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Add symbolic regression example
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‎source-code/symbolic-regression/create_data.py

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#!/usr/bin/env python
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import argparse
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import numpy as np
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def create_data(n: int, t_max: float, a: float, b: float, sigma: float) -> tuple[np.ndarray, np.ndarray]:
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t = np.linspace(0.0, t_max, n) + np.random.normal(scale=sigma, size=n)
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t[0] = 0.0
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x = a + b*np.sqrt(t) + np.random.normal(scale=sigma, size=n)
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return t, x
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def main():
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arg_parser = argparse.ArgumentParser(description='create noisy data set for a + b*sqrt(t)')
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arg_parser.add_argument('--n', type=int, default=100,
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help='number of points')
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arg_parser.add_argument('--t_max', type=float, default=30.0,
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help='maximum time')
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arg_parser.add_argument('--a', type=float, default=0.1,
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help='additive constant')
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arg_parser.add_argument('--b', type=float, default=0.5,
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help='multiplication factor')
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arg_parser.add_argument('--sigma', type=float, default=0.0,
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help='noise level')
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args = arg_parser.parse_args()
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for t, x in zip(*create_data(n=args.n, t_max=args.t_max, a=args.a, b=args.b, sigma=args.sigma)):
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print(f'{t},{x}')
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if __name__ == '__main__':
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main()

‎source-code/symbolic-regression/data.txt

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0.0,3.135792512413561
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0.04917507892521977,4.130354853733771
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0.38618397131377363,6.011067338531955
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0.3870133583739641,6.106184778902891
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0.7378723724895282,7.1722800673270966
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1.1083426898155673,8.25966345547244
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1.2965788974680286,8.754811817195248
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1.4664233095930943,9.024385334346336
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1.5567002255835847,9.140986767197862
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1.8805196710437433,9.86619642295168
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2.0403597484700136,10.183508718331238
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2.3880881183941485,10.720398260938284
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2.4404250954405926,10.762684435660642
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2.6093034588740007,11.089069692568328
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2.9903586429226374,11.809023895570325
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2.9319554439200126,11.492913194979257
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3.358514343416962,12.057295084737861
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3.463517627451456,12.185740397323244
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3.6503835099073654,12.717240550322568
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3.945825062960219,12.714905565999084
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4.140040738231665,13.238343742055978
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4.386959736676804,13.327826099430586
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4.571617086388203,13.72517932654574
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4.511110955419059,13.576192576128978
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4.8587757464378845,14.187086003381816
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5.101462904742424,14.406261191423873
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5.16555808652569,14.426383357760189
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5.430068339408772,14.529098652708946
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5.657757527774882,14.858290701837948
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5.902811659978236,15.044675412237089
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6.166886076950506,15.422188748780993
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6.077024895183746,15.164130636336493
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6.457555303195658,15.873068343918764
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6.670483139183774,15.799814154514008
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6.9349296999444725,16.133136042821537
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7.015670231413422,16.187639136111635
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7.053422373700981,16.183005526440013
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7.561850598673937,16.841619753513182
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7.5427949470946904,16.705985326188273
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7.846026776337292,17.01475047149082
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8.047323586909567,17.321619088060434
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8.449032560554086,17.430555610924777
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8.63280050792723,17.674342431080316
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8.651316710079197,17.86229565451557
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8.880416160966892,17.89130895746749
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8.961370090868897,18.01643142603243
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9.23635003920086,18.237081083268915
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9.408204030795556,18.362631806349274
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9.888658949654786,18.715292300715763
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9.757113151921999,18.446579392298386
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10.109408563570906,18.880702015074988
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10.267726986172564,19.147258680877094
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10.408741182428452,19.21668586221017
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10.767242128572184,19.426233750601277
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10.987099300762203,19.465720488657468
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11.148408093570783,19.618631014406855
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11.27762457753493,19.703681137156945
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11.52800497870441,19.920494671550465
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11.851678441109593,20.22533563427639
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12.16874006014594,20.39983531037478
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12.202677676417574,20.39100995525543
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12.57024556172086,20.73619431865826
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12.606423573707934,20.700608692958273
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12.949081834064543,20.947785946603847
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13.214885791532037,21.276328240212482
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13.782406055579965,21.571357507857144
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14.036286845447481,21.711368482874757
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14.341624764400732,21.748998351391375
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14.727438548026752,22.224193240741325
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14.649349056101203,22.06921676629916
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14.79729748379505,22.162070303714877
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15.172483223639146,22.332950462006693
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15.459180925022874,22.781678470794308
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15.543245773808717,22.893850930939387
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15.758482487249992,22.921799711637334
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15.86459513416048,22.75209350666247
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16.1956978570662,23.087753735311708
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16.24674748635097,23.401965639250722
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16.47384235930462,23.126800791150767
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16.78745969414955,23.56585310475394
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17.016115686136974,23.7533250657291
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16.97545954714283,23.487108147748426
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17.37206351448937,24.034121949776974
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17.73197263660408,24.10815489854129
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17.83020724040754,24.302119531279345
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17.908872587346675,24.128949627545918
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18.258436044287723,24.48187135131471
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18.290107701344205,24.53318590092017
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18.67462077271872,24.563537765146684
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18.53875882369785,24.48682113634027
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18.86242140013619,24.60026258893294
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19.250508467945654,24.845662570850287
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19.411781796757236,25.041372568062297
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19.686134796254237,25.094581620443236
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19.776467086699082,25.316712678356666
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19.87362597262397,25.36544920372383

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