├── requirements.txt
├── README.md
├── example.ipynb
├── EEGExtract.py
└── LICENSE


/requirements.txt:
--------------------------------------------------------------------------------
 1 | dit==1.5
 2 | numpy==1.24.3
 3 | pandas==2.0.1
 4 | PyWavelets==1.8.0
 5 | scikit-learn==1.7.2
 6 | scipy==1.15.3
 7 | statsmodels==0.14.5
 8 | pyod==2.0.5
 9 | librosa==0.11.0
10 | 


--------------------------------------------------------------------------------
/README.md:
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  1 | # EEGExtract 1.2.0
  2 | [Sari Saba-Sadiya](https://cse.msu.edu/~sadiyasa/)<sup>1,2</sup>,
  3 | [Eric Chantland]()<sup>2</sup>,
  4 | [Taosheng Liu](https://npal.psy.msu.edu/)<sup>2</sup>,
  5 | [Tuka Alhanai](https://talhanai.xyz/)<sup>3</sup>,
  6 | [Mohammad Ghassemi](https://ghassemi.xyz/)<sup>1</sup><br>
  7 | <sub>
  8 | <sup>1</sup> Human Augmentation and Artificial Intelligence lab, Michigan State University, Department of Computer Science<br>
  9 | <sup>2</sup> Neuroimaging of Perception and Attention Lab, Michigan State University, Department of Psychology<br>
 10 | <sup>3</sup> Computer Human Intelligence Lab, New York University Abu Dhabi, Department of Electrical and Computer Engineering<br>
 11 | </sub>
 12 | 
 13 | **2025 Update:** Thanks to [Alperen Kantarcı](https://github.com/Alpkant) for new update
 14 | 
 15 | 
 16 | A python package for extracting EEG features. First developed for the paper ["Unsupervised EEG Artifact Detection and Correction"](https://www.frontiersin.org/articles/10.3389/fdgth.2020.608920/abstract), published in Frontiers in Digital Health, Special issue on Machine Learning in Clinical Decision-Making. [Press here](https://www.frontiersin.org/articles/10.3389/fdgth.2020.608920/bibTex) for a BibTex citation (or scroll to the bottom of this page).
 17 | 
 18 | To the best of our knowledge EEGExtract is the most comprehensive library for EEG feature extraction currently available. This library is actively maintained, __please open an issue if you believe adding a specific feature will be of benefit for the community!__
 19 | 
 20 | 
 21 | ## Setup
 22 | 1. Make sure that you have the required packages listed in `requirements.txt`. Use `pip install -r requirements.txt` if unsure. 
 23 | 2. Simply download and place the `EEGExtract.py` file in the same folder as your repo. You can then use `import EEGExtract as eeg`.
 24 | 
 25 | ## License
 26 | 
 27 | <a href="https://www.gnu.org/licenses/gpl-3.0.en.html">
 28 | <img src="https://cdn2.iconfinder.com/data/icons/business-and-finance-311/32/Business_and_Finance_scale_weight_weights_scales_balance-256.png" alt="GPL-3.0 License" height="16" style="vertical-align:middle"> GPL-3.0 License </img></a>
 29 | 
 30 | Free to use and modify, but must cite the original publication below.
 31 | 
 32 | ## The Features
 33 | 
 34 | | _Signal Descriptor_                       | _Brief Description_ | _Function_ |
 35 | | --------------- | --------------- |  --------------- |
 36 | | __Complexity Features__                                 | _degree of randomness or irregularity_  |
 37 | | Shannon Entropy        | additive measure of signal stochasticity    | shannonEntropy |
 38 | | Tsalis Entropy (n=10)  | non-additive measure of signal stochasticity  | tsalisEntropy |
 39 | | Information Quantity  (δ,α,θ,β,γ)  | entropy of a wavelet decomposed signal         | filt_data + shannonEntropy |
 40 | | Cepstrum Coefficients (n=2)                        | rate of change in signal spectral band power   | mfcc |
 41 | | Lyapunov Exponent                                | separation between signals with similar trajectories   | lyapunov|
 42 | | Fractal Embedding Dimension                      | how signal properties change with scale | hFD |
 43 | | Hjorth Mobility                                  | mean signal frequency   | hjorthParameters |
 44 | | Hjorth Complexity                                | rate of change in mean signal frequency   | hjorthParameters |
 45 | | False Nearest Neighbor                           | signal continuity and smoothness | falseNearestNeighbor |
 46 | | ARMA Coefficients (n=2)                       | autoregressive coefficient of signal at (t-1) and (t-2)  | arma |
 47 | | __Continuity Features__                               | _clinically grounded signal characteristics_  |
 48 | | Median Frequency                               |   the median spectral power    | medianFreq |
 49 | | δ band Power                             |  spectral power in the 0-3Hz range  | bandPower |
 50 | | α band Power                             |  spectral power in the 4-7Hz range   | bandPower |
 51 | | θ band Power                             |  spectral power in the 8-15Hz range   | bandPower |
 52 | | β band Power                              |  spectral power in the 16-31Hz range   | bandPower |
 53 | | γ band Power                             |  spectral power above 32Hz | bandPower |
 54 | | Median Frequency                               |   median spectral power   | medianFreq |
 55 | | Standard Deviation                              | average difference between signal value and it's mean   | eegStd |
 56 | | α/δ Ratio                          | ratio of the power spectral density in α and δ bands | eegRatio |
 57 | | Regularity (burst-suppression)                 | measure of signal stationarity / spectral consistency  | eegRegularity |
 58 | | Voltage < (5μ, 10μ, 20μ)          |  low signal amplitude | eegVoltage |
 59 | | Normal EEG                                |        Peak spectral power textgreater= 8Hz   | |
 60 | | Diffuse Slowing                           |        indicator of peak power spectral density less than 8Hz   | diffuseSlowing |
 61 | | Spikes                                    |        signal amplitude exceeds μ by 3σ for 70 ms or less   | spikeNum |
 62 | | Delta Burst after spike                   |        Increased δ after spike, relative to δ before spike | burstAfterSpike |
 63 | | Sharp spike                               |        spikes lasting less than 70 ms   | shortSpikeNum |
 64 | | Number of Bursts                          |        number of amplitude bursts  | numBursts |
 65 | | Burst length μ and σ             |        statistical properties of bursts | burstLengthStats |
 66 | | Burst band powers (δ,α,θ,β,γ)   | spectral power of bursts  | burstBandPowers |
 67 | | Number of Suppressions                            | segments with contiguous amplitude suppression  | numSuppressions |
 68 | | Suppression length μ and σ             | statistical properties of suppressions | suppressionLengthStats |
 69 | | __Connectivity Features__                             |  _interactions between EEG electrode pairs_  |
 70 | | Coherence - δ                            | correlation in in 0-4 Hz power between signals    | filt_data + coherence |
 71 | | Coherence - All                                 | correlation in overall power between signals | coherence |
 72 | | Mutual Information                               | measure of dependence | calculate2Chan_MI |
 73 | | Granger causality - All                          | measure of causality | calcGrangerCausality |
 74 | | Phase Lag Index                                  | association between the instantaneous phase of signals | phaseLagIndex |
 75 | | Cross-correlation Magnitude                      | maximum correlation between two signals | crossCorrMag |
 76 | | Crosscorrelation - Lag                           | time-delay that maximizes correlation between signals | corrCorrLagAux |
 77 | 
 78 | Additionally, `EEGExtract` also contains implementations for a number of auxiliary functions
 79 | 
 80 | | _Function_  | params |  _Brief Description_ |
 81 | | --------------- | --------------- |  --------------- |
 82 | | filt_data | eegData, lowcut, highcut, fs, order=7 | midpass filter between lowcut and highcut |
 83 | | fcnRemoveShortEvents | z,n| z=[chan x samples ], n is threshold |
 84 | | get_intervals | A,B,endIdx | Find interval of consistent values in binary 1D numpy array |
 85 | 
 86 | ## Important Note
 87 | The feature extractor is an independent section that can be used with any artifact correction method (recently there have been quite a few including some notable example [1,2]). If you are interested in the specific setup that was used in the paper, as well as a link to the data, please visit [the following repository](https://github.com/sari-saba-sadiya/EEG-Artifact-Correction-Via-Completion).
 88 | 
 89 | [1] S. Phadikar, N. Sinha, and R. Ghosh, “Automatic eeg eyeblink artifact identification and removal technique using independent component analysis in combination with support vector machines and denoising autoencoder”
 90 | 
 91 | [2] B. Somers, T. Francart, and A. Bertrand, “A generic eeg artifact removal algorithm based on the multi-channel wiener filter.”
