polynomials_test
27-Feb-2019 08:54:01
polynomials_test
MATLAB version.
Test polynomials.
RANGE_BY_SAMPLING_TEST:
Use N sample values of each polynomial over its domain to estimate
its minimum Pmin and maximum Pmax
N Pmin Pmax
butcher: [-1.4393333333, +0.219]
16 -0.9392362348 0.1722153637
32 -1.096808774 0.1619794357
64 -1.218607005 0.1354705999
128 -1.146982586 0.200123647
256 -1.163550893 0.1864259985
512 -1.261186459 0.1643861716
1024 -1.301762549 0.181939832
2048 -1.328901868 0.1806981008
4096 -1.30398538 0.1970596662
8192 -1.333096962 0.1967859621
16384 -1.367394167 0.1955562743
32768 -1.347472355 0.2058122585
65536 -1.365699517 0.2125327583
131072 -1.355741449 0.2123066372
262144 -1.396926957 0.2177005289
524288 -1.397266108 0.2141781022
1048576 -1.39471054 0.2164118703
camel: [ -1.031628453489616, ? ]:
16 2.34293696 286.8335898
32 -0.5656567098 323.5035177
64 -0.9962010179 325.1266789
128 -1.027385874 379.3308185
256 -0.6818695846 307.3754905
512 -1.015374044 352.3236156
1024 -1.00287864 338.5134894
2048 -1.001644111 374.7228438
4096 -1.008459822 375.3418439
8192 -1.030057213 379.9255796
16384 -1.0315199 399.0081893
32768 -1.030716586 393.6800883
65536 -1.031499798 401.2157052
131072 -1.031604928 403.3259929
262144 -1.031451431 400.6543081
524288 -1.031561663 403.3561477
1048576 -1.03160806 403.9333421
camera: [-270397.4, +270202.6]
16 -46966.46863 87607.58773
32 -46583.37426 131880.9884
64 -107842.0561 96384.78574
128 -115095.894 102371.4783
256 -123199.992 125799.9772
512 -132145.0254 166292.1828
1024 -158207.0598 142974.8428
2048 -148419.6789 149261.7396
4096 -167042.0576 152023.3768
8192 -199173.1852 186346.3269
16384 -188996.5906 195186.7777
32768 -226765.1798 232225.4553
65536 -223290.0705 199323.1465
131072 -239475.7762 214594.9647
262144 -223937.433 219707.9062
524288 -226095.1346 221139.3738
1048576 -220739.0299 228089.0193
caprasse: [-3.1800966258, +4.4852773332]
16 -1.122640811 3.568584008
32 -1.647449732 3.56462884
64 -2.303226173 3.346400025
128 -1.409359901 3.38414889
256 -2.188055437 3.744646826
512 -2.156669132 3.949668106
1024 -2.681084075 3.871754895
2048 -2.508913074 3.954812721
4096 -2.708625627 4.240230838
8192 -2.917337055 4.252268658
16384 -2.863663818 4.295687111
32768 -3.057783765 4.344869033
65536 -2.983681702 4.280455175
131072 -3.054743761 4.401290811
262144 -3.026200759 4.387669535
524288 -3.087886456 4.408258398
1048576 -3.055552816 4.460833605
cyclic5: [-30000, +50000]
16 -9991.369907 6422.069083
32 -2145.460004 4624.181633
64 -4222.701274 7624.457565
128 -14992.43919 6112.12361
256 -8174.970236 11483.64356
512 -8628.718062 23099.33817
1024 -13808.80086 14629.6272
2048 -19021.72443 35545.02833
4096 -16946.40579 28357.55695
8192 -17621.7452 26592.28456
16384 -21133.52841 33712.66728
32768 -20793.87133 29474.87736
65536 -23036.08174 27816.00644
131072 -24933.06023 35863.25232
262144 -23580.77258 33465.41057
524288 -24018.55212 42566.08176
1048576 -25467.84219 39498.54646
cyclic7: [-5.0, +7.0]
16 -0.1818128315 0.2943232411
32 -0.1566307448 0.2425566252
64 -0.1613862091 0.5427491584
128 -0.6420509895 0.9047133214
256 -0.3866409939 0.4517013016
512 -0.9462007286 0.5831586333
1024 -1.5731949 0.9667101914
2048 -2.894077843 1.048015102
4096 -1.873678733 1.393726369
8192 -2.614966655 1.362242833
16384 -1.800746927 2.36379899
32768 -2.936911452 1.919211055
65536 -2.477698801 2.107552639
131072 -2.812458641 2.64886998
262144 -3.343510677 3.25534353
524288 -2.477821056 3.326030713
1048576 -2.669923467 3.303197282
cyclic8: [-8.0, +8.0]
16 -0.4040071044 0.05786917277
32 -0.08508165615 0.0622396526
64 -0.04506995837 0.118717916
128 -0.4218346391 0.2745799351
256 -0.2725731752 0.1953586594
512 -0.4612749938 0.4890045447
1024 -0.2750077722 0.55066444
2048 -0.6659820419 0.5284259662
4096 -0.7214659199 0.7541840231
8192 -2.193833684 1.286781661
16384 -0.9603117808 1.292588948
32768 -0.966085627 1.509452859
65536 -1.468336729 1.587438261
131072 -2.345419689 1.848147231
262144 -2.619592599 1.969771506
524288 -2.330561365 2.781625427
1048576 -2.384376073 2.303065784
goldstein_price: [ 3, ? ]:
16 51.12676154 820896.2479
32 105.5459688 203980.5891
64 10.92957343 724262.7837
128 3.817344807 798623.0425
256 9.765102979 867929.2964
512 8.221251128 969804.7232
1024 5.050014183 932723.5592
2048 4.492353885 940076.8531
4096 3.052169259 955370.7013
8192 3.052850987 1001207.627
16384 3.088965056 1004841.246
32768 3.00526769 1007141.08
65536 3.008620381 1012877.892
131072 3.002478186 1012477.438
262144 3.001078639 1014881.033
524288 3.001491298 1015031.333
1048576 3.000262585 1014524.015
hairer: [-1875.25, -48.25]
16 -926.0411179 -155.0324846
32 -1032.123614 -204.2213865
64 -923.2430733 -199.0450683
128 -1315.081641 -135.905696
256 -1023.718237 -114.4337671
512 -1309.290832 -112.6619642
1024 -1316.029618 -97.7389525
2048 -1525.32216 -93.39353897
4096 -1474.126644 -68.40662814
8192 -1491.76719 -73.46822717
16384 -1493.356889 -64.93141755
32768 -1594.938255 -74.16070942
65536 -1678.734462 -73.05326927
131072 -1611.06875 -67.44005
262144 -1659.385907 -58.2896173
524288 -1699.753406 -64.00018544
1048576 -1711.254178 -60.67348512
heart: [-1.36775, +1.74345327935
16 0.1140052593 1.007342859
32 0.3366754628 1.025957486
64 -0.3499218274 1.289240672
128 -0.07225874411 1.052502143
256 -0.4754486392 1.485554943
512 -0.3983935201 1.360331884
1024 -0.4679556199 1.460674034
2048 -0.5101981721 1.416384693
4096 -0.552286899 1.559009544
8192 -0.7789747658 1.575163714
16384 -0.7811037014 1.540810454
32768 -0.8293137161 1.640550256
65536 -0.7699449513 1.656784516
131072 -0.9025015425 1.654347059
262144 -0.9717289694 1.652736872
524288 -0.8253402394 1.63059713
1048576 -0.9570437895 1.685752139
himmelblau: [ 0, ? ]:
16 3.344612463 535.1187975
32 13.65550768 697.0243811
64 1.967193857 653.9187636
128 0.9391154232 833.246507
256 0.9589538353 657.0620917
512 0.7848869657 753.4085761
1024 0.03416051653 723.8703239
2048 0.008669694946 799.5137097
4096 0.09444232334 758.8565032
8192 0.01297949904 801.8225927
16384 0.01188193096 837.8470141
32768 0.006387915561 860.9489768
65536 0.008655583411 869.0417687
131072 6.034563755e-05 881.1186093
262144 0.0005764269044 874.9953325
524288 0.0008305200062 883.8135778
1048576 0.0003036544091 884.9308391
hunecke: [-1436.515078155, +161.120543283]
16 -787.374311 -37.15179156
32 -1101.766472 -73.77956751
64 -1145.158259 -1.121914179
128 -1187.430028 11.15542153
256 -1286.887026 -1.46343509
512 -1235.790156 42.27869517
1024 -1230.098017 66.51978582
2048 -1246.878481 98.97282175
4096 -1340.039759 85.46988876
8192 -1263.167011 98.62275376
16384 -1330.169829 129.8288892
32768 -1342.754365 98.77241454
65536 -1343.667596 116.1091694
131072 -1373.56007 123.7924842
262144 -1384.266376 135.977523
524288 -1412.494981 138.8953855
1048576 -1416.623171 139.3435011
kearfott: [ 0, ? ]:
16 1.890688428 73.3603846
32 0.6002071179 102.1437303
64 1.10893189 76.76005163
128 0.8683045935 97.6338526
256 0.4403239578 109.9642397
512 0.2045063378 122.7198361
1024 0.2308875819 130.9075302
2048 0.2923803795 151.9116666
4096 0.2187191028 158.5862868
8192 0.145415032 157.6793629
16384 0.04625697041 183.6609911
32768 0.06696469032 171.0181402
65536 0.03664279462 168.8297855
131072 0.03048870343 195.9865407
262144 0.01840079095 176.5833542
524288 0.002912729339 198.4442477
1048576 0.003118859558 207.6541432
lv3: [-9.35, +14.8 ]
16 -5.505976006 2.359192519
32 -2.411196489 4.221394903
64 -8.7249261 5.118580012
128 -6.196118255 5.045720063
256 -7.529919236 8.246773071
512 -7.992012879 6.563083491
1024 -6.584624644 8.049174981
2048 -8.76839483 8.190774113
4096 -7.471582786 7.949835791
8192 -8.519852729 8.063633439
16384 -8.789651166 8.158836837
32768 -8.920377623 8.475209322
65536 -9.046798181 8.147452917
131072 -9.009408155 8.498095034
262144 -9.060767317 8.530391987
524288 -8.969659498 8.503243629
1048576 -9.085109029 8.546697262
lv4: [-20.8, +22.8]
16 -6.884893684 4.151084073
32 -1.240729077 5.887408848
64 -8.377417891 8.796272966
128 -8.157045315 11.19769307
256 -8.607705406 7.948720738
512 -7.702569651 10.06555102
1024 -9.890049382 11.02818851
2048 -7.978823916 9.916188162
4096 -11.25760943 12.14712213
8192 -11.73914407 12.8606102
16384 -11.56105265 12.51808081
32768 -10.93875822 14.11446132
65536 -11.22992462 13.27660181
131072 -11.78153073 13.54132999
262144 -11.86689048 13.52270807
524288 -12.25617509 14.39611352
1048576 -12.5438857 13.73974981
magnetism6: [-0.25, +280.0]
16 56.49768538 176.9576672
32 20.37974721 155.4025017
64 13.068286 198.9760108
128 25.95516037 174.6717335
256 22.10666306 191.0768325
512 12.90162943 216.4283606
1024 7.597354659 194.5672584
2048 3.788502143 219.991467
4096 6.67575603 237.3487063
8192 4.261387053 219.9843987
16384 3.135742018 233.3861037
32768 4.552718225 241.1575989
65536 0.832176155 230.8975475
131072 2.191661966 252.8632361
262144 1.014809403 252.2550204
524288 1.238867148 245.623275
1048576 0.4762961256 249.9233468
magnetism7: [-0.25, +330.0]
16 2.61800899 8.614991166
32 0.8401354203 7.790561078
64 0.1041970534 9.155543046
128 0.8584411547 8.633176341
256 0.844812533 9.895126238
512 0.6488536823 9.918250127
1024 0.5583994316 10.07929211
2048 0.2170992297 11.76857085
4096 0.1689974334 10.57275424
8192 0.1073492634 11.30109414
16384 0.05507700358 10.79551285
32768 -0.1122765141 12.18196461
65536 -0.1082084514 10.75991951
131072 -0.1614776301 12.08280139
262144 -0.1262636206 12.31436106
524288 -0.1822241126 11.92265429
1048576 -0.154977993 12.44957874
quadratic: [ -2, ? ]:
16 14839.88234 48437.54628
32 9845.959905 38301.32847
64 9014.247013 42640.41569
128 8896.862825 51065.16435
256 7826.451775 52802.30423
512 5740.192882 50460.37355
1024 3763.537685 55927.90114
2048 4614.095632 56865.9075
4096 2543.616641 63334.06688
8192 3816.785264 67292.04963
16384 2150.438092 59774.27552
32768 2040.147525 64602.84142
65536 1472.641548 62707.54343
131072 737.0904958 65042.89241
262144 552.4597205 65332.71939
524288 1220.033859 67224.38646
1048576 779.2150834 67670.24279
rd: [-36.71269068, +10.40560403]
16 -25.28086805 4.497116297
32 -21.91160446 6.164186762
64 -31.84507985 5.314029372
128 -28.18593081 8.468599367
256 -32.2239576 9.280755427
512 -34.37184738 8.712661997
1024 -32.76607409 9.430387606
2048 -33.70567456 9.943244789
4096 -33.41258906 10.0578444
8192 -35.70089028 9.514725373
16384 -34.98116712 10.18877346
32768 -35.44273091 10.35038961
