Last updated on 2024-10-31 10:50:27 CET.
| Package | ERROR | NOTE | OK |
|---|---|---|---|
| Bessel | 13 | ||
| bitops | 13 | ||
| CLA | 13 | ||
| classGraph | 13 | ||
| cluster | 3 | 10 | |
| cobs | 2 | 11 | |
| copula | 6 | 7 | |
| diptest | 13 | ||
| DPQ | 13 | ||
| DPQmpfr | 13 | ||
| expm | 13 | ||
| fracdiff | 13 | ||
| lokern | 13 | ||
| longmemo | 1 | 12 | |
| lpridge | 13 | ||
| nor1mix | 13 | ||
| plugdensity | 13 | ||
| Rmpfr | 3 | 10 | |
| robustbase | 13 | ||
| robustX | 13 | ||
| round | 13 | ||
| sca | 13 | ||
| sfsmisc | 13 | ||
| stabledist | 13 | ||
| supclust | 13 | ||
| VLMC | 13 |
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: NOTE: 3, OK: 10
Version: 2.1.6
Check: tests
Result: NOTE
Running ‘agnes-ex.R’
Comparing ‘agnes-ex.Rout’ to ‘agnes-ex.Rout.save’ ... OK
Running ‘clara-NAs.R’
Comparing ‘clara-NAs.Rout’ to ‘clara-NAs.Rout.save’ ... OK
Running ‘clara-ex.R’
Comparing ‘clara-ex.Rout’ to ‘clara-ex.Rout.save’ ... OK
Running ‘clara-gower.R’
Running ‘clara.R’
Comparing ‘clara.Rout’ to ‘clara.Rout.save’ ... OK
Running ‘clusplot-out.R’
Comparing ‘clusplot-out.Rout’ to ‘clusplot-out.Rout.save’ ... OK
Running ‘daisy-ex.R’
Comparing ‘daisy-ex.Rout’ to ‘daisy-ex.Rout.save’ ... OK
Running ‘diana-boots.R’
Running ‘diana-ex.R’
Comparing ‘diana-ex.Rout’ to ‘diana-ex.Rout.save’ ... OK
Running ‘ellipsoid-ex.R’
Comparing ‘ellipsoid-ex.Rout’ to ‘ellipsoid-ex.Rout.save’ ... OK
Running ‘fanny-ex.R’
Comparing ‘fanny-ex.Rout’ to ‘fanny-ex.Rout.save’ ...194c194
< iterations 42
---
> iterations 45
Running ‘mona.R’
Comparing ‘mona.Rout’ to ‘mona.Rout.save’ ... OK
Running ‘pam.R’ [77s/114s]
Comparing ‘pam.Rout’ to ‘pam.Rout.save’ ... OK
Running ‘silhouette-default.R’
Comparing ‘silhouette-default.Rout’ to ‘silhouette-default.Rout.save’ ... OK
Running ‘sweep-ex.R’
Flavor: r-devel-linux-x86_64-fedora-clang
Version: 2.1.6
Check: tests
Result: NOTE
Running ‘agnes-ex.R’
Comparing ‘agnes-ex.Rout’ to ‘agnes-ex.Rout.save’ ... OK
Running ‘clara-NAs.R’
Comparing ‘clara-NAs.Rout’ to ‘clara-NAs.Rout.save’ ... OK
Running ‘clara-ex.R’
Comparing ‘clara-ex.Rout’ to ‘clara-ex.Rout.save’ ... OK
Running ‘clara-gower.R’
Running ‘clara.R’
Comparing ‘clara.Rout’ to ‘clara.Rout.save’ ... OK
Running ‘clusplot-out.R’
Comparing ‘clusplot-out.Rout’ to ‘clusplot-out.Rout.save’ ... OK
Running ‘daisy-ex.R’
Comparing ‘daisy-ex.Rout’ to ‘daisy-ex.Rout.save’ ... OK
Running ‘diana-boots.R’
Running ‘diana-ex.R’
Comparing ‘diana-ex.Rout’ to ‘diana-ex.Rout.save’ ... OK
Running ‘ellipsoid-ex.R’
Comparing ‘ellipsoid-ex.Rout’ to ‘ellipsoid-ex.Rout.save’ ... OK
Running ‘fanny-ex.R’
Comparing ‘fanny-ex.Rout’ to ‘fanny-ex.Rout.save’ ...194c194
< iterations 42
---
> iterations 45
Running ‘mona.R’
Comparing ‘mona.Rout’ to ‘mona.Rout.save’ ... OK
Running ‘pam.R’ [72s/87s]
Comparing ‘pam.Rout’ to ‘pam.Rout.save’ ... OK
Running ‘silhouette-default.R’
Comparing ‘silhouette-default.Rout’ to ‘silhouette-default.Rout.save’ ... OK
Running ‘sweep-ex.R’
Flavor: r-devel-linux-x86_64-fedora-gcc
Version: 2.1.6
Check: tests
Result: NOTE
Running 'agnes-ex.R' [2s]
Comparing 'agnes-ex.Rout' to 'agnes-ex.Rout.save' ... OK
Running 'clara-NAs.R' [0s]
Comparing 'clara-NAs.Rout' to 'clara-NAs.Rout.save' ... OK
Running 'clara-ex.R' [2s]
Comparing 'clara-ex.Rout' to 'clara-ex.Rout.save' ... OK
Running 'clara-gower.R' [0s]
Running 'clara.R' [3s]
Comparing 'clara.Rout' to 'clara.Rout.save' ... OK
Running 'clusplot-out.R' [1s]
Comparing 'clusplot-out.Rout' to 'clusplot-out.Rout.save' ... OK
Running 'daisy-ex.R' [1s]
Comparing 'daisy-ex.Rout' to 'daisy-ex.Rout.save' ... OK
Running 'diana-boots.R' [2s]
Running 'diana-ex.R' [0s]
Comparing 'diana-ex.Rout' to 'diana-ex.Rout.save' ... OK
Running 'ellipsoid-ex.R' [0s]
Comparing 'ellipsoid-ex.Rout' to 'ellipsoid-ex.Rout.save' ... OK
Running 'fanny-ex.R' [1s]
Comparing 'fanny-ex.Rout' to 'fanny-ex.Rout.save' ...194c194
< iterations 43
---
> iterations 45
1056c1056
< Converged after 46 iterations, obj = 2665.982
---
> Converged after 44 iterations, obj = 2665.982
Running 'mona.R' [1s]
Comparing 'mona.Rout' to 'mona.Rout.save' ... OK
Running 'pam.R' [31s]
Comparing 'pam.Rout' to 'pam.Rout.save' ... OK
Running 'silhouette-default.R' [2s]
Comparing 'silhouette-default.Rout' to 'silhouette-default.Rout.save' ... OK
Running 'sweep-ex.R' [0s]
Flavor: r-devel-windows-x86_64
Current CRAN status: ERROR: 2, OK: 11
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’ [3s/3s]
Running ‘ex1.R’ [4s/6s]
Running ‘ex2-long.R’ [5s/5s]
Running ‘ex3.R’ [2s/3s]
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [4s/5s]
Comparing ‘multi-constr.Rout’ to ‘multi-constr.Rout.save’ ... OK
Running ‘roof.R’ [4s/5s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ...24,40d23
< WARNING: Some lambdas had problems in rq.fit.sfnc():
< lambda icyc ifl fidel sum|res|_s k
< [1,] 6.094988e-03 1 25 889.5418 0 3
< [2,] 4.570597e-02 1 25 889.5418 0 3
< [3,] 8.946220e-02 1 25 889.5418 0 3
< [4,] 1.751081e-01 1 25 889.5418 0 3
< [5,] 3.427464e-01 1 25 889.5418 0 3
< [6,] 6.708718e-01 1 25 889.5418 0 3
< [7,] 5.030829e+00 1 25 889.5418 0 3
< [8,] 1.927405e+01 1 25 889.5418 0 3
< [9,] 7.384247e+01 1 25 889.5418 0 3
< [10,] 1.445350e+02 1 25 889.5418 0 3
< [11,] 5.537404e+02 1 25 889.5418 0 3
< [12,] 1.083859e+03 1 25 889.5418 0 3
< [13,] 2.121483e+03 1 25 889.5418 0 3
< [14,] 4.152467e+03 1 25 889.5418 0 3
< [15,] 8.127798e+03 1 25 889.5418 0 3
48,50d30
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 1125112525252525112512512525125252525251
54,56c34
< * Warning in algorithm: some ifl != 1
<
< {tau=0.5}-quantile; dimensionality of fit: 4 from {16,3,11,9,6,4}
---
> {tau=0.5}-quantile; dimensionality of fit: 5 from {16,11,9,8,6,5,4}
58c36
< lambda = 282.9043, selected via SIC, out of 25 ones.
---
> lambda = 19.27405, selected via SIC, out of 25 ones.
60,61c38,39
< coef[1:12]: 99.9071264, 98.9703735, 97.1887749, 95.6052671, 94.5143875, ... , 0.1239923
< R^2 = -13.39% ; empirical tau (over all): 81/153 = 0.5294118 (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)
75c53
< [3,] 6.09499e-03 1.80959
---
> [3,] 6.09499e-03 2.24395
78,82c56,60
< [6,] 4.57060e-02 1.80959
< [7,] 8.94622e-02 1.80959
< [8,] 1.75108e-01 1.80959
< [9,] 3.42746e-01 1.80959
< [10,] 6.70872e-01 1.80959
---
> [6,] 4.57060e-02 2.24395
> [7,] 8.94622e-02 2.24395
> [8,] 1.75108e-01 2.24424
> [9,] 3.42746e-01 2.24424
> [10,] 6.70872e-01 2.24535
85c63
< [13,] 5.03083e+00 1.80959
---
> [13,] 5.03083e+00 2.14329
87c65
< [15,] 1.92740e+01 1.80959
---
> [15,] 1.92740e+01 2.09955
89,90c67,68
< [17,] 7.38425e+01 1.80959
< [18,] 1.44535e+02 1.80959
---
> [17,] 7.38425e+01 2.10159
> [18,] 1.44535e+02 2.10170
92,96c70,74
< [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
---
> [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
103,105d80
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = lam0, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 25
109,113c84
<
< **** ERROR in algorithm: ifl = 25
<
<
< {tau=0.5}-quantile; dimensionality of fit: 3 from {3}
---
> {tau=0.5}-quantile; dimensionality of fit: 16 from {16}
117,118c88,89
< coef[1:12]: 99.26997, 78.11083, 91.25217, 89.64419, 84.14059, ... , 0.00000
< R^2 = 35.75% ; empirical tau (over all): 58/153 = 0.379085 (target tau= 0.5)
---
> coef[1:12]: 99.53956, 95.00000, 95.00000, 95.00000, 95.00000, ... , 76.69617
> R^2 = 1.48% ; empirical tau (over all): 78/153 = 0.5098039 (target tau= 0.5)
130,146d100
< 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 3
< [2,] 6.094988e-03 1 25 889.5418 0 3
< [3,] 1.192998e-02 1 25 889.5418 0 3
< [4,] 2.335104e-02 1 25 889.5418 0 3
< [5,] 4.570597e-02 1 25 889.5418 0 3
< [6,] 6.708718e-01 1 25 889.5418 0 3
< [7,] 1.313125e+00 1 25 889.5418 0 3
< [8,] 2.570235e+00 1 25 889.5418 0 3
< [9,] 1.927405e+01 1 25 889.5418 0 3
< [10,] 3.772589e+01 1 25 889.5418 0 3
< [11,] 7.384247e+01 1 25 889.5418 0 3
< [12,] 1.445350e+02 1 25 889.5418 0 3
< [13,] 5.537404e+02 1 25 889.5418 0 3
< [14,] 1.083859e+03 1 25 889.5418 0 3
< [15,] 1.590888e+04 1 25 889.5418 0 3
154,156d107
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 2512525252511125252511252525251252511125
160,162c111
< * Warning in algorithm: some ifl != 1
<
< {tau=0.25}-quantile; dimensionality of fit: 8 from {3,13,12,8,5}
---
> {tau=0.25}-quantile; dimensionality of fit: 5 from {13,12,11,10,8,7,6,5,3}
164c113
< lambda = 5.030829, selected via SIC, out of 25 ones.
---
> lambda = 73.84247, selected via SIC, out of 25 ones.
166,167c115,116
< coef[1:12]: 99.399386, 93.373943, 84.600792, 79.681901, 78.340386, ... , 3.379984
< 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)
184,199d132
< 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 3
< [2,] 3.113911e-03 1 25 889.5418 0 3
< [3,] 6.094988e-03 1 25 889.5418 0 3
< [4,] 1.192998e-02 1 25 889.5418 0 3
< [5,] 8.946220e-02 1 25 889.5418 0 3
< [6,] 1.751081e-01 1 25 889.5418 0 3
< [7,] 3.427464e-01 1 25 889.5418 0 3
< [8,] 1.313125e+00 1 25 889.5418 0 3
< [9,] 2.570235e+00 1 25 889.5418 0 3
< [10,] 5.030829e+00 1 25 889.5418 0 3
< [11,] 7.384247e+01 1 25 889.5418 0 3
< [12,] 1.083859e+03 1 25 889.5418 0 3
< [13,] 4.152467e+03 1 25 889.5418 0 3
< [14,] 8.127798e+03 1 25 889.5418 0 3
206,208d138
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 252525251125252512525251112511125125251
212,214c142
< * 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}
216c144
< lambda = 37.72589, selected via SIC, out of 25 ones.
---
> lambda = 5.030829, selected via SIC, out of 25 ones.
234,333c162,261
< [1,] 0.04998516 99.90713 73.08640 126.72785 82.70115 117.11310
< [2,] 0.20109657 99.62824 75.50652 123.74996 84.15373 115.10275
< [3,] 0.35220798 99.35219 77.04434 121.66004 85.04131 113.66307
< [4,] 0.50331939 99.07896 78.00986 120.14807 85.56276 112.59517
< [5,] 0.65443080 98.80857 78.68098 118.93617 85.89636 111.72078
< [6,] 0.80554221 98.54101 79.22790 117.85413 86.15131 110.93072
< [7,] 0.95665362 98.27628 79.66157 116.89100 86.33461 110.21796
< [8,] 1.10776504 98.01439 79.79619 116.23258 86.32709 109.70168
< [9,] 1.25887645 97.75532 79.50028 116.01036 86.04439 109.46625
< [10,] 1.40998786 97.49909 79.08062 115.91755 85.68331 109.31486
< [11,] 1.56109927 97.24568 78.78396 115.70740 85.40216 109.08921
< [12,] 1.71221068 96.99511 78.72291 115.26731 85.27317 108.71705
< [13,] 1.86332209 96.74737 78.88443 114.61031 85.28798 108.20676
< [14,] 2.01443350 96.50246 79.12177 113.88316 85.35244 107.65249
< [15,] 2.16554491 96.26038 79.13756 113.38320 85.27579 107.24498
< [16,] 2.31665632 96.02114 78.83792 113.20435 84.99780 107.04448
< [17,] 2.46776773 95.78472 78.54422 113.02522 84.72463 106.84481
< [18,] 2.61887914 95.55114 78.47291 112.62936 84.59515 106.50712
< [19,] 2.76999056 95.32038 78.69618 111.94459 84.65566 105.98511
< [20,] 2.92110197 95.09246 79.14289 111.04204 84.86053 105.32440
< [21,] 3.07221338 94.86737 79.56781 110.16693 85.05243 104.68231
< [22,] 3.22332479 94.64511 79.71258 109.57764 85.06563 104.22460
< [23,] 3.37443620 94.42569 79.71468 109.13669 84.98831 103.86306
< [24,] 3.52554761 94.20909 79.56635 108.85183 84.81551 103.60267
< [25,] 3.67665902 93.99533 79.00012 108.99053 84.37564 103.61501
< [26,] 3.82777043 93.78439 77.97137 109.59741 83.64006 103.92873
< [27,] 3.97888184 93.57629 76.77542 110.37716 82.79823 104.35435
< [28,] 4.12999325 93.37102 75.62426 111.11778 81.98616 104.75588
< [29,] 4.28110467 93.16858 74.64421 111.69295 81.28487 105.05229
< [30,] 4.43221608 92.96897 73.90129 112.03665 80.73671 105.20123
< [31,] 4.58332749 92.77219 73.41913 112.12526 80.35686 105.18753
< [32,] 4.73443890 92.57825 73.18769 111.96880 80.13886 105.01763
< [33,] 4.88555031 92.38713 73.16451 111.60976 80.05548 104.71879
< [34,] 5.03666172 92.19885 73.27028 111.12742 80.05584 104.34187
< [35,] 5.18777313 92.01340 73.38096 110.64584 80.06036 103.96644
< [36,] 5.33888454 91.83078 73.30423 110.35732 79.94567 103.71589
< [37,] 5.48999595 91.65099 72.89407 110.40791 79.61809 103.68389
< [38,] 5.64110736 91.47403 72.24854 110.69953 79.14054 103.80753
< [39,] 5.79221877 91.29991 71.47434 111.12548 78.58145 104.01836
< [40,] 5.94333019 91.12861 70.66018 111.59704 77.99775 104.25948
< [41,] 6.09444160 90.96015 69.87531 112.04499 77.43385 104.48645
< [42,] 6.24555301 90.79452 69.17182 112.41721 76.92317 104.66586
< [43,] 6.39666442 90.63171 68.58813 112.67530 76.49036 104.77307
< [44,] 6.54777583 90.47174 68.15210 112.79138 76.15330 104.79019
< [45,] 6.69888724 90.31461 67.88371 112.74550 75.92479 104.70442
< [46,] 6.84999865 90.16030 67.79678 112.52382 75.81371 104.50689
< [47,] 7.00111006 90.00882 67.90026 112.11739 75.82578 104.19186
< [48,] 7.15222147 89.86018 68.19883 111.52152 75.96404 103.75632
< [49,] 7.30333288 89.71437 68.69315 110.73559 76.22888 103.19985
< [50,] 7.45444429 89.57138 69.37937 109.76340 76.61785 102.52492
< [51,] 7.60555571 89.43123 70.24809 108.61438 77.12491 101.73756
< [52,] 7.75666712 89.29391 71.28208 107.30574 77.73900 100.84882
< [53,] 7.90777853 89.15943 72.45223 105.86662 78.44146 99.87739
< [54,] 8.05888994 89.02777 73.71025 104.34529 79.20131 98.85423
< [55,] 8.21000135 88.89894 74.97631 102.82158 79.96732 97.83057
< [56,] 8.36111276 88.77295 76.11975 101.42615 80.65570 96.89020
< [57,] 8.51222417 88.64979 76.93844 100.36114 81.13675 96.16283
< [58,] 8.66333558 88.52946 77.19289 99.86603 81.25685 95.80207
< [59,] 8.81444699 88.41196 77.00749 99.81642 81.09579 95.72812
< [60,] 8.96555840 88.29729 76.78849 99.80609 80.91419 95.68039
< [61,] 9.11666981 88.18545 76.74192 99.62898 80.84422 95.52668
< [62,] 9.26778123 88.07645 76.87136 99.28153 80.88819 95.26471
< [63,] 9.41889264 87.97027 76.97211 98.96843 80.91476 95.02579
< [64,] 9.57000405 87.86693 76.58903 99.14483 80.63195 95.10190
< [65,] 9.72111546 87.76642 75.63629 99.89654 79.98472 95.54811
< [66,] 9.87222687 87.66874 74.31434 101.02313 79.10165 96.23582
< [67,] 10.02333828 87.57389 72.79284 102.35493 78.09158 97.05619
< [68,] 10.17444969 87.48187 71.19072 103.77301 77.03081 97.93293
< [69,] 10.32556110 87.39268 69.58526 105.20010 75.96890 98.81646
< [70,] 10.47667251 87.30633 68.02574 106.58691 74.93749 99.67516
< [71,] 10.62778392 87.22280 66.54384 107.90176 73.95688 100.48872
< [72,] 10.77889533 87.14211 65.16024 109.12398 73.04035 101.24387
< [73,] 10.93000675 87.06425 63.88866 110.23984 72.19670 101.93180
< [74,] 11.08111816 86.98922 62.73827 111.24016 71.43181 102.54663
< [75,] 11.23222957 86.91702 61.71521 112.11883 70.74961 103.08443
< [76,] 11.38334098 86.84765 60.82345 112.87185 70.15266 103.54264
< [77,] 11.53445239 86.78112 60.06540 113.49683 69.64251 103.91972
< [78,] 11.68556380 86.71741 59.44225 113.99257 69.21991 104.21491
< [79,] 11.83667521 86.65654 58.95418 114.35890 68.88498 104.42809
< [80,] 11.98778662 86.59850 58.60044 114.59655 68.63725 104.55974
< [81,] 12.13889803 86.54328 58.37944 114.70712 68.47568 104.61089
< [82,] 12.29000944 86.49091 58.28868 114.69313 68.39868 104.58313
< [83,] 12.44112086 86.44136 58.32467 114.55804 68.40400 104.47871
< [84,] 12.59223227 86.39464 58.48278 114.30650 68.48869 104.30059
< [85,] 12.74334368 86.35075 58.75704 113.94446 68.64890 104.05261
< [86,] 12.89445509 86.30970 59.13981 113.47959 68.87973 103.73967
< [87,] 13.04556650 86.27148 59.62137 112.92158 69.17496 103.36799
< [88,] 13.19667791 86.23609 60.18940 112.28277 69.52668 102.94550
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---
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> [72,] 10.77889533 86.00000 62.36714 109.63286 71.96390 100.03610
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> [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
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336,435c264,363
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< [100,] 15.01001484 95.25846 80.38827 110.12865 84.74790 105.76901
---
> [1,] 0.04998516 99.53956 61.42903 137.65009 84.84354 114.23558
> [2,] 0.20109657 98.28282 64.00741 132.55823 85.06568 111.49995
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438,537c366,465
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---
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> [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/4s]
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’ [3s/3s]
Comparing ‘temp.Rout’ to ‘temp.Rout.save’ ...29,31d28
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
35,42c32,35
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
52,54d44
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
58,65c48,51
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
69,71d54
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
75,82c58,61
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.1}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.1)
---
> {tau=0.1}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.5700016, -0.1700000, -0.1700000, 0.1300024
> empirical tau (over all): 12/113 = 0.1061947 (target tau= 0.1)
85,87d63
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
91,98c67,70
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.9}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.9)
---
> {tau=0.9}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.2576939, 0.1300000, 0.1300000, 0.4961568
> empirical tau (over all): 104/113 = 0.920354 (target tau= 0.9)
101,103c73
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 74 102 111
105,108c75
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 28 38 39 85 86 92 95 97 113
113,225c80,192
< [1,] 1880 -0.393247953 -0.568567598 -0.217928308 -0.497693198 -0.2888027083