 92 | 
 93 | 
 94 | 
 95 | ## Cite
 96 | ```
 97 | @article{saba2020unsupervised,
 98 |   title={Unsupervised EEG Artifact Detection and Correction},
 99 |   author={Saba-Sadiya, Sari and Chantland, Eric and Alhanai, Tuka and Liu, Taosheng and Ghassemi, Mohammad Mahdi},
100 |   journal={Frontiers in Digital Health},
101 |   volume={2},
102 |   pages={57},
103 |   year={2020},
104 |   publisher={Frontiers}
105 | }
106 | ```
107 | 
108 | 


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/example.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {},
  7 |    "outputs": [],
  8 |    "source": [
  9 |     "%load_ext autoreload\n",
 10 |     "%autoreload 2\n",
 11 |     "import EEGExtract as eeg\n",
 12 |     "import glob\n",
 13 |     "import numpy as np"
 14 |    ]
 15 |   },
 16 |   {
 17 |    "cell_type": "code",
 18 |    "execution_count": 2,
 19 |    "metadata": {},
 20 |    "outputs": [],
 21 |    "source": [
 22 |     "# Export data from the BCI Competition Dataset IV 2a dataset\n",
 23 |     "# Code used from https://github.com/bregydoc/bcidatasetIV2a\n",
 24 |     "class MotorImageryDataset:\n",
 25 |     "    def __init__(self, dataset='A01T.npz'):\n",
 26 |     "        if not dataset.endswith('.npz'):\n",
 27 |     "            dataset += '.npz'\n",
 28 |     "\n",
 29 |     "        self.data = np.load(dataset)\n",
 30 |     "\n",
 31 |     "        self.Fs = 250 # 250Hz from original paper\n",
 32 |     "\n",
 33 |     "        # keys of data ['s', 'etyp', 'epos', 'edur', 'artifacts']\n",
 34 |     "        self.raw = self.data['s'].T\n",
 35 |     "        self.events_type = self.data['etyp'].T\n",
 36 |     "        self.events_position = self.data['epos'].T\n",
 37 |     "        self.events_duration = self.data['edur'].T\n",
 38 |     "        self.artifacts = self.data['artifacts'].T\n",
 39 |     "\n",
 40 |     "        # Types of motor imagery\n",
 41 |     "        self.mi_types = {769: 'left', 770: 'right', 771: 'foot',\n",
 42 |     "                         772: 'tongue', 783: 'unknown', 1023:'rejected'}\n",
 43 |     "\n",
 44 |     "    def get_trials_from_channel(self):\n",
 45 |     "\n",
 46 |     "        # Channel default is C3\n",
 47 |     "        startrial_code = 768\n",
 48 |     "        starttrial_events = self.events_type == startrial_code\n",
 49 |     "        idxs = [i for i, x in enumerate(starttrial_events[0]) if x]\n",
 50 |     "\n",
 51 |     "        trials = []\n",
 52 |     "        classes = []\n",
 53 |     "        artifacts = []\n",
 54 |     "        for ii, index in enumerate(idxs):\n",
 55 |     "            type_e = self.events_type[0, index+1]\n",
 56 |     "            if type_e not in self.mi_types.keys():\n",
 57 |     "                continue\n",
 58 |     "            class_e = self.mi_types[type_e]\n",
 59 |     "            if class_e == 'unknown':\n",
 60 |     "                continue\n",
 61 |     "            classes.append(type_e-769)\n",
 62 |     "\n",
 63 |     "            start = self.events_position[0, index] + 0.5 * self.Fs\n",
 64 |     "            stop = start + self.events_duration[0, index]\n",
 65 |     "            if stop < start + 2* self.Fs:\n",
 66 |     "                print(stop,start + 2* self.Fs)\n",
 67 |     "                raise '(MotorImageryDataset error): EEG is shorter than 2 sec'\n",
 68 |     "            trial = self.raw[0:22, int(start):int(start + 2* self.Fs)]\n",
 69 |     "            trials.append(trial)\n",
 70 |     "            artifacts.append(self.artifacts[0,ii])\n",
 71 |     "        return trials, classes, artifacts"
 72 |    ]
 73 |   },
 74 |   {
 75 |    "cell_type": "code",
 76 |    "execution_count": 3,
 77 |    "metadata": {},
 78 |    "outputs": [],
 79 |    "source": [
 80 |     "trials = []\n",
 81 |     "classes = []\n",
 82 |     "artifacts = []\n",
 83 |     "for file in glob.glob('../EEGExtract/bcidatasetIV2a/*.npz'):\n",
 84 |     "    datasetA1 = MotorImageryDataset(file)\n",
 85 |     "    # trials contains the N valid trials, and clases its related class.\n",
 86 |     "    tmp_trials, tmp_classes, tmp_artifacts = datasetA1.get_trials_from_channel()\n",
 87 |     "    trials.extend(tmp_trials)\n",
 88 |     "    classes.extend(tmp_classes)\n",
 89 |     "    artifacts.extend(tmp_artifacts)"
 90 |    ]
 91 |   },
 92 |   {
 93 |    "cell_type": "code",
 94 |    "execution_count": 4,
 95 |    "metadata": {},
 96 |    "outputs": [],
 97 |    "source": [
 98 |     "eegData = np.dstack(trials)"
 99 |    ]
100 |   },
101 |   {
102 |    "cell_type": "code",
103 |    "execution_count": 5,
104 |    "metadata": {},
105 |    "outputs": [],
106 |    "source": [
107 |     "fs = 250"
108 |    ]
109 |   },
110 |   {
111 |    "cell_type": "code",
112 |    "execution_count": 6,
113 |    "metadata": {},
114 |    "outputs": [
115 |     {
116 |      "data": {
117 |       "text/plain": [
118 |        "(22, 500, 2816)"
119 |       ]
120 |      },
121 |      "execution_count": 6,
122 |      "metadata": {},
123 |      "output_type": "execute_result"
124 |     }
125 |    ],
126 |    "source": [
127 |     "# eegData: 3D np array [chans x ms x epochs] \n",
128 |     "eegData.shape"
129 |    ]
130 |   },
131 |   {
132 |    "cell_type": "code",
133 |    "execution_count": 7,
134 |    "metadata": {},
135 |    "outputs": [],
136 |    "source": [
137 |     "feature_list = []"
138 |    ]
139 |   },
140 |   {
141 |    "cell_type": "markdown",
142 |    "metadata": {},
143 |    "source": [
144 |     "## Complexity Features"
145 |    ]
146 |   },
147 |   {
148 |    "cell_type": "code",
149 |    "execution_count": 34,
150 |    "metadata": {},
151 |    "outputs": [],
152 |    "source": [
153 |     "#Shannon Entropy\n",
154 |     "ShannonRes = eeg.shannonEntropy(eegData, bin_min=-200, bin_max=200, binWidth=2)"
155 |    ]
156 |   },
157 |   {
158 |    "cell_type": "code",
159 |    "execution_count": 35,
160 |    "metadata": {},
161 |    "outputs": [],
162 |    "source": [
163 |     "#Tsalis Entropy (n=10)\n",
164 |     "tsalisRes = eeg.tsalisEntropy(eegData, bin_min=-200, bin_max=200, binWidth=2,orders=list(range(1,10+1)))"
165 |    ]
166 |   },
167 |   {
168 |    "cell_type": "code",
169 |    "execution_count": 36,
170 |    "metadata": {},
171 |    "outputs": [],
172 |    "source": [
173 |     "# Subband Information Quantity\n",
174 |     "# delta (0.5–4 Hz)\n",
175 |     "eegData_delta = eeg.filt_data(eegData, 0.5, 4, fs)\n",
176 |     "ShannonRes_delta = eeg.shannonEntropy(eegData_delta, bin_min=-200, bin_max=200, binWidth=2)\n",
177 |     "# theta (4–8 Hz)\n",
178 |     "eegData_theta = eeg.filt_data(eegData, 4, 8, fs)\n",
179 |     "ShannonRes_theta = eeg.shannonEntropy(eegData_theta, bin_min=-200, bin_max=200, binWidth=2)\n",
180 |     "# alpha (8–12 Hz)\n",
181 |     "eegData_alpha = eeg.filt_data(eegData, 8, 12, fs)\n",
182 |     "ShannonRes_alpha = eeg.shannonEntropy(eegData_alpha, bin_min=-200, bin_max=200, binWidth=2)\n",
183 |     "# beta (12–30 Hz)\n",
184 |     "eegData_beta = eeg.filt_data(eegData, 12, 30, fs)\n",
185 |     "ShannonRes_beta = eeg.shannonEntropy(eegData_beta, bin_min=-200, bin_max=200, binWidth=2)\n",
186 |     "# gamma (30–100 Hz)\n",
187 |     "eegData_gamma = eeg.filt_data(eegData, 30, 100, fs)\n",
188 |     "ShannonRes_gamma = eeg.shannonEntropy(eegData_gamma, bin_min=-200, bin_max=200, binWidth=2)"
189 |    ]
190 |   },
191 |   {
192 |    "cell_type": "code",
193 |    "execution_count": 9,
194 |    "metadata": {},
195 |    "outputs": [
196 |     {
197 |      "name": "stderr",
198 |      "output_type": "stream",
199 |      "text": [
200 |       "/Users/alperen/miniconda3/envs/eegextract/lib/python3.11/site-packages/librosa/core/spectrum.py:266: UserWarning: n_fft=2048 is too large for input signal of length=500\n",
201 |       "  warnings.warn(\n"
202 |      ]
203 |     }
204 |    ],
205 |    "source": [
206 |     "# Cepstrum Coefficients (n=2)\n",
207 |     "CepstrumRes = eeg.mfcc(eegData, fs,order=2)"
208 |    ]
209 |   },
210 |   {
211 |    "cell_type": "code",
212 |    "execution_count": 10,
213 |    "metadata": {},
214 |    "outputs": [],
215 |    "source": [
216 |     "# Lyapunov Exponent\n",
217 |     "LyapunovRes = eeg.lyapunov(eegData)"
218 |    ]
219 |   },
220 |   {
221 |    "cell_type": "code",
222 |    "execution_count": 11,
223 |    "metadata": {},
224 |    "outputs": [
225 |     {
226 |      "name": "stderr",
227 |      "output_type": "stream",
228 |      "text": [
229 |       "/Users/alperen/Documents/Goethe/PhD/HONDA/eegextract_trial/EEGExtract.py:243: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
230 |       "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
231 |       "  (p, r1, r2, s)=np.linalg.lstsq(x, L)\n"
232 |      ]
233 |     }
234 |    ],
235 |    "source": [
236 |     "# Fractal Embedding Dimension\n",
237 |     "HiguchiFD_Res  = eeg.hFD(eegData[0,:,0],3)"
238 |    ]
239 |   },
240 |   {
241 |    "cell_type": "code",
242 |    "execution_count": 12,
243 |    "metadata": {},
244 |    "outputs": [],
245 |    "source": [
246 |     "# Hjorth Mobility\n",
247 |     "# Hjorth Complexity\n",
248 |     "HjorthMob, HjorthComp = eeg.hjorthParameters(eegData)"
249 |    ]
250 |   },
251 |   {
252 |    "cell_type": "code",
253 |    "execution_count": 13,
254 |    "metadata": {},
255 |    "outputs": [],
256 |    "source": [
257 |     "# False Nearest Neighbor\n",
258 |     "FalseNnRes = eeg.falseNearestNeighbor(eegData)"
259 |    ]
260 |   },
261 |   {
262 |    "cell_type": "code",
263 |    "execution_count": null,
264 |    "metadata": {},
265 |    "outputs": [],
266 |    "source": [
267 |     "# ARMA Coefficients (n=2)\n",
268 |     "armaRes = eeg.arma(eegData,order=2)"
269 |    ]
270 |   },
271 |   {
272 |    "cell_type": "markdown",
273 |    "metadata": {},
274 |    "source": [
275 |     "## Category Features"
276 |    ]
277 |   },
278 |   {
279 |    "cell_type": "code",
280 |    "execution_count": 16,
281 |    "metadata": {},
282 |    "outputs": [],
283 |    "source": [
284 |     "# Median Frequency\n",
285 |     "medianFreqRes = eeg.medianFreq(eegData,fs)"
286 |    ]
287 |   },
288 |   {
289 |    "cell_type": "code",
290 |    "execution_count": 17,
291 |    "metadata": {},
292 |    "outputs": [],
293 |    "source": [
294 |     "# δ band Power\n",
295 |     "bandPwr_delta = eeg.bandPower(eegData, 0.5, 4, fs)\n",
296 |     "# θ band Power\n",
297 |     "bandPwr_theta = eeg.bandPower(eegData, 4, 8, fs)\n",
298 |     "# α band Power\n",
299 |     "bandPwr_alpha = eeg.bandPower(eegData, 8, 12, fs)\n",
300 |     "# β band Power\n",
301 |     "bandPwr_beta = eeg.bandPower(eegData, 12, 30, fs)\n",
302 |     "# γ band Power\n",
303 |     "bandPwr_gamma = eeg.bandPower(eegData, 30, 100, fs)"
304 |    ]
305 |   },
306 |   {
307 |    "cell_type": "code",
308 |    "execution_count": 18,
309 |    "metadata": {},
310 |    "outputs": [],
311 |    "source": [
312 |     "# Standard Deviation\n",
313 |     "std_res = eeg.eegStd(eegData)"
314 |    ]
315 |   },
316 |   {
317 |    "cell_type": "code",
318 |    "execution_count": 19,
319 |    "metadata": {},
320 |    "outputs": [],
321 |    "source": [
322 |     "# α/δ Ratio\n",
323 |     "ratio_res = eeg.eegRatio(eegData,fs)"
324 |    ]
325 |   },
326 |   {
327 |    "cell_type": "code",
328 |    "execution_count": 20,
329 |    "metadata": {},
330 |    "outputs": [],
331 |    "source": [
332 |     "# Regularity (burst-suppression)\n",
333 |     "regularity_res = eeg.eegRegularity(eegData,fs)"
334 |    ]
335 |   },
336 |   {
337 |    "cell_type": "code",
338 |    "execution_count": 21,
339 |    "metadata": {},
340 |    "outputs": [],
341 |    "source": [
342 |     "# Voltage < 5μ\n",
343 |     "volt05_res = eeg.eegVoltage(eegData,voltage=5)\n",
344 |     "# Voltage < 10μ\n",
345 |     "volt10_res = eeg.eegVoltage(eegData,voltage=10)\n",
346 |     "# Voltage < 20μ\n",
347 |     "volt20_res = eeg.eegVoltage(eegData,voltage=20)"
348 |    ]
349 |   },
350 |   {
351 |    "cell_type": "code",
352 |    "execution_count": 22,
353 |    "metadata": {},
354 |    "outputs": [],
355 |    "source": [
356 |     "# Diffuse Slowing\n",
357 |     "df_res = eeg.diffuseSlowing(eegData)"
358 |    ]
359 |   },
360 |   {