65536 -35.46953288 10.30957117
131072 -36.174262 10.29443881
262144 -36.24836969 10.29016873
524288 -36.25222472 10.37149306
1048576 -36.45468642 10.31003619
reimer5: [-5.0, +5.0]
16 -2.361421916 2.704557987
32 -3.972695582 0.986257506
64 -3.217000685 2.032755989
128 -3.483504688 2.88951549
256 -3.194819989 2.763117113
512 -4.477395366 3.370369899
1024 -4.15838999 3.494604936
2048 -4.616521353 3.062676495
4096 -4.432506719 3.206821162
8192 -4.823650023 3.729307995
16384 -4.854054326 4.39754424
32768 -4.564112961 4.469575818
65536 -4.676685955 4.254240181
131072 -4.828277994 4.65359081
262144 -4.919769089 4.530616105
524288 -4.913618108 4.720229217
1048576 -4.925946223 4.699093241
reimer6: [-937501, +937499]
16 -216406.1196 143249.8505
32 -198041.2158 162876.8859
64 -259952.0084 263578.3623
128 -356140.0489 284512.089
256 -392049.9024 351816.816
512 -300184.011 381708.3474
1024 -344592.3377 401510.8525
2048 -318159.9736 405190.3427
4096 -397220.4826 396754.8119
8192 -435313.677 442697.448
16384 -511761.0618 425393.6531
32768 -465225.1855 515696.4921
65536 -537552.4335 470410.11
131072 -520920.8046 493498.4913
262144 -561643.7515 545348.9635
524288 -597021.9616 569344.228
1048576 -544521.8243 614558.7621
rosenbrock: [ 0, ? ]:
16 3279.0466 25302.94453
32 640.123231 37067.04753
64 251.7248232 49858.14266
128 724.1849479 39743.87575
256 111.0103696 53190.69659
512 90.86844074 52432.71283
1024 389.4488942 43715.11226
2048 30.91942906 58801.74504
4096 33.86417839 49426.12446
8192 62.22950547 58722.93201
16384 26.18954261 61525.89623
32768 40.23342493 55536.65555
65536 8.67362244 60633.10559
131072 8.558799195 65560.51067
262144 2.775330825 61103.6659
524288 3.201745928 64586.774
1048576 3.961061056 64452.94159
schwefel: [ 0, ? ]:
16 26.20698845 14952.37685
32 19.24332636 14409.12887
64 27.78131083 14362.91488
128 13.00573185 15596.643
256 2.693938057 18210.45926
512 6.329847001 17679.3988
1024 1.733246677 19542.94178
2048 1.711402766 20728.86981
4096 3.945633822 20875.80899
8192 1.0483197 22272.86669
16384 0.3575255246 22289.12026
32768 0.3632678296 23597.06074
65536 0.04075515688 23006.96345
131072 0.1780585259 23778.34825
262144 0.1595290857 23857.28458
524288 0.04910429572 23952.09488
1048576 0.02833273288 24137.65225
smith1: [ ?, ? ]:
16 31894.87703 261820.2815
32 20766.65283 181182.4803
64 18646.85718 274073.9985
128 8275.672143 401170.8701
256 9830.832006 279646.508
512 6128.948192 356302.3166
1024 4283.764101 374814.1959
2048 205.8468433 361051.7997
4096 1562.047289 429562.6929
8192 208.5012886 432714.4986
16384 2868.328443 441846.2972
32768 -1873.591333 457636.3338
65536 -676.3127945 500037.7835
131072 -1958.482913 490542.9343
262144 -1184.279241 488462.4813
524288 -2307.426881 485044.1633
1048576 -2052.432228 485447.6323
smith2: [ ?, ? ]:
16 -94691.41437 -755.5715445
32 -124454.0286 -70.64406169
64 -184497.4088 -117.3613514
128 -251690.6777 -7.368007913
256 -117923.9421 -13.40702833
512 -206312.4668 31.61313318
1024 -213457.5251 74.94191361
2048 -272728.3135 131.6697951
4096 -246718.7849 173.5016588
8192 -240054.6462 178.4586741
16384 -293327.4482 144.01461
32768 -326207.5833 206.2040368
65536 -304006.3419 221.7402841
131072 -313583.3811 231.3577427
262144 -305065.6922 242.2777611
524288 -321105.6831 279.4288612
1048576 -322752.2198 299.9506699
virasoro: [-29.0, +21.0]
16 -5.095535765 12.38910217
32 -9.328907304 10.02015178
64 -7.559487901 14.2265071
128 -11.84791997 16.42500861
256 -11.17145084 16.60232768
512 -14.35943061 16.91136634
1024 -14.55244956 17.37568103
2048 -15.72789536 18.57021816
4096 -18.10639705 19.24736744
8192 -16.22807994 19.66357965
16384 -17.44105986 19.83234891
32768 -16.99306248 19.93345155
65536 -20.41002263 19.78756216
131072 -19.94418466 20.22108268
262144 -21.62984907 20.42587032
524288 -20.97522433 20.31674168
1048576 -21.55233453 20.54891895
wright: [-30.25, 40.0 ]
16 -10.81769109 -8.325569794
32 -10.8993462 -8.701143985
64 -11.40451116 -8.469731443
128 -11.56755932 -7.667416737
256 -11.25778333 -8.065405719
512 -11.50224087 -8.193169379
1024 -11.63862276 -7.991977062
2048 -11.64480556 -7.742748387
4096 -11.78017849 -7.707492893
8192 -11.88695213 -7.684721959
16384 -11.982057 -7.557812121
32768 -12.0614065 -7.528100813
65536 -12.17380653 -7.464791433
131072 -12.15407048 -7.583746326
262144 -12.08196782 -7.49659552
524288 -12.08095527 -7.460238632
1048576 -12.1654111 -7.483117164
zakharov: [ 0, ? ]::
16 307.2572513 7805013.819
32 509.6723746 3601280.195
64 28.84753056 12197333.21
128 25.39264337 10302061.91
256 40.42131893 12283122.44
512 15.04679164 12467982.85
1024 16.1921555 15759352.47
2048 2.550197461 17513517.62
4096 10.20800089 16560273.83
8192 7.446913682 18107392.77
16384 5.984833934 23794094.48
32768 1.338112649 21106129.48
65536 2.364084421 22008999.36
131072 2.959038777 24757714.87
262144 1.130631563 25242079.72
524288 1.024112152 24810619.67
1048576 1.535256997 27185776.7
range_by_fmincon_test:
Use the MATLAB fmincon() function to seek range.
N Pmin Pmax
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the optimality tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the optimality tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
butcher known: [-1.4393333333, +0.219]
Butcher estimated: [ -1.439332949 0.2189993599]
polynomials_test
Normal end of execution.
27-Feb-2019 08:54:13
polynomials_test
27-Feb-2019 08:56:03
polynomials_test
MATLAB version.
Test polynomials.
RANGE_BY_SAMPLING_TEST:
Use N sample values of each polynomial over its domain to estimate
its minimum Pmin and maximum Pmax
N Pmin Pmax
butcher: [-1.4393333333, +0.219]
16 -0.9392362348 0.1722153637
32 -1.096808774 0.1619794357
64 -1.218607005 0.1354705999
128 -1.146982586 0.200123647
256 -1.163550893 0.1864259985
512 -1.261186459 0.1643861716
1024 -1.301762549 0.181939832
2048 -1.328901868 0.1806981008
4096 -1.30398538 0.1970596662
8192 -1.333096962 0.1967859621
16384 -1.367394167 0.1955562743
32768 -1.347472355 0.2058122585
65536 -1.365699517 0.2125327583
131072 -1.355741449 0.2123066372
262144 -1.396926957 0.2177005289
524288 -1.397266108 0.2141781022
1048576 -1.39471054 0.2164118703
camel: [ -1.031628453489616, ? ]:
16 2.34293696 286.8335898
32 -0.5656567098 323.5035177
64 -0.9962010179 325.1266789
128 -1.027385874 379.3308185
256 -0.6818695846 307.3754905
512 -1.015374044 352.3236156
1024 -1.00287864 338.5134894
2048 -1.001644111 374.7228438
4096 -1.008459822 375.3418439
8192 -1.030057213 379.9255796
16384 -1.0315199 399.0081893
32768 -1.030716586 393.6800883
65536 -1.031499798 401.2157052
131072 -1.031604928 403.3259929
262144 -1.031451431 400.6543081
524288 -1.031561663 403.3561477
1048576 -1.03160806 403.9333421
camera: [-270397.4, +270202.6]
16 -46966.46863 87607.58773
32 -46583.37426 131880.9884
64 -107842.0561 96384.78574
128 -115095.894 102371.4783
256 -123199.992 125799.9772
512 -132145.0254 166292.1828
1024 -158207.0598 142974.8428
2048 -148419.6789 149261.7396
4096 -167042.0576 152023.3768
8192 -199173.1852 186346.3269
16384 -188996.5906 195186.7777
32768 -226765.1798 232225.4553
65536 -223290.0705 199323.1465
131072 -239475.7762 214594.9647
262144 -223937.433 219707.9062
524288 -226095.1346 221139.3738
1048576 -220739.0299 228089.0193
caprasse: [-3.1800966258, +4.4852773332]
16 -1.122640811 3.568584008
32 -1.647449732 3.56462884
64 -2.303226173 3.346400025
128 -1.409359901 3.38414889
256 -2.188055437 3.744646826
512 -2.156669132 3.949668106
1024 -2.681084075 3.871754895
2048 -2.508913074 3.954812721
4096 -2.708625627 4.240230838
8192 -2.917337055 4.252268658
16384 -2.863663818 4.295687111
32768 -3.057783765 4.344869033
65536 -2.983681702 4.280455175
131072 -3.054743761 4.401290811
262144 -3.026200759 4.387669535
524288 -3.087886456 4.408258398
1048576 -3.055552816 4.460833605
cyclic5: [-30000, +50000]
16 -9991.369907 6422.069083
32 -2145.460004 4624.181633
64 -4222.701274 7624.457565
128 -14992.43919 6112.12361
256 -8174.970236 11483.64356
512 -8628.718062 23099.33817
1024 -13808.80086 14629.6272
2048 -19021.72443 35545.02833
4096 -16946.40579 28357.55695
8192 -17621.7452 26592.28456
16384 -21133.52841 33712.66728
32768 -20793.87133 29474.87736
65536 -23036.08174 27816.00644
131072 -24933.06023 35863.25232
262144 -23580.77258 33465.41057
524288 -24018.55212 42566.08176
1048576 -25467.84219 39498.54646
cyclic7: [-5.0, +7.0]
16 -0.1818128315 0.2943232411
32 -0.1566307448 0.2425566252
64 -0.1613862091 0.5427491584
128 -0.6420509895 0.9047133214
256 -0.3866409939 0.4517013016
512 -0.9462007286 0.5831586333
1024 -1.5731949 0.9667101914
2048 -2.894077843 1.048015102
4096 -1.873678733 1.393726369
8192 -2.614966655 1.362242833
16384 -1.800746927 2.36379899
32768 -2.936911452 1.919211055
65536 -2.477698801 2.107552639
131072 -2.812458641 2.64886998
262144 -3.343510677 3.25534353
524288 -2.477821056 3.326030713
1048576 -2.669923467 3.303197282
cyclic8: [-8.0, +8.0]
16 -0.4040071044 0.05786917277
32 -0.08508165615 0.0622396526
64 -0.04506995837 0.118717916
128 -0.4218346391 0.2745799351
256 -0.2725731752 0.1953586594
512 -0.4612749938 0.4890045447
1024 -0.2750077722 0.55066444
2048 -0.6659820419 0.5284259662
4096 -0.7214659199 0.7541840231
8192 -2.193833684 1.286781661
16384 -0.9603117808 1.292588948
32768 -0.966085627 1.509452859
65536 -1.468336729 1.587438261
131072 -2.345419689 1.848147231
262144 -2.619592599 1.969771506
524288 -2.330561365 2.781625427
1048576 -2.384376073 2.303065784
goldstein_price: [ 3, ? ]:
16 51.12676154 820896.2479
32 105.5459688 203980.5891
64 10.92957343 724262.7837
128 3.817344807 798623.0425
256 9.765102979 867929.2964
512 8.221251128 969804.7232
1024 5.050014183 932723.5592
2048 4.492353885 940076.8531
4096 3.052169259 955370.7013
8192 3.052850987 1001207.627
16384 3.088965056 1004841.246
32768 3.00526769 1007141.08
65536 3.008620381 1012877.892
131072 3.002478186 1012477.438
262144 3.001078639 1014881.033
524288 3.001491298 1015031.333
1048576 3.000262585 1014524.015
hairer: [-1875.25, -48.25]
16 -926.0411179 -155.0324846
32 -1032.123614 -204.2213865
64 -923.2430733 -199.0450683
128 -1315.081641 -135.905696
256 -1023.718237 -114.4337671
512 -1309.290832 -112.6619642
1024 -1316.029618 -97.7389525
2048 -1525.32216 -93.39353897
4096 -1474.126644 -68.40662814
8192 -1491.76719 -73.46822717
16384 -1493.356889 -64.93141755
32768 -1594.938255 -74.16070942
65536 -1678.734462 -73.05326927
