Last updated on 2024-11-22 03:52:32 CET.
| Flavor | Version | Tinstall | Tcheck | Ttotal | Status | Flags |
|---|---|---|---|---|---|---|
| r-devel-linux-x86_64-debian-clang | 1.3-8 | 9.91 | 112.79 | 122.70 | ERROR | |
| r-devel-linux-x86_64-debian-gcc | 1.3-8 | 7.34 | 87.74 | 95.08 | OK | |
| r-devel-linux-x86_64-fedora-clang | 1.3-8 | 198.59 | ERROR | |||
| r-devel-linux-x86_64-fedora-gcc | 1.3-8 | 203.68 | OK | |||
| r-devel-windows-x86_64 | 1.3-8 | 14.00 | 132.00 | 146.00 | OK | |
| r-patched-linux-x86_64 | 1.3-8 | 11.51 | 115.79 | 127.30 | OK | |
| r-release-linux-x86_64 | 1.3-8 | 10.40 | 114.40 | 124.80 | OK | |
| r-release-macos-arm64 | 1.3-8 | 69.00 | OK | |||
| r-release-macos-x86_64 | 1.3-8 | 96.00 | OK | |||
| r-release-windows-x86_64 | 1.3-8 | 14.00 | 131.00 | 145.00 | OK | |
| r-oldrel-macos-arm64 | 1.3-8 | 74.00 | OK | |||
| r-oldrel-macos-x86_64 | 1.3-8 | 160.00 | OK | |||
| r-oldrel-windows-x86_64 | 1.3-8 | 17.00 | 166.00 | 183.00 | OK |
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’ [2s/3s]
Running ‘ex1.R’ [3s/4s]
Running ‘ex2-long.R’ [5s/6s]
Running ‘ex3.R’ [2s/3s]
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [4s/5s]
Running ‘roof.R’ [4s/5s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ... OK
Running ‘small-ex.R’ [3s/3s]
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ...24,25d23
< Warning message:
< In cobs(x, y) : drqssbc2(): Not all flags are normal (== 1), ifl : 22
30,33d27
< WARNING! Since the number of 6 knots selected by AIC reached the
< upper bound during general knot selection, you might want to rerun
< cobs with a larger number of knots.
<
35,38d28
<
< WARNING! Since the number of 6 knots selected by AIC reached the
< upper bound during general knot selection, you might want to rerun
< cobs with a larger number of knots.
41,44c31,34
< {tau=0.5}-quantile; dimensionality of fit: 7 from {7}
< x$knots[1:6]: 0.999989, 2.000000, 3.000000, ... , 12.000011
< coef[1:7]: 7.99991, 11.99996, 20.00000, 32.00000, 44.00000, 72.00004, 96.00009
< R^2 = 99.88% ; empirical tau (over all): 5/7 = 0.714286 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 3 from {3}
> x$knots[1:2]: 0.999989, 12.000011
> coef[1:3]: 7.99991, 52.00000, 96.00009
> R^2 = 99.88% ; empirical tau (over all): 3/7 = 0.428571 (target tau= 0.5)
52,55c42,45
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:4]: 0.999989, 2.000000, 5.000000, 12.000011
< coef[1:5]: 6.9999, 11.5277, 29.4167, 68.5834, 96.0001
< R^2 = 99.87% ; empirical tau (over all): 3/7 = 0.428571 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 3 from {3}
> x$knots[1:2]: 0.999989, 12.000011
> coef[1:3]: 7.54157, 54.29167, 96.00008
> R^2 = 99.84% ; empirical tau (over all): 3/7 = 0.428571 (target tau= 0.5)
60c50
< [1] 7.66907
---
> [1] 9.71528
69,170c59,158
< [1,] 0.999989 7.99991 3.16725 12.8326 NaN NaN
< [2,] 1.111100 8.88880 4.38406 13.3935 NaN NaN
< [3,] 1.222212 9.77769 5.54416 14.0112 NaN NaN
< [4,] 1.333323 10.66658 6.65458 14.6786 NaN NaN
< [5,] 1.444434 11.55548 7.72267 15.3883 NaN NaN
< [6,] 1.555546 12.44437 8.75525 16.1335 NaN NaN
< [7,] 1.666657 13.33326 9.75780 16.9087 NaN NaN
< [8,] 1.777768 14.22215 10.73355 17.7107 NaN NaN
< [9,] 1.888880 15.11104 11.68294 18.5391 NaN NaN
< [10,] 1.999991 15.99993 12.60316 19.3967 NaN NaN
< [11,] 2.111102 16.88882 13.49193 20.2857 NaN NaN
< [12,] 2.222214 17.77771 14.35913 21.1963 NaN NaN
< [13,] 2.333325 18.66660 15.21538 22.1178 NaN NaN
< [14,] 2.444436 19.55549 16.06800 23.0430 NaN NaN
< [15,] 2.555548 20.44438 16.92094 23.9678 NaN NaN
< [16,] 2.666659 21.33327 17.77494 24.8916 NaN NaN
< [17,] 2.777770 22.22216 18.62769 25.8166 NaN NaN
< [18,] 2.888882 23.11105 19.47396 26.7481 NaN NaN
< [19,] 2.999993 23.99994 20.30585 27.6940 NaN NaN
< [20,] 3.111104 24.88884 21.11665 28.6610 NaN NaN
< [21,] 3.222216 25.77773 21.91370 29.6417 NaN NaN
< [22,] 3.333327 26.66662 22.70678 30.6265 NaN NaN
< [23,] 3.444438 27.55551 23.50362 31.6074 NaN NaN
< [24,] 3.555550 28.44440 24.31015 32.5786 NaN NaN
< [25,] 3.666661 29.33329 25.13073 33.5358 NaN NaN
< [26,] 3.777772 30.22218 25.96846 34.4759 NaN NaN
< [27,] 3.888884 31.11107 26.82535 35.3968 NaN NaN
< [28,] 3.999995 31.99996 27.70250 36.2974 NaN NaN
< [29,] 4.111106 32.88885 28.60016 37.1775 NaN NaN
< [30,] 4.222218 33.77774 29.51776 38.0377 NaN NaN
< [31,] 4.333329 34.66663 30.45390 38.8794 NaN NaN
< [32,] 4.444440 35.55552 31.40620 39.7049 NaN NaN
< [33,] 4.555552 36.44441 32.37120 40.5176 NaN NaN
< [34,] 4.666663 37.33330 33.34413 41.3225 NaN NaN
< [35,] 4.777774 38.22219 34.31867 42.1257 NaN NaN
< [36,] 4.888886 39.11109 35.28671 42.9355 NaN NaN
< [37,] 4.999997 39.99998 36.23821 43.7617 NaN NaN
< [38,] 5.111108 40.88887 37.16391 44.6138 NaN NaN
< [39,] 5.222220 41.77776 38.06991 45.4856 NaN NaN
< [40,] 5.333331 42.66665 38.96634 46.3670 NaN NaN
< [41,] 5.444442 43.55554 39.86104 47.2500 NaN NaN
< [42,] 5.555554 44.44443 40.75934 48.1295 NaN NaN
< [43,] 5.666665 45.33332 41.66407 49.0026 NaN NaN
< [44,] 5.777776 46.22221 42.57552 49.8689 NaN NaN
< [45,] 5.888888 47.11110 43.49145 50.7308 NaN NaN
< [46,] 5.999999 47.99999 44.40692 51.5931 NaN NaN
< [47,] 6.111110 48.88888 45.30640 52.4714 NaN NaN
< [48,] 6.222222 49.77777 46.18120 53.3744 NaN NaN
< [49,] 6.333333 50.66666 47.03479 54.2985 NaN NaN
< [50,] 6.444444 51.55555 47.87079 55.2403 NaN NaN
< [51,] 6.555556 52.44445 48.69275 56.1961 NaN NaN
< [52,] 6.666667 53.33334 49.50400 57.1627 NaN NaN
< [53,] 6.777778 54.22223 50.30760 58.1368 NaN NaN
< [54,] 6.888890 55.11112 51.10626 59.1160 NaN NaN
< [55,] 7.000001 56.00001 51.90233 60.0977 NaN NaN
< [56,] 7.111112 56.88890 52.69786 61.0799 NaN NaN
< [57,] 7.222224 57.77779 53.49457 62.0610 NaN NaN
< [58,] 7.333335 58.66668 54.29392 63.0394 NaN NaN
< [59,] 7.444446 59.55557 55.09714 64.0140 NaN NaN
< [60,] 7.555558 60.44446 55.90526 64.9837 NaN NaN
< [61,] 7.666669 61.33335 56.71912 65.9476 NaN NaN
< [62,] 7.777780 62.22224 57.53941 66.9051 NaN NaN
< [63,] 7.888892 63.11113 58.36670 67.8556 NaN NaN
< [64,] 8.000003 64.00002 59.20144 68.7986 NaN NaN
< [65,] 8.111114 64.88891 60.04398 69.7338 NaN NaN
< [66,] 8.222226 65.77781 60.89459 70.6610 NaN NaN
< [67,] 8.333337 66.66670 61.75345 71.5799 NaN NaN
< [68,] 8.444448 67.55559 62.62066 72.4905 NaN NaN
< [69,] 8.555560 68.44448 63.49628 73.3927 NaN NaN
< [70,] 8.666671 69.33337 64.38027 74.2865 NaN NaN
< [71,] 8.777782 70.22226 65.27254 75.1720 NaN NaN
< [72,] 8.888894 71.11115 66.17292 76.0494 NaN NaN
< [73,] 9.000005 72.00004 67.08118 76.9189 NaN NaN
< [74,] 9.111116 72.88893 67.99701 77.7808 NaN NaN
< [75,] 9.222228 73.77782 68.92003 78.6356 NaN NaN
< [76,] 9.333339 74.66671 69.84973 79.4837 NaN NaN
< [77,] 9.444450 75.55560 70.78555 80.3257 NaN NaN
< [78,] 9.555562 76.44449 71.72678 81.1622 NaN NaN
< [79,] 9.666673 77.33338 72.67260 81.9942 NaN NaN
< [80,] 9.777784 78.22227 73.62204 82.8225 NaN NaN
< [81,] 9.888896 79.11116 74.57397 83.6484 NaN NaN
< [82,] 10.000007 80.00006 75.52709 84.4730 NaN NaN
< [83,] 10.111118 80.88895 76.47989 85.2980 NaN NaN
< [84,] 10.222230 81.77784 77.43064 86.1250 NaN NaN
< [85,] 10.333341 82.66673 78.37741 86.9560 NaN NaN
< [86,] 10.444452 83.55562 79.31803 87.7932 NaN NaN
< [87,] 10.555564 84.44451 80.25011 88.6389 NaN NaN
< [88,] 10.666675 85.33340 81.17108 89.4957 NaN NaN
< [89,] 10.777786 86.22229 82.07825 90.3663 NaN NaN
< [90,] 10.888898 87.11118 82.96885 91.2535 NaN NaN
< [91,] 11.000009 88.00007 83.84016 92.1600 NaN NaN
< [92,] 11.111120 88.88896 84.68963 93.0883 NaN NaN
< [93,] 11.222232 89.77785 85.51498 94.0407 NaN NaN
< [94,] 11.333343 90.66674 86.31430 95.0192 NaN NaN
< [95,] 11.444454 91.55563 87.08618 96.0251 NaN NaN
< [96,] 11.555566 92.44452 87.82968 97.0594 NaN NaN
< [97,] 11.666677 93.33342 88.54435 98.1225 NaN NaN
< [98,] 11.777788 94.22231 89.23022 99.2144 NaN NaN
< [99,] 11.888900 95.11120 89.88765 100.3347 NaN NaN
< [100,] 12.000011 96.00009 90.51732 101.4829 NaN NaN
< Warning message:
< In qt((1 + level)/2, n - object$k) : NaNs produced
---
> [1,] 0.999989 7.99991 4.82789 11.1719 4.84949 11.1503
> [2,] 1.111100 8.88880 5.84444 11.9332 5.86518 11.9124
> [3,] 1.222212 9.77769 6.85519 12.7002 6.87510 12.6803
> [4,] 1.333323 10.66658 7.85994 13.4732 7.87905 13.4541
> [5,] 1.444434 11.55548 8.85846 14.2525 8.87683 14.2341
> [6,] 1.555546 12.44437 9.85054 15.0382 9.86821 15.0205
> [7,] 1.666657 13.33326 10.83596 15.8305 10.85297 15.8135
> [8,] 1.777768 14.22215 11.81451 16.6298 11.83091 16.6134
> [9,] 1.888880 15.11104 12.78598 17.4361 12.80181 17.4203
> [10,] 1.999991 15.99993 13.75019 18.2497 13.76551 18.2343
> [11,] 2.111102 16.88882 14.70699 19.0706 14.72185 19.0558
> [12,] 2.222214 17.77771 15.65628 19.8991 15.67072 19.8847
> [13,] 2.333325 18.66660 16.59799 20.7352 16.61208 20.7211
> [14,] 2.444436 19.55549 17.53215 21.5788 17.54593 21.5651
> [15,] 2.555548 20.44438 18.45883 22.4299 18.47235 22.4164
> [16,] 2.666659 21.33327 19.37817 23.2884 19.39149 23.2751
> [17,] 2.777770 22.22216 20.29043 24.1539 20.30359 24.1407
> [18,] 2.888882 23.11105 21.19590 25.0262 21.20894 25.0132
> [19,] 2.999993 23.99994 22.09496 25.9049 22.10793 25.8920
> [20,] 3.111104 24.88884 22.98804 26.7896 23.00099 26.7767
> [21,] 3.222216 25.77773 23.87563 27.6798 23.88858 27.6669
> [22,] 3.333327 26.66662 24.75824 28.5750 24.77123 28.5620
> [23,] 3.444438 27.55551 25.63639 29.4746 25.64946 29.4616
> [24,] 3.555550 28.44440 26.51062 30.3782 26.52379 30.3650
> [25,] 3.666661 29.33329 27.38147 31.2851 27.39476 31.2718
> [26,] 3.777772 30.22218 28.24944 32.1949 28.26287 32.1815
> [27,] 3.888884 31.11107 29.11501 33.1071 29.12861 33.0935
> [28,] 3.999995 31.99996 29.97866 34.0213 29.99243 34.0075
> [29,] 4.111106 32.88885 30.84080 34.9369 30.85475 34.9230
> [30,] 4.222218 33.77774 31.70184 35.8536 31.71597 35.8395
> [31,] 4.333329 34.66663 32.56212 36.7711 32.57645 36.7568
> [32,] 4.444440 35.55552 33.42197 37.6891 33.43650 37.6745
> [33,] 4.555552 36.44441 34.28170 38.6071 34.29643 38.5924
> [34,] 4.666663 37.33330 35.14155 39.5251 35.15648 39.5101
> [35,] 4.777774 38.22219 36.00178 40.4426 36.01690 40.4275
> [36,] 4.888886 39.11109 36.86257 41.3596 36.87789 41.3443
> [37,] 4.999997 39.99998 37.72413 42.2758 37.73963 42.2603
> [38,] 5.111108 40.88887 38.58661 43.1911 38.60229 43.1754
> [39,] 5.222220 41.77776 39.45015 44.1054 39.46601 44.0895
> [40,] 5.333331 42.66665 40.31488 45.0184 40.33090 45.0024
> [41,] 5.444442 43.55554 41.18091 45.9302 41.19708 45.9140
> [42,] 5.555554 44.44443 42.04831 46.8405 42.06463 46.8242
> [43,] 5.666665 45.33332 42.91718 47.7495 42.93363 47.7330
> [44,] 5.777776 46.22221 43.78757 48.6569 43.80415 48.6403
> [45,] 5.888888 47.11110 44.65953 49.5627 44.67622 49.5460
> [46,] 5.999999 47.99999 45.53310 50.4669 45.54990 50.4501
> [47,] 6.111110 48.88888 46.40831 51.3695 46.42520 51.3526
> [48,] 6.222222 49.77777 47.28517 52.2704 47.30215 52.2534
> [49,] 6.333333 50.66666 48.16370 53.1696 48.18074 53.1526
> [50,] 6.444444 51.55555 49.04388 54.0672 49.06099 54.0501
> [51,] 6.555556 52.44445 49.92572 54.9632 49.94287 54.9460
> [52,] 6.666667 53.33334 50.80918 55.8575 50.82637 55.8403
> [53,] 6.777778 54.22223 51.69424 56.7502 51.71145 56.7330
> [54,] 6.888890 55.11112 52.58085 57.6414 52.59808 57.6242
> [55,] 7.000001 56.00001 53.46896 58.5311 53.48620 58.5138
> [56,] 7.111112 56.88890 54.35852 59.4193 54.37575 59.4020
> [57,] 7.222224 57.77779 55.24944 60.3061 55.26666 60.2889
> [58,] 7.333335 58.66668 56.14166 61.1917 56.15886 61.1745
> [59,] 7.444446 59.55557 57.03507 62.0761 57.05224 62.0589
> [60,] 7.555558 60.44446 57.92957 62.9593 57.94670 62.9422
> [61,] 7.666669 61.33335 58.82505 63.8417 58.84213 63.8246
> [62,] 7.777780 62.22224 59.72137 64.7231 59.73840 64.7061
> [63,] 7.888892 63.11113 60.61839 65.6039 60.63536 65.5869
> [64,] 8.000003 64.00002 61.51595 66.4841 61.53286 66.4672
> [65,] 8.111114 64.88891 62.41387 67.3640 62.43073 67.3471
> [66,] 8.222226 65.77781 63.31198 68.2436 63.32877 68.2268
> [67,] 8.333337 66.66670 64.21005 69.1233 64.22678 69.1066
> [68,] 8.444448 67.55559 65.10788 70.0033 65.12455 69.9866
> [69,] 8.555560 68.44448 66.00522 70.8837 66.02184 70.8671
> [70,] 8.666671 69.33337 66.90183 71.7649 66.91839 71.7484
> [71,] 8.777782 70.22226 67.79742 72.6471 67.81393 72.6306
> [72,] 8.888894 71.11115 68.69171 73.5306 68.70819 73.5141
> [73,] 9.000005 72.00004 69.58441 74.4157 69.60086 74.3992
> [74,] 9.111116 72.88893 70.47520 75.3027 70.49164 75.2862
> [75,] 9.222228 73.77782 71.36376 76.1919 71.38020 76.1754
> [76,] 9.333339 74.66671 72.24976 77.0837 72.26622 77.0672
> [77,] 9.444450 75.55560 73.13285 77.9783 73.14935 77.9618
> [78,] 9.555562 76.44449 74.01272 78.8763 74.02928 78.8597
> [79,] 9.666673 77.33338 74.88902 79.7777 74.90567 79.7611
> [80,] 9.777784 78.22227 75.76143 80.6831 75.77819 80.6664
> [81,] 9.888896 79.11116 76.62965 81.5927 76.64655 81.5758
> [82,] 10.000007 80.00006 77.49337 82.5067 77.51044 82.4897
> [83,] 10.111118 80.88895 78.35232 83.4256 78.36960 83.4083
> [84,] 10.222230 81.77784 79.20626 84.3494 79.22378 84.3319
> [85,] 10.333341 82.66673 80.05498 85.2785 80.07276 85.2607
> [86,] 10.444452 83.55562 80.89827 86.2130 80.91637 86.1949
> [87,] 10.555564 84.44451 81.73600 87.1530 81.75445 87.1346
> [88,] 10.666675 85.33340 82.56803 88.0988 82.58687 88.0799
> [89,] 10.777786 86.22229 83.39429 89.0503 83.41355 89.0310
> [90,] 10.888898 87.11118 84.21470 90.0077 84.23443 89.9879
> [91,] 11.000009 88.00007 85.02924 90.9709 85.04947 90.9507
> [92,] 11.111120 88.88896 85.83791 91.9400 85.85868 91.9192
> [93,] 11.222232 89.77785 86.64072 92.9150 86.66208 92.8936
> [94,] 11.333343 90.66674 87.43771 93.8958 87.45970 93.8738
> [95,] 11.444454 91.55563 88.22894 94.8823 88.25160 94.8597
> [96,] 11.555566 92.44452 89.01448 95.8746 89.03784 95.8512
> [97,] 11.666677 93.33342 89.79440 96.8724 89.81850 96.8483
> [98,] 11.777788 94.22231 90.56880 97.8758 90.59368 97.8509
> [99,] 11.888900 95.11120 91.33776 98.8846 91.36346 98.8589
> [100,] 12.000011 96.00009 92.10139 99.8988 92.12794 99.8722
173,272c161,260
< [1,] 0.999989 6.99990 3.03158 10.9682 1.86823 12.1316
< [2,] 1.111100 8.00539 4.30309 11.7077 3.21772 12.7931
< [3,] 1.222212 9.00951 5.53158 12.4874 4.51198 13.5070
< [4,] 1.333323 10.01225 6.72328 13.3012 5.75908 14.2654
< [5,] 1.444434 11.01363 7.88455 14.1427 6.96722 15.0600
< [6,] 1.555546 12.01363 9.02114 15.0061 8.14386 15.8834
< [7,] 1.666657 13.01226 10.13756 15.8870 9.29481 16.7297
< [8,] 1.777768 14.00952 11.23638 16.7827 10.42341 17.5956
< [9,] 1.888880 15.00541 12.31766 17.6931 11.52972 18.4811
< [10,] 1.999991 15.99992 13.37843 18.6214 12.60991 19.3899
< [11,] 2.111102 16.99146 14.40588 19.5770 13.64789 20.3350
< [12,] 2.222214 17.97843 15.39456 20.5623 14.63706 21.3198
< [13,] 2.333325 18.96083 16.35072 21.5709 15.58553 22.3361
< [14,] 2.444436 19.93866 17.28099 22.5963 16.50186 23.3755
< [15,] 2.555548 20.91191 18.19172 23.6321 17.39427 24.4296
< [16,] 2.666659 21.88059 19.08863 24.6726 18.27014 25.4910
< [17,] 2.777770 22.84470 19.97659 25.7128 19.13577 26.5536
< [18,] 2.888882 23.80424 20.85962 26.7489 19.99637 27.6121
< [19,] 2.999993 24.75920 21.74097 27.7774 20.85614 28.6623
< [20,] 3.111104 25.70959 22.62322 28.7960 21.71841 29.7008
< [21,] 3.222216 26.65541 23.50837 29.8024 22.58579 30.7250
< [22,] 3.333327 27.59665 24.39799 30.7953 23.46026 31.7330
< [23,] 3.444438 28.53333 25.29322 31.7734 24.34335 32.7233
< [24,] 3.555550 29.46543 26.19492 32.7359 25.23614 33.6947
< [25,] 3.666661 30.39296 27.10367 33.6822 26.13938 34.6465
< [26,] 3.777772 31.31591 28.01980 34.6120 27.05351 35.5783
< [27,] 3.888884 32.23430 28.94342 35.5252 27.97867 36.4899
< [28,] 3.999995 33.14811 29.87444 36.4218 28.91473 37.3815
< [29,] 4.111106 34.05735 30.81254 37.3021 29.86129 38.2534
< [30,] 4.222218 34.96201 31.75717 38.1669 30.81763 39.1064
< [31,] 4.333329 35.86211 32.70749 39.0167 31.78268 39.9415
< [32,] 4.444440 36.75763 33.66238 39.8529 32.75497 40.7603
< [33,] 4.555552 37.64857 34.62032 40.6768 33.73256 41.5646
< [34,] 4.666663 38.53495 35.57935 41.4905 34.71289 42.3570
< [35,] 4.777774 39.41675 36.53696 42.2965 35.69271 43.1408
< [36,] 4.888886 40.29398 37.48996 43.0980 36.66793 43.9200
< [37,] 4.999997 41.16664 38.43442 43.8989 37.63343 44.6999
< [38,] 5.111108 42.03702 39.36327 44.7108 38.57944 45.4946
< [39,] 5.222220 42.90739 40.27308 45.5417 39.50080 46.3140
< [40,] 5.333331 43.77776 41.16494 46.3906 40.39897 47.1566
< [41,] 5.444442 44.64813 42.04034 47.2559 41.27584 48.0204
< [42,] 5.555554 45.51850 42.90102 48.1360 42.13367 48.9033
< [43,] 5.666665 46.38888 43.74886 49.0289 42.97491 49.8028
< [44,] 5.777776 47.25925 44.58585 49.9326 43.80212 50.7164
< [45,] 5.888888 48.12962 45.41393 50.8453 44.61780 51.6414
< [46,] 5.999999 48.99999 46.23496 51.7650 45.42435 52.5756
< [47,] 6.111110 49.87036 47.05065 52.6901 46.22401 53.5167
< [48,] 6.222222 50.74074 47.86256 53.6189 47.01879 54.4627
< [49,] 6.333333 51.61111 48.67208 54.5501 47.81047 55.4117
< [50,] 6.444444 52.48148 49.48043 55.4825 48.60064 56.3623
< [51,] 6.555556 53.35185 50.28866 56.4150 49.39065 57.3131
< [52,] 6.666667 54.22222 51.09768 57.3468 50.18168 58.2628
< [53,] 6.777778 55.09260 51.90827 58.2769 50.97474 59.2104
< [54,] 6.888890 55.96297 52.72109 59.2049 51.77069 60.1552
< [55,] 7.000001 56.83334 53.53669 60.1300 52.57024 61.0964
< [56,] 7.111112 57.70371 54.35556 61.0519 53.37401 62.0334
< [57,] 7.222224 58.57409 55.17808 61.9701 54.18250 62.9657
< [58,] 7.333335 59.44446 56.00457 62.8843 54.99612 63.8928
< [59,] 7.444446 60.31483 56.83529 63.7944 55.81523 64.8144
< [60,] 7.555558 61.18520 57.67046 64.6999 56.64008 65.7303
< [61,] 7.666669 62.05557 58.51024 65.6009 57.47089 66.6403
< [62,] 7.777780 62.92595 59.35475 66.4971 58.30781 67.5441
< [63,] 7.888892 63.79632 60.20406 67.3886 59.15095 68.4417
< [64,] 8.000003 64.66669 61.05822 68.2752 60.00036 69.3330
< [65,] 8.111114 65.53706 61.91723 69.1569 60.85603 70.2181
< [66,] 8.222226 66.40743 62.78106 70.0338 61.71794 71.0969
< [67,] 8.333337 67.27781 63.64964 70.9060 62.58601 71.9696
< [68,] 8.444448 68.14818 64.52289 71.7735 63.46009 72.8363
< [69,] 8.555560 69.01855 65.40065 72.6365 64.34002 73.6971
< [70,] 8.666671 69.88892 66.28276 73.4951 65.22557 74.5523
< [71,] 8.777782 70.75929 67.16899 74.3496 66.11645 75.4021
< [72,] 8.888894 71.62967 68.05909 75.2002 67.01234 76.2470
< [73,] 9.000005 72.50004 68.95275 76.0473 67.91282 77.0873
< [74,] 9.111116 73.37041 69.84961 76.8912 68.81744 77.9234
< [75,] 9.222228 74.24078 70.74924 77.7323 69.72566 78.7559
< [76,] 9.333339 75.11116 71.65117 78.5711 70.63683 79.5855
< [77,] 9.444450 75.98153 72.55483 79.4082 71.55026 80.4128
< [78,] 9.555562 76.85190 73.45961 80.2442 72.46512 81.2387
< [79,] 9.666673 77.72227 74.36478 81.0798 73.38049 82.0640
< [80,] 9.777784 78.59264 75.26955 81.9157 74.29534 82.8899
< [81,] 9.888896 79.46302 76.17301 82.7530 75.20851 83.7175
< [82,] 10.000007 80.33339 77.07419 83.5926 76.11871 84.5481
< [83,] 10.111118 81.20376 77.97198 84.4355 77.02455 85.3830
< [84,] 10.222230 82.07413 78.86522 85.2830 77.92449 86.2238
< [85,] 10.333341 82.94450 79.75265 86.1364 78.81693 87.0721
< [86,] 10.444452 83.81488 80.63296 86.9968 79.70014 87.9296
< [87,] 10.555564 84.68525 81.50479 87.8657 80.57240 88.7981
< [88,] 10.666675 85.55562 82.36678 88.7445 81.43193 89.6793
< [89,] 10.777786 86.42599 83.21762 89.6344 82.27705 90.5749
< [90,] 10.888898 87.29636 84.05606 90.5367 83.10613 91.4866
< [91,] 11.000009 88.16674 84.88099 91.4525 83.91773 92.4157
< [92,] 11.111120 89.03711 85.69142 92.3828 84.71060 93.3636
< [93,] 11.222232 89.90748 86.48660 93.3284 85.48373 94.3312
< [94,] 11.333343 90.77785 87.26593 94.2898 86.23637 95.3193
< [95,] 11.444454 91.64822 88.02905 95.2674 86.96805 96.3284
< [96,] 11.555566 92.51860 88.77578 96.2614 87.67853 97.3587
< [97,] 11.666677 93.38897 89.50614 97.2718 88.36784 98.4101
< [98,] 11.777788 94.25934 90.22026 98.2984 89.03616 99.4825
< [99,] 11.888900 95.12971 90.91843 99.3410 89.68385 100.5756
< [100,] 12.000011 96.00009 91.60102 100.3992 90.31138 101.6888
---
> [1,] 0.999989 7.54157 3.84088 11.2423 3.86608 11.2171
> [2,] 1.111100 8.48551 4.93375 12.0373 4.95794 12.0131
> [3,] 1.222212 9.42841 6.01883 12.8380 6.04205 12.8148
> [4,] 1.333323 10.37028 7.09586 13.6447 7.11816 13.6224
> [5,] 1.444434 11.31113 8.16461 14.4576 8.18604 14.4362
> [6,] 1.555546 12.25095 9.22482 15.2771 9.24543 15.2565
> [7,] 1.666657 13.18973 10.27623 16.1032 10.29607 16.0834
> [8,] 1.777768 14.12749 11.31858 16.9364 11.33771 16.9173
> [9,] 1.888880 15.06422 12.35165 17.7768 12.37013 17.7583
> [10,] 1.999991 15.99993 13.37523 18.6246 13.39310 18.6067
> [11,] 2.111102 16.93460 14.38913 19.4801 14.40646 19.4627
> [12,] 2.222214 17.86824 15.39324 20.3432 15.41009 20.3264
> [13,] 2.333325 18.80086 16.38748 21.2142 16.40392 21.1978
> [14,] 2.444436 19.73244 17.37188 22.0930 17.38795 22.0769
> [15,] 2.555548 20.66300 18.34652 22.9795 18.36229 22.9637
> [16,] 2.666659 21.59253 19.31158 23.8735 19.32712 23.8579
> [17,] 2.777770 22.52103 20.26734 24.7747 20.28269 24.7594
> [18,] 2.888882 23.44850 21.21415 25.6828 21.22937 25.6676
> [19,] 2.999993 24.37494 22.15246 26.5974 22.16759 26.5823
> [20,] 3.111104 25.30036 23.08276 27.5179 23.09787 27.5028
> [21,] 3.222216 26.22474 24.00563 28.4439 24.02074 28.4287
> [22,] 3.333327 27.14810 24.92165 29.3745 24.93682 29.3594
> [23,] 3.444438 28.07042 25.83145 30.3094 25.84670 30.2941
> [24,] 3.555550 28.99172 26.73565 31.2478 26.75102 31.2324
> [25,] 3.666661 29.91199 27.63487 32.1891 27.65038 32.1736
> [26,] 3.777772 30.83123 28.52970 33.1328 28.54537 33.1171
> [27,] 3.888884 31.74944 29.42071 34.0782 29.43657 34.0623
> [28,] 3.999995 32.66663 30.30844 35.0248 30.32450 35.0087
> [29,] 4.111106 33.58278 31.19339 35.9722 31.20966 35.9559
> [30,] 4.222218 34.49791 32.07601 36.9198 32.09251 36.9033
> [31,] 4.333329 35.41200 32.95673 37.8673 32.97345 37.8505
> [32,] 4.444440 36.32507 33.83593 38.8142 33.85288 38.7973
> [33,] 4.555552 37.23711 34.71394 39.7603 34.73112 39.7431
> [34,] 4.666663 38.14812 35.59108 40.7052 35.60849 40.6877
> [35,] 4.777774 39.05810 36.46761 41.6486 36.48525 41.6309
> [36,] 4.888886 39.96705 37.34379 42.5903 37.36165 42.5725
> [37,] 4.999997 40.87498 38.21982 43.5301 38.23791 43.5120
> [38,] 5.111108 41.78187 39.09591 44.4678 39.11420 44.4495
> [39,] 5.222220 42.68774 39.97220 45.4033 39.99069 45.3848
> [40,] 5.333331 43.59257 40.84885 46.3363 40.86754 46.3176
> [41,] 5.444442 44.49638 41.72598 47.2668 41.74485 47.2479
> [42,] 5.555554 45.39916 42.60369 48.1946 42.62273 48.1756
> [43,] 5.666665 46.30091 43.48208 49.1197 43.50128 49.1005
> [44,] 5.777776 47.20163 44.36122 50.0421 44.38056 50.0227
> [45,] 5.888888 48.10133 45.24116 50.9615 45.26064 50.9420
> [46,] 5.999999 48.99999 46.12195 51.8780 46.14155 51.8584
> [47,] 6.111110 49.89763 47.00362 52.7916 47.02333 52.7719
> [48,] 6.222222 50.79423 47.88620 53.7023 47.90600 53.6825
> [49,] 6.333333 51.68981 48.76968 54.6099 48.78957 54.5901
> [50,] 6.444444 52.58436 49.65408 55.5146 49.67404 55.4947
> [51,] 6.555556 53.47788 50.53937 56.4164 50.55938 56.3964
> [52,] 6.666667 54.37037 51.42553 57.3152 51.44558 57.2952
> [53,] 6.777778 55.26184 52.31252 58.2112 52.33260 58.1911
> [54,] 6.888890 56.15227 53.20029 59.1043 53.22039 59.0841
> [55,] 7.000001 57.04167 54.08879 59.9946 54.10890 59.9745
> [56,] 7.111112 57.93005 54.97794 60.8822 54.99804 60.8621
> [57,] 7.222224 58.81740 55.86766 61.7671 55.88775 61.7470
> [58,] 7.333335 59.70372 56.75786 62.6496 56.77792 62.6295
> [59,] 7.444446 60.58901 57.64842 63.5296 57.66845 63.5096
> [60,] 7.555558 61.47327 58.53923 64.4073 58.55921 64.3873
> [61,] 7.666669 62.35650 59.43015 65.2829 59.45008 65.2629
> [62,] 7.777780 63.23870 60.32102 66.1564 60.34089 66.1365
> [63,] 7.888892 64.11988 61.21168 67.0281 61.23148 67.0083
> [64,] 8.000003 65.00002 62.10193 67.8981 62.12167 67.8784
> [65,] 8.111114 65.87914 62.99159 68.7667 63.01126 68.7470
> [66,] 8.222226 66.75723 63.88043 69.6340 63.90002 69.6144
> [67,] 8.333337 67.63429 64.76820 70.5004 64.78772 70.4809
> [68,] 8.444448 68.51032 65.65466 71.3660 65.67411 71.3465
> [69,] 8.555560 69.38532 66.53952 72.2311 66.55890 72.2117
> [70,] 8.666671 70.25929 67.42249 73.0961 67.44181 73.0768
> [71,] 8.777782 71.13224 68.30326 73.9612 68.32252 73.9420
> [72,] 8.888894 72.00415 69.18148 74.8268 69.20070 74.8076
> [73,] 9.000005 72.87504 70.05681 75.6933 70.07600 75.6741
> [74,] 9.111116 73.74490 70.92888 76.5609 70.94806 76.5417
> [75,] 9.222228 74.61373 71.79732 77.4301 71.81650 77.4109
> [76,] 9.333339 75.48153 72.66174 78.3013 72.68095 78.2821
> [77,] 9.444450 76.34830 73.52176 79.1748 73.54101 79.1556
> [78,] 9.555562 77.21404 74.37697 80.0511 74.39629 80.0318
> [79,] 9.666673 78.07875 75.22700 80.9305 75.24642 80.9111
> [80,] 9.777784 78.94244 76.07146 81.8134 76.09101 81.7939
> [81,] 9.888896 79.80509 76.90999 82.7002 76.92971 82.6805
> [82,] 10.000007 80.66672 77.74225 83.5912 77.76217 83.5713
> [83,] 10.111118 81.52732 78.56792 84.4867 78.58808 84.4666
> [84,] 10.222230 82.38689 79.38672 85.3871 79.40715 85.3666
> [85,] 10.333341 83.24543 80.19839 86.2925 80.21914 86.2717
> [86,] 10.444452 84.10294 81.00271 87.2032 81.02382 87.1821
> [87,] 10.555564 84.95942 81.79950 88.1194 81.82102 88.0978
> [88,] 10.666675 85.81488 82.58862 89.0411 82.61059 89.0192
> [89,] 10.777786 86.66930 83.36997 89.9686 83.39244 89.9462
> [90,] 10.888898 87.52270 84.14347 90.9019 84.16649 90.8789
> [91,] 11.000009 88.37507 84.90910 91.8410 84.93270 91.8174
> [92,] 11.111120 89.22641 85.66684 92.7860 85.69108 92.7617
> [93,] 11.222232 90.07672 86.41672 93.7367 86.44165 93.7118
> [94,] 11.333343 90.92600 87.15879 94.6932 87.18445 94.6676
> [95,] 11.444454 91.77425 87.89311 95.6554 87.91954 95.6290
> [96,] 11.555566 92.62148 88.61975 96.6232 88.64701 96.5959
> [97,] 11.666677 93.46767 89.33882 97.5965 89.36694 97.5684
> [98,] 11.777788 94.31284 90.05041 98.5753 90.07944 98.5462
> [99,] 11.888900 95.15697 90.75463 99.5593 90.78461 99.5293
> [100,] 12.000011 96.00008 91.45160 100.5486 91.48257 100.5176
Running ‘spline-ex.R’ [2s/3s]
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’ [3s/5s]
Comparing ‘temp.Rout’ to ‘temp.Rout.save’ ...29,31d28
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
35,42c32,35
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
52,54d44
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
58,65c48,51
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
69,71d54
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
75,82c58,61
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.1}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.1)
---
> {tau=0.1}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.5700016, -0.1700000, -0.1700000, 0.1300024