< [2,] 1881 -0.389244486 -0.556686706 -0.221802266 -0.488996819 -0.2894921527
< [3,] 1882 -0.385241019 -0.544932639 -0.225549398 -0.480375996 -0.2901060418
< [4,] 1883 -0.381237552 -0.533324789 -0.229150314 -0.471842280 -0.2906328235
< [5,] 1884 -0.377234084 -0.521886218 -0.232581951 -0.463409410 -0.2910587589
< [6,] 1885 -0.373230617 -0.510644405 -0.235816829 -0.455093758 -0.2913674769
< [7,] 1886 -0.369227150 -0.499632120 -0.238822180 -0.446914845 -0.2915394558
< [8,] 1887 -0.365223683 -0.488888394 -0.241558972 -0.438895923 -0.2915514428
< [9,] 1888 -0.361220216 -0.478459556 -0.243980875 -0.431064594 -0.2913758376
< [10,] 1889 -0.357216749 -0.468400213 -0.246033284 -0.423453388 -0.2909801092
< [11,] 1890 -0.353213282 -0.458773976 -0.247652588 -0.416100202 -0.2903263615
< [12,] 1891 -0.349209814 -0.449653605 -0.248766024 -0.409048381 -0.2893712477
< [13,] 1892 -0.345206347 -0.441120098 -0.249292596 -0.402346180 -0.2880665146
< [14,] 1893 -0.341202880 -0.433260133 -0.249145628 -0.396045236 -0.2863605248
< [15,] 1894 -0.337199413 -0.426161346 -0.248237480 -0.390197757 -0.2842010691
< [16,] 1895 -0.333195946 -0.419905293 -0.246486599 -0.384852330 -0.2815395617
< [17,] 1896 -0.329192479 -0.414558712 -0.243826246 -0.380048714 -0.2783362437
< [18,] 1897 -0.325189012 -0.410164739 -0.240213284 -0.375812606 -0.2745654171
< [19,] 1898 -0.321185545 -0.406736420 -0.235634669 -0.372151779 -0.2702193101
< [20,] 1899 -0.317182077 -0.404254622 -0.230109533 -0.369054834 -0.2653093212
< [21,] 1900 -0.313178610 -0.402671075 -0.223686145 -0.366493014 -0.2598642062
< [22,] 1901 -0.309175143 -0.401915491 -0.216434795 -0.364424447 -0.2539258394
< [23,] 1902 -0.305171676 -0.401904507 -0.208438845 -0.362799469 -0.2475438831
< [24,] 1903 -0.301168209 -0.402550192 -0.199786225 -0.361565696 -0.2407707212
< [25,] 1904 -0.297164742 -0.403766666 -0.190562818 -0.360671966 -0.2336575172
< [26,] 1905 -0.293161275 -0.405474370 -0.180848179 -0.360070883 -0.2262516664
< [27,] 1906 -0.289157807 -0.407602268 -0.170713347 -0.359720126 -0.2185954887
< [28,] 1907 -0.285154340 -0.410088509 -0.160220171 -0.359582850 -0.2107258307
< [29,] 1908 -0.281150873 -0.412880143 -0.149421603 -0.359627508 -0.2026742377
< [30,] 1909 -0.268996808 -0.394836115 -0.143157501 -0.343964546 -0.1940290700
< [31,] 1910 -0.256842743 -0.376961386 -0.136724100 -0.328402442 -0.1852830438
< [32,] 1911 -0.244688678 -0.359281315 -0.130096042 -0.312956304 -0.1764210522
< [33,] 1912 -0.232534613 -0.341825431 -0.123243796 -0.297643724 -0.1674255025
< [34,] 1913 -0.220380548 -0.324627946 -0.116133151 -0.282485083 -0.1582760137
< [35,] 1914 -0.208226483 -0.307728160 -0.108724807 -0.267503793 -0.1489491732
< [36,] 1915 -0.196072418 -0.291170651 -0.100974185 -0.252726413 -0.1394184235
< [37,] 1916 -0.183918353 -0.275005075 -0.092831631 -0.238182523 -0.1296541835
< [38,] 1917 -0.171764288 -0.259285340 -0.084243236 -0.223904239 -0.1196243373
< [39,] 1918 -0.159610223 -0.244067933 -0.075152513 -0.209925213 -0.1092952334
< [40,] 1919 -0.147456158 -0.229409203 -0.065503113 -0.196279015 -0.0986333019
< [41,] 1920 -0.135302093 -0.215361603 -0.055242584 -0.182996891 -0.0876072953
< [42,] 1921 -0.123148028 -0.201969188 -0.044326869 -0.170105089 -0.0761909673
< [43,] 1922 -0.110993963 -0.189263062 -0.032724864 -0.157622139 -0.0643657877
< [44,] 1923 -0.098839898 -0.177257723 -0.020422074 -0.145556676 -0.0521231208
< [45,] 1924 -0.086685833 -0.165949224 -0.007422442 -0.133906350 -0.0394653164
< [46,] 1925 -0.074531768 -0.155315688 0.006252152 -0.122658128 -0.0264054087
< [47,] 1926 -0.062377703 -0.145320002 0.020564595 -0.111789900 -0.0129655072
< [48,] 1927 -0.050223638 -0.135913981 0.035466704 -0.101272959 0.0008256822
< [49,] 1928 -0.038069573 -0.127043003 0.050903856 -0.091074767 0.0149356198
< [50,] 1929 -0.025915508 -0.118650261 0.066819244 -0.081161479 0.0293304619
< [51,] 1930 -0.013761444 -0.110680090 0.083157203 -0.071499934 0.0439770474
< [52,] 1931 -0.001607379 -0.103080234 0.099865477 -0.062059002 0.0588442451
< [53,] 1932 0.010546686 -0.095803129 0.116896502 -0.052810346 0.0739037194
< [54,] 1933 0.022700751 -0.088806436 0.134207939 -0.043728744 0.0891302464
< [55,] 1934 0.034854816 -0.082053049 0.151762682 -0.034792088 0.1045017213
< [56,] 1935 0.047008881 -0.075510798 0.169528561 -0.025981216 0.1199989785
< [57,] 1936 0.059162946 -0.069151984 0.187477877 -0.017279624 0.1356055167
< [58,] 1937 0.054383856 -0.068135824 0.176903535 -0.018606241 0.1273739530
< [59,] 1938 0.049604765 -0.067303100 0.166512631 -0.020042139 0.1192516703
< [60,] 1939 0.044825675 -0.066681512 0.156332862 -0.021603820 0.1112551700
< [61,] 1940 0.040046585 -0.066303231 0.146396400 -0.023310448 0.1034036175
< [62,] 1941 0.035267494 -0.066205361 0.136740349 -0.025184129 0.0957191177
< [63,] 1942 0.030488404 -0.066430243 0.127407050 -0.027250087 0.0882268946
< [64,] 1943 0.025709313 -0.067025439 0.118444066 -0.029536657 0.0809552836
< [65,] 1944 0.020930223 -0.068043207 0.109903653 -0.032074970 0.0739354160
< [66,] 1945 0.016151132 -0.069539210 0.101841475 -0.034898188 0.0672004530
< [67,] 1946 0.011372042 -0.071570257 0.094314341 -0.038040154 0.0607842381
< [68,] 1947 0.006592951 -0.074190969 0.087376871 -0.041533408 0.0547193111
< [69,] 1948 0.001813861 -0.077449530 0.081077252 -0.045406656 0.0490343779
< [70,] 1949 -0.002965230 -0.081383054 0.075452595 -0.049682007 0.0437515481
< [71,] 1950 -0.007744320 -0.086013419 0.070524779 -0.054372496 0.0388838557
< [72,] 1951 -0.012523410 -0.091344570 0.066297749 -0.059480471 0.0344336506
< [73,] 1952 -0.017302501 -0.097362010 0.062757009 -0.064997299 0.0303922971
< [74,] 1953 -0.022081591 -0.104034636 0.059871454 -0.070904448 0.0267412650
< [75,] 1954 -0.026860682 -0.111318392 0.057597028 -0.077175672 0.0234543081
< [76,] 1955 -0.031639772 -0.119160824 0.055881280 -0.083779723 0.0205001786
< [77,] 1956 -0.036418863 -0.127505585 0.054667859 -0.090683032 0.0178453070
< [78,] 1957 -0.041197953 -0.136296186 0.053900280 -0.097851948 0.0154560415
< [79,] 1958 -0.045977044 -0.145478720 0.053524633 -0.105254354 0.0133002664
< [80,] 1959 -0.050756134 -0.155003532 0.053491263 -0.112860669 0.0113484004
< [81,] 1960 -0.055535225 -0.164826042 0.053755593 -0.120644335 0.0095738862
< [82,] 1961 -0.060314315 -0.174906951 0.054278321 -0.128581941 0.0079533109
< [83,] 1962 -0.065093405 -0.185212049 0.055025238 -0.136653105 0.0064662939
< [84,] 1963 -0.069872496 -0.195711803 0.055966811 -0.144840234 0.0050952422
< [85,] 1964 -0.074651586 -0.206380857 0.057077684 -0.153128222 0.0038250490
< [86,] 1965 -0.060832745 -0.185766914 0.064101424 -0.135261254 0.0135957648
< [87,] 1966 -0.047013903 -0.165458364 0.071430557 -0.117576222 0.0235484155
< [88,] 1967 -0.033195062 -0.145508157 0.079118034 -0.100104670 0.0337145466
< [89,] 1968 -0.019376220 -0.125978144 0.087225704 -0.082883444 0.0441310044
< [90,] 1969 -0.005557378 -0.106939362 0.095824605 -0.065954866 0.0548401092
< [91,] 1970 0.008261463 -0.088471368 0.104994294 -0.049366330 0.0658892560
< [92,] 1971 0.022080305 -0.070660043 0.114820653 -0.033168999 0.0773296085
< [93,] 1972 0.035899146 -0.053593318 0.125391611 -0.017415258 0.0892135504
< [94,] 1973 0.049717988 -0.037354556 0.136790532 -0.002154768 0.1015907442
< [95,] 1974 0.063536830 -0.022014046 0.149087705 0.012570595 0.1145030640
< [96,] 1975 0.077355671 -0.007620056 0.162331398 0.026732077 0.1279792657
< [97,] 1976 0.091174513 0.005808280 0.176540746 0.040318278 0.1420307479
< [98,] 1977 0.104993354 0.018284008 0.191702701 0.053336970 0.1566497385
< [99,] 1978 0.118812196 0.029850263 0.207774129 0.065813852 0.1718105399
< [100,] 1979 0.132631038 0.040573785 0.224688290 0.077788682 0.1874733929
< [101,] 1980 0.146449879 0.050536128 0.242363630 0.089310046 0.2035897119
< [102,] 1981 0.160268721 0.059824930 0.260712511 0.100430154 0.2201072876
< [103,] 1982 0.174087562 0.068526868 0.279648256 0.111200642 0.2369744825
< [104,] 1983 0.187906404 0.076722940 0.299089868 0.121669764 0.2541430435
< [105,] 1984 0.201725246 0.084485905 0.318964586 0.131880867 0.2715696238
< [106,] 1985 0.215544087 0.091879376 0.339208798 0.141871847 0.2892163274
< [107,] 1986 0.229362929 0.098957959 0.359767899 0.151675234 0.3070506231
< [108,] 1987 0.243181770 0.105767982 0.380595558 0.161318630 0.3250449108
< [109,] 1988 0.257000612 0.112348478 0.401652745 0.170825286 0.3431759375
< [110,] 1989 0.270819454 0.118732216 0.422906691 0.180214725 0.3614241817
< [111,] 1990 0.284638295 0.124946675 0.444329916 0.189503318 0.3797732721
< [112,] 1991 0.298457137 0.131014917 0.465899357 0.198704804 0.3982094699
< [113,] 1992 0.312275978 0.136956333 0.487595623 0.207830734 0.4167212231
---
> [1,] 1880 -0.470540541 -0.580395233 -0.360685849 -0.541226637 -0.399854444
> [2,] 1881 -0.462432432 -0.569650451 -0.355214414 -0.531421959 -0.393442906
> [3,] 1882 -0.454324324 -0.558928137 -0.349720511 -0.521631738 -0.387016910
> [4,] 1883 -0.446216216 -0.548230020 -0.344202412 -0.511857087 -0.380575346
> [5,] 1884 -0.438108108 -0.537557989 -0.338658227 -0.502099220 -0.374116996
> [6,] 1885 -0.430000000 -0.526914115 -0.333085885 -0.492359472 -0.367640528
> [7,] 1886 -0.421891892 -0.516300667 -0.327483116 -0.482639300 -0.361144484
> [8,] 1887 -0.413783784 -0.505720132 -0.321847435 -0.472940307 -0.354627261
> [9,] 1888 -0.405675676 -0.495175238 -0.316176113 -0.463264247 -0.348087105
> [10,] 1889 -0.397567568 -0.484668976 -0.310466159 -0.453613044 -0.341522091
> [11,] 1890 -0.389459459 -0.474204626 -0.304714293 -0.443988810 -0.334930108
> [12,] 1891 -0.381351351 -0.463785782 -0.298916920 -0.434393857 -0.328308845
> [13,] 1892 -0.373243243 -0.453416379 -0.293070107 -0.424830717 -0.321655770
> [14,] 1893 -0.365135135 -0.443100719 -0.287169552 -0.415302157 -0.314968113
> [15,] 1894 -0.357027027 -0.432843496 -0.281210558 -0.405811200 -0.308242854
> [16,] 1895 -0.348918919 -0.422649821 -0.275188017 -0.396361132 -0.301476706
> [17,] 1896 -0.340810811 -0.412525238 -0.269096384 -0.386955521 -0.294666101
> [18,] 1897 -0.332702703 -0.402475737 -0.262929668 -0.377598222 -0.287807183
> [19,] 1898 -0.324594595 -0.392507759 -0.256681430 -0.368293379 -0.280895810
> [20,] 1899 -0.316486486 -0.382628180 -0.250344793 -0.359045416 -0.273927557
> [21,] 1900 -0.308378378 -0.372844288 -0.243912468 -0.349859024 -0.266897733
> [22,] 1901 -0.300270270 -0.363163733 -0.237376807 -0.340739124 -0.259801417
> [23,] 1902 -0.292162162 -0.353594450 -0.230729874 -0.331690821 -0.252633503
> [24,] 1903 -0.284054054 -0.344144557 -0.223963551 -0.322719340 -0.245388768
> [25,] 1904 -0.275945946 -0.334822217 -0.217069675 -0.313829934 -0.238061958
> [26,] 1905 -0.267837838 -0.325635470 -0.210040206 -0.305027774 -0.230647901
> [27,] 1906 -0.259729730 -0.316592032 -0.202867427 -0.296317828 -0.223141632
> [28,] 1907 -0.251621622 -0.307699075 -0.195544168 -0.287704708 -0.215538535
> [29,] 1908 -0.243513514 -0.298962989 -0.188064038 -0.279192527 -0.207834500
> [30,] 1909 -0.235405405 -0.290389150 -0.180421661 -0.270784743 -0.200026067
> [31,] 1910 -0.227297297 -0.281981702 -0.172612893 -0.262484025 -0.192110570
> [32,] 1911 -0.219189189 -0.273743385 -0.164634993 -0.254292134 -0.184086245
> [33,] 1912 -0.211081081 -0.265675409 -0.156486753 -0.246209849 -0.175952313
> [34,] 1913 -0.202972973 -0.257777400 -0.148168546 -0.238236929 -0.167709017
> [35,] 1914 -0.194864865 -0.250047417 -0.139682313 -0.230372126 -0.159357604
> [36,] 1915 -0.186756757 -0.242482039 -0.131031475 -0.222613238 -0.150900276
> [37,] 1916 -0.178648649 -0.235076516 -0.122220781 -0.214957209 -0.142340088
> [38,] 1917 -0.170540541 -0.227824968 -0.113256113 -0.207400255 -0.133680826
> [39,] 1918 -0.162432432 -0.220720606 -0.104144259 -0.199938008 -0.124926856
> [40,] 1919 -0.154324324 -0.213755974 -0.094892674 -0.192565671 -0.116082978
> [41,] 1920 -0.146216216 -0.206923176 -0.085509256 -0.185278162 -0.107154270
> [42,] 1921 -0.138108108 -0.200214092 -0.076002124 -0.178070257 -0.098145959
> [43,] 1922 -0.130000000 -0.193620560 -0.066379440 -0.170936704 -0.089063296
> [44,] 1923 -0.121891892 -0.187134533 -0.056649251 -0.163872326 -0.079911458
> [45,] 1924 -0.113783784 -0.180748200 -0.046819367 -0.156872096 -0.070695472
> [46,] 1925 -0.105675676 -0.174454074 -0.036897277 -0.149931196 -0.061420156
> [47,] 1926 -0.097567568 -0.168245056 -0.026890080 -0.143045058 -0.052090077
> [48,] 1927 -0.089459459 -0.162114471 -0.016804448 -0.136209390 -0.042709529
> [49,] 1928 -0.081351351 -0.156056093 -0.006646610 -0.129420182 -0.033282521
> [50,] 1929 -0.073243243 -0.150064140 0.003577654 -0.122673716 -0.023812771
> [51,] 1930 -0.065135135 -0.144133276 0.013863006 -0.115966557 -0.014303713
> [52,] 1931 -0.057027027 -0.138258588 0.024204534 -0.109295545 -0.004758509
> [53,] 1932 -0.048918919 -0.132435569 0.034597732 -0.102657780 0.004819942
> [54,] 1933 -0.040810811 -0.126660095 0.045038473 -0.096050607 0.014428985
> [55,] 1934 -0.032702703 -0.120928393 0.055522988 -0.089471600 0.024066194
> [56,] 1935 -0.024594595 -0.115237021 0.066047832 -0.082918542 0.033729353
> [57,] 1936 -0.016486486 -0.109582838 0.076609865 -0.076389415 0.043416442
> [58,] 1937 -0.016486486 -0.105401253 0.072428280 -0.073698770 0.040725797
> [59,] 1938 -0.016486486 -0.101403226 0.068430253 -0.071126236 0.038153263
> [60,] 1939 -0.016486486 -0.097615899 0.064642926 -0.068689277 0.035716305
> [61,] 1940 -0.016486486 -0.094070136 0.061097163 -0.066407753 0.033434780
> [62,] 1941 -0.016486486 -0.090800520 0.057827547 -0.064303916 0.031330943
> [63,] 1942 -0.016486486 -0.087845022 0.054872049 -0.062402198 0.029429225
> [64,] 1943 -0.016486486 -0.085244160 0.052271187 -0.060728671 0.027755698
> [65,] 1944 -0.016486486 -0.083039523 0.050066550 -0.059310095 0.026337122
> [66,] 1945 -0.016486486 -0.081271575 0.048298602 -0.058172508 0.025199535
> [67,] 1946 -0.016486486 -0.079976806 0.047003833 -0.057339388 0.024366415
> [68,] 1947 -0.016486486 -0.079184539 0.046211566 -0.056829602 0.023856629
> [69,] 1948 -0.016486486 -0.078913907 0.045940934 -0.056655464 0.023682491
> [70,] 1949 -0.016486486 -0.079171667 0.046198694 -0.056821320 0.023848347
> [71,] 1950 -0.016486486 -0.079951382 0.046978409 -0.057323028 0.024350055
> [72,] 1951 -0.016486486 -0.081234197 0.048261224 -0.058148457 0.025175484
> [73,] 1952 -0.016486486 -0.082991006 0.050018033 -0.059278877 0.026305904
> [74,] 1953 -0.016486486 -0.085185454 0.052212481 -0.060690897 0.027717924
> [75,] 1954 -0.016486486 -0.087777140 0.054804167 -0.062358519 0.029385546
> [76,] 1955 -0.016486486 -0.090724471 0.057751498 -0.064254982 0.031282009
> [77,] 1956 -0.016486486 -0.093986883 0.061013910 -0.066354184 0.033381211
> [78,] 1957 -0.016486486 -0.097526332 0.064553359 -0.068631645 0.035658672
> [79,] 1958 -0.016486486 -0.101308145 0.068335172 -0.071065056 0.038092083
> [80,] 1959 -0.016486486 -0.105301366 0.072328393 -0.073634498 0.040661525
> [81,] 1960 -0.016486486 -0.109478765 0.076505793 -0.076322449 0.043349476
> [82,] 1961 -0.016486486 -0.113816631 0.080843658 -0.079113653 0.046140680
> [83,] 1962 -0.016486486 -0.118294454 0.085321481 -0.081994911 0.049021938
> [84,] 1963 -0.016486486 -0.122894566 0.089921593 -0.084954858 0.051981885
> [85,] 1964 -0.016486486 -0.127601781 0.094628808 -0.087983719 0.055010746
> [86,] 1965 -0.006054054 -0.111440065 0.099331957 -0.073864774 0.061756666
> [87,] 1966 0.004378378 -0.095541433 0.104298190 -0.059915111 0.068671868
> [88,] 1967 0.014810811 -0.079951422 0.109573043 -0.046164030 0.075785651
> [89,] 1968 0.025243243 -0.064723125 0.115209611 -0.032645694 0.083132181
> [90,] 1969 0.035675676 -0.049917365 0.121268716 -0.019399240 0.090750592
> [91,] 1970 0.046108108 -0.035602017 0.127818233 -0.006468342 0.098684559
> [92,] 1971 0.056540541 -0.021849988 0.134931069 0.006100087 0.106980994
> [93,] 1972 0.066972973 -0.008735416 0.142681362 0.018258345 0.115687601
> [94,] 1973 0.077405405 0.003672103 0.151138707 0.029961648 0.124849163
> [95,] 1974 0.087837838 0.015314778 0.160360898 0.041172812 0.134502863
> [96,] 1975 0.098270270 0.026154092 0.170386449 0.051867053 0.144673488
> [97,] 1976 0.108702703 0.036176523 0.181228883 0.062035669 0.155369736
> [98,] 1977 0.119135135 0.045395695 0.192874575 0.071687429 0.166582842
> [99,] 1978 0.129567568 0.053850212 0.205284923 0.080847170 0.178287965
> [100,] 1979 0.140000000 0.061597925 0.218402075 0.089552117 0.190447883
> [101,] 1980 0.150432432 0.068708461 0.232156404 0.097847072 0.203017792
> [102,] 1981 0.160864865 0.075255962 0.246473767 0.105779742 0.215949987
> [103,] 1982 0.171297297 0.081313324 0.261281271 0.113397031 0.229197563
> [104,] 1983 0.181729730 0.086948395 0.276511065 0.120742598 0.242716862
> [105,] 1984 0.192162162 0.092221970 0.292102355 0.127855559 0.256468766
> [106,] 1985 0.202594595 0.097187112 0.308002077 0.134770059 0.270419130
> [107,] 1986 0.213027027 0.101889333 0.324164721 0.141515381 0.284538673
> [108,] 1987 0.223459459 0.106367224 0.340551695 0.148116359 0.298802560
> [109,] 1988 0.233891892 0.110653299 0.357130484 0.154593913 0.313189871
> [110,] 1989 0.244324324 0.114774857 0.373873791 0.160965608 0.327683041
> [111,] 1990 0.254756757 0.118754798 0.390758715 0.167246179 0.342267335
> [112,] 1991 0.265189189 0.122612348 0.407766030 0.173447997 0.356930381
> [113,] 1992 0.275621622 0.126363680 0.424879564 0.179581470 0.371661774
228,340c195,307
< [1,] 1880 -0.393247953 -0.638616081 -0.147879825 -0.539424009 -0.247071897
< [2,] 1881 -0.389244486 -0.623587786 -0.154901186 -0.528852590 -0.249636382
< [3,] 1882 -0.385241019 -0.608736988 -0.161745049 -0.518386915 -0.252095123