131072 -1611.06875 -67.44005
262144 -1659.385907 -58.2896173
524288 -1699.753406 -64.00018544
1048576 -1711.254178 -60.67348512
heart: [-1.36775, +1.74345327935
16 0.1140052593 1.007342859
32 0.3366754628 1.025957486
64 -0.3499218274 1.289240672
128 -0.07225874411 1.052502143
256 -0.4754486392 1.485554943
512 -0.3983935201 1.360331884
1024 -0.4679556199 1.460674034
2048 -0.5101981721 1.416384693
4096 -0.552286899 1.559009544
8192 -0.7789747658 1.575163714
16384 -0.7811037014 1.540810454
32768 -0.8293137161 1.640550256
65536 -0.7699449513 1.656784516
131072 -0.9025015425 1.654347059
262144 -0.9717289694 1.652736872
524288 -0.8253402394 1.63059713
1048576 -0.9570437895 1.685752139
himmelblau: [ 0, ? ]:
16 3.344612463 535.1187975
32 13.65550768 697.0243811
64 1.967193857 653.9187636
128 0.9391154232 833.246507
256 0.9589538353 657.0620917
512 0.7848869657 753.4085761
1024 0.03416051653 723.8703239
2048 0.008669694946 799.5137097
4096 0.09444232334 758.8565032
8192 0.01297949904 801.8225927
16384 0.01188193096 837.8470141
32768 0.006387915561 860.9489768
65536 0.008655583411 869.0417687
131072 6.034563755e-05 881.1186093
262144 0.0005764269044 874.9953325
524288 0.0008305200062 883.8135778
1048576 0.0003036544091 884.9308391
hunecke: [-1436.515078155, +161.120543283]
16 -787.374311 -37.15179156
32 -1101.766472 -73.77956751
64 -1145.158259 -1.121914179
128 -1187.430028 11.15542153
256 -1286.887026 -1.46343509
512 -1235.790156 42.27869517
1024 -1230.098017 66.51978582
2048 -1246.878481 98.97282175
4096 -1340.039759 85.46988876
8192 -1263.167011 98.62275376
16384 -1330.169829 129.8288892
32768 -1342.754365 98.77241454
65536 -1343.667596 116.1091694
131072 -1373.56007 123.7924842
262144 -1384.266376 135.977523
524288 -1412.494981 138.8953855
1048576 -1416.623171 139.3435011
kearfott: [ 0, ? ]:
16 1.890688428 73.3603846
32 0.6002071179 102.1437303
64 1.10893189 76.76005163
128 0.8683045935 97.6338526
256 0.4403239578 109.9642397
512 0.2045063378 122.7198361
1024 0.2308875819 130.9075302
2048 0.2923803795 151.9116666
4096 0.2187191028 158.5862868
8192 0.145415032 157.6793629
16384 0.04625697041 183.6609911
32768 0.06696469032 171.0181402
65536 0.03664279462 168.8297855
131072 0.03048870343 195.9865407
262144 0.01840079095 176.5833542
524288 0.002912729339 198.4442477
1048576 0.003118859558 207.6541432
lv3: [-9.35, +14.8 ]
16 -5.505976006 2.359192519
32 -2.411196489 4.221394903
64 -8.7249261 5.118580012
128 -6.196118255 5.045720063
256 -7.529919236 8.246773071
512 -7.992012879 6.563083491
1024 -6.584624644 8.049174981
2048 -8.76839483 8.190774113
4096 -7.471582786 7.949835791
8192 -8.519852729 8.063633439
16384 -8.789651166 8.158836837
32768 -8.920377623 8.475209322
65536 -9.046798181 8.147452917
131072 -9.009408155 8.498095034
262144 -9.060767317 8.530391987
524288 -8.969659498 8.503243629
1048576 -9.085109029 8.546697262
lv4: [-20.8, +22.8]
16 -6.884893684 4.151084073
32 -1.240729077 5.887408848
64 -8.377417891 8.796272966
128 -8.157045315 11.19769307
256 -8.607705406 7.948720738
512 -7.702569651 10.06555102
1024 -9.890049382 11.02818851
2048 -7.978823916 9.916188162
4096 -11.25760943 12.14712213
8192 -11.73914407 12.8606102
16384 -11.56105265 12.51808081
32768 -10.93875822 14.11446132
65536 -11.22992462 13.27660181
131072 -11.78153073 13.54132999
262144 -11.86689048 13.52270807
524288 -12.25617509 14.39611352
1048576 -12.5438857 13.73974981
magnetism6: [-0.25, +280.0]
16 56.49768538 176.9576672
32 20.37974721 155.4025017
64 13.068286 198.9760108
128 25.95516037 174.6717335
256 22.10666306 191.0768325
512 12.90162943 216.4283606
1024 7.597354659 194.5672584
2048 3.788502143 219.991467
4096 6.67575603 237.3487063
8192 4.261387053 219.9843987
16384 3.135742018 233.3861037
32768 4.552718225 241.1575989
65536 0.832176155 230.8975475
131072 2.191661966 252.8632361
262144 1.014809403 252.2550204
524288 1.238867148 245.623275
1048576 0.4762961256 249.9233468
magnetism7: [-0.25, +330.0]
16 2.61800899 8.614991166
32 0.8401354203 7.790561078
64 0.1041970534 9.155543046
128 0.8584411547 8.633176341
256 0.844812533 9.895126238
512 0.6488536823 9.918250127
1024 0.5583994316 10.07929211
2048 0.2170992297 11.76857085
4096 0.1689974334 10.57275424
8192 0.1073492634 11.30109414
16384 0.05507700358 10.79551285
32768 -0.1122765141 12.18196461
65536 -0.1082084514 10.75991951
131072 -0.1614776301 12.08280139
262144 -0.1262636206 12.31436106
524288 -0.1822241126 11.92265429
1048576 -0.154977993 12.44957874
quadratic: [ -2, ? ]:
16 14839.88234 48437.54628
32 9845.959905 38301.32847
64 9014.247013 42640.41569
128 8896.862825 51065.16435
256 7826.451775 52802.30423
512 5740.192882 50460.37355
1024 3763.537685 55927.90114
2048 4614.095632 56865.9075
4096 2543.616641 63334.06688
8192 3816.785264 67292.04963
16384 2150.438092 59774.27552
32768 2040.147525 64602.84142
65536 1472.641548 62707.54343
131072 737.0904958 65042.89241
262144 552.4597205 65332.71939
524288 1220.033859 67224.38646
1048576 779.2150834 67670.24279
rd: [-36.71269068, +10.40560403]
16 -25.28086805 4.497116297
32 -21.91160446 6.164186762
64 -31.84507985 5.314029372
128 -28.18593081 8.468599367
256 -32.2239576 9.280755427
512 -34.37184738 8.712661997
1024 -32.76607409 9.430387606
2048 -33.70567456 9.943244789
4096 -33.41258906 10.0578444
8192 -35.70089028 9.514725373
16384 -34.98116712 10.18877346
32768 -35.44273091 10.35038961
65536 -35.46953288 10.30957117
131072 -36.174262 10.29443881
262144 -36.24836969 10.29016873
524288 -36.25222472 10.37149306
1048576 -36.45468642 10.31003619
reimer5: [-5.0, +5.0]
16 -2.361421916 2.704557987
32 -3.972695582 0.986257506
64 -3.217000685 2.032755989
128 -3.483504688 2.88951549
256 -3.194819989 2.763117113
512 -4.477395366 3.370369899
1024 -4.15838999 3.494604936
2048 -4.616521353 3.062676495
4096 -4.432506719 3.206821162
8192 -4.823650023 3.729307995
16384 -4.854054326 4.39754424
32768 -4.564112961 4.469575818
65536 -4.676685955 4.254240181
131072 -4.828277994 4.65359081
262144 -4.919769089 4.530616105
524288 -4.913618108 4.720229217
1048576 -4.925946223 4.699093241
reimer6: [-937501, +937499]
16 -216406.1196 143249.8505
32 -198041.2158 162876.8859
64 -259952.0084 263578.3623
128 -356140.0489 284512.089
256 -392049.9024 351816.816
512 -300184.011 381708.3474
1024 -344592.3377 401510.8525
2048 -318159.9736 405190.3427
4096 -397220.4826 396754.8119
8192 -435313.677 442697.448
16384 -511761.0618 425393.6531
32768 -465225.1855 515696.4921
65536 -537552.4335 470410.11
131072 -520920.8046 493498.4913
262144 -561643.7515 545348.9635
524288 -597021.9616 569344.228
1048576 -544521.8243 614558.7621
rosenbrock: [ 0, ? ]:
16 3279.0466 25302.94453
32 640.123231 37067.04753
64 251.7248232 49858.14266
128 724.1849479 39743.87575
256 111.0103696 53190.69659
512 90.86844074 52432.71283
1024 389.4488942 43715.11226
2048 30.91942906 58801.74504
4096 33.86417839 49426.12446
8192 62.22950547 58722.93201
16384 26.18954261 61525.89623
32768 40.23342493 55536.65555
65536 8.67362244 60633.10559
131072 8.558799195 65560.51067
262144 2.775330825 61103.6659
524288 3.201745928 64586.774
1048576 3.961061056 64452.94159
schwefel: [ 0, ? ]:
16 26.20698845 14952.37685
32 19.24332636 14409.12887
64 27.78131083 14362.91488
128 13.00573185 15596.643
256 2.693938057 18210.45926
512 6.329847001 17679.3988
1024 1.733246677 19542.94178
2048 1.711402766 20728.86981
4096 3.945633822 20875.80899
8192 1.0483197 22272.86669
16384 0.3575255246 22289.12026
32768 0.3632678296 23597.06074
65536 0.04075515688 23006.96345
131072 0.1780585259 23778.34825
262144 0.1595290857 23857.28458
524288 0.04910429572 23952.09488
1048576 0.02833273288 24137.65225
smith1: [ ?, ? ]:
16 31894.87703 261820.2815
32 20766.65283 181182.4803
64 18646.85718 274073.9985
128 8275.672143 401170.8701
256 9830.832006 279646.508
512 6128.948192 356302.3166
1024 4283.764101 374814.1959
2048 205.8468433 361051.7997
4096 1562.047289 429562.6929
8192 208.5012886 432714.4986
16384 2868.328443 441846.2972
32768 -1873.591333 457636.3338
65536 -676.3127945 500037.7835
131072 -1958.482913 490542.9343
262144 -1184.279241 488462.4813
524288 -2307.426881 485044.1633
1048576 -2052.432228 485447.6323
smith2: [ ?, ? ]:
16 -94691.41437 -755.5715445
32 -124454.0286 -70.64406169
64 -184497.4088 -117.3613514
128 -251690.6777 -7.368007913
256 -117923.9421 -13.40702833
512 -206312.4668 31.61313318
1024 -213457.5251 74.94191361
2048 -272728.3135 131.6697951
4096 -246718.7849 173.5016588
8192 -240054.6462 178.4586741
16384 -293327.4482 144.01461
32768 -326207.5833 206.2040368
65536 -304006.3419 221.7402841
131072 -313583.3811 231.3577427
262144 -305065.6922 242.2777611
524288 -321105.6831 279.4288612
1048576 -322752.2198 299.9506699
virasoro: [-29.0, +21.0]
16 -5.095535765 12.38910217
32 -9.328907304 10.02015178
64 -7.559487901 14.2265071
128 -11.84791997 16.42500861
256 -11.17145084 16.60232768
512 -14.35943061 16.91136634
1024 -14.55244956 17.37568103
2048 -15.72789536 18.57021816
4096 -18.10639705 19.24736744
8192 -16.22807994 19.66357965
16384 -17.44105986 19.83234891
32768 -16.99306248 19.93345155
65536 -20.41002263 19.78756216
131072 -19.94418466 20.22108268
262144 -21.62984907 20.42587032
524288 -20.97522433 20.31674168
1048576 -21.55233453 20.54891895
wright: [-30.25, 40.0 ]
16 -10.81769109 -8.325569794
32 -10.8993462 -8.701143985
64 -11.40451116 -8.469731443
128 -11.56755932 -7.667416737
256 -11.25778333 -8.065405719
512 -11.50224087 -8.193169379
1024 -11.63862276 -7.991977062
2048 -11.64480556 -7.742748387
4096 -11.78017849 -7.707492893
8192 -11.88695213 -7.684721959
16384 -11.982057 -7.557812121
32768 -12.0614065 -7.528100813
65536 -12.17380653 -7.464791433
131072 -12.15407048 -7.583746326
262144 -12.08196782 -7.49659552
524288 -12.08095527 -7.460238632
1048576 -12.1654111 -7.483117164
zakharov: [ 0, ? ]::
16 307.2572513 7805013.819
32 509.6723746 3601280.195
64 28.84753056 12197333.21
128 25.39264337 10302061.91
256 40.42131893 12283122.44
512 15.04679164 12467982.85
1024 16.1921555 15759352.47
2048 2.550197461 17513517.62
4096 10.20800089 16560273.83
8192 7.446913682 18107392.77
16384 5.984833934 23794094.48
32768 1.338112649 21106129.48
65536 2.364084421 22008999.36
131072 2.959038777 24757714.87
262144 1.130631563 25242079.72
524288 1.024112152 24810619.67
1048576 1.535256997 27185776.7
range_by_fmincon_test:
Use the MATLAB fmincon() function to seek range.
