weighted_ordinal_pattern_distribution: A function to compute weighted ordinal pattern statistics
In statcomp: Statistical Complexity and Information Measures for Time Series Analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
View source: R/weighted_ordinal_pattern_distribution.R
Description
Computation of weighted ordinal patterns of a time series. Weights can be generated by a user-specified function (e.g. variance-weighted, see Fadlallah et al 2013).
Usage
1
weighted_ordinal_pattern_distribution(x, ndemb)
Arguments
x
A numeric vector (e.g. a time series), from which the weighted ordinal pattern distribution is to be calculated
ndemb
Embedding dimension of the ordinal patterns (i.e. sliding window size). Should be chosen such as length(x) >> ndemb
Details
This function returns the distribution of weighted ordinal patterns using the Keller coding scheme, detailed in Physica A 356 (2005) 114-120. NA values are allowed.
The function uses old and slow R routines and is only maintained for comparability.
For faster routines, see weighted_ordinal_pattern_distribution.
Value
A character vector of length factorial(ndemb) is returned.
Author(s)
Sebastian Sippel
References
Fadlallah, B., Chen, B., Keil, A. and Principe, J., 2013. Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Physical Review E, 87(2), p.022911.
See Also
weighted_ordinal_pattern_distribution
Examples
1
2
x = arima.sim(model=list(ar = 0.3), n = 10^4)
weighted_ordinal_pattern_distribution(x = x, ndemb = 6)
Example output
[1] 35.1209130 28.5170067 27.2697483 24.9689948 25.1198458 11.5886040
[7] 27.5309845 12.9848797 45.3443771 31.3197923 12.5154578 14.3989571
[13] 11.6360282 13.9437976 30.3331540 29.6765890 25.2665533 17.5155359
[19] 7.3632532 12.3683906 8.6545123 9.9637387 18.0213507 16.4023793
[25] 4.7488853 6.8366009 4.7809144 8.5824980 14.3807481 24.6840268
[31] 26.7996915 11.7318864 18.8396026 13.4197722 9.0071136 14.5347591
[37] 17.3611373 3.6040206 8.3471890 14.2325918 19.8435298 9.7573870
[43] 24.4311176 18.8250351 16.8906408 28.6210958 24.0897279 22.3399754
[49] 8.5375725 8.6743653 11.2562648 10.2986377 15.4741318 17.2736540
[55] 4.4106275 5.8153301 13.2812979 7.6843866 12.4229269 23.0383680
[61] 12.8539735 10.5792353 10.5417385 7.4871112 4.4657572 2.9246969
[67] 11.3164354 7.6484541 7.0976271 10.1162948 6.0158522 8.2585371
[73] 10.2271679 10.0958164 7.5052580 7.4448603 8.4550747 8.5420239
[79] 9.1703486 9.8541772 14.0944658 19.1443026 8.1066467 21.4136953
[85] 9.6915959 6.3751024 10.0258539 20.0448876 16.2230158 29.9021678
[91] 18.3433465 4.1354301 1.6356447 3.8977091 0.7961022 5.0023420
[97] 7.3834077 4.7608655 2.8601137 5.8203051 6.1135089 5.1268603
[103] 11.6940100 3.5089820 3.5567403 6.5187226 5.3715028 10.7216812
[109] 5.3022955 7.3161049 13.7963613 20.7505360 9.4506635 14.4222051
[115] 8.6319109 13.4833067 12.2409263 19.7817091 27.2418570 29.5184897
[121] 25.8624892 27.9853316 29.9118856 9.4268062 15.5422288 15.8477606
[127] 12.5181780 10.6706295 10.8778658 8.5287317 13.1711853 7.9281410
[133] 5.0619575 6.5737501 5.9935029 9.5975092 6.2241719 6.9461358
[139] 9.9386764 4.5090062 2.9013164 6.7255560 7.2244252 12.9986012
[145] 5.5713437 4.7460412 7.4289013 5.2742952 12.1902938 12.5548832
[151] 19.2046889 17.9598404 5.2543673 3.8754050 3.1321197 9.5946678
[157] 5.5468496 4.7882147 2.5670693 5.1039326 5.5754275 2.8962079