> empirical tau (over all): 12/113 = 0.1061947 (target tau= 0.1)
85,87d63
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
91,98c67,70
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.9}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.9)
---
> {tau=0.9}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.2576939, 0.1300000, 0.1300000, 0.4961568
> empirical tau (over all): 104/113 = 0.920354 (target tau= 0.9)
101,103c73
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 74 102 111
105,108c75
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 28 38 39 85 86 92 95 97 113
113,225c80,192
< [1,] 1880 -0.393247953 -0.568567598 -0.217928308 -0.497693198 -0.2888027083
< [2,] 1881 -0.389244486 -0.556686706 -0.221802266 -0.488996819 -0.2894921527
< [3,] 1882 -0.385241019 -0.544932639 -0.225549398 -0.480375996 -0.2901060418
< [4,] 1883 -0.381237552 -0.533324789 -0.229150314 -0.471842280 -0.2906328235
< [5,] 1884 -0.377234084 -0.521886218 -0.232581951 -0.463409410 -0.2910587589
< [6,] 1885 -0.373230617 -0.510644405 -0.235816829 -0.455093758 -0.2913674769
< [7,] 1886 -0.369227150 -0.499632120 -0.238822180 -0.446914845 -0.2915394558
< [8,] 1887 -0.365223683 -0.488888394 -0.241558972 -0.438895923 -0.2915514428
< [9,] 1888 -0.361220216 -0.478459556 -0.243980875 -0.431064594 -0.2913758376
< [10,] 1889 -0.357216749 -0.468400213 -0.246033284 -0.423453388 -0.2909801092
< [11,] 1890 -0.353213282 -0.458773976 -0.247652588 -0.416100202 -0.2903263615
< [12,] 1891 -0.349209814 -0.449653605 -0.248766024 -0.409048381 -0.2893712477
< [13,] 1892 -0.345206347 -0.441120098 -0.249292596 -0.402346180 -0.2880665146
< [14,] 1893 -0.341202880 -0.433260133 -0.249145628 -0.396045236 -0.2863605248
< [15,] 1894 -0.337199413 -0.426161346 -0.248237480 -0.390197757 -0.2842010691
< [16,] 1895 -0.333195946 -0.419905293 -0.246486599 -0.384852330 -0.2815395617
< [17,] 1896 -0.329192479 -0.414558712 -0.243826246 -0.380048714 -0.2783362437
< [18,] 1897 -0.325189012 -0.410164739 -0.240213284 -0.375812606 -0.2745654171
< [19,] 1898 -0.321185545 -0.406736420 -0.235634669 -0.372151779 -0.2702193101
< [20,] 1899 -0.317182077 -0.404254622 -0.230109533 -0.369054834 -0.2653093212
< [21,] 1900 -0.313178610 -0.402671075 -0.223686145 -0.366493014 -0.2598642062
< [22,] 1901 -0.309175143 -0.401915491 -0.216434795 -0.364424447 -0.2539258394
< [23,] 1902 -0.305171676 -0.401904507 -0.208438845 -0.362799469 -0.2475438831
< [24,] 1903 -0.301168209 -0.402550192 -0.199786225 -0.361565696 -0.2407707212
< [25,] 1904 -0.297164742 -0.403766666 -0.190562818 -0.360671966 -0.2336575172
< [26,] 1905 -0.293161275 -0.405474370 -0.180848179 -0.360070883 -0.2262516664
< [27,] 1906 -0.289157807 -0.407602268 -0.170713347 -0.359720126 -0.2185954887
< [28,] 1907 -0.285154340 -0.410088509 -0.160220171 -0.359582850 -0.2107258307
< [29,] 1908 -0.281150873 -0.412880143 -0.149421603 -0.359627508 -0.2026742377
< [30,] 1909 -0.268996808 -0.394836115 -0.143157501 -0.343964546 -0.1940290700
< [31,] 1910 -0.256842743 -0.376961386 -0.136724100 -0.328402442 -0.1852830438
< [32,] 1911 -0.244688678 -0.359281315 -0.130096042 -0.312956304 -0.1764210522
< [33,] 1912 -0.232534613 -0.341825431 -0.123243796 -0.297643724 -0.1674255025
< [34,] 1913 -0.220380548 -0.324627946 -0.116133151 -0.282485083 -0.1582760137
< [35,] 1914 -0.208226483 -0.307728160 -0.108724807 -0.267503793 -0.1489491732
< [36,] 1915 -0.196072418 -0.291170651 -0.100974185 -0.252726413 -0.1394184235
< [37,] 1916 -0.183918353 -0.275005075 -0.092831631 -0.238182523 -0.1296541835
< [38,] 1917 -0.171764288 -0.259285340 -0.084243236 -0.223904239 -0.1196243373
< [39,] 1918 -0.159610223 -0.244067933 -0.075152513 -0.209925213 -0.1092952334
< [40,] 1919 -0.147456158 -0.229409203 -0.065503113 -0.196279015 -0.0986333019
< [41,] 1920 -0.135302093 -0.215361603 -0.055242584 -0.182996891 -0.0876072953
< [42,] 1921 -0.123148028 -0.201969188 -0.044326869 -0.170105089 -0.0761909673
< [43,] 1922 -0.110993963 -0.189263062 -0.032724864 -0.157622139 -0.0643657877
< [44,] 1923 -0.098839898 -0.177257723 -0.020422074 -0.145556676 -0.0521231208
< [45,] 1924 -0.086685833 -0.165949224 -0.007422442 -0.133906350 -0.0394653164
< [46,] 1925 -0.074531768 -0.155315688 0.006252152 -0.122658128 -0.0264054087
< [47,] 1926 -0.062377703 -0.145320002 0.020564595 -0.111789900 -0.0129655072
< [48,] 1927 -0.050223638 -0.135913981 0.035466704 -0.101272959 0.0008256822
< [49,] 1928 -0.038069573 -0.127043003 0.050903856 -0.091074767 0.0149356198
< [50,] 1929 -0.025915508 -0.118650261 0.066819244 -0.081161479 0.0293304619
< [51,] 1930 -0.013761444 -0.110680090 0.083157203 -0.071499934 0.0439770474
< [52,] 1931 -0.001607379 -0.103080234 0.099865477 -0.062059002 0.0588442451
< [53,] 1932 0.010546686 -0.095803129 0.116896502 -0.052810346 0.0739037194
< [54,] 1933 0.022700751 -0.088806436 0.134207939 -0.043728744 0.0891302464
< [55,] 1934 0.034854816 -0.082053049 0.151762682 -0.034792088 0.1045017213
< [56,] 1935 0.047008881 -0.075510798 0.169528561 -0.025981216 0.1199989785
< [57,] 1936 0.059162946 -0.069151984 0.187477877 -0.017279624 0.1356055167
< [58,] 1937 0.054383856 -0.068135824 0.176903535 -0.018606241 0.1273739530
< [59,] 1938 0.049604765 -0.067303100 0.166512631 -0.020042139 0.1192516703
< [60,] 1939 0.044825675 -0.066681512 0.156332862 -0.021603820 0.1112551700
< [61,] 1940 0.040046585 -0.066303231 0.146396400 -0.023310448 0.1034036175
< [62,] 1941 0.035267494 -0.066205361 0.136740349 -0.025184129 0.0957191177
< [63,] 1942 0.030488404 -0.066430243 0.127407050 -0.027250087 0.0882268946
< [64,] 1943 0.025709313 -0.067025439 0.118444066 -0.029536657 0.0809552836
< [65,] 1944 0.020930223 -0.068043207 0.109903653 -0.032074970 0.0739354160
< [66,] 1945 0.016151132 -0.069539210 0.101841475 -0.034898188 0.0672004530
< [67,] 1946 0.011372042 -0.071570257 0.094314341 -0.038040154 0.0607842381
< [68,] 1947 0.006592951 -0.074190969 0.087376871 -0.041533408 0.0547193111
< [69,] 1948 0.001813861 -0.077449530 0.081077252 -0.045406656 0.0490343779
< [70,] 1949 -0.002965230 -0.081383054 0.075452595 -0.049682007 0.0437515481
< [71,] 1950 -0.007744320 -0.086013419 0.070524779 -0.054372496 0.0388838557
< [72,] 1951 -0.012523410 -0.091344570 0.066297749 -0.059480471 0.0344336506
< [73,] 1952 -0.017302501 -0.097362010 0.062757009 -0.064997299 0.0303922971
< [74,] 1953 -0.022081591 -0.104034636 0.059871454 -0.070904448 0.0267412650
< [75,] 1954 -0.026860682 -0.111318392 0.057597028 -0.077175672 0.0234543081
< [76,] 1955 -0.031639772 -0.119160824 0.055881280 -0.083779723 0.0205001786
< [77,] 1956 -0.036418863 -0.127505585 0.054667859 -0.090683032 0.0178453070
< [78,] 1957 -0.041197953 -0.136296186 0.053900280 -0.097851948 0.0154560415
< [79,] 1958 -0.045977044 -0.145478720 0.053524633 -0.105254354 0.0133002664
< [80,] 1959 -0.050756134 -0.155003532 0.053491263 -0.112860669 0.0113484004
< [81,] 1960 -0.055535225 -0.164826042 0.053755593 -0.120644335 0.0095738862
< [82,] 1961 -0.060314315 -0.174906951 0.054278321 -0.128581941 0.0079533109
< [83,] 1962 -0.065093405 -0.185212049 0.055025238 -0.136653105 0.0064662939
< [84,] 1963 -0.069872496 -0.195711803 0.055966811 -0.144840234 0.0050952422
< [85,] 1964 -0.074651586 -0.206380857 0.057077684 -0.153128222 0.0038250490
< [86,] 1965 -0.060832745 -0.185766914 0.064101424 -0.135261254 0.0135957648
< [87,] 1966 -0.047013903 -0.165458364 0.071430557 -0.117576222 0.0235484155
< [88,] 1967 -0.033195062 -0.145508157 0.079118034 -0.100104670 0.0337145466
< [89,] 1968 -0.019376220 -0.125978144 0.087225704 -0.082883444 0.0441310044
< [90,] 1969 -0.005557378 -0.106939362 0.095824605 -0.065954866 0.0548401092
< [91,] 1970 0.008261463 -0.088471368 0.104994294 -0.049366330 0.0658892560
< [92,] 1971 0.022080305 -0.070660043 0.114820653 -0.033168999 0.0773296085
< [93,] 1972 0.035899146 -0.053593318 0.125391611 -0.017415258 0.0892135504
< [94,] 1973 0.049717988 -0.037354556 0.136790532 -0.002154768 0.1015907442
< [95,] 1974 0.063536830 -0.022014046 0.149087705 0.012570595 0.1145030640
< [96,] 1975 0.077355671 -0.007620056 0.162331398 0.026732077 0.1279792657
< [97,] 1976 0.091174513 0.005808280 0.176540746 0.040318278 0.1420307479
< [98,] 1977 0.104993354 0.018284008 0.191702701 0.053336970 0.1566497385
< [99,] 1978 0.118812196 0.029850263 0.207774129 0.065813852 0.1718105399
< [100,] 1979 0.132631038 0.040573785 0.224688290 0.077788682 0.1874733929
< [101,] 1980 0.146449879 0.050536128 0.242363630 0.089310046 0.2035897119
< [102,] 1981 0.160268721 0.059824930 0.260712511 0.100430154 0.2201072876
< [103,] 1982 0.174087562 0.068526868 0.279648256 0.111200642 0.2369744825
< [104,] 1983 0.187906404 0.076722940 0.299089868 0.121669764 0.2541430435
< [105,] 1984 0.201725246 0.084485905 0.318964586 0.131880867 0.2715696238
< [106,] 1985 0.215544087 0.091879376 0.339208798 0.141871847 0.2892163274
< [107,] 1986 0.229362929 0.098957959 0.359767899 0.151675234 0.3070506231
< [108,] 1987 0.243181770 0.105767982 0.380595558 0.161318630 0.3250449108
< [109,] 1988 0.257000612 0.112348478 0.401652745 0.170825286 0.3431759375
< [110,] 1989 0.270819454 0.118732216 0.422906691 0.180214725 0.3614241817
< [111,] 1990 0.284638295 0.124946675 0.444329916 0.189503318 0.3797732721
< [112,] 1991 0.298457137 0.131014917 0.465899357 0.198704804 0.3982094699
< [113,] 1992 0.312275978 0.136956333 0.487595623 0.207830734 0.4167212231
---
> [1,] 1880 -0.470540541 -0.580395233 -0.360685849 -0.541226637 -0.399854444
> [2,] 1881 -0.462432432 -0.569650451 -0.355214414 -0.531421959 -0.393442906
> [3,] 1882 -0.454324324 -0.558928137 -0.349720511 -0.521631738 -0.387016910
> [4,] 1883 -0.446216216 -0.548230020 -0.344202412 -0.511857087 -0.380575346
> [5,] 1884 -0.438108108 -0.537557989 -0.338658227 -0.502099220 -0.374116996
> [6,] 1885 -0.430000000 -0.526914115 -0.333085885 -0.492359472 -0.367640528
> [7,] 1886 -0.421891892 -0.516300667 -0.327483116 -0.482639300 -0.361144484
> [8,] 1887 -0.413783784 -0.505720132 -0.321847435 -0.472940307 -0.354627261
> [9,] 1888 -0.405675676 -0.495175238 -0.316176113 -0.463264247 -0.348087105
> [10,] 1889 -0.397567568 -0.484668976 -0.310466159 -0.453613044 -0.341522091
> [11,] 1890 -0.389459459 -0.474204626 -0.304714293 -0.443988810 -0.334930108
> [12,] 1891 -0.381351351 -0.463785782 -0.298916920 -0.434393857 -0.328308845
> [13,] 1892 -0.373243243 -0.453416379 -0.293070107 -0.424830717 -0.321655770
> [14,] 1893 -0.365135135 -0.443100719 -0.287169552 -0.415302157 -0.314968113
> [15,] 1894 -0.357027027 -0.432843496 -0.281210558 -0.405811200 -0.308242854
> [16,] 1895 -0.348918919 -0.422649821 -0.275188017 -0.396361132 -0.301476706
> [17,] 1896 -0.340810811 -0.412525238 -0.269096384 -0.386955521 -0.294666101
> [18,] 1897 -0.332702703 -0.402475737 -0.262929668 -0.377598222 -0.287807183
> [19,] 1898 -0.324594595 -0.392507759 -0.256681430 -0.368293379 -0.280895810
> [20,] 1899 -0.316486486 -0.382628180 -0.250344793 -0.359045416 -0.273927557
> [21,] 1900 -0.308378378 -0.372844288 -0.243912468 -0.349859024 -0.266897733
> [22,] 1901 -0.300270270 -0.363163733 -0.237376807 -0.340739124 -0.259801417
> [23,] 1902 -0.292162162 -0.353594450 -0.230729874 -0.331690821 -0.252633503
> [24,] 1903 -0.284054054 -0.344144557 -0.223963551 -0.322719340 -0.245388768
> [25,] 1904 -0.275945946 -0.334822217 -0.217069675 -0.313829934 -0.238061958
> [26,] 1905 -0.267837838 -0.325635470 -0.210040206 -0.305027774 -0.230647901
> [27,] 1906 -0.259729730 -0.316592032 -0.202867427 -0.296317828 -0.223141632
> [28,] 1907 -0.251621622 -0.307699075 -0.195544168 -0.287704708 -0.215538535
> [29,] 1908 -0.243513514 -0.298962989 -0.188064038 -0.279192527 -0.207834500
> [30,] 1909 -0.235405405 -0.290389150 -0.180421661 -0.270784743 -0.200026067
> [31,] 1910 -0.227297297 -0.281981702 -0.172612893 -0.262484025 -0.192110570
> [32,] 1911 -0.219189189 -0.273743385 -0.164634993 -0.254292134 -0.184086245
> [33,] 1912 -0.211081081 -0.265675409 -0.156486753 -0.246209849 -0.175952313
> [34,] 1913 -0.202972973 -0.257777400 -0.148168546 -0.238236929 -0.167709017
> [35,] 1914 -0.194864865 -0.250047417 -0.139682313 -0.230372126 -0.159357604
> [36,] 1915 -0.186756757 -0.242482039 -0.131031475 -0.222613238 -0.150900276
> [37,] 1916 -0.178648649 -0.235076516 -0.122220781 -0.214957209 -0.142340088
> [38,] 1917 -0.170540541 -0.227824968 -0.113256113 -0.207400255 -0.133680826
> [39,] 1918 -0.162432432 -0.220720606 -0.104144259 -0.199938008 -0.124926856
> [40,] 1919 -0.154324324 -0.213755974 -0.094892674 -0.192565671 -0.116082978
> [41,] 1920 -0.146216216 -0.206923176 -0.085509256 -0.185278162 -0.107154270
> [42,] 1921 -0.138108108 -0.200214092 -0.076002124 -0.178070257 -0.098145959
> [43,] 1922 -0.130000000 -0.193620560 -0.066379440 -0.170936704 -0.089063296
> [44,] 1923 -0.121891892 -0.187134533 -0.056649251 -0.163872326 -0.079911458
> [45,] 1924 -0.113783784 -0.180748200 -0.046819367 -0.156872096 -0.070695472
> [46,] 1925 -0.105675676 -0.174454074 -0.036897277 -0.149931196 -0.061420156
> [47,] 1926 -0.097567568 -0.168245056 -0.026890080 -0.143045058 -0.052090077
> [48,] 1927 -0.089459459 -0.162114471 -0.016804448 -0.136209390 -0.042709529
> [49,] 1928 -0.081351351 -0.156056093 -0.006646610 -0.129420182 -0.033282521
> [50,] 1929 -0.073243243 -0.150064140 0.003577654 -0.122673716 -0.023812771
> [51,] 1930 -0.065135135 -0.144133276 0.013863006 -0.115966557 -0.014303713
> [52,] 1931 -0.057027027 -0.138258588 0.024204534 -0.109295545 -0.004758509
> [53,] 1932 -0.048918919 -0.132435569 0.034597732 -0.102657780 0.004819942
> [54,] 1933 -0.040810811 -0.126660095 0.045038473 -0.096050607 0.014428985
> [55,] 1934 -0.032702703 -0.120928393 0.055522988 -0.089471600 0.024066194
> [56,] 1935 -0.024594595 -0.115237021 0.066047832 -0.082918542 0.033729353
> [57,] 1936 -0.016486486 -0.109582838 0.076609865 -0.076389415 0.043416442
> [58,] 1937 -0.016486486 -0.105401253 0.072428280 -0.073698770 0.040725797
> [59,] 1938 -0.016486486 -0.101403226 0.068430253 -0.071126236 0.038153263
> [60,] 1939 -0.016486486 -0.097615899 0.064642926 -0.068689277 0.035716305
> [61,] 1940 -0.016486486 -0.094070136 0.061097163 -0.066407753 0.033434780
> [62,] 1941 -0.016486486 -0.090800520 0.057827547 -0.064303916 0.031330943
> [63,] 1942 -0.016486486 -0.087845022 0.054872049 -0.062402198 0.029429225
> [64,] 1943 -0.016486486 -0.085244160 0.052271187 -0.060728671 0.027755698
> [65,] 1944 -0.016486486 -0.083039523 0.050066550 -0.059310095 0.026337122
> [66,] 1945 -0.016486486 -0.081271575 0.048298602 -0.058172508 0.025199535
> [67,] 1946 -0.016486486 -0.079976806 0.047003833 -0.057339388 0.024366415
> [68,] 1947 -0.016486486 -0.079184539 0.046211566 -0.056829602 0.023856629
> [69,] 1948 -0.016486486 -0.078913907 0.045940934 -0.056655464 0.023682491
> [70,] 1949 -0.016486486 -0.079171667 0.046198694 -0.056821320 0.023848347
> [71,] 1950 -0.016486486 -0.079951382 0.046978409 -0.057323028 0.024350055
> [72,] 1951 -0.016486486 -0.081234197 0.048261224 -0.058148457 0.025175484
> [73,] 1952 -0.016486486 -0.082991006 0.050018033 -0.059278877 0.026305904
> [74,] 1953 -0.016486486 -0.085185454 0.052212481 -0.060690897 0.027717924
> [75,] 1954 -0.016486486 -0.087777140 0.054804167 -0.062358519 0.029385546
> [76,] 1955 -0.016486486 -0.090724471 0.057751498 -0.064254982 0.031282009
> [77,] 1956 -0.016486486 -0.093986883 0.061013910 -0.066354184 0.033381211
> [78,] 1957 -0.016486486 -0.097526332 0.064553359 -0.068631645 0.035658672
> [79,] 1958 -0.016486486 -0.101308145 0.068335172 -0.071065056 0.038092083
> [80,] 1959 -0.016486486 -0.105301366 0.072328393 -0.073634498 0.040661525
> [81,] 1960 -0.016486486 -0.109478765 0.076505793 -0.076322449 0.043349476
> [82,] 1961 -0.016486486 -0.113816631 0.080843658 -0.079113653 0.046140680
> [83,] 1962 -0.016486486 -0.118294454 0.085321481 -0.081994911 0.049021938
> [84,] 1963 -0.016486486 -0.122894566 0.089921593 -0.084954858 0.051981885
> [85,] 1964 -0.016486486 -0.127601781 0.094628808 -0.087983719 0.055010746
> [86,] 1965 -0.006054054 -0.111440065 0.099331957 -0.073864774 0.061756666
> [87,] 1966 0.004378378 -0.095541433 0.104298190 -0.059915111 0.068671868
> [88,] 1967 0.014810811 -0.079951422 0.109573043 -0.046164030 0.075785651
> [89,] 1968 0.025243243 -0.064723125 0.115209611 -0.032645694 0.083132181
> [90,] 1969 0.035675676 -0.049917365 0.121268716 -0.019399240 0.090750592
> [91,] 1970 0.046108108 -0.035602017 0.127818233 -0.006468342 0.098684559
> [92,] 1971 0.056540541 -0.021849988 0.134931069 0.006100087 0.106980994
> [93,] 1972 0.066972973 -0.008735416 0.142681362 0.018258345 0.115687601
> [94,] 1973 0.077405405 0.003672103 0.151138707 0.029961648 0.124849163
> [95,] 1974 0.087837838 0.015314778 0.160360898 0.041172812 0.134502863
> [96,] 1975 0.098270270 0.026154092 0.170386449 0.051867053 0.144673488
> [97,] 1976 0.108702703 0.036176523 0.181228883 0.062035669 0.155369736
> [98,] 1977 0.119135135 0.045395695 0.192874575 0.071687429 0.166582842
> [99,] 1978 0.129567568 0.053850212 0.205284923 0.080847170 0.178287965
> [100,] 1979 0.140000000 0.061597925 0.218402075 0.089552117 0.190447883
> [101,] 1980 0.150432432 0.068708461 0.232156404 0.097847072 0.203017792
> [102,] 1981 0.160864865 0.075255962 0.246473767 0.105779742 0.215949987
> [103,] 1982 0.171297297 0.081313324 0.261281271 0.113397031 0.229197563
> [104,] 1983 0.181729730 0.086948395 0.276511065 0.120742598 0.242716862
> [105,] 1984 0.192162162 0.092221970 0.292102355 0.127855559 0.256468766
> [106,] 1985 0.202594595 0.097187112 0.308002077 0.134770059 0.270419130
> [107,] 1986 0.213027027 0.101889333 0.324164721 0.141515381 0.284538673
> [108,] 1987 0.223459459 0.106367224 0.340551695 0.148116359 0.298802560
> [109,] 1988 0.233891892 0.110653299 0.357130484 0.154593913 0.313189871
> [110,] 1989 0.244324324 0.114774857 0.373873791 0.160965608 0.327683041
> [111,] 1990 0.254756757 0.118754798 0.390758715 0.167246179 0.342267335
> [112,] 1991 0.265189189 0.122612348 0.407766030 0.173447997 0.356930381
> [113,] 1992 0.275621622 0.126363680 0.424879564 0.179581470 0.371661774
228,340c195,307
< [1,] 1880 -0.393247953 -0.638616081 -0.147879825 -0.539424009 -0.247071897
< [2,] 1881 -0.389244486 -0.623587786 -0.154901186 -0.528852590 -0.249636382
< [3,] 1882 -0.385241019 -0.608736988 -0.161745049 -0.518386915 -0.252095123
< [4,] 1883 -0.381237552 -0.594090828 -0.168384275 -0.508043150 -0.254431953
< [5,] 1884 -0.377234084 -0.579681581 -0.174786588 -0.497840525 -0.256627644
< [6,] 1885 -0.373230617 -0.565547708 -0.180913527 -0.487801951 -0.258659284
< [7,] 1886 -0.369227150 -0.551735068 -0.186719232 -0.477954750 -0.260499551
< [8,] 1887 -0.365223683 -0.538298290 -0.192149076 -0.468331465 -0.262115901
< [9,] 1888 -0.361220216 -0.525302213 -0.197138218 -0.458970724 -0.263469708
< [10,] 1889 -0.357216749 -0.512823261 -0.201610236 -0.449918056 -0.264515441
< [11,] 1890 -0.353213282 -0.500950461 -0.205476102 -0.441226498 -0.265200065
< [12,] 1891 -0.349209814 -0.489785646 -0.208633983 -0.432956717 -0.265462912
< [13,] 1892 -0.345206347 -0.479442174 -0.210970520 -0.425176244 -0.265236451
< [14,] 1893 -0.341202880 -0.470041356 -0.212364405 -0.417957348 -0.264448412
< [15,] 1894 -0.337199413 -0.461705842 -0.212692984 -0.411373100 -0.263025726
< [16,] 1895 -0.333195946 -0.454549774 -0.211842118 -0.405491497 -0.260900395
< [17,] 1896 -0.329192479 -0.448666556 -0.209718402 -0.400368183 -0.258016774
< [18,] 1897 -0.325189012 -0.444116558 -0.206261466 -0.396039125 -0.254338899
< [19,] 1898 -0.321185545 -0.440918038 -0.201453051 -0.392515198 -0.249855891
< [20,] 1899 -0.317182077 -0.439044218 -0.195319937 -0.389780451 -0.244583704
< [21,] 1900 -0.313178610 -0.438427544 -0.187929677 -0.387794638 -0.238562582
< [22,] 1901 -0.309175143 -0.438969642 -0.179380644 -0.386499155 -0.231851132
< [23,] 1902 -0.305171676 -0.440553844 -0.169789508 -0.385824495 -0.224518857
< [24,] 1903 -0.301168209 -0.443057086 -0.159279332 -0.385697347 -0.216639071
< [25,] 1904 -0.297164742 -0.446359172 -0.147970311 -0.386046103 -0.208283380
< [26,] 1905 -0.293161275 -0.450348759 -0.135973790 -0.386804433 -0.199518116
< [27,] 1906 -0.289157807 -0.454926427 -0.123389188 -0.387913107 -0.190402508
< [28,] 1907 -0.285154340 -0.460005614 -0.110303066 -0.389320557 -0.180988124
< [29,] 1908 -0.281150873 -0.465512212 -0.096789534 -0.390982633 -0.171319113
< [30,] 1909 -0.268996808 -0.445114865 -0.092878751 -0.373917700 -0.164075916
< [31,] 1910 -0.256842743 -0.424954461 -0.088731025 -0.356993924 -0.156691562
< [32,] 1911 -0.244688678 -0.405066488 -0.084310868 -0.340232447 -0.149144910
< [33,] 1912 -0.232534613 -0.385492277 -0.079576949 -0.323657890 -0.141411336
< [34,] 1913 -0.220380548 -0.366279707 -0.074481389 -0.307298779 -0.133462317
< [35,] 1914 -0.208226483 -0.347483782 -0.068969185 -0.291187880 -0.125265087
< [36,] 1915 -0.196072418 -0.329166890 -0.062977947 -0.275362361 -0.116782475
< [37,] 1916 -0.183918353 -0.311398525 -0.056438181 -0.259863623 -0.107973083
< [38,] 1917 -0.171764288 -0.294254136 -0.049274440 -0.244736614 -0.098791963
< [39,] 1918 -0.159610223 -0.277812779 -0.041407667 -0.230028429 -0.089192017
< [40,] 1919 -0.147456158 -0.262153318 -0.032758999 -0.215786053 -0.079126264
< [41,] 1920 -0.135302093 -0.247349160 -0.023255026 -0.202053217 -0.068550970
< [42,] 1921 -0.123148028 -0.233461966 -0.012834091 -0.188866654 -0.057429402
< [43,] 1922 -0.110993963 -0.220535266 -0.001452661 -0.176252299 -0.045735628
< [44,] 1923 -0.098839898 -0.208589350 0.010909553 -0.164222236 -0.033457560
< [45,] 1924 -0.086685833 -0.197618695 0.024247028 -0.152773178 -0.020598488
< [46,] 1925 -0.074531768 -0.187592682 0.038529145 -0.141886883 -0.007176654
< [47,] 1926 -0.062377703 -0.178459370 0.053703964 -0.131532407 0.006777000
< [48,] 1927 -0.050223638 -0.170151322 0.069704045 -0.121669575 0.021222298
< [49,] 1928 -0.038069573 -0.162592093 0.086452946 -0.112252846 0.036113699
< [50,] 1929 -0.025915508 -0.155702177 0.103871160 -0.103234855 0.051403838
< [51,] 1930 -0.013761444 -0.149403669 0.121880782 -0.094569190 0.067046303
< [52,] 1931 -0.001607379 -0.143623435 0.140408678 -0.086212283 0.082997525
< [53,] 1932 0.010546686 -0.138294906 0.159388279 -0.078124475 0.099217848
< [54,] 1933 0.022700751 -0.133358827 0.178760330 -0.070270466 0.115671969
< [55,] 1934 0.034854816 -0.128763266 0.198472899 -0.062619318 0.132328951
< [56,] 1935 0.047008881 -0.124463200 0.218480963 -0.055144209 0.149161972
< [57,] 1936 0.059162946 -0.120419862 0.238745755 -0.047822043 0.166147936
< [58,] 1937 0.054383856 -0.117088225 0.225855937 -0.047769234 0.156536946
< [59,] 1938 0.049604765 -0.114013317 0.213222848 -0.047869369 0.147078900
< [60,] 1939 0.044825675 -0.111233903 0.200885253 -0.048145542 0.137796893
< [61,] 1940 0.040046585 -0.108795008 0.188888177 -0.048624577 0.128717746
< [62,] 1941 0.035267494 -0.106748562 0.177283550 -0.049337410 0.119872398
< [63,] 1942 0.030488404 -0.105153822 0.166130629 -0.050319343 0.111296150
< [64,] 1943 0.025709313 -0.104077355 0.155495982 -0.051610033 0.103028659
< [65,] 1944 0.020930223 -0.103592297 0.145452743 -0.053253050 0.095113496
< [66,] 1945 0.016151132 -0.103776551 0.136078816 -0.055294804 0.087597069
< [67,] 1946 0.011372042 -0.104709625 0.127453709 -0.057782662 0.080526746
< [68,] 1947 0.006592951 -0.106467962 0.119653865 -0.060762163 0.073948066
< [69,] 1948 0.001813861 -0.109119001 0.112746722 -0.064273484 0.067901206
< [70,] 1949 -0.002965230 -0.112714681 0.106784222 -0.068347568 0.062417108
< [71,] 1950 -0.007744320 -0.117285623 0.101796983 -0.073002655 0.057514015
< [72,] 1951 -0.012523410 -0.122837348 0.097790527 -0.078242036 0.053195215
< [73,] 1952 -0.017302501 -0.129349568 0.094744566 -0.084053625 0.049448623
< [74,] 1953 -0.022081591 -0.136778751 0.092615568 -0.090411486 0.046248303
< [75,] 1954 -0.026860682 -0.145063238 0.091341874 -0.097278888 0.043557524
< [76,] 1955 -0.031639772 -0.154129620 0.090850076 -0.104612098 0.041332553
< [77,] 1956 -0.036418863 -0.163899035 0.091061309 -0.112364133 0.039526407
< [78,] 1957 -0.041197953 -0.174292425 0.091896518 -0.120487896 0.038091990
< [79,] 1958 -0.045977044 -0.185234342 0.093280255 -0.128938440 0.036984353
< [80,] 1959 -0.050756134 -0.196655293 0.095143025 -0.137674365 0.036162097
< [81,] 1960 -0.055535225 -0.208492888 0.097422439 -0.146658502 0.035588053
< [82,] 1961 -0.060314315 -0.220692125 0.100063495 -0.155858084 0.035229454
< [83,] 1962 -0.065093405 -0.233205123 0.103018312 -0.165244586 0.035057775
< [84,] 1963 -0.069872496 -0.245990553 0.106245561 -0.174793388 0.035048396
< [85,] 1964 -0.074651586 -0.259012925 0.109709752 -0.184483346 0.035180173
< [86,] 1965 -0.060832745 -0.235684019 0.114018529 -0.164998961 0.043333472
< [87,] 1966 -0.047013903 -0.212782523 0.118754717 -0.145769203 0.051741396
< [88,] 1967 -0.033195062 -0.190382546 0.123992423 -0.126838220 0.060448097
< [89,] 1968 -0.019376220 -0.168570650 0.129818210 -0.108257582 0.069505142
< [90,] 1969 -0.005557378 -0.147446255 0.136331499 -0.090086516 0.078971760
< [91,] 1970 0.008261463 -0.127120705 0.143643631 -0.072391356 0.088914283
< [92,] 1971 0.022080305 -0.107714195 0.151874804 -0.055243707 0.099404316
< [93,] 1972 0.035899146 -0.089349787 0.161148080 -0.038716881 0.110515174
< [94,] 1973 0.049717988 -0.072144153 0.171580129 -0.022880386 0.122316362
< [95,] 1974 0.063536830 -0.056195664 0.183269323 -0.007792824 0.134866483
< [96,] 1975 0.077355671 -0.041571875 0.196283217 0.006505558 0.148205784
< [97,] 1976 0.091174513 -0.028299564 0.210648590 0.019998808 0.162350217
< [98,] 1977 0.104993354 -0.016360474 0.226347183 0.032697804 0.177288905
< [99,] 1978 0.118812196 -0.005694233 0.243318625 0.044638509 0.192985883
< [100,] 1979 0.132631038 0.003792562 0.261469513 0.055876570 0.209385506
< [101,] 1980 0.146449879 0.012214052 0.280685706 0.066479983 0.226419775
< [102,] 1981 0.160268721 0.019692889 0.300844552 0.076521819 0.244015623
< [103,] 1982 0.174087562 0.026350383 0.321824742 0.086074346 0.262100779
< [104,] 1983 0.187906404 0.032299891 0.343512917 0.095205097 0.280607711
< [105,] 1984 0.201725246 0.037643248 0.365807243 0.103974737 0.299475754
< [106,] 1985 0.215544087 0.042469480 0.388618694 0.112436305 0.318651869
< [107,] 1986 0.229362929 0.046855011 0.411870847 0.120635329 0.338090528
< [108,] 1987 0.243181770 0.050864680 0.435498861 0.128610437 0.357753104
< [109,] 1988 0.257000612 0.054553115 0.459448109 0.136394171 0.377607052
< [110,] 1989 0.270819454 0.057966177 0.483672730 0.144013855 0.397625052
< [111,] 1990 0.284638295 0.061142326 0.508134265 0.151492399 0.417784191
< [112,] 1991 0.298457137 0.064113837 0.532800436 0.158849032 0.438065241
< [113,] 1992 0.312275978 0.066907850 0.557644107 0.166099922 0.458452034