{Error using optimoptions (line 124)
Invalid solver specified. Provide a solver name or handle (such as 'fmincon' or @fminunc).
Type DOC OPTIMOPTIONS for a list of solvers.
Error in range_by_fmincon_test (line 29)
options = optimoptions ( 'Display', 'off' );
Error in polynomials_test (line 28)
range_by_fmincon_test ( );
}
polynomials_test
27-Feb-2019 08:57:33
polynomials_test
MATLAB version.
Test polynomials.
RANGE_BY_SAMPLING_TEST:
Use N sample values of each polynomial over its domain to estimate
its minimum Pmin and maximum Pmax
N Pmin Pmax
butcher: [-1.4393333333, +0.219]
16 -0.9392362348 0.1722153637
32 -1.096808774 0.1619794357
64 -1.218607005 0.1354705999
128 -1.146982586 0.200123647
256 -1.163550893 0.1864259985
512 -1.261186459 0.1643861716
1024 -1.301762549 0.181939832
2048 -1.328901868 0.1806981008
4096 -1.30398538 0.1970596662
8192 -1.333096962 0.1967859621
16384 -1.367394167 0.1955562743
32768 -1.347472355 0.2058122585
65536 -1.365699517 0.2125327583
131072 -1.355741449 0.2123066372
262144 -1.396926957 0.2177005289
524288 -1.397266108 0.2141781022
1048576 -1.39471054 0.2164118703
camel: [ -1.031628453489616, ? ]:
16 2.34293696 286.8335898
32 -0.5656567098 323.5035177
64 -0.9962010179 325.1266789
128 -1.027385874 379.3308185
256 -0.6818695846 307.3754905
512 -1.015374044 352.3236156
1024 -1.00287864 338.5134894
2048 -1.001644111 374.7228438
4096 -1.008459822 375.3418439
8192 -1.030057213 379.9255796
16384 -1.0315199 399.0081893
32768 -1.030716586 393.6800883
65536 -1.031499798 401.2157052
131072 -1.031604928 403.3259929
262144 -1.031451431 400.6543081
524288 -1.031561663 403.3561477
1048576 -1.03160806 403.9333421
camera: [-270397.4, +270202.6]
16 -46966.46863 87607.58773
32 -46583.37426 131880.9884
64 -107842.0561 96384.78574
128 -115095.894 102371.4783
256 -123199.992 125799.9772
512 -132145.0254 166292.1828
1024 -158207.0598 142974.8428
2048 -148419.6789 149261.7396
4096 -167042.0576 152023.3768
8192 -199173.1852 186346.3269
16384 -188996.5906 195186.7777
32768 -226765.1798 232225.4553
65536 -223290.0705 199323.1465
131072 -239475.7762 214594.9647
262144 -223937.433 219707.9062
524288 -226095.1346 221139.3738
1048576 -220739.0299 228089.0193
caprasse: [-3.1800966258, +4.4852773332]
16 -1.122640811 3.568584008
32 -1.647449732 3.56462884
64 -2.303226173 3.346400025
128 -1.409359901 3.38414889
256 -2.188055437 3.744646826
512 -2.156669132 3.949668106
1024 -2.681084075 3.871754895
2048 -2.508913074 3.954812721
4096 -2.708625627 4.240230838
8192 -2.917337055 4.252268658
16384 -2.863663818 4.295687111
32768 -3.057783765 4.344869033
65536 -2.983681702 4.280455175
131072 -3.054743761 4.401290811
262144 -3.026200759 4.387669535
524288 -3.087886456 4.408258398
1048576 -3.055552816 4.460833605
cyclic5: [-30000, +50000]
16 -9991.369907 6422.069083
32 -2145.460004 4624.181633
64 -4222.701274 7624.457565
128 -14992.43919 6112.12361
256 -8174.970236 11483.64356
512 -8628.718062 23099.33817
1024 -13808.80086 14629.6272
2048 -19021.72443 35545.02833
4096 -16946.40579 28357.55695
8192 -17621.7452 26592.28456
16384 -21133.52841 33712.66728
32768 -20793.87133 29474.87736
65536 -23036.08174 27816.00644
131072 -24933.06023 35863.25232
262144 -23580.77258 33465.41057
524288 -24018.55212 42566.08176
1048576 -25467.84219 39498.54646
cyclic7: [-5.0, +7.0]
16 -0.1818128315 0.2943232411
32 -0.1566307448 0.2425566252
64 -0.1613862091 0.5427491584
128 -0.6420509895 0.9047133214
256 -0.3866409939 0.4517013016
512 -0.9462007286 0.5831586333
1024 -1.5731949 0.9667101914
2048 -2.894077843 1.048015102
4096 -1.873678733 1.393726369
8192 -2.614966655 1.362242833
16384 -1.800746927 2.36379899
32768 -2.936911452 1.919211055
65536 -2.477698801 2.107552639
131072 -2.812458641 2.64886998
262144 -3.343510677 3.25534353
524288 -2.477821056 3.326030713
1048576 -2.669923467 3.303197282
cyclic8: [-8.0, +8.0]
16 -0.4040071044 0.05786917277
32 -0.08508165615 0.0622396526
64 -0.04506995837 0.118717916
128 -0.4218346391 0.2745799351
256 -0.2725731752 0.1953586594
512 -0.4612749938 0.4890045447
1024 -0.2750077722 0.55066444
2048 -0.6659820419 0.5284259662
4096 -0.7214659199 0.7541840231
8192 -2.193833684 1.286781661
16384 -0.9603117808 1.292588948
32768 -0.966085627 1.509452859
65536 -1.468336729 1.587438261
131072 -2.345419689 1.848147231
262144 -2.619592599 1.969771506
524288 -2.330561365 2.781625427
1048576 -2.384376073 2.303065784
goldstein_price: [ 3, ? ]:
16 51.12676154 820896.2479
32 105.5459688 203980.5891
64 10.92957343 724262.7837
128 3.817344807 798623.0425
256 9.765102979 867929.2964
512 8.221251128 969804.7232
1024 5.050014183 932723.5592
2048 4.492353885 940076.8531
4096 3.052169259 955370.7013
8192 3.052850987 1001207.627
16384 3.088965056 1004841.246
32768 3.00526769 1007141.08
65536 3.008620381 1012877.892
131072 3.002478186 1012477.438
262144 3.001078639 1014881.033
524288 3.001491298 1015031.333
1048576 3.000262585 1014524.015
hairer: [-1875.25, -48.25]
16 -926.0411179 -155.0324846
32 -1032.123614 -204.2213865
64 -923.2430733 -199.0450683
128 -1315.081641 -135.905696
256 -1023.718237 -114.4337671
512 -1309.290832 -112.6619642
1024 -1316.029618 -97.7389525
2048 -1525.32216 -93.39353897
4096 -1474.126644 -68.40662814
8192 -1491.76719 -73.46822717
16384 -1493.356889 -64.93141755
32768 -1594.938255 -74.16070942
65536 -1678.734462 -73.05326927
131072 -1611.06875 -67.44005
262144 -1659.385907 -58.2896173
524288 -1699.753406 -64.00018544
1048576 -1711.254178 -60.67348512
heart: [-1.36775, +1.74345327935
16 0.1140052593 1.007342859
32 0.3366754628 1.025957486
64 -0.3499218274 1.289240672
128 -0.07225874411 1.052502143
256 -0.4754486392 1.485554943
512 -0.3983935201 1.360331884
1024 -0.4679556199 1.460674034
2048 -0.5101981721 1.416384693
4096 -0.552286899 1.559009544
8192 -0.7789747658 1.575163714
16384 -0.7811037014 1.540810454
32768 -0.8293137161 1.640550256
65536 -0.7699449513 1.656784516
131072 -0.9025015425 1.654347059
262144 -0.9717289694 1.652736872
524288 -0.8253402394 1.63059713
1048576 -0.9570437895 1.685752139
himmelblau: [ 0, ? ]:
16 3.344612463 535.1187975
32 13.65550768 697.0243811
64 1.967193857 653.9187636
128 0.9391154232 833.246507
256 0.9589538353 657.0620917
512 0.7848869657 753.4085761
1024 0.03416051653 723.8703239
2048 0.008669694946 799.5137097
4096 0.09444232334 758.8565032
8192 0.01297949904 801.8225927
16384 0.01188193096 837.8470141
32768 0.006387915561 860.9489768
65536 0.008655583411 869.0417687
131072 6.034563755e-05 881.1186093
262144 0.0005764269044 874.9953325
524288 0.0008305200062 883.8135778
1048576 0.0003036544091 884.9308391
hunecke: [-1436.515078155, +161.120543283]
16 -787.374311 -37.15179156
32 -1101.766472 -73.77956751
64 -1145.158259 -1.121914179
128 -1187.430028 11.15542153
256 -1286.887026 -1.46343509
512 -1235.790156 42.27869517
1024 -1230.098017 66.51978582
2048 -1246.878481 98.97282175
4096 -1340.039759 85.46988876
8192 -1263.167011 98.62275376
16384 -1330.169829 129.8288892
32768 -1342.754365 98.77241454
65536 -1343.667596 116.1091694
131072 -1373.56007 123.7924842
262144 -1384.266376 135.977523
524288 -1412.494981 138.8953855
1048576 -1416.623171 139.3435011
kearfott: [ 0, ? ]:
16 1.890688428 73.3603846
32 0.6002071179 102.1437303
64 1.10893189 76.76005163
128 0.8683045935 97.6338526
256 0.4403239578 109.9642397
512 0.2045063378 122.7198361
1024 0.2308875819 130.9075302
2048 0.2923803795 151.9116666
4096 0.2187191028 158.5862868
8192 0.145415032 157.6793629
16384 0.04625697041 183.6609911
32768 0.06696469032 171.0181402
65536 0.03664279462 168.8297855
131072 0.03048870343 195.9865407
262144 0.01840079095 176.5833542
524288 0.002912729339 198.4442477
1048576 0.003118859558 207.6541432
lv3: [-9.35, +14.8 ]
16 -5.505976006 2.359192519
32 -2.411196489 4.221394903
64 -8.7249261 5.118580012
128 -6.196118255 5.045720063
256 -7.529919236 8.246773071
512 -7.992012879 6.563083491
1024 -6.584624644 8.049174981
2048 -8.76839483 8.190774113
4096 -7.471582786 7.949835791
8192 -8.519852729 8.063633439
16384 -8.789651166 8.158836837
32768 -8.920377623 8.475209322
65536 -9.046798181 8.147452917