361 |    "cell_type": "code",
362 |    "execution_count": 23,
363 |    "metadata": {},
364 |    "outputs": [],
365 |    "source": [
366 |     "# Spikes\n",
367 |     "minNumSamples = int(70*fs/1000)\n",
368 |     "spikeNum_res = eeg.spikeNum(eegData,minNumSamples)"
369 |    ]
370 |   },
371 |   {
372 |    "cell_type": "code",
373 |    "execution_count": 24,
374 |    "metadata": {},
375 |    "outputs": [],
376 |    "source": [
377 |     "# Delta burst after Spike\n",
378 |     "deltaBurst_res = eeg.burstAfterSpike(eegData,eegData_delta,minNumSamples=7,stdAway = 3)"
379 |    ]
380 |   },
381 |   {
382 |    "cell_type": "code",
383 |    "execution_count": 25,
384 |    "metadata": {},
385 |    "outputs": [],
386 |    "source": [
387 |     "# Sharp spike\n",
388 |     "sharpSpike_res = eeg.shortSpikeNum(eegData,minNumSamples)"
389 |    ]
390 |   },
391 |   {
392 |    "cell_type": "code",
393 |    "execution_count": 26,
394 |    "metadata": {},
395 |    "outputs": [],
396 |    "source": [
397 |     "# Number of Bursts\n",
398 |     "numBursts_res = eeg.numBursts(eegData,fs)"
399 |    ]
400 |   },
401 |   {
402 |    "cell_type": "code",
403 |    "execution_count": 27,
404 |    "metadata": {},
405 |    "outputs": [
406 |     {
407 |      "name": "stderr",
408 |      "output_type": "stream",
409 |      "text": [
410 |       "/Users/alperen/miniconda3/envs/eegextract/lib/python3.11/site-packages/numpy/core/fromnumeric.py:3464: RuntimeWarning: Mean of empty slice.\n",
411 |       "  return _methods._mean(a, axis=axis, dtype=dtype,\n",
412 |       "/Users/alperen/miniconda3/envs/eegextract/lib/python3.11/site-packages/numpy/core/_methods.py:269: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
413 |       "  ret = _var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,\n"
414 |      ]
415 |     }
416 |    ],
417 |    "source": [
418 |     "# Burst length μ and σ\n",
419 |     "burstLenMean_res,burstLenStd_res = eeg.burstLengthStats(eegData,fs)"
420 |    ]
421 |   },
422 |   {
423 |    "cell_type": "code",
424 |    "execution_count": 28,
425 |    "metadata": {},
426 |    "outputs": [],
427 |    "source": [
428 |     "# Burst Band Power for δ\n",
429 |     "burstBandPwrAlpha = eeg.burstBandPowers(eegData, 0.5, 4, fs)"
430 |    ]
431 |   },
432 |   {
433 |    "cell_type": "code",
434 |    "execution_count": 29,
435 |    "metadata": {},
436 |    "outputs": [],
437 |    "source": [
438 |     "# Number of Suppressions\n",
439 |     "numSupps_res = eeg.numSuppressions(eegData,fs)"
440 |    ]
441 |   },
442 |   {
443 |    "cell_type": "code",
444 |    "execution_count": 30,
445 |    "metadata": {},
446 |    "outputs": [],
447 |    "source": [
448 |     "# Suppression length μ and σ\n",
449 |     "suppLenMean_res,suppLenStd_res = eeg.suppressionLengthStats(eegData,fs)"
450 |    ]
451 |   },
452 |   {
453 |    "cell_type": "markdown",
454 |    "metadata": {},
455 |    "source": [
456 |     "##    Connectivity features"
457 |    ]
458 |   },
459 |   {
460 |    "cell_type": "code",
461 |    "execution_count": 31,
462 |    "metadata": {},
463 |    "outputs": [],
464 |    "source": [
465 |     "# Coherence - δ\n",
466 |     "coherence_res = eeg.coherence(eegData,fs)"
467 |    ]
468 |   },
469 |   {
470 |    "cell_type": "code",
471 |    "execution_count": 32,
472 |    "metadata": {},
473 |    "outputs": [],
474 |    "source": [
475 |     "#import importlib\n",
476 |     "#importlib.reload(eeg)"
477 |    ]
478 |   },
479 |   {
480 |    "cell_type": "code",
481 |    "execution_count": 37,
482 |    "metadata": {},
483 |    "outputs": [],
484 |    "source": [
485 |     "feature_list = []\n",
486 |     "feature_list.append(ShannonRes)\n",
487 |     "feature_list.append(ShannonRes_delta)\n",
488 |     "feature_list.append(ShannonRes_theta)\n",
489 |     "#feature_list.append(ShannonRes_alpha)\n",
490 |     "#feature_list.append(ShannonRes_beta)\n",
491 |     "feature_list.append(ShannonRes_gamma)\n",
492 |     "feature_list.append(bandPwr_delta)\n",
493 |     "feature_list.append(bandPwr_theta)\n",
494 |     "#feature_list.append(bandPwr_alpha)\n",
495 |     "#feature_list.append(bandPwr_beta)\n",
496 |     "feature_list.append(bandPwr_gamma)\n",
497 |     "feature_list.append(std_res)\n",
498 |     "#feature_list.append(ratio_res)\n",
499 |     "feature_list.append(regularity_res)\n",
500 |     "feature_list.append(volt05_res)\n",
501 |     "feature_list.append(volt10_res)\n",
502 |     "feature_list.append(volt20_res)\n",
503 |     "feature_list.append(df_res)\n",
504 |     "feature_list.append(spikeNum_res)\n",
505 |     "feature_list.append(deltaBurst_res)\n",
506 |     "feature_list.append(sharpSpike_res)\n",
507 |     "feature_list.append(numBursts_res)\n",
508 |     "#feature_list.append(burstLenMean_res)\n",
509 |     "#feature_list.append(burstLenStd_res)\n",
510 |     "feature_list.append(numSupps_res)\n",
511 |     "#feature_list.append(coherence_res)"
512 |    ]
513 |   },
514 |   {
515 |    "cell_type": "code",
516 |    "execution_count": 38,
517 |    "metadata": {},
518 |    "outputs": [],
519 |    "source": [
520 |     "feature_arr  = np.vstack(feature_list).transpose()"
521 |    ]
522 |   },
523 |   {
524 |    "cell_type": "code",
525 |    "execution_count": 39,
526 |    "metadata": {},
527 |    "outputs": [
528 |     {
529 |      "data": {
530 |       "text/plain": [
531 |        "(2816, 396)"
532 |       ]
533 |      },
534 |      "execution_count": 39,
535 |      "metadata": {},
536 |      "output_type": "execute_result"
537 |     }
538 |    ],
539 |    "source": [
540 |     "feature_arr.shape"
541 |    ]
542 |   },
543 |   {
544 |    "cell_type": "code",
545 |    "execution_count": 40,
546 |    "metadata": {},
547 |    "outputs": [
548 |     {
549 |      "data": {
550 |       "text/plain": [
551 |        "18"
552 |       ]
553 |      },
554 |      "execution_count": 40,
555 |      "metadata": {},
556 |      "output_type": "execute_result"
557 |     }
558 |    ],
559 |    "source": [
560 |     "len(feature_list)"
561 |    ]
562 |   },
563 |   {
564 |    "cell_type": "code",
565 |    "execution_count": 41,
566 |    "metadata": {},
567 |    "outputs": [
568 |     {
569 |      "data": {
570 |       "text/plain": [
571 |        "0.17329545454545456"
572 |       ]
573 |      },
574 |      "execution_count": 41,
575 |      "metadata": {},
576 |      "output_type": "execute_result"
577 |     }
578 |    ],
579 |    "source": [
580 |     "sum(artifacts) / len(artifacts)"
581 |    ]
582 |   },
583 |   {
584 |    "cell_type": "code",
585 |    "execution_count": 45,
586 |    "metadata": {},
587 |    "outputs": [],
588 |    "source": [
589 |     "# https://pyod.readthedocs.io/en/latest/pyod.models.html\n",
590 |     "from pyod import models\n",
591 |     "from pyod.models import hbos,auto_encoder,lof,so_gaal,lscp,vae,abod,ocsvm,xgbod,pca"
592 |    ]
593 |   },
594 |   {
595 |    "cell_type": "code",
596 |    "execution_count": 46,
597 |    "metadata": {},
598 |    "outputs": [
599 |     {
600 |      "data": {
601 |       "text/plain": [
602 |        "HBOS(alpha=0.07, contamination=0.15, n_bins=17, tol=0.5)"
603 |       ]
604 |      },
605 |      "execution_count": 46,
606 |      "metadata": {},
607 |      "output_type": "execute_result"
608 |     }
609 |    ],
610 |    "source": [
611 |     "clf = hbos.HBOS(n_bins=17, alpha=0.07, tol=0.5,contamination=.15)\n",
612 |     "clf.fit(feature_arr)"
613 |    ]
614 |   },
615 |   {
616 |    "cell_type": "code",
617 |    "execution_count": 47,
618 |    "metadata": {},
619 |    "outputs": [],
620 |    "source": [
621 |     "from sklearn.metrics import confusion_matrix,cohen_kappa_score,f1_score"
622 |    ]
623 |   },
624 |   {
625 |    "cell_type": "code",
626 |    "execution_count": 48,
627 |    "metadata": {},
628 |    "outputs": [
629 |     {
630 |      "data": {
631 |       "text/plain": [
632 |        "array([[2025,  303],\n",
633 |        "       [ 368,  120]])"
634 |       ]
635 |      },
636 |      "execution_count": 48,
637 |      "metadata": {},
638 |      "output_type": "execute_result"
639 |     }
640 |    ],
641 |    "source": [
642 |     "confusion_matrix(artifacts, clf.labels_)"
643 |    ]
644 |   },
645 |   {
646 |    "cell_type": "code",
647 |    "execution_count": 49,
648 |    "metadata": {},
649 |    "outputs": [
650 |     {
651 |      "data": {
652 |       "text/plain": [
653 |        "0.12217820163082671"
654 |       ]
655 |      },
656 |      "execution_count": 49,
657 |      "metadata": {},
658 |      "output_type": "execute_result"
659 |     }
660 |    ],
661 |    "source": [
662 |     "cohen_kappa_score(artifacts, clf.labels_)"
663 |    ]
664 |   },
665 |   {
666 |    "cell_type": "code",
667 |    "execution_count": 50,
668 |    "metadata": {},
669 |    "outputs": [
670 |     {
671 |      "data": {
672 |       "text/plain": [
673 |        "0.26344676180021953"
674 |       ]
675 |      },
676 |      "execution_count": 50,
677 |      "metadata": {},
678 |      "output_type": "execute_result"
679 |     }
680 |    ],
681 |    "source": [
682 |     "f1_score(artifacts, clf.labels_)"
683 |    ]
684 |   },
685 |   {
686 |    "cell_type": "code",
687 |    "execution_count": null,
688 |    "metadata": {},
689 |    "outputs": [],
690 |    "source": []
691 |   },
692 |   {
693 |    "cell_type": "code",
694 |    "execution_count": null,
695 |    "metadata": {},
696 |    "outputs": [],
697 |    "source": []
698 |   }
699 |  ],
700 |  "metadata": {
701 |   "kernelspec": {
702 |    "display_name": "eegextract",
703 |    "language": "python",
704 |    "name": "python3"
705 |   },
706 |   "language_info": {
707 |    "codemirror_mode": {
708 |     "name": "ipython",
709 |     "version": 3
710 |    },
711 |    "file_extension": ".py",
712 |    "mimetype": "text/x-python",
713 |    "name": "python",
714 |    "nbconvert_exporter": "python",
715 |    "pygments_lexer": "ipython3",
716 |    "version": "3.11.14"
717 |   }
718 |  },
719 |  "nbformat": 4,
720 |  "nbformat_minor": 2
721 | }
722 | 


--------------------------------------------------------------------------------
/EEGExtract.py:
--------------------------------------------------------------------------------
  1 | import bisect
  2 | import numpy as np
  3 | import pandas as pd
  4 | import pywt
  5 | from scipy import stats, signal, integrate
  6 | from dit.other import tsallis_entropy
  7 | import dit
  8 | import librosa
  9 | import statsmodels.api as sm
 10 | import itertools
 11 | from statsmodels import tsa
 12 | from sklearn.metrics import mutual_info_score
 13 | import numpy as np
 14 | from scipy import signal,integrate
 15 | from sklearn.metrics.cluster import normalized_mutual_info_score as normed_mutual_info 
 16 | 
 17 | ################################################
 18 | #	Auxiliary Functions
 19 | ################################################
 20 | 
 21 | ##########
 22 | # Filter the eegData, midpass filter 
 23 | #	eegData: 3D np array [chans x ms x epochs] 
 24 | def filt_data(eegData, lowcut, highcut, fs, order=7):
 25 |     nyq = 0.5 * fs
 26 |     low = lowcut / nyq
 27 |     high = highcut / nyq
 28 |     b, a = signal.butter(order, [low, high], btype='band')
 29 |     filt_eegData = signal.lfilter(b, a, eegData, axis = 1)
 30 |     return filt_eegData
 31 | 
 32 | #########
 33 | # remove short bursts / spikes 
 34 | def fcnRemoveShortEvents(z,n):
 35 |     for chan in range(z.shape[0]):
 36 |         # check for too-short suppressions
 37 |         ct=0
 38 |         i0=1
 39 |         i1=1 
 40 |         for i in range(2,len(z[chan,:])):
 41 |             if z[chan,i]==z[chan,i-1]:
 42 |                 ct=ct+1
 43 |                 i1=i
 44 |             else:
 45 |                 if ct<n:
 46 |                     z[chan,i0:i1] = 0
 47 |                     z[chan,i1] = 0 #nasty little bug
 48 |                 ct=0
 49 |                 i0=i
 50 |                 i1=i
 51 |         if z[chan,0] == 1 and z[chan,1] == 0:
 52 |             z[chan,0] = 0
 53 |     return z
 54 | 
 55 | ##########
 56 | # Find interval of consistent values in binary 1D numpy array
 57 | def get_intervals(A,B,endIdx=500):
 58 |     # This function gives you intervals (a1,b1), (a2,b3) for every a in A=[a1,a2,a3,..]
