Last updated on 2024-11-08 07:50:11 CET.
| Flavor | Version | Tinstall | Tcheck | Ttotal | Status | Flags |
|---|---|---|---|---|---|---|
| r-devel-linux-x86_64-debian-clang | 1.3-8 | 10.84 | 115.93 | 126.77 | ERROR | |
| r-devel-linux-x86_64-debian-gcc | 1.3-8 | 8.68 | 87.09 | 95.77 | OK | |
| r-devel-linux-x86_64-fedora-clang | 1.3-8 | 220.76 | ERROR | |||
| r-devel-linux-x86_64-fedora-gcc | 1.3-8 | 206.09 | OK | |||
| r-devel-windows-x86_64 | 1.3-8 | 15.00 | 131.00 | 146.00 | OK | |
| r-patched-linux-x86_64 | 1.3-8 | 10.05 | 115.25 | 125.30 | OK | |
| r-release-linux-x86_64 | 1.3-8 | 10.08 | 115.40 | 125.48 | 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 | 16.00 | 136.00 | 152.00 | 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 | 171.00 | 188.00 | OK |
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’ [3s/3s]
Running ‘ex1.R’ [4s/5s]
Running ‘ex2-long.R’ [7s/10s]
Running ‘ex3.R’ [2s/3s]
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ...15,16c15,16
< Warning messages:
< 1: In cobs(weight, height, knots = weight, nknots = length(weight)) :
---
> Warning message:
> In cobs(weight, height, knots = weight, nknots = length(weight)) :
19,20d18
< 2: In cobs(weight, height, knots = weight, nknots = length(weight)) :
< drqssbc2(): Not all flags are normal (== 1), ifl : 23
Running ‘multi-constr.R’ [4s/5s]
Running ‘roof.R’ [4s/5s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ...24,45d23
< WARNING: Some lambdas had problems in rq.fit.sfnc():
< lambda icyc ifl fidel sum|res|_s k
< [1,] 1.590888e-03 1 25 889.5418 0.00000 3
< [2,] 3.113911e-03 1 25 889.5418 0.00000 3
< [3,] 1.192998e-02 1 25 889.5418 0.00000 3
< [4,] 2.335104e-02 1 25 889.5418 0.00000 3
< [5,] 4.570597e-02 1 25 889.5418 0.00000 3
< [6,] 1.751081e-01 1 25 889.5418 0.00000 3
< [7,] 6.708718e-01 18 21 1110.8511 64.93351 4
< [8,] 1.313125e+00 1 25 889.5418 0.00000 3
< [9,] 2.570235e+00 1 25 889.5418 0.00000 3
< [10,] 9.847052e+00 1 25 889.5418 0.00000 3
< [11,] 1.927405e+01 1 25 889.5418 0.00000 3
< [12,] 3.772589e+01 1 25 889.5418 0.00000 3
< [13,] 7.384247e+01 1 25 889.5418 0.00000 3
< [14,] 2.829043e+02 1 25 889.5418 0.00000 3
< [15,] 5.537404e+02 1 25 889.5418 0.00000 3
< [16,] 1.083859e+03 1 25 889.5418 0.00000 3
< [17,] 2.121483e+03 1 25 889.5418 0.00000 3
< [18,] 4.152467e+03 1 25 889.5418 0.00000 3
< [19,] 8.127798e+03 1 25 889.5418 0.00000 3
< [20,] 1.590888e+04 1 25 889.5418 0.00000 3
47,48c25
< WARNING! Since the optimal lambda chosen by SIC
< reached the smoothest possible fit at `lambda.hi', you should
---
> The algorithm has converged. You might
50,52c27,29
< and possibly consider doing one of the following:
< (1) reduce 'lambda.lo', increase 'lambda.hi', increase 'lambda.length' or all of the above;
< (2) decrease the number of knots.
---
> 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.
54,56d30
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 252512525251251212525125252525125252525252525
60,62c34
< * Warning in algorithm: some ifl != 1
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {3,16,4,8,5}
---
> {tau=0.5}-quantile; dimensionality of fit: 5 from {16,11,9,8,6,5,4}
64c36
< lambda = 144.535, selected via SIC, out of 25 ones.
---
> lambda = 19.27405, selected via SIC, out of 25 ones.
66,67c38,39
< coef[1:12]: 99.8592496, 98.4410072, 95.8601794, 93.6911524, 92.2856863, ... , 0.2997177
< R^2 = -6.47% ; empirical tau (over all): 79/153 = 0.5163399 (target tau= 0.5)
---
> coef[1:12]: 99.8569569, 98.4177329, 95.9739856, 94.1164468, 93.0604245, ... , 0.4726201
> R^2 = -5.6% ; empirical tau (over all): 78/153 = 0.5098039 (target tau= 0.5)
79,80c51,52
< [1,] 1.59089e-03 1.80959
< [2,] 3.11391e-03 1.80959
---
> [1,] 1.59089e-03 2.24395
> [2,] 3.11391e-03 2.24395
82,84c54,56
< [4,] 1.19300e-02 1.80959
< [5,] 2.33510e-02 1.80959
< [6,] 4.57060e-02 1.80959
---
> [4,] 1.19300e-02 2.24395
> [5,] 2.33510e-02 2.24395
> [6,] 4.57060e-02 2.24395
86c58
< [8,] 1.75108e-01 1.80959
---
> [8,] 1.75108e-01 2.24424
88,90c60,62
< [10,] 6.70872e-01 2.04820
< [11,] 1.31313e+00 1.80959
< [12,] 2.57024e+00 1.80959
---