131072 -9.009408155 8.498095034
262144 -9.060767317 8.530391987
524288 -8.969659498 8.503243629
1048576 -9.085109029 8.546697262
lv4: [-20.8, +22.8]
16 -6.884893684 4.151084073
32 -1.240729077 5.887408848
64 -8.377417891 8.796272966
128 -8.157045315 11.19769307
256 -8.607705406 7.948720738
512 -7.702569651 10.06555102
1024 -9.890049382 11.02818851
2048 -7.978823916 9.916188162
4096 -11.25760943 12.14712213
8192 -11.73914407 12.8606102
16384 -11.56105265 12.51808081
32768 -10.93875822 14.11446132
65536 -11.22992462 13.27660181
131072 -11.78153073 13.54132999
262144 -11.86689048 13.52270807
524288 -12.25617509 14.39611352
1048576 -12.5438857 13.73974981
magnetism6: [-0.25, +280.0]
16 56.49768538 176.9576672
32 20.37974721 155.4025017
64 13.068286 198.9760108
128 25.95516037 174.6717335
256 22.10666306 191.0768325
512 12.90162943 216.4283606
1024 7.597354659 194.5672584
2048 3.788502143 219.991467
4096 6.67575603 237.3487063
8192 4.261387053 219.9843987
16384 3.135742018 233.3861037
32768 4.552718225 241.1575989
65536 0.832176155 230.8975475
131072 2.191661966 252.8632361
262144 1.014809403 252.2550204
524288 1.238867148 245.623275
1048576 0.4762961256 249.9233468
magnetism7: [-0.25, +330.0]
16 2.61800899 8.614991166
32 0.8401354203 7.790561078
64 0.1041970534 9.155543046
128 0.8584411547 8.633176341
256 0.844812533 9.895126238
512 0.6488536823 9.918250127
1024 0.5583994316 10.07929211
2048 0.2170992297 11.76857085
4096 0.1689974334 10.57275424
8192 0.1073492634 11.30109414
16384 0.05507700358 10.79551285
32768 -0.1122765141 12.18196461
65536 -0.1082084514 10.75991951
131072 -0.1614776301 12.08280139
262144 -0.1262636206 12.31436106
524288 -0.1822241126 11.92265429
1048576 -0.154977993 12.44957874
quadratic: [ -2, ? ]:
16 14839.88234 48437.54628
32 9845.959905 38301.32847
64 9014.247013 42640.41569
128 8896.862825 51065.16435
256 7826.451775 52802.30423
512 5740.192882 50460.37355
1024 3763.537685 55927.90114
2048 4614.095632 56865.9075
4096 2543.616641 63334.06688
8192 3816.785264 67292.04963
16384 2150.438092 59774.27552
32768 2040.147525 64602.84142
65536 1472.641548 62707.54343
131072 737.0904958 65042.89241
262144 552.4597205 65332.71939
524288 1220.033859 67224.38646
1048576 779.2150834 67670.24279
rd: [-36.71269068, +10.40560403]
16 -25.28086805 4.497116297
32 -21.91160446 6.164186762
64 -31.84507985 5.314029372
128 -28.18593081 8.468599367
256 -32.2239576 9.280755427
512 -34.37184738 8.712661997
1024 -32.76607409 9.430387606
2048 -33.70567456 9.943244789
4096 -33.41258906 10.0578444
8192 -35.70089028 9.514725373
16384 -34.98116712 10.18877346
32768 -35.44273091 10.35038961
65536 -35.46953288 10.30957117
131072 -36.174262 10.29443881
262144 -36.24836969 10.29016873
524288 -36.25222472 10.37149306
1048576 -36.45468642 10.31003619
reimer5: [-5.0, +5.0]
16 -2.361421916 2.704557987
32 -3.972695582 0.986257506
64 -3.217000685 2.032755989
128 -3.483504688 2.88951549
256 -3.194819989 2.763117113
512 -4.477395366 3.370369899
1024 -4.15838999 3.494604936
2048 -4.616521353 3.062676495
4096 -4.432506719 3.206821162
8192 -4.823650023 3.729307995
16384 -4.854054326 4.39754424
32768 -4.564112961 4.469575818
65536 -4.676685955 4.254240181
131072 -4.828277994 4.65359081
262144 -4.919769089 4.530616105
524288 -4.913618108 4.720229217
1048576 -4.925946223 4.699093241
reimer6: [-937501, +937499]
16 -216406.1196 143249.8505
32 -198041.2158 162876.8859
64 -259952.0084 263578.3623
128 -356140.0489 284512.089
256 -392049.9024 351816.816
512 -300184.011 381708.3474
1024 -344592.3377 401510.8525
2048 -318159.9736 405190.3427
4096 -397220.4826 396754.8119
8192 -435313.677 442697.448
16384 -511761.0618 425393.6531
32768 -465225.1855 515696.4921
65536 -537552.4335 470410.11
131072 -520920.8046 493498.4913
262144 -561643.7515 545348.9635
524288 -597021.9616 569344.228
1048576 -544521.8243 614558.7621
rosenbrock: [ 0, ? ]:
16 3279.0466 25302.94453
32 640.123231 37067.04753
64 251.7248232 49858.14266
128 724.1849479 39743.87575
256 111.0103696 53190.69659
512 90.86844074 52432.71283
1024 389.4488942 43715.11226
2048 30.91942906 58801.74504
4096 33.86417839 49426.12446
8192 62.22950547 58722.93201
16384 26.18954261 61525.89623
32768 40.23342493 55536.65555
65536 8.67362244 60633.10559
131072 8.558799195 65560.51067
262144 2.775330825 61103.6659
524288 3.201745928 64586.774
1048576 3.961061056 64452.94159
schwefel: [ 0, ? ]:
16 26.20698845 14952.37685
32 19.24332636 14409.12887
64 27.78131083 14362.91488
128 13.00573185 15596.643
256 2.693938057 18210.45926
512 6.329847001 17679.3988
1024 1.733246677 19542.94178
2048 1.711402766 20728.86981
4096 3.945633822 20875.80899
8192 1.0483197 22272.86669
16384 0.3575255246 22289.12026
32768 0.3632678296 23597.06074
65536 0.04075515688 23006.96345
131072 0.1780585259 23778.34825
262144 0.1595290857 23857.28458
524288 0.04910429572 23952.09488
1048576 0.02833273288 24137.65225
smith1: [ ?, ? ]:
16 31894.87703 261820.2815
32 20766.65283 181182.4803
64 18646.85718 274073.9985
128 8275.672143 401170.8701
256 9830.832006 279646.508
512 6128.948192 356302.3166
1024 4283.764101 374814.1959
2048 205.8468433 361051.7997
4096 1562.047289 429562.6929
8192 208.5012886 432714.4986
16384 2868.328443 441846.2972
32768 -1873.591333 457636.3338
65536 -676.3127945 500037.7835
131072 -1958.482913 490542.9343
262144 -1184.279241 488462.4813
524288 -2307.426881 485044.1633
1048576 -2052.432228 485447.6323
smith2: [ ?, ? ]:
16 -94691.41437 -755.5715445
32 -124454.0286 -70.64406169
64 -184497.4088 -117.3613514
128 -251690.6777 -7.368007913
256 -117923.9421 -13.40702833
512 -206312.4668 31.61313318
1024 -213457.5251 74.94191361
2048 -272728.3135 131.6697951
4096 -246718.7849 173.5016588
8192 -240054.6462 178.4586741
16384 -293327.4482 144.01461
32768 -326207.5833 206.2040368
65536 -304006.3419 221.7402841
131072 -313583.3811 231.3577427
262144 -305065.6922 242.2777611
524288 -321105.6831 279.4288612
1048576 -322752.2198 299.9506699
virasoro: [-29.0, +21.0]
16 -5.095535765 12.38910217
32 -9.328907304 10.02015178
64 -7.559487901 14.2265071
128 -11.84791997 16.42500861
256 -11.17145084 16.60232768
512 -14.35943061 16.91136634
1024 -14.55244956 17.37568103
2048 -15.72789536 18.57021816
4096 -18.10639705 19.24736744
8192 -16.22807994 19.66357965
16384 -17.44105986 19.83234891
32768 -16.99306248 19.93345155
65536 -20.41002263 19.78756216
131072 -19.94418466 20.22108268
262144 -21.62984907 20.42587032
524288 -20.97522433 20.31674168
1048576 -21.55233453 20.54891895
wright: [-30.25, 40.0 ]
16 -10.81769109 -8.325569794
32 -10.8993462 -8.701143985
64 -11.40451116 -8.469731443
128 -11.56755932 -7.667416737
256 -11.25778333 -8.065405719
512 -11.50224087 -8.193169379
1024 -11.63862276 -7.991977062
2048 -11.64480556 -7.742748387
4096 -11.78017849 -7.707492893
8192 -11.88695213 -7.684721959
16384 -11.982057 -7.557812121
32768 -12.0614065 -7.528100813
65536 -12.17380653 -7.464791433
131072 -12.15407048 -7.583746326
262144 -12.08196782 -7.49659552
524288 -12.08095527 -7.460238632
1048576 -12.1654111 -7.483117164
zakharov: [ 0, ? ]::
16 307.2572513 7805013.819
32 509.6723746 3601280.195
64 28.84753056 12197333.21
128 25.39264337 10302061.91
256 40.42131893 12283122.44
512 15.04679164 12467982.85
1024 16.1921555 15759352.47
2048 2.550197461 17513517.62
4096 10.20800089 16560273.83
8192 7.446913682 18107392.77
16384 5.984833934 23794094.48
32768 1.338112649 21106129.48
65536 2.364084421 22008999.36
131072 2.959038777 24757714.87
262144 1.130631563 25242079.72
524288 1.024112152 24810619.67
1048576 1.535256997 27185776.7
range_by_fmincon_test:
Use the MATLAB fmincon() function to seek range.
{Error using optimfcnchk (line 99)
NONLCON must be a function.
Error in fmincon (line 421)
confcn = optimfcnchk(NONLCON,'fmincon',length(varargin),funValCheck,flags.gradconst,false,true);
Error in range_by_fmincon_test (line 36)
[ x_min, f_min ] = fmincon ( @butcher_min_fun, x0, [], [], [], [], lb, ub, options );
Error in polynomials_test (line 28)
range_by_fmincon_test ( );
}
polynomials_test
27-Feb-2019 08:58:11
polynomials_test
MATLAB version.
Test polynomials.