[163] 2.9995874 7.2587284 4.2995215 4.0830989 7.3934924 9.4559952
[169] 4.7869742 5.7500695 1.6846159 7.2396724 14.3836267 11.1362194
[175] 6.2315744 3.8684823 4.8141987 12.9758471 9.7581664 18.8167119
[181] 16.8553549 11.0156107 9.2031767 7.2467628 4.9338128 5.3632388
[187] 13.3478030 3.6669982 4.0013900 7.9354016 8.3678706 8.9457136
[193] 6.9078676 5.7591493 9.7189809 9.4232175 5.0822622 7.5838827
[199] 4.2566860 4.9771655 12.4549862 9.4282958 14.9095871 13.4437326
[205] 6.7735724 7.9101707 9.4819733 16.8692083 27.6690307 18.1314945
[211] 5.8628490 7.7898534 3.2157202 6.6340937 7.3835295 6.4253159
[217] 10.8861956 6.5812678 6.9101767 8.3230395 3.4215342 5.0449765
[223] 5.7289833 6.9645163 6.7737635 10.4645643 11.3166709 8.9626071
[229] 12.5602147 8.1838345 11.3272876 19.2501948 7.5747769 19.9500813
[235] 8.1303572 8.4725885 12.9382518 25.0920699 32.4886318 20.9772632
[241] 26.9155888 17.7415601 13.5193079 7.4829115 5.2474072 2.0950005
[247] 11.6777702 7.3537787 9.0991449 6.4124923 6.3387554 8.3073196
[253] 9.9865662 7.5744737 4.8361629 6.6313819 2.2755114 4.6885269
[259] 4.6353870 3.5151573 2.6608469 1.5185920 2.6770252 7.8523177
[265] 4.5319270 3.7463981 3.3170378 0.6466043 9.5359557 10.9306823
[271] 19.8269637 6.1270240 6.7168459 4.4258462 3.0000098 3.9981561
[277] 8.5920166 5.8774418 5.8815020 3.1714171 5.5903779 2.2921633
[283] 6.6448022 1.8478074 3.1838236 3.4513578 6.9712095 7.0149844
[289] 5.2862791 5.1925710 5.5492605 6.9064212 3.0561801 14.1128576
[295] 7.3014404 1.6832178 3.0846099 8.6876544 11.6925399 11.8633406
[301] 20.3239662 13.3869156 4.7421063 10.2674605 5.8281637 7.5892773
[307] 15.2060112 9.7274292 7.9349396 5.8724071 4.0768784 7.0736349
[313] 9.3729176 11.6001941 18.5938923 8.6012679 9.1229656 15.2862100
[319] 4.8063084 3.8047911 14.0224133 8.1581934 8.6655204 13.7615127
[325] 5.9092009 4.3981782 10.4010155 9.4454393 16.2932788 20.0840573
[331] 15.9608698 20.4306775 7.4431607 4.2527446 7.7158053 4.1302094
[337] 23.2049987 6.6856140 8.0971991 11.6752237 4.8665418 14.1632569
[343] 8.8595116 10.7665301 21.6593473 13.1227780 13.2928453 18.6539387
[349] 15.9088922 16.5730100 16.7772374 29.9563051 27.4314551 23.5313781
[355] 16.6898597 10.1568770 16.5366310 26.6557984 33.3757817 31.5321349
[361] 32.0548583 35.3574444 32.0418756 19.2652336 11.4821985 7.0290823
[367] 20.1968471 18.1117066 41.8175555 15.1718126 13.1982829 11.5987973
[373] 14.0367224 14.3300494 8.1293336 11.4269350 15.4265620 17.3892696
[379] 6.1556527 8.5630747 6.3342873 8.7247626 13.0554831 12.7621986
[385] 3.8328630 4.7150930 7.5094507 4.6397605 19.0579702 17.6530478
[391] 32.5744073 17.3973878 9.7767070 5.8826174 3.5351979 4.0555956
[397] 12.9083993 3.7066744 5.3404706 10.0859220 5.9782773 8.3636444
[403] 13.2926440 11.2125418 10.7174341 12.0511540 10.5155244 13.7403212
[409] 6.0756551 5.6292796 8.7168647 6.2822847 4.7839214 13.1709468
[415] 5.5248841 5.7979099 4.9867517 6.9594110 13.2675038 20.7582850
[421] 14.1433587 9.8896554 8.5394873 5.1474885 6.9834805 5.3862901
[427] 5.2986212 6.4968789 9.0237059 3.3267998 2.3297010 5.1039461
[433] 8.1972936 5.2425847 3.0460600 5.3012660 5.1516304 8.2316341
[439] 4.7117951 4.1191076 5.1204872 2.3290207 4.6425767 6.8314992
[445] 4.0899797 4.7513672 5.9341110 9.5954581 14.1951769 13.5596434
[451] 11.6897449 9.6686920 9.1139474 2.6466160 5.0933950 4.8885603