---
> [1,] 1880 -0.570000000 -0.7989007 -0.3410992837 -0.71728636 -0.422713636
> [2,] 1881 -0.562857143 -0.7862639 -0.3394503795 -0.70660842 -0.419105867
> [3,] 1882 -0.555714286 -0.7736739 -0.3377546582 -0.69596060 -0.415467975
> [4,] 1883 -0.548571429 -0.7611343 -0.3360085204 -0.68534522 -0.411797641
> [5,] 1884 -0.541428571 -0.7486491 -0.3342080272 -0.67476481 -0.408092333
> [6,] 1885 -0.534285714 -0.7362226 -0.3323488643 -0.66422216 -0.404349273
> [7,] 1886 -0.527142857 -0.7238594 -0.3304263043 -0.65372029 -0.400565421
> [8,] 1887 -0.520000000 -0.7115648 -0.3284351643 -0.64326256 -0.396737440
> [9,] 1888 -0.512857143 -0.6993445 -0.3263697605 -0.63285261 -0.392861675
> [10,] 1889 -0.505714286 -0.6872047 -0.3242238599 -0.62249446 -0.388934114
> [11,] 1890 -0.498571429 -0.6751522 -0.3219906288 -0.61219250 -0.384950360
> [12,] 1891 -0.491428571 -0.6631946 -0.3196625782 -0.60195155 -0.380905594
> [13,] 1892 -0.484285714 -0.6513399 -0.3172315093 -0.59177689 -0.376794541
> [14,] 1893 -0.477142857 -0.6395973 -0.3146884583 -0.58167428 -0.372611433
> [15,] 1894 -0.470000000 -0.6279764 -0.3120236430 -0.57165002 -0.368349976
> [16,] 1895 -0.462857143 -0.6164879 -0.3092264155 -0.56171097 -0.364003318
> [17,] 1896 -0.455714286 -0.6051433 -0.3062852230 -0.55186455 -0.359564026
> [18,] 1897 -0.448571429 -0.5939553 -0.3031875831 -0.54211879 -0.355024067
> [19,] 1898 -0.441428571 -0.5829371 -0.2999200783 -0.53248233 -0.350374809
> [20,] 1899 -0.434285714 -0.5721031 -0.2964683783 -0.52296440 -0.345607030
> [21,] 1900 -0.427142857 -0.5614684 -0.2928172976 -0.51357475 -0.340710959
> [22,] 1901 -0.420000000 -0.5510491 -0.2889508980 -0.50432366 -0.335676342
> [23,] 1902 -0.412857143 -0.5408616 -0.2848526441 -0.49522175 -0.330492537
> [24,] 1903 -0.405714286 -0.5309229 -0.2805056214 -0.48627991 -0.325148662
> [25,] 1904 -0.398571429 -0.5212500 -0.2758928205 -0.47750909 -0.319633772
> [26,] 1905 -0.391428571 -0.5118597 -0.2709974894 -0.46892006 -0.313937087
> [27,] 1906 -0.384285714 -0.5027679 -0.2658035488 -0.46052317 -0.308048262
> [28,] 1907 -0.377142857 -0.4939897 -0.2602960562 -0.45232803 -0.301957682
> [29,] 1908 -0.370000000 -0.4855383 -0.2544616963 -0.44434322 -0.295656778
> [30,] 1909 -0.362857143 -0.4774250 -0.2482892691 -0.43657594 -0.289138345
> [31,] 1910 -0.355714286 -0.4696584 -0.2417701364 -0.42903175 -0.282396824
> [32,] 1911 -0.348571429 -0.4622443 -0.2348985912 -0.42171431 -0.275428543
> [33,] 1912 -0.341428571 -0.4551850 -0.2276721117 -0.41462526 -0.268231879
> [34,] 1913 -0.334285714 -0.4484800 -0.2200914777 -0.40776409 -0.260807334
> [35,] 1914 -0.327142857 -0.4421250 -0.2121607344 -0.40112820 -0.253157511
> [36,] 1915 -0.320000000 -0.4361130 -0.2038870084 -0.39471301 -0.245286995
> [37,] 1916 -0.312857143 -0.4304341 -0.1952801960 -0.38851213 -0.237202155
> [38,] 1917 -0.305714286 -0.4250760 -0.1863525523 -0.38251770 -0.228910875
> [39,] 1918 -0.298571429 -0.4200246 -0.1771182205 -0.37672060 -0.220422257
> [40,] 1919 -0.291428571 -0.4152644 -0.1675927388 -0.37111085 -0.211746298
> [41,] 1920 -0.284285714 -0.4107789 -0.1577925583 -0.36567785 -0.202893584
> [42,] 1921 -0.277142857 -0.4065511 -0.1477346004 -0.36041071 -0.193875002
> [43,] 1922 -0.270000000 -0.4025641 -0.1374358695 -0.35529850 -0.184701495
> [44,] 1923 -0.262857143 -0.3988012 -0.1269131329 -0.35033043 -0.175383852
> [45,] 1924 -0.255714286 -0.3952459 -0.1161826679 -0.34549603 -0.165932545
> [46,] 1925 -0.248571429 -0.3918828 -0.1052600744 -0.34078524 -0.156357614
> [47,] 1926 -0.241428571 -0.3886970 -0.0941601449 -0.33618857 -0.146668575
> [48,] 1927 -0.234285714 -0.3856746 -0.0828967845 -0.33169705 -0.136874376
> [49,] 1928 -0.227142857 -0.3828027 -0.0714829715 -0.32730235 -0.126983369
> [50,] 1929 -0.220000000 -0.3800693 -0.0599307484 -0.32299670 -0.117003301
> [51,] 1930 -0.212857143 -0.3774630 -0.0482512378 -0.31877296 -0.106941331
> [52,] 1931 -0.205714286 -0.3749739 -0.0364546744 -0.31462453 -0.096804042
> [53,] 1932 -0.198571429 -0.3725924 -0.0245504487 -0.31054538 -0.086597478
> [54,] 1933 -0.191428571 -0.3703100 -0.0125471577 -0.30652997 -0.076327171
> [55,] 1934 -0.184285714 -0.3681188 -0.0004526588 -0.30257325 -0.065998175
> [56,] 1935 -0.177142857 -0.3660116 0.0117258745 -0.29867061 -0.055615108
> [57,] 1936 -0.170000000 -0.3639819 0.0239818977 -0.29481782 -0.045182180
> [58,] 1937 -0.170000000 -0.3552689 0.0152688616 -0.28921141 -0.050788591
> [59,] 1938 -0.170000000 -0.3469383 0.0069383006 -0.28385110 -0.056148897
> [60,] 1939 -0.170000000 -0.3390468 -0.0009532311 -0.27877329 -0.061226710
> [61,] 1940 -0.170000000 -0.3316586 -0.0083414258 -0.27401935 -0.065980650
> [62,] 1941 -0.170000000 -0.3248458 -0.0151542191 -0.26963565 -0.070364348
> [63,] 1942 -0.170000000 -0.3186875 -0.0213124962 -0.26567310 -0.074326897
> [64,] 1943 -0.170000000 -0.3132682 -0.0267318303 -0.26218603 -0.077813972
> [65,] 1944 -0.170000000 -0.3086744 -0.0313255619 -0.25923019 -0.080769813
> [66,] 1945 -0.170000000 -0.3049906 -0.0350093787 -0.25685983 -0.083140168
> [67,] 1946 -0.170000000 -0.3022928 -0.0377072467 -0.25512389 -0.084876113
> [68,] 1947 -0.170000000 -0.3006419 -0.0393580695 -0.25406166 -0.085938337
> [69,] 1948 -0.170000000 -0.3000780 -0.0399219767 -0.25369882 -0.086301183
> [70,] 1949 -0.170000000 -0.3006151 -0.0393848898 -0.25404441 -0.085955594
> [71,] 1950 -0.170000000 -0.3022398 -0.0377602233 -0.25508980 -0.084910201
> [72,] 1951 -0.170000000 -0.3049127 -0.0350872623 -0.25680972 -0.083190282
> [73,] 1952 -0.170000000 -0.3085733 -0.0314266558 -0.25916514 -0.080834862
> [74,] 1953 -0.170000000 -0.3131458 -0.0268541535 -0.26210732 -0.077892681
> [75,] 1954 -0.170000000 -0.3185461 -0.0214539408 -0.26558209 -0.074417909
> [76,] 1955 -0.170000000 -0.3246873 -0.0153126807 -0.26953369 -0.070466310
> [77,] 1956 -0.170000000 -0.3314851 -0.0085148970 -0.27390773 -0.066092271
> [78,] 1957 -0.170000000 -0.3388601 -0.0011398598 -0.27865320 -0.061346797
> [79,] 1958 -0.170000000 -0.3467402 0.0067401824 -0.28372362 -0.056276377
> [80,] 1959 -0.170000000 -0.3550607 0.0150607304 -0.28907749 -0.050922513
> [81,] 1960 -0.170000000 -0.3637650 0.0237650445 -0.29467829 -0.045321714
> [82,] 1961 -0.170000000 -0.3728037 0.0328037172 -0.30049423 -0.039505772
> [83,] 1962 -0.170000000 -0.3821340 0.0421340134 -0.30649781 -0.033502185
> [84,] 1963 -0.170000000 -0.3917191 0.0517191202 -0.31266536 -0.027334640
> [85,] 1964 -0.170000000 -0.4015274 0.0615273928 -0.31897650 -0.021023499
> [86,] 1965 -0.159285714 -0.3788752 0.0603037544 -0.30058075 -0.017990680
> [87,] 1966 -0.148571429 -0.3567712 0.0596282943 -0.28253772 -0.014605137
> [88,] 1967 -0.137857143 -0.3353102 0.0595958975 -0.26490847 -0.010805813
> [89,] 1968 -0.127142857 -0.3146029 0.0603171930 -0.24776419 -0.006521525
> [90,] 1969 -0.116428571 -0.2947761 0.0619189162 -0.23118642 -0.001670726
> [91,] 1970 -0.105714286 -0.2759711 0.0645424939 -0.21526616 0.003837587
> [92,] 1971 -0.095000000 -0.2583398 0.0683398431 -0.20010116 0.010101164
> [93,] 1972 -0.084285714 -0.2420369 0.0734654391 -0.18579083 0.017219402
> [94,] 1973 -0.073571429 -0.2272072 0.0800643002 -0.17242847 0.025285614
> [95,] 1974 -0.062857143 -0.2139711 0.0882568427 -0.16009157 0.034377282
> [96,] 1975 -0.052142857 -0.2024090 0.0981233226 -0.14883176 0.044546046
> [97,] 1976 -0.041428571 -0.1925491 0.1096919157 -0.13866718 0.055810037
> [98,] 1977 -0.030714286 -0.1843628 0.1229342326 -0.12957956 0.068150987
> [99,] 1978 -0.020000000 -0.1777698 0.1377698370 -0.12151714 0.081517138
> [100,] 1979 -0.009285714 -0.1726496 0.1540781875 -0.11440236 0.095830930
> [101,] 1980 0.001428571 -0.1688571 0.1717142023 -0.10814187 0.110999008
> [102,] 1981 0.012142857 -0.1662377 0.1905233955 -0.10263625 0.126921969
> [103,] 1982 0.022857143 -0.1646396 0.2103538775 -0.09778779 0.143502079
> [104,] 1983 0.033571429 -0.1639214 0.2310642722 -0.09350551 0.160648370
> [105,] 1984 0.044285714 -0.1639565 0.2525279044 -0.08970790 0.178279332
> [106,] 1985 0.055000000 -0.1646342 0.2746342071 -0.08632382 0.196323821
> [107,] 1986 0.065714286 -0.1658598 0.2972883534 -0.08329225 0.214720820
> [108,] 1987 0.076428571 -0.1675528 0.3204099260 -0.08056144 0.233418585
> [109,] 1988 0.087142857 -0.1696455 0.3439311798 -0.07808781 0.252373526
> [110,] 1989 0.097857143 -0.1720809 0.3677952332 -0.07583476 0.271549041
> [111,] 1990 0.108571429 -0.1748115 0.3919543697 -0.07377157 0.290914428
> [112,] 1991 0.119285714 -0.1777971 0.4163685288 -0.07187248 0.310443909
> [113,] 1992 0.130000000 -0.1810040 0.4410040109 -0.07011580 0.330115800
343,455c310,422
< [1,] 1880 -0.393247953 -0.693805062 -0.092690844 -0.572302393 -0.214193513
< [2,] 1881 -0.389244486 -0.676297026 -0.102191945 -0.560253689 -0.218235282
< [3,] 1882 -0.385241019 -0.659006413 -0.111475624 -0.548334514 -0.222147524
< [4,] 1883 -0.381237552 -0.641966465 -0.120508639 -0.536564669 -0.225910434
< [5,] 1884 -0.377234084 -0.625216717 -0.129251452 -0.524967709 -0.229500459
< [6,] 1885 -0.373230617 -0.608804280 -0.137656955 -0.513571700 -0.232889535
< [7,] 1886 -0.369227150 -0.592785330 -0.145668970 -0.502410107 -0.236044193
< [8,] 1887 -0.365223683 -0.577226782 -0.153220584 -0.491522795 -0.238924571
< [9,] 1888 -0.361220216 -0.562208058 -0.160232373 -0.480957079 -0.241483352
< [10,] 1889 -0.357216749 -0.547822773 -0.166610724 -0.470768729 -0.243664768
< [11,] 1890 -0.353213282 -0.534179978 -0.172246585 -0.461022711 -0.245403852
< [12,] 1891 -0.349209814 -0.521404410 -0.177015219 -0.451793336 -0.246626293
< [13,] 1892 -0.345206347 -0.509634924 -0.180777771 -0.443163327 -0.247249368
< [14,] 1893 -0.341202880 -0.499020116 -0.183385645 -0.435221208 -0.247184553
< [15,] 1894 -0.337199413 -0.489710224 -0.184688602 -0.428056482 -0.246342344
< [16,] 1895 -0.333195946 -0.481845064 -0.184546828 -0.421752442 -0.244639450
< [17,] 1896 -0.329192479 -0.475539046 -0.182845912 -0.416377249 -0.242007708
< [18,] 1897 -0.325189012 -0.470866120 -0.179511904 -0.411974957 -0.238403066
< [19,] 1898 -0.321185545 -0.467848651 -0.174522438 -0.408558891 -0.233812198
< [20,] 1899 -0.317182077 -0.466453839 -0.167910316 -0.406109508 -0.228254646
< [21,] 1900 -0.313178610 -0.466598933 -0.159758288 -0.404577513 -0.221779708
< [22,] 1901 -0.309175143 -0.468163434 -0.150186852 -0.403891117 -0.214459169
< [23,] 1902 -0.305171676 -0.471004432 -0.139338920 -0.403965184 -0.206378168
< [24,] 1903 -0.301168209 -0.474971184 -0.127365234 -0.404709910 -0.197626508
< [25,] 1904 -0.297164742 -0.479916458 -0.114413025 -0.406037582 -0.188291901
< [26,] 1905 -0.293161275 -0.485703869 -0.100618680 -0.407866950 -0.178455599
< [27,] 1906 -0.289157807 -0.492211633 -0.086103982 -0.410125463 -0.168190151
< [28,] 1907 -0.285154340 -0.499333719 -0.070974961 -0.412749954 -0.157558727
< [29,] 1908 -0.281150873 -0.506979351 -0.055322395 -0.415686342 -0.146615404
< [30,] 1909 -0.268996808 -0.484727899 -0.053265717 -0.397516841 -0.140476775
< [31,] 1910 -0.256842743 -0.462766683 -0.050918803 -0.379520246 -0.134165240
< [32,] 1911 -0.244688678 -0.441139176 -0.048238181 -0.361722455 -0.127654901
< [33,] 1912 -0.232534613 -0.419896002 -0.045173225 -0.344153628 -0.120915598
< [34,] 1913 -0.220380548 -0.399095811 -0.041665286 -0.326848704 -0.113912392
< [35,] 1914 -0.208226483 -0.378805976 -0.037646990 -0.309847821 -0.106605145
< [36,] 1915 -0.196072418 -0.359102922 -0.033041915 -0.293196507 -0.098948329
< [37,] 1916 -0.183918353 -0.340071771 -0.027764935 -0.276945475 -0.090891232
< [38,] 1917 -0.171764288 -0.321804943 -0.021723634 -0.261149781 -0.082378795
< [39,] 1918 -0.159610223 -0.304399275 -0.014821172 -0.245867116 -0.073353330
< [40,] 1919 -0.147456158 -0.287951368 -0.006960949 -0.231155030 -0.063757286
< [41,] 1920 -0.135302093 -0.272551143 0.001946957 -0.217067092 -0.053537094
< [42,] 1921 -0.123148028 -0.258274127 0.011978071 -0.203648297 -0.042647760
< [43,] 1922 -0.110993963 -0.245173645 0.023185718 -0.190930411 -0.031057516
< [44,] 1923 -0.098839898 -0.233274545 0.035594749 -0.178928240 -0.018751557
< [45,] 1924 -0.086685833 -0.222570067 0.049198400 -0.167637754 -0.005733912
< [46,] 1925 -0.074531768 -0.213022703 0.063959166 -0.157036610 0.007973073
< [47,] 1926 -0.062377703 -0.204568828 0.079813422 -0.147086903 0.022331496
< [48,] 1927 -0.050223638 -0.197125838 0.096678562 -0.137739423 0.037292146
< [49,] 1928 -0.038069573 -0.190600095 0.114460948 -0.128938384 0.052799237
< [50,] 1929 -0.025915508 -0.184894207 0.133063191 -0.120625768 0.068794751
< [51,] 1930 -0.013761444 -0.179912750 0.152389863 -0.112744726 0.085221839
< [52,] 1931 -0.001607379 -0.175566138 0.172351381 -0.105241887 0.102027130
< [53,] 1932 0.010546686 -0.171772831 0.192866204 -0.098068675 0.119162048
< [54,] 1933 0.022700751 -0.168460244 0.213861747 -0.091181848 0.136583351
< [55,] 1934 0.034854816 -0.165564766 0.235274399 -0.084543511 0.154253144
< [56,] 1935 0.047008881 -0.163031246 0.257049009 -0.078120807 0.172138570
< [57,] 1936 0.059162946 -0.160812199 0.279138092 -0.071885448 0.190211340
< [58,] 1937 0.054383856 -0.155656272 0.264423984 -0.070745832 0.179513544
< [59,] 1938 0.049604765 -0.150814817 0.250024348 -0.069793562 0.169003093
< [60,] 1939 0.044825675 -0.146335320 0.235986670 -0.069056925 0.158708275
< [61,] 1940 0.040046585 -0.142272933 0.222366102 -0.068568777 0.148661946
< [62,] 1941 0.035267494 -0.138691265 0.209226254 -0.068367014 0.138902002
< [63,] 1942 0.030488404 -0.135662903 0.196639710 -0.068494879 0.129471686
< [64,] 1943 0.025709313 -0.133269386 0.184688012 -0.069000947 0.120419573
< [65,] 1944 0.020930223 -0.131600299 0.173460744 -0.069938588 0.111799033
< [66,] 1945 0.016151132 -0.130751068 0.163053332 -0.071364652 0.103666917
< [67,] 1946 0.011372042 -0.130819083 0.153563167 -0.073337158 0.096081242
< [68,] 1947 0.006592951 -0.131897983 0.145083886 -0.075911890 0.089097793
< [69,] 1948 0.001813861 -0.134070373 0.137698095 -0.079138060 0.082765782
< [70,] 1949 -0.002965230 -0.137399877 0.131469418 -0.083053571 0.077123112
< [71,] 1950 -0.007744320 -0.141924001 0.126435361 -0.087680768 0.072192128
< [72,] 1951 -0.012523410 -0.147649510 0.122602689 -0.093023679 0.067976858
< [73,] 1952 -0.017302501 -0.154551551 0.119946549 -0.099067500 0.064462498
< [74,] 1953 -0.022081591 -0.162576801 0.118413618 -0.105780463 0.061617281
< [75,] 1954 -0.026860682 -0.171649733 0.117928369 -0.113117575 0.059396211
< [76,] 1955 -0.031639772 -0.181680427 0.118400882 -0.121025265 0.057745721
< [77,] 1956 -0.036418863 -0.192572281 0.119734555 -0.129445984 0.056608259
< [78,] 1957 -0.041197953 -0.204228457 0.121832550 -0.138322042 0.055926136
< [79,] 1958 -0.045977044 -0.216556537 0.124602449 -0.147598382 0.055644294
< [80,] 1959 -0.050756134 -0.229471397 0.127959128 -0.157224290 0.055712022
< [81,] 1960 -0.055535225 -0.242896613 0.131826164 -0.167154239 0.056083790
< [82,] 1961 -0.060314315 -0.256764812 0.136136182 -0.177348092 0.056719462
< [83,] 1962 -0.065093405 -0.271017346 0.140830535 -0.187770909 0.057584098
< [84,] 1963 -0.069872496 -0.285603587 0.145858595 -0.198392529 0.058647537
< [85,] 1964 -0.074651586 -0.300480064 0.151176891 -0.209187055 0.059883882
< [86,] 1965 -0.060832745 -0.275012124 0.153346634 -0.188428358 0.066762869
< [87,] 1966 -0.047013903 -0.250067729 0.156039922 -0.167981559 0.073953753
< [88,] 1967 -0.033195062 -0.225737656 0.159347533 -0.147900737 0.081510614
< [89,] 1968 -0.019376220 -0.202127937 0.163375497 -0.128249061 0.089496621
< [90,] 1969 -0.005557378 -0.179360353 0.168245596 -0.109099079 0.097984322
< [91,] 1970 0.008261463 -0.157571293 0.174094219 -0.090532045 0.107054971
< [92,] 1971 0.022080305 -0.136907986 0.181068596 -0.072635669 0.116796279
< [93,] 1972 0.035899146 -0.117521176 0.189319469 -0.055499756 0.127298049
< [94,] 1973 0.049717988 -0.099553773 0.198989749 -0.039209443 0.138645419
< [95,] 1974 0.063536830 -0.083126277 0.210199936 -0.023836517 0.150910176
< [96,] 1975 0.077355671 -0.068321437 0.223032779 -0.009430275 0.164141617
< [97,] 1976 0.091174513 -0.055172054 0.237521080 0.003989742 0.178359283
< [98,] 1977 0.104993354 -0.043655763 0.253642472 0.016436858 0.193549851
< [99,] 1978 0.118812196 -0.033698615 0.271323007 0.027955127 0.209669265
< [100,] 1979 0.132631038 -0.025186198 0.290448273 0.038612710 0.226649365
< [101,] 1980 0.146449879 -0.017978697 0.310878456 0.048492899 0.244406859
< [102,] 1981 0.160268721 -0.011925874 0.332463316 0.057685199 0.262852243
< [103,] 1982 0.174087562 -0.006879134 0.355054259 0.066278133 0.281896992
< [104,] 1983 0.187906404 -0.002699621 0.378512429 0.074354424 0.301458384
< [105,] 1984 0.201725246 0.000737403 0.402713088 0.081988382 0.321462109
< [106,] 1985 0.215544087 0.003540988 0.427547186 0.089244975 0.341843199
< [107,] 1986 0.229362929 0.005804749 0.452921108 0.096179971 0.362545886
< [108,] 1987 0.243181770 0.007608108 0.478755433 0.102840688 0.383522853
< [109,] 1988 0.257000612 0.009017980 0.504983244 0.109266987 0.404734237
< [110,] 1989 0.270819454 0.010090540 0.531548367 0.115492336 0.426146571
< [111,] 1990 0.284638295 0.010872901 0.558403689 0.121544800 0.447731790
< [112,] 1991 0.298457137 0.011404596 0.585509677 0.127447933 0.469466340
< [113,] 1992 0.312275978 0.011718869 0.612833087 0.133221539 0.491330418
---
> [1,] 1880 -0.257692308 -3.867500e-01 -0.128634653 -0.340734568 -0.174650048
> [2,] 1881 -0.250769231 -3.767293e-01 -0.124809149 -0.331818355 -0.169720107
> [3,] 1882 -0.243846154 -3.667351e-01 -0.120957249 -0.322919126 -0.164773181
> [4,] 1883 -0.236923077 -3.567692e-01 -0.117076923 -0.314038189 -0.159807965
> [5,] 1884 -0.230000000 -3.468340e-01 -0.113165951 -0.305176970 -0.154823030
> [6,] 1885 -0.223076923 -3.369319e-01 -0.109221900 -0.296337036 -0.149816810
> [7,] 1886 -0.216153846 -3.270656e-01 -0.105242105 -0.287520102 -0.144787590
> [8,] 1887 -0.209230769 -3.172379e-01 -0.101223643 -0.278728048 -0.139733491
> [9,] 1888 -0.202307692 -3.074521e-01 -0.097163311 -0.269962936 -0.134652449
> [10,] 1889 -0.195384615 -2.977116e-01 -0.093057593 -0.261227027 -0.129542204
> [11,] 1890 -0.188461539 -2.880204e-01 -0.088902637 -0.252522800 -0.124400277
> [12,] 1891 -0.181538462 -2.783827e-01 -0.084694220 -0.243852973 -0.119223950
> [13,] 1892 -0.174615385 -2.688030e-01 -0.080427720 -0.235220519 -0.114010250
> [14,] 1893 -0.167692308 -2.592865e-01 -0.076098083 -0.226628691 -0.108755924
> [15,] 1894 -0.160769231 -2.498387e-01 -0.071699793 -0.218081038 -0.103457424
> [16,] 1895 -0.153846154 -2.404655e-01 -0.067226847 -0.209581422 -0.098110886
> [17,] 1896 -0.146923077 -2.311734e-01 -0.062672732 -0.201134035 -0.092712119
> [18,] 1897 -0.140000000 -2.219696e-01 -0.058030409 -0.192743405 -0.087256595
> [19,] 1898 -0.133076923 -2.128615e-01 -0.053292314 -0.184414399 -0.081739447
> [20,] 1899 -0.126153846 -2.038573e-01 -0.048450366 -0.176152218 -0.076155475
> [21,] 1900 -0.119230769 -1.949655e-01 -0.043496005 -0.167962369 -0.070499170
> [22,] 1901 -0.112307692 -1.861951e-01 -0.038420244 -0.159850635 -0.064764750
> [23,] 1902 -0.105384615 -1.775555e-01 -0.033213760 -0.151823015 -0.058946216
> [24,] 1903 -0.098461539 -1.690561e-01 -0.027867017 -0.143885645 -0.053037432
> [25,] 1904 -0.091538462 -1.607065e-01 -0.022370423 -0.136044696 -0.047032227
> [26,] 1905 -0.084615385 -1.525162e-01 -0.016714535 -0.128306245 -0.040924524
> [27,] 1906 -0.077692308 -1.444943e-01 -0.010890287 -0.120676126 -0.034708490
> [28,] 1907 -0.070769231 -1.366492e-01 -0.004889253 -0.113159760 -0.028378702
> [29,] 1908 -0.063846154 -1.289884e-01 0.001296074 -0.105761977 -0.021930331
> [30,] 1909 -0.056923077 -1.215182e-01 0.007672008 -0.098486840 -0.015359314
> [31,] 1910 -0.050000000 -1.142434e-01 0.014243419 -0.091337484 -0.008662516
> [32,] 1911 -0.043076923 -1.071674e-01 0.021013527 -0.084315978 -0.001837868
> [33,] 1912 -0.036153846 -1.002914e-01 0.027983751 -0.077423239 0.005115546
> [34,] 1913 -0.029230769 -9.361519e-02 0.035153653 -0.070658982 0.012197443
> [35,] 1914 -0.022307692 -8.713634e-02 0.042520952 -0.064021740 0.019406355
> [36,] 1915 -0.015384615 -8.085086e-02 0.050081630 -0.057508928 0.026739697
> [37,] 1916 -0.008461538 -7.475318e-02 0.057830107 -0.051116955 0.034193878
> [38,] 1917 -0.001538462 -6.883640e-02 0.065759473 -0.044841376 0.041764453
> [39,] 1918 0.005384615 -6.309252e-02 0.073861755 -0.038677059 0.049446290
> [40,] 1919 0.012307692 -5.751281e-02 0.082128191 -0.032618368 0.057233753
> [41,] 1920 0.019230769 -5.208797e-02 0.090549507 -0.026659334 0.065120873
> [42,] 1921 0.026153846 -4.680847e-02 0.099116161 -0.020793819 0.073101511
> [43,] 1922 0.033076923 -4.166472e-02 0.107818567 -0.015015652 0.081169499
> [44,] 1923 0.040000000 -3.664727e-02 0.116647271 -0.009318753 0.089318753
> [45,] 1924 0.046923077 -3.174694e-02 0.125593095 -0.003697214 0.097543368
> [46,] 1925 0.053846154 -2.695494e-02 0.134647244 0.001854623 0.105837685
> [47,] 1926 0.060769231 -2.226292e-02 0.143801377 0.007342124 0.114196337
> [48,] 1927 0.067692308 -1.766304e-02 0.153047656 0.012770335 0.122614280
> [49,] 1928 0.074615385 -1.314799e-02 0.162378762 0.018143964 0.131086806
> [50,] 1929 0.081538462 -8.710982e-03 0.171787905 0.023467379 0.139609544
> [51,] 1930 0.088461538 -4.345738e-03 0.181268815 0.028744616 0.148178461
> [52,] 1931 0.095384615 -4.649065e-05 0.190815721 0.033979388 0.156789843
> [53,] 1932 0.102307692 4.192055e-03 0.200423329 0.039175101 0.165440284
> [54,] 1933 0.109230769 8.374747e-03 0.210086792 0.044334874 0.174126664
> [55,] 1934 0.116153846 1.250601e-02 0.219801679 0.049461559 0.182846134
> [56,] 1935 0.123076923 1.658990e-02 0.229563945 0.054557757 0.191596090
> [57,] 1936 0.130000000 2.063010e-02 0.239369902 0.059625842 0.200374158
> [58,] 1937 0.130000000 2.554264e-02 0.234457361 0.062786820 0.197213180
> [59,] 1938 0.130000000 3.023953e-02 0.229760466 0.065809042 0.194190958
> [60,] 1939 0.130000000 3.468890e-02 0.225311102 0.068671989 0.191328011
> [61,] 1940 0.130000000 3.885447e-02 0.221145527 0.071352331 0.188647669
> [62,] 1941 0.130000000 4.269563e-02 0.217304372 0.073823926 0.186176074
> [63,] 1942 0.130000000 4.616776e-02 0.213832244 0.076058070 0.183941930
> [64,] 1943 0.130000000 4.922326e-02 0.210776742 0.078024136 0.181975864
> [65,] 1944 0.130000000 5.181327e-02 0.208186727 0.079690683 0.180309317
> [66,] 1945 0.130000000 5.389026e-02 0.206109736 0.081027125 0.178972875
> [67,] 1946 0.130000000 5.541136e-02 0.204588637 0.082005877 0.177994123
> [68,] 1947 0.130000000 5.634212e-02 0.203657879 0.082604774 0.177395226
> [69,] 1948 0.130000000 5.666006e-02 0.203339939 0.082809352 0.177190648
> [70,] 1949 0.130000000 5.635724e-02 0.203642757 0.082614504 0.177385496
> [71,] 1950 0.130000000 5.544123e-02 0.204558768 0.082025096 0.177974904
> [72,] 1951 0.130000000 5.393418e-02 0.206065824 0.081055380 0.178944620
> [73,] 1952 0.130000000 5.187027e-02 0.208129729 0.079727358 0.180272642
> [74,] 1953 0.130000000 4.929223e-02 0.210707774 0.078068513 0.181931487
> [75,] 1954 0.130000000 4.624751e-02 0.213752495 0.076109385 0.183890615
> [76,] 1955 0.130000000 4.278497e-02 0.217215029 0.073881414 0.186118586
> [77,] 1956 0.130000000 3.895228e-02 0.221047722 0.071415265 0.188584735
> [78,] 1957 0.130000000 3.479412e-02 0.225205878 0.068739695 0.191260305
> [79,] 1958 0.130000000 3.035124e-02 0.229648764 0.065880916 0.194119084
> [80,] 1959 0.130000000 2.565999e-02 0.234340014 0.062862328 0.197137672
> [81,] 1960 0.130000000 2.075236e-02 0.239247637 0.059704514 0.200295486
> [82,] 1961 0.130000000 1.565622e-02 0.244343776 0.056425398 0.203574602
> [83,] 1962 0.130000000 1.039566e-02 0.249604337 0.053040486 0.206959514
> [84,] 1963 0.130000000 4.991436e-03 0.255008564 0.049563131 0.210436869
> [85,] 1964 0.130000000 -5.386147e-04 0.260538615 0.046004815 0.213995185
> [86,] 1965 0.143076923 1.926909e-02 0.266884757 0.063412665 0.222741181
> [87,] 1966 0.156153846 3.876772e-02 0.273539971 0.080621643 0.231686050
> [88,] 1967 0.169230769 5.790379e-02 0.280557753 0.097597325 0.240864213
> [89,] 1968 0.182307692 7.661491e-02 0.288000479 0.114299577 0.250315807
> [90,] 1969 0.195384615 9.482963e-02 0.295939602 0.130682422 0.260086809
> [91,] 1970 0.208461538 1.124682e-01 0.304454863 0.146694551 0.270228526
> [92,] 1971 0.221538461 1.294450e-01 0.313631914 0.162280850 0.280796073
> [93,] 1972 0.234615385 1.456729e-01 0.323557850 0.177385278 0.291845491
> [94,] 1973 0.247692308 1.610702e-01 0.334314435 0.191955225 0.303429390
> [95,] 1974 0.260769231 1.755689e-01 0.345969561 0.205947004 0.315591457
> [96,] 1975 0.273846154 1.891238e-01 0.358568478 0.219331501 0.328360807
> [97,] 1976 0.286923077 2.017191e-01 0.372127073 0.232098492 0.341747662
> [98,] 1977 0.300000000 2.133707e-01 0.386629338 0.244258277 0.355741722
> [99,] 1978 0.313076923 2.241239e-01 0.402029922 0.255840039 0.370313807
> [100,] 1979 0.326153846 2.340468e-01 0.418260863 0.266887506 0.385420186
> [101,] 1980 0.339230769 2.432212e-01 0.435240360 0.277453314 0.401008224
> [102,] 1981 0.352307692 2.517341e-01 0.452881314 0.287593508 0.417021876
> [103,] 1982 0.365384615 2.596711e-01 0.471098085 0.297363192 0.433406039
> [104,] 1983 0.378461538 2.671121e-01 0.489810964 0.306813654 0.450109423
> [105,] 1984 0.391538461 2.741284e-01 0.508948530 0.315990851 0.467086072
> [106,] 1985 0.404615384 2.807823e-01 0.528448443 0.324934896 0.484295873
> [107,] 1986 0.417692308 2.871274e-01 0.548257238 0.333680190 0.501704425
> [108,] 1987 0.430769231 2.932089e-01 0.568329576 0.342255907 0.519282554
> [109,] 1988 0.443846154 2.990650e-01 0.588627259 0.350686626 0.537005682
> [110,] 1989 0.456923077 3.047279e-01 0.609118218 0.358992981 0.554853173
> [111,] 1990 0.470000000 3.102244e-01 0.629775550 0.367192284 0.572807716
> [112,] 1991 0.483076923 3.155772e-01 0.650576667 0.375299067 0.590854778
> [113,] 1992 0.496153846 3.208051e-01 0.671502569 0.383325558 0.608982134
478,480d444
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
490,492d453
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
496,499d456
<
< **** ERROR in algorithm: ifl = 22
<
<
502,503c459,460
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> coef[1:5]: -0.40655906, -0.31473700, 0.05651823, -0.05681818, 0.28681956
> R^2 = 72.56% ; empirical tau (over all): 54/113 = 0.4778761 (target tau= 0.5)
509,512d465
<
< **** ERROR in algorithm: ifl = 22
<
<
515,517d467
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
522,525d471
<
< **** ERROR in algorithm: ifl = 22
<
<
528,530d473
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
532,534c475
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 68 74 78 79 102 111
536,539c477
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 38 39 50 54 77 85 97 113
Running ‘wind.R’ [6s/7s]
Running the tests in ‘tests/ex1.R’ failed.