RANGE_BY_SAMPLING_TEST:
Use N sample values of each polynomial over its domain to estimate
its minimum Pmin and maximum Pmax
N Pmin Pmax
butcher: [-1.4393333333, +0.219]
16 -0.9392362348 0.1722153637
32 -1.096808774 0.1619794357
64 -1.218607005 0.1354705999
128 -1.146982586 0.200123647
256 -1.163550893 0.1864259985
512 -1.261186459 0.1643861716
1024 -1.301762549 0.181939832
2048 -1.328901868 0.1806981008
4096 -1.30398538 0.1970596662
8192 -1.333096962 0.1967859621
16384 -1.367394167 0.1955562743
32768 -1.347472355 0.2058122585
65536 -1.365699517 0.2125327583
131072 -1.355741449 0.2123066372
262144 -1.396926957 0.2177005289
524288 -1.397266108 0.2141781022
1048576 -1.39471054 0.2164118703
camel: [ -1.031628453489616, ? ]:
16 2.34293696 286.8335898
32 -0.5656567098 323.5035177
64 -0.9962010179 325.1266789
128 -1.027385874 379.3308185
256 -0.6818695846 307.3754905
512 -1.015374044 352.3236156
1024 -1.00287864 338.5134894
2048 -1.001644111 374.7228438
4096 -1.008459822 375.3418439
8192 -1.030057213 379.9255796
16384 -1.0315199 399.0081893
32768 -1.030716586 393.6800883
65536 -1.031499798 401.2157052
131072 -1.031604928 403.3259929
262144 -1.031451431 400.6543081
524288 -1.031561663 403.3561477
1048576 -1.03160806 403.9333421
camera: [-270397.4, +270202.6]
16 -46966.46863 87607.58773
32 -46583.37426 131880.9884
64 -107842.0561 96384.78574
128 -115095.894 102371.4783
256 -123199.992 125799.9772
512 -132145.0254 166292.1828
1024 -158207.0598 142974.8428
2048 -148419.6789 149261.7396
4096 -167042.0576 152023.3768
8192 -199173.1852 186346.3269
16384 -188996.5906 195186.7777
32768 -226765.1798 232225.4553
65536 -223290.0705 199323.1465
131072 -239475.7762 214594.9647
262144 -223937.433 219707.9062
524288 -226095.1346 221139.3738
1048576 -220739.0299 228089.0193
caprasse: [-3.1800966258, +4.4852773332]
16 -1.122640811 3.568584008
32 -1.647449732 3.56462884
64 -2.303226173 3.346400025
128 -1.409359901 3.38414889
256 -2.188055437 3.744646826
512 -2.156669132 3.949668106
1024 -2.681084075 3.871754895
2048 -2.508913074 3.954812721
4096 -2.708625627 4.240230838
8192 -2.917337055 4.252268658
16384 -2.863663818 4.295687111
32768 -3.057783765 4.344869033
65536 -2.983681702 4.280455175
131072 -3.054743761 4.401290811
262144 -3.026200759 4.387669535
524288 -3.087886456 4.408258398
1048576 -3.055552816 4.460833605
cyclic5: [-30000, +50000]
16 -9991.369907 6422.069083
32 -2145.460004 4624.181633
64 -4222.701274 7624.457565
128 -14992.43919 6112.12361
256 -8174.970236 11483.64356
512 -8628.718062 23099.33817
1024 -13808.80086 14629.6272
2048 -19021.72443 35545.02833
4096 -16946.40579 28357.55695
8192 -17621.7452 26592.28456
16384 -21133.52841 33712.66728
32768 -20793.87133 29474.87736
65536 -23036.08174 27816.00644
131072 -24933.06023 35863.25232
262144 -23580.77258 33465.41057
524288 -24018.55212 42566.08176
1048576 -25467.84219 39498.54646
cyclic7: [-5.0, +7.0]
16 -0.1818128315 0.2943232411
32 -0.1566307448 0.2425566252
64 -0.1613862091 0.5427491584
128 -0.6420509895 0.9047133214
256 -0.3866409939 0.4517013016
512 -0.9462007286 0.5831586333
1024 -1.5731949 0.9667101914
2048 -2.894077843 1.048015102
4096 -1.873678733 1.393726369
8192 -2.614966655 1.362242833
16384 -1.800746927 2.36379899
32768 -2.936911452 1.919211055
65536 -2.477698801 2.107552639
131072 -2.812458641 2.64886998
262144 -3.343510677 3.25534353
524288 -2.477821056 3.326030713
1048576 -2.669923467 3.303197282
cyclic8: [-8.0, +8.0]
16 -0.4040071044 0.05786917277
32 -0.08508165615 0.0622396526
64 -0.04506995837 0.118717916
128 -0.4218346391 0.2745799351
256 -0.2725731752 0.1953586594
512 -0.4612749938 0.4890045447
1024 -0.2750077722 0.55066444
2048 -0.6659820419 0.5284259662
4096 -0.7214659199 0.7541840231
8192 -2.193833684 1.286781661
16384 -0.9603117808 1.292588948
32768 -0.966085627 1.509452859
65536 -1.468336729 1.587438261
131072 -2.345419689 1.848147231
262144 -2.619592599 1.969771506
524288 -2.330561365 2.781625427
1048576 -2.384376073 2.303065784
goldstein_price: [ 3, ? ]:
16 51.12676154 820896.2479
32 105.5459688 203980.5891
64 10.92957343 724262.7837
128 3.817344807 798623.0425
256 9.765102979 867929.2964
512 8.221251128 969804.7232
1024 5.050014183 932723.5592
2048 4.492353885 940076.8531
4096 3.052169259 955370.7013
8192 3.052850987 1001207.627
16384 3.088965056 1004841.246
32768 3.00526769 1007141.08
65536 3.008620381 1012877.892
131072 3.002478186 1012477.438
262144 3.001078639 1014881.033
524288 3.001491298 1015031.333
1048576 3.000262585 1014524.015
hairer: [-1875.25, -48.25]
16 -926.0411179 -155.0324846
32 -1032.123614 -204.2213865
64 -923.2430733 -199.0450683
128 -1315.081641 -135.905696
256 -1023.718237 -114.4337671
512 -1309.290832 -112.6619642
1024 -1316.029618 -97.7389525
2048 -1525.32216 -93.39353897
4096 -1474.126644 -68.40662814
8192 -1491.76719 -73.46822717
16384 -1493.356889 -64.93141755
32768 -1594.938255 -74.16070942
65536 -1678.734462 -73.05326927
131072 -1611.06875 -67.44005
262144 -1659.385907 -58.2896173
524288 -1699.753406 -64.00018544
1048576 -1711.254178 -60.67348512
heart: [-1.36775, +1.74345327935
16 0.1140052593 1.007342859
32 0.3366754628 1.025957486
64 -0.3499218274 1.289240672
128 -0.07225874411 1.052502143
256 -0.4754486392 1.485554943
512 -0.3983935201 1.360331884
1024 -0.4679556199 1.460674034
2048 -0.5101981721 1.416384693
4096 -0.552286899 1.559009544
8192 -0.7789747658 1.575163714
16384 -0.7811037014 1.540810454
32768 -0.8293137161 1.640550256
65536 -0.7699449513 1.656784516
131072 -0.9025015425 1.654347059
262144 -0.9717289694 1.652736872
524288 -0.8253402394 1.63059713
1048576 -0.9570437895 1.685752139
himmelblau: [ 0, ? ]:
16 3.344612463 535.1187975
32 13.65550768 697.0243811
64 1.967193857 653.9187636
128 0.9391154232 833.246507
256 0.9589538353 657.0620917
512 0.7848869657 753.4085761
1024 0.03416051653 723.8703239
2048 0.008669694946 799.5137097
4096 0.09444232334 758.8565032
8192 0.01297949904 801.8225927
16384 0.01188193096 837.8470141
32768 0.006387915561 860.9489768
65536 0.008655583411 869.0417687
131072 6.034563755e-05 881.1186093
262144 0.0005764269044 874.9953325
524288 0.0008305200062 883.8135778
1048576 0.0003036544091 884.9308391
hunecke: [-1436.515078155, +161.120543283]
16 -787.374311 -37.15179156
32 -1101.766472 -73.77956751
64 -1145.158259 -1.121914179
128 -1187.430028 11.15542153
256 -1286.887026 -1.46343509
512 -1235.790156 42.27869517
1024 -1230.098017 66.51978582
2048 -1246.878481 98.97282175
4096 -1340.039759 85.46988876
8192 -1263.167011 98.62275376
16384 -1330.169829 129.8288892
32768 -1342.754365 98.77241454
65536 -1343.667596 116.1091694
131072 -1373.56007 123.7924842
262144 -1384.266376 135.977523
524288 -1412.494981 138.8953855
1048576 -1416.623171 139.3435011
kearfott: [ 0, ? ]:
16 1.890688428 73.3603846
32 0.6002071179 102.1437303
64 1.10893189 76.76005163
128 0.8683045935 97.6338526
256 0.4403239578 109.9642397
512 0.2045063378 122.7198361
1024 0.2308875819 130.9075302
2048 0.2923803795 151.9116666
4096 0.2187191028 158.5862868
8192 0.145415032 157.6793629
16384 0.04625697041 183.6609911
32768 0.06696469032 171.0181402
65536 0.03664279462 168.8297855
131072 0.03048870343 195.9865407
262144 0.01840079095 176.5833542
524288 0.002912729339 198.4442477
1048576 0.003118859558 207.6541432
lv3: [-9.35, +14.8 ]
16 -5.505976006 2.359192519
32 -2.411196489 4.221394903
64 -8.7249261 5.118580012
128 -6.196118255 5.045720063
256 -7.529919236 8.246773071
512 -7.992012879 6.563083491
1024 -6.584624644 8.049174981
2048 -8.76839483 8.190774113
4096 -7.471582786 7.949835791
8192 -8.519852729 8.063633439
16384 -8.789651166 8.158836837
32768 -8.920377623 8.475209322
65536 -9.046798181 8.147452917
131072 -9.009408155 8.498095034
262144 -9.060767317 8.530391987
524288 -8.969659498 8.503243629
1048576 -9.085109029 8.546697262
lv4: [-20.8, +22.8]
16 -6.884893684 4.151084073
32 -1.240729077 5.887408848
64 -8.377417891 8.796272966
128 -8.157045315 11.19769307
256 -8.607705406 7.948720738
512 -7.702569651 10.06555102
1024 -9.890049382 11.02818851
2048 -7.978823916 9.916188162
4096 -11.25760943 12.14712213
8192 -11.73914407 12.8606102
16384 -11.56105265 12.51808081
32768 -10.93875822 14.11446132
65536 -11.22992462 13.27660181
131072 -11.78153073 13.54132999
262144 -11.86689048 13.52270807
524288 -12.25617509 14.39611352
1048576 -12.5438857 13.73974981
magnetism6: [-0.25, +280.0]
16 56.49768538 176.9576672
32 20.37974721 155.4025017
64 13.068286 198.9760108
128 25.95516037 174.6717335
256 22.10666306 191.0768325
512 12.90162943 216.4283606
1024 7.597354659 194.5672584
2048 3.788502143 219.991467
4096 6.67575603 237.3487063
8192 4.261387053 219.9843987
16384 3.135742018 233.3861037
32768 4.552718225 241.1575989
65536 0.832176155 230.8975475
131072 2.191661966 252.8632361
262144 1.014809403 252.2550204
524288 1.238867148 245.623275
1048576 0.4762961256 249.9233468
magnetism7: [-0.25, +330.0]
16 2.61800899 8.614991166
32 0.8401354203 7.790561078
64 0.1041970534 9.155543046
128 0.8584411547 8.633176341
256 0.844812533 9.895126238
512 0.6488536823 9.918250127
1024 0.5583994316 10.07929211
2048 0.2170992297 11.76857085
4096 0.1689974334 10.57275424
8192 0.1073492634 11.30109414
16384 0.05507700358 10.79551285
32768 -0.1122765141 12.18196461
65536 -0.1082084514 10.75991951
131072 -0.1614776301 12.08280139
262144 -0.1262636206 12.31436106
524288 -0.1822241126 11.92265429
1048576 -0.154977993 12.44957874
quadratic: [ -2, ? ]:
16 14839.88234 48437.54628
32 9845.959905 38301.32847
64 9014.247013 42640.41569
128 8896.862825 51065.16435
256 7826.451775 52802.30423
512 5740.192882 50460.37355
1024 3763.537685 55927.90114
2048 4614.095632 56865.9075
4096 2543.616641 63334.06688
8192 3816.785264 67292.04963
16384 2150.438092 59774.27552
32768 2040.147525 64602.84142
65536 1472.641548 62707.54343
131072 737.0904958 65042.89241
262144 552.4597205 65332.71939
524288 1220.033859 67224.38646
1048576 779.2150834 67670.24279
rd: [-36.71269068, +10.40560403]
16 -25.28086805 4.497116297
32 -21.91160446 6.164186762
64 -31.84507985 5.314029372
128 -28.18593081 8.468599367
256 -32.2239576 9.280755427
512 -34.37184738 8.712661997
1024 -32.76607409 9.430387606
2048 -33.70567456 9.943244789
4096 -33.41258906 10.0578444
8192 -35.70089028 9.514725373
16384 -34.98116712 10.18877346
32768 -35.44273091 10.35038961
65536 -35.46953288 10.30957117