< [4,] 1883 -0.381237552 -0.594090828 -0.168384275 -0.508043150 -0.254431953
< [5,] 1884 -0.377234084 -0.579681581 -0.174786588 -0.497840525 -0.256627644
< [6,] 1885 -0.373230617 -0.565547708 -0.180913527 -0.487801951 -0.258659284
< [7,] 1886 -0.369227150 -0.551735068 -0.186719232 -0.477954750 -0.260499551
< [8,] 1887 -0.365223683 -0.538298290 -0.192149076 -0.468331465 -0.262115901
< [9,] 1888 -0.361220216 -0.525302213 -0.197138218 -0.458970724 -0.263469708
< [10,] 1889 -0.357216749 -0.512823261 -0.201610236 -0.449918056 -0.264515441
< [11,] 1890 -0.353213282 -0.500950461 -0.205476102 -0.441226498 -0.265200065
< [12,] 1891 -0.349209814 -0.489785646 -0.208633983 -0.432956717 -0.265462912
< [13,] 1892 -0.345206347 -0.479442174 -0.210970520 -0.425176244 -0.265236451
< [14,] 1893 -0.341202880 -0.470041356 -0.212364405 -0.417957348 -0.264448412
< [15,] 1894 -0.337199413 -0.461705842 -0.212692984 -0.411373100 -0.263025726
< [16,] 1895 -0.333195946 -0.454549774 -0.211842118 -0.405491497 -0.260900395
< [17,] 1896 -0.329192479 -0.448666556 -0.209718402 -0.400368183 -0.258016774
< [18,] 1897 -0.325189012 -0.444116558 -0.206261466 -0.396039125 -0.254338899
< [19,] 1898 -0.321185545 -0.440918038 -0.201453051 -0.392515198 -0.249855891
< [20,] 1899 -0.317182077 -0.439044218 -0.195319937 -0.389780451 -0.244583704
< [21,] 1900 -0.313178610 -0.438427544 -0.187929677 -0.387794638 -0.238562582
< [22,] 1901 -0.309175143 -0.438969642 -0.179380644 -0.386499155 -0.231851132
< [23,] 1902 -0.305171676 -0.440553844 -0.169789508 -0.385824495 -0.224518857
< [24,] 1903 -0.301168209 -0.443057086 -0.159279332 -0.385697347 -0.216639071
< [25,] 1904 -0.297164742 -0.446359172 -0.147970311 -0.386046103 -0.208283380
< [26,] 1905 -0.293161275 -0.450348759 -0.135973790 -0.386804433 -0.199518116
< [27,] 1906 -0.289157807 -0.454926427 -0.123389188 -0.387913107 -0.190402508
< [28,] 1907 -0.285154340 -0.460005614 -0.110303066 -0.389320557 -0.180988124
< [29,] 1908 -0.281150873 -0.465512212 -0.096789534 -0.390982633 -0.171319113
< [30,] 1909 -0.268996808 -0.445114865 -0.092878751 -0.373917700 -0.164075916
< [31,] 1910 -0.256842743 -0.424954461 -0.088731025 -0.356993924 -0.156691562
< [32,] 1911 -0.244688678 -0.405066488 -0.084310868 -0.340232447 -0.149144910
< [33,] 1912 -0.232534613 -0.385492277 -0.079576949 -0.323657890 -0.141411336
< [34,] 1913 -0.220380548 -0.366279707 -0.074481389 -0.307298779 -0.133462317
< [35,] 1914 -0.208226483 -0.347483782 -0.068969185 -0.291187880 -0.125265087
< [36,] 1915 -0.196072418 -0.329166890 -0.062977947 -0.275362361 -0.116782475
< [37,] 1916 -0.183918353 -0.311398525 -0.056438181 -0.259863623 -0.107973083
< [38,] 1917 -0.171764288 -0.294254136 -0.049274440 -0.244736614 -0.098791963
< [39,] 1918 -0.159610223 -0.277812779 -0.041407667 -0.230028429 -0.089192017
< [40,] 1919 -0.147456158 -0.262153318 -0.032758999 -0.215786053 -0.079126264
< [41,] 1920 -0.135302093 -0.247349160 -0.023255026 -0.202053217 -0.068550970
< [42,] 1921 -0.123148028 -0.233461966 -0.012834091 -0.188866654 -0.057429402
< [43,] 1922 -0.110993963 -0.220535266 -0.001452661 -0.176252299 -0.045735628
< [44,] 1923 -0.098839898 -0.208589350 0.010909553 -0.164222236 -0.033457560
< [45,] 1924 -0.086685833 -0.197618695 0.024247028 -0.152773178 -0.020598488
< [46,] 1925 -0.074531768 -0.187592682 0.038529145 -0.141886883 -0.007176654
< [47,] 1926 -0.062377703 -0.178459370 0.053703964 -0.131532407 0.006777000
< [48,] 1927 -0.050223638 -0.170151322 0.069704045 -0.121669575 0.021222298
< [49,] 1928 -0.038069573 -0.162592093 0.086452946 -0.112252846 0.036113699
< [50,] 1929 -0.025915508 -0.155702177 0.103871160 -0.103234855 0.051403838
< [51,] 1930 -0.013761444 -0.149403669 0.121880782 -0.094569190 0.067046303
< [52,] 1931 -0.001607379 -0.143623435 0.140408678 -0.086212283 0.082997525
< [53,] 1932 0.010546686 -0.138294906 0.159388279 -0.078124475 0.099217848
< [54,] 1933 0.022700751 -0.133358827 0.178760330 -0.070270466 0.115671969
< [55,] 1934 0.034854816 -0.128763266 0.198472899 -0.062619318 0.132328951
< [56,] 1935 0.047008881 -0.124463200 0.218480963 -0.055144209 0.149161972
< [57,] 1936 0.059162946 -0.120419862 0.238745755 -0.047822043 0.166147936
< [58,] 1937 0.054383856 -0.117088225 0.225855937 -0.047769234 0.156536946
< [59,] 1938 0.049604765 -0.114013317 0.213222848 -0.047869369 0.147078900
< [60,] 1939 0.044825675 -0.111233903 0.200885253 -0.048145542 0.137796893
< [61,] 1940 0.040046585 -0.108795008 0.188888177 -0.048624577 0.128717746
< [62,] 1941 0.035267494 -0.106748562 0.177283550 -0.049337410 0.119872398
< [63,] 1942 0.030488404 -0.105153822 0.166130629 -0.050319343 0.111296150
< [64,] 1943 0.025709313 -0.104077355 0.155495982 -0.051610033 0.103028659
< [65,] 1944 0.020930223 -0.103592297 0.145452743 -0.053253050 0.095113496
< [66,] 1945 0.016151132 -0.103776551 0.136078816 -0.055294804 0.087597069
< [67,] 1946 0.011372042 -0.104709625 0.127453709 -0.057782662 0.080526746
< [68,] 1947 0.006592951 -0.106467962 0.119653865 -0.060762163 0.073948066
< [69,] 1948 0.001813861 -0.109119001 0.112746722 -0.064273484 0.067901206
< [70,] 1949 -0.002965230 -0.112714681 0.106784222 -0.068347568 0.062417108
< [71,] 1950 -0.007744320 -0.117285623 0.101796983 -0.073002655 0.057514015
< [72,] 1951 -0.012523410 -0.122837348 0.097790527 -0.078242036 0.053195215
< [73,] 1952 -0.017302501 -0.129349568 0.094744566 -0.084053625 0.049448623
< [74,] 1953 -0.022081591 -0.136778751 0.092615568 -0.090411486 0.046248303
< [75,] 1954 -0.026860682 -0.145063238 0.091341874 -0.097278888 0.043557524
< [76,] 1955 -0.031639772 -0.154129620 0.090850076 -0.104612098 0.041332553
< [77,] 1956 -0.036418863 -0.163899035 0.091061309 -0.112364133 0.039526407
< [78,] 1957 -0.041197953 -0.174292425 0.091896518 -0.120487896 0.038091990
< [79,] 1958 -0.045977044 -0.185234342 0.093280255 -0.128938440 0.036984353
< [80,] 1959 -0.050756134 -0.196655293 0.095143025 -0.137674365 0.036162097
< [81,] 1960 -0.055535225 -0.208492888 0.097422439 -0.146658502 0.035588053
< [82,] 1961 -0.060314315 -0.220692125 0.100063495 -0.155858084 0.035229454
< [83,] 1962 -0.065093405 -0.233205123 0.103018312 -0.165244586 0.035057775
< [84,] 1963 -0.069872496 -0.245990553 0.106245561 -0.174793388 0.035048396
< [85,] 1964 -0.074651586 -0.259012925 0.109709752 -0.184483346 0.035180173
< [86,] 1965 -0.060832745 -0.235684019 0.114018529 -0.164998961 0.043333472
< [87,] 1966 -0.047013903 -0.212782523 0.118754717 -0.145769203 0.051741396
< [88,] 1967 -0.033195062 -0.190382546 0.123992423 -0.126838220 0.060448097
< [89,] 1968 -0.019376220 -0.168570650 0.129818210 -0.108257582 0.069505142
< [90,] 1969 -0.005557378 -0.147446255 0.136331499 -0.090086516 0.078971760
< [91,] 1970 0.008261463 -0.127120705 0.143643631 -0.072391356 0.088914283
< [92,] 1971 0.022080305 -0.107714195 0.151874804 -0.055243707 0.099404316
< [93,] 1972 0.035899146 -0.089349787 0.161148080 -0.038716881 0.110515174
< [94,] 1973 0.049717988 -0.072144153 0.171580129 -0.022880386 0.122316362
< [95,] 1974 0.063536830 -0.056195664 0.183269323 -0.007792824 0.134866483
< [96,] 1975 0.077355671 -0.041571875 0.196283217 0.006505558 0.148205784
< [97,] 1976 0.091174513 -0.028299564 0.210648590 0.019998808 0.162350217
< [98,] 1977 0.104993354 -0.016360474 0.226347183 0.032697804 0.177288905
< [99,] 1978 0.118812196 -0.005694233 0.243318625 0.044638509 0.192985883
< [100,] 1979 0.132631038 0.003792562 0.261469513 0.055876570 0.209385506
< [101,] 1980 0.146449879 0.012214052 0.280685706 0.066479983 0.226419775
< [102,] 1981 0.160268721 0.019692889 0.300844552 0.076521819 0.244015623
< [103,] 1982 0.174087562 0.026350383 0.321824742 0.086074346 0.262100779
< [104,] 1983 0.187906404 0.032299891 0.343512917 0.095205097 0.280607711
< [105,] 1984 0.201725246 0.037643248 0.365807243 0.103974737 0.299475754
< [106,] 1985 0.215544087 0.042469480 0.388618694 0.112436305 0.318651869
< [107,] 1986 0.229362929 0.046855011 0.411870847 0.120635329 0.338090528
< [108,] 1987 0.243181770 0.050864680 0.435498861 0.128610437 0.357753104
< [109,] 1988 0.257000612 0.054553115 0.459448109 0.136394171 0.377607052
< [110,] 1989 0.270819454 0.057966177 0.483672730 0.144013855 0.397625052
< [111,] 1990 0.284638295 0.061142326 0.508134265 0.151492399 0.417784191
< [112,] 1991 0.298457137 0.064113837 0.532800436 0.158849032 0.438065241
< [113,] 1992 0.312275978 0.066907850 0.557644107 0.166099922 0.458452034
---
> [1,] 1880 -0.570000000 -0.7989007 -0.3410992837 -0.71728636 -0.422713636
> [2,] 1881 -0.562857143 -0.7862639 -0.3394503795 -0.70660842 -0.419105867
> [3,] 1882 -0.555714286 -0.7736739 -0.3377546582 -0.69596060 -0.415467975
> [4,] 1883 -0.548571429 -0.7611343 -0.3360085204 -0.68534522 -0.411797641
> [5,] 1884 -0.541428571 -0.7486491 -0.3342080272 -0.67476481 -0.408092333
> [6,] 1885 -0.534285714 -0.7362226 -0.3323488643 -0.66422216 -0.404349273
> [7,] 1886 -0.527142857 -0.7238594 -0.3304263043 -0.65372029 -0.400565421
> [8,] 1887 -0.520000000 -0.7115648 -0.3284351643 -0.64326256 -0.396737440
> [9,] 1888 -0.512857143 -0.6993445 -0.3263697605 -0.63285261 -0.392861675
> [10,] 1889 -0.505714286 -0.6872047 -0.3242238599 -0.62249446 -0.388934114
> [11,] 1890 -0.498571429 -0.6751522 -0.3219906288 -0.61219250 -0.384950360
> [12,] 1891 -0.491428571 -0.6631946 -0.3196625782 -0.60195155 -0.380905594
> [13,] 1892 -0.484285714 -0.6513399 -0.3172315093 -0.59177689 -0.376794541
> [14,] 1893 -0.477142857 -0.6395973 -0.3146884583 -0.58167428 -0.372611433
> [15,] 1894 -0.470000000 -0.6279764 -0.3120236430 -0.57165002 -0.368349976
> [16,] 1895 -0.462857143 -0.6164879 -0.3092264155 -0.56171097 -0.364003318
> [17,] 1896 -0.455714286 -0.6051433 -0.3062852230 -0.55186455 -0.359564026
> [18,] 1897 -0.448571429 -0.5939553 -0.3031875831 -0.54211879 -0.355024067
> [19,] 1898 -0.441428571 -0.5829371 -0.2999200783 -0.53248233 -0.350374809
> [20,] 1899 -0.434285714 -0.5721031 -0.2964683783 -0.52296440 -0.345607030
> [21,] 1900 -0.427142857 -0.5614684 -0.2928172976 -0.51357475 -0.340710959
> [22,] 1901 -0.420000000 -0.5510491 -0.2889508980 -0.50432366 -0.335676342
> [23,] 1902 -0.412857143 -0.5408616 -0.2848526441 -0.49522175 -0.330492537
> [24,] 1903 -0.405714286 -0.5309229 -0.2805056214 -0.48627991 -0.325148662
> [25,] 1904 -0.398571429 -0.5212500 -0.2758928205 -0.47750909 -0.319633772
> [26,] 1905 -0.391428571 -0.5118597 -0.2709974894 -0.46892006 -0.313937087
> [27,] 1906 -0.384285714 -0.5027679 -0.2658035488 -0.46052317 -0.308048262
> [28,] 1907 -0.377142857 -0.4939897 -0.2602960562 -0.45232803 -0.301957682
> [29,] 1908 -0.370000000 -0.4855383 -0.2544616963 -0.44434322 -0.295656778
> [30,] 1909 -0.362857143 -0.4774250 -0.2482892691 -0.43657594 -0.289138345
> [31,] 1910 -0.355714286 -0.4696584 -0.2417701364 -0.42903175 -0.282396824
> [32,] 1911 -0.348571429 -0.4622443 -0.2348985912 -0.42171431 -0.275428543
> [33,] 1912 -0.341428571 -0.4551850 -0.2276721117 -0.41462526 -0.268231879
> [34,] 1913 -0.334285714 -0.4484800 -0.2200914777 -0.40776409 -0.260807334
> [35,] 1914 -0.327142857 -0.4421250 -0.2121607344 -0.40112820 -0.253157511
> [36,] 1915 -0.320000000 -0.4361130 -0.2038870084 -0.39471301 -0.245286995
> [37,] 1916 -0.312857143 -0.4304341 -0.1952801960 -0.38851213 -0.237202155
> [38,] 1917 -0.305714286 -0.4250760 -0.1863525523 -0.38251770 -0.228910875
> [39,] 1918 -0.298571429 -0.4200246 -0.1771182205 -0.37672060 -0.220422257
> [40,] 1919 -0.291428571 -0.4152644 -0.1675927388 -0.37111085 -0.211746298
> [41,] 1920 -0.284285714 -0.4107789 -0.1577925583 -0.36567785 -0.202893584
> [42,] 1921 -0.277142857 -0.4065511 -0.1477346004 -0.36041071 -0.193875002
> [43,] 1922 -0.270000000 -0.4025641 -0.1374358695 -0.35529850 -0.184701495
> [44,] 1923 -0.262857143 -0.3988012 -0.1269131329 -0.35033043 -0.175383852
> [45,] 1924 -0.255714286 -0.3952459 -0.1161826679 -0.34549603 -0.165932545
> [46,] 1925 -0.248571429 -0.3918828 -0.1052600744 -0.34078524 -0.156357614
> [47,] 1926 -0.241428571 -0.3886970 -0.0941601449 -0.33618857 -0.146668575
> [48,] 1927 -0.234285714 -0.3856746 -0.0828967845 -0.33169705 -0.136874376
> [49,] 1928 -0.227142857 -0.3828027 -0.0714829715 -0.32730235 -0.126983369
> [50,] 1929 -0.220000000 -0.3800693 -0.0599307484 -0.32299670 -0.117003301
> [51,] 1930 -0.212857143 -0.3774630 -0.0482512378 -0.31877296 -0.106941331
> [52,] 1931 -0.205714286 -0.3749739 -0.0364546744 -0.31462453 -0.096804042
> [53,] 1932 -0.198571429 -0.3725924 -0.0245504487 -0.31054538 -0.086597478
> [54,] 1933 -0.191428571 -0.3703100 -0.0125471577 -0.30652997 -0.076327171
> [55,] 1934 -0.184285714 -0.3681188 -0.0004526588 -0.30257325 -0.065998175
> [56,] 1935 -0.177142857 -0.3660116 0.0117258745 -0.29867061 -0.055615108
> [57,] 1936 -0.170000000 -0.3639819 0.0239818977 -0.29481782 -0.045182180
> [58,] 1937 -0.170000000 -0.3552689 0.0152688616 -0.28921141 -0.050788591
> [59,] 1938 -0.170000000 -0.3469383 0.0069383006 -0.28385110 -0.056148897
> [60,] 1939 -0.170000000 -0.3390468 -0.0009532311 -0.27877329 -0.061226710
> [61,] 1940 -0.170000000 -0.3316586 -0.0083414258 -0.27401935 -0.065980650
> [62,] 1941 -0.170000000 -0.3248458 -0.0151542191 -0.26963565 -0.070364348
> [63,] 1942 -0.170000000 -0.3186875 -0.0213124962 -0.26567310 -0.074326897
> [64,] 1943 -0.170000000 -0.3132682 -0.0267318303 -0.26218603 -0.077813972
> [65,] 1944 -0.170000000 -0.3086744 -0.0313255619 -0.25923019 -0.080769813
> [66,] 1945 -0.170000000 -0.3049906 -0.0350093787 -0.25685983 -0.083140168
> [67,] 1946 -0.170000000 -0.3022928 -0.0377072467 -0.25512389 -0.084876113
> [68,] 1947 -0.170000000 -0.3006419 -0.0393580695 -0.25406166 -0.085938337
> [69,] 1948 -0.170000000 -0.3000780 -0.0399219767 -0.25369882 -0.086301183
> [70,] 1949 -0.170000000 -0.3006151 -0.0393848898 -0.25404441 -0.085955594
> [71,] 1950 -0.170000000 -0.3022398 -0.0377602233 -0.25508980 -0.084910201
> [72,] 1951 -0.170000000 -0.3049127 -0.0350872623 -0.25680972 -0.083190282
> [73,] 1952 -0.170000000 -0.3085733 -0.0314266558 -0.25916514 -0.080834862
> [74,] 1953 -0.170000000 -0.3131458 -0.0268541535 -0.26210732 -0.077892681
> [75,] 1954 -0.170000000 -0.3185461 -0.0214539408 -0.26558209 -0.074417909
> [76,] 1955 -0.170000000 -0.3246873 -0.0153126807 -0.26953369 -0.070466310
> [77,] 1956 -0.170000000 -0.3314851 -0.0085148970 -0.27390773 -0.066092271
> [78,] 1957 -0.170000000 -0.3388601 -0.0011398598 -0.27865320 -0.061346797
> [79,] 1958 -0.170000000 -0.3467402 0.0067401824 -0.28372362 -0.056276377
> [80,] 1959 -0.170000000 -0.3550607 0.0150607304 -0.28907749 -0.050922513
> [81,] 1960 -0.170000000 -0.3637650 0.0237650445 -0.29467829 -0.045321714
> [82,] 1961 -0.170000000 -0.3728037 0.0328037172 -0.30049423 -0.039505772
> [83,] 1962 -0.170000000 -0.3821340 0.0421340134 -0.30649781 -0.033502185
> [84,] 1963 -0.170000000 -0.3917191 0.0517191202 -0.31266536 -0.027334640
> [85,] 1964 -0.170000000 -0.4015274 0.0615273928 -0.31897650 -0.021023499
> [86,] 1965 -0.159285714 -0.3788752 0.0603037544 -0.30058075 -0.017990680
> [87,] 1966 -0.148571429 -0.3567712 0.0596282943 -0.28253772 -0.014605137
> [88,] 1967 -0.137857143 -0.3353102 0.0595958975 -0.26490847 -0.010805813
> [89,] 1968 -0.127142857 -0.3146029 0.0603171930 -0.24776419 -0.006521525
> [90,] 1969 -0.116428571 -0.2947761 0.0619189162 -0.23118642 -0.001670726
> [91,] 1970 -0.105714286 -0.2759711 0.0645424939 -0.21526616 0.003837587
> [92,] 1971 -0.095000000 -0.2583398 0.0683398431 -0.20010116 0.010101164
> [93,] 1972 -0.084285714 -0.2420369 0.0734654391 -0.18579083 0.017219402
> [94,] 1973 -0.073571429 -0.2272072 0.0800643002 -0.17242847 0.025285614
> [95,] 1974 -0.062857143 -0.2139711 0.0882568427 -0.16009157 0.034377282
> [96,] 1975 -0.052142857 -0.2024090 0.0981233226 -0.14883176 0.044546046
> [97,] 1976 -0.041428571 -0.1925491 0.1096919157 -0.13866718 0.055810037
> [98,] 1977 -0.030714286 -0.1843628 0.1229342326 -0.12957956 0.068150987
> [99,] 1978 -0.020000000 -0.1777698 0.1377698370 -0.12151714 0.081517138
> [100,] 1979 -0.009285714 -0.1726496 0.1540781875 -0.11440236 0.095830930
> [101,] 1980 0.001428571 -0.1688571 0.1717142023 -0.10814187 0.110999008
> [102,] 1981 0.012142857 -0.1662377 0.1905233955 -0.10263625 0.126921969
> [103,] 1982 0.022857143 -0.1646396 0.2103538775 -0.09778779 0.143502079
> [104,] 1983 0.033571429 -0.1639214 0.2310642722 -0.09350551 0.160648370
> [105,] 1984 0.044285714 -0.1639565 0.2525279044 -0.08970790 0.178279332
> [106,] 1985 0.055000000 -0.1646342 0.2746342071 -0.08632382 0.196323821
> [107,] 1986 0.065714286 -0.1658598 0.2972883534 -0.08329225 0.214720820
> [108,] 1987 0.076428571 -0.1675528 0.3204099260 -0.08056144 0.233418585
> [109,] 1988 0.087142857 -0.1696455 0.3439311798 -0.07808781 0.252373526
> [110,] 1989 0.097857143 -0.1720809 0.3677952332 -0.07583476 0.271549041
> [111,] 1990 0.108571429 -0.1748115 0.3919543697 -0.07377157 0.290914428
> [112,] 1991 0.119285714 -0.1777971 0.4163685288 -0.07187248 0.310443909
> [113,] 1992 0.130000000 -0.1810040 0.4410040109 -0.07011580 0.330115800
343,455c310,422
< [1,] 1880 -0.393247953 -0.693805062 -0.092690844 -0.572302393 -0.214193513
< [2,] 1881 -0.389244486 -0.676297026 -0.102191945 -0.560253689 -0.218235282
< [3,] 1882 -0.385241019 -0.659006413 -0.111475624 -0.548334514 -0.222147524
< [4,] 1883 -0.381237552 -0.641966465 -0.120508639 -0.536564669 -0.225910434
< [5,] 1884 -0.377234084 -0.625216717 -0.129251452 -0.524967709 -0.229500459
< [6,] 1885 -0.373230617 -0.608804280 -0.137656955 -0.513571700 -0.232889535
< [7,] 1886 -0.369227150 -0.592785330 -0.145668970 -0.502410107 -0.236044193