[457] 6.8710538 3.2294488 6.5292781 1.5107479 5.2987406 6.0162369
[463] 2.9628681 6.7914769 3.1973397 3.7848241 7.2623938 5.1606124
[469] 11.0906344 6.3227462 8.9577227 13.3964945 8.2961408 10.6934876
[475] 6.8602872 12.6079223 9.1030338 15.9112996 22.9130718 13.4459796
[481] 34.8370144 23.1912402 34.0914419 19.7707883 8.7510113 6.3899459
[487] 21.6359023 16.5961024 19.4134671 13.0109934 7.8803539 10.2242420
[493] 10.2885559 11.5579260 5.8029123 7.6271100 3.2879614 8.2505724
[499] 4.6098370 4.4172806 3.7078658 1.9991004 6.9370432 9.8930633
[505] 1.1399343 1.3509878 5.7456050 6.9821256 8.0758623 16.0354911
[511] 25.7680990 25.8117913 17.8635380 11.6928684 4.9914711 3.9903662
[517] 12.3506078 10.9440485 18.5431574 9.5276424 5.5190079 8.8572265
[523] 6.1533653 9.7321058 5.7262592 11.0022409 4.9354135 10.7510261
[529] 9.6837819 5.0530177 6.7187558 3.1566858 6.4919478 8.2920048
[535] 4.7198428 11.0089622 3.3683565 4.7952767 10.0097729 8.6582982
[541] 21.1306763 12.3060098 4.2363557 1.5673765 6.4807889 6.1992594
[547] 19.8498046 4.2311949 6.5225303 4.7056368 7.0724330 6.7366316
[553] 10.4270557 3.5520449 4.9792157 2.3770509 10.8316743 5.5702951
[559] 4.9556253 5.6202306 4.3815235 5.0289847 8.3564232 9.4847043
[565] 6.3590222 13.0932896 10.1510483 4.4742243 20.4763457 18.5660821
[571] 12.4968352 13.3714751 3.3454232 8.0550356 2.7247927 6.3512235
[577] 8.3202882 4.9490641 5.8701985 4.2304967 4.7312747 8.2258889
[583] 6.7219439 7.1134445 5.6021551 5.1148427 4.2166693 12.7827286
[589] 9.8550506 9.7898406 12.4154164 10.9742304 20.1501267 12.3096647
[595] 8.8398580 18.7668711 8.3953098 12.7666632 24.0155662 22.8605636
[601] 21.0450443 26.2580875 12.5732984 5.4093547 10.8914734 5.8918538
[607] 13.2104045 5.8182733 20.4054977 9.8634741 8.6171402 12.9941584
[613] 8.6708413 5.9195304 4.7404241 9.0525713 5.2367203 5.3216983
[619] 9.1056870 5.7104100 3.7398599 11.8228379 3.6710705 10.3778858
[625] 5.9410259 2.6092421 1.9044290 7.5302931 9.3549069 15.5700888
[631] 31.9767288 20.8816144 15.0560935 12.6984154 10.5141772 7.8432266
[637] 13.9410674 15.7644540 11.9989027 11.0761089 9.9281595 5.9685919
[643] 6.7416309 9.8832243 12.2475697 7.9513820 9.5515401 9.6133197
[649] 11.6448435 8.2438065 4.6851289 6.8739650 8.8928290 15.5565450
[655] 6.9575605 7.0050056 10.9781723 7.5395905 15.9865403 26.1689467
[661] 25.9809335 21.8932025 15.1230352 8.6789650 4.4631167 3.2341900
[667] 20.8037623 15.2538226 16.2486269 10.5069285 10.7537073 8.0306509
[673] 28.2652174 23.0624951 14.5613288 20.1536869 15.3485773 11.1058212
[679] 14.1238494 12.6749629 18.2375078 7.8837276 10.6031456 22.8756422
[685] 7.5404642 13.9559405 11.6067291 10.5262934 21.8627603 18.6745788
[691] 13.7302745 10.9491951 10.5697239 7.9766717 6.4185228 4.9739268
[697] 18.0944616 9.9590908 11.4028426 11.3677097 5.9253235 13.6364128
[703] 14.5487736 26.2766802 19.0249346 16.2844089 19.9230368 14.9176742
[709] 20.4782843 12.2295738 28.8312608 39.1748043 21.0265860 22.0293753
[715] 6.2237565 7.3864153 20.1067050 33.0470349 25.0596236 44.8354463
statcomp documentation built on Oct. 30, 2019, 11:15 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/weighted_ordinal_pattern_distribution.R
Description
Computation of weighted ordinal patterns of a time series. Weights can be generated by a user-specified function (e.g. variance-weighted, see Fadlallah et al 2013).