> [10,] 6.70872e-01 2.24535
> [11,] 1.31313e+00 2.18317
> [12,] 2.57024e+00 2.15738
92,95c64,67
< [14,] 9.84705e+00 1.80959
< [15,] 1.92740e+01 1.80959
< [16,] 3.77259e+01 1.80959
< [17,] 7.38425e+01 1.80959
---
> [14,] 9.84705e+00 2.11165
> [15,] 1.92740e+01 2.09955
> [16,] 3.77259e+01 2.11706
> [17,] 7.38425e+01 2.10159
97,103c69,75
< [19,] 2.82904e+02 1.80959
< [20,] 5.53740e+02 1.80959
< [21,] 1.08386e+03 1.80959
< [22,] 2.12148e+03 1.80959
< [23,] 4.15247e+03 1.80959
< [24,] 8.12780e+03 1.80959
< [25,] 1.59089e+04 1.80959
---
> [19,] 2.82904e+02 2.10095
> [20,] 5.53740e+02 2.12696
> [21,] 1.08386e+03 2.12696
> [22,] 2.12148e+03 2.12696
> [23,] 4.15247e+03 2.12696
> [24,] 8.12780e+03 2.12696
> [25,] 1.59089e+04 2.12696
129,150d100
< WARNING: Some lambdas had problems in rq.fit.sfnc():
< lambda icyc ifl fidel sum|res|_s k
< [1,] 3.113911e-03 1 25 889.5418 0.00000 3
< [2,] 1.192998e-02 17 21 981.4627 106.09537 3
< [3,] 8.946220e-02 1 25 889.5418 0.00000 3
< [4,] 1.751081e-01 1 25 889.5418 0.00000 3
< [5,] 3.427464e-01 1 25 889.5418 0.00000 3
< [6,] 6.708718e-01 10 21 1003.6100 21.11754 3
< [7,] 2.570235e+00 1 25 889.5418 0.00000 3
< [8,] 5.030829e+00 1 24 889.5418 0.00000 3
< [9,] 9.847052e+00 1 25 889.5418 0.00000 3
< [10,] 1.927405e+01 1 25 889.5418 0.00000 3
< [11,] 3.772589e+01 1 25 889.5418 0.00000 3
< [12,] 7.384247e+01 1 25 889.5418 0.00000 3
< [13,] 1.445350e+02 1 25 889.5418 0.00000 3
< [14,] 2.829043e+02 1 25 889.5418 0.00000 3
< [15,] 5.537404e+02 1 25 889.5418 0.00000 3
< [16,] 1.083859e+03 1 25 889.5418 0.00000 3
< [17,] 2.121483e+03 1 25 889.5418 0.00000 3
< [18,] 4.152467e+03 1 25 889.5418 0.00000 3
< [19,] 8.127798e+03 1 25 889.5418 0.00000 3
< [20,] 1.590888e+04 1 25 889.5418 0.00000 3
152,153c102
< WARNING! Since the optimal lambda chosen by SIC
< rests on a flat portion, you might
---
> The algorithm has converged. You might
155c104,106
< to see if you want to reduce 'lambda.lo' and/or increase 'lambda.ho'
---
> 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.
157,159d107
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 125121112525252112524252525252525252525252525
163,165c111
< * Warning in algorithm: some ifl != 1
<
< {tau=0.25}-quantile; dimensionality of fit: 10 from {13,3,10}
---
> {tau=0.25}-quantile; dimensionality of fit: 5 from {13,12,11,10,8,7,6,5,3}
167c113
< lambda = 1.313125, selected via SIC, out of 25 ones.
---
> lambda = 73.84247, selected via SIC, out of 25 ones.
169,170c115,116
< coef[1:12]: 99.254957, 91.804860, 82.972707, 80.841558, 80.841558, ... , 6.116351
< empirical tau (over all): 40/153 = 0.2614379 (target tau= 0.25)
---
> coef[1:12]: 99.6189624, 95.7795144, 88.7927299, 82.9207676, 79.1159073, ... , 0.8113919
> empirical tau (over all): 44/153 = 0.2875817 (target tau= 0.25)
187,206d132
< WARNING: Some lambdas had problems in rq.fit.sfnc():
< lambda icyc ifl fidel sum|res|_s k
< [1,] 1.590888e-03 1 25 889.5418 0.00000 3
< [2,] 3.113911e-03 5 21 657.3322 95.00356 3
< [3,] 6.094988e-03 1 25 889.5418 0.00000 3
< [4,] 1.192998e-02 1 25 889.5418 0.00000 3
< [5,] 2.335104e-02 1 25 889.5418 0.00000 3
< [6,] 4.570597e-02 1 25 889.5418 0.00000 3
< [7,] 3.427464e-01 1 25 889.5418 0.00000 3
< [8,] 6.708718e-01 1 25 889.5418 0.00000 3
< [9,] 2.570235e+00 1 25 889.5418 0.00000 3
< [10,] 5.030829e+00 1 25 889.5418 0.00000 3
< [11,] 9.847052e+00 1 25 889.5418 0.00000 3
< [12,] 1.445350e+02 1 25 889.5418 0.00000 3
< [13,] 2.829043e+02 1 25 889.5418 0.00000 3
< [14,] 5.537404e+02 1 25 889.5418 0.00000 3
< [15,] 2.121483e+03 1 25 889.5418 0.00000 3
< [16,] 4.152467e+03 1 25 889.5418 0.00000 3
< [17,] 8.127798e+03 1 25 889.5418 0.00000 3
< [18,] 1.590888e+04 1 25 889.5418 0.00000 3
213,215d138
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 2521252525251125251252525111252525125252525
219,221c142
< * Warning in algorithm: some ifl != 1
<
< {tau=0.75}-quantile; dimensionality of fit: 70 from {3,70}
---
> {tau=0.75}-quantile; dimensionality of fit: 70 from {70}
223c144
< lambda = 19.27405, selected via SIC, out of 25 ones.
---
> lambda = 5.030829, selected via SIC, out of 25 ones.