Complete output:
> #### OOps! Running this in 'CMD check' or in *R* __for the first time__
> #### ===== gives a wrong result (at the end) than when run a 2nd time
> ####-- problem disappears with introduction of if (psw) call ... in Fortran
>
> suppressMessages(library(cobs))
> options(digits = 6)
> if(!dev.interactive(orNone=TRUE)) pdf("ex1.pdf")
>
> source(system.file("util.R", package = "cobs"))
>
> ## Simple example from example(cobs)
> set.seed(908)
> x <- seq(-1,1, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> ## specify constraints (boundary conditions)
> con <- rbind(c( 1,min(x),0),
+ c(-1,max(x),1),
+ c( 0, 0, 0.5))
> ## obtain the median *regression* B-spline using automatically selected knots
> coR <- cobs(x,y,constraint = "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning message:
In cobs(x, y, constraint = "increase", pointwise = con) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
> summaryCobs(coR)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", pointwise = con)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : chr "AIC"
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:50] -1 -0.959 -0.918 -0.878 -0.837 ...
$ y : num [1:50] 0.2254 0.0916 0.0803 -0.0272 -0.0454 ...
$ resid : num [1:50] 0.148 0.019 0.0105 -0.0962 -0.1156 ...
$ fitted : num [1:50] 0.0774 0.0726 0.0698 0.069 0.0702 ...
$ coef : num [1:4] 0.0774 0.0226 0.8067 1.074
$ knots : num [1:3] -1 -0.224 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : num 0
$ icyc : int 1
$ ifl : int 21
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 -0.02569206 0.0153529 0.0773974 0.139442 0.180487
2 -0.02467377 0.0149258 0.0747853 0.134645 0.174244
3 -0.02343992 0.0148223 0.0726602 0.130498 0.168760
4 -0.02198644 0.0150449 0.0710223 0.127000 0.164031
5 -0.02030765 0.0155971 0.0698714 0.124146 0.160050
6 -0.01839614 0.0164832 0.0692075 0.121932 0.156811
7 -0.01624274 0.0177089 0.0690308 0.120353 0.154304
8 -0.01383648 0.0192806 0.0693410 0.119401 0.152519
9 -0.01116467 0.0212061 0.0701384 0.119071 0.151441
10 -0.00821304 0.0234939 0.0714227 0.119352 0.151059
11 -0.00496594 0.0261535 0.0731942 0.120235 0.151354
12 -0.00140661 0.0291949 0.0754527 0.121711 0.152312
13 0.00248257 0.0326287 0.0781983 0.123768 0.153914
14 0.00671972 0.0364659 0.0814309 0.126396 0.156142
15 0.01132316 0.0407175 0.0851506 0.129584 0.158978
16 0.01631107 0.0453944 0.0893573 0.133320 0.162404
17 0.02170124 0.0505073 0.0940511 0.137595 0.166401
18 0.02751079 0.0560665 0.0992320 0.142397 0.170953
19 0.03375595 0.0620819 0.1048999 0.147718 0.176044
20 0.04045190 0.0685624 0.1110549 0.153547 0.181658
21 0.04761262 0.0755166 0.1176969 0.159877 0.187781
22 0.05525079 0.0829521 0.1248260 0.166700 0.194401
23 0.06337769 0.0908757 0.1324422 0.174009 0.201507
24 0.07200318 0.0992932 0.1405454 0.181798 0.209088
25 0.08113560 0.1082098 0.1491357 0.190062 0.217136
26 0.09078179 0.1176295 0.1582130 0.198797 0.225644
27 0.10094701 0.1275555 0.1677774 0.207999 0.234608
28 0.11163490 0.1379900 0.1778288 0.217668 0.244023
29 0.12284746 0.1489342 0.1883674 0.227801 0.253887
30 0.13458491 0.1603882 0.1993929 0.238398 0.264201
31 0.14684569 0.1723511 0.2109056 0.249460 0.274965
32 0.15962625 0.1848207 0.2229052 0.260990 0.286184
33 0.17292100 0.1977938 0.2353920 0.272990 0.297863
34 0.18672210 0.2112655 0.2483658 0.285466 0.310009
35 0.20101931 0.2252297 0.2618267 0.298424 0.322634
36 0.21579978 0.2396787 0.2757746 0.311870 0.335749
37 0.23104789 0.2546031 0.2902096 0.325816 0.349371
38 0.24674505 0.2699916 0.3051316 0.340272 0.363518
39 0.26286963 0.2858313 0.3205407 0.355250 0.378212
40 0.27927345 0.3019880 0.3363239 0.370660 0.393374
41 0.29546082 0.3179864 0.3520365 0.386087 0.408612
42 0.31139379 0.3337855 0.3676333 0.401481 0.423873
43 0.32708550 0.3493933 0.3831143 0.416835 0.439143
44 0.34254943 0.3648179 0.3984794 0.432141 0.454409
45 0.35779910 0.3800674 0.4137287 0.447390 0.469658
46 0.37284780 0.3951499 0.4288622 0.462574 0.484877
47 0.38770842 0.4100730 0.4438798 0.477687 0.500051
48 0.40239320 0.4248442 0.4587815 0.492719 0.515170
49 0.41691367 0.4394703 0.4735674 0.507665 0.530221
50 0.43128050 0.4539579 0.4882375 0.522517 0.545195
51 0.44550348 0.4683128 0.5027918 0.537271 0.560080
52 0.45959144 0.4825403 0.5172301 0.551920 0.574869
53 0.47355229 0.4966451 0.5315527 0.566460 0.589553
54 0.48739298 0.5106315 0.5457594 0.580887 0.604126
55 0.50111956 0.5245032 0.5598503 0.595197 0.618581
56 0.51473718 0.5382631 0.5738253 0.609388 0.632913
57 0.52825014 0.5519139 0.5876845 0.623455 0.647119
58 0.54166189 0.5654577 0.6014278 0.637398 0.661194
59 0.55497510 0.5788960 0.6150553 0.651215 0.675136
60 0.56819166 0.5922301 0.6285670 0.664904 0.688942
61 0.58131273 0.6054605 0.6419628 0.678465 0.702613
62 0.59433873 0.6185876 0.6552428 0.691898 0.716147
63 0.60726940 0.6316113 0.6684069 0.705203 0.729544
64 0.62010376 0.6445308 0.6814552 0.718380 0.742807
65 0.63284018 0.6573453 0.6943876 0.731430 0.755935
66 0.64547632 0.6700533 0.7072042 0.744355 0.768932
67 0.65800921 0.6826530 0.7199050 0.757157 0.781801
68 0.67043520 0.6951423 0.7324899 0.769838 0.794545
69 0.68274995 0.7075185 0.7449590 0.782400 0.807168
70 0.69494850 0.7197786 0.7573122 0.794846 0.819676
71 0.70702523 0.7319193 0.7695496 0.807180 0.832074
72 0.71897385 0.7439368 0.7816712 0.819406 0.844369
73 0.73078747 0.7558269 0.7936769 0.831527 0.856566
74 0.74245861 0.7675851 0.8055668 0.843548 0.868675
75 0.75397921 0.7792066 0.8173408 0.855475 0.880702
76 0.76534070 0.7906862 0.8289990 0.867312 0.892657
77 0.77653408 0.8020185 0.8405413 0.879064 0.904549
78 0.78754996 0.8131979 0.8519678 0.890738 0.916386
79 0.79837866 0.8242185 0.8632785 0.902338 0.928178
80 0.80901036 0.8350744 0.8744733 0.913872 0.939936
81 0.81943516 0.8457597 0.8855523 0.925345 0.951669
82 0.82964324 0.8562684 0.8965154 0.936762 0.963388
83 0.83962502 0.8665947 0.9073627 0.948131 0.975100
84 0.84937122 0.8767332 0.9180941 0.959455 0.986817
85 0.85887309 0.8866785 0.9287098 0.970741 0.998546
86 0.86812243 0.8964257 0.9392095 0.981993 1.010297
87 0.87711179 0.9059703 0.9495934 0.993217 1.022075
88 0.88583447 0.9153083 0.9598615 1.004415 1.033889
89 0.89428462 0.9244361 0.9700138 1.015591 1.045743
90 0.90245726 0.9333508 0.9800502 1.026749 1.057643
91 0.91034831 0.9420499 0.9899707 1.037891 1.069593
92 0.91795453 0.9505315 0.9997754 1.049019 1.081596
93 0.92527350 0.9587940 1.0094643 1.060135 1.093655
94 0.93230358 0.9668366 1.0190373 1.071238 1.105771
95 0.93904380 0.9746586 1.0284945 1.082330 1.117945
96 0.94549385 0.9822598 1.0378359 1.093412 1.130178
97 0.95165390 0.9896403 1.0470614 1.104482 1.142469
98 0.95752462 0.9968006 1.0561710 1.115541 1.154817
99 0.96310704 1.0037413 1.0651648 1.126588 1.167223
100 0.96840246 1.0104631 1.0740428 1.137623 1.179683
knots :
[1] -1.00000 -0.22449 1.00000
coef :
[1] 0.0773974 0.0225871 0.8067413 1.0740429
> coR1 <- cobs(x,y,constraint = "increase", pointwise = con, degree = 1)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning message:
In cobs(x, y, constraint = "increase", pointwise = con, degree = 1) :
drqssbc2(): Not all flags are normal (== 1), ifl : 20
> summary(coR1)
COBS regression spline (degree = 1) from call:
cobs(x = x, y = y, constraint = "increase", degree = 1, pointwise = con)
**** ERROR in algorithm: ifl = 20
{tau=0.5}-quantile; dimensionality of fit: 3 from {3}
x$knots[1:3]: -1.000002, -0.632653, 1.000002
with 3 pointwise constraints
coef[1:3]: 0.0781509, 0.0820419, 1.1196697
R^2 = 94.72% ; empirical tau (over all): 25/50 = 0.5 (target tau= 0.5)
>
> ## compute the median *smoothing* B-spline using automatically chosen lambda
> coS <- cobs(x,y,constraint = "increase", pointwise = con,
+ lambda = -1, trace = 3)
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
loo.design2(): -> Xeq 51 x 22 (nz = 151 =^= 0.13%)
Xieq 62 x 22 (nz = 224 =^= 0.16%)
........................
Error in drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda, :
The problem is degenerate for the range of lambda specified.
Calls: cobs -> drqssbc2
In addition: Warning message:
In min(sol1["k", i.keep]) : no non-missing arguments to min; returning Inf
Execution halted
Running the tests in ‘tests/ex2-long.R’ failed.
Complete output:
> ####
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time()
Time (user system elapsed): 0.001 0 0.002
>
> options(digits = 5)
> if(!dev.interactive(orNone=TRUE)) pdf("ex2.pdf")
>
> set.seed(821)
> x <- round(sort(rnorm(200)), 3) # rounding -> multiple values
> sum(duplicated(x)) # 9
[1] 3
> y <- (fx <- exp(-x)) + rt(200,4)/4
> summaryCobs(cxy <- cobs(x,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0.72 -0.149 0 -0.195 0.545 ...
$ fitted : num [1:200] 11.98 8.39 6.67 6.07 5.87 ...
$ coef : num [1:5] 11.9769 3.5917 1.0544 0.0295 0.0295
$ knots : num [1:4] -2.557 -0.813 0.418 2.573
$ k0 : num 5
$ k : num 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0
$ icyc : int 11
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 11.4448128 11.6875576 11.976923 12.26629 12.50903
2 10.9843366 11.2126114 11.484728 11.75684 11.98512
3 10.5344633 10.7489871 11.004712 11.26044 11.47496
4 10.0951784 10.2966768 10.536874 10.77707 10.97857
5 9.6664684 9.8556730 10.081215 10.30676 10.49596
6 9.2483213 9.4259693 9.637736 9.84950 10.02715
7 8.8407282 9.0075609 9.206435 9.40531 9.57214
8 8.4436848 8.6004453 8.787313 8.97418 9.13094
9 8.0571928 8.2046236 8.380369 8.55612 8.70355
10 7.6812627 7.8201015 7.985605 8.15111 8.28995
11 7.3159159 7.4468904 7.603020 7.75915 7.89012
12 6.9611870 7.0850095 7.232613 7.38022 7.50404
13 6.6171269 6.7344861 6.874385 7.01428 7.13164
14 6.2838041 6.3953578 6.528336 6.66131 6.77287
15 5.9613061 6.0676719 6.194466 6.32126 6.42763
16 5.6497392 5.7514863 5.872775 5.99406 6.09581
17 5.3492272 5.4468683 5.563262 5.67966 5.77730
18 5.0599086 5.1538933 5.265928 5.37796 5.47195
19 4.7819325 4.8726424 4.980774 5.08891 5.17961
20 4.5154542 4.6031999 4.707798 4.81240 4.90014
21 4.2606295 4.3456507 4.447001 4.54835 4.63337
22 4.0176099 4.1000771 4.198383 4.29669 4.37916
23 3.7865383 3.8665567 3.961943 4.05733 4.13735
24 3.5675443 3.6451602 3.737683 3.83021 3.90782
25 3.3607413 3.4359491 3.525601 3.61525 3.69046
26 3.1662231 3.2389744 3.325698 3.41242 3.48517
27 2.9840608 3.0542750 3.137974 3.22167 3.29189
28 2.8142997 2.8818753 2.962429 3.04298 3.11056
29 2.6569546 2.7217833 2.799063 2.87634 2.94117
30 2.5120031 2.5739870 2.647875 2.72176 2.78375
31 2.3793776 2.4384496 2.508867 2.57928 2.63836
32 2.2589520 2.3151025 2.382037 2.44897 2.50512
33 2.1505256 2.2038366 2.267386 2.33094 2.38425
34 2.0538038 2.1044916 2.164914 2.22534 2.27602
35 1.9677723 2.0162522 2.074043 2.13183 2.18031
36 1.8846710 1.9316617 1.987677 2.04369 2.09068
37 1.8024456 1.8486425 1.903712 1.95878 2.00498
38 1.7213655 1.7673410 1.822146 1.87695 1.92293
39 1.6417290 1.6879196 1.742982 1.79804 1.84423
40 1.5638322 1.6105393 1.666217 1.72189 1.76860
41 1.4879462 1.5353474 1.591852 1.64836 1.69576
42 1.4143040 1.4624707 1.519888 1.57731 1.62547
43 1.3430975 1.3920136 1.450324 1.50864 1.55755
44 1.2744792 1.3240589 1.383161 1.44226 1.49184
45 1.2085658 1.2586702 1.318397 1.37812 1.42823
46 1.1454438 1.1958944 1.256034 1.31617 1.36662
47 1.0851730 1.1357641 1.196072 1.25638 1.30697
48 1.0277900 1.0782992 1.138509 1.19872 1.24923
49 0.9733099 1.0235079 1.083347 1.14319 1.19338
50 0.9217268 0.9713870 1.030585 1.08978 1.13944
51 0.8730129 0.9219214 0.980223 1.03852 1.08743
52 0.8271160 0.8750827 0.932262 0.98944 1.03741
53 0.7839554 0.8308269 0.886700 0.94257 0.98945
54 0.7434158 0.7890916 0.843540 0.89799 0.94366
55 0.7053406 0.7497913 0.802779 0.85577 0.90022
56 0.6695233 0.7128138 0.764419 0.81602 0.85931
57 0.6357022 0.6780170 0.728459 0.77890 0.82121
58 0.6035616 0.6452289 0.694899 0.74457 0.78624
59 0.5724566 0.6139693 0.663455 0.71294 0.75445
60 0.5410437 0.5829503 0.632905 0.68286 0.72477
61 0.5094333 0.5521679 0.603110 0.65405 0.69679
62 0.4778879 0.5217649 0.574069 0.62637 0.67025
63 0.4466418 0.4918689 0.545782 0.59970 0.64492
64 0.4158910 0.4625864 0.518250 0.57391 0.62061
65 0.3857918 0.4340022 0.491472 0.54894 0.59715
66 0.3564634 0.4061813 0.465448 0.52471 0.57443
67 0.3279928 0.3791711 0.440179 0.50119 0.55236
68 0.3004403 0.3530042 0.415663 0.47832 0.53089
69 0.2738429 0.3277009 0.391903 0.45610 0.50996
70 0.2482184 0.3032707 0.368896 0.43452 0.48957
71 0.2235676 0.2797141 0.346644 0.41357 0.46972
72 0.1998762 0.2570233 0.325146 0.39327 0.45042
73 0.1771158 0.2351830 0.304402 0.37362 0.43169
74 0.1552452 0.2141706 0.284413 0.35466 0.41358
75 0.1342101 0.1939567 0.265178 0.33640 0.39615
76 0.1139444 0.1745054 0.246697 0.31889 0.37945
77 0.0943704 0.1557743 0.228971 0.30217 0.36357
78 0.0753996 0.1377153 0.211999 0.28628 0.34860
79 0.0569347 0.1202755 0.195781 0.27129 0.33463
80 0.0388708 0.1033980 0.180318 0.25724 0.32177
81 0.0210989 0.0870233 0.165609 0.24419 0.31012
82 0.0035089 0.0710917 0.151654 0.23222 0.29980
83 -0.0140062 0.0555449 0.138454 0.22136 0.29091
84 -0.0315470 0.0403283 0.126008 0.21169 0.28356
85 -0.0492034 0.0253928 0.114316 0.20324 0.27783
86 -0.0670524 0.0106968 0.103378 0.19606 0.27381
87 -0.0851561 -0.0037936 0.093195 0.19018 0.27155
88 -0.1035613 -0.0181039 0.083766 0.18564 0.27109
89 -0.1223000 -0.0322515 0.075091 0.18243 0.27248
90 -0.1413914 -0.0462467 0.067171 0.18059 0.27573
91 -0.1608432 -0.0600938 0.060005 0.18010 0.28085
92 -0.1806546 -0.0737923 0.053594 0.18098 0.28784
93 -0.2008180 -0.0873382 0.047936 0.18321 0.29669
94 -0.2213213 -0.1007247 0.043033 0.18679 0.30739
95 -0.2421494 -0.1139438 0.038884 0.19171 0.31992
96 -0.2632855 -0.1269863 0.035490 0.19797 0.33427
97 -0.2847123 -0.1398427 0.032850 0.20554 0.35041
98 -0.3064126 -0.1525038 0.030964 0.21443 0.36834
99 -0.3283696 -0.1649603 0.029833 0.22463 0.38804
100 -0.3505674 -0.1772037 0.029456 0.23611 0.40948
knots :
[1] -2.557 -0.813 0.418 2.573
coef :
[1] 11.976924 3.591747 1.054378 0.029456 0.029456
> 1 - sum(cxy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 97.6%
[1] 0.95969
> showProc.time()
Time (user system elapsed): 0.445 0.013 0.716
>
> if(doExtra) {
+ ## Interpolation
+ cxyI <- cobs(x,y, "decrease", knots = unique(x))
+ ## takes quite long : 63 sec. (Pent. III, 700 MHz) --- this is because
+ ## each knot is added sequentially... {{improve!}}
+
+ summaryCobs(cxyI)# only 7 knots remaining!
+ showProc.time()
+ }
>
> summaryCobs(cxy1 <- cobs(x,y, "decrease", lambda = 0.1))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", lambda = 0.1)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 -0.315 0 -0.161 0.586 ...
$ fitted : num [1:200] 12.7 8.56 6.67 6.04 5.83 ...
$ coef : num [1:22] 12.7 5.78 3.16 2.43 2.11 ...
$ knots : num [1:20] -2.557 -1.34 -1.03 -0.901 -0.772 ...
$ k0 : int 15
$ k : int 15
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0.1
$ icyc : int 23
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0912847 12.4849933 12.6970034 12.90901 13.30272
2 11.5452819 11.9166521 12.1166331 12.31661 12.68798
3 11.0146966 11.3650966 11.5537853 11.74247 12.09287
4 10.4995535 10.8303355 11.0084599 11.18658 11.51737
5 9.9998870 10.3123808 10.4806571 10.64893 10.96143
6 9.5157430 9.8112485 9.9703768 10.12951 10.42501
7 9.0471805 9.3269594 9.4776191 9.62828 9.90806
8 8.5942728 8.8595392 9.0023838 9.14523 9.41049
9 8.1571088 8.4090188 8.5446710 8.68032 8.93223
10 7.7357927 7.9754347 8.1044808 8.23353 8.47317
11 7.3304438 7.5588289 7.6818131 7.80480 8.03318
12 6.9411951 7.1592477 7.2766679 7.39409 7.61214
13 6.5681906 6.7767415 6.8890452 7.00135 7.20990
14 6.2115819 6.4113636 6.5189450 6.62653 6.82631
15 5.8715240 6.0631680 6.1663674 6.26957 6.46121
16 5.5481704 5.7322086 5.8313123 5.93042 6.11445
17 5.2416676 5.4185366 5.5137796 5.60902 5.78589
18 4.9521494 5.1221988 5.2137695 5.30534 5.47539
19 4.6797308 4.8432355 4.9312819 5.01933 5.18283
20 4.4245017 4.5816781 4.6663169 4.75096 4.90813
21 4.1865199 4.3375470 4.4188743 4.50020 4.65123
22 3.9658032 4.1108482 4.1889542 4.26706 4.41211
23 3.7623206 3.9015710 3.9765567 4.05154 4.19079
24 3.5759813 3.7096836 3.7816817 3.85368 3.98738
25 3.4043771 3.5329043 3.6021155 3.67133 3.79985
26 3.2347309 3.3585931 3.4252922 3.49199 3.61585
27 3.0652721 3.1848437 3.2492325 3.31362 3.43319
28 2.8962030 3.0117271 3.0739363 3.13615 3.25167
29 2.7276530 2.8392885 2.8994037 2.95952 3.07115
30 2.5596612 2.6675415 2.7256346 2.78373 2.89161
31 2.3944947 2.4988186 2.5549966 2.61117 2.71550
32 2.2444821 2.3455939 2.4000421 2.45449 2.55560
33 2.1114672 2.2097080 2.2626102 2.31551 2.41375
34 1.9954176 2.0911496 2.1427009 2.19425 2.28998
35 1.8963846 1.9899366 2.0403140 2.09069 2.18424
36 1.8125024 1.9041996 1.9535781 2.00296 2.09465
37 1.7347658 1.8248332 1.8733340 1.92183 2.01190
38 1.6620975 1.7506630 1.7983550 1.84605 1.93461
39 1.5945123 1.6816941 1.7286411 1.77559 1.86277
40 1.5278221 1.6138190 1.6601279 1.70644 1.79243
41 1.4573347 1.5423451 1.5881227 1.63390 1.71891
42 1.3839943 1.4682138 1.5135655 1.55892 1.64314
43 1.3227219 1.4063482 1.4513806 1.49641 1.58004
44 1.2787473 1.3619265 1.4067181 1.45151 1.53469
45 1.2488624 1.3317463 1.3763789 1.42101 1.50390
46 1.2168724 1.2994789 1.3439621 1.38845 1.47105
47 1.1806389 1.2628708 1.3071522 1.35143 1.43367
48 1.1401892 1.2219316 1.2659495 1.30997 1.39171
49 1.0941843 1.1754044 1.2191410 1.26288 1.34410
50 1.0326549 1.1134412 1.1569442 1.20045 1.28123
51 0.9535058 1.0339215 1.0772249 1.12053 1.20094
52 0.8632281 0.9433870 0.9865521 1.02972 1.10988
53 0.7875624 0.8676441 0.9107678 0.95389 1.03397
54 0.7267897 0.8069673 0.8501425 0.89332 0.97350
55 0.6673925 0.7477244 0.7909827 0.83424 0.91457
56 0.6072642 0.6877460 0.7310850 0.77442 0.85491
57 0.5471548 0.6278279 0.6712700 0.71471 0.79539
58 0.4995140 0.5804770 0.6240752 0.66767 0.74864
59 0.4686435 0.5499607 0.5937495 0.63754 0.71886
60 0.4531016 0.5348803 0.5789177 0.62296 0.70473
61 0.4381911 0.5206110 0.5649937 0.60938 0.69180
62 0.4199957 0.5032331 0.5480561 0.59288 0.67612
63 0.4036491 0.4879280 0.5333117 0.57870 0.66297
64 0.3952493 0.4807890 0.5268517 0.57291 0.65845
65 0.3926229 0.4796600 0.5265291 0.57340 0.66044
66 0.3900185 0.4787485 0.5265291 0.57431 0.66304
67 0.3870480 0.4776752 0.5264774 0.57528 0.66591
68 0.3738545 0.4665585 0.5164792 0.56640 0.65910
69 0.3432056 0.4380737 0.4891596 0.54025 0.63511
70 0.2950830 0.3922142 0.4445189 0.49682 0.59395
71 0.2295290 0.3291123 0.3827373 0.43636 0.53595
72 0.1670195 0.2693294 0.3244228 0.37952 0.48183
73 0.1216565 0.2269375 0.2836308 0.34032 0.44561
74 0.0934100 0.2019260 0.2603613 0.31880 0.42731
75 0.0787462 0.1907702 0.2510947 0.31142 0.42344
76 0.0658428 0.1813823 0.2435998 0.30582 0.42136
77 0.0538230 0.1727768 0.2368329 0.30089 0.41984
78 0.0427388 0.1649719 0.2307938 0.29662 0.41885
79 0.0325663 0.1579592 0.2254827 0.29301 0.41840
80 0.0232151 0.1517072 0.2208995 0.29009 0.41858
81 0.0145359 0.1461634 0.2170442 0.28792 0.41955
82 0.0063272 0.1412575 0.2139168 0.28658 0.42151
83 -0.0016568 0.1369034 0.2115173 0.28613 0.42469
84 -0.0096967 0.1330028 0.2098457 0.28669 0.42939
85 -0.0180957 0.1294496 0.2089021 0.28835 0.43590
86 -0.0272134 0.1260791 0.2086264 0.29117 0.44447
87 -0.0387972 0.1210358 0.2071052 0.29317 0.45301
88 -0.0534279 0.1135207 0.2034217 0.29332 0.46027
89 -0.0709531 0.1035871 0.1975762 0.29157 0.46611
90 -0.0912981 0.0912612 0.1895684 0.28788 0.47043
91 -0.1144525 0.0765465 0.1793985 0.28225 0.47325
92 -0.1404576 0.0594287 0.1670665 0.27470 0.47459
93 -0.1693951 0.0398791 0.1525723 0.26527 0.47454
94 -0.2013769 0.0178586 0.1359159 0.25397 0.47321
95 -0.2365365 -0.0066795 0.1170974 0.24087 0.47073
96 -0.2750210 -0.0337868 0.0961167 0.22602 0.46725
97 -0.3169840 -0.0635170 0.0729738 0.20946 0.46293
98 -0.3625797 -0.0959240 0.0476688 0.19126 0.45792
99 -0.4119579 -0.1310604 0.0202016 0.17146 0.45236
100 -0.4652595 -0.1689754 -0.0094278 0.15012 0.44640
knots :
[1] -2.557 -1.340 -1.030 -0.901 -0.772 -0.586 -0.448 -0.305 -0.092 0.054
[11] 0.163 0.329 0.481 0.606 0.722 0.859 1.065 1.244 1.837 2.573
coef :
[1] 12.6970048 5.7788265 3.1620633 2.4291174 2.1069607 1.8462166
[7] 1.6371062 1.4304905 1.3348346 1.1758220 0.9413974 0.7863913
[13] 0.5998958 0.5697029 0.5265291 0.5265291 0.5265291 0.2707227
[19] 0.2086712 0.2086712 -0.0094278 6.5257497
> 1 - sum(cxy1 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.2%
[1] 0.96169
>
> summaryCobs(cxy2 <- cobs(x,y, "decrease", lambda = 1e-2))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", lambda = 0.01)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 -0.146 0.1468 -0.0463 0.6868 ...
$ fitted : num [1:200] 12.7 8.39 6.52 5.92 5.73 ...
$ coef : num [1:22] 12.7 5.34 3.59 2.19 2.13 ...
$ knots : num [1:20] -2.557 -1.34 -1.03 -0.901 -0.772 ...