< [8,] 1887 -0.365223683 -0.577226782 -0.153220584 -0.491522795 -0.238924571
< [9,] 1888 -0.361220216 -0.562208058 -0.160232373 -0.480957079 -0.241483352
< [10,] 1889 -0.357216749 -0.547822773 -0.166610724 -0.470768729 -0.243664768
< [11,] 1890 -0.353213282 -0.534179978 -0.172246585 -0.461022711 -0.245403852
< [12,] 1891 -0.349209814 -0.521404410 -0.177015219 -0.451793336 -0.246626293
< [13,] 1892 -0.345206347 -0.509634924 -0.180777771 -0.443163327 -0.247249368
< [14,] 1893 -0.341202880 -0.499020116 -0.183385645 -0.435221208 -0.247184553
< [15,] 1894 -0.337199413 -0.489710224 -0.184688602 -0.428056482 -0.246342344
< [16,] 1895 -0.333195946 -0.481845064 -0.184546828 -0.421752442 -0.244639450
< [17,] 1896 -0.329192479 -0.475539046 -0.182845912 -0.416377249 -0.242007708
< [18,] 1897 -0.325189012 -0.470866120 -0.179511904 -0.411974957 -0.238403066
< [19,] 1898 -0.321185545 -0.467848651 -0.174522438 -0.408558891 -0.233812198
< [20,] 1899 -0.317182077 -0.466453839 -0.167910316 -0.406109508 -0.228254646
< [21,] 1900 -0.313178610 -0.466598933 -0.159758288 -0.404577513 -0.221779708
< [22,] 1901 -0.309175143 -0.468163434 -0.150186852 -0.403891117 -0.214459169
< [23,] 1902 -0.305171676 -0.471004432 -0.139338920 -0.403965184 -0.206378168
< [24,] 1903 -0.301168209 -0.474971184 -0.127365234 -0.404709910 -0.197626508
< [25,] 1904 -0.297164742 -0.479916458 -0.114413025 -0.406037582 -0.188291901
< [26,] 1905 -0.293161275 -0.485703869 -0.100618680 -0.407866950 -0.178455599
< [27,] 1906 -0.289157807 -0.492211633 -0.086103982 -0.410125463 -0.168190151
< [28,] 1907 -0.285154340 -0.499333719 -0.070974961 -0.412749954 -0.157558727
< [29,] 1908 -0.281150873 -0.506979351 -0.055322395 -0.415686342 -0.146615404
< [30,] 1909 -0.268996808 -0.484727899 -0.053265717 -0.397516841 -0.140476775
< [31,] 1910 -0.256842743 -0.462766683 -0.050918803 -0.379520246 -0.134165240
< [32,] 1911 -0.244688678 -0.441139176 -0.048238181 -0.361722455 -0.127654901
< [33,] 1912 -0.232534613 -0.419896002 -0.045173225 -0.344153628 -0.120915598
< [34,] 1913 -0.220380548 -0.399095811 -0.041665286 -0.326848704 -0.113912392
< [35,] 1914 -0.208226483 -0.378805976 -0.037646990 -0.309847821 -0.106605145
< [36,] 1915 -0.196072418 -0.359102922 -0.033041915 -0.293196507 -0.098948329
< [37,] 1916 -0.183918353 -0.340071771 -0.027764935 -0.276945475 -0.090891232
< [38,] 1917 -0.171764288 -0.321804943 -0.021723634 -0.261149781 -0.082378795
< [39,] 1918 -0.159610223 -0.304399275 -0.014821172 -0.245867116 -0.073353330
< [40,] 1919 -0.147456158 -0.287951368 -0.006960949 -0.231155030 -0.063757286
< [41,] 1920 -0.135302093 -0.272551143 0.001946957 -0.217067092 -0.053537094
< [42,] 1921 -0.123148028 -0.258274127 0.011978071 -0.203648297 -0.042647760
< [43,] 1922 -0.110993963 -0.245173645 0.023185718 -0.190930411 -0.031057516
< [44,] 1923 -0.098839898 -0.233274545 0.035594749 -0.178928240 -0.018751557
< [45,] 1924 -0.086685833 -0.222570067 0.049198400 -0.167637754 -0.005733912
< [46,] 1925 -0.074531768 -0.213022703 0.063959166 -0.157036610 0.007973073
< [47,] 1926 -0.062377703 -0.204568828 0.079813422 -0.147086903 0.022331496
< [48,] 1927 -0.050223638 -0.197125838 0.096678562 -0.137739423 0.037292146
< [49,] 1928 -0.038069573 -0.190600095 0.114460948 -0.128938384 0.052799237
< [50,] 1929 -0.025915508 -0.184894207 0.133063191 -0.120625768 0.068794751
< [51,] 1930 -0.013761444 -0.179912750 0.152389863 -0.112744726 0.085221839
< [52,] 1931 -0.001607379 -0.175566138 0.172351381 -0.105241887 0.102027130
< [53,] 1932 0.010546686 -0.171772831 0.192866204 -0.098068675 0.119162048
< [54,] 1933 0.022700751 -0.168460244 0.213861747 -0.091181848 0.136583351
< [55,] 1934 0.034854816 -0.165564766 0.235274399 -0.084543511 0.154253144
< [56,] 1935 0.047008881 -0.163031246 0.257049009 -0.078120807 0.172138570
< [57,] 1936 0.059162946 -0.160812199 0.279138092 -0.071885448 0.190211340
< [58,] 1937 0.054383856 -0.155656272 0.264423984 -0.070745832 0.179513544
< [59,] 1938 0.049604765 -0.150814817 0.250024348 -0.069793562 0.169003093
< [60,] 1939 0.044825675 -0.146335320 0.235986670 -0.069056925 0.158708275
< [61,] 1940 0.040046585 -0.142272933 0.222366102 -0.068568777 0.148661946
< [62,] 1941 0.035267494 -0.138691265 0.209226254 -0.068367014 0.138902002
< [63,] 1942 0.030488404 -0.135662903 0.196639710 -0.068494879 0.129471686
< [64,] 1943 0.025709313 -0.133269386 0.184688012 -0.069000947 0.120419573
< [65,] 1944 0.020930223 -0.131600299 0.173460744 -0.069938588 0.111799033
< [66,] 1945 0.016151132 -0.130751068 0.163053332 -0.071364652 0.103666917
< [67,] 1946 0.011372042 -0.130819083 0.153563167 -0.073337158 0.096081242
< [68,] 1947 0.006592951 -0.131897983 0.145083886 -0.075911890 0.089097793
< [69,] 1948 0.001813861 -0.134070373 0.137698095 -0.079138060 0.082765782
< [70,] 1949 -0.002965230 -0.137399877 0.131469418 -0.083053571 0.077123112
< [71,] 1950 -0.007744320 -0.141924001 0.126435361 -0.087680768 0.072192128
< [72,] 1951 -0.012523410 -0.147649510 0.122602689 -0.093023679 0.067976858
< [73,] 1952 -0.017302501 -0.154551551 0.119946549 -0.099067500 0.064462498
< [74,] 1953 -0.022081591 -0.162576801 0.118413618 -0.105780463 0.061617281
< [75,] 1954 -0.026860682 -0.171649733 0.117928369 -0.113117575 0.059396211
< [76,] 1955 -0.031639772 -0.181680427 0.118400882 -0.121025265 0.057745721
< [77,] 1956 -0.036418863 -0.192572281 0.119734555 -0.129445984 0.056608259
< [78,] 1957 -0.041197953 -0.204228457 0.121832550 -0.138322042 0.055926136
< [79,] 1958 -0.045977044 -0.216556537 0.124602449 -0.147598382 0.055644294
< [80,] 1959 -0.050756134 -0.229471397 0.127959128 -0.157224290 0.055712022
< [81,] 1960 -0.055535225 -0.242896613 0.131826164 -0.167154239 0.056083790
< [82,] 1961 -0.060314315 -0.256764812 0.136136182 -0.177348092 0.056719462
< [83,] 1962 -0.065093405 -0.271017346 0.140830535 -0.187770909 0.057584098
< [84,] 1963 -0.069872496 -0.285603587 0.145858595 -0.198392529 0.058647537
< [85,] 1964 -0.074651586 -0.300480064 0.151176891 -0.209187055 0.059883882
< [86,] 1965 -0.060832745 -0.275012124 0.153346634 -0.188428358 0.066762869
< [87,] 1966 -0.047013903 -0.250067729 0.156039922 -0.167981559 0.073953753
< [88,] 1967 -0.033195062 -0.225737656 0.159347533 -0.147900737 0.081510614
< [89,] 1968 -0.019376220 -0.202127937 0.163375497 -0.128249061 0.089496621
< [90,] 1969 -0.005557378 -0.179360353 0.168245596 -0.109099079 0.097984322
< [91,] 1970 0.008261463 -0.157571293 0.174094219 -0.090532045 0.107054971
< [92,] 1971 0.022080305 -0.136907986 0.181068596 -0.072635669 0.116796279
< [93,] 1972 0.035899146 -0.117521176 0.189319469 -0.055499756 0.127298049
< [94,] 1973 0.049717988 -0.099553773 0.198989749 -0.039209443 0.138645419
< [95,] 1974 0.063536830 -0.083126277 0.210199936 -0.023836517 0.150910176
< [96,] 1975 0.077355671 -0.068321437 0.223032779 -0.009430275 0.164141617
< [97,] 1976 0.091174513 -0.055172054 0.237521080 0.003989742 0.178359283
< [98,] 1977 0.104993354 -0.043655763 0.253642472 0.016436858 0.193549851
< [99,] 1978 0.118812196 -0.033698615 0.271323007 0.027955127 0.209669265
< [100,] 1979 0.132631038 -0.025186198 0.290448273 0.038612710 0.226649365
< [101,] 1980 0.146449879 -0.017978697 0.310878456 0.048492899 0.244406859
< [102,] 1981 0.160268721 -0.011925874 0.332463316 0.057685199 0.262852243
< [103,] 1982 0.174087562 -0.006879134 0.355054259 0.066278133 0.281896992
< [104,] 1983 0.187906404 -0.002699621 0.378512429 0.074354424 0.301458384
< [105,] 1984 0.201725246 0.000737403 0.402713088 0.081988382 0.321462109
< [106,] 1985 0.215544087 0.003540988 0.427547186 0.089244975 0.341843199
< [107,] 1986 0.229362929 0.005804749 0.452921108 0.096179971 0.362545886
< [108,] 1987 0.243181770 0.007608108 0.478755433 0.102840688 0.383522853
< [109,] 1988 0.257000612 0.009017980 0.504983244 0.109266987 0.404734237
< [110,] 1989 0.270819454 0.010090540 0.531548367 0.115492336 0.426146571
< [111,] 1990 0.284638295 0.010872901 0.558403689 0.121544800 0.447731790
< [112,] 1991 0.298457137 0.011404596 0.585509677 0.127447933 0.469466340
< [113,] 1992 0.312275978 0.011718869 0.612833087 0.133221539 0.491330418
---
> [1,] 1880 -0.257692308 -3.867500e-01 -0.128634653 -0.340734568 -0.174650048
> [2,] 1881 -0.250769231 -3.767293e-01 -0.124809149 -0.331818355 -0.169720107
> [3,] 1882 -0.243846154 -3.667351e-01 -0.120957249 -0.322919126 -0.164773181
> [4,] 1883 -0.236923077 -3.567692e-01 -0.117076923 -0.314038189 -0.159807965
> [5,] 1884 -0.230000000 -3.468340e-01 -0.113165951 -0.305176970 -0.154823030
> [6,] 1885 -0.223076923 -3.369319e-01 -0.109221900 -0.296337036 -0.149816810
> [7,] 1886 -0.216153846 -3.270656e-01 -0.105242105 -0.287520102 -0.144787590
> [8,] 1887 -0.209230769 -3.172379e-01 -0.101223643 -0.278728048 -0.139733491
> [9,] 1888 -0.202307692 -3.074521e-01 -0.097163311 -0.269962936 -0.134652449
> [10,] 1889 -0.195384615 -2.977116e-01 -0.093057593 -0.261227027 -0.129542204
> [11,] 1890 -0.188461539 -2.880204e-01 -0.088902637 -0.252522800 -0.124400277
> [12,] 1891 -0.181538462 -2.783827e-01 -0.084694220 -0.243852973 -0.119223950
> [13,] 1892 -0.174615385 -2.688030e-01 -0.080427720 -0.235220519 -0.114010250
> [14,] 1893 -0.167692308 -2.592865e-01 -0.076098083 -0.226628691 -0.108755924
> [15,] 1894 -0.160769231 -2.498387e-01 -0.071699793 -0.218081038 -0.103457424
> [16,] 1895 -0.153846154 -2.404655e-01 -0.067226847 -0.209581422 -0.098110886
> [17,] 1896 -0.146923077 -2.311734e-01 -0.062672732 -0.201134035 -0.092712119
> [18,] 1897 -0.140000000 -2.219696e-01 -0.058030409 -0.192743405 -0.087256595
> [19,] 1898 -0.133076923 -2.128615e-01 -0.053292314 -0.184414399 -0.081739447
> [20,] 1899 -0.126153846 -2.038573e-01 -0.048450366 -0.176152218 -0.076155475
> [21,] 1900 -0.119230769 -1.949655e-01 -0.043496005 -0.167962369 -0.070499170
> [22,] 1901 -0.112307692 -1.861951e-01 -0.038420244 -0.159850635 -0.064764750
> [23,] 1902 -0.105384615 -1.775555e-01 -0.033213760 -0.151823015 -0.058946216
> [24,] 1903 -0.098461539 -1.690561e-01 -0.027867017 -0.143885645 -0.053037432
> [25,] 1904 -0.091538462 -1.607065e-01 -0.022370423 -0.136044696 -0.047032227
> [26,] 1905 -0.084615385 -1.525162e-01 -0.016714535 -0.128306245 -0.040924524
> [27,] 1906 -0.077692308 -1.444943e-01 -0.010890287 -0.120676126 -0.034708490
> [28,] 1907 -0.070769231 -1.366492e-01 -0.004889253 -0.113159760 -0.028378702
> [29,] 1908 -0.063846154 -1.289884e-01 0.001296074 -0.105761977 -0.021930331
> [30,] 1909 -0.056923077 -1.215182e-01 0.007672008 -0.098486840 -0.015359314
> [31,] 1910 -0.050000000 -1.142434e-01 0.014243419 -0.091337484 -0.008662516
> [32,] 1911 -0.043076923 -1.071674e-01 0.021013527 -0.084315978 -0.001837868
> [33,] 1912 -0.036153846 -1.002914e-01 0.027983751 -0.077423239 0.005115546
> [34,] 1913 -0.029230769 -9.361519e-02 0.035153653 -0.070658982 0.012197443
> [35,] 1914 -0.022307692 -8.713634e-02 0.042520952 -0.064021740 0.019406355
> [36,] 1915 -0.015384615 -8.085086e-02 0.050081630 -0.057508928 0.026739697
> [37,] 1916 -0.008461538 -7.475318e-02 0.057830107 -0.051116955 0.034193878
> [38,] 1917 -0.001538462 -6.883640e-02 0.065759473 -0.044841376 0.041764453
> [39,] 1918 0.005384615 -6.309252e-02 0.073861755 -0.038677059 0.049446290
> [40,] 1919 0.012307692 -5.751281e-02 0.082128191 -0.032618368 0.057233753
> [41,] 1920 0.019230769 -5.208797e-02 0.090549507 -0.026659334 0.065120873
> [42,] 1921 0.026153846 -4.680847e-02 0.099116161 -0.020793819 0.073101511
> [43,] 1922 0.033076923 -4.166472e-02 0.107818567 -0.015015652 0.081169499
> [44,] 1923 0.040000000 -3.664727e-02 0.116647271 -0.009318753 0.089318753
> [45,] 1924 0.046923077 -3.174694e-02 0.125593095 -0.003697214 0.097543368
> [46,] 1925 0.053846154 -2.695494e-02 0.134647244 0.001854623 0.105837685
> [47,] 1926 0.060769231 -2.226292e-02 0.143801377 0.007342124 0.114196337
> [48,] 1927 0.067692308 -1.766304e-02 0.153047656 0.012770335 0.122614280
> [49,] 1928 0.074615385 -1.314799e-02 0.162378762 0.018143964 0.131086806
> [50,] 1929 0.081538462 -8.710982e-03 0.171787905 0.023467379 0.139609544
> [51,] 1930 0.088461538 -4.345738e-03 0.181268815 0.028744616 0.148178461
> [52,] 1931 0.095384615 -4.649065e-05 0.190815721 0.033979388 0.156789843
> [53,] 1932 0.102307692 4.192055e-03 0.200423329 0.039175101 0.165440284
> [54,] 1933 0.109230769 8.374747e-03 0.210086792 0.044334874 0.174126664
> [55,] 1934 0.116153846 1.250601e-02 0.219801679 0.049461559 0.182846134
> [56,] 1935 0.123076923 1.658990e-02 0.229563945 0.054557757 0.191596090
> [57,] 1936 0.130000000 2.063010e-02 0.239369902 0.059625842 0.200374158
> [58,] 1937 0.130000000 2.554264e-02 0.234457361 0.062786820 0.197213180
> [59,] 1938 0.130000000 3.023953e-02 0.229760466 0.065809042 0.194190958
> [60,] 1939 0.130000000 3.468890e-02 0.225311102 0.068671989 0.191328011
> [61,] 1940 0.130000000 3.885447e-02 0.221145527 0.071352331 0.188647669
> [62,] 1941 0.130000000 4.269563e-02 0.217304372 0.073823926 0.186176074
> [63,] 1942 0.130000000 4.616776e-02 0.213832244 0.076058070 0.183941930
> [64,] 1943 0.130000000 4.922326e-02 0.210776742 0.078024136 0.181975864
> [65,] 1944 0.130000000 5.181327e-02 0.208186727 0.079690683 0.180309317
> [66,] 1945 0.130000000 5.389026e-02 0.206109736 0.081027125 0.178972875
> [67,] 1946 0.130000000 5.541136e-02 0.204588637 0.082005877 0.177994123
> [68,] 1947 0.130000000 5.634212e-02 0.203657879 0.082604774 0.177395226
> [69,] 1948 0.130000000 5.666006e-02 0.203339939 0.082809352 0.177190648
> [70,] 1949 0.130000000 5.635724e-02 0.203642757 0.082614504 0.177385496
> [71,] 1950 0.130000000 5.544123e-02 0.204558768 0.082025096 0.177974904
> [72,] 1951 0.130000000 5.393418e-02 0.206065824 0.081055380 0.178944620
> [73,] 1952 0.130000000 5.187027e-02 0.208129729 0.079727358 0.180272642
> [74,] 1953 0.130000000 4.929223e-02 0.210707774 0.078068513 0.181931487
> [75,] 1954 0.130000000 4.624751e-02 0.213752495 0.076109385 0.183890615
> [76,] 1955 0.130000000 4.278497e-02 0.217215029 0.073881414 0.186118586
> [77,] 1956 0.130000000 3.895228e-02 0.221047722 0.071415265 0.188584735
> [78,] 1957 0.130000000 3.479412e-02 0.225205878 0.068739695 0.191260305
> [79,] 1958 0.130000000 3.035124e-02 0.229648764 0.065880916 0.194119084
> [80,] 1959 0.130000000 2.565999e-02 0.234340014 0.062862328 0.197137672
> [81,] 1960 0.130000000 2.075236e-02 0.239247637 0.059704514 0.200295486
> [82,] 1961 0.130000000 1.565622e-02 0.244343776 0.056425398 0.203574602
> [83,] 1962 0.130000000 1.039566e-02 0.249604337 0.053040486 0.206959514
> [84,] 1963 0.130000000 4.991436e-03 0.255008564 0.049563131 0.210436869
> [85,] 1964 0.130000000 -5.386147e-04 0.260538615 0.046004815 0.213995185
> [86,] 1965 0.143076923 1.926909e-02 0.266884757 0.063412665 0.222741181
> [87,] 1966 0.156153846 3.876772e-02 0.273539971 0.080621643 0.231686050
> [88,] 1967 0.169230769 5.790379e-02 0.280557753 0.097597325 0.240864213
> [89,] 1968 0.182307692 7.661491e-02 0.288000479 0.114299577 0.250315807
> [90,] 1969 0.195384615 9.482963e-02 0.295939602 0.130682422 0.260086809
> [91,] 1970 0.208461538 1.124682e-01 0.304454863 0.146694551 0.270228526
> [92,] 1971 0.221538461 1.294450e-01 0.313631914 0.162280850 0.280796073
> [93,] 1972 0.234615385 1.456729e-01 0.323557850 0.177385278 0.291845491
> [94,] 1973 0.247692308 1.610702e-01 0.334314435 0.191955225 0.303429390
> [95,] 1974 0.260769231 1.755689e-01 0.345969561 0.205947004 0.315591457
> [96,] 1975 0.273846154 1.891238e-01 0.358568478 0.219331501 0.328360807
> [97,] 1976 0.286923077 2.017191e-01 0.372127073 0.232098492 0.341747662
> [98,] 1977 0.300000000 2.133707e-01 0.386629338 0.244258277 0.355741722
> [99,] 1978 0.313076923 2.241239e-01 0.402029922 0.255840039 0.370313807
> [100,] 1979 0.326153846 2.340468e-01 0.418260863 0.266887506 0.385420186
> [101,] 1980 0.339230769 2.432212e-01 0.435240360 0.277453314 0.401008224
> [102,] 1981 0.352307692 2.517341e-01 0.452881314 0.287593508 0.417021876
> [103,] 1982 0.365384615 2.596711e-01 0.471098085 0.297363192 0.433406039
> [104,] 1983 0.378461538 2.671121e-01 0.489810964 0.306813654 0.450109423
> [105,] 1984 0.391538461 2.741284e-01 0.508948530 0.315990851 0.467086072
> [106,] 1985 0.404615384 2.807823e-01 0.528448443 0.324934896 0.484295873
> [107,] 1986 0.417692308 2.871274e-01 0.548257238 0.333680190 0.501704425
> [108,] 1987 0.430769231 2.932089e-01 0.568329576 0.342255907 0.519282554
> [109,] 1988 0.443846154 2.990650e-01 0.588627259 0.350686626 0.537005682
> [110,] 1989 0.456923077 3.047279e-01 0.609118218 0.358992981 0.554853173
> [111,] 1990 0.470000000 3.102244e-01 0.629775550 0.367192284 0.572807716
> [112,] 1991 0.483076923 3.155772e-01 0.650576667 0.375299067 0.590854778
> [113,] 1992 0.496153846 3.208051e-01 0.671502569 0.383325558 0.608982134
478,480d444
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
490,492d453
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
496,499d456
<
< **** ERROR in algorithm: ifl = 22
<
<
502,503c459,460
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> coef[1:5]: -0.40655906, -0.31473700, 0.05651823, -0.05681818, 0.28681956
> R^2 = 72.56% ; empirical tau (over all): 54/113 = 0.4778761 (target tau= 0.5)
509,512d465
<
< **** ERROR in algorithm: ifl = 22
<
<
515,517d467
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
522,525d471
<
< **** ERROR in algorithm: ifl = 22
<
<
528,530d473
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
532,534c475
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 68 74 78 79 102 111
536,539c477
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 38 39 50 54 77 85 97 113
Running ‘wind.R’ [6s/7s]
Running the tests in ‘tests/ex1.R’ failed.