241,340c162,261
< [1,] 0.04998516 99.85925 70.45262 129.26588 82.39397 117.32453
< [2,] 0.20109657 99.43830 72.99090 125.88569 83.73058 115.14602
< [3,] 0.35220798 99.02419 74.56555 123.48283 84.49763 113.55074
< [4,] 0.50331939 98.61692 75.51646 121.71738 84.89702 112.33682
< [5,] 0.65443080 98.21650 76.14832 120.28468 85.10969 111.32331
< [6,] 0.80554221 97.82292 76.64775 118.99810 85.24650 110.39935
< [7,] 0.95665362 97.43619 77.02675 117.84563 85.31455 109.55783
< [8,] 1.10776504 97.05630 77.08161 117.03099 85.19287 108.91973
< [9,] 1.25887645 96.68325 76.66817 116.69834 84.79583 108.57068
< [10,] 1.40998786 96.31705 76.12279 116.51132 84.32321 108.31090
< [11,] 1.56109927 95.95770 75.71600 116.19939 83.93569 107.97971
< [12,] 1.71221068 95.60518 75.57128 115.63908 83.70659 107.50378
< [13,] 1.86332209 95.25951 75.67433 114.84469 83.62742 106.89160
< [14,] 2.01443350 94.92069 75.86425 113.97713 83.60262 106.23875
< [15,] 2.16554491 94.58870 75.81500 113.36241 83.43857 105.73884
< [16,] 2.31665632 94.26357 75.42364 113.10349 83.07410 105.45303
< [17,] 2.46776773 93.94527 75.04254 112.84800 82.71850 105.17204
< [18,] 2.61887914 93.63382 74.90902 112.35863 82.51273 104.75492
< [19,] 2.76999056 93.32922 75.10220 111.55623 82.50377 104.15467
< [20,] 2.92110197 93.03146 75.54412 110.51879 82.64532 103.41759
< [21,] 3.07221338 92.74054 75.96589 109.51519 82.77768 102.70339
< [22,] 3.22332479 92.45646 76.08423 108.82870 82.73261 102.18031
< [23,] 3.37443620 92.17923 76.04988 108.30859 82.59963 101.75883
< [24,] 3.52554761 91.90885 75.85434 107.96335 82.37370 101.44399
< [25,] 3.67665902 91.64530 75.20435 108.08626 81.88064 101.40997
< [26,] 3.82777043 91.38861 74.05098 108.72623 81.09139 101.68582
< [27,] 3.97888184 91.13875 72.71804 109.55946 80.19826 102.07924
< [28,] 4.12999325 90.89574 71.43794 110.35354 79.33930 102.45218
< [29,] 4.28110467 90.65957 70.34919 110.96995 78.59677 102.72238
< [30,] 4.43221608 90.43025 69.52417 111.33633 78.01365 102.84686
< [31,] 4.58332749 90.20777 68.98880 111.42675 77.60533 102.81022
< [32,] 4.73443890 89.99214 68.73206 111.25222 77.36528 102.61899
< [33,] 4.88555031 89.78335 68.70739 110.85931 77.26585 102.30085
< [34,] 5.03666172 89.58140 68.82785 110.33496 77.25538 101.90742
< [35,] 5.18777313 89.38630 68.95743 109.81517 77.25312 101.51948
< [36,] 5.33888454 89.19804 68.88527 109.51081 77.13382 101.26226
< [37,] 5.48999595 89.01663 68.45127 109.58198 76.80238 101.23087
< [38,] 5.64110736 88.84205 67.76295 109.92116 76.32269 101.36142
< [39,] 5.79221877 88.67433 66.93729 110.41136 75.76420 101.58446
< [40,] 5.94333019 88.51344 66.07156 110.95533 75.18469 101.84220
< [41,] 6.09444160 88.35941 65.24169 111.47712 74.62926 102.08955
< [42,] 6.24555301 88.21221 64.50479 111.91963 74.13182 102.29260
< [43,] 6.39666442 88.07186 63.90296 112.24076 73.71739 102.42633
< [44,] 6.54777583 87.93835 63.46678 112.40992 73.40412 102.47259
< [45,] 6.69888724 87.81169 63.21814 112.40524 73.20501 102.41837
< [46,] 6.84999865 87.69187 63.17219 112.21155 73.12906 102.25467
< [47,] 7.00111006 87.57889 63.33875 111.81904 73.18211 101.97568
< [48,] 7.15222147 87.47276 63.72296 111.22257 73.36720 101.57832
< [49,] 7.30333288 87.37348 64.32551 110.42144 73.68476 101.06220
< [50,] 7.45444429 87.28103 65.14222 109.41984 74.13228 100.42979
< [51,] 7.60555571 87.19543 66.16276 108.22810 74.70364 99.68722
< [52,] 7.75666712 87.11668 67.36825 106.86510 75.38763 98.84572
< [53,] 7.90777853 87.04476 68.72676 105.36277 76.16528 97.92425
< [54,] 8.05888994 86.97970 70.18536 103.77404 77.00515 96.95425
< [55,] 8.21000135 86.92147 71.65649 102.18645 77.85525 95.98770
< [56,] 8.36111276 86.87009 72.99694 100.74324 78.63051 95.10968
< [57,] 8.51222417 86.82556 73.98507 99.66605 79.19929 94.45182
< [58,] 8.66333558 86.78787 74.35829 99.21744 79.40565 94.17008
< [59,] 8.81444699 86.75702 74.25300 99.26103 79.33059 94.18344
< [60,] 8.96555840 86.73301 74.11460 99.35143 79.23865 94.22738
< [61,] 9.11666981 86.71585 74.16900 99.26270 79.26399 94.16772
< [62,] 9.26778123 86.70554 74.42013 98.99095 79.40895 94.00213
< [63,] 9.41889264 86.70207 74.64353 98.76060 79.54022 93.86391
< [64,] 9.57000405 86.70207 74.33682 99.06731 79.35806 94.04607
< [65,] 9.72111546 86.70207 73.40242 100.00171 78.80310 94.60103
< [66,] 9.87222687 86.70207 72.06011 101.34402 78.00587 95.39826
< [67,] 10.02333828 86.70207 70.49592 102.90822 77.07686 96.32727
< [68,] 10.17444969 86.70207 68.84022 104.56391 76.09350 97.31063
< [69,] 10.32556110 86.70207 67.17776 106.22638 75.10613 98.29801
< [70,] 10.47667251 86.70207 65.56256 107.84157 74.14682 99.25731
< [71,] 10.62778392 86.70207 64.02936 109.37477 73.23622 100.16791
< [72,] 10.77889533 86.70207 62.60084 110.80330 72.38779 101.01635
< [73,] 10.93000675 86.70207 61.29202 112.11211 71.61045 101.79368
< [74,] 11.08111816 86.70207 60.11299 113.29114 70.91020 102.49394
< [75,] 11.23222957 86.70207 59.07044 114.33369 70.29100 103.11313
< [76,] 11.38334098 86.70207 58.16876 115.23537 69.75547 103.64866
< [77,] 11.53445239 86.70207 57.41058 115.99355 69.30517 104.09896
< [78,] 11.68556380 86.70207 56.79720 116.60693 68.94087 104.46326
< [79,] 11.83667521 86.70207 56.32881 117.07532 68.66268 104.74145