 59 |     # and the smallest element in b that is larger than a.
 60 |     intervals = []
 61 |     for ii,A_idx_lst in enumerate(A):
 62 |         B_idx_lst = [bisect.bisect_left(B[ii], idx) for idx in A_idx_lst]
 63 |         chan_intervals = []
 64 |         for jj,idx_l in enumerate(B_idx_lst):
 65 |             if idx_l == len(B[ii]):
 66 |                 chan_intervals.append((A_idx_lst[jj],endIdx))
 67 |             else:
 68 |                 chan_intervals.append((A_idx_lst[jj],B[ii][idx_l]))
 69 |         intervals.append(chan_intervals)
 70 |         # previous code already takes care of the [] possibility
 71 |         #if B_idx_lst == []:
 72 |         #    intervals.append([])
 73 |     return intervals
 74 | 
 75 | ##########
 76 | # Detect bursts and supressions in eeg data
 77 | def burst_supression_detection(x,fs,suppression_threshold = 10):
 78 | 	'''
 79 | 	# DETECT EMG ARTIFACTS.
 80 | 	nyq = 0.5 * fs
 81 | 	low = low / nyq
 82 | 	high = high / nyq
 83 | 	be, ae = signal.butter(order, [low, high], btype='band')
 84 | 	'''
 85 | 	# CALCULATE ENVELOPE
 86 | 	e = abs(signal.hilbert(x,axis=1));
 87 | 	# same as smooth(e,Fs/4) in MATLAB, apply 1/2 second smoothing
 88 | 	ME = np.array([np.convolve(el,np.ones(int(fs/4))/(fs/4),'same') for el in e.tolist()])
 89 | 	e = ME
 90 | 	# DETECT SUPRESSIONS
 91 | 	# apply threshold -- 10uv
 92 | 	z = (ME<suppression_threshold)
 93 | 	# remove too-short suppression segments
 94 | 	z = fcnRemoveShortEvents(z,fs/2)
 95 | 	# remove too-short burst segments
 96 | 	b = fcnRemoveShortEvents(1-z,fs/2)
 97 | 	z = 1-b
 98 | 	went_high = [np.where(np.array(chD[:-1]) < np.array(chD[1:]))[0].tolist() for chD in z.tolist()]
 99 | 	went_low = [np.where(np.array(chD[:-1]) > np.array(chD[1:]))[0].tolist() for chD in z.tolist()]
100 | 
101 | 	bursts = get_intervals(went_high,went_low)
102 | 	supressions = get_intervals(went_low,went_high)
103 | 
104 | 	return bursts,supressions
105 | 
106 | ##########
107 | # Coherence in the Delta Band
108 | def CoherenceDelta(eegData, i, j, fs=100):
109 |     nfft=eegData.shape[1]
110 |     f, Cxy = signal.coherence(eegData[i,:,:], eegData[j,:,:], fs=fs, nfft=nfft, axis=0)#, window=np.hanning(nfft))
111 |     out = np.mean(Cxy[np.all([f >= 0.5, f<=4], axis=0)], axis=0)
112 |     return out
113 | 
114 | ##########
115 | # correlation across channels
116 | def PhaseLagIndex(eegData, i, j):
117 |     hxi = ss.hilbert(eegData[i,:,:])
118 |     hxj = ss.hilbert(eegData[j,:,:])
119 |     # calculating the INSTANTANEOUS PHASE
120 |     inst_phasei = np.arctan(np.angle(hxi))
121 |     inst_phasej = np.arctan(np.angle(hxj))
122 | 
123 |     out = np.abs(np.mean(np.sign(inst_phasej - inst_phasei), axis=0))
124 |     return out
125 | 
126 | ##########
127 | # Cross Correlation
128 | def crossCorrelation(eegData, i, j):
129 |     out = np.zeros(eegData.shape[2])
130 |     for epoch in range(eegData.shape[2]):
131 |         ccor = np.correlate(eegData[i,:,epoch], eegData[j,:,epoch], mode="full")
132 |         absccor = np.abs(ccor)
133 |         out[epoch] = (np.max(absccor) - np.mean(absccor)) / np.std(absccor)
134 |     return out
135 | 
136 | ##########
137 | # Auxilary Cross-correlation Lag
138 | def corrCorrLagAux(eegData,ii,jj,Fs=100):
139 |     out = np.zeros(eegData.shape[2])
140 |     lagCorr = []
141 |     for lag in range(0,eegData.shape[1],int(0.2*Fs)):
142 |         tmp = eegData.copy()
143 |         tmp[jj,:,:] = np.roll(tmp[jj,:,:], lag, axis=0)
144 |         lagCorr.append(CrossCorrelation(tmp, ii, jj, Fs))
145 |     return np.argmax(lagCorr,axis=0)
146 | 
147 | ################################################
148 | #	bandpower Functions
149 | ################################################
150 | 
151 | ##########
152 | # compute the bandpower (area under segment (from fband[0] to fband[1] in Hz)
153 | # of curve in freqency domain) of data, at sampling frequency of Fs (100 ussually)
154 | def bandpower(data, fs, fband):
155 |     freqs, powers = periodogram(data, fs)
156 |     idx_min = np.argmax(freqs > fband[0]) - 1
157 |     idx_max = np.argmax(freqs > fband[1]) - 1
158 |     idx_delta = np.zeros(dtype=bool, shape=freqs.shape)
159 |     idx_delta[idx_min:idx_max] = True
160 |     bpower = simps(powers[idx_delta], freqs[idx_delta])
161 |     return bpower
162 | 
163 | ##########
164 | # computes the same thing as vecbandpower but with a loop
165 | def pfvecbandpower(data, fs, fband):
166 |     bpowers = np.zeros((data.shape[0], data.shape[2]))
167 |     for i in range(data.shape[0]):
168 |         freqs, powers = periodogram(data[i, :, :], fs, axis=0)
169 |         idx_min = np.argmax(freqs > fband[0]) - 1
170 |         idx_max = np.argmax(freqs > fband[1]) - 1
171 |         idx_delta = np.zeros(dtype=bool, shape=freqs.shape)
172 |         idx_delta[idx_min:idx_max] = True
173 |        
174 |         bpower = simps(powers[idx_delta, :], freqs[idx_delta], axis=0)
175 |         bpowers[i, :] = bpower
176 | 
177 |     return bpowers
178 | 
179 | ################################################
180 | #	Complexity features
181 | ################################################    
182 | 
183 | ##########
184 | # Extract the Shannon Entropy
185 | # threshold the signal and make it discrete, normalize it and then compute entropy
186 | def shannonEntropy(eegData, bin_min, bin_max, binWidth):
187 |     H = np.zeros((eegData.shape[0], eegData.shape[2]))
188 |     for chan in range(H.shape[0]):
189 |         for epoch in range(H.shape[1]):
190 |             counts, binCenters = np.histogram(eegData[chan,:,epoch], bins=np.arange(bin_min+1, bin_max, binWidth))
191 |             nz = counts > 0
192 |             prob = counts[nz] / np.sum(counts[nz])
193 |             H[chan, epoch] = -np.dot(prob, np.log2(prob/binWidth))
194 |     return H
195 |     
196 | ##########
197 | # Extract the tsalis Entropy
198 | def tsalisEntropy(eegData, bin_min, bin_max, binWidth, orders = [1]):
199 |     H = [np.zeros((eegData.shape[0], eegData.shape[2]))]*len(orders)
200 |     for chan in range(H[0].shape[0]):
201 |         for epoch in range(H[0].shape[1]):
202 |             counts, bins = np.histogram(eegData[chan,:,epoch], bins=np.arange(-200+1, 200, 2))
203 |             dist = dit.Distribution([str(bc).zfill(5) for bc in bins[:-1]],counts/sum(counts))
204 |             for ii,order in enumerate(orders):
205 |                 H[ii][chan,epoch] = tsallis_entropy(dist,order)
206 |     return H
207 | 
208 | ##########
209 | # Cepstrum Coefficients (n=2)
210 | def mfcc(eegData,fs,order=2):
211 |     H = np.zeros((eegData.shape[0], eegData.shape[2],order))
212 |     for chan in range(H.shape[0]):
213 |         for epoch in range(H.shape[1]):
214 |             H[chan, epoch, : ] = librosa.feature.mfcc(y=np.asfortranarray(eegData[chan,:,epoch]), sr=fs)[0:order].T
215 |     return H
216 | 
217 | ##########
218 | # Lyapunov exponent
219 | def lyapunov(eegData):
220 |     return np.mean(np.log(np.abs(np.gradient(eegData,axis=1))),axis=1)
221 |     
222 | ##########
223 | # Fractal Embedding Dimension
224 | # From pyrem: packadge for sleep scoring from EEG data
225 | # https://github.com/gilestrolab/pyrem/blob/master/src/pyrem/univariate.py
226 | def hFD(a, k_max): #Higuchi FD
227 |     L = []
228 |     x = []
229 |     N = len(a)
230 | 
231 |     for k in range(1,k_max):
232 |         Lk = 0
233 |         for m in range(0,k):
234 |             #we pregenerate all idxs
235 |             idxs = np.arange(1,int(np.floor((N-m)/k)),dtype=np.int32)
236 |             Lmk = np.sum(np.abs(a[m+idxs*k] - a[m+k*(idxs-1)]))
237 |             Lmk = (Lmk*(N - 1)/(((N - m)/ k)* k)) / k
238 |             Lk += Lmk
239 | 
240 |         L.append(np.log(Lk/(m+1)))
241 |         x.append([np.log(1.0/ k), 1])
242 | 
243 |     (p, r1, r2, s)=np.linalg.lstsq(x, L)
244 |     return p[0]
245 |     
246 | ##########
247 | # Hjorth Mobility
248 | # Hjorth Complexity
249 | # variance = mean(signal^2) iff mean(signal)=0
250 | # which it is be because I normalized the signal
251 | # Assuming signals have mean 0
252 | # Mobility = sqrt( mean(dx^2) / mean(x^2) )
253 | def hjorthParameters(xV):
254 |     dxV = np.diff(xV, axis=1)
255 |     ddxV = np.diff(dxV, axis=1)
256 | 
257 |     mx2 = np.mean(np.square(xV), axis=1)
258 |     mdx2 = np.mean(np.square(dxV), axis=1)
259 |     mddx2 = np.mean(np.square(ddxV), axis=1)
260 | 
261 |     mob = mdx2 / mx2
262 |     complexity = np.sqrt((mddx2 / mdx2) / mob)
263 |     mobility = np.sqrt(mob)
264 | 
265 |     # PLEASE NOTE that Mohammad did NOT ACTUALLY use hjorth complexity,
266 |     # in the matlab code for hjorth complexity subtraction by mob not division was used 
267 |     return mobility, complexity
268 | 
269 | ##########
270 | # false nearest neighbor descriptor
271 | def falseNearestNeighbor(eegData, fast=True):
272 |     # Average Mutual Information
273 |     # There exist good arguments that if the time delayed mutual
274 |     # information exhibits a marked minimum at a certain value of tex2html_wrap_inline6553,
275 |     # then this is a good candidate for a reasonable time delay.