$ k0 : int 21
$ k : int 21
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0.01
$ icyc : int 35
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0477594 12.4997491 12.6970071 12.89427 13.34625
2 11.4687308 11.8950752 12.0811411 12.26721 12.69355
3 10.9090823 11.3113523 11.4869116 11.66247 12.06474
4 10.3688404 10.7485883 10.9143185 11.08005 11.45980
5 9.8480420 10.2067945 10.3633618 10.51993 10.87868
6 9.3467363 9.6859859 9.8340417 9.98210 10.32135
7 8.8649866 9.1861815 9.3263579 9.46653 9.78773
8 8.4028715 8.7074055 8.8403106 8.97322 9.27775
9 7.9604861 8.2496865 8.3758998 8.50211 8.79131
10 7.5379421 7.8130586 7.9331254 8.05319 8.32831
11 7.1353676 7.3975607 7.5119874 7.62641 7.88861
12 6.7529050 7.0032361 7.1124859 7.22174 7.47207
13 6.3907086 6.6301316 6.7346209 6.83911 7.07853
14 6.0489410 6.2782966 6.3783923 6.47849 6.70784
15 5.7277684 5.9477816 6.0438001 6.13982 6.35983
16 5.4273551 5.6386366 5.7308444 5.82305 6.03433
17 5.1478583 5.3509094 5.4395252 5.52814 5.73119
18 4.8894214 5.0846433 5.1698424 5.25504 5.45026
19 4.6521676 4.8398760 4.9217960 5.00372 5.19142
20 4.4361933 4.6166367 4.6953861 4.77414 4.95458
21 4.2415605 4.4149443 4.4906127 4.56628 4.73966
22 4.0682883 4.2348044 4.3074756 4.38015 4.54666
23 3.9163432 4.0762071 4.1459751 4.21574 4.37561
24 3.7856282 3.9391227 4.0061110 4.07310 4.22659
25 3.6683774 3.8159306 3.8803259 3.94472 4.09227
26 3.5214653 3.6636629 3.7257209 3.78778 3.92998
27 3.3383583 3.4756303 3.5355387 3.59545 3.73272
28 3.1192735 3.2518988 3.3097793 3.36766 3.50028
29 2.8643493 2.9925103 3.0484425 3.10437 3.23254
30 2.5736278 2.6974778 2.7515286 2.80558 2.92943
31 2.2696062 2.3893733 2.4416422 2.49391 2.61368
32 2.0718959 2.1879754 2.2386350 2.28929 2.40537
33 1.9979346 2.1107181 2.1599392 2.20916 2.32194
34 1.9710324 2.0809358 2.1288999 2.17686 2.28677
35 1.9261503 2.0335510 2.0804229 2.12729 2.23470
36 1.8645775 1.9698487 2.0157914 2.06173 2.16701
37 1.7927585 1.8961587 1.9412848 1.98641 2.08981
38 1.7116948 1.8133707 1.8577443 1.90212 2.00379
39 1.6214021 1.7214896 1.7651699 1.80885 1.90894
40 1.5242004 1.6229275 1.6660141 1.70910 1.80783
41 1.4229217 1.5205162 1.5631086 1.60570 1.70330
42 1.3194940 1.4161806 1.4583766 1.50057 1.59726
43 1.2442053 1.3402109 1.3821098 1.42401 1.52001
44 1.2075941 1.3030864 1.3447613 1.38644 1.48193
45 1.2023778 1.2975311 1.3390581 1.38059 1.47574
46 1.1914924 1.2863272 1.3277152 1.36910 1.46394
47 1.1698641 1.2642688 1.3054691 1.34667 1.44107
48 1.1375221 1.2313649 1.2723199 1.31327 1.40712
49 1.0934278 1.1866710 1.2273643 1.26806 1.36130
50 1.0300956 1.1228408 1.1633168 1.20379 1.29654
51 0.9459780 1.0382977 1.0785880 1.11888 1.21120
52 0.8492712 0.9412961 0.9814577 1.02162 1.11364
53 0.7724392 0.8643755 0.9044985 0.94462 1.03656
54 0.7154255 0.8074718 0.8476428 0.88781 0.97986
55 0.6587891 0.7510125 0.7912608 0.83151 0.92373
56 0.5994755 0.6918710 0.7321944 0.77252 0.86491
57 0.5383570 0.6309722 0.6713915 0.71181 0.80443
58 0.4898228 0.5827709 0.6233354 0.66390 0.75685
59 0.4588380 0.5521926 0.5929345 0.63368 0.72703
60 0.4438719 0.5377564 0.5787296 0.61970 0.71359
61 0.4293281 0.5239487 0.5652432 0.60654 0.70116
62 0.4110511 0.5066103 0.5483143 0.59002 0.68558
63 0.3944126 0.4911673 0.5333932 0.57562 0.67237
64 0.3857958 0.4839980 0.5268556 0.56971 0.66792
65 0.3830000 0.4829213 0.5265291 0.57014 0.67006
66 0.3802084 0.4820731 0.5265291 0.57099 0.67285
67 0.3770181 0.4810608 0.5264673 0.57187 0.67592
68 0.3616408 0.4680678 0.5145149 0.56096 0.66739
69 0.3254129 0.4343244 0.4818557 0.52939 0.63830
70 0.2683149 0.3798245 0.4284897 0.47715 0.58866
71 0.1904294 0.3047541 0.3546478 0.40454 0.51887
72 0.1179556 0.2354105 0.2866704 0.33793 0.45539
73 0.0689088 0.1897746 0.2425231 0.29527 0.41614
74 0.0432569 0.1678366 0.2222059 0.27658 0.40115
75 0.0359906 0.1645977 0.2207246 0.27685 0.40546
76 0.0301934 0.1628364 0.2207246 0.27861 0.41126
77 0.0245630 0.1611257 0.2207246 0.28032 0.41689
78 0.0191553 0.1594827 0.2207246 0.28197 0.42229
79 0.0139446 0.1578996 0.2207246 0.28355 0.42750
80 0.0088340 0.1563468 0.2207246 0.28510 0.43262
81 0.0036634 0.1547759 0.2207246 0.28667 0.43779
82 -0.0017830 0.1531211 0.2207246 0.28833 0.44323
83 -0.0077688 0.1513025 0.2207246 0.29015 0.44922
84 -0.0145948 0.1492286 0.2207246 0.29222 0.45604
85 -0.0225859 0.1468007 0.2207246 0.29465 0.46404
86 -0.0321107 0.1438739 0.2206774 0.29748 0.47347
87 -0.0445016 0.1389916 0.2190720 0.29915 0.48265
88 -0.0601227 0.1315395 0.2151851 0.29883 0.49049
89 -0.0788103 0.1215673 0.2090164 0.29647 0.49684
90 -0.1004844 0.1090993 0.2005661 0.29203 0.50162
91 -0.1251339 0.0941388 0.1898342 0.28553 0.50480
92 -0.1528032 0.0766725 0.1768206 0.27697 0.50644
93 -0.1835797 0.0566736 0.1615253 0.26638 0.50663
94 -0.2175834 0.0341058 0.1439484 0.25379 0.50548
95 -0.2549574 0.0089256 0.1240898 0.23925 0.50314
96 -0.2958592 -0.0189149 0.1019496 0.22281 0.49976
97 -0.3404537 -0.0494657 0.0775277 0.20452 0.49551
98 -0.3889062 -0.0827771 0.0508241 0.18443 0.49055
99 -0.4413769 -0.1188979 0.0218389 0.16258 0.48505
100 -0.4980173 -0.1578738 -0.0094279 0.13902 0.47916
knots :
[1] -2.557 -1.340 -1.030 -0.901 -0.772 -0.586 -0.448 -0.305 -0.092 0.054
[11] 0.163 0.329 0.481 0.606 0.722 0.859 1.065 1.244 1.837 2.573
coef :
[1] 12.697009 5.337850 3.591398 2.187733 2.133993 1.936435 1.631856
[8] 1.340650 1.340650 1.185401 0.931750 0.789326 0.598245 0.570221
[15] 0.526529 0.526529 0.526529 0.220725 0.220725 0.220725 -0.009428
[22] 46.342964
> 1 - sum(cxy2 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.2% (tiny bit better)
[1] 0.96257
>
> summaryCobs(cxy3 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 60))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", nknots = 60, lambda = 1e-06)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 0 0 -0.382 0.309 ...
$ fitted : num [1:200] 12.7 8.24 6.67 6.26 6.11 ...
$ coef : num [1:62] 12.7 7.69 6.09 4.35 3.73 3.73 2.74 2.57 2.57 2.25 ...
$ knots : num [1:60] -2.56 -1.81 -1.73 -1.38 -1.23 ...
$ k0 : int 61
$ k : int 61
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 1e-06
$ icyc : int 46
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0247124 12.56890432 12.6970139 12.825123 13.36932
2 11.3797843 11.89599414 12.0175164 12.139039 12.65525
3 10.7668218 11.25721357 11.3726579 11.488102 11.97849
4 10.1860204 10.65259986 10.7624385 10.872277 11.33886
5 9.6375946 10.08219388 10.1868581 10.291522 10.73612
6 9.1217734 9.54603927 9.6459167 9.745794 10.17006
7 8.6387946 9.04418136 9.1396144 9.235048 9.64043
8 8.1888978 8.57666578 8.6679512 8.759237 9.14700
9 7.7723156 8.14353686 8.2309270 8.318317 8.68954
10 7.3892646 7.74483589 7.8285418 7.912248 8.26782
11 7.0399352 7.38059913 7.4607957 7.540992 7.88166
12 6.7244802 7.05085572 7.1276886 7.204521 7.53090
13 6.4430029 6.75562533 6.8292205 6.902816 7.21544
14 6.1955428 6.49491547 6.5653915 6.635868 6.93524
15 5.9820595 6.26871848 6.3362016 6.403685 6.69034
16 5.7696526 6.04428975 6.1089428 6.173596 6.44823
17 5.4339991 5.69759119 5.7596440 5.821697 6.08529
18 5.0454361 5.29908138 5.3587927 5.418504 5.67215
19 4.6993977 4.94405130 5.0016458 5.059240 5.30389
20 4.3963458 4.63268699 4.6883247 4.743962 4.98030
21 4.1365583 4.36504142 4.4188292 4.472617 4.70110
22 3.9202312 4.14115193 4.1931594 4.245167 4.46609
23 3.7474595 3.96103662 4.0113153 4.061594 4.27517
24 3.6182953 3.82478434 3.8733944 3.922005 4.12849
25 3.5335861 3.73343196 3.7804782 3.827524 4.02737
26 3.4937186 3.68729597 3.7328665 3.778437 3.97201
27 3.4752667 3.66292175 3.7070981 3.751274 3.93893
28 3.3043525 3.48641351 3.5292729 3.572132 3.75419
29 2.9458452 3.12249549 3.1640812 3.205667 3.38232
30 2.4899112 2.66132542 2.7016785 2.742031 2.91345
31 2.3652956 2.53186083 2.5710724 2.610284 2.77685
32 2.2382402 2.40029503 2.4384448 2.476594 2.63865
33 2.0486975 2.20653724 2.2436947 2.280852 2.43869
34 2.0511798 2.20522276 2.2414864 2.277750 2.43179
35 2.0553528 2.20601792 2.2414864 2.276955 2.42762
36 2.0385642 2.18623332 2.2209965 2.255760 2.40343
37 1.8391470 1.98414706 2.0182819 2.052417 2.19742
38 1.6312788 1.77395114 1.8075380 1.841125 1.98380
39 1.5314449 1.67192652 1.7049976 1.738069 1.87855
40 1.5208780 1.65927041 1.6918497 1.724429 1.86282
41 1.4986364 1.63513027 1.6672626 1.699395 1.83589
42 1.4498027 1.58470514 1.6164629 1.648221 1.78312
43 1.2247043 1.35830771 1.3897596 1.421211 1.55481
44 1.1772885 1.30980813 1.3410049 1.372202 1.50472
45 1.1781750 1.30997706 1.3410049 1.372033 1.50383
46 1.1786125 1.31005757 1.3410014 1.371945 1.50339
47 1.1644262 1.29555858 1.3264288 1.357299 1.48843
48 1.1223208 1.25286982 1.2836027 1.314336 1.44488
49 1.0583227 1.18805529 1.2185960 1.249137 1.37887
50 1.0360396 1.16504088 1.1954094 1.225778 1.35478
51 1.0366880 1.16516444 1.1954094 1.225654 1.35413
52 0.9728290 1.10089058 1.1310379 1.161185 1.28925
53 0.6458992 0.77387319 0.8039998 0.834127 0.96210
54 0.6278378 0.75589463 0.7860408 0.816187 0.94424
55 0.6233664 0.75144260 0.7815933 0.811744 0.93982
56 0.6203139 0.74853170 0.7787158 0.808900 0.93712
57 0.4831205 0.61171664 0.6419898 0.672263 0.80086
58 0.4152141 0.54435194 0.5747526 0.605153 0.73429
59 0.4143942 0.54419570 0.5747526 0.605309 0.73511
60 0.4133407 0.54399495 0.5747526 0.605510 0.73616
61 0.3912541 0.52305164 0.5540784 0.585105 0.71690
62 0.3615872 0.49479624 0.5261553 0.557514 0.69072
63 0.3595156 0.49440150 0.5261553 0.557909 0.69279
64 0.3572502 0.49396981 0.5261553 0.558341 0.69506
65 0.3545874 0.49346241 0.5261553 0.558848 0.69772
66 0.3515435 0.49288238 0.5261553 0.559428 0.70077
67 0.3482098 0.49224713 0.5261553 0.560063 0.70410
68 0.3447026 0.49157882 0.5261553 0.560732 0.70761
69 0.3265062 0.47651151 0.5118246 0.547138 0.69714
70 0.2579257 0.41132297 0.4474346 0.483546 0.63694
71 0.2081857 0.36515737 0.4021105 0.439064 0.59604
72 0.1349572 0.29569526 0.3335350 0.371375 0.53211
73 0.0020438 0.16674762 0.2055209 0.244294 0.40900
74 -0.0243664 0.14460810 0.1843868 0.224166 0.39314
75 -0.0362635 0.13720915 0.1780468 0.218884 0.39236
76 -0.0421115 0.13609478 0.1780468 0.219999 0.39820
77 -0.0482083 0.13493301 0.1780468 0.221161 0.40430
78 -0.0546034 0.13371440 0.1780468 0.222379 0.41070
79 -0.0610386 0.13248816 0.1780468 0.223605 0.41713
80 -0.0674722 0.13126221 0.1780468 0.224831 0.42357
81 -0.0740291 0.13001276 0.1780468 0.226081 0.43012
82 -0.0809567 0.12869267 0.1780468 0.227401 0.43705
83 -0.0885308 0.12724941 0.1780468 0.228844 0.44462
84 -0.0966886 0.12569491 0.1780468 0.230399 0.45278
85 -0.1053882 0.12403716 0.1780468 0.232056 0.46148
86 -0.1147206 0.12225885 0.1780468 0.233835 0.47081
87 -0.1248842 0.12032213 0.1780468 0.235771 0.48098
88 -0.1360096 0.11820215 0.1780468 0.237891 0.49210
89 -0.1480747 0.11590310 0.1780468 0.240190 0.50417
90 -0.1611528 0.11337745 0.1780053 0.242633 0.51716
91 -0.1772967 0.10838384 0.1756366 0.242889 0.52857
92 -0.1976403 0.09964452 0.1696291 0.239614 0.53690
93 -0.2221958 0.08715720 0.1599828 0.232808 0.54216
94 -0.2510614 0.07090314 0.1466976 0.222492 0.54446
95 -0.2844042 0.05085051 0.1297736 0.208697 0.54395
96 -0.3224450 0.02695723 0.1092109 0.191465 0.54087
97 -0.3654434 -0.00082617 0.0850093 0.170845 0.53546
98 -0.4136843 -0.03255395 0.0571689 0.146892 0.52802
99 -0.4674640 -0.06828261 0.0256897 0.119662 0.51884
100 -0.5270786 -0.10806856 -0.0094284 0.089212 0.50822
knots :
[1] -2.557 -1.812 -1.726 -1.384 -1.233 -1.082 -1.046 -1.009 -0.932 -0.902
[11] -0.877 -0.838 -0.813 -0.765 -0.707 -0.665 -0.568 -0.498 -0.460 -0.413
[21] -0.347 -0.333 -0.299 -0.274 -0.226 -0.089 -0.024 -0.011 0.063 0.094
[31] 0.118 0.136 0.231 0.285 0.328 0.392 0.460 0.473 0.517 0.551
[41] 0.602 0.623 0.692 0.715 0.742 0.787 0.812 0.892 0.934 0.988
[51] 1.070 1.162 1.178 1.276 1.402 1.655 1.877 1.988 2.047 2.573
coef :
[1] 12.6970155 7.6878537 6.0937652 4.3540061 3.7259911 3.7259911
[7] 2.7408131 2.5727608 2.5727608 2.2478639 2.2414864 2.2414864
[13] 2.2414864 2.2414864 2.2414864 1.9875889 1.6964374 1.6964374
[19] 1.6623718 1.6623718 1.3410049 1.3410049 1.3410049 1.3410049
[25] 1.3410049 1.3410049 1.1954094 1.1954094 1.1954094 1.1954094
[31] 0.9829296 0.8091342 0.7815933 0.7815933 0.7815933 0.5747526
[37] 0.5747526 0.5747526 0.5747526 0.5747526 0.5261553 0.5261553
[43] 0.5261553 0.5261553 0.5261553 0.5261553 0.5261553 0.5261553
[49] 0.5261553 0.5261553 0.4273578 0.3741431 0.2060752 0.1780468
[55] 0.1780468 0.1780468 0.1780468 0.1780468 0.1780468 0.1780468
[61] -0.0094285 432.6957871
> 1 - sum(cxy3 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.36%
[1] 0.96502
> showProc.time()
Time (user system elapsed): 0.156 0.008 0.2
>
> cpuTime(cxy4 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 100))# ~ 3 sec.
Time elapsed: 0.053
> 1 - sum(cxy4 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.443%
[1] 0.96603
>
> cpuTime(cxy5 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 150))# ~ 8.7 sec.
Time elapsed: 0.03
> 1 - sum(cxy5 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.4396%
[1] 0.96835
> showProc.time()
Time (user system elapsed): 0.408 0.004 0.513
>
>
> ## regularly spaced x :
> X <- seq(-1,1, len = 201)
> xx <- c(seq(-1.1, -1, len = 11), X,
+ seq( 1, 1.1, len = 11))
> y <- (fx <- exp(-X)) + rt(201,4)/4
> summaryCobs(cXy <- cobs(X,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = X, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:201] -1 -0.99 -0.98 -0.97 -0.96 -0.95 -0.94 -0.93 -0.92 -0.91 ...
$ y : num [1:201] 2.67 2.77 3.46 3.14 1.79 ...
$ resid : num [1:201] 0 0.125 0.84 0.555 -0.77 ...
$ fitted : num [1:201] 2.67 2.64 2.62 2.59 2.56 ...
$ coef : num [1:4] 2.672 1.556 0.7 0.356
$ knots : num [1:3] -1 -0.2 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 100
$ lambda : num 0
$ icyc : int 9
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 2.46750 2.55064 2.67153 2.79242 2.87556
2 2.42251 2.50122 2.61568 2.73013 2.80884
3 2.37783 2.45240 2.56081 2.66923 2.74379
4 2.33345 2.40414 2.50694 2.60973 2.68043
5 2.28933 2.35645 2.45404 2.55164 2.61876
6 2.24548 2.30932 2.40214 2.49496 2.55879
7 2.20189 2.26274 2.35122 2.43970 2.50055
8 2.15855 2.21672 2.30129 2.38586 2.44402
9 2.11547 2.17124 2.25234 2.33344 2.38922
10 2.07265 2.12633 2.20438 2.28244 2.33611
11 2.03013 2.08199 2.15741 2.23283 2.28470
12 1.98791 2.03824 2.11142 2.18461 2.23494
13 1.94605 1.99510 2.06642 2.13775 2.18680
14 1.90459 1.95260 2.02241 2.09222 2.14023
15 1.86359 1.91078 1.97938 2.04799 2.09517
16 1.82311 1.86966 1.93734 2.00502 2.05157
17 1.78322 1.82929 1.89629 1.96328 2.00936
18 1.74397 1.78971 1.85622 1.92273 1.96847
19 1.70544 1.75096 1.81714 1.88332 1.92883
20 1.66769 1.71307 1.77904 1.84502 1.89039
21 1.63079 1.67608 1.74193 1.80779 1.85308
22 1.59478 1.64002 1.70581 1.77160 1.81684
23 1.55972 1.60493 1.67067 1.73642 1.78163
24 1.52564 1.57083 1.63653 1.70222 1.74741
25 1.49260 1.53773 1.60336 1.66899 1.71412
26 1.46062 1.50567 1.57118 1.63670 1.68175
27 1.42972 1.47466 1.53999 1.60533 1.65026
28 1.39994 1.44470 1.50979 1.57488 1.61964
29 1.37128 1.41581 1.48057 1.54533 1.58987
30 1.34375 1.38800 1.45234 1.51668 1.56093
31 1.31736 1.36126 1.42510 1.48893 1.53283
32 1.29211 1.33560 1.39884 1.46207 1.50556
33 1.26800 1.31101 1.37357 1.43612 1.47914
34 1.24500 1.28749 1.34928 1.41107 1.45356
35 1.22310 1.26502 1.32598 1.38694 1.42886
36 1.20228 1.24360 1.30367 1.36374 1.40505
37 1.18250 1.22319 1.28234 1.34150 1.38218
38 1.16372 1.20377 1.26200 1.32023 1.36028
39 1.14589 1.18532 1.24265 1.29998 1.33941
40 1.12894 1.16779 1.22428 1.28077 1.31962
41 1.11271 1.15106 1.20683 1.26259 1.30094
42 1.09639 1.13439 1.18963 1.24488 1.28287
43 1.07982 1.11760 1.17253 1.22747 1.26525
44 1.06303 1.10072 1.15553 1.21034 1.24803
45 1.04607 1.08378 1.13862 1.19346 1.23117
46 1.02898 1.06681 1.12181 1.17681 1.21463
47 1.01180 1.04982 1.10509 1.16037 1.19838
48 0.99458 1.03284 1.08847 1.14411 1.18237
49 0.97734 1.01589 1.07195 1.12801 1.16656
50 0.96011 0.99899 1.05552 1.11205 1.15092
51 0.94294 0.98216 1.03919 1.09621 1.13543
52 0.92585 0.96541 1.02295 1.08049 1.12005
53 0.90885 0.94877 1.00681 1.06485 1.10477
54 0.89197 0.93223 0.99076 1.04930 1.08956
55 0.87523 0.91581 0.97482 1.03382 1.07440
56 0.85865 0.89952 0.95896 1.01840 1.05928
57 0.84223 0.88337 0.94321 1.00304 1.04419
58 0.82598 0.86736 0.92755 0.98773 1.02911
59 0.80991 0.85150 0.91198 0.97246 1.01405
60 0.79403 0.83579 0.89651 0.95723 0.99899
61 0.77834 0.82023 0.88114 0.94205 0.98394
62 0.76284 0.80482 0.86586 0.92690 0.96888
63 0.74753 0.78956 0.85068 0.91180 0.95383
64 0.73241 0.77446 0.83559 0.89673 0.93878
65 0.71747 0.75950 0.82060 0.88171 0.92374
66 0.70271 0.74468 0.80571 0.86674 0.90871
67 0.68812 0.73001 0.79091 0.85182 0.89371
68 0.67368 0.71546 0.77621 0.83696 0.87874
69 0.65939 0.70104 0.76161 0.82217 0.86382
70 0.64523 0.68674 0.74710 0.80745 0.84896
71 0.63118 0.67254 0.73268 0.79282 0.83419
72 0.61722 0.65844 0.71836 0.77829 0.81951
73 0.60333 0.64441 0.70414 0.76388 0.80495
74 0.58948 0.63045 0.69002 0.74958 0.79055
75 0.57565 0.61654 0.67599 0.73544 0.77632
76 0.56181 0.60266 0.66205 0.72145 0.76230
77 0.54792 0.58879 0.64821 0.70764 0.74851
78 0.53395 0.57491 0.63447 0.69403 0.73500
79 0.51986 0.56100 0.62083 0.68065 0.72179
80 0.50563 0.54705 0.60728 0.66750 0.70892
81 0.49121 0.53302 0.59382 0.65462 0.69643
82 0.47657 0.51891 0.58046 0.64202 0.68435
83 0.46169 0.50468 0.56720 0.62972 0.67271
84 0.44652 0.49033 0.55403 0.61774 0.66155
85 0.43105 0.47584 0.54096 0.60609 0.65087
86 0.41526 0.46119 0.52799 0.59478 0.64072
87 0.39912 0.44638 0.51511 0.58383 0.63109
88 0.38264 0.43141 0.50233 0.57324 0.62202
89 0.36579 0.41626 0.48964 0.56302 0.61349
90 0.34858 0.40093 0.47705 0.55317 0.60552
91 0.33101 0.38542 0.46455 0.54368 0.59810
92 0.31307 0.36975 0.45215 0.53456 0.59123
93 0.29478 0.35390 0.43985 0.52580 0.58492
94 0.27615 0.33788 0.42764 0.51741 0.57914
95 0.25717 0.32170 0.41553 0.50936 0.57389
96 0.23787 0.30536 0.40352 0.50167 0.56917
97 0.21824 0.28888 0.39160 0.49431 0.56495
98 0.19830 0.27225 0.37977 0.48730 0.56125
99 0.17806 0.25547 0.36804 0.48062 0.55803
100 0.15752 0.23857 0.35641 0.47426 0.55531
knots :
[1] -1.0 -0.2 1.0
coef :
[1] 2.67153 1.55592 0.70045 0.35641
> 1 - sum(cXy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 77.2%
[1] 0.77644
> showProc.time()
Time (user system elapsed): 0.108 0 0.258
>
> (cXy.9 <- cobs(X,y, "decrease", tau = 0.9))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.9)
{tau=0.9}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:5]: -1.0, -0.6, -0.2, 0.2, 1.0
> (cXy.1 <- cobs(X,y, "decrease", tau = 0.1))
qbsks2():
Performing general knot selection ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
Deleting unnecessary knots ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.1)
{tau=0.1}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:3]: -1.0, 0.6, 1.0
> (cXy.99<- cobs(X,y, "decrease", tau = 0.99))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.99)
{tau=0.99}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:3]: -1.0, -0.2, 1.0
> (cXy.01<- cobs(X,y, "decrease", tau = 0.01))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.01)
{tau=0.01}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:5]: -1.0, -0.6, -0.2, 0.2, 1.0
> plot(X,y, xlim = range(xx),
+ main = "cobs(*, \"decrease\"), N=201, tau = 50% (Med.), 1,10, 90,99%")
> lines(predict(cXy, xx), col = 2)
> lines(predict(cXy.1, xx), col = 3)
> lines(predict(cXy.9, xx), col = 3)
> lines(predict(cXy.01, xx), col = 4)
> lines(predict(cXy.99, xx), col = 4)
>
> showProc.time()
Time (user system elapsed): 0.5 0 0.686
>
> ## Interpolation
> cpuTime(cXyI <- cobs(X,y, "decrease", knots = unique(X)))
qbsks2():
Performing general knot selection ...
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cpuTime ... cobs -> qbsks2 -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
In addition: Warning message:
In cobs(X, y, "decrease", knots = unique(X)) :
The number of knots can't be equal to the number of unique x for degree = 2.
'cobs' has automatically deleted the middle knot.
Timing stopped at: 0.699 0.012 0.788
Execution halted
Running the tests in ‘tests/multi-constr.R’ failed.
Complete output:
> #### Examples which use the new feature of more than one 'constraint'.
>
> suppressMessages(library(cobs))
>
> ## do *not* show platform info here (as have *.Rout.save), but in 0_pt-ex.R
> options(digits = 6)
>
> if(!dev.interactive(orNone=TRUE)) pdf("multi-constr.pdf")
>
> source(system.file("util.R", package = "cobs"))
> source(system.file(package="Matrix", "test-tools-1.R", mustWork=TRUE))
Loading required package: tools
> ##--> tryCatch.W.E(), showProc.time(), assertError(), relErrV(), ...
> Lnx <- Sys.info()[["sysname"]] == "Linux"
> isMac <- Sys.info()[["sysname"]] == "Darwin"
> x86 <- (arch <- Sys.info()[["machine"]]) == "x86_64"
> noLdbl <- (.Machine$sizeof.longdouble <= 8) ## TRUE when --disable-long-double
> ## IGNORE_RDIFF_BEGIN
> Sys.info()
sysname
"Linux"
release
"6.10.11-amd64"
version
"#1 SMP PREEMPT_DYNAMIC Debian 6.10.11-1 (2024-09-22)"
nodename
"gimli2"
machine
"x86_64"
login
"hornik"
user
"hornik"
effective_user
"hornik"
> noLdbl
[1] FALSE
> ## IGNORE_RDIFF_END
>
>
> Rsq <- function(obj) {
+ stopifnot(inherits(obj, "cobs"), is.numeric(res <- obj$resid))
+ 1 - sum(res^2)/obj$SSy
+ }
> list_ <- function (...) `names<-`(list(...), vapply(sys.call()[-1L], as.character, ""))
> is.cobs <- function(x) inherits(x, "cobs")
>
> set.seed(908)
> x <- seq(-1,2, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> plot(x,y); lines(x, f.true, col="gray", lwd=2, lty=3)
>
> ## constraint on derivative at right end:
> (con <- rbind(c(2 , max(x), 0))) # f'(x_n) == 0
[,1] [,2] [,3]
[1,] 2 2 0
>
> ## Using 'trace = 3' --> 'trace = 2' inside drqssbc2()
>
> ## Regression splines (lambda = 0)
> c2 <- cobs(x,y, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
> c2i <- cobs(x,y, constraint = c("increase"), trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 2 x 3 (nz = 6 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 5 x 6 (nz = 15 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 6 x 7 (nz = 18 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
> c2c <- cobs(x,y, constraint = c("concave"), trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 1 x 3 (nz = 3 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 3 x 5 (nz = 9 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 4 x 6 (nz = 12 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 5 x 7 (nz = 15 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 1 x 3 (nz = 3 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
>
> c2IC <- cobs(x,y, constraint = c("inc", "concave"), trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 5 x 4 (nz = 15 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 7 x 5 (nz = 21 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 9 x 6 (nz = 27 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 11 x 7 (nz = 33 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
> ## here, it's the same as just "i":
> all.equal(fitted(c2i), fitted(c2IC))
[1] "Mean relative difference: 0.0808156"
>
> c1 <- cobs(x,y, degree = 1, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
> c1i <- cobs(x,y, degree = 1, constraint = c("increase"), trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 1 x 2 (nz = 2 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 2 x 3 (nz = 4 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 4 x 5 (nz = 8 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 5 x 6 (nz = 10 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 4 x 5 (nz = 8 =^= 0.4%)
> c1c <- cobs(x,y, degree = 1, constraint = c("concave"), trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 3 x 5 (nz = 9 =^= 0.6%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 4 x 6 (nz = 12 =^= 0.5%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
>
> plot(c1)
> lines(predict(c1i), col="forest green")
> all.equal(fitted(c1), fitted(c1i), tol = 1e-9)# but not 1e-10
[1] TRUE
>
> ## now gives warning (not error):
> c1IC <- cobs(x,y, degree = 1, constraint = c("inc", "concave"), trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 1 x 2 (nz = 2 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 12 =^= 0.6%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 7 x 5 (nz = 17 =^= 0.49%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 9 x 6 (nz = 22 =^= 0.41%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 1 x 2 (nz = 2 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
Warning messages:
1: In l1.design2(x, w, constraint, ptConstr, knots, pw, nrq = n, nl1, :
too few knots ==> nk <= 4; could not add constraint 'concave'
2: In l1.design2(x, w, constraint, ptConstr, knots, pw, nrq = n, nl1, :
too few knots ==> nk <= 4; could not add constraint 'concave'
>
> cp2 <- cobs(x,y, pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 2 x 3 (nz = 6 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 2 x 5 (nz = 6 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 2 x 6 (nz = 6 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 2 x 7 (nz = 6 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 2 x 5 (nz = 6 =^= 0.6%)
>
> ## Here, warning ".. 'ifl'.. " on *some* platforms (e.g. Windows 32bit) :
> r2i <- tryCatch.W.E( cobs(x,y, constraint = "increase", pointwise = con) )
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> cp2i <- r2i$value
> ## IGNORE_RDIFF_BEGIN
> r2i$warning
NULL
> ## IGNORE_RDIFF_END
> ## when plotting it, we see that it gave a trivial constant!!
> cp2c <- cobs(x,y, constraint = "concave", pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 4 x 4 (nz = 12 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 5 x 5 (nz = 15 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 6 x 6 (nz = 18 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 7 x 7 (nz = 21 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
>
> ## now gives warning (not error): but no warning on M1 mac -> IGNORE
> ## IGNORE_RDIFF_BEGIN
> cp2IC <- cobs(x,y, constraint = c("inc", "concave"), pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 5 x 3 (nz = 15 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 7 x 4 (nz = 21 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 9 x 5 (nz = 27 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 11 x 6 (nz = 33 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 13 x 7 (nz = 39 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 5 x 3 (nz = 15 =^= 1%)
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> qbsks2 -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Running the tests in ‘tests/wind.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time() # timing here (to be faster by default)
Time (user system elapsed): 0.002 0 0.002
>
> data(DublinWind)
> attach(DublinWind)##-> speed & day (instead of "wind.x" & "DUB.")
> iday <- sort.list(day)
>
> if(!dev.interactive(orNone=TRUE)) pdf("wind.pdf", width=10)
>
> stopifnot(identical(day,c(rep(c(rep(1:365,3),1:366),4),
+ rep(1:365,2))))
> co50.1 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 1)
> co50.2 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 2)
>
> showProc.time()
Time (user system elapsed): 0.437 0.009 0.453
>
> plot(day,speed, pch = ".", col = "gray20")
> lines(day[iday], fitted(co50.1)[iday], col="orange", lwd = 2)
> lines(day[iday], fitted(co50.2)[iday], col="sky blue", lwd = 2)
> rug(knots(co50.1), col=3, lwd=2)
>
> nknots <- 13
>
>
> if(doExtra) {
+ ## Compute the quadratic median smoothing B-spline using SIC
+ ## lambda selection
+ co.o50 <-
+ cobs(day, speed, knots.add = TRUE, constraint="periodic", nknots = nknots,
+ tau = .5, lambda = -1, method = "uniform")
+ summary(co.o50) # [does print]
+
+ showProc.time()
+
+ op <- par(mfrow = c(3,1), mgp = c(1.5, 0.6,0), mar=.1 + c(3,3:1))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o",
+ col=2, log = "x", main = "co.o50: periodic"))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o", ylim = robrng(pp.sic),
+ col=2, log = "x", main = "co.o50: periodic"))
+ of <- 0.64430538125795
+ with(co.o50, plot(pp.sic - of ~ pp.lambda, type ="o", ylim = c(6e-15, 8e-15),
+ ylab = paste("sic -",formatC(of, dig=14, small.m = "'")),
+ col=2, log = "x", main = "co.o50: periodic"))
+ par(op)
+ }
>
> showProc.time()
Time (user system elapsed): 0.034 0 0.038
>
> ## cobs99: Since SIC chooses a lambda that corresponds to the smoothest
> ## possible fit, rerun cobs with a larger lstart value
> ## (lstart <- log(.Machine$double.xmax)^3) # 3.57 e9
> ##
> co.o50. <-
+ cobs(day,speed, knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
The algorithm has converged. You might
plot() the returned object (which plots 'sic' against 'lambda')
to see if you have found the global minimum of the information criterion
so that you can determine if you need to adjust any or all of
'lambda.lo', 'lambda.hi' and 'lambda.length' and refit the model.
> summary(co.o50.)
COBS smoothing spline (degree = 2) from call:
cobs(x = day, y = speed, constraint = "periodic", nknots = 10, method = "quantile", tau = 0.5, lambda = -1, knots.add = TRUE)
{tau=0.5}-quantile; dimensionality of fit: 7 from {14,13,11,8,7,30}
x$knots[1:10]: 0.999635, 41.000000, 82.000000, ... , 366.000365
lambda = 101002.6, selected via SIC, out of 25 ones.
coef[1:12]: 1.121550e+01, 1.139573e+01, 1.089025e+01, 9.954427e+00, 8.148158e+00, ... , 5.373106e-04
R^2 = 8.22% ; empirical tau (over all): 3287/6574 = 0.5 (target tau= 0.5)
> summary(pc.5 <- predict(co.o50., interval = "both"))
z fit cb.lo cb.up
Min. : 0.9996 Min. : 7.212 Min. : 6.351 Min. : 7.951
1st Qu.: 92.2498 1st Qu.: 7.790 1st Qu.: 7.000 1st Qu.: 8.600
Median :183.5000 Median : 9.436 Median : 8.555 Median :10.326
Mean :183.5000 Mean : 9.314 Mean : 8.388 Mean :10.241
3rd Qu.:274.7502 3rd Qu.:10.798 3rd Qu.: 9.716 3rd Qu.:11.787
Max. :366.0004 Max. :11.290 Max. :10.347 Max. :13.416
ci.lo ci.up
Min. : 6.782 Min. : 7.598
1st Qu.: 7.370 1st Qu.: 8.213
Median : 8.974 Median : 9.901
Mean : 8.830 Mean : 9.798
3rd Qu.:10.197 3rd Qu.:11.311
Max. :10.797 Max. :12.366
>
> showProc.time()
Time (user system elapsed): 1.747 0.003 2.061
>
> if(doExtra) { ## + repeat.delete.add
+ co.o50.. <- cobs(day,speed, knots.add = TRUE, repeat.delete.add=TRUE,
+ constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
+ summary(co.o50..)