131072 -36.174262 10.29443881
262144 -36.24836969 10.29016873
524288 -36.25222472 10.37149306
1048576 -36.45468642 10.31003619
reimer5: [-5.0, +5.0]
16 -2.361421916 2.704557987
32 -3.972695582 0.986257506
64 -3.217000685 2.032755989
128 -3.483504688 2.88951549
256 -3.194819989 2.763117113
512 -4.477395366 3.370369899
1024 -4.15838999 3.494604936
2048 -4.616521353 3.062676495
4096 -4.432506719 3.206821162
8192 -4.823650023 3.729307995
16384 -4.854054326 4.39754424
32768 -4.564112961 4.469575818
65536 -4.676685955 4.254240181
131072 -4.828277994 4.65359081
262144 -4.919769089 4.530616105
524288 -4.913618108 4.720229217
1048576 -4.925946223 4.699093241
reimer6: [-937501, +937499]
16 -216406.1196 143249.8505
32 -198041.2158 162876.8859
64 -259952.0084 263578.3623
128 -356140.0489 284512.089
256 -392049.9024 351816.816
512 -300184.011 381708.3474
1024 -344592.3377 401510.8525
2048 -318159.9736 405190.3427
4096 -397220.4826 396754.8119
8192 -435313.677 442697.448
16384 -511761.0618 425393.6531
32768 -465225.1855 515696.4921
65536 -537552.4335 470410.11
131072 -520920.8046 493498.4913
262144 -561643.7515 545348.9635
524288 -597021.9616 569344.228
1048576 -544521.8243 614558.7621
rosenbrock: [ 0, ? ]:
16 3279.0466 25302.94453
32 640.123231 37067.04753
64 251.7248232 49858.14266
128 724.1849479 39743.87575
256 111.0103696 53190.69659
512 90.86844074 52432.71283
1024 389.4488942 43715.11226
2048 30.91942906 58801.74504
4096 33.86417839 49426.12446
8192 62.22950547 58722.93201
16384 26.18954261 61525.89623
32768 40.23342493 55536.65555
65536 8.67362244 60633.10559
131072 8.558799195 65560.51067
262144 2.775330825 61103.6659
524288 3.201745928 64586.774
1048576 3.961061056 64452.94159
schwefel: [ 0, ? ]:
16 26.20698845 14952.37685
32 19.24332636 14409.12887
64 27.78131083 14362.91488
128 13.00573185 15596.643
256 2.693938057 18210.45926
512 6.329847001 17679.3988
1024 1.733246677 19542.94178
2048 1.711402766 20728.86981
4096 3.945633822 20875.80899
8192 1.0483197 22272.86669
16384 0.3575255246 22289.12026
32768 0.3632678296 23597.06074
65536 0.04075515688 23006.96345
131072 0.1780585259 23778.34825
262144 0.1595290857 23857.28458
524288 0.04910429572 23952.09488
1048576 0.02833273288 24137.65225
smith1: [ ?, ? ]:
16 31894.87703 261820.2815
32 20766.65283 181182.4803
64 18646.85718 274073.9985
128 8275.672143 401170.8701
256 9830.832006 279646.508
512 6128.948192 356302.3166
1024 4283.764101 374814.1959
2048 205.8468433 361051.7997
4096 1562.047289 429562.6929
8192 208.5012886 432714.4986
16384 2868.328443 441846.2972
32768 -1873.591333 457636.3338
65536 -676.3127945 500037.7835
131072 -1958.482913 490542.9343
262144 -1184.279241 488462.4813
524288 -2307.426881 485044.1633
1048576 -2052.432228 485447.6323
smith2: [ ?, ? ]:
16 -94691.41437 -755.5715445
32 -124454.0286 -70.64406169
64 -184497.4088 -117.3613514
128 -251690.6777 -7.368007913
256 -117923.9421 -13.40702833
512 -206312.4668 31.61313318
1024 -213457.5251 74.94191361
2048 -272728.3135 131.6697951
4096 -246718.7849 173.5016588
8192 -240054.6462 178.4586741
16384 -293327.4482 144.01461
32768 -326207.5833 206.2040368
65536 -304006.3419 221.7402841
131072 -313583.3811 231.3577427
262144 -305065.6922 242.2777611
524288 -321105.6831 279.4288612
1048576 -322752.2198 299.9506699
virasoro: [-29.0, +21.0]
16 -5.095535765 12.38910217
32 -9.328907304 10.02015178
64 -7.559487901 14.2265071
128 -11.84791997 16.42500861
256 -11.17145084 16.60232768
512 -14.35943061 16.91136634
1024 -14.55244956 17.37568103
2048 -15.72789536 18.57021816
4096 -18.10639705 19.24736744
8192 -16.22807994 19.66357965
16384 -17.44105986 19.83234891
32768 -16.99306248 19.93345155
65536 -20.41002263 19.78756216
131072 -19.94418466 20.22108268
262144 -21.62984907 20.42587032
524288 -20.97522433 20.31674168
1048576 -21.55233453 20.54891895
wright: [-30.25, 40.0 ]
16 -10.81769109 -8.325569794
32 -10.8993462 -8.701143985
64 -11.40451116 -8.469731443
128 -11.56755932 -7.667416737
256 -11.25778333 -8.065405719
512 -11.50224087 -8.193169379
1024 -11.63862276 -7.991977062
2048 -11.64480556 -7.742748387
4096 -11.78017849 -7.707492893
8192 -11.88695213 -7.684721959
16384 -11.982057 -7.557812121
32768 -12.0614065 -7.528100813
65536 -12.17380653 -7.464791433
131072 -12.15407048 -7.583746326
262144 -12.08196782 -7.49659552
524288 -12.08095527 -7.460238632
1048576 -12.1654111 -7.483117164
zakharov: [ 0, ? ]::
16 307.2572513 7805013.819
32 509.6723746 3601280.195
64 28.84753056 12197333.21
128 25.39264337 10302061.91
256 40.42131893 12283122.44
512 15.04679164 12467982.85
1024 16.1921555 15759352.47
2048 2.550197461 17513517.62
4096 10.20800089 16560273.83
8192 7.446913682 18107392.77
16384 5.984833934 23794094.48
32768 1.338112649 21106129.48
65536 2.364084421 22008999.36
131072 2.959038777 24757714.87
262144 1.130631563 25242079.72
524288 1.024112152 24810619.67
1048576 1.535256997 27185776.7
range_by_fmincon_test:
Use the MATLAB fmincon() function to seek range.
butcher known: [-1.4393333333, +0.219]
Butcher estimated: [ -1.439332949 0.2189993599]
polynomials_test
Normal end of execution.
27-Feb-2019 08:58:22
polynomials_test
27-Feb-2019 08:59:20
polynomials_test
MATLAB version.
Test polynomials.
RANGE_BY_SAMPLING_TEST:
Use N sample values of each polynomial over its domain to estimate
its minimum Pmin and maximum Pmax
N Pmin Pmax
butcher: [-1.4393333333, +0.219]
16 -0.9392362348 0.1722153637
32 -1.096808774 0.1619794357
64 -1.218607005 0.1354705999
128 -1.146982586 0.200123647
256 -1.163550893 0.1864259985
512 -1.261186459 0.1643861716
1024 -1.301762549 0.181939832
2048 -1.328901868 0.1806981008
4096 -1.30398538 0.1970596662
8192 -1.333096962 0.1967859621
16384 -1.367394167 0.1955562743
32768 -1.347472355 0.2058122585
65536 -1.365699517 0.2125327583
131072 -1.355741449 0.2123066372
262144 -1.396926957 0.2177005289
524288 -1.397266108 0.2141781022
1048576 -1.39471054 0.2164118703
camel: [ -1.031628453489616, ? ]:
16 2.34293696 286.8335898
32 -0.5656567098 323.5035177
64 -0.9962010179 325.1266789
128 -1.027385874 379.3308185
256 -0.6818695846 307.3754905
512 -1.015374044 352.3236156
1024 -1.00287864 338.5134894
2048 -1.001644111 374.7228438
4096 -1.008459822 375.3418439
8192 -1.030057213 379.9255796
16384 -1.0315199 399.0081893
32768 -1.030716586 393.6800883
65536 -1.031499798 401.2157052
131072 -1.031604928 403.3259929
262144 -1.031451431 400.6543081
524288 -1.031561663 403.3561477
1048576 -1.03160806 403.9333421
camera: [-270397.4, +270202.6]
16 -46966.46863 87607.58773
32 -46583.37426 131880.9884
64 -107842.0561 96384.78574
128 -115095.894 102371.4783
256 -123199.992 125799.9772
512 -132145.0254 166292.1828
1024 -158207.0598 142974.8428
2048 -148419.6789 149261.7396
4096 -167042.0576 152023.3768
8192 -199173.1852 186346.3269
16384 -188996.5906 195186.7777
32768 -226765.1798 232225.4553
65536 -223290.0705 199323.1465
131072 -239475.7762 214594.9647
262144 -223937.433 219707.9062
524288 -226095.1346 221139.3738
1048576 -220739.0299 228089.0193
caprasse: [-3.1800966258, +4.4852773332]
16 -1.122640811 3.568584008
32 -1.647449732 3.56462884
64 -2.303226173 3.346400025
128 -1.409359901 3.38414889
256 -2.188055437 3.744646826
512 -2.156669132 3.949668106
1024 -2.681084075 3.871754895
2048 -2.508913074 3.954812721
4096 -2.708625627 4.240230838
8192 -2.917337055 4.252268658
16384 -2.863663818 4.295687111
32768 -3.057783765 4.344869033
65536 -2.983681702 4.280455175
131072 -3.054743761 4.401290811
262144 -3.026200759 4.387669535
524288 -3.087886456 4.408258398
1048576 -3.055552816 4.460833605
cyclic5: [-30000, +50000]
16 -9991.369907 6422.069083
32 -2145.460004 4624.181633
64 -4222.701274 7624.457565
128 -14992.43919 6112.12361
256 -8174.970236 11483.64356
512 -8628.718062 23099.33817
1024 -13808.80086 14629.6272
2048 -19021.72443 35545.02833
4096 -16946.40579 28357.55695
8192 -17621.7452 26592.28456
16384 -21133.52841 33712.66728
32768 -20793.87133 29474.87736
65536 -23036.08174 27816.00644
131072 -24933.06023 35863.25232
262144 -23580.77258 33465.41057
524288 -24018.55212 42566.08176
1048576 -25467.84219 39498.54646
cyclic7: [-5.0, +7.0]
16 -0.1818128315 0.2943232411
32 -0.1566307448 0.2425566252
64 -0.1613862091 0.5427491584
128 -0.6420509895 0.9047133214
256 -0.3866409939 0.4517013016
512 -0.9462007286 0.5831586333
1024 -1.5731949 0.9667101914
2048 -2.894077843 1.048015102
4096 -1.873678733 1.393726369
8192 -2.614966655 1.362242833
16384 -1.800746927 2.36379899
32768 -2.936911452 1.919211055
65536 -2.477698801 2.107552639
131072 -2.812458641 2.64886998
262144 -3.343510677 3.25534353
524288 -2.477821056 3.326030713
1048576 -2.669923467 3.303197282
cyclic8: [-8.0, +8.0]
16 -0.4040071044 0.05786917277
32 -0.08508165615 0.0622396526
64 -0.04506995837 0.118717916
128 -0.4218346391 0.2745799351
256 -0.2725731752 0.1953586594
512 -0.4612749938 0.4890045447
1024 -0.2750077722 0.55066444
2048 -0.6659820419 0.5284259662
4096 -0.7214659199 0.7541840231
8192 -2.193833684 1.286781661
16384 -0.9603117808 1.292588948
32768 -0.966085627 1.509452859
65536 -1.468336729 1.587438261
131072 -2.345419689 1.848147231
262144 -2.619592599 1.969771506
524288 -2.330561365 2.781625427
1048576 -2.384376073 2.303065784
goldstein_price: [ 3, ? ]:
16 51.12676154 820896.2479
32 105.5459688 203980.5891
64 10.92957343 724262.7837
128 3.817344807 798623.0425
256 9.765102979 867929.2964
512 8.221251128 969804.7232
1024 5.050014183 932723.5592
2048 4.492353885 940076.8531
4096 3.052169259 955370.7013
8192 3.052850987 1001207.627
16384 3.088965056 1004841.246
32768 3.00526769 1007141.08
65536 3.008620381 1012877.892
131072 3.002478186 1012477.438
262144 3.001078639 1014881.033
524288 3.001491298 1015031.333
1048576 3.000262585 1014524.015
hairer: [-1875.25, -48.25]
16 -926.0411179 -155.0324846
32 -1032.123614 -204.2213865
64 -923.2430733 -199.0450683
128 -1315.081641 -135.905696
256 -1023.718237 -114.4337671
512 -1309.290832 -112.6619642
1024 -1316.029618 -97.7389525
2048 -1525.32216 -93.39353897
4096 -1474.126644 -68.40662814
8192 -1491.76719 -73.46822717
16384 -1493.356889 -64.93141755
32768 -1594.938255 -74.16070942
65536 -1678.734462 -73.05326927
131072 -1611.06875 -67.44005
262144 -1659.385907 -58.2896173
524288 -1699.753406 -64.00018544
1048576 -1711.254178 -60.67348512
heart: [-1.36775, +1.74345327935
16 0.1140052593 1.007342859