Complete output:
> #### OOps! Running this in 'CMD check' or in *R* __for the first time__
> #### ===== gives a wrong result (at the end) than when run a 2nd time
> ####-- problem disappears with introduction of if (psw) call ... in Fortran
>
> suppressMessages(library(cobs))
> options(digits = 6)
> if(!dev.interactive(orNone=TRUE)) pdf("ex1.pdf")
>
> source(system.file("util.R", package = "cobs"))
>
> ## Simple example from example(cobs)
> set.seed(908)
> x <- seq(-1,1, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> ## specify constraints (boundary conditions)
> con <- rbind(c( 1,min(x),0),
+ c(-1,max(x),1),
+ c( 0, 0, 0.5))
> ## obtain the median *regression* B-spline using automatically selected knots
> coR <- cobs(x,y,constraint = "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> 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/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): 0.002 0 0.002
>
> options(digits = 5)
> if(!dev.interactive(orNone=TRUE)) pdf("ex2.pdf")
>
> set.seed(821)
> x <- round(sort(rnorm(200)), 3) # rounding -> multiple values
> sum(duplicated(x)) # 9
[1] 3
> y <- (fx <- exp(-x)) + rt(200,4)/4
> summaryCobs(cxy <- cobs(x,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0.72 -0.149 0 -0.195 0.545 ...
$ fitted : num [1:200] 11.98 8.39 6.67 6.07 5.87 ...
$ coef : num [1:5] 11.9769 3.5917 1.0544 0.0295 0.0295
$ knots : num [1:4] -2.557 -0.813 0.418 2.573
$ k0 : num 5
$ k : num 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0
$ icyc : int 11
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 11.4448128 11.6875576 11.976923 12.26629 12.50903
2 10.9843366 11.2126114 11.484728 11.75684 11.98512
3 10.5344633 10.7489871 11.004712 11.26044 11.47496
4 10.0951784 10.2966768 10.536874 10.77707 10.97857
5 9.6664684 9.8556730 10.081215 10.30676 10.49596
6 9.2483213 9.4259693 9.637736 9.84950 10.02715
7 8.8407282 9.0075609 9.206435 9.40531 9.57214
8 8.4436848 8.6004453 8.787313 8.97418 9.13094
9 8.0571928 8.2046236 8.380369 8.55612 8.70355
10 7.6812627 7.8201015 7.985605 8.15111 8.28995
11 7.3159159 7.4468904 7.603020 7.75915 7.89012
12 6.9611870 7.0850095 7.232613 7.38022 7.50404
13 6.6171269 6.7344861 6.874385 7.01428 7.13164
14 6.2838041 6.3953578 6.528336 6.66131 6.77287
15 5.9613061 6.0676719 6.194466 6.32126 6.42763
16 5.6497392 5.7514863 5.872775 5.99406 6.09581
17 5.3492272 5.4468683 5.563262 5.67966 5.77730
18 5.0599086 5.1538933 5.265928 5.37796 5.47195
19 4.7819325 4.8726424 4.980774 5.08891 5.17961
20 4.5154542 4.6031999 4.707798 4.81240 4.90014
21 4.2606295 4.3456507 4.447001 4.54835 4.63337
22 4.0176099 4.1000771 4.198383 4.29669 4.37916
23 3.7865383 3.8665567 3.961943 4.05733 4.13735
24 3.5675443 3.6451602 3.737683 3.83021 3.90782
25 3.3607413 3.4359491 3.525601 3.61525 3.69046
26 3.1662231 3.2389744 3.325698 3.41242 3.48517
27 2.9840608 3.0542750 3.137974 3.22167 3.29189
28 2.8142997 2.8818753 2.962429 3.04298 3.11056
29 2.6569546 2.7217833 2.799063 2.87634 2.94117
30 2.5120031 2.5739870 2.647875 2.72176 2.78375
31 2.3793776 2.4384496 2.508867 2.57928 2.63836
32 2.2589520 2.3151025 2.382037 2.44897 2.50512
33 2.1505256 2.2038366 2.267386 2.33094 2.38425
34 2.0538038 2.1044916 2.164914 2.22534 2.27602
35 1.9677723 2.0162522 2.074043 2.13183 2.18031
36 1.8846710 1.9316617 1.987677 2.04369 2.09068
37 1.8024456 1.8486425 1.903712 1.95878 2.00498
38 1.7213655 1.7673410 1.822146 1.87695 1.92293
39 1.6417290 1.6879196 1.742982 1.79804 1.84423
40 1.5638322 1.6105393 1.666217 1.72189 1.76860
41 1.4879462 1.5353474 1.591852 1.64836 1.69576
42 1.4143040 1.4624707 1.519888 1.57731 1.62547
43 1.3430975 1.3920136 1.450324 1.50864 1.55755
44 1.2744792 1.3240589 1.383161 1.44226 1.49184
45 1.2085658 1.2586702 1.318397 1.37812 1.42823
46 1.1454438 1.1958944 1.256034 1.31617 1.36662
47 1.0851730 1.1357641 1.196072 1.25638 1.30697
48 1.0277900 1.0782992 1.138509 1.19872 1.24923
49 0.9733099 1.0235079 1.083347 1.14319 1.19338
50 0.9217268 0.9713870 1.030585 1.08978 1.13944
51 0.8730129 0.9219214 0.980223 1.03852 1.08743
52 0.8271160 0.8750827 0.932262 0.98944 1.03741
53 0.7839554 0.8308269 0.886700 0.94257 0.98945
54 0.7434158 0.7890916 0.843540 0.89799 0.94366
55 0.7053406 0.7497913 0.802779 0.85577 0.90022
56 0.6695233 0.7128138 0.764419 0.81602 0.85931
57 0.6357022 0.6780170 0.728459 0.77890 0.82121
58 0.6035616 0.6452289 0.694899 0.74457 0.78624
59 0.5724566 0.6139693 0.663455 0.71294 0.75445
60 0.5410437 0.5829503 0.632905 0.68286 0.72477
61 0.5094333 0.5521679 0.603110 0.65405 0.69679
62 0.4778879 0.5217649 0.574069 0.62637 0.67025
63 0.4466418 0.4918689 0.545782 0.59970 0.64492
64 0.4158910 0.4625864 0.518250 0.57391 0.62061
65 0.3857918 0.4340022 0.491472 0.54894 0.59715
66 0.3564634 0.4061813 0.465448 0.52471 0.57443
67 0.3279928 0.3791711 0.440179 0.50119 0.55236
68 0.3004403 0.3530042 0.415663 0.47832 0.53089
69 0.2738429 0.3277009 0.391903 0.45610 0.50996
70 0.2482184 0.3032707 0.368896 0.43452 0.48957
71 0.2235676 0.2797141 0.346644 0.41357 0.46972
72 0.1998762 0.2570233 0.325146 0.39327 0.45042
73 0.1771158 0.2351830 0.304402 0.37362 0.43169
74 0.1552452 0.2141706 0.284413 0.35466 0.41358
75 0.1342101 0.1939567 0.265178 0.33640 0.39615
76 0.1139444 0.1745054 0.246697 0.31889 0.37945
77 0.0943704 0.1557743 0.228971 0.30217 0.36357
78 0.0753996 0.1377153 0.211999 0.28628 0.34860
79 0.0569347 0.1202755 0.195781 0.27129 0.33463
80 0.0388708 0.1033980 0.180318 0.25724 0.32177
81 0.0210989 0.0870233 0.165609 0.24419 0.31012
82 0.0035089 0.0710917 0.151654 0.23222 0.29980
83 -0.0140062 0.0555449 0.138454 0.22136 0.29091
84 -0.0315470 0.0403283 0.126008 0.21169 0.28356
85 -0.0492034 0.0253928 0.114316 0.20324 0.27783
86 -0.0670524 0.0106968 0.103378 0.19606 0.27381
87 -0.0851561 -0.0037936 0.093195 0.19018 0.27155
88 -0.1035613 -0.0181039 0.083766 0.18564 0.27109
89 -0.1223000 -0.0322515 0.075091 0.18243 0.27248
90 -0.1413914 -0.0462467 0.067171 0.18059 0.27573
91 -0.1608432 -0.0600938 0.060005 0.18010 0.28085
92 -0.1806546 -0.0737923 0.053594 0.18098 0.28784
93 -0.2008180 -0.0873382 0.047936 0.18321 0.29669
94 -0.2213213 -0.1007247 0.043033 0.18679 0.30739
95 -0.2421494 -0.1139438 0.038884 0.19171 0.31992
96 -0.2632855 -0.1269863 0.035490 0.19797 0.33427
97 -0.2847123 -0.1398427 0.032850 0.20554 0.35041
98 -0.3064126 -0.1525038 0.030964 0.21443 0.36834
99 -0.3283696 -0.1649603 0.029833 0.22463 0.38804
100 -0.3505674 -0.1772037 0.029456 0.23611 0.40948
knots :
[1] -2.557 -0.813 0.418 2.573
coef :
[1] 11.976924 3.591747 1.054378 0.029456 0.029456
> 1 - sum(cxy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 97.6%
[1] 0.95969
> showProc.time()
Time (user system elapsed): 0.411 0.016 0.475
>
> 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): 0.159 0 0.16
>
> cpuTime(cxy4 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 100))# ~ 3 sec.
Time elapsed: 0.042
> 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: 0.037
> 1 - sum(cxy5 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.4396%
[1] 0.96835
> showProc.time()
Time (user system elapsed): 0.42 0.003 0.45
>
>
> ## regularly spaced x :
> X <- seq(-1,1, len = 201)
> xx <- c(seq(-1.1, -1, len = 11), X,
+ seq( 1, 1.1, len = 11))
> y <- (fx <- exp(-X)) + rt(201,4)/4
> summaryCobs(cXy <- cobs(X,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = X, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:201] -1 -0.99 -0.98 -0.97 -0.96 -0.95 -0.94 -0.93 -0.92 -0.91 ...
$ y : num [1:201] 2.67 2.77 3.46 3.14 1.79 ...
$ resid : num [1:201] 0 0.125 0.84 0.555 -0.77 ...
$ fitted : num [1:201] 2.67 2.64 2.62 2.59 2.56 ...
$ coef : num [1:4] 2.672 1.556 0.7 0.356
$ knots : num [1:3] -1 -0.2 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 100
$ lambda : num 0
$ icyc : int 9
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 2.46750 2.55064 2.67153 2.79242 2.87556
2 2.42251 2.50122 2.61568 2.73013 2.80884
3 2.37783 2.45240 2.56081 2.66923 2.74379
4 2.33345 2.40414 2.50694 2.60973 2.68043
5 2.28933 2.35645 2.45404 2.55164 2.61876
6 2.24548 2.30932 2.40214 2.49496 2.55879
7 2.20189 2.26274 2.35122 2.43970 2.50055
8 2.15855 2.21672 2.30129 2.38586 2.44402
9 2.11547 2.17124 2.25234 2.33344 2.38922
10 2.07265 2.12633 2.20438 2.28244 2.33611
11 2.03013 2.08199 2.15741 2.23283 2.28470
12 1.98791 2.03824 2.11142 2.18461 2.23494
13 1.94605 1.99510 2.06642 2.13775 2.18680
14 1.90459 1.95260 2.02241 2.09222 2.14023
15 1.86359 1.91078 1.97938 2.04799 2.09517
16 1.82311 1.86966 1.93734 2.00502 2.05157
17 1.78322 1.82929 1.89629 1.96328 2.00936
18 1.74397 1.78971 1.85622 1.92273 1.96847
19 1.70544 1.75096 1.81714 1.88332 1.92883
20 1.66769 1.71307 1.77904 1.84502 1.89039
21 1.63079 1.67608 1.74193 1.80779 1.85308
22 1.59478 1.64002 1.70581 1.77160 1.81684
23 1.55972 1.60493 1.67067 1.73642 1.78163
24 1.52564 1.57083 1.63653 1.70222 1.74741
25 1.49260 1.53773 1.60336 1.66899 1.71412
26 1.46062 1.50567 1.57118 1.63670 1.68175
27 1.42972 1.47466 1.53999 1.60533 1.65026
28 1.39994 1.44470 1.50979 1.57488 1.61964
29 1.37128 1.41581 1.48057 1.54533 1.58987
30 1.34375 1.38800 1.45234 1.51668 1.56093
31 1.31736 1.36126 1.42510 1.48893 1.53283
32 1.29211 1.33560 1.39884 1.46207 1.50556
33 1.26800 1.31101 1.37357 1.43612 1.47914
34 1.24500 1.28749 1.34928 1.41107 1.45356
35 1.22310 1.26502 1.32598 1.38694 1.42886
36 1.20228 1.24360 1.30367 1.36374 1.40505
37 1.18250 1.22319 1.28234 1.34150 1.38218
38 1.16372 1.20377 1.26200 1.32023 1.36028
39 1.14589 1.18532 1.24265 1.29998 1.33941
40 1.12894 1.16779 1.22428 1.28077 1.31962
41 1.11271 1.15106 1.20683 1.26259 1.30094
42 1.09639 1.13439 1.18963 1.24488 1.28287
43 1.07982 1.11760 1.17253 1.22747 1.26525
44 1.06303 1.10072 1.15553 1.21034 1.24803
45 1.04607 1.08378 1.13862 1.19346 1.23117
46 1.02898 1.06681 1.12181 1.17681 1.21463
47 1.01180 1.04982 1.10509 1.16037 1.19838
48 0.99458 1.03284 1.08847 1.14411 1.18237
49 0.97734 1.01589 1.07195 1.12801 1.16656
50 0.96011 0.99899 1.05552 1.11205 1.15092
51 0.94294 0.98216 1.03919 1.09621 1.13543
52 0.92585 0.96541 1.02295 1.08049 1.12005
53 0.90885 0.94877 1.00681 1.06485 1.10477
54 0.89197 0.93223 0.99076 1.04930 1.08956
55 0.87523 0.91581 0.97482 1.03382 1.07440
56 0.85865 0.89952 0.95896 1.01840 1.05928
57 0.84223 0.88337 0.94321 1.00304 1.04419
58 0.82598 0.86736 0.92755 0.98773 1.02911
59 0.80991 0.85150 0.91198 0.97246 1.01405
60 0.79403 0.83579 0.89651 0.95723 0.99899
61 0.77834 0.82023 0.88114 0.94205 0.98394
62 0.76284 0.80482 0.86586 0.92690 0.96888
63 0.74753 0.78956 0.85068 0.91180 0.95383
64 0.73241 0.77446 0.83559 0.89673 0.93878
65 0.71747 0.75950 0.82060 0.88171 0.92374
66 0.70271 0.74468 0.80571 0.86674 0.90871
67 0.68812 0.73001 0.79091 0.85182 0.89371
68 0.67368 0.71546 0.77621 0.83696 0.87874
69 0.65939 0.70104 0.76161 0.82217 0.86382
70 0.64523 0.68674 0.74710 0.80745 0.84896
71 0.63118 0.67254 0.73268 0.79282 0.83419
72 0.61722 0.65844 0.71836 0.77829 0.81951
73 0.60333 0.64441 0.70414 0.76388 0.80495
74 0.58948 0.63045 0.69002 0.74958 0.79055
75 0.57565 0.61654 0.67599 0.73544 0.77632
76 0.56181 0.60266 0.66205 0.72145 0.76230
77 0.54792 0.58879 0.64821 0.70764 0.74851
78 0.53395 0.57491 0.63447 0.69403 0.73500
79 0.51986 0.56100 0.62083 0.68065 0.72179
80 0.50563 0.54705 0.60728 0.66750 0.70892
81 0.49121 0.53302 0.59382 0.65462 0.69643
82 0.47657 0.51891 0.58046 0.64202 0.68435
83 0.46169 0.50468 0.56720 0.62972 0.67271
84 0.44652 0.49033 0.55403 0.61774 0.66155
85 0.43105 0.47584 0.54096 0.60609 0.65087
86 0.41526 0.46119 0.52799 0.59478 0.64072
87 0.39912 0.44638 0.51511 0.58383 0.63109
88 0.38264 0.43141 0.50233 0.57324 0.62202
89 0.36579 0.41626 0.48964 0.56302 0.61349
90 0.34858 0.40093 0.47705 0.55317 0.60552
91 0.33101 0.38542 0.46455 0.54368 0.59810
92 0.31307 0.36975 0.45215 0.53456 0.59123
93 0.29478 0.35390 0.43985 0.52580 0.58492
94 0.27615 0.33788 0.42764 0.51741 0.57914
95 0.25717 0.32170 0.41553 0.50936 0.57389
96 0.23787 0.30536 0.40352 0.50167 0.56917
97 0.21824 0.28888 0.39160 0.49431 0.56495
98 0.19830 0.27225 0.37977 0.48730 0.56125
99 0.17806 0.25547 0.36804 0.48062 0.55803
100 0.15752 0.23857 0.35641 0.47426 0.55531
knots :
[1] -1.0 -0.2 1.0
coef :
[1] 2.67153 1.55592 0.70045 0.35641
> 1 - sum(cXy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 77.2%
[1] 0.77644
> showProc.time()
Time (user system elapsed): 0.108 0.001 0.205
>
> (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): 0.528 0 0.658
>
> ## Interpolation
> cpuTime(cXyI <- cobs(X,y, "decrease", knots = unique(X)))
qbsks2():
Performing general knot selection ...