276 |     npts = 1000   # not sure about this?
277 |     maxdims = 50
278 |     max_delay = 2 # max_delay = 200  # TODO: need to use 200, but also need to speed this up
279 |     distance_thresh = 0.5
280 |     
281 |     out = np.zeros((eegData.shape[0], eegData.shape[2]))
282 |     for chan in range(eegData.shape[0]):
283 |         for epoch in range(eegData.shape[2]):
284 |             if fast:
285 |                 out[chan, epoch] = 0
286 |             else:
287 |                 cur_eegData = eegData[chan, :, epoch]
288 |                 lagidx = 0  # we are looking for the index of the lag that makes the signal maximally uncorrelated to the original
289 |                 # # minNMI = 1  # normed_mutual_info is from 1 (perfectly correlated) to 0 (not at all correlated) 
290 |                 # # for lag in range(1, max_delay):
291 |                 # #     x = cur_eegData[:-lag]
292 |                 # #     xlag = cur_eegData[lag:]
293 |                 # #     # convert float data into histogram bins
294 |                 # #     nbins = int(np.floor(1 + np.log2(len(x)) + 0.5))
295 |                 # #     x_discrete = np.histogram(x, bins=nbins)[0]
296 |                 # #     xlag_discrete = np.histogram(xlag, bins=nbins)[0]
297 |                 # #     cNMI = normed_mutual_info(x_discrete, xlag_discrete)
298 |                 # #     if cNMI < minNMI:
299 |                 # #         minNMI = cNMI
300 |                 # #         lagidx = lag
301 |                 # nearest neighbors part
302 |                 knn = int(max(2, 6*lagidx))  # heuristic (number of nearest neighbors to look up)
303 |                 m = 1 # lagidx + 1
304 | 
305 |                 # y is the embedded version of the signal
306 |                 y = np.zeros((maxdims+1, npts))
307 |                 for d in range(maxdims+1):
308 |                     tmp = cur_eegData[d*m:d*m + npts]
309 |                     y[d, :tmp.shape[0]] = tmp
310 |                 
311 |                 nnd = np.ones((npts, maxdims))
312 |                 nnz = np.zeros((npts, maxdims))
313 |                 
314 |                 # see where it tends to settle
315 |                 for d in range(1, maxdims):
316 |                     for k in range(0, npts):
317 |                         # get the distances to all points in the window (distance given embedding dimension)
318 |                         dists = []
319 |                         for nextpt in range(1, knn+1):
320 |                             if k+nextpt < npts:
321 |                                 dists.append(np.linalg.norm(y[:d, k] - y[:d, k+nextpt]))
322 |                         if len(dists) > 0:
323 |                             minIdx = np.argmin(dists)
324 |                             if dists[minIdx] == 0:
325 |                                 dists[minIdx] = 0.0000001  # essentially 0 just silence the error
326 |                             nnd[k, d-1] = dists[minIdx]
327 |                             nnz[k, d-1] = np.abs( y[d+1, k] - y[d+1, minIdx+1+k] )
328 |                 # aggregate results
329 |                 mindim = np.mean(nnz/nnd > distance_thresh, axis=0) < 0.1
330 |                 # get the index of the first occurence of the value true
331 |                 # (a 1 in the binary representation of true and false)
332 |                 out[chan, epoch] = np.argmax(mindim)
333 |         
334 |     return out 
335 | 
336 | ##########
337 | # ARMA coefficients
338 | def arma(eegData,order=2):
339 |     H = np.zeros((eegData.shape[0], eegData.shape[2],order))
340 |     for chan in range(H.shape[0]):
341 |         for epoch in range(H.shape[1]):
342 |             # ARMA is deprecated, use ARIMA with d=0 instead
343 |             arma_mod = sm.tsa.ARIMA(eegData[chan,:,epoch], order=(order, 0, order), trend='n')
344 |             arma_res = arma_mod.fit(method_kwargs={'disp': False})
345 |             H[chan, epoch, : ] = arma_res.arparams
346 |     return H
347 | 
348 | ################################################
349 | #	Continuity features
350 | ################################################  
351 | 
352 | ##########
353 | # median frequency
354 | def medianFreq(eegData,fs):
355 |     H = np.zeros((eegData.shape[0], eegData.shape[2]))
356 |     for chan in range(H.shape[0]):
357 |         freqs, powers = signal.periodogram(eegData[chan, :, :], fs, axis=0)
358 |         H[chan,:] = freqs[np.argsort(powers,axis=0)[len(powers)//2]]
359 |     return H
360 | 
361 | ##########
362 | # calculate band power
363 | def bandPower(eegData, lowcut, highcut, fs):
364 | 	eegData_band = filt_data(eegData, lowcut, highcut, fs, order=7)
365 | 	freqs, powers = signal.periodogram(eegData_band, fs, axis=1)
366 | 	bandPwr = np.mean(powers,axis=1)
367 | 	return bandPwr
368 | 
369 | ##########
370 | # numberOfSpikes    
371 | def spikeNum(eegData,minNumSamples=7,stdAway = 3):
372 |     H = np.zeros((eegData.shape[0], eegData.shape[2]))
373 |     for chan in range(H.shape[0]):
374 |         for epoch in range(H.shape[1]):
375 |             mean = np.mean(eegData[chan, :, epoch])
376 |             std = np.std(eegData[chan,:,epoch],axis=1)
377 |             H[chan,epoch] = len(signal.find_peaks(abs(eegData[chan,:,epoch]-mean), 3*std,epoch,width=7)[0])
378 |     return H
379 | 
380 | ##########    
381 | # Standard Deviation
382 | def eegStd(eegData):
383 | 	std_res = np.std(eegData,axis=1)
384 | 	return std_res
385 | 
386 | ##########
387 | # α/δ Ratio
388 | def eegRatio(eegData,fs):
389 | 	# alpha (8–12 Hz)
390 | 	eegData_alpha = filt_data(eegData, 8, 12, fs)
391 | 	# delta (0.5–4 Hz)
392 | 	eegData_delta = filt_data(eegData, 0.5, 4, fs)
393 | 	# calculate the power
394 | 	powers_alpha = bandPower(eegData, 8, 12, fs)
395 | 	powers_delta = bandPower(eegData, 0.5, 4, fs)
396 | 	ratio_res = np.sum(powers_alpha,axis=0) / np.sum(powers_delta,axis=0)
397 | 	return np.expand_dims(ratio_res, axis=0)
398 | 
399 | ###########
400 | # Regularity (burst-suppression)
401 | # Regularity of eeg
402 | # filter with a window of 0.5 seconds to create a nonnegative smooth signal.
403 | # In this technique, we first squared the signal and applied a moving-average
404 | # The window length of the moving average was set at 0.5 seconds.
405 | def eegRegularity(eegData, Fs=100):
406 |     in_x = np.square(eegData)  # square signal
407 |     num_wts = Fs//2  # find the filter length in samples - we want 0.5 seconds.