< [80,] 11.98778662 86.70207 56.00460 117.39953 68.47013 104.93400
< [81,] 12.13889803 86.70207 55.82283 117.58130 68.36217 105.04196
< [82,] 12.29000944 86.70207 55.78075 117.62338 68.33718 105.06695
< [83,] 12.44112086 86.70207 55.87453 117.52960 68.39288 105.01125
< [84,] 12.59223227 86.70207 56.09911 117.30502 68.52626 104.87787
< [85,] 12.74334368 86.70207 56.44793 116.95620 68.73343 104.67070
< [86,] 12.89445509 86.70207 56.91262 116.49152 69.00942 104.39471
< [87,] 13.04556650 86.70207 57.48251 115.92162 69.34790 104.05624
< [88,] 13.19667791 86.70207 58.14411 115.26002 69.74083 103.66330
< [89,] 13.34778932 86.70207 58.88027 114.52387 70.17805 103.22608
< [90,] 13.49890073 86.70207 59.66924 113.73489 70.64664 102.75749
< [91,] 13.65001214 86.70207 60.48356 112.92057 71.13029 102.27385
< [92,] 13.80112355 86.70207 61.28872 112.11542 71.60849 101.79564
< [93,] 13.95223496 86.70207 62.04196 111.36217 72.05586 101.34827
< [94,] 14.10334638 86.70207 62.69152 110.71261 72.44165 100.96248
< [95,] 14.25445779 86.70207 63.17698 110.22715 72.72997 100.67416
< [96,] 14.40556920 86.70207 63.43166 109.97247 72.88123 100.52290
< [97,] 14.55668061 86.70207 63.38768 110.01645 72.85511 100.54902
< [98,] 14.70779202 86.70207 62.98352 110.42062 72.61507 100.78906
< [99,] 14.85890343 86.70207 62.17212 111.23201 72.13316 101.27097
< [100,] 15.01001484 86.70207 60.92663 112.47750 71.39344 102.01069
---
> [1,] 0.04998516 99.85696 71.02180 128.69211 82.73109 116.98282
> [2,] 0.20109657 99.43170 73.49827 125.36513 84.02923 114.83416
> [3,] 0.35220798 99.01723 75.03391 123.00056 84.77298 113.26149
> [4,] 0.50331939 98.61356 75.96202 121.26510 85.16029 112.06684
> [5,] 0.65443080 98.22068 76.58136 119.86000 85.36859 111.07277
> [6,] 0.80554221 97.83859 77.07493 118.60226 85.50657 110.17061
> [7,] 0.95665362 97.46729 77.45448 117.48011 85.58122 109.35337
> [8,] 1.10776504 97.10679 77.52028 116.69330 85.47391 108.73967
> [9,] 1.25887645 96.75708 77.13096 116.38320 85.10067 108.41349
> [10,] 1.40998786 96.41816 76.61633 116.21998 84.65740 108.17892
> [11,] 1.56109927 96.09003 76.24170 115.93835 84.30165 107.87841
> [12,] 1.71221068 95.77269 76.12812 115.41726 84.10533 107.44006
> [13,] 1.86332209 95.46615 76.26158 114.67072 84.06011 106.87219
> [14,] 2.01443350 95.17040 76.48429 113.85650 84.07228 106.26851
> [15,] 2.16554491 94.88544 76.47657 113.29430 83.95199 105.81889
> [16,] 2.31665632 94.61127 76.13747 113.08507 83.63925 105.58329
> [17,] 2.46776773 94.34789 75.81251 112.88328 83.33930 105.35649
> [18,] 2.61887914 94.09531 75.73439 112.45623 83.19034 105.00029
> [19,] 2.76999056 93.85352 75.98072 111.72632 83.23845 104.46859
> [20,] 2.92110197 93.62252 76.47502 110.77002 83.43822 103.80682
> [21,] 3.07221338 93.40231 76.95365 109.85097 83.63307 103.17155
> [22,] 3.22332479 93.19290 77.13883 109.24697 83.65802 102.72778
> [23,] 3.37443620 92.99428 77.17837 108.81018 83.60084 102.38771
> [24,] 3.52554761 92.80644 77.06394 108.54895 83.45660 102.15629
> [25,] 3.67665902 92.62499 76.50354 108.74644 83.05009 102.19989
> [26,] 3.82777043 92.43415 75.43346 109.43484 82.33704 102.53125
> [27,] 3.97888184 92.23251 74.16977 110.29524 81.50463 102.96039
> [28,] 4.12999325 92.02008 72.94041 111.09975 80.68822 103.35194
> [29,] 4.28110467 91.79686 71.88118 111.71254 79.96847 103.62524
> [30,] 4.43221608 91.56284 71.06304 112.06265 79.38754 103.73815
> [31,] 4.58332749 91.31804 70.51142 112.12465 78.96051 103.67557
> [32,] 4.73443890 91.06244 70.21552 111.90936 78.68097 103.44391
> [33,] 4.88555031 90.79605 70.12967 111.46243 78.52181 103.07029
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> [35,] 5.18777313 90.23090 70.19903 110.26276 78.33351 102.12828
> [36,] 5.33888454 89.93586 70.01785 109.85388 78.10609 101.76564
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> [40,] 5.94333019 88.85633 66.85058 110.86209 75.78661 101.92606
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> [42,] 6.24555301 88.38132 65.13462 111.62803 74.57457 102.18808
> [43,] 6.39666442 88.16001 64.46079 111.85922 74.08449 102.23552
> [44,] 6.54777583 87.94948 63.95348 111.94548 73.69770 102.20126
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> [46,] 6.84999865 87.56081 63.51763 111.60398 73.28101 101.84060
> [47,] 7.00111006 87.38266 63.61358 111.15173 73.26565 101.49966
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> [50,] 7.45444429 86.91296 65.20438 108.62154 74.01973 99.80619
> [51,] 7.60555571 86.77798 66.15405 107.40191 74.52895 99.02701
> [52,] 7.75666712 86.65379 67.28915 106.01844 75.15268 98.15491
> [53,] 7.90777853 86.54040 68.57837 104.50242 75.87233 97.20846
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> [58,] 8.66333558 86.13530 73.94727 98.32332 78.89655 93.37405
> [59,] 8.81444699 86.08665 73.82563 98.34767 78.80455 93.36876
> [60,] 8.96555840 86.04880 73.67561 98.42200 78.70008 93.39753
> [61,] 9.11666981 86.02174 73.71872 98.32476 78.71469 93.32879
> [62,] 9.26778123 86.00548 73.95881 98.05214 78.85068 93.16027
> [63,] 9.41889264 86.00000 74.17580 97.82420 78.97733 93.02267
> [64,] 9.57000405 86.00000 73.87505 98.12495 78.79871 93.20129
> [65,] 9.72111546 86.00000 72.95882 99.04118 78.25454 93.74546