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cpuTime ... cobs -> qbsks2 -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
In addition: Warning message:
In cobs(X, y, "decrease", knots = unique(X)) :
The number of knots can't be equal to the number of unique x for degree = 2.
'cobs' has automatically deleted the middle knot.
Timing stopped at: 0.671 0.015 0.868
Execution halted
Running the tests in ‘tests/wind.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time() # timing here (to be faster by default)
Time (user system elapsed): 0.002 0.001 0.001
>
> 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)
> co50.2 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 2)
>
> showProc.time()
Time (user system elapsed): 0.406 0.03 0.503
>
> 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): 0.033 0 0.033
>
> ## cobs99: Since SIC chooses a lambda that corresponds to the smoothest
> ## possible fit, rerun cobs with a larger lstart value
> ## (lstart <- log(.Machine$double.xmax)^3) # 3.57 e9
> ##
> co.o50. <-
+ cobs(day,speed, knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
The algorithm has converged. You might
plot() the returned object (which plots 'sic' against 'lambda')
to see if you have found the global minimum of the information criterion
so that you can determine if you need to adjust any or all of
'lambda.lo', 'lambda.hi' and 'lambda.length' and refit the model.
> summary(co.o50.)
COBS smoothing spline (degree = 2) from call:
cobs(x = day, y = speed, constraint = "periodic", nknots = 10, method = "quantile", tau = 0.5, lambda = -1, knots.add = TRUE)
{tau=0.5}-quantile; dimensionality of fit: 7 from {14,13,11,8,7,30}
x$knots[1:10]: 0.999635, 41.000000, 82.000000, ... , 366.000365
lambda = 101002.6, selected via SIC, out of 25 ones.
coef[1:12]: 1.121550e+01, 1.139573e+01, 1.089025e+01, 9.954427e+00, 8.148158e+00, ... , 5.373106e-04
R^2 = 8.22% ; empirical tau (over all): 3287/6574 = 0.5 (target tau= 0.5)
> summary(pc.5 <- predict(co.o50., interval = "both"))
z fit cb.lo cb.up
Min. : 0.9996 Min. : 7.212 Min. : 6.351 Min. : 7.951
1st Qu.: 92.2498 1st Qu.: 7.790 1st Qu.: 7.000 1st Qu.: 8.600
Median :183.5000 Median : 9.436 Median : 8.555 Median :10.326
Mean :183.5000 Mean : 9.314 Mean : 8.388 Mean :10.241
3rd Qu.:274.7502 3rd Qu.:10.798 3rd Qu.: 9.716 3rd Qu.:11.787
Max. :366.0004 Max. :11.290 Max. :10.347 Max. :13.416
ci.lo ci.up
Min. : 6.782 Min. : 7.598
1st Qu.: 7.370 1st Qu.: 8.213
Median : 8.974 Median : 9.901
Mean : 8.830 Mean : 9.798
3rd Qu.:10.197 3rd Qu.:11.311
Max. :10.797 Max. :12.366
>
> showProc.time()
Time (user system elapsed): 1.779 0.203 2.292
>
> if(doExtra) { ## + repeat.delete.add
+ co.o50.. <- cobs(day,speed, knots.add = TRUE, repeat.delete.add=TRUE,
+ constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
+ summary(co.o50..)
+ showProc.time()
+ }
>
> co.o9 <- ## Compute the .9 quantile smoothing B-spline
+ cobs(day,speed,knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .9,lambda = -1, method = "uniform")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Flavor: r-devel-linux-x86_64-debian-clang
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’
Running ‘ex1.R’ [6s/12s]
Running ‘ex2-long.R’ [16s/26s]
Running ‘ex3.R’
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’
Running ‘roof.R’
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ...24,40d23
< 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 9 24 1135.8839 8.07831 3
< [5,] 1.313125e+00 1 25 889.5418 0.00000 3
< [6,] 2.570235e+00 1 25 889.5418 0.00000 3
< [7,] 1.927405e+01 1 24 889.5418 0.00000 3
< [8,] 3.772589e+01 1 25 889.5418 0.00000 3
< [9,] 7.384247e+01 1 25 889.5418 0.00000 3
< [10,] 1.445350e+02 1 25 889.5418 0.00000 3
< [11,] 1.083859e+03 1 25 889.5418 0.00000 3
< [12,] 2.121483e+03 1 25 889.5418 0.00000 3
< [13,] 4.152467e+03 1 25 889.5418 0.00000 3
< [14,] 8.127798e+03 1 25 889.5418 0.00000 3
< [15,] 1.590888e+04 1 25 889.5418 0.00000 3
48,50d30
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 2525125241111125251124252525112525252525
54,56c34
< * Warning in algorithm: some ifl != 1
<
< {tau=0.5}-quantile; dimensionality of fit: 4 from {3,16,8,6,4}
---
> {tau=0.5}-quantile; dimensionality of fit: 5 from {16,11,9,8,6,5,4}
58c36
< lambda = 282.9043, selected via SIC, out of 25 ones.
---
> lambda = 19.27405, selected via SIC, out of 25 ones.
60,61c38,39
< coef[1:12]: 99.9071264, 98.9703735, 97.1887749, 95.6052671, 94.5143875, ... , 0.1239923
< R^2 = -13.39% ; empirical tau (over all): 81/153 = 0.5294118 (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)
73,74c51,52
< [1,] 1.59089e-03 1.80959
< [2,] 3.11391e-03 1.80959
---
> [1,] 1.59089e-03 2.24395
> [2,] 3.11391e-03 2.24395
76,77c54,55
< [4,] 1.19300e-02 1.80959
< [5,] 2.33510e-02 2.05405
---
> [4,] 1.19300e-02 2.24395
> [5,] 2.33510e-02 2.24395
83,84c61,62
< [11,] 1.31313e+00 1.80959
< [12,] 2.57024e+00 1.80959
---
> [11,] 1.31313e+00 2.18317
> [12,] 2.57024e+00 2.15738
87,90c65,68
< [15,] 1.92740e+01 1.80959
< [16,] 3.77259e+01 1.80959
< [17,] 7.38425e+01 1.80959
< [18,] 1.44535e+02 1.80959
---
> [15,] 1.92740e+01 2.09955
> [16,] 3.77259e+01 2.11706
> [17,] 7.38425e+01 2.10159
> [18,] 1.44535e+02 2.10170
93,97c71,75
< [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
---
> [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
123,136d100
< 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 3
< [2,] 6.094988e-03 1 25 889.5418 0 3
< [3,] 1.751081e-01 1 25 889.5418 0 3
< [4,] 6.708718e-01 1 25 889.5418 0 3
< [5,] 5.030829e+00 1 25 889.5418 0 3
< [6,] 9.847052e+00 1 25 889.5418 0 3
< [7,] 1.927405e+01 1 25 889.5418 0 3
< [8,] 3.772589e+01 1 25 889.5418 0 3
< [9,] 1.445350e+02 1 25 889.5418 0 3
< [10,] 2.829043e+02 1 25 889.5418 0 3
< [11,] 8.127798e+03 1 25 889.5418 0 3
< [12,] 1.590888e+04 1 25 889.5418 0 3
144,146d107
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 1252511112512511252525251252511112525
150,152c111
< * Warning in algorithm: some ifl != 1
<
< {tau=0.25}-quantile; dimensionality of fit: 5 from {13,3,12,10,5}
---
> {tau=0.25}-quantile; dimensionality of fit: 5 from {13,12,11,10,8,7,6,5,3}
174,189d132
< WARNING: Some lambdas had problems in rq.fit.sfnc():
< lambda icyc ifl fidel sum|res|_s k
< [1,] 3.113911e-03 6 21 679.9659 96.9949 3
< [2,] 6.094988e-03 1 25 889.5418 0.0000 3
< [3,] 1.192998e-02 1 25 889.5418 0.0000 3
< [4,] 4.570597e-02 1 25 889.5418 0.0000 3
< [5,] 8.946220e-02 1 25 889.5418 0.0000 3
< [6,] 2.570235e+00 1 25 889.5418 0.0000 3
< [7,] 1.927405e+01 1 25 889.5418 0.0000 3
< [8,] 3.772589e+01 1 25 889.5418 0.0000 3
< [9,] 7.384247e+01 1 25 889.5418 0.0000 3
< [10,] 1.445350e+02 1 25 889.5418 0.0000 3
< [11,] 1.083859e+03 1 24 889.5418 0.0000 3
< [12,] 2.121483e+03 1 25 889.5418 0.0000 3
< [13,] 4.152467e+03 1 25 889.5418 0.0000 3
< [14,] 1.590888e+04 1 25 889.5418 0.0000 3
196,198d138
< Warning message:
< In cobs(age, fci, constraint = "decrease", lambda = -1, nknots = 10, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 121252512525111125112525252511242525125
202,204c142
< * Warning in algorithm: some ifl != 1
<
< {tau=0.75}-quantile; dimensionality of fit: 70 from {70,3}
---
> {tau=0.75}-quantile; dimensionality of fit: 70 from {70}
206c144
< lambda = 1.313125, selected via SIC, out of 25 ones.
---
> lambda = 5.030829, selected via SIC, out of 25 ones.
224,323c162,261
< [1,] 0.04998516 99.90713 73.08640 126.72785 82.70115 117.11310
< [2,] 0.20109657 99.62824 75.50652 123.74996 84.15373 115.10275
< [3,] 0.35220798 99.35219 77.04434 121.66004 85.04131 113.66307
< [4,] 0.50331939 99.07896 78.00986 120.14807 85.56276 112.59517
< [5,] 0.65443080 98.80857 78.68098 118.93617 85.89636 111.72078
< [6,] 0.80554221 98.54101 79.22790 117.85413 86.15131 110.93072
< [7,] 0.95665362 98.27628 79.66157 116.89100 86.33461 110.21796
< [8,] 1.10776504 98.01439 79.79619 116.23258 86.32709 109.70168
< [9,] 1.25887645 97.75532 79.50028 116.01036 86.04439 109.46625
< [10,] 1.40998786 97.49909 79.08062 115.91755 85.68331 109.31486
< [11,] 1.56109927 97.24568 78.78396 115.70740 85.40216 109.08921
< [12,] 1.71221068 96.99511 78.72291 115.26731 85.27317 108.71705
< [13,] 1.86332209 96.74737 78.88443 114.61031 85.28798 108.20676
< [14,] 2.01443350 96.50246 79.12177 113.88316 85.35244 107.65249
< [15,] 2.16554491 96.26038 79.13756 113.38320 85.27579 107.24498
< [16,] 2.31665632 96.02114 78.83792 113.20435 84.99780 107.04448
< [17,] 2.46776773 95.78472 78.54422 113.02522 84.72463 106.84481
< [18,] 2.61887914 95.55114 78.47291 112.62936 84.59515 106.50712
< [19,] 2.76999056 95.32038 78.69618 111.94459 84.65566 105.98511
< [20,] 2.92110197 95.09246 79.14289 111.04204 84.86053 105.32440
< [21,] 3.07221338 94.86737 79.56781 110.16693 85.05243 104.68231
< [22,] 3.22332479 94.64511 79.71258 109.57764 85.06563 104.22460
< [23,] 3.37443620 94.42569 79.71468 109.13669 84.98831 103.86306
< [24,] 3.52554761 94.20909 79.56635 108.85183 84.81551 103.60267
< [25,] 3.67665902 93.99533 79.00012 108.99053 84.37564 103.61501
< [26,] 3.82777043 93.78439 77.97137 109.59741 83.64006 103.92873
< [27,] 3.97888184 93.57629 76.77542 110.37716 82.79823 104.35435
< [28,] 4.12999325 93.37102 75.62426 111.11778 81.98616 104.75588
< [29,] 4.28110467 93.16858 74.64421 111.69295 81.28487 105.05229
< [30,] 4.43221608 92.96897 73.90129 112.03665 80.73671 105.20123
< [31,] 4.58332749 92.77219 73.41913 112.12526 80.35686 105.18753
< [32,] 4.73443890 92.57825 73.18769 111.96880 80.13886 105.01763
< [33,] 4.88555031 92.38713 73.16451 111.60976 80.05548 104.71879
< [34,] 5.03666172 92.19885 73.27028 111.12742 80.05584 104.34187
< [35,] 5.18777313 92.01340 73.38096 110.64584 80.06036 103.96644
< [36,] 5.33888454 91.83078 73.30423 110.35732 79.94567 103.71589
< [37,] 5.48999595 91.65099 72.89407 110.40791 79.61809 103.68389
< [38,] 5.64110736 91.47403 72.24854 110.69953 79.14054 103.80753
< [39,] 5.79221877 91.29991 71.47434 111.12548 78.58145 104.01836
< [40,] 5.94333019 91.12861 70.66018 111.59704 77.99775 104.25948
< [41,] 6.09444160 90.96015 69.87531 112.04499 77.43385 104.48645
< [42,] 6.24555301 90.79452 69.17182 112.41721 76.92317 104.66586
< [43,] 6.39666442 90.63171 68.58813 112.67530 76.49036 104.77307
< [44,] 6.54777583 90.47174 68.15210 112.79138 76.15330 104.79019
< [45,] 6.69888724 90.31461 67.88371 112.74550 75.92479 104.70442
< [46,] 6.84999865 90.16030 67.79678 112.52382 75.81371 104.50689
< [47,] 7.00111006 90.00882 67.90026 112.11739 75.82578 104.19186
< [48,] 7.15222147 89.86018 68.19883 111.52152 75.96404 103.75632
< [49,] 7.30333288 89.71437 68.69315 110.73559 76.22888 103.19985
< [50,] 7.45444429 89.57138 69.37937 109.76340 76.61785 102.52492
< [51,] 7.60555571 89.43123 70.24809 108.61438 77.12491 101.73756
< [52,] 7.75666712 89.29391 71.28208 107.30574 77.73900 100.84882
< [53,] 7.90777853 89.15943 72.45223 105.86662 78.44146 99.87739
< [54,] 8.05888994 89.02777 73.71025 104.34529 79.20131 98.85423
< [55,] 8.21000135 88.89894 74.97631 102.82158 79.96732 97.83057
< [56,] 8.36111276 88.77295 76.11975 101.42615 80.65570 96.89020
< [57,] 8.51222417 88.64979 76.93844 100.36114 81.13675 96.16283
< [58,] 8.66333558 88.52946 77.19289 99.86603 81.25685 95.80207
< [59,] 8.81444699 88.41196 77.00749 99.81642 81.09579 95.72812
< [60,] 8.96555840 88.29729 76.78849 99.80609 80.91419 95.68039
< [61,] 9.11666981 88.18545 76.74192 99.62898 80.84422 95.52668
< [62,] 9.26778123 88.07645 76.87136 99.28153 80.88819 95.26471
< [63,] 9.41889264 87.97027 76.97211 98.96843 80.91476 95.02579
< [64,] 9.57000405 87.86693 76.58903 99.14483 80.63195 95.10190
< [65,] 9.72111546 87.76642 75.63629 99.89654 79.98472 95.54811
< [66,] 9.87222687 87.66874 74.31434 101.02313 79.10165 96.23582
< [67,] 10.02333828 87.57389 72.79284 102.35493 78.09158 97.05619
< [68,] 10.17444969 87.48187 71.19072 103.77301 77.03081 97.93293
< [69,] 10.32556110 87.39268 69.58526 105.20010 75.96890 98.81646
< [70,] 10.47667251 87.30633 68.02574 106.58691 74.93749 99.67516
< [71,] 10.62778392 87.22280 66.54384 107.90176 73.95688 100.48872
< [72,] 10.77889533 87.14211 65.16024 109.12398 73.04035 101.24387
< [73,] 10.93000675 87.06425 63.88866 110.23984 72.19670 101.93180
< [74,] 11.08111816 86.98922 62.73827 111.24016 71.43181 102.54663
< [75,] 11.23222957 86.91702 61.71521 112.11883 70.74961 103.08443
< [76,] 11.38334098 86.84765 60.82345 112.87185 70.15266 103.54264
< [77,] 11.53445239 86.78112 60.06540 113.49683 69.64251 103.91972
< [78,] 11.68556380 86.71741 59.44225 113.99257 69.21991 104.21491
< [79,] 11.83667521 86.65654 58.95418 114.35890 68.88498 104.42809
< [80,] 11.98778662 86.59850 58.60044 114.59655 68.63725 104.55974
< [81,] 12.13889803 86.54328 58.37944 114.70712 68.47568 104.61089
< [82,] 12.29000944 86.49091 58.28868 114.69313 68.39868 104.58313
< [83,] 12.44112086 86.44136 58.32467 114.55804 68.40400 104.47871
< [84,] 12.59223227 86.39464 58.48278 114.30650 68.48869 104.30059
< [85,] 12.74334368 86.35075 58.75704 113.94446 68.64890 104.05261
< [86,] 12.89445509 86.30970 59.13981 113.47959 68.87973 103.73967
< [87,] 13.04556650 86.27148 59.62137 112.92158 69.17496 103.36799
< [88,] 13.19667791 86.23609 60.18940 112.28277 69.52668 102.94550
< [89,] 13.34778932 86.20353 60.82826 111.57879 69.92484 102.48221
< [90,] 13.49890073 86.17380 61.51813 110.82947 70.35675 101.99085
< [91,] 13.65001214 86.14690 62.23394 110.05986 70.80631 101.48749
< [92,] 13.80112355 86.12283 62.94423 109.30144 71.25335 100.99232
< [93,] 13.95223496 86.10160 63.61000 108.59319 71.67284 100.53036
< [94,] 14.10334638 86.08319 64.18404 107.98235 72.03450 100.13189
< [95,] 14.25445779 86.06762 64.61124 107.52400 72.30297 99.83227
< [96,] 14.40556920 86.05488 64.83078 107.27898 72.43924 99.67052
< [97,] 14.55668061 86.04497 64.78076 107.30919 72.40360 99.68634
< [98,] 14.70779202 86.03789 64.40506 107.67073 72.16004 99.91574
< [99,] 14.85890343 86.03365 63.66076 108.40653 71.68104 100.38625
< [100,] 15.01001484 86.03223 62.52339 109.54108 70.95089 101.11357
---
> [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
> [34,] 5.03666172 90.51887 70.16863 110.86911 78.43239 102.60535
> [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
> [37,] 5.48999595 89.64979 69.48409 109.81549 77.67292 101.62667
> [38,] 5.64110736 89.37451 68.70505 110.04398 77.09844 101.65059
> [39,] 5.79221877 89.11003 67.79542 110.42464 76.45079 101.76927
> [40,] 5.94333019 88.85633 66.85058 110.86209 75.78661 101.92606
> [41,] 6.09444160 88.61343 65.94497 111.28189 75.15011 102.07676
> [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
> [45,] 6.69888724 87.74975 63.63413 111.86536 73.42693 102.07257
> [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
> [48,] 7.15222147 87.21530 63.92703 110.50356 73.38386 101.04674
> [49,] 7.30333288 87.05874 64.45867 109.65880 73.63603 100.48144
> [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
> [54,] 8.05888994 86.43779 69.96982 102.90576 76.65708 96.21850
> [55,] 8.21000135 86.34598 71.37765 101.31431 77.45594 95.23602
> [56,] 8.36111276 86.26496 72.66142 99.86851 78.18550 94.34442
> [57,] 8.51222417 86.19473 73.60378 98.78569 78.71667 93.67279
> [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
> [95,] 14.25445779 86.00000 62.93209 109.06791 72.29944 99.70056
> [96,] 14.40556920 86.00000 63.18182 108.81818 72.44775 99.55225
> [97,] 14.55668061 86.00000 63.13869 108.86131 72.42214 99.57786
> [98,] 14.70779202 86.00000 62.74238 109.25762 72.18676 99.81324
> [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
Running ‘small-ex.R’
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
Running ‘spline-ex.R’
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’ [6s/11s]
Comparing ‘temp.Rout’ to ‘temp.Rout.save’ ... OK
Running ‘wind.R’ [13s/18s]
Running the tests in ‘tests/0_pt-ex.R’ failed.
Complete output:
> suppressMessages(library(cobs))
> options(digits = 6, warn = 2) ## << all warnings to errors!
>
> ## When 'R CMD check'ing, we may want to see exact package information:
> sessionInfo() # plus the details of the major dependent packages:
R Under development (unstable) (2024-10-30 r87277)
Platform: x86_64-pc-linux-gnu
Running under: Fedora Linux 36 (Workstation Edition)
Matrix products: default
BLAS: /data/gannet/ripley/R/R-clang/lib/libRblas.so
LAPACK: /data/gannet/ripley/R/R-clang/lib/libRlapack.so; LAPACK version 3.12.0
locale:
[1] LC_CTYPE=en_GB.utf8 LC_NUMERIC=C
[3] LC_TIME=en_GB.UTF-8 LC_COLLATE=C
[5] LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
[7] LC_PAPER=en_GB.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
time zone: Europe/London
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] cobs_1.3-8
loaded via a namespace (and not attached):
[1] MASS_7.3-61 compiler_4.5.0 Matrix_1.7-1 quantreg_5.99
[5] SparseM_1.84-2 survival_3.7-0 MatrixModels_0.5-3 splines_4.5.0
[9] grid_4.5.0 lattice_0.22-6
> packageDescription("SparseM")
Package: SparseM
Version: 1.84-2
Authors@R: c( person("Roger", "Koenker", role = c("cre","aut"), email =
"rkoenker@uiuc.edu"), person(c("Pin", "Tian"), "Ng", role =
c("ctb"), comment = "Contributions to Sparse QR code", email =
"pin.ng@nau.edu") , person("Yousef", "Saad", role = c("ctb"),
comment = "author of sparskit2") , person("Ben", "Shaby", role
= c("ctb"), comment = "author of chol2csr") , person("Martin",
"Maechler", role = "ctb", comment = c("chol() tweaks; S4",
ORCID = "0000-0002-8685-9910")) )
Maintainer: Roger Koenker <rkoenker@uiuc.edu>
Depends: R (>= 2.15), methods
Imports: graphics, stats, utils
VignetteBuilder: knitr
Suggests: knitr
Description: Some basic linear algebra functionality for sparse
matrices is provided: including Cholesky decomposition and
backsolving as well as standard R subsetting and Kronecker
products.
