 6.73055980e-03, 8.61060936e-03,
1.04788857e-02, 1.23147839e-02, 1.56306574e-02,
1.87118249e-02, 2.12461678e-02, 2.56479572e-02,
3.05641053e-02, 3.62309399e-02, 4.08826236e-02,
4.93068431e-02, 5.73786087e-02, 6.70094435e-02,
7.80975453e-02, 8.85867316e-02, 9.97965662e-02,
1.13123710e-01, 1.25876664e-01, 1.42376196e-01,
1.62244613e-01, 1.83208974e-01, 2.05366050e-01,
2.29556330e-01, 2.53282959e-01, 2.77540635e-01,
3.05427136e-01, 3.36100492e-01, 3.63831154e-01,
3.94043118e-01, 4.25583501e-01, 4.55163960e-01,
4.86837208e-01, 5.20599620e-01, 5.48129193e-01,
5.78151849e-01, 6.08547876e-01, 6.40669188e-01,
6.70746937e-01, 7.01026286e-01, 7.25971707e-01,
7.51021605e-01, 7.77398045e-01, 8.00059380e-01,
8.22450308e-01, 8.40847440e-01, 8.57498407e-01,
8.75729509e-01, 8.91310252e-01, 9.05933655e-01,
9.18565943e-01, 9.29274795e-01, 9.40657581e-01,
9.48881056e-01, 9.57538817e-01, 9.63601434e-01,
9.70164957e-01, 9.75166523e-01, 9.79733128e-01,
9.83692163e-01, 9.86929642e-01, 9.89432271e-01,
9.91544580e-01, 9.93344271e-01, 9.94115203e-01,
9.95269177e-01, 9.96206415e-01, 9.97047263e-01,
9.97575959e-01, 9.98237416e-01, 9.98678170e-01,
9.98903131e-01, 9.99062383e-01, 9.99389219e-01,
9.99710548e-01, 9.99739859e-01, 9.99802006e-01,
9.99820441e-01, 9.99861218e-01, 9.99912599e-01,
9.99946445e-01, 9.99963921e-01, 9.99975528e-01,
9.99981646e-01, 9.99987764e-01, 9.99993882e-01,
1.00000000e+00])
u = self.data
cdf = percentile(u, numbins=100)
np.testing.assert_array_almost_equal(r_bins, cdf.bin_edges)
np.testing.assert_array_almost_equal(r_percentiles, cdf.percentiles)