32 0.3366754628 1.025957486
64 -0.3499218274 1.289240672
128 -0.07225874411 1.052502143
256 -0.4754486392 1.485554943
512 -0.3983935201 1.360331884
1024 -0.4679556199 1.460674034
2048 -0.5101981721 1.416384693
4096 -0.552286899 1.559009544
8192 -0.7789747658 1.575163714
16384 -0.7811037014 1.540810454
32768 -0.8293137161 1.640550256
65536 -0.7699449513 1.656784516
131072 -0.9025015425 1.654347059
262144 -0.9717289694 1.652736872
524288 -0.8253402394 1.63059713
1048576 -0.9570437895 1.685752139
himmelblau: [ 0, ? ]:
16 3.344612463 535.1187975
32 13.65550768 697.0243811
64 1.967193857 653.9187636
128 0.9391154232 833.246507
256 0.9589538353 657.0620917
512 0.7848869657 753.4085761
1024 0.03416051653 723.8703239
2048 0.008669694946 799.5137097
4096 0.09444232334 758.8565032
8192 0.01297949904 801.8225927
16384 0.01188193096 837.8470141
32768 0.006387915561 860.9489768
65536 0.008655583411 869.0417687
131072 6.034563755e-05 881.1186093
262144 0.0005764269044 874.9953325
524288 0.0008305200062 883.8135778
1048576 0.0003036544091 884.9308391
hunecke: [-1436.515078155, +161.120543283]
16 -787.374311 -37.15179156
32 -1101.766472 -73.77956751
64 -1145.158259 -1.121914179
128 -1187.430028 11.15542153
256 -1286.887026 -1.46343509
512 -1235.790156 42.27869517
1024 -1230.098017 66.51978582
2048 -1246.878481 98.97282175
4096 -1340.039759 85.46988876
8192 -1263.167011 98.62275376
16384 -1330.169829 129.8288892
32768 -1342.754365 98.77241454
65536 -1343.667596 116.1091694
131072 -1373.56007 123.7924842
262144 -1384.266376 135.977523
524288 -1412.494981 138.8953855
1048576 -1416.623171 139.3435011
kearfott: [ 0, ? ]:
16 1.890688428 73.3603846
32 0.6002071179 102.1437303
64 1.10893189 76.76005163
128 0.8683045935 97.6338526
256 0.4403239578 109.9642397
512 0.2045063378 122.7198361
1024 0.2308875819 130.9075302
2048 0.2923803795 151.9116666
4096 0.2187191028 158.5862868
8192 0.145415032 157.6793629
16384 0.04625697041 183.6609911
32768 0.06696469032 171.0181402
65536 0.03664279462 168.8297855
131072 0.03048870343 195.9865407
262144 0.01840079095 176.5833542
524288 0.002912729339 198.4442477
1048576 0.003118859558 207.6541432
lv3: [-9.35, +14.8 ]
16 -5.505976006 2.359192519
32 -2.411196489 4.221394903
64 -8.7249261 5.118580012
128 -6.196118255 5.045720063
256 -7.529919236 8.246773071
512 -7.992012879 6.563083491
1024 -6.584624644 8.049174981
2048 -8.76839483 8.190774113
4096 -7.471582786 7.949835791
8192 -8.519852729 8.063633439
16384 -8.789651166 8.158836837
32768 -8.920377623 8.475209322
65536 -9.046798181 8.147452917
131072 -9.009408155 8.498095034
262144 -9.060767317 8.530391987
524288 -8.969659498 8.503243629
1048576 -9.085109029 8.546697262
lv4: [-20.8, +22.8]
16 -6.884893684 4.151084073
32 -1.240729077 5.887408848
64 -8.377417891 8.796272966
128 -8.157045315 11.19769307
256 -8.607705406 7.948720738
512 -7.702569651 10.06555102
1024 -9.890049382 11.02818851
2048 -7.978823916 9.916188162
4096 -11.25760943 12.14712213
8192 -11.73914407 12.8606102
16384 -11.56105265 12.51808081
32768 -10.93875822 14.11446132
65536 -11.22992462 13.27660181
131072 -11.78153073 13.54132999
262144 -11.86689048 13.52270807
524288 -12.25617509 14.39611352
1048576 -12.5438857 13.73974981
magnetism6: [-0.25, +280.0]
16 56.49768538 176.9576672
32 20.37974721 155.4025017
64 13.068286 198.9760108
128 25.95516037 174.6717335
256 22.10666306 191.0768325
512 12.90162943 216.4283606
1024 7.597354659 194.5672584
2048 3.788502143 219.991467
4096 6.67575603 237.3487063
8192 4.261387053 219.9843987
16384 3.135742018 233.3861037
32768 4.552718225 241.1575989
65536 0.832176155 230.8975475
131072 2.191661966 252.8632361
262144 1.014809403 252.2550204
524288 1.238867148 245.623275
1048576 0.4762961256 249.9233468
magnetism7: [-0.25, +330.0]
16 2.61800899 8.614991166
32 0.8401354203 7.790561078
64 0.1041970534 9.155543046
128 0.8584411547 8.633176341
256 0.844812533 9.895126238
512 0.6488536823 9.918250127
1024 0.5583994316 10.07929211
2048 0.2170992297 11.76857085
4096 0.1689974334 10.57275424
8192 0.1073492634 11.30109414
16384 0.05507700358 10.79551285
32768 -0.1122765141 12.18196461
65536 -0.1082084514 10.75991951
131072 -0.1614776301 12.08280139
262144 -0.1262636206 12.31436106
524288 -0.1822241126 11.92265429
1048576 -0.154977993 12.44957874
quadratic: [ -2, ? ]:
16 14839.88234 48437.54628
32 9845.959905 38301.32847
64 9014.247013 42640.41569
128 8896.862825 51065.16435
256 7826.451775 52802.30423
512 5740.192882 50460.37355
1024 3763.537685 55927.90114
2048 4614.095632 56865.9075
4096 2543.616641 63334.06688
8192 3816.785264 67292.04963
16384 2150.438092 59774.27552
32768 2040.147525 64602.84142
65536 1472.641548 62707.54343
131072 737.0904958 65042.89241
262144 552.4597205 65332.71939
524288 1220.033859 67224.38646
1048576 779.2150834 67670.24279
rd: [-36.71269068, +10.40560403]
16 -25.28086805 4.497116297
32 -21.91160446 6.164186762
64 -31.84507985 5.314029372
128 -28.18593081 8.468599367
256 -32.2239576 9.280755427
512 -34.37184738 8.712661997
1024 -32.76607409 9.430387606
2048 -33.70567456 9.943244789
4096 -33.41258906 10.0578444
8192 -35.70089028 9.514725373
16384 -34.98116712 10.18877346
32768 -35.44273091 10.35038961
65536 -35.46953288 10.30957117
131072 -36.174262 10.29443881
262144 -36.24836969 10.29016873
524288 -36.25222472 10.37149306
1048576 -36.45468642 10.31003619
reimer5: [-5.0, +5.0]
16 -2.361421916 2.704557987
32 -3.972695582 0.986257506
64 -3.217000685 2.032755989
128 -3.483504688 2.88951549
256 -3.194819989 2.763117113
512 -4.477395366 3.370369899
1024 -4.15838999 3.494604936
2048 -4.616521353 3.062676495
4096 -4.432506719 3.206821162
8192 -4.823650023 3.729307995
16384 -4.854054326 4.39754424
32768 -4.564112961 4.469575818
65536 -4.676685955 4.254240181
131072 -4.828277994 4.65359081
262144 -4.919769089 4.530616105
524288 -4.913618108 4.720229217
1048576 -4.925946223 4.699093241
reimer6: [-937501, +937499]
16 -216406.1196 143249.8505
32 -198041.2158 162876.8859
64 -259952.0084 263578.3623
128 -356140.0489 284512.089
256 -392049.9024 351816.816
512 -300184.011 381708.3474
1024 -344592.3377 401510.8525
2048 -318159.9736 405190.3427
4096 -397220.4826 396754.8119
8192 -435313.677 442697.448
16384 -511761.0618 425393.6531
32768 -465225.1855 515696.4921
65536 -537552.4335 470410.11
131072 -520920.8046 493498.4913
262144 -561643.7515 545348.9635
524288 -597021.9616 569344.228
1048576 -544521.8243 614558.7621
rosenbrock: [ 0, ? ]:
16 3279.0466 25302.94453
32 640.123231 37067.04753
64 251.7248232 49858.14266
128 724.1849479 39743.87575
256 111.0103696 53190.69659
512 90.86844074 52432.71283
1024 389.4488942 43715.11226
2048 30.91942906 58801.74504
4096 33.86417839 49426.12446
8192 62.22950547 58722.93201
16384 26.18954261 61525.89623
32768 40.23342493 55536.65555
65536 8.67362244 60633.10559
131072 8.558799195 65560.51067
262144 2.775330825 61103.6659
524288 3.201745928 64586.774
1048576 3.961061056 64452.94159
schwefel: [ 0, ? ]:
16 26.20698845 14952.37685
32 19.24332636 14409.12887
64 27.78131083 14362.91488
128 13.00573185 15596.643
256 2.693938057 18210.45926
512 6.329847001 17679.3988
1024 1.733246677 19542.94178
2048 1.711402766 20728.86981
4096 3.945633822 20875.80899
8192 1.0483197 22272.86669
16384 0.3575255246 22289.12026
32768 0.3632678296 23597.06074
65536 0.04075515688 23006.96345
131072 0.1780585259 23778.34825
262144 0.1595290857 23857.28458
524288 0.04910429572 23952.09488
1048576 0.02833273288 24137.65225
smith1: [ ?, ? ]:
16 31894.87703 261820.2815
32 20766.65283 181182.4803
64 18646.85718 274073.9985
128 8275.672143 401170.8701
256 9830.832006 279646.508
512 6128.948192 356302.3166
1024 4283.764101 374814.1959
2048 205.8468433 361051.7997
4096 1562.047289 429562.6929
8192 208.5012886 432714.4986
16384 2868.328443 441846.2972
32768 -1873.591333 457636.3338
65536 -676.3127945 500037.7835
131072 -1958.482913 490542.9343
262144 -1184.279241 488462.4813
524288 -2307.426881 485044.1633
1048576 -2052.432228 485447.6323
smith2: [ ?, ? ]:
16 -94691.41437 -755.5715445
32 -124454.0286 -70.64406169
64 -184497.4088 -117.3613514
128 -251690.6777 -7.368007913
256 -117923.9421 -13.40702833
512 -206312.4668 31.61313318
1024 -213457.5251 74.94191361
2048 -272728.3135 131.6697951
4096 -246718.7849 173.5016588
8192 -240054.6462 178.4586741
16384 -293327.4482 144.01461
32768 -326207.5833 206.2040368
65536 -304006.3419 221.7402841
131072 -313583.3811 231.3577427
262144 -305065.6922 242.2777611
524288 -321105.6831 279.4288612
1048576 -322752.2198 299.9506699
virasoro: [-29.0, +21.0]
16 -5.095535765 12.38910217
32 -9.328907304 10.02015178
64 -7.559487901 14.2265071
128 -11.84791997 16.42500861
256 -11.17145084 16.60232768
512 -14.35943061 16.91136634
1024 -14.55244956 17.37568103
2048 -15.72789536 18.57021816
4096 -18.10639705 19.24736744
8192 -16.22807994 19.66357965
16384 -17.44105986 19.83234891
32768 -16.99306248 19.93345155
65536 -20.41002263 19.78756216
131072 -19.94418466 20.22108268
262144 -21.62984907 20.42587032
524288 -20.97522433 20.31674168
1048576 -21.55233453 20.54891895
wright: [-30.25, 40.0 ]
16 -10.81769109 -8.325569794
32 -10.8993462 -8.701143985
64 -11.40451116 -8.469731443
128 -11.56755932 -7.667416737
256 -11.25778333 -8.065405719
512 -11.50224087 -8.193169379
1024 -11.63862276 -7.991977062
2048 -11.64480556 -7.742748387
4096 -11.78017849 -7.707492893
8192 -11.88695213 -7.684721959
16384 -11.982057 -7.557812121
32768 -12.0614065 -7.528100813
65536 -12.17380653 -7.464791433
131072 -12.15407048 -7.583746326
262144 -12.08196782 -7.49659552
524288 -12.08095527 -7.460238632
1048576 -12.1654111 -7.483117164
zakharov: [ 0, ? ]::
16 307.2572513 7805013.819
32 509.6723746 3601280.195
64 28.84753056 12197333.21
128 25.39264337 10302061.91
256 40.42131893 12283122.44
512 15.04679164 12467982.85
1024 16.1921555 15759352.47
2048 2.550197461 17513517.62
4096 10.20800089 16560273.83
8192 7.446913682 18107392.77
16384 5.984833934 23794094.48
32768 1.338112649 21106129.48
65536 2.364084421 22008999.36
131072 2.959038777 24757714.87
262144 1.130631563 25242079.72
524288 1.024112152 24810619.67
1048576 1.535256997 27185776.7
range_by_fmincon_test:
Use the MATLAB fmincon() function to seek range.
butcher known: [ -1.439333333 0.219]
Butcher estimated: [ -1.439332949 0.2189993599]
polynomials_test
Normal end of execution.
27-Feb-2019 08:59:31
diary