License: GPL (>= 2)
Title: Sparse Linear Algebra
URL: http://www.econ.uiuc.edu/~roger/research/sparse/sparse.html
NeedsCompilation: yes
Packaged: 2024-07-17 11:01:25 UTC; ripley
Author: Roger Koenker [cre, aut], Pin Tian Ng [ctb] (Contributions to
Sparse QR code), Yousef Saad [ctb] (author of sparskit2), Ben
Shaby [ctb] (author of chol2csr), Martin Maechler [ctb] (chol()
tweaks; S4, <https://orcid.org/0000-0002-8685-9910>)
Repository: CRAN
Date/Publication: 2024-07-17 16:10:06 UTC
Built: R 4.5.0; x86_64-pc-linux-gnu; 2024-10-25 17:46:41 UTC; unix
-- File: /data/gannet/ripley/R/test-clang/SparseM/Meta/package.rds
> packageDescription("quantreg")
Package: quantreg
Title: Quantile Regression
Description: Estimation and inference methods for models for
conditional quantile functions: Linear and nonlinear parametric
and non-parametric (total variation penalized) models for
conditional quantiles of a univariate response and several
methods for handling censored survival data. Portfolio
selection methods based on expected shortfall risk are also now
included. See Koenker, R. (2005) Quantile Regression, Cambridge
U. Press, <doi:10.1017/CBO9780511754098> and Koenker, R. et al.
(2017) Handbook of Quantile Regression, CRC Press,
<doi:10.1201/9781315120256>.
Version: 5.99
Authors@R: c( person("Roger", "Koenker", role = c("cre","aut"), email =
"rkoenker@illinois.edu"), person("Stephen", "Portnoy", role =
c("ctb"), comment = "Contributions to Censored QR code", email
= "sportnoy@illinois.edu"), person(c("Pin", "Tian"), "Ng", role
= c("ctb"), comment = "Contributions to Sparse QR code", email
= "pin.ng@nau.edu"), person("Blaise", "Melly", role = c("ctb"),
comment = "Contributions to preprocessing code", email =
"mellyblaise@gmail.com"), person("Achim", "Zeileis", role =
c("ctb"), comment = "Contributions to dynrq code essentially
identical to his dynlm code", email =
"Achim.Zeileis@uibk.ac.at"), person("Philip", "Grosjean", role
= c("ctb"), comment = "Contributions to nlrq code", email =
"phgrosjean@sciviews.org"), person("Cleve", "Moler", role =
c("ctb"), comment = "author of several linpack routines"),
person("Yousef", "Saad", role = c("ctb"), comment = "author of
sparskit2"), person("Victor", "Chernozhukov", role = c("ctb"),
comment = "contributions to extreme value inference code"),
person("Ivan", "Fernandez-Val", role = c("ctb"), comment =
"contributions to extreme value inference code"),
person(c("Brian", "D"), "Ripley", role = c("trl","ctb"),
comment = "Initial (2001) R port from S (to my everlasting
shame -- how could I have been so slow to adopt R!) and for
numerous other suggestions and useful advice", email =
"ripley@stats.ox.ac.uk"))
Maintainer: Roger Koenker <rkoenker@illinois.edu>
Repository: CRAN
Depends: R (>= 3.5), stats, SparseM
Imports: methods, graphics, Matrix, MatrixModels, survival, MASS
Suggests: interp, rgl, logspline, nor1mix, Formula, zoo, R.rsp, conquer
License: GPL (>= 2)
URL: https://www.r-project.org
NeedsCompilation: yes
VignetteBuilder: R.rsp
Packaged: 2024-10-22 10:53:40 UTC; roger
Author: Roger Koenker [cre, aut], Stephen Portnoy [ctb] (Contributions
to Censored QR code), Pin Tian Ng [ctb] (Contributions to
Sparse QR code), Blaise Melly [ctb] (Contributions to
preprocessing code), Achim Zeileis [ctb] (Contributions to
dynrq code essentially identical to his dynlm code), Philip
Grosjean [ctb] (Contributions to nlrq code), Cleve Moler [ctb]
(author of several linpack routines), Yousef Saad [ctb] (author
of sparskit2), Victor Chernozhukov [ctb] (contributions to
extreme value inference code), Ivan Fernandez-Val [ctb]
(contributions to extreme value inference code), Brian D Ripley
[trl, ctb] (Initial (2001) R port from S (to my everlasting
shame -- how could I have been so slow to adopt R!) and for
numerous other suggestions and useful advice)
Date/Publication: 2024-10-22 12:50:02 UTC
Built: R 4.5.0; x86_64-pc-linux-gnu; 2024-10-25 18:51:22 UTC; unix
-- File: /data/gannet/ripley/R/test-clang/quantreg/Meta/package.rds
> packageDescription("cobs")
Package: cobs
Version: 1.3-8
VersionNote: Released 1.3-7 on 2024-02-03
Date: 2024-03-05
Title: Constrained B-Splines (Sparse Matrix Based)
Description: Qualitatively Constrained (Regression) Smoothing Splines
via Linear Programming and Sparse Matrices.
Author: Pin T. Ng <Pin.Ng@nau.edu> and Martin Maechler
Maintainer: Martin Maechler <maechler@stat.math.ethz.ch>
Imports: SparseM (>= 1.6), quantreg (>= 4.65), grDevices, graphics,
splines, stats, methods
Suggests: Matrix
LazyData: yes
BuildResaveData: no
URL: https://curves-etc.r-forge.r-project.org/,
https://r-forge.r-project.org/R/?group_id=846,
https://r-forge.r-project.org/scm/viewvc.php/pkg/cobs/?root=curves-etc,
https://www2.nau.edu/PinNg/cobs.html,
svn://svn.r-forge.r-project.org/svnroot/curves-etc/pkg/cobs
BugReports: https://r-forge.r-project.org/R/?group_id=846
License: GPL (>= 2)
NeedsCompilation: yes
Packaged: 2024-03-05 22:24:30 UTC; maechler
Repository: CRAN
Date/Publication: 2024-03-06 12:50:02 UTC
Built: R 4.5.0; x86_64-pc-linux-gnu; 2024-10-30 17:23:50 UTC; unix
-- File: /data/gannet/ripley/R/packages/tests-clang/cobs.Rcheck/cobs/Meta/package.rds
> ##
>
> str(.M <- .Machine, digits = 8)
List of 29
$ double.eps : num 2.220446e-16
$ double.neg.eps : num 1.110223e-16
$ double.xmin : num 2.2250739e-308
$ double.xmax : num 1.7976931e+308
$ double.base : int 2
$ double.digits : int 53
$ double.rounding : int 5
$ double.guard : int 0
$ double.ulp.digits : int -52
$ double.neg.ulp.digits : int -53
$ double.exponent : int 11
$ double.min.exp : int -1022
$ double.max.exp : int 1024
$ integer.max : int 2147483647
$ sizeof.long : int 8
$ sizeof.longlong : int 8
$ sizeof.longdouble : int 16
$ sizeof.pointer : int 8
$ sizeof.time_t : int 8
$ longdouble.eps : num 1.0842022e-19
$ longdouble.neg.eps : num 5.4210109e-20
$ longdouble.digits : int 64
$ longdouble.rounding : int 5
$ longdouble.guard : int 0
$ longdouble.ulp.digits : int -63
$ longdouble.neg.ulp.digits: int -64
$ longdouble.exponent : int 15
$ longdouble.min.exp : int -16382
$ longdouble.max.exp : int 16384
> capabilities()
jpeg png tiff tcltk X11 aqua
TRUE TRUE TRUE TRUE TRUE FALSE
http/ftp sockets libxml fifo cledit iconv
TRUE TRUE FALSE TRUE FALSE TRUE
NLS Rprof profmem cairo ICU long.double
TRUE TRUE FALSE TRUE TRUE TRUE
libcurl
TRUE
> str(.M[grep("^sizeof", names(.M))]) ## also differentiate long-double..
List of 5
$ sizeof.long : int 8
$ sizeof.longlong : int 8
$ sizeof.longdouble: int 16
$ sizeof.pointer : int 8
$ sizeof.time_t : int 8
> (b64 <- .M$sizeof.pointer == 8)
[1] TRUE
> (arch <- Sys.info()[["machine"]])
[1] "x86_64"
> (onWindows <- .Platform$OS.type == "windows")
[1] FALSE
> (win32 <- onWindows && !b64)
[1] FALSE
>
> op <- options(warn = 2) ## << all warnings to errors!
>
> set.seed(101)
> x <- seq(-2,2, length = 100)
> y <- x^2 + 0.5*rnorm(100)
> ## Constraints -- choosing ones that are true for f(x) = x^2
> PW <- rbind(
+ c(0, -3,9), # f(-3) = 9
+ c(0, 3,9), # f(3 ) = 9
+ c(2, 0,0)) # f'(0) = 0
>
> mod <- cobs (x,y,constraint = "convex", pointwise = PW)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Error in cobs(x, y, constraint = "convex", pointwise = PW) :
(converted from warning) drqssbc2(): Not all flags are normal (== 1), ifl : 20
Execution halted
Running the tests in ‘tests/ex1.R’ failed.
Complete output:
> #### OOps! Running this in 'CMD check' or in *R* __for the first time__
> #### ===== gives a wrong result (at the end) than when run a 2nd time
> ####-- problem disappears with introduction of if (psw) call ... in Fortran
>
> suppressMessages(library(cobs))
> options(digits = 6)
> if(!dev.interactive(orNone=TRUE)) pdf("ex1.pdf")
>
> source(system.file("util.R", package = "cobs"))
>
> ## Simple example from example(cobs)
> set.seed(908)
> x <- seq(-1,1, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> ## specify constraints (boundary conditions)
> con <- rbind(c( 1,min(x),0),
+ c(-1,max(x),1),
+ c( 0, 0, 0.5))
> ## obtain the median *regression* B-spline using automatically selected knots
> coR <- cobs(x,y,constraint = "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> summaryCobs(coR)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", pointwise = con)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : chr "AIC"
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:50] -1 -0.959 -0.918 -0.878 -0.837 ...
$ y : num [1:50] 0.2254 0.0916 0.0803 -0.0272 -0.0454 ...
$ resid : num [1:50] 0.1976 0.063 0.0491 -0.0626 -0.0868 ...
$ fitted : num [1:50] 0.0278 0.0287 0.0312 0.0354 0.0414 ...
$ coef : num [1:4] 0.0278 0.0278 0.8154 1
$ knots : num [1:3] -1 -0.224 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : num 0
$ icyc : int 7
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 -6.77514e-02 -0.029701622 0.0278152 0.0853320 0.123382
2 -6.41787e-02 -0.027468888 0.0280224 0.0835138 0.120224
3 -6.04433e-02 -0.024973163 0.0286442 0.0822615 0.117732
4 -5.65412e-02 -0.022212175 0.0296803 0.0815728 0.115902
5 -5.24674e-02 -0.019182756 0.0311310 0.0814447 0.114729
6 -4.82149e-02 -0.015880775 0.0329961 0.0818729 0.114207
7 -4.37751e-02 -0.012301110 0.0352757 0.0828524 0.114326
8 -3.91381e-02 -0.008437641 0.0379697 0.0843771 0.115077
9 -3.42918e-02 -0.004283290 0.0410782 0.0864397 0.116448
10 -2.92233e-02 0.000169901 0.0446012 0.0890325 0.118426
11 -2.39179e-02 0.004930665 0.0485387 0.0921467 0.120995
12 -1.83600e-02 0.010008360 0.0528906 0.0957728 0.124141
13 -1.25335e-02 0.015412811 0.0576570 0.0999012 0.127847
14 -6.42140e-03 0.021154129 0.0628378 0.1045216 0.132097
15 -6.81378e-06 0.027242531 0.0684332 0.1096238 0.136873
16 6.72715e-03 0.033688168 0.0744430 0.1151978 0.142159
17 1.37970e-02 0.040500961 0.0808672 0.1212335 0.147938
18 2.12185e-02 0.047690461 0.0877060 0.1277215 0.154193
19 2.90068e-02 0.055265726 0.0949592 0.1346527 0.160912
20 3.71760e-02 0.063235225 0.1026269 0.1420185 0.168078
21 4.57390e-02 0.071606758 0.1107090 0.1498113 0.175679
22 5.47075e-02 0.080387396 0.1192056 0.1580238 0.183704
23 6.40921e-02 0.089583438 0.1281167 0.1666500 0.192141
24 7.39018e-02 0.099200377 0.1374422 0.1756841 0.200983
25 8.41444e-02 0.109242876 0.1471823 0.1851216 0.210220
26 9.48262e-02 0.119714746 0.1573367 0.1949588 0.219847
27 1.05952e-01 0.130618921 0.1679057 0.2051925 0.229859
28 1.17526e-01 0.141957438 0.1788891 0.2158208 0.240253
29 1.29548e-01 0.153731401 0.1902870 0.2268426 0.251026
30 1.42021e-01 0.165940947 0.2020994 0.2382578 0.262178
31 1.54941e-01 0.178585191 0.2143262 0.2500672 0.273711
32 1.68306e-01 0.191662165 0.2269675 0.2622729 0.285629
33 1.82111e-01 0.205168744 0.2400233 0.2748778 0.297936
34 1.96348e-01 0.219100556 0.2534935 0.2878865 0.310639
35 2.11008e-01 0.233451886 0.2673782 0.3013046 0.323748
36 2.26079e-01 0.248215565 0.2816774 0.3151392 0.337276
37 2.41547e-01 0.263382876 0.2963910 0.3293992 0.351235
38 2.57393e-01 0.278943451 0.3115191 0.3440948 0.365645
39 2.73599e-01 0.294885220 0.3270617 0.3592382 0.380524
40 2.90023e-01 0.311080514 0.3429107 0.3747410 0.395798
41 3.06194e-01 0.327075735 0.3586411 0.3902065 0.411088
42 3.22074e-01 0.342831649 0.3742095 0.4055873 0.426345
43 3.37676e-01 0.358355597 0.3896158 0.4208761 0.441556
44 3.53012e-01 0.373655096 0.4048602 0.4360653 0.456709
45 3.68094e-01 0.388737688 0.4199426 0.4511475 0.471791
46 3.82936e-01 0.403610792 0.4348630 0.4661151 0.486790
47 3.97549e-01 0.418281590 0.4496214 0.4809611 0.501694
48 4.11944e-01 0.432756923 0.4642177 0.4956786 0.516491
49 4.26133e-01 0.447043216 0.4786521 0.5102611 0.531172
50 4.40124e-01 0.461146429 0.4929245 0.5247027 0.545725
51 4.53927e-01 0.475072016 0.5070350 0.5389979 0.560143
52 4.67551e-01 0.488824911 0.5209834 0.5531418 0.574416
53 4.81002e-01 0.502409521 0.5347698 0.5671300 0.588538
54 4.94287e-01 0.515829730 0.5483942 0.5809587 0.602501
55 5.07412e-01 0.529088909 0.5618566 0.5946243 0.616302
56 5.20381e-01 0.542189933 0.5751571 0.6081242 0.629933
57 5.33198e-01 0.555135196 0.5882955 0.6214558 0.643393
58 5.45867e-01 0.567926630 0.6012719 0.6346172 0.656677
59 5.58390e-01 0.580565721 0.6140864 0.6476070 0.669782
60 5.70769e-01 0.593053527 0.6267388 0.6604241 0.682708
61 5.83005e-01 0.605390690 0.6392293 0.6730679 0.695454
62 5.95098e-01 0.617577451 0.6515577 0.6855380 0.708017
63 6.07048e-01 0.629613656 0.6637242 0.6978347 0.720400
64 6.18854e-01 0.641498766 0.6757287 0.7099586 0.732603
65 6.30515e-01 0.653231865 0.6875711 0.7219104 0.744627
66 6.42028e-01 0.664811658 0.6992516 0.7336916 0.756475
67 6.53391e-01 0.676236478 0.7107701 0.7453037 0.768149
68 6.64600e-01 0.687504287 0.7221266 0.7567489 0.779653
69 6.75652e-01 0.698612675 0.7333211 0.7680295 0.790991
70 6.86541e-01 0.709558867 0.7443536 0.7791483 0.802166
71 6.97262e-01 0.720339721 0.7552241 0.7901084 0.813186
72 7.07810e-01 0.730951740 0.7659326 0.8009134 0.824055
73 7.18179e-01 0.741391078 0.7764791 0.8115671 0.834779
74 7.28361e-01 0.751653555 0.7868636 0.8220736 0.845367
75 7.38348e-01 0.761734678 0.7970861 0.8324375 0.855824
76 7.48134e-01 0.771629669 0.8071466 0.8426636 0.866160
77 7.57709e-01 0.781333498 0.8170452 0.8527568 0.876382
78 7.67065e-01 0.790840929 0.8267817 0.8627224 0.886499
79 7.76192e-01 0.800146569 0.8363562 0.8725659 0.896520
80 7.85083e-01 0.809244928 0.8457688 0.8822926 0.906455
81 7.93727e-01 0.818130488 0.8550193 0.8919081 0.916312
82 8.02116e-01 0.826797774 0.8641079 0.9014179 0.926100
83 8.10240e-01 0.835241429 0.8730344 0.9108274 0.935829
84 8.18091e-01 0.843456291 0.8817990 0.9201417 0.945507
85 8.25661e-01 0.851437463 0.8904015 0.9293656 0.955142
86 8.32942e-01 0.859180385 0.8988421 0.9385038 0.964742
87 8.39928e-01 0.866680887 0.9071207 0.9475605 0.974313
88 8.46612e-01 0.873935236 0.9152373 0.9565393 0.983862
89 8.52989e-01 0.880940170 0.9231918 0.9654435 0.993395
90 8.59054e-01 0.887692913 0.9309844 0.9742760 1.002915
91 8.64803e-01 0.894191180 0.9386150 0.9830389 1.012427
92 8.70233e-01 0.900433167 0.9460836 0.9917341 1.021934
93 8.75343e-01 0.906417527 0.9533902 1.0003629 1.031437
94 8.80130e-01 0.912143340 0.9605348 1.0089263 1.040939
95 8.84594e-01 0.917610075 0.9675174 1.0174248 1.050441
96 8.88735e-01 0.922817542 0.9743381 1.0258586 1.059942
97 8.92551e-01 0.927765853 0.9809967 1.0342275 1.069442
98 8.96045e-01 0.932455371 0.9874933 1.0425312 1.078941
99 8.99218e-01 0.936886669 0.9938279 1.0507692 1.088438
100 9.02069e-01 0.941060487 1.0000006 1.0589406 1.097932
knots :
[1] -1.00000 -0.22449 1.00000
coef :
[1] 0.0278152 0.0278152 0.8153868 1.0000006
> coR1 <- cobs(x,y,constraint = "increase", pointwise = con, degree = 1)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> summary(coR1)
COBS regression spline (degree = 1) from call:
cobs(x = x, y = y, constraint = "increase", degree = 1, pointwise = con)
{tau=0.5}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:4]: -1.000002, -0.632653, 0.183673, 1.000002
with 3 pointwise constraints
coef[1:4]: 0.0504467, 0.0504467, 0.6305155, 1.0000009
R^2 = 93.83% ; empirical tau (over all): 21/50 = 0.42 (target tau= 0.5)
>
> ## compute the median *smoothing* B-spline using automatically chosen lambda
> coS <- cobs(x,y,constraint = "increase", pointwise = con,
+ lambda = -1, trace = 3)
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
loo.design2(): -> Xeq 51 x 22 (nz = 151 =^= 0.13%)
Xieq 62 x 22 (nz = 224 =^= 0.16%)
........................
The algorithm has converged. You might
plot() the returned object (which plots 'sic' against 'lambda')
to see if you have found the global minimum of the information criterion
so that you can determine if you need to adjust any or all of
'lambda.lo', 'lambda.hi' and 'lambda.length' and refit the model.
> with(coS, cbind(pp.lambda, pp.sic, k0, ifl, icyc))
pp.lambda pp.sic k0 ifl icyc
[1,] 3.54019e-05 -2.64644 22 1 21
[2,] 6.92936e-05 -2.64644 22 1 21
[3,] 1.35631e-04 -2.64644 22 1 20
[4,] 2.65477e-04 -2.64644 22 1 22
[5,] 5.19629e-04 -2.64644 22 1 22
[6,] 1.01709e-03 -2.64644 22 1 23
[7,] 1.99080e-03 -2.68274 21 1 20
[8,] 3.89667e-03 -2.75212 19 1 18
[9,] 7.62711e-03 -2.73932 19 1 14
[10,] 1.49289e-02 -2.85261 16 1 13
[11,] 2.92209e-02 -2.97873 12 1 12
[12,] 5.71953e-02 -3.01058 11 1 12
[13,] 1.11951e-01 -3.04364 10 1 11
[14,] 2.19126e-01 -3.11242 8 1 12
[15,] 4.28904e-01 -3.17913 6 1 12
[16,] 8.39512e-01 -3.18824 5 1 11
[17,] 1.64321e+00 -3.01467 5 1 12
[18,] 3.21633e+00 -3.01380 4 1 11
[19,] 6.29545e+00 -3.01380 4 1 10
[20,] 1.23223e+01 -3.01380 4 1 11
[21,] 2.41190e+01 -3.01380 4 1 11
[22,] 4.72092e+01 -3.01380 4 1 10
[23,] 9.24046e+01 -3.01380 4 1 10
[24,] 1.80867e+02 -3.01380 4 1 10
[25,] 3.54019e+02 -3.01380 4 1 10
> with(coS, plot(pp.sic ~ pp.lambda, type = "b", log = "x", col=2,
+ main = deparse(call)))
> ##-> very nice minimum close to 1
>
> summaryCobs(coS)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", lambda = -1, pointwise = con, trace = 3)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : NULL
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi TRUE
$ x : num [1:50] -1 -0.959 -0.918 -0.878 -0.837 ...