> [66,] 9.87222687 86.00000 71.64259 100.35741 77.47280 94.52720
> [67,] 10.02333828 86.00000 70.10879 101.89121 76.56184 95.43816
> [68,] 10.17444969 86.00000 68.48528 103.51472 75.59760 96.40240
> [69,] 10.32556110 86.00000 66.85512 105.14488 74.62941 97.37059
> [70,] 10.47667251 86.00000 65.27131 106.72869 73.68875 98.31125
> [71,] 10.62778392 86.00000 63.76791 108.23209 72.79584 99.20416
> [72,] 10.77889533 86.00000 62.36714 109.63286 71.96390 100.03610
> [73,] 10.93000675 86.00000 61.08376 110.91624 71.20167 100.79833
> [74,] 11.08111816 86.00000 59.92764 112.07236 70.51502 101.48498
> [75,] 11.23222957 86.00000 58.90536 113.09464 69.90786 102.09214
> [76,] 11.38334098 86.00000 58.02120 113.97880 69.38274 102.61726
> [77,] 11.53445239 86.00000 57.27775 114.72225 68.94119 103.05881
> [78,] 11.68556380 86.00000 56.67629 115.32371 68.58397 103.41603
> [79,] 11.83667521 86.00000 56.21700 115.78300 68.31119 103.68881
> [80,] 11.98778662 86.00000 55.89910 116.10090 68.12238 103.87762
> [81,] 12.13889803 86.00000 55.72086 116.27914 68.01652 103.98348
> [82,] 12.29000944 86.00000 55.67959 116.32041 67.99201 104.00799
> [83,] 12.44112086 86.00000 55.77155 116.22845 68.04662 103.95338
> [84,] 12.59223227 86.00000 55.99177 116.00823 68.17741 103.82259
> [85,] 12.74334368 86.00000 56.33381 115.66619 68.38056 103.61944
> [86,] 12.89445509 86.00000 56.78946 115.21054 68.65118 103.34882
> [87,] 13.04556650 86.00000 57.34829 114.65171 68.98308 103.01692
> [88,] 13.19667791 86.00000 57.99703 114.00297 69.36839 102.63161
> [89,] 13.34778932 86.00000 58.71888 113.28112 69.79711 102.20289
> [90,] 13.49890073 86.00000 59.49252 112.50748 70.25659 101.74341
> [91,] 13.65001214 86.00000 60.29101 111.70899 70.73083 101.26917
> [92,] 13.80112355 86.00000 61.08052 110.91948 71.19974 100.80026
> [93,] 13.95223496 86.00000 61.81913 110.18087 71.63842 100.36158
> [94,] 14.10334638 86.00000 62.45607 109.54393 72.01671 99.98329
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> [99,] 14.85890343 86.00000 61.94676 110.05324 71.71422 100.28578
> [100,] 15.01001484 86.00000 60.72548 111.27452 70.98887 101.01113
445,544c366,465
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< [2,] 0.20109657 97.09552 68.34722 125.84383 83.81418 110.37687
< [3,] 0.35220798 95.07576 68.48923 121.66229 82.79312 107.35840
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< [7,] 0.95665362 88.39334 66.20829 110.57839 78.14413 98.64255
< [8,] 1.10776504 87.07190 65.35942 108.78438 77.04101 97.10279
< [9,] 1.25887645 85.89012 64.13374 107.64651 75.83895 95.94129
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< [11,] 1.56109927 83.94556 61.94285 105.94827 73.78059 94.11053
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< [13,] 1.86332209 82.55966 61.27058 103.84874 72.72438 92.39494
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< [15,] 2.16554491 81.72655 61.31955 102.13356 72.29878 91.15433
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< [34,] 5.03666172 77.04712 54.48802 99.60622 66.62511 87.46914
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< [38,] 5.64110736 73.64293 50.72995 96.55590 63.05742 84.22843
< [39,] 5.79221877 72.85528 49.22714 96.48343 61.93938 83.77118
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< [41,] 6.09444160 71.39162 46.26268 96.52057 59.78237 83.00088
< [42,] 6.24555301 70.71561 44.94565 96.48556 58.81022 82.62100
< [43,] 6.39666442 70.07680 43.80522 96.34839 57.93967 82.21394
< [44,] 6.54777583 69.47521 42.87463 96.07579 57.18608 81.76434
< [45,] 6.69888724 68.91082 42.17765 95.64400 56.56044 81.26121
< [46,] 6.84999865 68.38365 41.73078 95.03652 56.07036 80.69694
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< [100,] 15.01001484 64.99235 36.97448 93.01023 52.04845 77.93626
---
> [1,] 0.04998516 99.61896 71.09477 128.14315 82.67778 116.56014
> [2,] 0.20109657 98.47936 72.82560 124.13312 83.24300 113.71572
> [3,] 0.35220798 97.35829 73.63361 121.08298 83.26765 111.44893
> [4,] 0.50331939 96.25575 73.84849 118.66301 82.94756 109.56394
> [5,] 0.65443080 95.17173 73.76577 116.57769 82.45824 107.88523
> [6,] 0.80554221 94.10624 73.56650 114.64599 81.90721 106.30528
> [7,] 0.95665362 93.05929 73.26229 112.85628 81.30139 104.81718
> [8,] 1.10776504 92.03085 72.65556 111.40614 80.52342 103.53829
> [9,] 1.25887645 91.02095 71.60648 110.43542 79.49025 102.55165
> [10,] 1.40998786 90.02957 70.44130 109.61785 78.39564 101.66351
> [11,] 1.56109927 89.05672 69.42245 108.69100 77.39547 100.71798
> [12,] 1.71221068 88.10240 68.66968 107.53512 76.56086 99.64395
> [13,] 1.86332209 87.16661 68.16915 106.16408 75.88358 98.44965
> [14,] 2.01443350 86.24935 67.76475 104.73394 75.27092 97.22778
> [15,] 2.16554491 85.35061 67.14027 103.56095 74.53507 96.16615
> [16,] 2.31665632 84.47040 66.19583 102.74498 73.61671 95.32409
> [17,] 2.46776773 83.60872 65.27323 101.94421 72.71884 94.49860
> [18,] 2.61887914 82.76557 64.60266 100.92848 71.97819 93.55294
> [19,] 2.76999056 81.94094 64.26088 99.62100 71.44034 92.44154
> [20,] 2.92110197 81.13484 64.17227 98.09742 71.06037 91.20931
> [21,] 3.07221338 80.34727 64.07600 96.61855 70.68338 90.01116
> [22,] 3.22332479 79.57823 63.69729 95.45917 70.14617 89.01029