408 |     q = signal.lfilter(np.ones(num_wts) / num_wts, 1, in_x, axis=1)
409 |     q = -np.sort(-q, axis=1) # descending sort on smooth signal
410 |     N = q.shape[1]
411 |     u2 = np.square(np.arange(1, N+1))
412 |     # COMPUTE THE Regularity
413 |     # dot each 5min epoch with the quadratic data points and then normalize by the size of the dotted things    
414 |     reg = np.sqrt( np.einsum('ijk,j->ik', q, u2) / (np.sum(q, axis=1)*(N**2)/3) )
415 |     return reg
416 | 
417 | ###########
418 | # Voltage < (5μ, 10μ, 20μ)
419 | def eegVoltage(eegData,voltage=20):
420 | 	eegFilt = eegData.copy()
421 | 	eegFilt[abs(eegFilt) > voltage] = np.nan
422 | 	volt_res = np.nanmean(eegFilt,axis=1)
423 | 	return volt_res
424 | 
425 | ##########
426 | # Diffuse Slowing
427 | # look for diffuse slowing (bandpower max from frequency domain integral)
428 | # repeated integration of a huge tensor is really expensive
429 | def diffuseSlowing(eegData, Fs=100, fast=True):
430 |     maxBP = np.zeros((eegData.shape[0], eegData.shape[2]))
431 |     idx = np.zeros((eegData.shape[0], eegData.shape[2]))
432 |     if fast:
433 |         return idx
434 |     for j in range(1, Fs//2):
435 |         print("BP", j)
436 |         cbp = bandpower(eegData, Fs, [j-1, j])
437 |         biggerCIdx = cbp > maxBP
438 |         idx[biggerCIdx] = j
439 |         maxBP[biggerCIdx] = cbp[biggerCIdx]
440 |     return (idx < 8)
441 | 
442 | ##########
443 | # Spikes
444 | def spikeNum(eegData,minNumSamples=7,stdAway = 3):
445 |     H = np.zeros((eegData.shape[0], eegData.shape[2]))
446 |     for chan in range(H.shape[0]):
447 |         for epoch in range(H.shape[1]):
448 |             mean = np.mean(eegData[chan, :, epoch])
449 |             std = np.std(eegData[chan,:,epoch])
450 |             H[chan,epoch] = len(signal.find_peaks(abs(eegData[chan,:,epoch]-mean), 3*std,epoch,width=7)[0])
451 |     return H
452 | 
453 | ##########
454 | # Delta Burst after spike
455 | def burstAfterSpike(eegData,eegData_subband,minNumSamples=7,stdAway = 3):
456 |     H = np.zeros((eegData.shape[0], eegData.shape[2]))
457 |     for chan in range(H.shape[0]):
458 |         for epoch in range(H.shape[1]):
459 |             preBurst = 0
460 |             postBurst = 0
461 |             mean = np.mean(eegData[chan, :, epoch])
462 |             std = np.std(eegData[chan,:,epoch])
463 |             idxList = signal.find_peaks(abs(eegData[chan,:,epoch]-mean), stdAway*std,epoch,width=minNumSamples)[0]
464 |             for idx in idxList:
465 |                 preBurst += np.mean(eegData_subband[chan,idx-7:idx-1,epoch])
466 |                 postBurst += np.mean(eegData_subband[chan,idx+1:idx+7,epoch])
467 |             H[chan,epoch] = postBurst - preBurst
468 |     return H
469 | 
470 | ##########
471 | # Sharp spike
472 | def shortSpikeNum(eegData,minNumSamples=7,stdAway = 3):
473 |     H = np.zeros((eegData.shape[0], eegData.shape[2]))
474 |     for chan in range(H.shape[0]):
475 |         for epoch in range(H.shape[1]):
476 |             mean = np.mean(eegData[chan, :, epoch])
477 |             std = np.std(eegData[chan,:,epoch])
478 |             longSpikes = set(signal.find_peaks(abs(eegData[chan,:,epoch]-mean), 3*std,epoch,width=7)[0])
479 |             shortSpikes = set(signal.find_peaks(abs(eegData[chan,:,epoch]-mean), 3*std,epoch,width=1)[0])
480 |             H[chan,epoch] = len(shortSpikes.difference(longSpikes))
481 |     return H
482 | 
483 | ##########
484 | # Number of Bursts
485 | def numBursts(eegData,fs):
486 | 	bursts = []
487 | 	supressions = []
488 | 	for epoch in range(eegData.shape[2]):
489 | 		epochBurst,epochSupressions = burst_supression_detection(eegData[:,:,epoch],fs,suppression_threshold=10)#,low=30,high=49)
490 | 		bursts.append(epochBurst)
491 | 		supressions.append(epochSupressions)
492 | 	# Number of Bursts
493 | 	numBursts_res = np.zeros((eegData.shape[0], eegData.shape[2]))
494 | 	for chan in range(numBursts_res.shape[0]):
495 | 		for epoch in range(numBursts_res.shape[1]):
496 | 			numBursts_res[chan,epoch] = len(bursts[epoch][chan])
497 | 	return numBursts_res
498 | 	
499 | ##########
500 | # Burst length μ and σ
501 | def burstLengthStats(eegData,fs):
502 | 	bursts = []
503 | 	supressions = []
504 | 	for epoch in range(eegData.shape[2]):
505 | 		epochBurst,epochSupressions = burst_supression_detection(eegData[:,:,epoch],fs,suppression_threshold=10)#,low=30,high=49)
506 | 		bursts.append(epochBurst)
507 | 		supressions.append(epochSupressions)
508 | 	# Number of Bursts
509 | 	burstMean_res = np.zeros((eegData.shape[0], eegData.shape[2]))
510 | 	burstStd_res = np.zeros((eegData.shape[0], eegData.shape[2]))
511 | 	for chan in range(burstMean_res.shape[0]):
512 | 		for epoch in range(burstMean_res.shape[1]):
513 | 			burstMean_res[chan,epoch] = np.mean([burst[1]-burst[0] for burst in bursts[epoch][chan]])
514 | 			burstStd_res[chan,epoch] = np.std([burst[1]-burst[0] for burst in bursts[epoch][chan]])
515 | 	burstMean_res = np.nan_to_num(burstMean_res)
516 | 	burstStd_res = np.nan_to_num(burstStd_res)
517 | 	return burstMean_res,burstStd_res
518 | 
519 | ##########
520 | # Burst band powers (δ, α, θ, β, γ)
521 | def burstBandPowers(eegData, lowcut, highcut, fs, order=7):
522 | 	band_burst_powers = np.zeros((eegData.shape[0], eegData.shape[2]))
523 | 	bursts = []
524 | 	supressions = []
525 | 	for epoch in range(eegData.shape[2]):
526 | 		epochBurst,epochSupressions = burst_supression_detection(eegData[:,:,epoch],fs,suppression_threshold=10)#,low=30,high=49)
527 | 		bursts.append(epochBurst)
528 | 		supressions.append(epochSupressions)
529 | 	eegData_band = filt_data(eegData, lowcut, highcut, fs, order=7)
530 | 	for epoch,epochBursts in enumerate(bursts):
531 | 		for chan,chanBursts in enumerate(epochBursts):
532 | 			epochPowers = []  
533 | 			for burst in chanBursts:
534 | 				if burst[1] == eegData.shape[1]:
535 | 					burstData =  eegData_band[:,burst[0]:,epoch]
536 | 				else:
537 | 					burstData =  eegData_band[:,burst[0]:burst[1],epoch]
538 | 				freqs, powers = signal.periodogram(burstData, fs, axis=1)
539 | 				epochPowers.append(np.mean(powers,axis=1))
540 | 			band_burst_powers[chan,epoch] = np.mean(epochPowers)	
541 | 	return band_burst_powers
542 | 
543 | ##########
544 | # Number of Suppressions
545 | def numSuppressions(eegData,fs,suppression_threshold=10):
546 | 	bursts = []
547 | 	supressions = []
548 | 	for epoch in range(eegData.shape[2]):
549 | 		epochBurst,epochSupressions = burst_supression_detection(eegData[:,:,epoch],fs,suppression_threshold=suppression_threshold)#,low=30,high=49)
550 | 		bursts.append(epochBurst)
551 | 		supressions.append(epochSupressions)
552 | 	numSupprs_res = np.zeros((eegData.shape[0], eegData.shape[2]))
553 | 	for chan in range(numSupprs_res.shape[0]):
554 | 		for epoch in range(numSupprs_res.shape[1]):
555 | 			numSupprs_res[chan,epoch] = len(supressions[epoch][chan])
556 | 	return numSupprs_res
557 | 
558 | ##########
559 | # Suppression length μ and σ
560 | def suppressionLengthStats(eegData,fs,suppression_threshold=10):
561 | 	bursts = []
562 | 	supressions = []
563 | 	for epoch in range(eegData.shape[2]):
564 | 		epochBurst,epochSupressions = burst_supression_detection(eegData[:,:,epoch],fs,suppression_threshold=suppression_threshold)#,low=30,high=49)
565 | 		bursts.append(epochBurst)
566 | 		supressions.append(epochSupressions)
567 | 	supressionMean_res = np.zeros((eegData.shape[0], eegData.shape[2]))
568 | 	supressionStd_res = np.zeros((eegData.shape[0], eegData.shape[2]))
569 | 	for chan in range(supressionMean_res.shape[0]):
570 | 		for epoch in range(supressionMean_res.shape[1]):
571 | 			supressionMean_res[chan,epoch] = np.mean([suppr[1]-suppr[0] for suppr in supressions[epoch][chan]])
572 | 			supressionStd_res[chan,epoch] = np.std([suppr[1]-suppr[0] for suppr in supressions[epoch][chan]])
573 | 	supressionMean_res = np.nan_to_num(supressionMean_res)
574 | 	supressionStd_res = np.nan_to_num(supressionStd_res)
575 | 	return supressionMean_res, supressionStd_res
576 | 
577 | ################################################
578 | #	Connectivity features
579 | ################################################
580 | 
581 | ##########
582 | # Coherence - δ
583 | def coherence(eegData,fs):
584 | 	coh_res = []
585 | 	for ii, jj in itertools.combinations(range(eegData.shape[0]), 2):
586 | 		coh_res.append(CoherenceDelta(eegData, ii, jj, fs=fs))
587 | 	coh_res = np.array(coh_res)
588 | 	return coh_res
589 | 
590 | ##########
591 | # Mutual information
592 | def calculate2Chan_MI(eegData,ii,jj,bin_min=-200, bin_max=200, binWidth=2):
593 |     H = np.zeros(eegData.shape[2])
594 |     bins = np.arange(bin_min+1, bin_max, binWidth)
595 |     for epoch in range(eegData.shape[2]):
596 |         c_xy = np.histogram2d(eegData[ii,:,epoch],eegData[jj,:,epoch],bins)[0]
597 |         H[epoch] = mutual_info_score(None, None, contingency=c_xy)
598 |     return H
599 | 
600 | ##########
601 | # Granger causality
602 | def calcGrangerCausality(eegData,ii,jj):
603 |     H = np.zeros(eegData.shape[2])
604 |     for epoch in range(eegData.shape[2]):
605 |         X = np.vstack([eegData[ii,:,epoch],eegData[jj,:,epoch]]).T
606 |         H[epoch] = tsa.stattools.grangercausalitytests(X, 1, addconst=True, verbose=False)[1][0]['ssr_ftest'][0]
607 |     return H
608 | 
609 | ##########
610 | # phase Lag Index
611 | def phaseLagIndex(eegData, i, j):
612 |     hxi = ss.hilbert(eegData[i,:,:])
613 |     hxj = ss.hilbert(eegData[j,:,:])
614 |     # calculating the INSTANTANEOUS PHASE
615 |     inst_phasei = np.arctan(np.angle(hxi))
616 |     inst_phasej = np.arctan(np.angle(hxj))
617 | 
618 |     out = np.abs(np.mean(np.sign(inst_phasej - inst_phasei), axis=0))
619 |     return out
620 | 
621 | ##########
622 | # Cross-correlation Magnitude
623 | def crossCorrMag(eegData,ii,jj):
624 | 	crossCorr_res = []
625 | 	for ii, jj in itertools.combinations(range(eegData.shape[0]), 2):
626 | 		crossCorr_res.append(crossCorrelation(eegData, ii, jj))
627 | 	crossCorr_res = np.array(crossCorr_res)
628 | 	return crossCorr_res
629 | 
630 | ##########
631 | # Cross-correlation Lag
632 | def corrCorrLag(eegData,ii,jj,fs=100):
633 | 	crossCorrLag_res = []
634 | 	for ii, jj in itertools.combinations(range(eegData.shape[0]), 2):
635 | 		crossCorrLag_res.append(corrCorrLag(eegData, ii, jj, fs))
636 | 	crossCorrLag_res = np.array(crossCorrLag_res)
637 | 	return crossCorrLag_res
638 | 


--------------------------------------------------------------------------------
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123 |   The "System Libraries" of an executable work include anything, other
124 | than the work as a whole, that (a) is included in the normal form of
125 | packaging a Major Component, but which is not part of that Major
126 | Component, and (b) serves only to enable use of the work with that
127 | Major Component, or to implement a Standard Interface for which an
128 | implementation is available to the public in source code form.  A
129 | "Major Component", in this context, means a major essential component
130 | (kernel, window system, and so on) of the specific operating system
131 | (if any) on which the executable work runs, or a compiler used to
132 | produce the work, or an object code interpreter used to run it.
133 | 
134 |   The "Corresponding Source" for a work in object code form means all
135 | the source code needed to generate, install, and (for an executable
136 | work) run the object code and to modify the work, including scripts to
137 | control those activities.  However, it does not include the work's
138 | System Libraries, or general-purpose tools or generally available free
139 | programs which are used unmodified in performing those activities but
140 | which are not part of the work.  For example, Corresponding Source
141 | includes interface definition files associated with source files for
142 | the work, and the source code for shared libraries and dynamically
143 | linked subprograms that the work is specifically designed to require,
144 | such as by intimate data communication or control flow between those
145 | subprograms and other parts of the work.
146 | 
147 |   The Corresponding Source need not include anything that users
148 | can regenerate automatically from other parts of the Corresponding
149 | Source.