$ y : num [1:50] 0.2254 0.0916 0.0803 -0.0272 -0.0454 ...
$ resid : num [1:50] 0.2254 0.0829 0.062 -0.0562 -0.0862 ...
$ fitted : num [1:50] 0 0.00869 0.01837 0.02906 0.04075 ...
$ coef : num [1:22] 0 0.00819 0.03365 0.06662 0.10458 ...
$ knots : num [1:20] -1 -0.918 -0.796 -0.714 -0.592 ...
$ k0 : int [1:25] 22 22 22 22 22 22 21 19 19 16 ...
$ k : int 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : Named num 0.84
..- attr(*, "names")= chr "lambda"
$ icyc : int [1:25] 21 21 20 22 22 23 20 18 14 13 ...
$ ifl : int [1:25] 1 1 1 1 1 1 1 1 1 1 ...
$ pp.lambda : num [1:25] 0 0 0 0 0.001 0.001 0.002 0.004 0.008 0.015 ...
$ pp.sic : num [1:25] -2.65 -2.65 -2.65 -2.65 -2.65 ...
$ i.mask : logi [1:25] TRUE TRUE TRUE TRUE TRUE TRUE ...
cb.lo ci.lo fit ci.up cb.up
1 -0.07071332 -0.03907635 -3.77249e-07 0.0390756 0.0707126
2 -0.06555125 -0.03435600 4.17438e-03 0.0427048 0.0739000
3 -0.06016465 -0.02940203 8.59400e-03 0.0465900 0.0773526
4 -0.05455349 -0.02421442 1.32585e-02 0.0507314 0.0810704
5 -0.04871809 -0.01879334 1.81678e-02 0.0551289 0.0850537
6 -0.04265897 -0.01313909 2.33220e-02 0.0597831 0.0893029
7 -0.03637554 -0.00725134 2.87210e-02 0.0646934 0.0938176
8 -0.02986704 -0.00112966 3.43649e-02 0.0698595 0.0985969
9 -0.02313305 0.00522618 4.02537e-02 0.0752812 0.1036404
10 -0.01617351 0.01181620 4.63873e-02 0.0809584 0.1089481
11 -0.00898880 0.01864020 5.27658e-02 0.0868914 0.1145204
12 -0.00157983 0.02569768 5.93891e-02 0.0930806 0.1203581
13 0.00605308 0.03298846 6.62573e-02 0.0995262 0.1264615
14 0.01391000 0.04051257 7.33704e-02 0.1062282 0.1328307
15 0.02199057 0.04826981 8.07283e-02 0.1131867 0.1394660
16 0.03029461 0.05626010 8.83310e-02 0.1204020 0.1463675
17 0.03882336 0.06448412 9.61787e-02 0.1278732 0.1535339
18 0.04757769 0.07294234 1.04271e-01 0.1355999 0.1609646
19 0.05655804 0.08163500 1.12608e-01 0.1435819 0.1686589
20 0.06576441 0.09056212 1.21191e-01 0.1518192 0.1766169
21 0.07519637 0.09972344 1.30018e-01 0.1603120 0.1848391
22 0.08485262 0.10911826 1.39090e-01 0.1690610 0.1933266
23 0.09473211 0.11874598 1.48406e-01 0.1780668 0.2020807
24 0.10483493 0.12860668 1.57968e-01 0.1873294 0.2111011
25 0.11516076 0.13870015 1.67775e-01 0.1968489 0.2203882
26 0.12570956 0.14902638 1.77826e-01 0.2066253 0.2299421
27 0.13648327 0.15958645 1.88122e-01 0.2166576 0.2397608
28 0.14748286 0.17038090 1.98663e-01 0.2269453 0.2498433
29 0.15870881 0.18140998 2.09449e-01 0.2374880 0.2601892
30 0.17016110 0.19267368 2.20480e-01 0.2482859 0.2707984
31 0.18183922 0.20417172 2.31755e-01 0.2593391 0.2816716
32 0.19374227 0.21590361 2.43276e-01 0.2706482 0.2928095
33 0.20587062 0.22786955 2.55041e-01 0.2822129 0.3042118
34 0.21822524 0.24007008 2.67051e-01 0.2940328 0.3158776
35 0.23080666 0.25250549 2.79306e-01 0.3061075 0.3278063
36 0.24361488 0.26517577 2.91806e-01 0.3184370 0.3399979
37 0.25664938 0.27808064 3.04551e-01 0.3310217 0.3524530
38 0.26990862 0.29121926 3.17541e-01 0.3438624 0.3651730
39 0.28339034 0.30459037 3.30775e-01 0.3569602 0.3781603
40 0.29709467 0.31819405 3.44255e-01 0.3703152 0.3914146
41 0.31102144 0.33203019 3.57979e-01 0.3839275 0.4049363
42 0.32517059 0.34609876 3.71948e-01 0.3977971 0.4187252
43 0.33954481 0.36040126 3.86162e-01 0.4119224 0.4327789
44 0.35414537 0.37493839 4.00621e-01 0.4263028 0.4470958
45 0.36897279 0.38971043 4.15324e-01 0.4409381 0.4616757
46 0.38402708 0.40471738 4.30273e-01 0.4558281 0.4765184
47 0.39930767 0.41995895 4.45466e-01 0.4709732 0.4916245
48 0.41479557 0.43541678 4.60887e-01 0.4863568 0.5069780
49 0.43039487 0.45099622 4.76442e-01 0.5018872 0.5224885
50 0.44609197 0.46668362 4.92117e-01 0.5175506 0.5381422
51 0.46188684 0.48247895 5.07913e-01 0.5333471 0.5539392
52 0.47773555 0.49833835 5.23786e-01 0.5492329 0.5698357
53 0.49336687 0.51398935 5.39461e-01 0.5649325 0.5855550
54 0.50873469 0.52938518 5.54891e-01 0.5803975 0.6010480
55 0.52383955 0.54452615 5.70077e-01 0.5956277 0.6163143
56 0.53868141 0.55941225 5.85018e-01 0.6106231 0.6313539
57 0.55325974 0.57404316 5.99714e-01 0.6253839 0.6461673
58 0.56757320 0.58841816 6.14165e-01 0.6399109 0.6607558
59 0.58161907 0.60253574 6.28371e-01 0.6542056 0.6751223
60 0.59539741 0.61639593 6.42332e-01 0.6682680 0.6892665
61 0.60890835 0.62999881 6.56048e-01 0.6820980 0.7031884
62 0.62215175 0.64334429 6.69520e-01 0.6956957 0.7168882
63 0.63512996 0.65643368 6.82747e-01 0.7090597 0.7303634
64 0.64784450 0.66926783 6.95729e-01 0.7221893 0.7436126
65 0.66029589 0.68184700 7.08466e-01 0.7350841 0.7566352
66 0.67248408 0.69417118 7.20958e-01 0.7477442 0.7694313
67 0.68440855 0.70624008 7.33205e-01 0.7601699 0.7820014
68 0.69606829 0.71805313 7.45207e-01 0.7723617 0.7943465
69 0.70746295 0.72961016 7.56965e-01 0.7843198 0.8064670
70 0.71859343 0.74091165 7.68478e-01 0.7960438 0.8183620
71 0.72946023 0.75195789 7.79746e-01 0.8075332 0.8300309
72 0.74006337 0.76274887 7.90769e-01 0.8187883 0.8414738
73 0.75040233 0.77328433 8.01547e-01 0.8298091 0.8526911
74 0.76047612 0.78356369 8.12080e-01 0.8405963 0.8636839
75 0.77028266 0.79358583 8.22368e-01 0.8511510 0.8744542
76 0.77982200 0.80335076 8.32412e-01 0.8614732 0.8850020
77 0.78909446 0.81285866 8.42211e-01 0.8715627 0.8953269
78 0.79809990 0.82210946 8.51765e-01 0.8814196 0.9054292
79 0.80683951 0.83110382 8.61074e-01 0.8910433 0.9153076
80 0.81531459 0.83984244 8.70138e-01 0.9004329 0.9249608
81 0.82352559 0.84832559 8.78957e-01 0.9095884 0.9343884
82 0.83147249 0.85655324 8.87531e-01 0.9185095 0.9435903
83 0.83915483 0.86452515 8.95861e-01 0.9271968 0.9525671
84 0.84657171 0.87224082 9.03946e-01 0.9356505 0.9613196
85 0.85372180 0.87969951 9.11786e-01 0.9438715 0.9698492
86 0.86060525 0.88690131 9.19381e-01 0.9518597 0.9781558
87 0.86722242 0.89384640 9.26731e-01 0.9596149 0.9862389
88 0.87357322 0.90053476 9.33836e-01 0.9671371 0.9940986
89 0.87965804 0.90696658 9.40696e-01 0.9744261 1.0017347
90 0.88547781 0.91314239 9.47312e-01 0.9814814 1.0091460
91 0.89103290 0.91906239 9.53683e-01 0.9883028 1.0163323
92 0.89632328 0.92472655 9.59808e-01 0.9948904 1.0232937
93 0.90134850 0.93013464 9.65689e-01 1.0012443 1.0300304
94 0.90610776 0.93528622 9.71326e-01 1.0073650 1.0365434
95 0.91060065 0.94018104 9.76717e-01 1.0132527 1.0428331
96 0.91482784 0.94481950 9.81863e-01 1.0189071 1.0488987
97 0.91878971 0.94920179 9.86765e-01 1.0243279 1.0547400
98 0.92248624 0.95332789 9.91422e-01 1.0295152 1.0603569
99 0.92591703 0.95719761 9.95833e-01 1.0344692 1.0657498
100 0.92908136 0.96081053 1.00000e+00 1.0391902 1.0709194
knots :
[1] -1.0000020 -0.9183673 -0.7959184 -0.7142857 -0.5918367 -0.5102041
[7] -0.3877551 -0.2653061 -0.1836735 -0.0612245 0.0204082 0.1428571
[13] 0.2244898 0.3469388 0.4693878 0.5510204 0.6734694 0.7551020
[19] 0.8775510 1.0000020
coef :
[1] -4.01161e-07 8.18714e-03 3.36534e-02 6.66159e-02 1.04576e-01
[6] 1.50032e-01 2.00486e-01 2.70027e-01 3.35473e-01 4.05918e-01
[11] 4.83858e-01 5.64259e-01 6.37163e-01 7.05069e-01 7.77561e-01
[16] 8.30474e-01 8.78390e-01 9.18810e-01 9.54232e-01 9.87743e-01
[21] 1.00000e+00 5.99960e-01
>
> plot(x, y, main = "cobs(x,y, constraint=\"increase\", pointwise = *)")
> matlines(x, cbind(fitted(coR), fitted(coR1), fitted(coS)),
+ col = 2:4, lty=1)
>
> ##-- real data example (still n = 50)
> data(cars)
> attach(cars)
> co1 <- cobs(speed, dist, "increase")
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> co1.1 <- cobs(speed, dist, "increase", knots.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> co1.2 <- cobs(speed, dist, "increase", knots.add = TRUE, repeat.delete.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> ## These three all give the same -- only remaining knots (outermost data):
> ic <- which("call" == names(co1))
> stopifnot(all.equal(co1[-ic], co1.1[-ic]),
+ all.equal(co1[-ic], co1.2[-ic]))
> 1 - sum(co1 $ resid ^2) / sum((dist - mean(dist))^2) # R^2 = 64.2%
[1] 0.642288
>
> co2 <- cobs(speed, dist, "increase", lambda = -1)# 6 warnings
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Running the tests in ‘tests/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$sizeof.longdouble <= 8) ## TRUE when --disable-long-double
> ## IGNORE_RDIFF_BEGIN
> Sys.info()
sysname
"Linux"
release
"6.2.15-100.fc36.x86_64"
version
"#1 SMP PREEMPT_DYNAMIC Thu May 11 16:51:53 UTC 2023"
nodename
"gannet.stats.ox.ac.uk"
machine
"x86_64"
login
"ripley"
user
"ripley"
effective_user
"ripley"
> noLdbl
[1] FALSE
> ## IGNORE_RDIFF_END
>
>
> Rsq <- function(obj) {
+ stopifnot(inherits(obj, "cobs"), is.numeric(res <- obj$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 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%)
Warning message:
In cobs(x, y, constraint = c("increase"), trace = 3) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
> 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: 0.0609687"
>
> 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 ...
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.
> cp2i <- r2i$value
> ## IGNORE_RDIFF_BEGIN
> r2i$warning
<simpleWarning in cobs(x, y, constraint = "increase", pointwise = con): drqssbc2(): Not all flags are normal (== 1), ifl : 20>
> ## 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 5 (nz = 150 =^= 0.6%)
Xieq 5 x 5 (nz = 15 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 5 x 5 (nz = 15 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 5 x 5 (nz = 15 =^= 0.6%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 4 x 4 (nz = 12 =^= 0.75%)
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%)
>
> ## 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%)
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 5 x 3 (nz = 15 =^= 1%)
Warning message:
In cobs(x, y, constraint = c("inc", "concave"), pointwise = con, :
drqssbc2(): Not all flags are normal (== 1), ifl : 18
> ## IGNORE_RDIFF_END
> cp1 <- cobs(x,y, degree = 1, pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 2 x 2 (nz = 4 =^= 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 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 2 x 5 (nz = 4 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 2 x 6 (nz = 4 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 2 x 5 (nz = 4 =^= 0.4%)
Warning message:
In cobs(x, y, degree = 1, pointwise = con, trace = 3) :
drqssbc2(): Not all flags are normal (== 1), ifl : 22
> cp1i <- cobs(x,y, degree = 1, constraint = "increase", pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 3 x 2 (nz = 6 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 4 x 3 (nz = 8 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 6 x 5 (nz = 12 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 7 x 6 (nz = 14 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 6 x 5 (nz = 12 =^= 0.4%)
> cp1c <- cobs(x,y, degree = 1, constraint = "concave", pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 2 x 2 (nz = 4 =^= 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 4 x 4 (nz = 10 =^= 0.62%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 5 x 5 (nz = 13 =^= 0.52%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 6 x 6 (nz = 16 =^= 0.44%)
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 2 x 2 (nz = 4 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
>
> cp1IC <- cobs(x,y, degree = 1, constraint = c("inc", "concave"), pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 3 x 2 (nz = 6 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 7 x 4 (nz = 16 =^= 0.57%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 9 x 5 (nz = 21 =^= 0.47%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 11 x 6 (nz = 26 =^= 0.39%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 3 x 2 (nz = 6 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
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'
3: In cobs(x, y, degree = 1, constraint = c("inc", "concave"), pointwise = con, :
drqssbc2(): Not all flags are normal (== 1), ifl : 20
>
> ## Named list of all cobs() results above -- sort() collation order matters for ls() !
> (curLC <- Sys.getlocale("LC_COLLATE"))
[1] "C"
> Sys.setlocale("LC_COLLATE", "C")
[1] "C"
> cobsL <- mget(Filter(\(nm) is.cobs(.GlobalEnv[[nm]]), ls(patt="c[12p]")),
+ envir = .GlobalEnv)
> Sys.setlocale("LC_COLLATE", curLC) # reverting
[1] "C"
>
> knL <- lapply(cobsL, `[[`, "knots")
> str(knL[order(lengths(knL))])
List of 16
$ c2IC : num [1:2] -1 2
$ cp2IC: num [1:2] -1 2
$ c1IC : num [1:3] -1 0.776 2
$ c1c : num [1:3] -1 0.776 2
$ c2 : num [1:3] -1 -0.449 2
$ c2c : num [1:3] -1 0.163 2
$ c2i : num [1:3] -1 -0.449 2
$ cp1IC: num [1:3] -1 0.776 2
$ cp1c : num [1:3] -1 0.776 2
$ cp2 : num [1:4] -1 -0.449 0.776 2
$ cp2c : num [1:4] -1 -0.449 0.776 2
$ c1 : num [1:5] -1 -0.449 0.163 0.776 2
$ c1i : num [1:5] -1 -0.449 0.163 0.776 2
$ cp1 : num [1:5] -1 -0.449 0.163 0.776 2
$ cp1i : num [1:5] -1 -0.449 0.163 0.776 2
$ cp2i : num [1:6] -1 -0.449 0.163 0.776 1.388 ...
>
> gotRsqrs <- sapply(cobsL, Rsq)
> Rsqrs <- c(c1 = 0.95079126, c1IC = 0.92974549, c1c = 0.92974549, c1i = 0.95079126,
+ c2 = 0.94637437, c2IC = 0.91375404, c2c = 0.92505977, c2i = 0.95022829,
+ cp1 = 0.9426453, cp1IC = 0.92223149, cp1c = 0.92223149, cp1i = 0.9426453,
+ cp2 = 0.94988863, cp2IC= 0.90051964, cp2c = 0.91375409, cp2i = 0.93611487)
> ## M1 mac " = " , cp2IC= 0.91704726, " = " , cp2i = 0.94620178
> ## noLD " = " , cp2IC=-0.08244284, " = " , cp2i = 0.94636815
> ## ATLAS " = " , cp2IC= 0.91471729, " = " , cp2i = 0.94506339
> ## openBLAS " = " , cp2IC= 0.91738019, " = " , cp2i = 0.93589404
> ## MKL " = " , cp2IC= 0.91765403, " = " , cp2i = 0.94501205
> ## Intel " = " , cp2IC= 0.91765403, " = " , cp2i = 0.94501205
> ## ^^^^^^^^^^ ^^^^^^^^^^
> ## remove these two from testing, notably for the M1 Mac & noLD .. :
> ##iR2 <- if(!x86 || noLdbl) setdiff(names(cobsL), c("cp2IC", "cp2i")) else TRUE
> ## actually everywhere, because of ATLAS, openBLAS, MKL, Intel... :
> iR2 <- setdiff(names(cobsL), nR2 <- c("cp2IC", "cp2i"))
> ## IGNORE_RDIFF_BEGIN
> dput(signif(gotRsqrs, digits=8))
c(c1 = 0.95079126, c1IC = 0.92974549, c1c = 0.92974549, c1i = 0.95079126,
c2 = 0.94637437, c2IC = 0.91375404, c2c = 0.92505977, c2i = 0.94864721,
cp1 = 0.95341697, cp1IC = 0.93470747, cp1c = 0.92223149, cp1i = 0.9426453,
cp2 = 0.94988863, cp2IC = 0.90051964, cp2c = 0.91867996, cp2i = 0.94580766
)
> all.equal(Rsqrs[iR2], gotRsqrs[iR2], tolerance=0)# 2.6277e-9 (Lnx F 38); 2.6898e-9 (M1 mac)
[1] "Mean relative difference: 0.0022731"
> all.equal(Rsqrs[nR2], gotRsqrs[nR2], tolerance=0)# differ; drastically only for 'noLD'
[1] "Mean relative difference: 0.00527747"
> ## IGNORE_RDIFF_END
> stopifnot(exprs = {
+ all.equal(Rsqrs[iR2], gotRsqrs[iR2])
+ identical(c(5L, 3L, 3L, 5L,
+ 3L, 2L, 3L, 4L,
+ 5L, 3L, 3L, 5L,
+ 4L, 2L, 2L, 4L), unname(lengths(knL)))
+ })
Error: Rsqrs[iR2] and gotRsqrs[iR2] are not equal:
Mean relative difference: 0.0022731
Execution halted
Flavor: r-devel-linux-x86_64-fedora-clang
Current CRAN status: NOTE: 6, OK: 7
Version: 1.1-4
Check: installed package size
Result: NOTE
installed size is 7.8Mb
sub-directories of 1Mb or more:
R 2.4Mb
doc 3.2Mb
Flavors: r-release-macos-arm64, r-release-macos-x86_64, r-oldrel-macos-arm64, r-oldrel-macos-x86_64
Version: 1.1-4
Flags: --no-vignettes
Check: installed package size
Result: NOTE
installed size is 7.3Mb
sub-directories of 1Mb or more:
R 2.1Mb
doc 3.2Mb
Flavors: r-release-windows-x86_64, r-oldrel-windows-x86_64
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: NOTE: 1, OK: 12
Version: 1.1-3
Check: tests
Result: NOTE
Running 'FEXP-ex.R' [1s]
Comparing 'FEXP-ex.Rout' to 'FEXP-ex.Rout.save' ... OK
Running 'ceta-ex.R' [3s]
Comparing 'ceta-ex.Rout' to 'ceta-ex.Rout.save' ...75c75
< [2,] -8.5705517 13.00507 -5.2497156
---
> [2,] -8.5705518 13.00507 -5.2497156
86c86
< [1,] 7.4008136 -7.25886 0.0763714
---
> [1,] 7.4008136 -7.25886 0.0763715
88c88
< [3,] 0.0763714 -5.38985 6.8074697
---
> [3,] 0.0763715 -5.38985 6.8074697
111c111
< [2,] -6.6156657 11.346062 -5.4359093
---
> [2,] -6.6156658 11.346062 -5.4359093
116c116
< [1,] 6.6254802 -6.577171 0.1320888
---
> [1,] 6.6254801 -6.577171 0.1320888
Running 'sim-ex.R' [0s]
Comparing 'sim-ex.Rout' to 'sim-ex.Rout.save' ... OK
Running 'spec-ex.R' [14s]
Flavor: r-devel-windows-x86_64
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: NOTE: 3, OK: 10
Version: 0.9-5
Check: Rd cross-references
Result: NOTE
Found the following Rd file(s) with Rd \link{} targets missing package
anchors:
mpfr-class.Rd: is.whole
mpfr-utils.Rd: asNumeric
mpfr.Rd: asNumeric
mpfrArray.Rd: asNumeric
mpfrMatrix-utils.Rd: asNumeric
pbetaI.Rd: bigq
utils.Rd: is.whole
Please provide package anchors for all Rd \link{} targets not in the
package itself and the base packages.
Flavors: r-devel-linux-x86_64-debian-clang, r-devel-linux-x86_64-debian-gcc, r-devel-windows-x86_64
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13