+ showProc.time()
+ }
>
> co.o9 <- ## Compute the .9 quantile smoothing B-spline
+ cobs(day,speed,knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .9,lambda = -1, method = "uniform")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Flavor: r-devel-linux-x86_64-debian-clang
Version: 1.3-8
Check: examples
Result: ERROR
Running examples in ‘cobs-Ex.R’ failed
The error most likely occurred in:
> ### Name: cobs-methods
> ### Title: Methods for COBS Objects
> ### Aliases: coef.cobs fitted.cobs knots.cobs print.cobs residuals.cobs
> ### summary.cobs
> ### Keywords: print
>
> ### ** Examples
>
> example(cobs)
cobs> x <- seq(-1,3,,150)
cobs> y <- (f.true <- pnorm(2*x)) + rnorm(150)/10
cobs> ## specify pointwise constraints (boundary conditions)
cobs> con <- rbind(c( 1,min(x),0), # f(min(x)) >= 0
cobs+ c(-1,max(x),1), # f(max(x)) <= 1
cobs+ c(0, 0, 0.5))# f(0) = 0.5
cobs> ## obtain the median REGRESSION B-spline using automatically selected knots
cobs> Rbs <- cobs(x,y, constraint= "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning in cobs(x, y, constraint = "increase", pointwise = con) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
cobs> Rbs
COBS regression spline (degree = 2) from call:
cobs(x = x, y = y, constraint = "increase", pointwise = con)
**** ERROR in algorithm: ifl = 21
{tau=0.5}-quantile; dimensionality of fit: 5 from {5}
x$knots[1:4]: -1.0000040, -0.2214765, 1.3892617, 3.0000040
cobs> plot(Rbs, lwd = 2.5)
cobs> lines(spline(x, f.true), col = "gray40")
cobs> lines(predict(cobs(x,y)), col = "blue")
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning in cobs(x, y) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
cobs> mtext("cobs(x,y) # completely unconstrained", 3, col= "blue")
cobs> ## compute the median SMOOTHING B-spline using automatically chosen lambda
cobs> Sbs <- cobs(x,y, constraint="increase", pointwise= con, lambda= -1)
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Warning in min(sol1["k", i.keep]) :
no non-missing arguments to min; returning Inf
Error in drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda, :
The problem is degenerate for the range of lambda specified.
Calls: example ... source -> withVisible -> eval -> eval -> cobs -> drqssbc2
Execution halted
Flavor: r-devel-linux-x86_64-fedora-clang
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’
Running ‘ex1.R’
Running ‘ex2-long.R’ [12s/16s]
Running ‘ex3.R’
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [7s/11s]
Comparing ‘multi-constr.Rout’ to ‘multi-constr.Rout.save’ ... OK
Running ‘roof.R’ [6s/12s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ... OK
Running ‘small-ex.R’
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
Running ‘spline-ex.R’
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’
Comparing ‘temp.Rout’ to ‘temp.Rout.save’ ...29,31d28
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 20
35,42c32,35
<
< **** ERROR in algorithm: ifl = 20
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.40707639, -0.31455702, 0.05463725, -0.05314932, 0.29190009
< R^2 = 72.54% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
52,54d44
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
58,65c48,51
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
72,75c58,61
< {tau=0.1}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.5515010, -0.4255000, -0.1700000, -0.1700000, 0.1300024
< empirical tau (over all): 11/113 = 0.09734513 (target tau= 0.1)
---
> {tau=0.1}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.5700016, -0.1700000, -0.1700000, 0.1300024
> empirical tau (over all): 12/113 = 0.1061947 (target tau= 0.1)
78,80d63
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
84,91c67,70
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.9}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.9)
---
> {tau=0.9}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.2576939, 0.1300000, 0.1300000, 0.4961568
> empirical tau (over all): 104/113 = 0.920354 (target tau= 0.9)
94,96c73
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 74 102 111
98c75
< [1] 5 8 25 38 39 77 85 86 92 95 97
---
> [1] 5 8 25 28 38 39 85 86 92 95 97 113
103,215c80,192
< [1,] 1880 -0.393247953 -0.568567598 -0.217928308 -0.497693198 -0.2888027083
< [2,] 1881 -0.389244486 -0.556686706 -0.221802266 -0.488996819 -0.2894921527
< [3,] 1882 -0.385241019 -0.544932639 -0.225549398 -0.480375996 -0.2901060418
< [4,] 1883 -0.381237552 -0.533324789 -0.229150314 -0.471842280 -0.2906328235
< [5,] 1884 -0.377234084 -0.521886218 -0.232581951 -0.463409410 -0.2910587589
< [6,] 1885 -0.373230617 -0.510644405 -0.235816829 -0.455093758 -0.2913674769
< [7,] 1886 -0.369227150 -0.499632120 -0.238822180 -0.446914845 -0.2915394558
< [8,] 1887 -0.365223683 -0.488888394 -0.241558972 -0.438895923 -0.2915514428
< [9,] 1888 -0.361220216 -0.478459556 -0.243980875 -0.431064594 -0.2913758376
< [10,] 1889 -0.357216749 -0.468400213 -0.246033284 -0.423453388 -0.2909801092
< [11,] 1890 -0.353213282 -0.458773976 -0.247652588 -0.416100202 -0.2903263615
< [12,] 1891 -0.349209814 -0.449653605 -0.248766024 -0.409048381 -0.2893712477
< [13,] 1892 -0.345206347 -0.441120098 -0.249292596 -0.402346180 -0.2880665146
< [14,] 1893 -0.341202880 -0.433260133 -0.249145628 -0.396045236 -0.2863605248
< [15,] 1894 -0.337199413 -0.426161346 -0.248237480 -0.390197757 -0.2842010691
< [16,] 1895 -0.333195946 -0.419905293 -0.246486599 -0.384852330 -0.2815395617
< [17,] 1896 -0.329192479 -0.414558712 -0.243826246 -0.380048714 -0.2783362437
< [18,] 1897 -0.325189012 -0.410164739 -0.240213284 -0.375812606 -0.2745654171
< [19,] 1898 -0.321185545 -0.406736420 -0.235634669 -0.372151779 -0.2702193101
< [20,] 1899 -0.317182077 -0.404254622 -0.230109533 -0.369054834 -0.2653093212
< [21,] 1900 -0.313178610 -0.402671075 -0.223686145 -0.366493014 -0.2598642062
< [22,] 1901 -0.309175143 -0.401915491 -0.216434795 -0.364424447 -0.2539258394
< [23,] 1902 -0.305171676 -0.401904507 -0.208438845 -0.362799469 -0.2475438831
< [24,] 1903 -0.301168209 -0.402550192 -0.199786225 -0.361565696 -0.2407707212
< [25,] 1904 -0.297164742 -0.403766666 -0.190562818 -0.360671966 -0.2336575172
< [26,] 1905 -0.293161275 -0.405474370 -0.180848179 -0.360070883 -0.2262516664
< [27,] 1906 -0.289157807 -0.407602268 -0.170713347 -0.359720126 -0.2185954887
< [28,] 1907 -0.285154340 -0.410088509 -0.160220171 -0.359582850 -0.2107258307
< [29,] 1908 -0.281150873 -0.412880143 -0.149421603 -0.359627508 -0.2026742377
< [30,] 1909 -0.268996808 -0.394836115 -0.143157501 -0.343964546 -0.1940290700
< [31,] 1910 -0.256842743 -0.376961386 -0.136724100 -0.328402442 -0.1852830438
< [32,] 1911 -0.244688678 -0.359281315 -0.130096042 -0.312956304 -0.1764210522
< [33,] 1912 -0.232534613 -0.341825431 -0.123243796 -0.297643724 -0.1674255025
< [34,] 1913 -0.220380548 -0.324627946 -0.116133151 -0.282485083 -0.1582760137
< [35,] 1914 -0.208226483 -0.307728160 -0.108724807 -0.267503793 -0.1489491732
< [36,] 1915 -0.196072418 -0.291170651 -0.100974185 -0.252726413 -0.1394184235
< [37,] 1916 -0.183918353 -0.275005075 -0.092831631 -0.238182523 -0.1296541835
< [38,] 1917 -0.171764288 -0.259285340 -0.084243236 -0.223904239 -0.1196243373
< [39,] 1918 -0.159610223 -0.244067933 -0.075152513 -0.209925213 -0.1092952334
< [40,] 1919 -0.147456158 -0.229409203 -0.065503113 -0.196279015 -0.0986333019
< [41,] 1920 -0.135302093 -0.215361603 -0.055242584 -0.182996891 -0.0876072953
< [42,] 1921 -0.123148028 -0.201969188 -0.044326869 -0.170105089 -0.0761909673
< [43,] 1922 -0.110993963 -0.189263062 -0.032724864 -0.157622139 -0.0643657877
< [44,] 1923 -0.098839898 -0.177257723 -0.020422074 -0.145556676 -0.0521231208
< [45,] 1924 -0.086685833 -0.165949224 -0.007422442 -0.133906350 -0.0394653164
< [46,] 1925 -0.074531768 -0.155315688 0.006252152 -0.122658128 -0.0264054087
< [47,] 1926 -0.062377703 -0.145320002 0.020564595 -0.111789900 -0.0129655072
< [48,] 1927 -0.050223638 -0.135913981 0.035466704 -0.101272959 0.0008256822
< [49,] 1928 -0.038069573 -0.127043003 0.050903856 -0.091074767 0.0149356198
< [50,] 1929 -0.025915508 -0.118650261 0.066819244 -0.081161479 0.0293304619
< [51,] 1930 -0.013761444 -0.110680090 0.083157203 -0.071499934 0.0439770474
< [52,] 1931 -0.001607379 -0.103080234 0.099865477 -0.062059002 0.0588442451
< [53,] 1932 0.010546686 -0.095803129 0.116896502 -0.052810346 0.0739037194
< [54,] 1933 0.022700751 -0.088806436 0.134207939 -0.043728744 0.0891302464
< [55,] 1934 0.034854816 -0.082053049 0.151762682 -0.034792088 0.1045017213
< [56,] 1935 0.047008881 -0.075510798 0.169528561 -0.025981216 0.1199989785
< [57,] 1936 0.059162946 -0.069151984 0.187477877 -0.017279624 0.1356055167
< [58,] 1937 0.054383856 -0.068135824 0.176903535 -0.018606241 0.1273739530
< [59,] 1938 0.049604765 -0.067303100 0.166512631 -0.020042139 0.1192516703
< [60,] 1939 0.044825675 -0.066681512 0.156332862 -0.021603820 0.1112551700
< [61,] 1940 0.040046585 -0.066303231 0.146396400 -0.023310448 0.1034036175
< [62,] 1941 0.035267494 -0.066205361 0.136740349 -0.025184129 0.0957191177
< [63,] 1942 0.030488404 -0.066430243 0.127407050 -0.027250087 0.0882268946
< [64,] 1943 0.025709313 -0.067025439 0.118444066 -0.029536657 0.0809552836
< [65,] 1944 0.020930223 -0.068043207 0.109903653 -0.032074970 0.0739354160
< [66,] 1945 0.016151132 -0.069539210 0.101841475 -0.034898188 0.0672004530
< [67,] 1946 0.011372042 -0.071570257 0.094314341 -0.038040154 0.0607842381
< [68,] 1947 0.006592951 -0.074190969 0.087376871 -0.041533408 0.0547193111
< [69,] 1948 0.001813861 -0.077449530 0.081077252 -0.045406656 0.0490343779
< [70,] 1949 -0.002965230 -0.081383054 0.075452595 -0.049682007 0.0437515481
< [71,] 1950 -0.007744320 -0.086013419 0.070524779 -0.054372496 0.0388838557
< [72,] 1951 -0.012523410 -0.091344570 0.066297749 -0.059480471 0.0344336506
< [73,] 1952 -0.017302501 -0.097362010 0.062757009 -0.064997299 0.0303922971
< [74,] 1953 -0.022081591 -0.104034636 0.059871454 -0.070904448 0.0267412650
< [75,] 1954 -0.026860682 -0.111318392 0.057597028 -0.077175672 0.0234543081
< [76,] 1955 -0.031639772 -0.119160824 0.055881280 -0.083779723 0.0205001786
< [77,] 1956 -0.036418863 -0.127505585 0.054667859 -0.090683032 0.0178453070
< [78,] 1957 -0.041197953 -0.136296186 0.053900280 -0.097851948 0.0154560415
< [79,] 1958 -0.045977044 -0.145478720 0.053524633 -0.105254354 0.0133002664
< [80,] 1959 -0.050756134 -0.155003532 0.053491263 -0.112860669 0.0113484004
< [81,] 1960 -0.055535225 -0.164826042 0.053755593 -0.120644335 0.0095738862
< [82,] 1961 -0.060314315 -0.174906951 0.054278321 -0.128581941 0.0079533109
< [83,] 1962 -0.065093405 -0.185212049 0.055025238 -0.136653105 0.0064662939
< [84,] 1963 -0.069872496 -0.195711803 0.055966811 -0.144840234 0.0050952422
< [85,] 1964 -0.074651586 -0.206380857 0.057077684 -0.153128222 0.0038250490
< [86,] 1965 -0.060832745 -0.185766914 0.064101424 -0.135261254 0.0135957648
< [87,] 1966 -0.047013903 -0.165458364 0.071430557 -0.117576222 0.0235484155
< [88,] 1967 -0.033195062 -0.145508157 0.079118034 -0.100104670 0.0337145466
< [89,] 1968 -0.019376220 -0.125978144 0.087225704 -0.082883444 0.0441310044
< [90,] 1969 -0.005557378 -0.106939362 0.095824605 -0.065954866 0.0548401092
< [91,] 1970 0.008261463 -0.088471368 0.104994294 -0.049366330 0.0658892560
< [92,] 1971 0.022080305 -0.070660043 0.114820653 -0.033168999 0.0773296085
< [93,] 1972 0.035899146 -0.053593318 0.125391611 -0.017415258 0.0892135504
< [94,] 1973 0.049717988 -0.037354556 0.136790532 -0.002154768 0.1015907442
< [95,] 1974 0.063536830 -0.022014046 0.149087705 0.012570595 0.1145030640
< [96,] 1975 0.077355671 -0.007620056 0.162331398 0.026732077 0.1279792657
< [97,] 1976 0.091174513 0.005808280 0.176540746 0.040318278 0.1420307479
< [98,] 1977 0.104993354 0.018284008 0.191702701 0.053336970 0.1566497385
< [99,] 1978 0.118812196 0.029850263 0.207774129 0.065813852 0.1718105399
< [100,] 1979 0.132631038 0.040573785 0.224688290 0.077788682 0.1874733929
< [101,] 1980 0.146449879 0.050536128 0.242363630 0.089310046 0.2035897119
< [102,] 1981 0.160268721 0.059824930 0.260712511 0.100430154 0.2201072876
< [103,] 1982 0.174087562 0.068526868 0.279648256 0.111200642 0.2369744825
< [104,] 1983 0.187906404 0.076722940 0.299089868 0.121669764 0.2541430435
< [105,] 1984 0.201725246 0.084485905 0.318964586 0.131880867 0.2715696238
< [106,] 1985 0.215544087 0.091879376 0.339208798 0.141871847 0.2892163274
< [107,] 1986 0.229362929 0.098957959 0.359767899 0.151675234 0.3070506231
< [108,] 1987 0.243181770 0.105767982 0.380595558 0.161318630 0.3250449108
< [109,] 1988 0.257000612 0.112348478 0.401652745 0.170825286 0.3431759375
< [110,] 1989 0.270819454 0.118732216 0.422906691 0.180214725 0.3614241817
< [111,] 1990 0.284638295 0.124946675 0.444329916 0.189503318 0.3797732721
< [112,] 1991 0.298457137 0.131014917 0.465899357 0.198704804 0.3982094699
< [113,] 1992 0.312275978 0.136956333 0.487595623 0.207830734 0.4167212231
---
> [1,] 1880 -0.470540541 -0.580395233 -0.360685849 -0.541226637 -0.399854444
> [2,] 1881 -0.462432432 -0.569650451 -0.355214414 -0.531421959 -0.393442906
> [3,] 1882 -0.454324324 -0.558928137 -0.349720511 -0.521631738 -0.387016910
> [4,] 1883 -0.446216216 -0.548230020 -0.344202412 -0.511857087 -0.380575346
> [5,] 1884 -0.438108108 -0.537557989 -0.338658227 -0.502099220 -0.374116996
> [6,] 1885 -0.430000000 -0.526914115 -0.333085885 -0.492359472 -0.367640528
> [7,] 1886 -0.421891892 -0.516300667 -0.327483116 -0.482639300 -0.361144484
> [8,] 1887 -0.413783784 -0.505720132 -0.321847435 -0.472940307 -0.354627261
> [9,] 1888 -0.405675676 -0.495175238 -0.316176113 -0.463264247 -0.348087105
> [10,] 1889 -0.397567568 -0.484668976 -0.310466159 -0.453613044 -0.341522091
> [11,] 1890 -0.389459459 -0.474204626 -0.304714293 -0.443988810 -0.334930108
> [12,] 1891 -0.381351351 -0.463785782 -0.298916920 -0.434393857 -0.328308845
> [13,] 1892 -0.373243243 -0.453416379 -0.293070107 -0.424830717 -0.321655770
> [14,] 1893 -0.365135135 -0.443100719 -0.287169552 -0.415302157 -0.314968113
> [15,] 1894 -0.357027027 -0.432843496 -0.281210558 -0.405811200 -0.308242854
> [16,] 1895 -0.348918919 -0.422649821 -0.275188017 -0.396361132 -0.301476706
> [17,] 1896 -0.340810811 -0.412525238 -0.269096384 -0.386955521 -0.294666101
> [18,] 1897 -0.332702703 -0.402475737 -0.262929668 -0.377598222 -0.287807183
> [19,] 1898 -0.324594595 -0.392507759 -0.256681430 -0.368293379 -0.280895810
> [20,] 1899 -0.316486486 -0.382628180 -0.250344793 -0.359045416 -0.273927557
> [21,] 1900 -0.308378378 -0.372844288 -0.243912468 -0.349859024 -0.266897733
> [22,] 1901 -0.300270270 -0.363163733 -0.237376807 -0.340739124 -0.259801417
> [23,] 1902 -0.292162162 -0.353594450 -0.230729874 -0.331690821 -0.252633503
> [24,] 1903 -0.284054054 -0.344144557 -0.223963551 -0.322719340 -0.245388768
> [25,] 1904 -0.275945946 -0.334822217 -0.217069675 -0.313829934 -0.238061958
> [26,] 1905 -0.267837838 -0.325635470 -0.210040206 -0.305027774 -0.230647901
> [27,] 1906 -0.259729730 -0.316592032 -0.202867427 -0.296317828 -0.223141632
> [28,] 1907 -0.251621622 -0.307699075 -0.195544168 -0.287704708 -0.215538535
> [29,] 1908 -0.243513514 -0.298962989 -0.188064038 -0.279192527 -0.207834500
> [30,] 1909 -0.235405405 -0.290389150 -0.180421661 -0.270784743 -0.200026067
> [31,] 1910 -0.227297297 -0.281981702 -0.172612893 -0.262484025 -0.192110570
> [32,] 1911 -0.219189189 -0.273743385 -0.164634993 -0.254292134 -0.184086245
> [33,] 1912 -0.211081081 -0.265675409 -0.156486753 -0.246209849 -0.175952313
> [34,] 1913 -0.202972973 -0.257777400 -0.148168546 -0.238236929 -0.167709017
> [35,] 1914 -0.194864865 -0.250047417 -0.139682313 -0.230372126 -0.159357604
> [36,] 1915 -0.186756757 -0.242482039 -0.131031475 -0.222613238 -0.150900276
> [37,] 1916 -0.178648649 -0.235076516 -0.122220781 -0.214957209 -0.142340088
> [38,] 1917 -0.170540541 -0.227824968 -0.113256113 -0.207400255 -0.133680826
> [39,] 1918 -0.162432432 -0.220720606 -0.104144259 -0.199938008 -0.124926856
> [40,] 1919 -0.154324324 -0.213755974 -0.094892674 -0.192565671 -0.116082978
> [41,] 1920 -0.146216216 -0.206923176 -0.085509256 -0.185278162 -0.107154270
> [42,] 1921 -0.138108108 -0.200214092 -0.076002124 -0.178070257 -0.098145959
> [43,] 1922 -0.130000000 -0.193620560 -0.066379440 -0.170936704 -0.089063296
> [44,] 1923 -0.121891892 -0.187134533 -0.056649251 -0.163872326 -0.079911458
> [45,] 1924 -0.113783784 -0.180748200 -0.046819367 -0.156872096 -0.070695472
> [46,] 1925 -0.105675676 -0.174454074 -0.036897277 -0.149931196 -0.061420156
> [47,] 1926 -0.097567568 -0.168245056 -0.026890080 -0.143045058 -0.052090077
> [48,] 1927 -0.089459459 -0.162114471 -0.016804448 -0.136209390 -0.042709529
> [49,] 1928 -0.081351351 -0.156056093 -0.006646610 -0.129420182 -0.033282521
> [50,] 1929 -0.073243243 -0.150064140 0.003577654 -0.122673716 -0.023812771
> [51,] 1930 -0.065135135 -0.144133276 0.013863006 -0.115966557 -0.014303713
> [52,] 1931 -0.057027027 -0.138258588 0.024204534 -0.109295545 -0.004758509
> [53,] 1932 -0.048918919 -0.132435569 0.034597732 -0.102657780 0.004819942
> [54,] 1933 -0.040810811 -0.126660095 0.045038473 -0.096050607 0.014428985
> [55,] 1934 -0.032702703 -0.120928393 0.055522988 -0.089471600 0.024066194
> [56,] 1935 -0.024594595 -0.115237021 0.066047832 -0.082918542 0.033729353
> [57,] 1936 -0.016486486 -0.109582838 0.076609865 -0.076389415 0.043416442
> [58,] 1937 -0.016486486 -0.105401253 0.072428280 -0.073698770 0.040725797
> [59,] 1938 -0.016486486 -0.101403226 0.068430253 -0.071126236 0.038153263
> [60,] 1939 -0.016486486 -0.097615899 0.064642926 -0.068689277 0.035716305
> [61,] 1940 -0.016486486 -0.094070136 0.061097163 -0.066407753 0.033434780
> [62,] 1941 -0.016486486 -0.090800520 0.057827547 -0.064303916 0.031330943
> [63,] 1942 -0.016486486 -0.087845022 0.054872049 -0.062402198 0.029429225
> [64,] 1943 -0.016486486 -0.085244160 0.052271187 -0.060728671 0.027755698
> [65,] 1944 -0.016486486 -0.083039523 0.050066550 -0.059310095 0.026337122
> [66,] 1945 -0.016486486 -0.081271575 0.048298602 -0.058172508 0.025199535
> [67,] 1946 -0.016486486 -0.079976806 0.047003833 -0.057339388 0.024366415
> [68,] 1947 -0.016486486 -0.079184539 0.046211566 -0.056829602 0.023856629
> [69,] 1948 -0.016486486 -0.078913907 0.045940934 -0.056655464 0.023682491
> [70,] 1949 -0.016486486 -0.079171667 0.046198694 -0.056821320 0.023848347
> [71,] 1950 -0.016486486 -0.079951382 0.046978409 -0.057323028 0.024350055
> [72,] 1951 -0.016486486 -0.081234197 0.048261224 -0.058148457 0.025175484
> [73,] 1952 -0.016486486 -0.082991006 0.050018033 -0.059278877 0.026305904
> [74,] 1953 -0.016486486 -0.085185454 0.052212481 -0.060690897 0.027717924
> [75,] 1954 -0.016486486 -0.087777140 0.054804167 -0.062358519 0.029385546
> [76,] 1955 -0.016486486 -0.090724471 0.057751498 -0.064254982 0.031282009
> [77,] 1956 -0.016486486 -0.093986883 0.061013910 -0.066354184 0.033381211
> [78,] 1957 -0.016486486 -0.097526332 0.064553359 -0.068631645 0.035658672
> [79,] 1958 -0.016486486 -0.101308145 0.068335172 -0.071065056 0.038092083
> [80,] 1959 -0.016486486 -0.105301366 0.072328393 -0.073634498 0.040661525
> [81,] 1960 -0.016486486 -0.109478765 0.076505793 -0.076322449 0.043349476
> [82,] 1961 -0.016486486 -0.113816631 0.080843658 -0.079113653 0.046140680
> [83,] 1962 -0.016486486 -0.118294454 0.085321481 -0.081994911 0.049021938
> [84,] 1963 -0.016486486 -0.122894566 0.089921593 -0.084954858 0.051981885
> [85,] 1964 -0.016486486 -0.127601781 0.094628808 -0.087983719 0.055010746
> [86,] 1965 -0.006054054 -0.111440065 0.099331957 -0.073864774 0.061756666
> [87,] 1966 0.004378378 -0.095541433 0.104298190 -0.059915111 0.068671868
> [88,] 1967 0.014810811 -0.079951422 0.109573043 -0.046164030 0.075785651
> [89,] 1968 0.025243243 -0.064723125 0.115209611 -0.032645694 0.083132181
> [90,] 1969 0.035675676 -0.049917365 0.121268716 -0.019399240 0.090750592
> [91,] 1970 0.046108108 -0.035602017 0.127818233 -0.006468342 0.098684559
> [92,] 1971 0.056540541 -0.021849988 0.134931069 0.006100087 0.106980994
> [93,] 1972 0.066972973 -0.008735416 0.142681362 0.018258345 0.115687601
> [94,] 1973 0.077405405 0.003672103 0.151138707 0.029961648 0.124849163
> [95,] 1974 0.087837838 0.015314778 0.160360898 0.041172812 0.134502863
> [96,] 1975 0.098270270 0.026154092 0.170386449 0.051867053 0.144673488
> [97,] 1976 0.108702703 0.036176523 0.181228883 0.062035669 0.155369736
> [98,] 1977 0.119135135 0.045395695 0.192874575 0.071687429 0.166582842
> [99,] 1978 0.129567568 0.053850212 0.205284923 0.080847170 0.178287965
> [100,] 1979 0.140000000 0.061597925 0.218402075 0.089552117 0.190447883
> [101,] 1980 0.150432432 0.068708461 0.232156404 0.097847072 0.203017792
> [102,] 1981 0.160864865 0.075255962 0.246473767 0.105779742 0.215949987
> [103,] 1982 0.171297297 0.081313324 0.261281271 0.113397031 0.229197563
> [104,] 1983 0.181729730 0.086948395 0.276511065 0.120742598 0.242716862
> [105,] 1984 0.192162162 0.092221970 0.292102355 0.127855559 0.256468766
> [106,] 1985 0.202594595 0.097187112 0.308002077 0.134770059 0.270419130
> [107,] 1986 0.213027027 0.101889333 0.324164721 0.141515381 0.284538673
> [108,] 1987 0.223459459 0.106367224 0.340551695 0.148116359 0.298802560
> [109,] 1988 0.233891892 0.110653299 0.357130484 0.154593913 0.313189871
> [110,] 1989 0.244324324 0.114774857 0.373873791 0.160965608 0.327683041
> [111,] 1990 0.254756757 0.118754798 0.390758715 0.167246179 0.342267335
> [112,] 1991 0.265189189 0.122612348 0.407766030 0.173447997 0.356930381
> [113,] 1992 0.275621622 0.126363680 0.424879564 0.179581470 0.371661774
218,330c195,307
< [1,] 1880 -0.551500000 -0.8692435 -0.233756532 -0.74079307 -0.362206927
< [2,] 1881 -0.547000000 -0.8504667 -0.243533314 -0.72778780 -0.366212204
< [3,] 1882 -0.542500000 -0.8319198 -0.253080242 -0.71491945 -0.370080546
< [4,] 1883 -0.538000000 -0.8136378 -0.262362171 -0.70220898 -0.373791017
< [5,] 1884 -0.533500000 -0.7956627 -0.271337305 -0.68968128 -0.377318719
< [6,] 1885 -0.529000000 -0.7780442 -0.279955841 -0.67736602 -0.380633979
< [7,] 1886 -0.524500000 -0.7608416 -0.288158389 -0.66529858 -0.383701418
< [8,] 1887 -0.520000000 -0.7441258 -0.295874209 -0.65352111 -0.386478893
< [9,] 1888 -0.515500000 -0.7279807 -0.303019336 -0.64208362 -0.388916382
< [10,] 1889 -0.511000000 -0.7125052 -0.309494803 -0.63104507 -0.390954927
< [11,] 1890 -0.506500000 -0.6978147 -0.315185325 -0.62047415 -0.392525847
< [12,] 1891 -0.502000000 -0.6840410 -0.319959029 -0.61044942 -0.393550580
< [13,] 1892 -0.497500000 -0.6713309 -0.323669122 -0.60105832 -0.393941676
< [14,] 1893 -0.493000000 -0.6598415 -0.326158511 -0.59239445 -0.393605547
< [15,] 1894 -0.488500000 -0.6497316 -0.327268365 -0.58455243 -0.392447572
< [16,] 1895 -0.484000000 -0.6411491 -0.326850877 -0.57762031 -0.390379695
< [17,] 1896 -0.479500000 -0.6342149 -0.324785091 -0.57167014 -0.387329858
< [18,] 1897 -0.475000000 -0.6290072 -0.320992831 -0.56674851 -0.383251488
< [19,] 1898 -0.470500000 -0.6255495 -0.315450451 -0.56286950 -0.378130499
< [20,] 1899 -0.466000000 -0.6238074 -0.308192629 -0.56001245 -0.371987550
< [21,] 1900 -0.461500000 -0.6236932 -0.299306846 -0.55812524 -0.364874755
< [22,] 1901 -0.457000000 -0.6250795 -0.288920492 -0.55713199 -0.356868008
< [23,] 1902 -0.452500000 -0.6278154 -0.277184649 -0.55694269 -0.348057313
< [24,] 1903 -0.448000000 -0.6317413 -0.264258680 -0.55746239 -0.338537611
< [25,] 1904 -0.443500000 -0.6367018 -0.250298234 -0.55859837 -0.328401628
< [26,] 1905 -0.439000000 -0.6425525 -0.235447498 -0.56026474 -0.317735261
< [27,] 1906 -0.434500000 -0.6491648 -0.219835216 -0.56238479 -0.306615211
< [28,] 1907 -0.430000000 -0.6564265 -0.203573485 -0.56489174 -0.295108256
< [29,] 1908 -0.425500000 -0.6642417 -0.186758271 -0.56772843 -0.283271568
< [30,] 1909 -0.416375000 -0.6444420 -0.188308043 -0.55224402 -0.280505976
< [31,] 1910 -0.407250000 -0.6249490 -0.189550984 -0.53694241 -0.277557591
< [32,] 1911 -0.398125000 -0.6058089 -0.190441134 -0.52185096 -0.274399035
< [33,] 1912 -0.389000000 -0.5870750 -0.190924973 -0.50700158 -0.270998423
< [34,] 1913 -0.379875000 -0.5688095 -0.190940499 -0.49243118 -0.267318816
< [35,] 1914 -0.370750000 -0.5510835 -0.190416485 -0.47818222 -0.263317783
< [36,] 1915 -0.361625000 -0.5339779 -0.189272139 -0.46430281 -0.258947192
< [37,] 1916 -0.352500000 -0.5175825 -0.187417468 -0.45084657 -0.254153431
< [38,] 1917 -0.343375000 -0.5019952 -0.184754769 -0.43787171 -0.248878295
< [39,] 1918 -0.334250000 -0.4873183 -0.181181668 -0.42543921 -0.243060793
< [40,] 1919 -0.325125000 -0.4736540 -0.176596039 -0.41360991 -0.236640086
< [41,] 1920 -0.316000000 -0.4610972 -0.170902819 -0.40244046 -0.229559541
< [42,] 1921 -0.306875000 -0.4497278 -0.164022164 -0.39197841 -0.221771591
< [43,] 1922 -0.297750000 -0.4396023 -0.155897699 -0.38225735 -0.213242652
< [44,] 1923 -0.288625000 -0.4307468 -0.146503154 -0.37329293 -0.203957073
< [45,] 1924 -0.279500000 -0.4231543 -0.135845678 -0.36508089 -0.193919112
< [46,] 1925 -0.270375000 -0.4167851 -0.123964922 -0.35759761 -0.183152393
< [47,] 1926 -0.261250000 -0.4115719 -0.110928148 -0.35080301 -0.171696986
< [48,] 1927 -0.252125000 -0.4074273 -0.096822686 -0.34464508 -0.159604916
< [49,] 1928 -0.243000000 -0.4042525 -0.081747527 -0.33906484 -0.146935158
< [50,] 1929 -0.233875000 -0.4019444 -0.065805632 -0.33400095 -0.133749048
< [51,] 1930 -0.224750000 -0.4004021 -0.049097883 -0.32939331 -0.120106687
< [52,] 1931 -0.215625000 -0.3995310 -0.031718987 -0.32518550 -0.106064496
< [53,] 1932 -0.206500000 -0.3992449 -0.013755146 -0.32132617 -0.091673830
< [54,] 1933 -0.197374999 -0.3994669 0.004716902 -0.31776960 -0.076980402
< [55,] 1934 -0.188249999 -0.4001299 0.023629911 -0.31447572 -0.062024276
< [56,] 1935 -0.179124999 -0.4011756 0.042925575 -0.31140981 -0.046840186
< [57,] 1936 -0.169999999 -0.4025537 0.062553694 -0.30854196 -0.031458039
< [58,] 1937 -0.169999999 -0.3920506 0.052050575 -0.30228481 -0.037715186
< [59,] 1938 -0.169999999 -0.3818799 0.041879911 -0.29622572 -0.043774276
< [60,] 1939 -0.169999999 -0.3720919 0.032091902 -0.29039460 -0.049605402
< [61,] 1940 -0.169999999 -0.3627449 0.022744854 -0.28482617 -0.055173829
< [62,] 1941 -0.169999999 -0.3539060 0.013906014 -0.27956050 -0.060439496
< [63,] 1942 -0.169999999 -0.3456521 0.005652118 -0.27464331 -0.065356687
< [64,] 1943 -0.169999999 -0.3380694 -0.001930632 -0.27012595 -0.069874048
< [65,] 1944 -0.169999999 -0.3312525 -0.008747527 -0.26606484 -0.073935158
< [66,] 1945 -0.169999999 -0.3253023 -0.014697685 -0.26252008 -0.077479916
< [67,] 1946 -0.169999999 -0.3203219 -0.019678148 -0.25955301 -0.080446986
< [68,] 1947 -0.169999999 -0.3164101 -0.023589921 -0.25722261 -0.082777393
< [69,] 1948 -0.169999999 -0.3136543 -0.026345677 -0.25558089 -0.084419112
< [70,] 1949 -0.169999999 -0.3121218 -0.027878154 -0.25466793 -0.085332072
< [71,] 1950 -0.169999999 -0.3118523 -0.028147699 -0.25450735 -0.085492652
< [72,] 1951 -0.169999999 -0.3128528 -0.027147163 -0.25510341 -0.084896591
< [73,] 1952 -0.169999999 -0.3150972 -0.024902819 -0.25644046 -0.083559541
< [74,] 1953 -0.169999999 -0.3185290 -0.021471038 -0.25848491 -0.081515086
< [75,] 1954 -0.169999999 -0.3230683 -0.016931668 -0.26118921 -0.078810793
< [76,] 1955 -0.169999999 -0.3286202 -0.011379769 -0.26449670 -0.075503294
< [77,] 1956 -0.169999999 -0.3350825 -0.004917467 -0.26834657 -0.071653431
< [78,] 1957 -0.169999999 -0.3423529 0.002352862 -0.27267781 -0.067322192
< [79,] 1958 -0.169999999 -0.3503335 0.010333515 -0.27743222 -0.062567783
< [80,] 1959 -0.169999999 -0.3589345 0.018934501 -0.28255618 -0.057443816
< [81,] 1960 -0.169999999 -0.3680750 0.028075027 -0.28800158 -0.051998422
< [82,] 1961 -0.169999999 -0.3776839 0.037683867 -0.29372596 -0.046274035
< [83,] 1962 -0.169999999 -0.3876990 0.047699017 -0.29969241 -0.040307591
< [84,] 1963 -0.169999999 -0.3980670 0.058066957 -0.30586902 -0.034130975
< [85,] 1964 -0.169999999 -0.4087417 0.068741729 -0.31222843 -0.027771567
< [86,] 1965 -0.159285714 -0.3857122 0.067140801 -0.29417746 -0.024393969
< [87,] 1966 -0.148571428 -0.3632362 0.066093356 -0.27645622 -0.020686639
< [88,] 1967 -0.137857142 -0.3414096 0.065695360 -0.25912188 -0.016592404
< [89,] 1968 -0.127142857 -0.3203446 0.066058909 -0.24224123 -0.012044485
< [90,] 1969 -0.116428571 -0.3001699 0.067312749 -0.22589096 -0.006966182