150 | 
151 |   The Corresponding Source for a work in source code form is that
152 | same work.
153 | 
154 |   2. Basic Permissions.
155 | 
156 |   All rights granted under this License are granted for the term of
157 | copyright on the Program, and are irrevocable provided the stated
158 | conditions are met.  This License explicitly affirms your unlimited
159 | permission to run the unmodified Program.  The output from running a
160 | covered work is covered by this License only if the output, given its
161 | content, constitutes a covered work.  This License acknowledges your
162 | rights of fair use or other equivalent, as provided by copyright law.
163 | 
164 |   You may make, run and propagate covered works that you do not
165 | convey, without conditions so long as your license otherwise remains
166 | in force.  You may convey covered works to others for the sole purpose
167 | of having them make modifications exclusively for you, or provide you
168 | with facilities for running those works, provided that you comply with
169 | the terms of this License in conveying all material for which you do
170 | not control copyright.  Those thus making or running the covered works
171 | for you must do so exclusively on your behalf, under your direction
172 | and control, on terms that prohibit them from making any copies of
173 | your copyrighted material outside their relationship with you.
174 | 
175 |   Conveying under any other circumstances is permitted solely under
176 | the conditions stated below.  Sublicensing is not allowed; section 10
177 | makes it unnecessary.
178 | 
179 |   3. Protecting Users' Legal Rights From Anti-Circumvention Law.
180 | 
181 |   No covered work shall be deemed part of an effective technological
182 | measure under any applicable law fulfilling obligations under article
183 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or
184 | similar laws prohibiting or restricting circumvention of such
185 | measures.
186 | 
187 |   When you convey a covered work, you waive any legal power to forbid
188 | circumvention of technological measures to the extent such circumvention
189 | is effected by exercising rights under this License with respect to
190 | the covered work, and you disclaim any intention to limit operation or
191 | modification of the work as a means of enforcing, against the work's
192 | users, your or third parties' legal rights to forbid circumvention of
193 | technological measures.
194 | 
195 |   4. Conveying Verbatim Copies.
196 | 
197 |   You may convey verbatim copies of the Program's source code as you
198 | receive it, in any medium, provided that you conspicuously and
199 | appropriately publish on each copy an appropriate copyright notice;
200 | keep intact all notices stating that this License and any
201 | non-permissive terms added in accord with section 7 apply to the code;
202 | keep intact all notices of the absence of any warranty; and give all
203 | recipients a copy of this License along with the Program.
204 | 
205 |   You may charge any price or no price for each copy that you convey,
206 | and you may offer support or warranty protection for a fee.
207 | 
208 |   5. Conveying Modified Source Versions.
209 | 
210 |   You may convey a work based on the Program, or the modifications to
211 | produce it from the Program, in the form of source code under the
212 | terms of section 4, provided that you also meet all of these conditions:
213 | 
214 |     a) The work must carry prominent notices stating that you modified
215 |     it, and giving a relevant date.
216 | 
217 |     b) The work must carry prominent notices stating that it is
218 |     released under this License and any conditions added under section
219 |     7.  This requirement modifies the requirement in section 4 to
220 |     "keep intact all notices".
221 | 
222 |     c) You must license the entire work, as a whole, under this
223 |     License to anyone who comes into possession of a copy.  This
224 |     License will therefore apply, along with any applicable section 7
225 |     additional terms, to the whole of the work, and all its parts,
226 |     regardless of how they are packaged.  This License gives no
227 |     permission to license the work in any other way, but it does not
228 |     invalidate such permission if you have separately received it.
229 | 
230 |     d) If the work has interactive user interfaces, each must display
231 |     Appropriate Legal Notices; however, if the Program has interactive
232 |     interfaces that do not display Appropriate Legal Notices, your
233 |     work need not make them do so.
234 | 
235 |   A compilation of a covered work with other separate and independent
236 | works, which are not by their nature extensions of the covered work,
237 | and which are not combined with it such as to form a larger program,
238 | in or on a volume of a storage or distribution medium, is called an
239 | "aggregate" if the compilation and its resulting copyright are not
240 | used to limit the access or legal rights of the compilation's users
241 | beyond what the individual works permit.  Inclusion of a covered work
242 | in an aggregate does not cause this License to apply to the other
243 | parts of the aggregate.
244 | 
245 |   6. Conveying Non-Source Forms.
246 | 
247 |   You may convey a covered work in object code form under the terms
248 | of sections 4 and 5, provided that you also convey the
249 | machine-readable Corresponding Source under the terms of this License,
250 | in one of these ways:
251 | 
252 |     a) Convey the object code in, or embodied in, a physical product
253 |     (including a physical distribution medium), accompanied by the
254 |     Corresponding Source fixed on a durable physical medium
255 |     customarily used for software interchange.
256 | 
257 |     b) Convey the object code in, or embodied in, a physical product
258 |     (including a physical distribution medium), accompanied by a
259 |     written offer, valid for at least three years and valid for as
260 |     long as you offer spare parts or customer support for that product
261 |     model, to give anyone who possesses the object code either (1) a
262 |     copy of the Corresponding Source for all the software in the
263 |     product that is covered by this License, on a durable physical
264 |     medium customarily used for software interchange, for a price no
265 |     more than your reasonable cost of physically performing this
266 |     conveying of source, or (2) access to copy the
267 |     Corresponding Source from a network server at no charge.
268 | 
269 |     c) Convey individual copies of the object code with a copy of the
270 |     written offer to provide the Corresponding Source.  This
271 |     alternative is allowed only occasionally and noncommercially, and
272 |     only if you received the object code with such an offer, in accord
273 |     with subsection 6b.
274 | 
275 |     d) Convey the object code by offering access from a designated
276 |     place (gratis or for a charge), and offer equivalent access to the
277 |     Corresponding Source in the same way through the same place at no
278 |     further charge.  You need not require recipients to copy the
279 |     Corresponding Source along with the object code.  If the place to
280 |     copy the object code is a network server, the Corresponding Source
281 |     may be on a different server (operated by you or a third party)
282 |     that supports equivalent copying facilities, provided you maintain
283 |     clear directions next to the object code saying where to find the
284 |     Corresponding Source.  Regardless of what server hosts the
285 |     Corresponding Source, you remain obligated to ensure that it is
286 |     available for as long as needed to satisfy these requirements.
287 | 
288 |     e) Convey the object code using peer-to-peer transmission, provided
289 |     you inform other peers where the object code and Corresponding
290 |     Source of the work are being offered to the general public at no
291 |     charge under subsection 6d.
292 | 
293 |   A separable portion of the object code, whose source code is excluded
294 | from the Corresponding Source as a System Library, need not be
295 | included in conveying the object code work.
296 | 
297 |   A "User Product" is either (1) a "consumer product", which means any
298 | tangible personal property which is normally used for personal, family,
299 | or household purposes, or (2) anything designed or sold for incorporation
300 | into a dwelling.  In determining whether a product is a consumer product,
301 | doubtful cases shall be resolved in favor of coverage.  For a particular
302 | product received by a particular user, "normally used" refers to a
303 | typical or common use of that class of product, regardless of the status
304 | of the particular user or of the way in which the particular user
305 | actually uses, or expects or is expected to use, the product.  A product
306 | is a consumer product regardless of whether the product has substantial
307 | commercial, industrial or non-consumer uses, unless such uses represent
308 | the only significant mode of use of the product.
309 | 
310 |   "Installation Information" for a User Product means any methods,
311 | procedures, authorization keys, or other information required to install
312 | and execute modified versions of a covered work in that User Product from
313 | a modified version of its Corresponding Source.  The information must
314 | suffice to ensure that the continued functioning of the modified object
315 | code is in no case prevented or interfered with solely because
316 | modification has been made.
317 | 
318 |   If you convey an object code work under this section in, or with, or
319 | specifically for use in, a User Product, and the conveying occurs as
320 | part of a transaction in which the right of possession and use of the
321 | User Product is transferred to the recipient in perpetuity or for a
322 | fixed term (regardless of how the transaction is characterized), the
323 | Corresponding Source conveyed under this section must be accompanied
324 | by the Installation Information.  But this requirement does not apply
325 | if neither you nor any third party retains the ability to install
326 | modified object code on the User Product (for example, the work has
327 | been installed in ROM).
328 | 
329 |   The requirement to provide Installation Information does not include a
330 | requirement to continue to provide support service, warranty, or updates
331 | for a work that has been modified or installed by the recipient, or for
332 | the User Product in which it has been modified or installed.  Access to a
333 | network may be denied when the modification itself materially and
334 | adversely affects the operation of the network or violates the rules and
335 | protocols for communication across the network.
336 | 
337 |   Corresponding Source conveyed, and Installation Information provided,
338 | in accord with this section must be in a format that is publicly
339 | documented (and with an implementation available to the public in
340 | source code form), and must require no special password or key for
341 | unpacking, reading or copying.
342 | 
343 |   7. Additional Terms.
344 | 
345 |   "Additional permissions" are terms that supplement the terms of this
346 | License by making exceptions from one or more of its conditions.
347 | Additional permissions that are applicable to the entire Program shall
348 | be treated as though they were included in this License, to the extent
349 | that they are valid under applicable law.  If additional permissions
350 | apply only to part of the Program, that part may be used separately
351 | under those permissions, but the entire Program remains governed by
352 | this License without regard to the additional permissions.
353 | 
354 |   When you convey a copy of a covered work, you may at your option
355 | remove any additional permissions from that copy, or from any part of
356 | it.  (Additional permissions may be written to require their own
357 | removal in certain cases when you modify the work.)  You may place
358 | additional permissions on material, added by you to a covered work,
359 | for which you have or can give appropriate copyright permission.
360 | 
361 |   Notwithstanding any other provision of this License, for material you
362 | add to a covered work, you may (if authorized by the copyright holders of
363 | that material) supplement the terms of this License with terms:
364 | 
365 |     a) Disclaiming warranty or limiting liability differently from the
366 |     terms of sections 15 and 16 of this License; or
367 | 
368 |     b) Requiring preservation of specified reasonable legal notices or
369 |     author attributions in that material or in the Appropriate Legal
370 |     Notices displayed by works containing it; or
371 | 
372 |     c) Prohibiting misrepresentation of the origin of that material, or
373 |     requiring that modified versions of such material be marked in
374 |     reasonable ways as different from the original version; or
375 | 
376 |     d) Limiting the use for publicity purposes of names of licensors or
377 |     authors of the material; or
378 | 
379 |     e) Declining to grant rights under trademark law for use of some
380 |     trade names, trademarks, or service marks; or
381 | 
382 |     f) Requiring indemnification of licensors and authors of that
383 |     material by anyone who conveys the material (or modified versions of
384 |     it) with contractual assumptions of liability to the recipient, for
385 |     any liability that these contractual assumptions directly impose on
386 |     those licensors and authors.
387 | 
388 |   All other non-permissive additional terms are considered "further
389 | restrictions" within the meaning of section 10.  If the Program as you
390 | received it, or any part of it, contains a notice stating that it is
391 | governed by this License along with a term that is a further
392 | restriction, you may remove that term.  If a license document contains
393 | a further restriction but permits relicensing or conveying under this
394 | License, you may add to a covered work material governed by the terms
395 | of that license document, provided that the further restriction does
396 | not survive such relicensing or conveying.
397 | 
398 |   If you add terms to a covered work in accord with this section, you
399 | must place, in the relevant source files, a statement of the
400 | additional terms that apply to those files, or a notice indicating
401 | where to find the applicable terms.
402 | 
403 |   Additional terms, permissive or non-permissive, may be stated in the
404 | form of a separately written license, or stated as exceptions;
405 | the above requirements apply either way.
406 | 
407 |   8. Termination.