> [23,] 3.37443620 78.82772 63.18237 94.47306 69.53558 88.11985
> [24,] 3.52554761 78.09573 62.52299 93.66847 68.84672 87.34474
> [25,] 3.67665902 77.38227 61.43468 93.32987 67.91063 86.85392
> [26,] 3.82777043 76.68734 59.86999 93.50470 66.69913 86.67556
> [27,] 3.97888184 76.01094 58.14300 93.87888 65.39875 86.62313
> [28,] 4.12999325 75.35307 56.47916 94.22697 64.14341 86.56272
> [29,] 4.28110467 74.71372 55.01281 94.41462 63.01289 86.41454
> [30,] 4.43221608 74.09290 53.81417 94.37163 62.04889 86.13691
> [31,] 4.58332749 73.49061 52.90837 94.07284 61.26634 85.71488
> [32,] 4.73443890 72.90685 52.28474 93.52895 60.65890 85.15479
> [33,] 4.88555031 72.34161 51.89810 92.78512 60.19973 84.48349
> [34,] 5.03666172 71.79490 51.66412 91.92568 59.83877 83.75104
> [35,] 5.18777313 71.26672 51.45089 91.08256 59.49764 83.03581
> [36,] 5.33888454 70.75707 51.05385 90.46029 59.05487 82.45927
> [37,] 5.48999595 70.26595 50.31772 90.21418 58.41823 82.11366
> [38,] 5.64110736 69.79335 49.34679 90.23991 57.64966 81.93704
> [39,] 5.79221877 69.33928 48.25453 90.42403 56.81656 81.86200
> [40,] 5.94333019 68.90374 47.13530 90.67219 55.97496 81.83253
> [41,] 6.09444160 68.48673 46.06273 90.91073 55.16859 81.80486
> [42,] 6.24555301 68.08824 45.09223 91.08425 54.43038 81.74611
> [43,] 6.39666442 67.70829 44.26465 91.15193 53.78457 81.63201
> [44,] 6.54777583 67.34686 43.60963 91.08408 53.24877 81.44495
> [45,] 6.69888724 67.00396 43.14841 90.85950 52.83559 81.17232
> [46,] 6.84999865 66.67958 42.89570 90.46347 52.55378 80.80539
> [47,] 7.00111006 66.37374 42.86099 89.88649 52.40897 80.33850
> [48,] 7.15222147 66.08642 43.04930 89.12354 52.40414 79.76870
> [49,] 7.30333288 65.81763 43.46129 88.17397 52.53968 79.09558
> [50,] 7.45444429 65.56737 44.09290 87.04184 52.81318 78.32156
> [51,] 7.60555571 65.33564 44.93411 85.73716 53.21870 77.45257
> [52,] 7.75666712 65.12243 45.96662 84.27824 53.74535 76.49951
> [53,] 7.90777853 64.92775 47.15943 82.69607 54.37473 75.48077
> [54,] 8.05888994 64.75160 48.46122 81.04198 55.07637 74.42683
> [55,] 8.21000135 64.59398 49.78707 79.40088 55.79981 73.38814
> [56,] 8.36111276 64.45488 50.99804 77.91173 56.46255 72.44721
> [57,] 8.51222417 64.33432 51.87914 76.78949 56.93690 71.73173
> [58,] 8.66333558 64.23228 52.17569 76.28887 57.07159 71.39297
> [59,] 8.81444699 64.14877 52.01997 76.27756 56.94519 71.35234
> [60,] 8.96555840 64.08378 51.84402 76.32354 56.81431 71.35326
> [61,] 9.11666981 64.03733 51.86698 76.20767 56.80908 71.26558
> [62,] 9.26778123 64.00940 52.09265 75.92615 56.93177 71.08704
> [63,] 9.41889264 64.00000 52.30332 75.69669 57.05307 70.94693
> [64,] 9.57000405 64.00000 52.00581 75.99419 56.87637 71.12363
> [65,] 9.72111546 64.00000 51.09945 76.90055 56.33807 71.66193
> [66,] 9.87222687 64.00000 49.79742 78.20258 55.56476 72.43524
> [67,] 10.02333828 64.00000 48.28016 79.71984 54.66363 73.33637
> [68,] 10.17444969 64.00000 46.67416 81.32584 53.70978 74.29022
> [69,] 10.32556110 64.00000 45.06158 82.93842 52.75203 75.24797
> [70,] 10.47667251 64.00000 43.49485 84.50515 51.82152 76.17848
> [71,] 10.62778392 64.00000 42.00766 85.99234 50.93824 77.06176
> [72,] 10.77889533 64.00000 40.62200 87.37800 50.11526 77.88474
> [73,] 10.93000675 64.00000 39.35246 88.64754 49.36126 78.63874
> [74,] 11.08111816 64.00000 38.20881 89.79119 48.68201 79.31799
> [75,] 11.23222957 64.00000 37.19755 90.80245 48.08140 79.91860
> [76,] 11.38334098 64.00000 36.32292 91.67708 47.56194 80.43806
> [77,] 11.53445239 64.00000 35.58749 92.41251 47.12515 80.87485
> [78,] 11.68556380 64.00000 34.99252 93.00748 46.77178 81.22822
> [79,] 11.83667521 64.00000 34.53818 93.46182 46.50194 81.49806
> [80,] 11.98778662 64.00000 34.22371 93.77629 46.31517 81.68483
> [81,] 12.13889803 64.00000 34.04739 93.95261 46.21045 81.78955
> [82,] 12.29000944 64.00000 34.00657 93.99343 46.18621 81.81379
> [83,] 12.44112086 64.00000 34.09754 93.90246 46.24024 81.75976
> [84,] 12.59223227 64.00000 34.31538 93.68462 46.36962 81.63038
> [85,] 12.74334368 64.00000 34.65373 93.34627 46.57057 81.42943
> [86,] 12.89445509 64.00000 35.10447 92.89553 46.83828 81.16172
> [87,] 13.04556650 64.00000 35.65727 92.34273 47.16660 80.83340
> [88,] 13.19667791 64.00000 36.29902 91.70098 47.54774 80.45226
> [89,] 13.34778932 64.00000 37.01308 90.98692 47.97184 80.02816
> [90,] 13.49890073 64.00000 37.77838 90.22162 48.42637 79.57363
> [91,] 13.65001214 64.00000 38.56826 89.43174 48.89550 79.10450
> [92,] 13.80112355 64.00000 39.34926 88.65074 49.35935 78.64065
> [93,] 13.95223496 64.00000 40.07990 87.92010 49.79330 78.20670
> [94,] 14.10334638 64.00000 40.70997 87.29003 50.16751 77.83249
> [95,] 14.25445779 64.00000 41.18086 86.81914 50.44718 77.55282
> [96,] 14.40556920 64.00000 41.42789 86.57211 50.59390 77.40610
> [97,] 14.55668061 64.00000 41.38523 86.61477 50.56856 77.43144
> [98,] 14.70779202 64.00000 40.99320 87.00680 50.33573 77.66427
> [99,] 14.85890343 64.00000 40.20615 87.79385 49.86828 78.13172
> [100,] 15.01001484 64.00000 38.99804 89.00196 49.15076 78.84924
Running ‘small-ex.R’ [3s/3s]
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
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’ [4s/5s]
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.