Usage
1 | weighted_ordinal_pattern_distribution(x, ndemb)
|
Arguments
x |
A numeric vector (e.g. a time series), from which the weighted ordinal pattern distribution is to be calculated |
ndemb |
Embedding dimension of the ordinal patterns (i.e. sliding window size). Should be chosen such as length(x) >> ndemb |
Details
This function returns the distribution of weighted ordinal patterns using the Keller coding scheme, detailed in Physica A 356 (2005) 114-120. NA values are allowed. The function uses old and slow R routines and is only maintained for comparability. For faster routines, see weighted_ordinal_pattern_distribution.
Value
A character vector of length factorial(ndemb) is returned.
Author(s)
Sebastian Sippel
References
Fadlallah, B., Chen, B., Keil, A. and Principe, J., 2013. Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Physical Review E, 87(2), p.022911.
See Also
weighted_ordinal_pattern_distribution
Examples
1 2 | x = arima.sim(model=list(ar = 0.3), n = 10^4)
weighted_ordinal_pattern_distribution(x = x, ndemb = 6)
|
Example output
[1] 35.1209130 28.5170067 27.2697483 24.9689948 25.1198458 11.5886040
[7] 27.5309845 12.9848797 45.3443771 31.3197923 12.5154578 14.3989571
[13] 11.6360282 13.9437976 30.3331540 29.6765890 25.2665533 17.5155359
[19] 7.3632532 12.3683906 8.6545123 9.9637387 18.0213507 16.4023793
[25] 4.7488853 6.8366009 4.7809144 8.5824980 14.3807481 24.6840268
[31] 26.7996915 11.7318864 18.8396026 13.4197722 9.0071136 14.5347591
[37] 17.3611373 3.6040206 8.3471890 14.2325918 19.8435298 9.7573870
[43] 24.4311176 18.8250351 16.8906408 28.6210958 24.0897279 22.3399754
[49] 8.5375725 8.6743653 11.2562648 10.2986377 15.4741318 17.2736540
[55] 4.4106275 5.8153301 13.2812979 7.6843866 12.4229269 23.0383680
[61] 12.8539735 10.5792353 10.5417385 7.4871112 4.4657572 2.9246969
[67] 11.3164354 7.6484541 7.0976271 10.1162948 6.0158522 8.2585371
[73] 10.2271679 10.0958164 7.5052580 7.4448603 8.4550747 8.5420239
[79] 9.1703486 9.8541772 14.0944658 19.1443026 8.1066467 21.4136953
[85] 9.6915959 6.3751024 10.0258539 20.0448876 16.2230158 29.9021678
[91] 18.3433465 4.1354301 1.6356447 3.8977091 0.7961022 5.0023420
[97] 7.3834077 4.7608655 2.8601137 5.8203051 6.1135089 5.1268603
[103] 11.6940100 3.5089820 3.5567403 6.5187226 5.3715028 10.7216812
[109] 5.3022955 7.3161049 13.7963613 20.7505360 9.4506635 14.4222051
[115] 8.6319109 13.4833067 12.2409263 19.7817091 27.2418570 29.5184897
[121] 25.8624892 27.9853316 29.9118856 9.4268062 15.5422288 15.8477606
[127] 12.5181780 10.6706295 10.8778658 8.5287317 13.1711853 7.9281410
[133] 5.0619575 6.5737501 5.9935029 9.5975092 6.2241719 6.9461358
[139] 9.9386764 4.5090062 2.9013164 6.7255560 7.2244252 12.9986012
[145] 5.5713437 4.7460412 7.4289013 5.2742952 12.1902938 12.5548832
[151] 19.2046889 17.9598404 5.2543673 3.8754050 3.1321197 9.5946678
[157] 5.5468496 4.7882147 2.5670693 5.1039326 5.5754275 2.8962079
[163] 2.9995874 7.2587284 4.2995215 4.0830989 7.3934924 9.4559952
[169] 4.7869742 5.7500695 1.6846159 7.2396724 14.3836267 11.1362194
[175] 6.2315744 3.8684823 4.8141987 12.9758471 9.7581664 18.8167119