408 | 
409 |   You may not propagate or modify a covered work except as expressly
410 | provided under this License.  Any attempt otherwise to propagate or
411 | modify it is void, and will automatically terminate your rights under
412 | this License (including any patent licenses granted under the third
413 | paragraph of section 11).
414 | 
415 |   However, if you cease all violation of this License, then your
416 | license from a particular copyright holder is reinstated (a)
417 | provisionally, unless and until the copyright holder explicitly and
418 | finally terminates your license, and (b) permanently, if the copyright
419 | holder fails to notify you of the violation by some reasonable means
420 | prior to 60 days after the cessation.
421 | 
422 |   Moreover, your license from a particular copyright holder is
423 | reinstated permanently if the copyright holder notifies you of the
424 | violation by some reasonable means, this is the first time you have
425 | received notice of violation of this License (for any work) from that
426 | copyright holder, and you cure the violation prior to 30 days after
427 | your receipt of the notice.
428 | 
429 |   Termination of your rights under this section does not terminate the
430 | licenses of parties who have received copies or rights from you under
431 | this License.  If your rights have been terminated and not permanently
432 | reinstated, you do not qualify to receive new licenses for the same
433 | material under section 10.
434 | 
435 |   9. Acceptance Not Required for Having Copies.
436 | 
437 |   You are not required to accept this License in order to receive or
438 | run a copy of the Program.  Ancillary propagation of a covered work
439 | occurring solely as a consequence of using peer-to-peer transmission
440 | to receive a copy likewise does not require acceptance.  However,
441 | nothing other than this License grants you permission to propagate or
442 | modify any covered work.  These actions infringe copyright if you do
443 | not accept this License.  Therefore, by modifying or propagating a
444 | covered work, you indicate your acceptance of this License to do so.
445 | 
446 |   10. Automatic Licensing of Downstream Recipients.
447 | 
448 |   Each time you convey a covered work, the recipient automatically
449 | receives a license from the original licensors, to run, modify and
450 | propagate that work, subject to this License.  You are not responsible
451 | for enforcing compliance by third parties with this License.
452 | 
453 |   An "entity transaction" is a transaction transferring control of an
454 | organization, or substantially all assets of one, or subdividing an
455 | organization, or merging organizations.  If propagation of a covered
456 | work results from an entity transaction, each party to that
457 | transaction who receives a copy of the work also receives whatever
458 | licenses to the work the party's predecessor in interest had or could
459 | give under the previous paragraph, plus a right to possession of the
460 | Corresponding Source of the work from the predecessor in interest, if
461 | the predecessor has it or can get it with reasonable efforts.
462 | 
463 |   You may not impose any further restrictions on the exercise of the
464 | rights granted or affirmed under this License.  For example, you may
465 | not impose a license fee, royalty, or other charge for exercise of
466 | rights granted under this License, and you may not initiate litigation
467 | (including a cross-claim or counterclaim in a lawsuit) alleging that
468 | any patent claim is infringed by making, using, selling, offering for
469 | sale, or importing the Program or any portion of it.
470 | 
471 |   11. Patents.
472 | 
473 |   A "contributor" is a copyright holder who authorizes use under this
474 | License of the Program or a work on which the Program is based.  The
475 | work thus licensed is called the contributor's "contributor version".
476 | 
477 |   A contributor's "essential patent claims" are all patent claims
478 | owned or controlled by the contributor, whether already acquired or
479 | hereafter acquired, that would be infringed by some manner, permitted
480 | by this License, of making, using, or selling its contributor version,
481 | but do not include claims that would be infringed only as a
482 | consequence of further modification of the contributor version.  For
483 | purposes of this definition, "control" includes the right to grant
484 | patent sublicenses in a manner consistent with the requirements of
485 | this License.
486 | 
487 |   Each contributor grants you a non-exclusive, worldwide, royalty-free
488 | patent license under the contributor's essential patent claims, to
489 | make, use, sell, offer for sale, import and otherwise run, modify and
490 | propagate the contents of its contributor version.
491 | 
492 |   In the following three paragraphs, a "patent license" is any express
493 | agreement or commitment, however denominated, not to enforce a patent
494 | (such as an express permission to practice a patent or covenant not to
495 | sue for patent infringement).  To "grant" such a patent license to a
496 | party means to make such an agreement or commitment not to enforce a
497 | patent against the party.
498 | 
499 |   If you convey a covered work, knowingly relying on a patent license,
500 | and the Corresponding Source of the work is not available for anyone
501 | to copy, free of charge and under the terms of this License, through a
502 | publicly available network server or other readily accessible means,
503 | then you must either (1) cause the Corresponding Source to be so
504 | available, or (2) arrange to deprive yourself of the benefit of the
505 | patent license for this particular work, or (3) arrange, in a manner
506 | consistent with the requirements of this License, to extend the patent
507 | license to downstream recipients.  "Knowingly relying" means you have
508 | actual knowledge that, but for the patent license, your conveying the
509 | covered work in a country, or your recipient's use of the covered work
510 | in a country, would infringe one or more identifiable patents in that
511 | country that you have reason to believe are valid.
512 | 
513 |   If, pursuant to or in connection with a single transaction or
514 | arrangement, you convey, or propagate by procuring conveyance of, a
515 | covered work, and grant a patent license to some of the parties
516 | receiving the covered work authorizing them to use, propagate, modify
517 | or convey a specific copy of the covered work, then the patent license
518 | you grant is automatically extended to all recipients of the covered
519 | work and works based on it.
520 | 
521 |   A patent license is "discriminatory" if it does not include within
522 | the scope of its coverage, prohibits the exercise of, or is
523 | conditioned on the non-exercise of one or more of the rights that are
524 | specifically granted under this License.  You may not convey a covered
525 | work if you are a party to an arrangement with a third party that is
526 | in the business of distributing software, under which you make payment
527 | to the third party based on the extent of your activity of conveying
528 | the work, and under which the third party grants, to any of the
529 | parties who would receive the covered work from you, a discriminatory
530 | patent license (a) in connection with copies of the covered work
531 | conveyed by you (or copies made from those copies), or (b) primarily
532 | for and in connection with specific products or compilations that
533 | contain the covered work, unless you entered into that arrangement,
534 | or that patent license was granted, prior to 28 March 2007.
535 | 
536 |   Nothing in this License shall be construed as excluding or limiting
537 | any implied license or other defenses to infringement that may
538 | otherwise be available to you under applicable patent law.
539 | 
540 |   12. No Surrender of Others' Freedom.
541 | 
542 |   If conditions are imposed on you (whether by court order, agreement or
543 | otherwise) that contradict the conditions of this License, they do not
544 | excuse you from the conditions of this License.  If you cannot convey a
545 | covered work so as to satisfy simultaneously your obligations under this
546 | License and any other pertinent obligations, then as a consequence you may
547 | not convey it at all.  For example, if you agree to terms that obligate you
548 | to collect a royalty for further conveying from those to whom you convey
549 | the Program, the only way you could satisfy both those terms and this
550 | License would be to refrain entirely from conveying the Program.
551 | 
552 |   13. Use with the GNU Affero General Public License.
553 | 
554 |   Notwithstanding any other provision of this License, you have
555 | permission to link or combine any covered work with a work licensed
556 | under version 3 of the GNU Affero General Public License into a single
557 | combined work, and to convey the resulting work.  The terms of this
558 | License will continue to apply to the part which is the covered work,
559 | but the special requirements of the GNU Affero General Public License,
560 | section 13, concerning interaction through a network will apply to the
561 | combination as such.
562 | 
563 |   14. Revised Versions of this License.
564 | 
565 |   The Free Software Foundation may publish revised and/or new versions of
566 | the GNU General Public License from time to time.  Such new versions will
567 | be similar in spirit to the present version, but may differ in detail to
568 | address new problems or concerns.
569 | 
570 |   Each version is given a distinguishing version number.  If the
571 | Program specifies that a certain numbered version of the GNU General
572 | Public License "or any later version" applies to it, you have the
573 | option of following the terms and conditions either of that numbered
574 | version or of any later version published by the Free Software
575 | Foundation.  If the Program does not specify a version number of the
576 | GNU General Public License, you may choose any version ever published
577 | by the Free Software Foundation.
578 | 
579 |   If the Program specifies that a proxy can decide which future
580 | versions of the GNU General Public License can be used, that proxy's
581 | public statement of acceptance of a version permanently authorizes you
582 | to choose that version for the Program.
583 | 
584 |   Later license versions may give you additional or different
585 | permissions.  However, no additional obligations are imposed on any
586 | author or copyright holder as a result of your choosing to follow a
587 | later version.
588 | 
589 |   15. Disclaimer of Warranty.
590 | 
591 |   THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
592 | APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
596 | PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
597 | IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
599 | 
600 |   16. Limitation of Liability.
601 | 
602 |   IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
610 | SUCH DAMAGES.
611 | 
612 |   17. Interpretation of Sections 15 and 16.
613 | 
614 |   If the disclaimer of warranty and limitation of liability provided
615 | above cannot be given local legal effect according to their terms,
616 | reviewing courts shall apply local law that most closely approximates
617 | an absolute waiver of all civil liability in connection with the
618 | Program, unless a warranty or assumption of liability accompanies a
619 | copy of the Program in return for a fee.
620 | 
621 |                      END OF TERMS AND CONDITIONS
622 | 
623 |             How to Apply These Terms to Your New Programs
624 | 
625 |   If you develop a new program, and you want it to be of the greatest
626 | possible use to the public, the best way to achieve this is to make it
627 | free software which everyone can redistribute and change under these terms.
628 | 
629 |   To do so, attach the following notices to the program.  It is safest
630 | to attach them to the start of each source file to most effectively
631 | state the exclusion of warranty; and each file should have at least
632 | the "copyright" line and a pointer to where the full notice is found.
633 | 
634 |     <one line to give the program's name and a brief idea of what it does.>
635 |     Copyright (C) <year>  <name of author>
636 | 
637 |     This program is free software: you can redistribute it and/or modify
638 |     it under the terms of the GNU General Public License as published by
639 |     the Free Software Foundation, either version 3 of the License, or
640 |     (at your option) any later version.
641 | 
642 |     This program is distributed in the hope that it will be useful,
643 |     but WITHOUT ANY WARRANTY; without even the implied warranty of
644 |     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
645 |     GNU General Public License for more details.
646 | 
647 |     You should have received a copy of the GNU General Public License
648 |     along with this program.  If not, see <https://www.gnu.org/licenses/>.
649 | 
650 | Also add information on how to contact you by electronic and paper mail.
651 | 
652 |   If the program does terminal interaction, make it output a short
653 | notice like this when it starts in an interactive mode:
654 | 
655 |     <program>  Copyright (C) <year>  <name of author>
656 |     This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
657 |     This is free software, and you are welcome to redistribute it
658 |     under certain conditions; type `show c' for details.
659 | 
660 | The hypothetical commands `show w' and `show c' should show the appropriate
661 | parts of the General Public License.  Of course, your program's commands
662 | might be different; for a GUI interface, you would use an "about box".
663 | 
664 |   You should also get your employer (if you work as a programmer) or school,
665 | if any, to sign a "copyright disclaimer" for the program, if necessary.
666 | For more information on this, and how to apply and follow the GNU GPL, see
667 | <https://www.gnu.org/licenses/>.
668 | 
669 |   The GNU General Public License does not permit incorporating your program
670 | into proprietary programs.  If your program is a subroutine library, you
671 | may consider it more useful to permit linking proprietary applications with
672 | the library.  If this is what you want to do, use the GNU Lesser General
673 | Public License instead of this License.  But first, please read
674 | <https://www.gnu.org/licenses/why-not-lgpl.html>.
675 | 


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