WARNING: Some lambdas had problems in rq.fit.sfnc():
lambda icyc ifl fidel sum|res|_s k
[1,] 2.30776 16 23 250.3 7.5999 11
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.
Warning message:
In cobs(speed, dist, "increase", lambda = -1) :
drqssbc2(): Not all flags are normal (== 1), ifl : 11111111112311111111111111
> summaryCobs(co2)
List of 24
$ call : language cobs(x = speed, y = dist, constraint = "increase", lambda = -1)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi TRUE
$ x : num [1:50] 4 4 7 7 8 9 10 10 10 11 ...
$ y : num [1:50] 2 10 4 22 16 10 18 26 34 17 ...
$ resid : num [1:50] -4.86 3.14 -9.75 8.25 0 ...
$ fitted : num [1:50] 6.86 6.86 13.75 13.75 16 ...
$ coef : num [1:20] 6.86 10.37 14.88 17.12 19.55 ...
$ knots : num [1:18] 4 7 8 9 10 ...
$ k0 : int [1:25] 16 16 16 16 16 16 15 15 14 12 ...
$ k : int 3
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 32539
$ lambda : Named num 66.3
..- attr(*, "names")= chr "lambda"
$ icyc : int [1:25] 17 17 15 16 16 16 18 16 17 19 ...
$ ifl : int [1:25] 1 1 1 1 1 1 1 1 1 1 ...
$ pp.lambda : num [1:25] 0 0.01 0.01 0.02 0.04 0.08 0.16 0.31 0.6 1.18 ...
$ pp.sic : num [1:25] 2.23 2.23 2.23 2.23 2.23 ...
$ i.mask : logi [1:25] TRUE TRUE TRUE TRUE TRUE TRUE ...
cb.lo ci.lo fit ci.up cb.up
1 -18.0106902 -9.829675 6.86289 23.5554 31.7365
2 -15.9869427 -8.308682 7.35806 23.0248 30.7031
3 -14.7253903 -7.299595 7.85201 23.0036 30.4294
4 -14.0304377 -6.671152 8.34475 23.3607 30.7199
5 -13.6842238 -6.277147 8.83627 23.9497 31.3568
6 -13.4881973 -5.984332 9.32657 24.6375 32.1413
7 -13.2846859 -5.686895 9.81565 25.3182 32.9160
8 -12.9604500 -5.308840 10.30352 25.9159 33.5675
9 -12.4418513 -4.800750 10.79017 26.3811 34.0222
10 -11.6889866 -4.135844 11.27560 26.6871 34.2402
11 -10.6923973 -3.307777 11.75982 26.8274 34.2120
12 -9.4739641 -2.331232 12.24282 26.8169 33.9596
13 -8.0930597 -1.246053 12.72459 26.6952 33.5422
14 -6.6587120 -0.125409 13.20516 26.5357 33.0690
15 -5.3461743 0.913089 13.68450 26.4559 32.7152
16 -4.3525007 1.737247 14.16278 26.5883 32.6781
17 -3.5579640 2.427497 14.64024 26.8530 32.8385
18 -2.7821201 3.104937 15.11690 27.1289 33.0159
19 -1.9790693 3.800369 15.59275 27.3851 33.1646
20 -1.2507247 4.445431 16.06788 27.6903 33.3865
21 -0.6706167 4.992698 16.54814 28.1036 33.7669
22 -0.0321786 5.581929 17.03697 28.4920 34.1061
23 0.7878208 6.295824 17.53436 28.7729 34.2809
24 1.7680338 7.120056 18.04033 28.9606 34.3126
25 2.7272662 7.933027 18.55487 29.1767 34.3825
26 3.5589282 8.663206 19.07798 29.4928 34.5970
27 4.4415126 9.430376 19.60966 29.7890 34.7778
28 5.4482980 10.283717 20.14992 30.0161 34.8515
29 6.4928117 11.165196 20.69874 30.2323 34.9047
30 7.3396986 11.916867 21.25613 30.5954 35.1726
31 8.0441586 12.575775 21.82210 31.0684 35.6000
32 8.8220660 13.286792 22.39663 31.5065 35.9712
33 9.7293382 14.087444 22.97973 31.8720 36.2301
34 10.6439776 14.895860 23.57141 32.2470 36.4988
35 11.3712676 15.581364 24.17165 32.7619 36.9720
36 12.0903660 16.264191 24.78047 33.2968 37.4706
37 12.9621618 17.052310 25.39786 33.7434 37.8336
38 13.9690548 17.933912 26.02382 34.1137 38.0786
39 14.8961150 18.764757 26.65834 34.5519 38.4206
40 15.5880299 19.440617 27.30144 35.1623 39.0149
41 16.2838155 20.121892 27.95311 35.7843 39.6224
42 17.1058166 20.890689 28.61335 36.3360 40.1209
43 17.9817714 21.698514 29.28216 36.8658 40.5826
44 18.6610233 22.377150 29.95954 37.5419 41.2581
45 19.1808813 22.951637 30.64550 38.3394 42.1101
46 19.7841459 23.584917 31.34002 39.0951 42.8959
47 20.5213873 24.310926 32.04311 39.7753 43.5648
48 21.2465778 25.031668 32.75477 40.4779 44.2630
49 21.7264172 25.590574 33.47501 41.3594 45.2236
50 22.1476742 26.112985 34.20381 42.2946 46.2600
51 22.6982036 26.724968 34.94119 43.1574 47.1842
52 23.3692423 27.420644 35.68713 43.9536 48.0050
53 23.9709413 28.072605 36.44165 44.8107 48.9124
54 24.3957772 28.608693 37.20474 45.8008 50.0137
55 24.9012324 29.201704 37.97639 46.7511 51.0516
56 25.6136292 29.936410 38.75662 47.5768 51.8996
57 26.4819493 30.778576 39.54542 48.3123 52.6089
58 27.2901515 31.583215 40.34279 49.1024 53.3954
59 28.0053951 32.328289 41.14873 49.9692 54.2921
60 28.8530207 33.165023 41.96324 50.7615 55.0735
61 29.9067993 34.142924 42.78632 51.4297 55.6658
62 31.0646746 35.193503 43.61797 52.0424 56.1713
63 32.0654071 36.141443 44.45820 52.7749 56.8510
64 32.9512818 37.015121 45.30699 53.5989 57.6627
65 33.9291102 37.953328 46.16435 54.3754 58.3996
66 35.0297017 38.976740 47.03029 55.0838 59.0309
67 36.0927814 39.977797 47.90479 55.8318 59.7168
68 36.9113073 40.817553 48.78787 56.7582 60.6644
69 37.7036248 41.642540 49.67951 57.7165 61.6554
70 38.6422928 42.568561 50.57973 58.5909 62.5172
71 39.7057083 43.581119 51.48852 59.3959 63.2713
72 40.6774154 44.534950 52.40587 60.2768 64.1343
73 41.4311354 45.345310 53.33180 61.3183 65.2325
74 42.1677718 46.147024 54.26630 62.3856 66.3648
75 42.9301723 46.968847 55.20937 63.4499 67.4886