[181] 16.8553549 11.0156107 9.2031767 7.2467628 4.9338128 5.3632388
[187] 13.3478030 3.6669982 4.0013900 7.9354016 8.3678706 8.9457136
[193] 6.9078676 5.7591493 9.7189809 9.4232175 5.0822622 7.5838827
[199] 4.2566860 4.9771655 12.4549862 9.4282958 14.9095871 13.4437326
[205] 6.7735724 7.9101707 9.4819733 16.8692083 27.6690307 18.1314945
[211] 5.8628490 7.7898534 3.2157202 6.6340937 7.3835295 6.4253159
[217] 10.8861956 6.5812678 6.9101767 8.3230395 3.4215342 5.0449765
[223] 5.7289833 6.9645163 6.7737635 10.4645643 11.3166709 8.9626071
[229] 12.5602147 8.1838345 11.3272876 19.2501948 7.5747769 19.9500813
[235] 8.1303572 8.4725885 12.9382518 25.0920699 32.4886318 20.9772632
[241] 26.9155888 17.7415601 13.5193079 7.4829115 5.2474072 2.0950005
[247] 11.6777702 7.3537787 9.0991449 6.4124923 6.3387554 8.3073196
[253] 9.9865662 7.5744737 4.8361629 6.6313819 2.2755114 4.6885269
[259] 4.6353870 3.5151573 2.6608469 1.5185920 2.6770252 7.8523177
[265] 4.5319270 3.7463981 3.3170378 0.6466043 9.5359557 10.9306823
[271] 19.8269637 6.1270240 6.7168459 4.4258462 3.0000098 3.9981561
[277] 8.5920166 5.8774418 5.8815020 3.1714171 5.5903779 2.2921633
[283] 6.6448022 1.8478074 3.1838236 3.4513578 6.9712095 7.0149844
[289] 5.2862791 5.1925710 5.5492605 6.9064212 3.0561801 14.1128576
[295] 7.3014404 1.6832178 3.0846099 8.6876544 11.6925399 11.8633406
[301] 20.3239662 13.3869156 4.7421063 10.2674605 5.8281637 7.5892773
[307] 15.2060112 9.7274292 7.9349396 5.8724071 4.0768784 7.0736349
[313] 9.3729176 11.6001941 18.5938923 8.6012679 9.1229656 15.2862100
[319] 4.8063084 3.8047911 14.0224133 8.1581934 8.6655204 13.7615127
[325] 5.9092009 4.3981782 10.4010155 9.4454393 16.2932788 20.0840573
[331] 15.9608698 20.4306775 7.4431607 4.2527446 7.7158053 4.1302094
[337] 23.2049987 6.6856140 8.0971991 11.6752237 4.8665418 14.1632569
[343] 8.8595116 10.7665301 21.6593473 13.1227780 13.2928453 18.6539387
[349] 15.9088922 16.5730100 16.7772374 29.9563051 27.4314551 23.5313781
[355] 16.6898597 10.1568770 16.5366310 26.6557984 33.3757817 31.5321349
[361] 32.0548583 35.3574444 32.0418756 19.2652336 11.4821985 7.0290823
[367] 20.1968471 18.1117066 41.8175555 15.1718126 13.1982829 11.5987973
[373] 14.0367224 14.3300494 8.1293336 11.4269350 15.4265620 17.3892696
[379] 6.1556527 8.5630747 6.3342873 8.7247626 13.0554831 12.7621986
[385] 3.8328630 4.7150930 7.5094507 4.6397605 19.0579702 17.6530478
[391] 32.5744073 17.3973878 9.7767070 5.8826174 3.5351979 4.0555956
[397] 12.9083993 3.7066744 5.3404706 10.0859220 5.9782773 8.3636444
[403] 13.2926440 11.2125418 10.7174341 12.0511540 10.5155244 13.7403212
[409] 6.0756551 5.6292796 8.7168647 6.2822847 4.7839214 13.1709468
[415] 5.5248841 5.7979099 4.9867517 6.9594110 13.2675038 20.7582850
[421] 14.1433587 9.8896554 8.5394873 5.1474885 6.9834805 5.3862901
[427] 5.2986212 6.4968789 9.0237059 3.3267998 2.3297010 5.1039461
[433] 8.1972936 5.2425847 3.0460600 5.3012660 5.1516304 8.2316341
[439] 4.7117951 4.1191076 5.1204872 2.3290207 4.6425767 6.8314992
[445] 4.0899797 4.7513672 5.9341110 9.5954581 14.1951769 13.5596434
[451] 11.6897449 9.6686920 9.1139474 2.6466160 5.0933950 4.8885603