< [91,] 1970 -0.105714285 -0.2810296 0.069601066 -0.21015697 -0.001271599
< [92,] 1971 -0.095000000 -0.2630795 0.073079509 -0.19513199 0.005131993
< [93,] 1972 -0.084285714 -0.2464789 0.077907440 -0.18091096 0.012339531
< [94,] 1973 -0.073571428 -0.2313788 0.084235942 -0.16758388 0.020441022
< [95,] 1974 -0.062857142 -0.2179067 0.092192406 -0.15522664 0.029512358
< [96,] 1975 -0.052142857 -0.2061500 0.101864313 -0.14389137 0.039605655
< [97,] 1976 -0.041428571 -0.1961435 0.113286338 -0.13359871 0.050741570
< [98,] 1977 -0.030714285 -0.1878634 0.126434838 -0.12433459 0.062906020
< [99,] 1978 -0.020000000 -0.1812316 0.141231635 -0.11605243 0.076052428
< [100,] 1979 -0.009285714 -0.1761272 0.157555775 -0.10868017 0.090108739
< [101,] 1980 0.001428572 -0.1724023 0.175259450 -0.10212975 0.104986896
< [102,] 1981 0.012142857 -0.1698981 0.194183828 -0.09630656 0.120592277
< [103,] 1982 0.022857143 -0.1684575 0.214171819 -0.09111701 0.136831296
< [104,] 1983 0.033571429 -0.1679338 0.235076625 -0.08647364 0.153616502
< [105,] 1984 0.044285714 -0.1681949 0.256766379 -0.08229790 0.170869332
< [106,] 1985 0.055000000 -0.1691258 0.279125791 -0.07852111 0.188521107
< [107,] 1986 0.065714286 -0.1706273 0.302055897 -0.07508430 0.206512868
< [108,] 1987 0.076428572 -0.1726156 0.325472731 -0.07193745 0.224794593
< [109,] 1988 0.087142857 -0.1750198 0.349305552 -0.06903842 0.243324139
< [110,] 1989 0.097857143 -0.1777807 0.373494972 -0.06635184 0.262066125
< [111,] 1990 0.108571429 -0.1808483 0.397991187 -0.06384803 0.280990883
< [112,] 1991 0.119285714 -0.1841810 0.422752400 -0.06150208 0.300073511
< [113,] 1992 0.130000000 -0.1877435 0.447743468 -0.05929307 0.319293073
---
> [1,] 1880 -0.570000000 -0.7989007 -0.3410992837 -0.71728636 -0.422713636
> [2,] 1881 -0.562857143 -0.7862639 -0.3394503795 -0.70660842 -0.419105867
> [3,] 1882 -0.555714286 -0.7736739 -0.3377546582 -0.69596060 -0.415467975
> [4,] 1883 -0.548571429 -0.7611343 -0.3360085204 -0.68534522 -0.411797641
> [5,] 1884 -0.541428571 -0.7486491 -0.3342080272 -0.67476481 -0.408092333
> [6,] 1885 -0.534285714 -0.7362226 -0.3323488643 -0.66422216 -0.404349273
> [7,] 1886 -0.527142857 -0.7238594 -0.3304263043 -0.65372029 -0.400565421
> [8,] 1887 -0.520000000 -0.7115648 -0.3284351643 -0.64326256 -0.396737440
> [9,] 1888 -0.512857143 -0.6993445 -0.3263697605 -0.63285261 -0.392861675
> [10,] 1889 -0.505714286 -0.6872047 -0.3242238599 -0.62249446 -0.388934114
> [11,] 1890 -0.498571429 -0.6751522 -0.3219906288 -0.61219250 -0.384950360
> [12,] 1891 -0.491428571 -0.6631946 -0.3196625782 -0.60195155 -0.380905594
> [13,] 1892 -0.484285714 -0.6513399 -0.3172315093 -0.59177689 -0.376794541
> [14,] 1893 -0.477142857 -0.6395973 -0.3146884583 -0.58167428 -0.372611433
> [15,] 1894 -0.470000000 -0.6279764 -0.3120236430 -0.57165002 -0.368349976
> [16,] 1895 -0.462857143 -0.6164879 -0.3092264155 -0.56171097 -0.364003318
> [17,] 1896 -0.455714286 -0.6051433 -0.3062852230 -0.55186455 -0.359564026
> [18,] 1897 -0.448571429 -0.5939553 -0.3031875831 -0.54211879 -0.355024067
> [19,] 1898 -0.441428571 -0.5829371 -0.2999200783 -0.53248233 -0.350374809
> [20,] 1899 -0.434285714 -0.5721031 -0.2964683783 -0.52296440 -0.345607030
> [21,] 1900 -0.427142857 -0.5614684 -0.2928172976 -0.51357475 -0.340710959
> [22,] 1901 -0.420000000 -0.5510491 -0.2889508980 -0.50432366 -0.335676342
> [23,] 1902 -0.412857143 -0.5408616 -0.2848526441 -0.49522175 -0.330492537
> [24,] 1903 -0.405714286 -0.5309229 -0.2805056214 -0.48627991 -0.325148662
> [25,] 1904 -0.398571429 -0.5212500 -0.2758928205 -0.47750909 -0.319633772
> [26,] 1905 -0.391428571 -0.5118597 -0.2709974894 -0.46892006 -0.313937087
> [27,] 1906 -0.384285714 -0.5027679 -0.2658035488 -0.46052317 -0.308048262
> [28,] 1907 -0.377142857 -0.4939897 -0.2602960562 -0.45232803 -0.301957682
> [29,] 1908 -0.370000000 -0.4855383 -0.2544616963 -0.44434322 -0.295656778
> [30,] 1909 -0.362857143 -0.4774250 -0.2482892691 -0.43657594 -0.289138345
> [31,] 1910 -0.355714286 -0.4696584 -0.2417701364 -0.42903175 -0.282396824
> [32,] 1911 -0.348571429 -0.4622443 -0.2348985912 -0.42171431 -0.275428543
> [33,] 1912 -0.341428571 -0.4551850 -0.2276721117 -0.41462526 -0.268231879
> [34,] 1913 -0.334285714 -0.4484800 -0.2200914777 -0.40776409 -0.260807334
> [35,] 1914 -0.327142857 -0.4421250 -0.2121607344 -0.40112820 -0.253157511
> [36,] 1915 -0.320000000 -0.4361130 -0.2038870084 -0.39471301 -0.245286995
> [37,] 1916 -0.312857143 -0.4304341 -0.1952801960 -0.38851213 -0.237202155
> [38,] 1917 -0.305714286 -0.4250760 -0.1863525523 -0.38251770 -0.228910875
> [39,] 1918 -0.298571429 -0.4200246 -0.1771182205 -0.37672060 -0.220422257
> [40,] 1919 -0.291428571 -0.4152644 -0.1675927388 -0.37111085 -0.211746298
> [41,] 1920 -0.284285714 -0.4107789 -0.1577925583 -0.36567785 -0.202893584
> [42,] 1921 -0.277142857 -0.4065511 -0.1477346004 -0.36041071 -0.193875002
> [43,] 1922 -0.270000000 -0.4025641 -0.1374358695 -0.35529850 -0.184701495
> [44,] 1923 -0.262857143 -0.3988012 -0.1269131329 -0.35033043 -0.175383852
> [45,] 1924 -0.255714286 -0.3952459 -0.1161826679 -0.34549603 -0.165932545
> [46,] 1925 -0.248571429 -0.3918828 -0.1052600744 -0.34078524 -0.156357614
> [47,] 1926 -0.241428571 -0.3886970 -0.0941601449 -0.33618857 -0.146668575
> [48,] 1927 -0.234285714 -0.3856746 -0.0828967845 -0.33169705 -0.136874376
> [49,] 1928 -0.227142857 -0.3828027 -0.0714829715 -0.32730235 -0.126983369
> [50,] 1929 -0.220000000 -0.3800693 -0.0599307484 -0.32299670 -0.117003301
> [51,] 1930 -0.212857143 -0.3774630 -0.0482512378 -0.31877296 -0.106941331
> [52,] 1931 -0.205714286 -0.3749739 -0.0364546744 -0.31462453 -0.096804042
> [53,] 1932 -0.198571429 -0.3725924 -0.0245504487 -0.31054538 -0.086597478
> [54,] 1933 -0.191428571 -0.3703100 -0.0125471577 -0.30652997 -0.076327171
> [55,] 1934 -0.184285714 -0.3681188 -0.0004526588 -0.30257325 -0.065998175
> [56,] 1935 -0.177142857 -0.3660116 0.0117258745 -0.29867061 -0.055615108
> [57,] 1936 -0.170000000 -0.3639819 0.0239818977 -0.29481782 -0.045182180
> [58,] 1937 -0.170000000 -0.3552689 0.0152688616 -0.28921141 -0.050788591
> [59,] 1938 -0.170000000 -0.3469383 0.0069383006 -0.28385110 -0.056148897
> [60,] 1939 -0.170000000 -0.3390468 -0.0009532311 -0.27877329 -0.061226710
> [61,] 1940 -0.170000000 -0.3316586 -0.0083414258 -0.27401935 -0.065980650
> [62,] 1941 -0.170000000 -0.3248458 -0.0151542191 -0.26963565 -0.070364348
> [63,] 1942 -0.170000000 -0.3186875 -0.0213124962 -0.26567310 -0.074326897
> [64,] 1943 -0.170000000 -0.3132682 -0.0267318303 -0.26218603 -0.077813972
> [65,] 1944 -0.170000000 -0.3086744 -0.0313255619 -0.25923019 -0.080769813
> [66,] 1945 -0.170000000 -0.3049906 -0.0350093787 -0.25685983 -0.083140168
> [67,] 1946 -0.170000000 -0.3022928 -0.0377072467 -0.25512389 -0.084876113
> [68,] 1947 -0.170000000 -0.3006419 -0.0393580695 -0.25406166 -0.085938337
> [69,] 1948 -0.170000000 -0.3000780 -0.0399219767 -0.25369882 -0.086301183
> [70,] 1949 -0.170000000 -0.3006151 -0.0393848898 -0.25404441 -0.085955594
> [71,] 1950 -0.170000000 -0.3022398 -0.0377602233 -0.25508980 -0.084910201
> [72,] 1951 -0.170000000 -0.3049127 -0.0350872623 -0.25680972 -0.083190282
> [73,] 1952 -0.170000000 -0.3085733 -0.0314266558 -0.25916514 -0.080834862
> [74,] 1953 -0.170000000 -0.3131458 -0.0268541535 -0.26210732 -0.077892681
> [75,] 1954 -0.170000000 -0.3185461 -0.0214539408 -0.26558209 -0.074417909
> [76,] 1955 -0.170000000 -0.3246873 -0.0153126807 -0.26953369 -0.070466310
> [77,] 1956 -0.170000000 -0.3314851 -0.0085148970 -0.27390773 -0.066092271
> [78,] 1957 -0.170000000 -0.3388601 -0.0011398598 -0.27865320 -0.061346797
> [79,] 1958 -0.170000000 -0.3467402 0.0067401824 -0.28372362 -0.056276377
> [80,] 1959 -0.170000000 -0.3550607 0.0150607304 -0.28907749 -0.050922513
> [81,] 1960 -0.170000000 -0.3637650 0.0237650445 -0.29467829 -0.045321714
> [82,] 1961 -0.170000000 -0.3728037 0.0328037172 -0.30049423 -0.039505772
> [83,] 1962 -0.170000000 -0.3821340 0.0421340134 -0.30649781 -0.033502185
> [84,] 1963 -0.170000000 -0.3917191 0.0517191202 -0.31266536 -0.027334640
> [85,] 1964 -0.170000000 -0.4015274 0.0615273928 -0.31897650 -0.021023499
> [86,] 1965 -0.159285714 -0.3788752 0.0603037544 -0.30058075 -0.017990680
> [87,] 1966 -0.148571429 -0.3567712 0.0596282943 -0.28253772 -0.014605137
> [88,] 1967 -0.137857143 -0.3353102 0.0595958975 -0.26490847 -0.010805813
> [89,] 1968 -0.127142857 -0.3146029 0.0603171930 -0.24776419 -0.006521525
> [90,] 1969 -0.116428571 -0.2947761 0.0619189162 -0.23118642 -0.001670726
> [91,] 1970 -0.105714286 -0.2759711 0.0645424939 -0.21526616 0.003837587
> [92,] 1971 -0.095000000 -0.2583398 0.0683398431 -0.20010116 0.010101164
> [93,] 1972 -0.084285714 -0.2420369 0.0734654391 -0.18579083 0.017219402
> [94,] 1973 -0.073571429 -0.2272072 0.0800643002 -0.17242847 0.025285614
> [95,] 1974 -0.062857143 -0.2139711 0.0882568427 -0.16009157 0.034377282
> [96,] 1975 -0.052142857 -0.2024090 0.0981233226 -0.14883176 0.044546046
> [97,] 1976 -0.041428571 -0.1925491 0.1096919157 -0.13866718 0.055810037
> [98,] 1977 -0.030714286 -0.1843628 0.1229342326 -0.12957956 0.068150987
> [99,] 1978 -0.020000000 -0.1777698 0.1377698370 -0.12151714 0.081517138
> [100,] 1979 -0.009285714 -0.1726496 0.1540781875 -0.11440236 0.095830930
> [101,] 1980 0.001428571 -0.1688571 0.1717142023 -0.10814187 0.110999008
> [102,] 1981 0.012142857 -0.1662377 0.1905233955 -0.10263625 0.126921969
> [103,] 1982 0.022857143 -0.1646396 0.2103538775 -0.09778779 0.143502079
> [104,] 1983 0.033571429 -0.1639214 0.2310642722 -0.09350551 0.160648370
> [105,] 1984 0.044285714 -0.1639565 0.2525279044 -0.08970790 0.178279332
> [106,] 1985 0.055000000 -0.1646342 0.2746342071 -0.08632382 0.196323821
> [107,] 1986 0.065714286 -0.1658598 0.2972883534 -0.08329225 0.214720820
> [108,] 1987 0.076428571 -0.1675528 0.3204099260 -0.08056144 0.233418585
> [109,] 1988 0.087142857 -0.1696455 0.3439311798 -0.07808781 0.252373526
> [110,] 1989 0.097857143 -0.1720809 0.3677952332 -0.07583476 0.271549041
> [111,] 1990 0.108571429 -0.1748115 0.3919543697 -0.07377157 0.290914428
> [112,] 1991 0.119285714 -0.1777971 0.4163685288 -0.07187248 0.310443909
> [113,] 1992 0.130000000 -0.1810040 0.4410040109 -0.07011580 0.330115800
333,445c310,422
< [1,] 1880 -0.393247953 -0.693805062 -0.092690844 -0.572302393 -0.214193513
< [2,] 1881 -0.389244486 -0.676297026 -0.102191945 -0.560253689 -0.218235282
< [3,] 1882 -0.385241019 -0.659006413 -0.111475624 -0.548334514 -0.222147524
< [4,] 1883 -0.381237552 -0.641966465 -0.120508639 -0.536564669 -0.225910434
< [5,] 1884 -0.377234084 -0.625216717 -0.129251452 -0.524967709 -0.229500459
< [6,] 1885 -0.373230617 -0.608804280 -0.137656955 -0.513571700 -0.232889535
< [7,] 1886 -0.369227150 -0.592785330 -0.145668970 -0.502410107 -0.236044193
< [8,] 1887 -0.365223683 -0.577226782 -0.153220584 -0.491522795 -0.238924571
< [9,] 1888 -0.361220216 -0.562208058 -0.160232373 -0.480957079 -0.241483352
< [10,] 1889 -0.357216749 -0.547822773 -0.166610724 -0.470768729 -0.243664768
< [11,] 1890 -0.353213282 -0.534179978 -0.172246585 -0.461022711 -0.245403852
< [12,] 1891 -0.349209814 -0.521404410 -0.177015219 -0.451793336 -0.246626293
< [13,] 1892 -0.345206347 -0.509634924 -0.180777771 -0.443163327 -0.247249368
< [14,] 1893 -0.341202880 -0.499020116 -0.183385645 -0.435221208 -0.247184553
< [15,] 1894 -0.337199413 -0.489710224 -0.184688602 -0.428056482 -0.246342344
< [16,] 1895 -0.333195946 -0.481845064 -0.184546828 -0.421752442 -0.244639450
< [17,] 1896 -0.329192479 -0.475539046 -0.182845912 -0.416377249 -0.242007708
< [18,] 1897 -0.325189012 -0.470866120 -0.179511904 -0.411974957 -0.238403066
< [19,] 1898 -0.321185545 -0.467848651 -0.174522438 -0.408558891 -0.233812198
< [20,] 1899 -0.317182077 -0.466453839 -0.167910316 -0.406109508 -0.228254646
< [21,] 1900 -0.313178610 -0.466598933 -0.159758288 -0.404577513 -0.221779708
< [22,] 1901 -0.309175143 -0.468163434 -0.150186852 -0.403891117 -0.214459169
< [23,] 1902 -0.305171676 -0.471004432 -0.139338920 -0.403965184 -0.206378168
< [24,] 1903 -0.301168209 -0.474971184 -0.127365234 -0.404709910 -0.197626508
< [25,] 1904 -0.297164742 -0.479916458 -0.114413025 -0.406037582 -0.188291901
< [26,] 1905 -0.293161275 -0.485703869 -0.100618680 -0.407866950 -0.178455599
< [27,] 1906 -0.289157807 -0.492211633 -0.086103982 -0.410125463 -0.168190151
< [28,] 1907 -0.285154340 -0.499333719 -0.070974961 -0.412749954 -0.157558727
< [29,] 1908 -0.281150873 -0.506979351 -0.055322395 -0.415686342 -0.146615404
< [30,] 1909 -0.268996808 -0.484727899 -0.053265717 -0.397516841 -0.140476775
< [31,] 1910 -0.256842743 -0.462766683 -0.050918803 -0.379520246 -0.134165240
< [32,] 1911 -0.244688678 -0.441139176 -0.048238181 -0.361722455 -0.127654901
< [33,] 1912 -0.232534613 -0.419896002 -0.045173225 -0.344153628 -0.120915598
< [34,] 1913 -0.220380548 -0.399095811 -0.041665286 -0.326848704 -0.113912392
< [35,] 1914 -0.208226483 -0.378805976 -0.037646990 -0.309847821 -0.106605145
< [36,] 1915 -0.196072418 -0.359102922 -0.033041915 -0.293196507 -0.098948329
< [37,] 1916 -0.183918353 -0.340071771 -0.027764935 -0.276945475 -0.090891232
< [38,] 1917 -0.171764288 -0.321804943 -0.021723634 -0.261149781 -0.082378795
< [39,] 1918 -0.159610223 -0.304399275 -0.014821172 -0.245867116 -0.073353330
< [40,] 1919 -0.147456158 -0.287951368 -0.006960949 -0.231155030 -0.063757286
< [41,] 1920 -0.135302093 -0.272551143 0.001946957 -0.217067092 -0.053537094
< [42,] 1921 -0.123148028 -0.258274127 0.011978071 -0.203648297 -0.042647760
< [43,] 1922 -0.110993963 -0.245173645 0.023185718 -0.190930411 -0.031057516
< [44,] 1923 -0.098839898 -0.233274545 0.035594749 -0.178928240 -0.018751557
< [45,] 1924 -0.086685833 -0.222570067 0.049198400 -0.167637754 -0.005733912
< [46,] 1925 -0.074531768 -0.213022703 0.063959166 -0.157036610 0.007973073
< [47,] 1926 -0.062377703 -0.204568828 0.079813422 -0.147086903 0.022331496
< [48,] 1927 -0.050223638 -0.197125838 0.096678562 -0.137739423 0.037292146
< [49,] 1928 -0.038069573 -0.190600095 0.114460948 -0.128938384 0.052799237
< [50,] 1929 -0.025915508 -0.184894207 0.133063191 -0.120625768 0.068794751
< [51,] 1930 -0.013761444 -0.179912750 0.152389863 -0.112744726 0.085221839
< [52,] 1931 -0.001607379 -0.175566138 0.172351381 -0.105241887 0.102027130
< [53,] 1932 0.010546686 -0.171772831 0.192866204 -0.098068675 0.119162048
< [54,] 1933 0.022700751 -0.168460244 0.213861747 -0.091181848 0.136583351
< [55,] 1934 0.034854816 -0.165564766 0.235274399 -0.084543511 0.154253144
< [56,] 1935 0.047008881 -0.163031246 0.257049009 -0.078120807 0.172138570
< [57,] 1936 0.059162946 -0.160812199 0.279138092 -0.071885448 0.190211340
< [58,] 1937 0.054383856 -0.155656272 0.264423984 -0.070745832 0.179513544
< [59,] 1938 0.049604765 -0.150814817 0.250024348 -0.069793562 0.169003093
< [60,] 1939 0.044825675 -0.146335320 0.235986670 -0.069056925 0.158708275
< [61,] 1940 0.040046585 -0.142272933 0.222366102 -0.068568777 0.148661946
< [62,] 1941 0.035267494 -0.138691265 0.209226254 -0.068367014 0.138902002
< [63,] 1942 0.030488404 -0.135662903 0.196639710 -0.068494879 0.129471686
< [64,] 1943 0.025709313 -0.133269386 0.184688012 -0.069000947 0.120419573
< [65,] 1944 0.020930223 -0.131600299 0.173460744 -0.069938588 0.111799033
< [66,] 1945 0.016151132 -0.130751068 0.163053332 -0.071364652 0.103666917
< [67,] 1946 0.011372042 -0.130819083 0.153563167 -0.073337158 0.096081242
< [68,] 1947 0.006592951 -0.131897983 0.145083886 -0.075911890 0.089097793
< [69,] 1948 0.001813861 -0.134070373 0.137698095 -0.079138060 0.082765782
< [70,] 1949 -0.002965230 -0.137399877 0.131469418 -0.083053571 0.077123112
< [71,] 1950 -0.007744320 -0.141924001 0.126435361 -0.087680768 0.072192128
< [72,] 1951 -0.012523410 -0.147649510 0.122602689 -0.093023679 0.067976858
< [73,] 1952 -0.017302501 -0.154551551 0.119946549 -0.099067500 0.064462498
< [74,] 1953 -0.022081591 -0.162576801 0.118413618 -0.105780463 0.061617281
< [75,] 1954 -0.026860682 -0.171649733 0.117928369 -0.113117575 0.059396211
< [76,] 1955 -0.031639772 -0.181680427 0.118400882 -0.121025265 0.057745721
< [77,] 1956 -0.036418863 -0.192572281 0.119734555 -0.129445984 0.056608259
< [78,] 1957 -0.041197953 -0.204228457 0.121832550 -0.138322042 0.055926136
< [79,] 1958 -0.045977044 -0.216556537 0.124602449 -0.147598382 0.055644294
< [80,] 1959 -0.050756134 -0.229471397 0.127959128 -0.157224290 0.055712022
< [81,] 1960 -0.055535225 -0.242896613 0.131826164 -0.167154239 0.056083790
< [82,] 1961 -0.060314315 -0.256764812 0.136136182 -0.177348092 0.056719462
< [83,] 1962 -0.065093405 -0.271017346 0.140830535 -0.187770909 0.057584098
< [84,] 1963 -0.069872496 -0.285603587 0.145858595 -0.198392529 0.058647537
< [85,] 1964 -0.074651586 -0.300480064 0.151176891 -0.209187055 0.059883882
< [86,] 1965 -0.060832745 -0.275012124 0.153346634 -0.188428358 0.066762869
< [87,] 1966 -0.047013903 -0.250067729 0.156039922 -0.167981559 0.073953753
< [88,] 1967 -0.033195062 -0.225737656 0.159347533 -0.147900737 0.081510614
< [89,] 1968 -0.019376220 -0.202127937 0.163375497 -0.128249061 0.089496621
< [90,] 1969 -0.005557378 -0.179360353 0.168245596 -0.109099079 0.097984322
< [91,] 1970 0.008261463 -0.157571293 0.174094219 -0.090532045 0.107054971
< [92,] 1971 0.022080305 -0.136907986 0.181068596 -0.072635669 0.116796279
< [93,] 1972 0.035899146 -0.117521176 0.189319469 -0.055499756 0.127298049
< [94,] 1973 0.049717988 -0.099553773 0.198989749 -0.039209443 0.138645419
< [95,] 1974 0.063536830 -0.083126277 0.210199936 -0.023836517 0.150910176
< [96,] 1975 0.077355671 -0.068321437 0.223032779 -0.009430275 0.164141617
< [97,] 1976 0.091174513 -0.055172054 0.237521080 0.003989742 0.178359283
< [98,] 1977 0.104993354 -0.043655763 0.253642472 0.016436858 0.193549851
< [99,] 1978 0.118812196 -0.033698615 0.271323007 0.027955127 0.209669265
< [100,] 1979 0.132631038 -0.025186198 0.290448273 0.038612710 0.226649365
< [101,] 1980 0.146449879 -0.017978697 0.310878456 0.048492899 0.244406859
< [102,] 1981 0.160268721 -0.011925874 0.332463316 0.057685199 0.262852243
< [103,] 1982 0.174087562 -0.006879134 0.355054259 0.066278133 0.281896992
< [104,] 1983 0.187906404 -0.002699621 0.378512429 0.074354424 0.301458384
< [105,] 1984 0.201725246 0.000737403 0.402713088 0.081988382 0.321462109
< [106,] 1985 0.215544087 0.003540988 0.427547186 0.089244975 0.341843199
< [107,] 1986 0.229362929 0.005804749 0.452921108 0.096179971 0.362545886
< [108,] 1987 0.243181770 0.007608108 0.478755433 0.102840688 0.383522853
< [109,] 1988 0.257000612 0.009017980 0.504983244 0.109266987 0.404734237
< [110,] 1989 0.270819454 0.010090540 0.531548367 0.115492336 0.426146571
< [111,] 1990 0.284638295 0.010872901 0.558403689 0.121544800 0.447731790
< [112,] 1991 0.298457137 0.011404596 0.585509677 0.127447933 0.469466340
< [113,] 1992 0.312275978 0.011718869 0.612833087 0.133221539 0.491330418
---
> [1,] 1880 -0.257692308 -3.867500e-01 -0.128634653 -0.340734568 -0.174650048
> [2,] 1881 -0.250769231 -3.767293e-01 -0.124809149 -0.331818355 -0.169720107
> [3,] 1882 -0.243846154 -3.667351e-01 -0.120957249 -0.322919126 -0.164773181
> [4,] 1883 -0.236923077 -3.567692e-01 -0.117076923 -0.314038189 -0.159807965
> [5,] 1884 -0.230000000 -3.468340e-01 -0.113165951 -0.305176970 -0.154823030
> [6,] 1885 -0.223076923 -3.369319e-01 -0.109221900 -0.296337036 -0.149816810
> [7,] 1886 -0.216153846 -3.270656e-01 -0.105242105 -0.287520102 -0.144787590
> [8,] 1887 -0.209230769 -3.172379e-01 -0.101223643 -0.278728048 -0.139733491
> [9,] 1888 -0.202307692 -3.074521e-01 -0.097163311 -0.269962936 -0.134652449
> [10,] 1889 -0.195384615 -2.977116e-01 -0.093057593 -0.261227027 -0.129542204
> [11,] 1890 -0.188461539 -2.880204e-01 -0.088902637 -0.252522800 -0.124400277
> [12,] 1891 -0.181538462 -2.783827e-01 -0.084694220 -0.243852973 -0.119223950
> [13,] 1892 -0.174615385 -2.688030e-01 -0.080427720 -0.235220519 -0.114010250
> [14,] 1893 -0.167692308 -2.592865e-01 -0.076098083 -0.226628691 -0.108755924
> [15,] 1894 -0.160769231 -2.498387e-01 -0.071699793 -0.218081038 -0.103457424
> [16,] 1895 -0.153846154 -2.404655e-01 -0.067226847 -0.209581422 -0.098110886
> [17,] 1896 -0.146923077 -2.311734e-01 -0.062672732 -0.201134035 -0.092712119
> [18,] 1897 -0.140000000 -2.219696e-01 -0.058030409 -0.192743405 -0.087256595
> [19,] 1898 -0.133076923 -2.128615e-01 -0.053292314 -0.184414399 -0.081739447
> [20,] 1899 -0.126153846 -2.038573e-01 -0.048450366 -0.176152218 -0.076155475
> [21,] 1900 -0.119230769 -1.949655e-01 -0.043496005 -0.167962369 -0.070499170
> [22,] 1901 -0.112307692 -1.861951e-01 -0.038420244 -0.159850635 -0.064764750
> [23,] 1902 -0.105384615 -1.775555e-01 -0.033213760 -0.151823015 -0.058946216
> [24,] 1903 -0.098461539 -1.690561e-01 -0.027867017 -0.143885645 -0.053037432
> [25,] 1904 -0.091538462 -1.607065e-01 -0.022370423 -0.136044696 -0.047032227
> [26,] 1905 -0.084615385 -1.525162e-01 -0.016714535 -0.128306245 -0.040924524
> [27,] 1906 -0.077692308 -1.444943e-01 -0.010890287 -0.120676126 -0.034708490
> [28,] 1907 -0.070769231 -1.366492e-01 -0.004889253 -0.113159760 -0.028378702
> [29,] 1908 -0.063846154 -1.289884e-01 0.001296074 -0.105761977 -0.021930331
> [30,] 1909 -0.056923077 -1.215182e-01 0.007672008 -0.098486840 -0.015359314
> [31,] 1910 -0.050000000 -1.142434e-01 0.014243419 -0.091337484 -0.008662516
> [32,] 1911 -0.043076923 -1.071674e-01 0.021013527 -0.084315978 -0.001837868
> [33,] 1912 -0.036153846 -1.002914e-01 0.027983751 -0.077423239 0.005115546
> [34,] 1913 -0.029230769 -9.361519e-02 0.035153653 -0.070658982 0.012197443
> [35,] 1914 -0.022307692 -8.713634e-02 0.042520952 -0.064021740 0.019406355
> [36,] 1915 -0.015384615 -8.085086e-02 0.050081630 -0.057508928 0.026739697
> [37,] 1916 -0.008461538 -7.475318e-02 0.057830107 -0.051116955 0.034193878
> [38,] 1917 -0.001538462 -6.883640e-02 0.065759473 -0.044841376 0.041764453
> [39,] 1918 0.005384615 -6.309252e-02 0.073861755 -0.038677059 0.049446290
> [40,] 1919 0.012307692 -5.751281e-02 0.082128191 -0.032618368 0.057233753
> [41,] 1920 0.019230769 -5.208797e-02 0.090549507 -0.026659334 0.065120873
> [42,] 1921 0.026153846 -4.680847e-02 0.099116161 -0.020793819 0.073101511
> [43,] 1922 0.033076923 -4.166472e-02 0.107818567 -0.015015652 0.081169499
> [44,] 1923 0.040000000 -3.664727e-02 0.116647271 -0.009318753 0.089318753
> [45,] 1924 0.046923077 -3.174694e-02 0.125593095 -0.003697214 0.097543368
> [46,] 1925 0.053846154 -2.695494e-02 0.134647244 0.001854623 0.105837685
> [47,] 1926 0.060769231 -2.226292e-02 0.143801377 0.007342124 0.114196337
> [48,] 1927 0.067692308 -1.766304e-02 0.153047656 0.012770335 0.122614280
> [49,] 1928 0.074615385 -1.314799e-02 0.162378762 0.018143964 0.131086806
> [50,] 1929 0.081538462 -8.710982e-03 0.171787905 0.023467379 0.139609544
> [51,] 1930 0.088461538 -4.345738e-03 0.181268815 0.028744616 0.148178461
> [52,] 1931 0.095384615 -4.649065e-05 0.190815721 0.033979388 0.156789843
> [53,] 1932 0.102307692 4.192055e-03 0.200423329 0.039175101 0.165440284
> [54,] 1933 0.109230769 8.374747e-03 0.210086792 0.044334874 0.174126664
> [55,] 1934 0.116153846 1.250601e-02 0.219801679 0.049461559 0.182846134
> [56,] 1935 0.123076923 1.658990e-02 0.229563945 0.054557757 0.191596090
> [57,] 1936 0.130000000 2.063010e-02 0.239369902 0.059625842 0.200374158
> [58,] 1937 0.130000000 2.554264e-02 0.234457361 0.062786820 0.197213180
> [59,] 1938 0.130000000 3.023953e-02 0.229760466 0.065809042 0.194190958
> [60,] 1939 0.130000000 3.468890e-02 0.225311102 0.068671989 0.191328011
> [61,] 1940 0.130000000 3.885447e-02 0.221145527 0.071352331 0.188647669
> [62,] 1941 0.130000000 4.269563e-02 0.217304372 0.073823926 0.186176074
> [63,] 1942 0.130000000 4.616776e-02 0.213832244 0.076058070 0.183941930
> [64,] 1943 0.130000000 4.922326e-02 0.210776742 0.078024136 0.181975864
> [65,] 1944 0.130000000 5.181327e-02 0.208186727 0.079690683 0.180309317
> [66,] 1945 0.130000000 5.389026e-02 0.206109736 0.081027125 0.178972875
> [67,] 1946 0.130000000 5.541136e-02 0.204588637 0.082005877 0.177994123
> [68,] 1947 0.130000000 5.634212e-02 0.203657879 0.082604774 0.177395226
> [69,] 1948 0.130000000 5.666006e-02 0.203339939 0.082809352 0.177190648
> [70,] 1949 0.130000000 5.635724e-02 0.203642757 0.082614504 0.177385496
> [71,] 1950 0.130000000 5.544123e-02 0.204558768 0.082025096 0.177974904
> [72,] 1951 0.130000000 5.393418e-02 0.206065824 0.081055380 0.178944620
> [73,] 1952 0.130000000 5.187027e-02 0.208129729 0.079727358 0.180272642
> [74,] 1953 0.130000000 4.929223e-02 0.210707774 0.078068513 0.181931487
> [75,] 1954 0.130000000 4.624751e-02 0.213752495 0.076109385 0.183890615
> [76,] 1955 0.130000000 4.278497e-02 0.217215029 0.073881414 0.186118586
> [77,] 1956 0.130000000 3.895228e-02 0.221047722 0.071415265 0.188584735
> [78,] 1957 0.130000000 3.479412e-02 0.225205878 0.068739695 0.191260305
> [79,] 1958 0.130000000 3.035124e-02 0.229648764 0.065880916 0.194119084
> [80,] 1959 0.130000000 2.565999e-02 0.234340014 0.062862328 0.197137672
> [81,] 1960 0.130000000 2.075236e-02 0.239247637 0.059704514 0.200295486
> [82,] 1961 0.130000000 1.565622e-02 0.244343776 0.056425398 0.203574602
> [83,] 1962 0.130000000 1.039566e-02 0.249604337 0.053040486 0.206959514
> [84,] 1963 0.130000000 4.991436e-03 0.255008564 0.049563131 0.210436869
> [85,] 1964 0.130000000 -5.386147e-04 0.260538615 0.046004815 0.213995185
> [86,] 1965 0.143076923 1.926909e-02 0.266884757 0.063412665 0.222741181
> [87,] 1966 0.156153846 3.876772e-02 0.273539971 0.080621643 0.231686050
> [88,] 1967 0.169230769 5.790379e-02 0.280557753 0.097597325 0.240864213
> [89,] 1968 0.182307692 7.661491e-02 0.288000479 0.114299577 0.250315807
> [90,] 1969 0.195384615 9.482963e-02 0.295939602 0.130682422 0.260086809
> [91,] 1970 0.208461538 1.124682e-01 0.304454863 0.146694551 0.270228526
> [92,] 1971 0.221538461 1.294450e-01 0.313631914 0.162280850 0.280796073
> [93,] 1972 0.234615385 1.456729e-01 0.323557850 0.177385278 0.291845491
> [94,] 1973 0.247692308 1.610702e-01 0.334314435 0.191955225 0.303429390
> [95,] 1974 0.260769231 1.755689e-01 0.345969561 0.205947004 0.315591457
> [96,] 1975 0.273846154 1.891238e-01 0.358568478 0.219331501 0.328360807
> [97,] 1976 0.286923077 2.017191e-01 0.372127073 0.232098492 0.341747662
> [98,] 1977 0.300000000 2.133707e-01 0.386629338 0.244258277 0.355741722
> [99,] 1978 0.313076923 2.241239e-01 0.402029922 0.255840039 0.370313807
> [100,] 1979 0.326153846 2.340468e-01 0.418260863 0.266887506 0.385420186
> [101,] 1980 0.339230769 2.432212e-01 0.435240360 0.277453314 0.401008224
> [102,] 1981 0.352307692 2.517341e-01 0.452881314 0.287593508 0.417021876
> [103,] 1982 0.365384615 2.596711e-01 0.471098085 0.297363192 0.433406039
> [104,] 1983 0.378461538 2.671121e-01 0.489810964 0.306813654 0.450109423
> [105,] 1984 0.391538461 2.741284e-01 0.508948530 0.315990851 0.467086072
> [106,] 1985 0.404615384 2.807823e-01 0.528448443 0.324934896 0.484295873
> [107,] 1986 0.417692308 2.871274e-01 0.548257238 0.333680190 0.501704425
> [108,] 1987 0.430769231 2.932089e-01 0.568329576 0.342255907 0.519282554
> [109,] 1988 0.443846154 2.990650e-01 0.588627259 0.350686626 0.537005682
> [110,] 1989 0.456923077 3.047279e-01 0.609118218 0.358992981 0.554853173
> [111,] 1990 0.470000000 3.102244e-01 0.629775550 0.367192284 0.572807716
> [112,] 1991 0.483076923 3.155772e-01 0.650576667 0.375299067 0.590854778
> [113,] 1992 0.496153846 3.208051e-01 0.671502569 0.383325558 0.608982134
468,470d444
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 19
480,482d453
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
486,489d456
<
< **** ERROR in algorithm: ifl = 22
<
<
492,493c459,460
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> coef[1:5]: -0.40655906, -0.31473700, 0.05651823, -0.05681818, 0.28681956
> R^2 = 72.56% ; empirical tau (over all): 54/113 = 0.4778761 (target tau= 0.5)
499,502d465
<
< **** ERROR in algorithm: ifl = 22
<
<
505,507d467
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
512,515d471
<
< **** ERROR in algorithm: ifl = 22
<
<
518,520d473
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
522,524c475
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 68 74 78 79 102 111
526,529c477
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 38 39 50 54 77 85 97 113
Running ‘wind.R’ [10s/12s]
Running the tests in ‘tests/ex1.R’ failed.