76 43.5601364 47.704612 56.16101 64.6174 68.7619
77 43.7706750 48.161720 57.12122 66.0807 70.4718
78 43.6707129 48.413272 58.09000 67.7667 72.5093
79 43.5686662 48.666244 59.06735 69.4685 74.5660
80 43.6408522 49.038961 60.05327 71.0676 76.4657
81 43.9707369 49.587438 61.04777 72.5081 78.1248
82 44.5808788 50.326813 62.05083 73.7748 79.5208
83 45.4473581 51.241035 63.06246 74.8839 80.6776
84 46.5017521 52.284184 64.08267 75.8812 81.6636
85 47.6254964 53.376692 65.11144 76.8462 82.5974
86 48.6454643 54.402376 66.14879 77.8952 83.6521
87 49.6079288 55.392288 67.19471 78.9971 84.7815
88 50.7825571 56.527401 68.24919 79.9710 85.7158
89 52.2754967 57.878951 69.31225 80.7456 86.3490
90 54.0486439 59.421366 70.38388 81.3464 86.7191
91 55.8745252 61.001989 71.46408 81.9262 87.0536
92 57.4111269 62.391297 72.55285 82.7144 87.6946
93 58.7265102 63.634965 73.65019 83.6654 88.5739
94 59.8812030 64.773613 74.75610 84.7386 89.6310
95 60.8442106 65.786441 75.87058 85.9547 90.8969
96 61.4961859 66.593355 76.99363 87.3939 92.4911
97 61.6555082 67.072471 78.12525 89.1780 94.5950
98 61.1305173 67.095165 79.26545 91.4357 97.4004
99 59.7777137 66.565137 80.41421 94.2633 101.0507
100 57.5292654 65.436863 81.57154 97.7062 105.6138
knots :
[1] 3.99998 7.00000 8.00000 9.00000 10.00000 11.00000 12.00000 13.00000
[9] 14.00000 15.00000 16.00000 17.00000 18.00000 19.00000 20.00000 22.00000
[17] 23.00000 25.00002
coef :
[1] 6.862887 10.368778 14.880952 17.119048 19.547619 22.166667 24.976190
[8] 27.976190 31.166667 34.547619 38.119048 41.880952 45.833333 49.976190
[15] 54.309524 61.095238 68.452381 76.095292 81.571544 0.190476
> 1 - sum(co2 $ resid ^2) / sum((dist - mean(dist))^2)# R^2= 67.4%
[1] 0.652418
>
> co3 <- cobs(speed, dist, "convex", lambda = -1)# 3 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/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): 0.001 0 0.001
>
> 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)
Warning message:
In cobs(day, speed, constraint = "periodic", tau = 0.5, lambda = 2.2, :
drqssbc2(): Not all flags are normal (== 1), ifl : 37
> co50.2 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 2)
Warning message:
In cobs(day, speed, constraint = "periodic", tau = 0.5, lambda = 2.2, :
drqssbc2(): Not all flags are normal (== 1), ifl : 38
>
> showProc.time()
Time (user system elapsed): 0.416 0.012 0.502
>
> 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): 0.026 0.008 0.092
>
> ## 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.
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
Flavor: r-devel-linux-x86_64-debian-clang
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’ [4s/12s]
Running ‘ex1.R’ [12s/60s]
Running ‘ex2-long.R’ [8s/29s]
Running ‘ex3.R’
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [7s/22s]
Comparing ‘multi-constr.Rout’ to ‘multi-constr.Rout.save’ ... OK
Running ‘roof.R’ [5s/20s]
Running ‘small-ex.R’ [5s/18s]
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
Running ‘spline-ex.R’ [4s/21s]
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’ [5s/25s]
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’ [10s/29s]
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): 0.003 0 0.066
>
> 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): 0.751 0.039 3.036
>
> 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): 0.26 0.015 0.277
>
> cpuTime(cxy4 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 100))# ~ 3 sec.
Time elapsed: 0.281
> 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: 0.273
> 1 - sum(cxy5 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.4396%
[1] 0.96835
> showProc.time()
Time (user system elapsed): 0.575 0.008 2.819
>
>
> ## 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): 0.169 0.003 0.174
>
> (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): 0.81 0.001 0.979
>
> ## 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: 1.843 0.024 7.219
Execution halted
Running the tests in ‘tests/roof.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> data(USArmyRoofs)
> attach(USArmyRoofs)#-> "age" and "fci"
>
> if(!dev.interactive(orNone=TRUE)) pdf("roof.pdf", width=10)
>
> ## Compute the quadratic median smoothing B-spline with SIC
> ## chosen lambda
> a50 <- cobs(age,fci,constraint = "decrease",lambda = -1,nknots = 10,
+ degree = 2,pointwise = rbind(c(0,0,100)),
+ trace = 2)# trace > 1 : more tracing
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.
fieq=TRUE -> Tnobs = 184, n0 = 29, |ptConstr| = 2
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/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): 0.001 0.002 0.032
>
> 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): 0.722 0.048 2.589
>
> 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 0.003 0.144
>
> ## 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): 2.897 0.029 5.435
>
> 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