[457] 6.8710538 3.2294488 6.5292781 1.5107479 5.2987406 6.0162369
[463] 2.9628681 6.7914769 3.1973397 3.7848241 7.2623938 5.1606124
[469] 11.0906344 6.3227462 8.9577227 13.3964945 8.2961408 10.6934876
[475] 6.8602872 12.6079223 9.1030338 15.9112996 22.9130718 13.4459796
[481] 34.8370144 23.1912402 34.0914419 19.7707883 8.7510113 6.3899459
[487] 21.6359023 16.5961024 19.4134671 13.0109934 7.8803539 10.2242420
[493] 10.2885559 11.5579260 5.8029123 7.6271100 3.2879614 8.2505724
[499] 4.6098370 4.4172806 3.7078658 1.9991004 6.9370432 9.8930633
[505] 1.1399343 1.3509878 5.7456050 6.9821256 8.0758623 16.0354911
[511] 25.7680990 25.8117913 17.8635380 11.6928684 4.9914711 3.9903662
[517] 12.3506078 10.9440485 18.5431574 9.5276424 5.5190079 8.8572265
[523] 6.1533653 9.7321058 5.7262592 11.0022409 4.9354135 10.7510261
[529] 9.6837819 5.0530177 6.7187558 3.1566858 6.4919478 8.2920048
[535] 4.7198428 11.0089622 3.3683565 4.7952767 10.0097729 8.6582982
[541] 21.1306763 12.3060098 4.2363557 1.5673765 6.4807889 6.1992594
[547] 19.8498046 4.2311949 6.5225303 4.7056368 7.0724330 6.7366316
[553] 10.4270557 3.5520449 4.9792157 2.3770509 10.8316743 5.5702951
[559] 4.9556253 5.6202306 4.3815235 5.0289847 8.3564232 9.4847043
[565] 6.3590222 13.0932896 10.1510483 4.4742243 20.4763457 18.5660821
[571] 12.4968352 13.3714751 3.3454232 8.0550356 2.7247927 6.3512235
[577] 8.3202882 4.9490641 5.8701985 4.2304967 4.7312747 8.2258889
[583] 6.7219439 7.1134445 5.6021551 5.1148427 4.2166693 12.7827286
[589] 9.8550506 9.7898406 12.4154164 10.9742304 20.1501267 12.3096647
[595] 8.8398580 18.7668711 8.3953098 12.7666632 24.0155662 22.8605636
[601] 21.0450443 26.2580875 12.5732984 5.4093547 10.8914734 5.8918538
[607] 13.2104045 5.8182733 20.4054977 9.8634741 8.6171402 12.9941584
[613] 8.6708413 5.9195304 4.7404241 9.0525713 5.2367203 5.3216983
[619] 9.1056870 5.7104100 3.7398599 11.8228379 3.6710705 10.3778858
[625] 5.9410259 2.6092421 1.9044290 7.5302931 9.3549069 15.5700888
[631] 31.9767288 20.8816144 15.0560935 12.6984154 10.5141772 7.8432266
[637] 13.9410674 15.7644540 11.9989027 11.0761089 9.9281595 5.9685919
[643] 6.7416309 9.8832243 12.2475697 7.9513820 9.5515401 9.6133197
[649] 11.6448435 8.2438065 4.6851289 6.8739650 8.8928290 15.5565450
[655] 6.9575605 7.0050056 10.9781723 7.5395905 15.9865403 26.1689467
[661] 25.9809335 21.8932025 15.1230352 8.6789650 4.4631167 3.2341900
[667] 20.8037623 15.2538226 16.2486269 10.5069285 10.7537073 8.0306509
[673] 28.2652174 23.0624951 14.5613288 20.1536869 15.3485773 11.1058212
[679] 14.1238494 12.6749629 18.2375078 7.8837276 10.6031456 22.8756422
[685] 7.5404642 13.9559405 11.6067291 10.5262934 21.8627603 18.6745788
[691] 13.7302745 10.9491951 10.5697239 7.9766717 6.4185228 4.9739268
[697] 18.0944616 9.9590908 11.4028426 11.3677097 5.9253235 13.6364128
[703] 14.5487736 26.2766802 19.0249346 16.2844089 19.9230368 14.9176742
[709] 20.4782843 12.2295738 28.8312608 39.1748043 21.0265860 22.0293753
[715] 6.2237565 7.3864153 20.1067050 33.0470349 25.0596236 44.8354463
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