Complete output:
> #### OOps! Running this in 'CMD check' or in *R* __for the first time__
> #### ===== gives a wrong result (at the end) than when run a 2nd time
> ####-- problem disappears with introduction of if (psw) call ... in Fortran
>
> suppressMessages(library(cobs))
> options(digits = 6)
> if(!dev.interactive(orNone=TRUE)) pdf("ex1.pdf")
>
> source(system.file("util.R", package = "cobs"))
>
> ## Simple example from example(cobs)
> set.seed(908)
> x <- seq(-1,1, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> ## specify constraints (boundary conditions)
> con <- rbind(c( 1,min(x),0),
+ c(-1,max(x),1),
+ c( 0, 0, 0.5))
> ## obtain the median *regression* B-spline using automatically selected knots
> coR <- cobs(x,y,constraint = "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> summaryCobs(coR)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", pointwise = con)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : chr "AIC"
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:50] -1 -0.959 -0.918 -0.878 -0.837 ...
$ y : num [1:50] 0.2254 0.0916 0.0803 -0.0272 -0.0454 ...
$ resid : num [1:50] 0.1976 0.063 0.0491 -0.0626 -0.0868 ...
$ fitted : num [1:50] 0.0278 0.0287 0.0312 0.0354 0.0414 ...
$ coef : num [1:4] 0.0278 0.0278 0.8154 1
$ knots : num [1:3] -1 -0.224 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : num 0
$ icyc : int 7
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 -6.77514e-02 -0.029701622 0.0278152 0.0853320 0.123382
2 -6.41787e-02 -0.027468888 0.0280224 0.0835138 0.120224
3 -6.04433e-02 -0.024973163 0.0286442 0.0822615 0.117732
4 -5.65412e-02 -0.022212175 0.0296803 0.0815728 0.115902
5 -5.24674e-02 -0.019182756 0.0311310 0.0814447 0.114729
6 -4.82149e-02 -0.015880775 0.0329961 0.0818729 0.114207
7 -4.37751e-02 -0.012301110 0.0352757 0.0828524 0.114326
8 -3.91381e-02 -0.008437641 0.0379697 0.0843771 0.115077
9 -3.42918e-02 -0.004283290 0.0410782 0.0864397 0.116448
10 -2.92233e-02 0.000169901 0.0446012 0.0890325 0.118426
11 -2.39179e-02 0.004930665 0.0485387 0.0921467 0.120995
12 -1.83600e-02 0.010008360 0.0528906 0.0957728 0.124141
13 -1.25335e-02 0.015412811 0.0576570 0.0999012 0.127847
14 -6.42140e-03 0.021154129 0.0628378 0.1045216 0.132097
15 -6.81378e-06 0.027242531 0.0684332 0.1096238 0.136873
16 6.72715e-03 0.033688168 0.0744430 0.1151978 0.142159
17 1.37970e-02 0.040500961 0.0808672 0.1212335 0.147938
18 2.12185e-02 0.047690461 0.0877060 0.1277215 0.154193
19 2.90068e-02 0.055265726 0.0949592 0.1346527 0.160912
20 3.71760e-02 0.063235225 0.1026269 0.1420185 0.168078
21 4.57390e-02 0.071606758 0.1107090 0.1498113 0.175679
22 5.47075e-02 0.080387396 0.1192056 0.1580238 0.183704
23 6.40921e-02 0.089583438 0.1281167 0.1666500 0.192141
24 7.39018e-02 0.099200377 0.1374422 0.1756841 0.200983
25 8.41444e-02 0.109242876 0.1471823 0.1851216 0.210220
26 9.48262e-02 0.119714746 0.1573367 0.1949588 0.219847
27 1.05952e-01 0.130618921 0.1679057 0.2051925 0.229859
28 1.17526e-01 0.141957438 0.1788891 0.2158208 0.240253
29 1.29548e-01 0.153731401 0.1902870 0.2268426 0.251026
30 1.42021e-01 0.165940947 0.2020994 0.2382578 0.262178
31 1.54941e-01 0.178585191 0.2143262 0.2500672 0.273711
32 1.68306e-01 0.191662165 0.2269675 0.2622729 0.285629
33 1.82111e-01 0.205168744 0.2400233 0.2748778 0.297936
34 1.96348e-01 0.219100556 0.2534935 0.2878865 0.310639
35 2.11008e-01 0.233451886 0.2673782 0.3013046 0.323748
36 2.26079e-01 0.248215565 0.2816774 0.3151392 0.337276
37 2.41547e-01 0.263382876 0.2963910 0.3293992 0.351235
38 2.57393e-01 0.278943451 0.3115191 0.3440948 0.365645
39 2.73599e-01 0.294885220 0.3270617 0.3592382 0.380524
40 2.90023e-01 0.311080514 0.3429107 0.3747410 0.395798
41 3.06194e-01 0.327075735 0.3586411 0.3902065 0.411088
42 3.22074e-01 0.342831649 0.3742095 0.4055873 0.426345
43 3.37676e-01 0.358355597 0.3896158 0.4208761 0.441556
44 3.53012e-01 0.373655096 0.4048602 0.4360653 0.456709
45 3.68094e-01 0.388737688 0.4199426 0.4511475 0.471791
46 3.82936e-01 0.403610792 0.4348630 0.4661151 0.486790
47 3.97549e-01 0.418281590 0.4496214 0.4809611 0.501694
48 4.11944e-01 0.432756923 0.4642177 0.4956786 0.516491
49 4.26133e-01 0.447043216 0.4786521 0.5102611 0.531172
50 4.40124e-01 0.461146429 0.4929245 0.5247027 0.545725
51 4.53927e-01 0.475072016 0.5070350 0.5389979 0.560143
52 4.67551e-01 0.488824911 0.5209834 0.5531418 0.574416
53 4.81002e-01 0.502409521 0.5347698 0.5671300 0.588538
54 4.94287e-01 0.515829730 0.5483942 0.5809587 0.602501
55 5.07412e-01 0.529088909 0.5618566 0.5946243 0.616302
56 5.20381e-01 0.542189933 0.5751571 0.6081242 0.629933
57 5.33198e-01 0.555135196 0.5882955 0.6214558 0.643393
58 5.45867e-01 0.567926630 0.6012719 0.6346172 0.656677
59 5.58390e-01 0.580565721 0.6140864 0.6476070 0.669782
60 5.70769e-01 0.593053527 0.6267388 0.6604241 0.682708
61 5.83005e-01 0.605390690 0.6392293 0.6730679 0.695454
62 5.95098e-01 0.617577451 0.6515577 0.6855380 0.708017
63 6.07048e-01 0.629613656 0.6637242 0.6978347 0.720400
64 6.18854e-01 0.641498766 0.6757287 0.7099586 0.732603
65 6.30515e-01 0.653231865 0.6875711 0.7219104 0.744627
66 6.42028e-01 0.664811658 0.6992516 0.7336916 0.756475
67 6.53391e-01 0.676236478 0.7107701 0.7453037 0.768149
68 6.64600e-01 0.687504287 0.7221266 0.7567489 0.779653
69 6.75652e-01 0.698612675 0.7333211 0.7680295 0.790991
70 6.86541e-01 0.709558867 0.7443536 0.7791483 0.802166
71 6.97262e-01 0.720339721 0.7552241 0.7901084 0.813186
72 7.07810e-01 0.730951740 0.7659326 0.8009134 0.824055
73 7.18179e-01 0.741391078 0.7764791 0.8115671 0.834779
74 7.28361e-01 0.751653555 0.7868636 0.8220736 0.845367
75 7.38348e-01 0.761734678 0.7970861 0.8324375 0.855824
76 7.48134e-01 0.771629669 0.8071466 0.8426636 0.866160
77 7.57709e-01 0.781333498 0.8170452 0.8527568 0.876382
78 7.67065e-01 0.790840929 0.8267817 0.8627224 0.886499
79 7.76192e-01 0.800146569 0.8363562 0.8725659 0.896520
80 7.85083e-01 0.809244928 0.8457688 0.8822926 0.906455
81 7.93727e-01 0.818130488 0.8550193 0.8919081 0.916312
82 8.02116e-01 0.826797774 0.8641079 0.9014179 0.926100
83 8.10240e-01 0.835241429 0.8730344 0.9108274 0.935829
84 8.18091e-01 0.843456291 0.8817990 0.9201417 0.945507
85 8.25661e-01 0.851437463 0.8904015 0.9293656 0.955142
86 8.32942e-01 0.859180385 0.8988421 0.9385038 0.964742
87 8.39928e-01 0.866680887 0.9071207 0.9475605 0.974313
88 8.46612e-01 0.873935236 0.9152373 0.9565393 0.983862
89 8.52989e-01 0.880940170 0.9231918 0.9654435 0.993395
90 8.59054e-01 0.887692913 0.9309844 0.9742760 1.002915
91 8.64803e-01 0.894191180 0.9386150 0.9830389 1.012427
92 8.70233e-01 0.900433167 0.9460836 0.9917341 1.021934
93 8.75343e-01 0.906417527 0.9533902 1.0003629 1.031437
94 8.80130e-01 0.912143340 0.9605348 1.0089263 1.040939
95 8.84594e-01 0.917610075 0.9675174 1.0174248 1.050441
96 8.88735e-01 0.922817542 0.9743381 1.0258586 1.059942
97 8.92551e-01 0.927765853 0.9809967 1.0342275 1.069442
98 8.96045e-01 0.932455371 0.9874933 1.0425312 1.078941
99 8.99218e-01 0.936886669 0.9938279 1.0507692 1.088438
100 9.02069e-01 0.941060487 1.0000006 1.0589406 1.097932
knots :
[1] -1.00000 -0.22449 1.00000
coef :
[1] 0.0278152 0.0278152 0.8153868 1.0000006
> coR1 <- cobs(x,y,constraint = "increase", pointwise = con, degree = 1)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> summary(coR1)
COBS regression spline (degree = 1) from call:
cobs(x = x, y = y, constraint = "increase", degree = 1, pointwise = con)
{tau=0.5}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:4]: -1.000002, -0.632653, 0.183673, 1.000002
with 3 pointwise constraints
coef[1:4]: 0.0504467, 0.0504467, 0.6305155, 1.0000009
R^2 = 93.83% ; empirical tau (over all): 21/50 = 0.42 (target tau= 0.5)
>
> ## compute the median *smoothing* B-spline using automatically chosen lambda
> coS <- cobs(x,y,constraint = "increase", pointwise = con,
+ lambda = -1, trace = 3)
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
loo.design2(): -> Xeq 51 x 22 (nz = 151 =^= 0.13%)
Xieq 62 x 22 (nz = 224 =^= 0.16%)
........................
The algorithm has converged. You might
plot() the returned object (which plots 'sic' against 'lambda')
to see if you have found the global minimum of the information criterion
so that you can determine if you need to adjust any or all of
'lambda.lo', 'lambda.hi' and 'lambda.length' and refit the model.
> with(coS, cbind(pp.lambda, pp.sic, k0, ifl, icyc))
pp.lambda pp.sic k0 ifl icyc
[1,] 3.54019e-05 -2.64644 22 1 21
[2,] 6.92936e-05 -2.64644 22 1 21
[3,] 1.35631e-04 -2.64644 22 1 20
[4,] 2.65477e-04 -2.64644 22 1 22
[5,] 5.19629e-04 -2.64644 22 1 22
[6,] 1.01709e-03 -2.64644 22 1 23
[7,] 1.99080e-03 -2.68274 21 1 20
[8,] 3.89667e-03 -2.75212 19 1 18
[9,] 7.62711e-03 -2.73932 19 1 14
[10,] 1.49289e-02 -2.85261 16 1 13
[11,] 2.92209e-02 -2.97873 12 1 12
[12,] 5.71953e-02 -3.01058 11 1 12
[13,] 1.11951e-01 -3.04364 10 1 11
[14,] 2.19126e-01 -3.11242 8 1 12
[15,] 4.28904e-01 -3.17913 6 1 12
[16,] 8.39512e-01 -3.18824 5 1 11
[17,] 1.64321e+00 -3.01467 5 1 12
[18,] 3.21633e+00 -3.01380 4 1 11
[19,] 6.29545e+00 -3.01380 4 1 10
[20,] 1.23223e+01 -3.01380 4 1 11
[21,] 2.41190e+01 -3.01380 4 1 11
[22,] 4.72092e+01 -3.01380 4 1 10
[23,] 9.24046e+01 -3.01380 4 1 10
[24,] 1.80867e+02 -3.01380 4 1 10
[25,] 3.54019e+02 -3.01380 4 1 10
> with(coS, plot(pp.sic ~ pp.lambda, type = "b", log = "x", col=2,
+ main = deparse(call)))
> ##-> very nice minimum close to 1
>
> summaryCobs(coS)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", lambda = -1, pointwise = con, trace = 3)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : NULL
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi TRUE
$ x : num [1:50] -1 -0.959 -0.918 -0.878 -0.837 ...
$ y : num [1:50] 0.2254 0.0916 0.0803 -0.0272 -0.0454 ...
$ resid : num [1:50] 0.2254 0.0829 0.062 -0.0562 -0.0862 ...
$ fitted : num [1:50] 0 0.00869 0.01837 0.02906 0.04075 ...
$ coef : num [1:22] 0 0.00819 0.03365 0.06662 0.10458 ...
$ knots : num [1:20] -1 -0.918 -0.796 -0.714 -0.592 ...
$ k0 : int [1:25] 22 22 22 22 22 22 21 19 19 16 ...
$ k : int 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : Named num 0.84
..- attr(*, "names")= chr "lambda"
$ icyc : int [1:25] 21 21 20 22 22 23 20 18 14 13 ...
$ ifl : int [1:25] 1 1 1 1 1 1 1 1 1 1 ...
$ pp.lambda : num [1:25] 0 0 0 0 0.001 0.001 0.002 0.004 0.008 0.015 ...
$ pp.sic : num [1:25] -2.65 -2.65 -2.65 -2.65 -2.65 ...
$ i.mask : logi [1:25] TRUE TRUE TRUE TRUE TRUE TRUE ...
cb.lo ci.lo fit ci.up cb.up
1 -0.07071332 -0.03907635 -3.77249e-07 0.0390756 0.0707126
2 -0.06555125 -0.03435600 4.17438e-03 0.0427048 0.0739000
3 -0.06016465 -0.02940203 8.59400e-03 0.0465900 0.0773526
4 -0.05455349 -0.02421442 1.32585e-02 0.0507314 0.0810704
5 -0.04871809 -0.01879334 1.81678e-02 0.0551289 0.0850537
6 -0.04265897 -0.01313909 2.33220e-02 0.0597831 0.0893029
7 -0.03637554 -0.00725134 2.87210e-02 0.0646934 0.0938176
8 -0.02986704 -0.00112966 3.43649e-02 0.0698595 0.0985969
9 -0.02313305 0.00522618 4.02537e-02 0.0752812 0.1036404
10 -0.01617351 0.01181620 4.63873e-02 0.0809584 0.1089481
11 -0.00898880 0.01864020 5.27658e-02 0.0868914 0.1145204
12 -0.00157983 0.02569768 5.93891e-02 0.0930806 0.1203581
13 0.00605308 0.03298846 6.62573e-02 0.0995262 0.1264615
14 0.01391000 0.04051257 7.33704e-02 0.1062282 0.1328307
15 0.02199057 0.04826981 8.07283e-02 0.1131867 0.1394660
16 0.03029461 0.05626010 8.83310e-02 0.1204020 0.1463675
17 0.03882336 0.06448412 9.61787e-02 0.1278732 0.1535339
18 0.04757769 0.07294234 1.04271e-01 0.1355999 0.1609646
19 0.05655804 0.08163500 1.12608e-01 0.1435819 0.1686589
20 0.06576441 0.09056212 1.21191e-01 0.1518192 0.1766169
21 0.07519637 0.09972344 1.30018e-01 0.1603120 0.1848391
22 0.08485262 0.10911826 1.39090e-01 0.1690610 0.1933266
23 0.09473211 0.11874598 1.48406e-01 0.1780668 0.2020807
24 0.10483493 0.12860668 1.57968e-01 0.1873294 0.2111011
25 0.11516076 0.13870015 1.67775e-01 0.1968489 0.2203882
26 0.12570956 0.14902638 1.77826e-01 0.2066253 0.2299421
27 0.13648327 0.15958645 1.88122e-01 0.2166576 0.2397608
28 0.14748286 0.17038090 1.98663e-01 0.2269453 0.2498433
29 0.15870881 0.18140998 2.09449e-01 0.2374880 0.2601892
30 0.17016110 0.19267368 2.20480e-01 0.2482859 0.2707984
31 0.18183922 0.20417172 2.31755e-01 0.2593391 0.2816716
32 0.19374227 0.21590361 2.43276e-01 0.2706482 0.2928095
33 0.20587062 0.22786955 2.55041e-01 0.2822129 0.3042118
34 0.21822524 0.24007008 2.67051e-01 0.2940328 0.3158776
35 0.23080666 0.25250549 2.79306e-01 0.3061075 0.3278063
36 0.24361488 0.26517577 2.91806e-01 0.3184370 0.3399979
37 0.25664938 0.27808064 3.04551e-01 0.3310217 0.3524530
38 0.26990862 0.29121926 3.17541e-01 0.3438624 0.3651730
39 0.28339034 0.30459037 3.30775e-01 0.3569602 0.3781603
40 0.29709467 0.31819405 3.44255e-01 0.3703152 0.3914146
41 0.31102144 0.33203019 3.57979e-01 0.3839275 0.4049363
42 0.32517059 0.34609876 3.71948e-01 0.3977971 0.4187252
43 0.33954481 0.36040126 3.86162e-01 0.4119224 0.4327789
44 0.35414537 0.37493839 4.00621e-01 0.4263028 0.4470958
45 0.36897279 0.38971043 4.15324e-01 0.4409381 0.4616757
46 0.38402708 0.40471738 4.30273e-01 0.4558281 0.4765184
47 0.39930767 0.41995895 4.45466e-01 0.4709732 0.4916245
48 0.41479557 0.43541678 4.60887e-01 0.4863568 0.5069780
49 0.43039487 0.45099622 4.76442e-01 0.5018872 0.5224885
50 0.44609197 0.46668362 4.92117e-01 0.5175506 0.5381422
51 0.46188684 0.48247895 5.07913e-01 0.5333471 0.5539392
52 0.47773555 0.49833835 5.23786e-01 0.5492329 0.5698357
53 0.49336687 0.51398935 5.39461e-01 0.5649325 0.5855550
54 0.50873469 0.52938518 5.54891e-01 0.5803975 0.6010480
55 0.52383955 0.54452615 5.70077e-01 0.5956277 0.6163143
56 0.53868141 0.55941225 5.85018e-01 0.6106231 0.6313539
57 0.55325974 0.57404316 5.99714e-01 0.6253839 0.6461673
58 0.56757320 0.58841816 6.14165e-01 0.6399109 0.6607558
59 0.58161907 0.60253574 6.28371e-01 0.6542056 0.6751223
60 0.59539741 0.61639593 6.42332e-01 0.6682680 0.6892665
61 0.60890835 0.62999881 6.56048e-01 0.6820980 0.7031884
62 0.62215175 0.64334429 6.69520e-01 0.6956957 0.7168882
63 0.63512996 0.65643368 6.82747e-01 0.7090597 0.7303634
64 0.64784450 0.66926783 6.95729e-01 0.7221893 0.7436126
65 0.66029589 0.68184700 7.08466e-01 0.7350841 0.7566352
66 0.67248408 0.69417118 7.20958e-01 0.7477442 0.7694313
67 0.68440855 0.70624008 7.33205e-01 0.7601699 0.7820014
68 0.69606829 0.71805313 7.45207e-01 0.7723617 0.7943465
69 0.70746295 0.72961016 7.56965e-01 0.7843198 0.8064670
70 0.71859343 0.74091165 7.68478e-01 0.7960438 0.8183620
71 0.72946023 0.75195789 7.79746e-01 0.8075332 0.8300309
72 0.74006337 0.76274887 7.90769e-01 0.8187883 0.8414738
73 0.75040233 0.77328433 8.01547e-01 0.8298091 0.8526911
74 0.76047612 0.78356369 8.12080e-01 0.8405963 0.8636839
75 0.77028266 0.79358583 8.22368e-01 0.8511510 0.8744542
76 0.77982200 0.80335076 8.32412e-01 0.8614732 0.8850020
77 0.78909446 0.81285866 8.42211e-01 0.8715627 0.8953269
78 0.79809990 0.82210946 8.51765e-01 0.8814196 0.9054292
79 0.80683951 0.83110382 8.61074e-01 0.8910433 0.9153076
80 0.81531459 0.83984244 8.70138e-01 0.9004329 0.9249608
81 0.82352559 0.84832559 8.78957e-01 0.9095884 0.9343884
82 0.83147249 0.85655324 8.87531e-01 0.9185095 0.9435903
83 0.83915483 0.86452515 8.95861e-01 0.9271968 0.9525671
84 0.84657171 0.87224082 9.03946e-01 0.9356505 0.9613196
85 0.85372180 0.87969951 9.11786e-01 0.9438715 0.9698492
86 0.86060525 0.88690131 9.19381e-01 0.9518597 0.9781558
87 0.86722242 0.89384640 9.26731e-01 0.9596149 0.9862389
88 0.87357322 0.90053476 9.33836e-01 0.9671371 0.9940986
89 0.87965804 0.90696658 9.40696e-01 0.9744261 1.0017347
90 0.88547781 0.91314239 9.47312e-01 0.9814814 1.0091460
91 0.89103290 0.91906239 9.53683e-01 0.9883028 1.0163323
92 0.89632328 0.92472655 9.59808e-01 0.9948904 1.0232937
93 0.90134850 0.93013464 9.65689e-01 1.0012443 1.0300304
94 0.90610776 0.93528622 9.71326e-01 1.0073650 1.0365434
95 0.91060065 0.94018104 9.76717e-01 1.0132527 1.0428331
96 0.91482784 0.94481950 9.81863e-01 1.0189071 1.0488987
97 0.91878971 0.94920179 9.86765e-01 1.0243279 1.0547400
98 0.92248624 0.95332789 9.91422e-01 1.0295152 1.0603569
99 0.92591703 0.95719761 9.95833e-01 1.0344692 1.0657498
100 0.92908136 0.96081053 1.00000e+00 1.0391902 1.0709194
knots :
[1] -1.0000020 -0.9183673 -0.7959184 -0.7142857 -0.5918367 -0.5102041
[7] -0.3877551 -0.2653061 -0.1836735 -0.0612245 0.0204082 0.1428571
[13] 0.2244898 0.3469388 0.4693878 0.5510204 0.6734694 0.7551020
[19] 0.8775510 1.0000020
coef :
[1] -4.01161e-07 8.18714e-03 3.36534e-02 6.66159e-02 1.04576e-01
[6] 1.50032e-01 2.00486e-01 2.70027e-01 3.35473e-01 4.05918e-01
[11] 4.83858e-01 5.64259e-01 6.37163e-01 7.05069e-01 7.77561e-01
[16] 8.30474e-01 8.78390e-01 9.18810e-01 9.54232e-01 9.87743e-01
[21] 1.00000e+00 5.99960e-01
>
> plot(x, y, main = "cobs(x,y, constraint=\"increase\", pointwise = *)")
> matlines(x, cbind(fitted(coR), fitted(coR1), fitted(coS)),
+ col = 2:4, lty=1)
>
> ##-- real data example (still n = 50)
> data(cars)
> attach(cars)
> co1 <- cobs(speed, dist, "increase")
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> co1.1 <- cobs(speed, dist, "increase", knots.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> co1.2 <- cobs(speed, dist, "increase", knots.add = TRUE, repeat.delete.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> ## These three all give the same -- only remaining knots (outermost data):
> ic <- which("call" == names(co1))
> stopifnot(all.equal(co1[-ic], co1.1[-ic]),
+ all.equal(co1[-ic], co1.2[-ic]))
> 1 - sum(co1 $ resid ^2) / sum((dist - mean(dist))^2) # R^2 = 64.2%
[1] 0.642288
>
> co2 <- cobs(speed, dist, "increase", lambda = -1)# 6 warnings
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Running the tests in ‘tests/wind.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time() # timing here (to be faster by default)
Time (user system elapsed): 0.002 0.001 0.002
>
> data(DublinWind)
> attach(DublinWind)##-> speed & day (instead of "wind.x" & "DUB.")
> iday <- sort.list(day)
>
> if(!dev.interactive(orNone=TRUE)) pdf("wind.pdf", width=10)
>
> stopifnot(identical(day,c(rep(c(rep(1:365,3),1:366),4),
+ rep(1:365,2))))
> co50.1 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 1)
> co50.2 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 2)
>
> showProc.time()
Time (user system elapsed): 0.681 0.035 1.101
>
> plot(day,speed, pch = ".", col = "gray20")
> lines(day[iday], fitted(co50.1)[iday], col="orange", lwd = 2)
> lines(day[iday], fitted(co50.2)[iday], col="sky blue", lwd = 2)
> rug(knots(co50.1), col=3, lwd=2)
>
> nknots <- 13
>
>
> if(doExtra) {
+ ## Compute the quadratic median smoothing B-spline using SIC
+ ## lambda selection
+ co.o50 <-
+ cobs(day, speed, knots.add = TRUE, constraint="periodic", nknots = nknots,
+ tau = .5, lambda = -1, method = "uniform")
+ summary(co.o50) # [does print]
+
+ showProc.time()
+
+ op <- par(mfrow = c(3,1), mgp = c(1.5, 0.6,0), mar=.1 + c(3,3:1))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o",
+ col=2, log = "x", main = "co.o50: periodic"))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o", ylim = robrng(pp.sic),
+ col=2, log = "x", main = "co.o50: periodic"))
+ of <- 0.64430538125795
+ with(co.o50, plot(pp.sic - of ~ pp.lambda, type ="o", ylim = c(6e-15, 8e-15),
+ ylab = paste("sic -",formatC(of, dig=14, small.m = "'")),
+ col=2, log = "x", main = "co.o50: periodic"))
+ par(op)
+ }
>
> showProc.time()
Time (user system elapsed): 0.049 0 0.05
>
> ## cobs99: Since SIC chooses a lambda that corresponds to the smoothest
> ## possible fit, rerun cobs with a larger lstart value
> ## (lstart <- log(.Machine$double.xmax)^3) # 3.57 e9
> ##
> co.o50. <-
+ cobs(day,speed, knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
The algorithm has converged. You might
plot() the returned object (which plots 'sic' against 'lambda')
to see if you have found the global minimum of the information criterion
so that you can determine if you need to adjust any or all of
'lambda.lo', 'lambda.hi' and 'lambda.length' and refit the model.
> summary(co.o50.)
COBS smoothing spline (degree = 2) from call:
cobs(x = day, y = speed, constraint = "periodic", nknots = 10, method = "quantile", tau = 0.5, lambda = -1, knots.add = TRUE)
{tau=0.5}-quantile; dimensionality of fit: 7 from {14,13,11,8,7,30}
x$knots[1:10]: 0.999635, 41.000000, 82.000000, ... , 366.000365
lambda = 101002.6, selected via SIC, out of 25 ones.
coef[1:12]: 1.121550e+01, 1.139573e+01, 1.089025e+01, 9.954427e+00, 8.148158e+00, ... , 5.373106e-04
R^2 = 8.22% ; empirical tau (over all): 3287/6574 = 0.5 (target tau= 0.5)
> summary(pc.5 <- predict(co.o50., interval = "both"))
z fit cb.lo cb.up
Min. : 0.9996 Min. : 7.212 Min. : 6.351 Min. : 7.951
1st Qu.: 92.2498 1st Qu.: 7.790 1st Qu.: 7.000 1st Qu.: 8.600
Median :183.5000 Median : 9.436 Median : 8.555 Median :10.326
Mean :183.5000 Mean : 9.314 Mean : 8.388 Mean :10.241
3rd Qu.:274.7502 3rd Qu.:10.798 3rd Qu.: 9.716 3rd Qu.:11.787
Max. :366.0004 Max. :11.290 Max. :10.347 Max. :13.416
ci.lo ci.up
Min. : 6.782 Min. : 7.598
1st Qu.: 7.370 1st Qu.: 8.213
Median : 8.974 Median : 9.901
Mean : 8.830 Mean : 9.798
3rd Qu.:10.197 3rd Qu.:11.311
Max. :10.797 Max. :12.366
>
> showProc.time()
Time (user system elapsed): 2.83 0.017 3.206
>
> if(doExtra) { ## + repeat.delete.add
+ co.o50.. <- cobs(day,speed, knots.add = TRUE, repeat.delete.add=TRUE,
+ constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
+ summary(co.o50..)
+ showProc.time()
+ }
>
> co.o9 <- ## Compute the .9 quantile smoothing B-spline
+ cobs(day,speed,knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .9,lambda = -1, method = "uniform")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Flavor: r-devel-linux-x86_64-fedora-clang