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jlindsey@alpha.luc.ac.be

1999-Nov-16 07:57 UTC

spikes in contour and persp (PR#327)

The following matrix of normed likelihoods should give a smooth
surface but instead gives a series of spikes in both persp and contour
(the dim labels are the axes values). I know an algorithm cannot be
infallible but it would be nice to have some parameters to control the
smoothing. (It takes close to an hour to produce this matrix on a
Pentium II 300mh. It was after that that it crashed with the Inf in my
previous bug message...)
  Jim

"like" <-
structure(c(0.00176391675079333, 0.00146923361143409, 0.000118873942550920, 
2.60033028913311e-06, 1.36792992686478e-07, 1.8246691363054e-08, 
3.70167824680542e-09, 9.3435105158372e-10, 2.65488573122080e-10, 
8.02477512258327e-11, 2.49374837366522e-11, 7.79989625462184e-12, 
2.42313836128e-12, 7.41635672535047e-13, 2.22582213352616e-13, 
6.53529934129183e-14, 1.87592482515789e-14, 5.26673348630621e-15, 
1.44811282825086e-15, 3.90678315206886e-16, 1.03661464711976e-16, 
0.000357163904115257, 0.00646880985207886, 0.00663283207618763, 
0.0006059775621534, 1.21364454274087e-05, 1.80805906201527e-07, 
4.32774824739439e-08, 7.10745665416504e-09, 1.49838488962873e-09, 
3.63085812144783e-10, 9.50968657445326e-11, 2.5947561761174e-11, 
7.20856405305296e-12, 2.00980008827208e-12, 5.57310934761386e-13, 
1.52876329921416e-13, 4.13626490878394e-14, 1.10248761462956e-14, 
2.89491661046771e-15, 7.49510768794562e-16, 1.91634151378621e-16, 
3.07815510765707e-06, 0.000842181964429961, 0.0191090902323545, 
0.0242142517038679, 0.0025500207241197, 5.00789710794291e-05, 
2.23383985740275e-07, 2.32292942996531e-10, 1.46732078349253e-13, 
3.68779458410766e-16, 4.40310716451135e-10, 1.00615855772164e-10, 
2.42780131405657e-11, 6.03418238957602e-12, 1.52070970641775e-12, 
3.84738608832168e-13, 9.7118421208109e-14, 2.43727608742882e-14, 
6.0703200390455e-15, 1.49975407591609e-15, 3.67743639034840e-16, 
1.73726268058860e-08, 5.6077403337573e-06, 0.00165385022367381, 
0.0459164322410669, 0.0716297725686465, 0.00882904283150518, 
0.000179278272111563, 1.60177707812379e-06, 1.64900664911929e-07, 
1.78009575764431e-08, 2.65523682169734e-09, 4.76742738255559e-10, 
9.5704507548558e-11, 2.05674605214745e-11, 4.60601964796226e-12, 
1.05660190825881e-12, 2.45557822201462e-13, 5.74149524761638e-14, 
1.34489585256116e-14, 3.14879289081088e-15, 7.36195777222565e-16, 
4.89497216471075e-10, 3.81542617663398e-08, 9.09401919276533e-06, 
0.00275857826337638, 0.0909868934673163, 0.172758831413262, 0.0251503663306111, 
0.000549189356381134, 6.31352952358429e-06, 2.68961061449807e-07, 
2.3542509728124e-08, 2.97462447665947e-09, 4.64066856401819e-10, 
8.2401204449613e-11, 1.58824099088396e-11, 3.22710254273834e-12, 
6.78416160046776e-13, 1.45781121121843e-13, 3.17710965274086e-14, 
6.98813199754939e-15, 1.54686370477970e-15, 3.47818999816463e-11, 
1.24676135382412e-09, 7.47555356513558e-08, 1.33070547402354e-05, 
0.00398944889318836, 0.151170953683526, 0.343008298678816, 0.0591272231401392, 
0.00142894699562673, 1.33907834497016e-05, 3.93659041601088e-07, 
2.78925562712552e-08, 2.99820042629106e-09, 4.08906587960769e-10, 
6.46521841575397e-11, 1.12526828683000e-11, 2.08843221915706e-12, 
4.0497894062659e-13, 8.09694435253555e-14, 1.65467499310321e-14, 
3.4370548505308e-15, 2.36576283045907e-18, 9.6063453887084e-11, 
2.77556814791118e-09, 1.30655321075467e-07, 1.77439204853078e-05, 
0.00510559845838645, 0.214466920173550, 0.567639160458647, 0.115409841304071, 
0.00314993314454434, 2.62121724290019e-05, 5.22127208541793e-07, 
2.98270603284278e-08, 2.73794692447261e-09, 3.28356740333764e-10, 
4.65286665769768e-11, 7.36102946837208e-12, 1.25596058135938e-12, 
2.26061516010492e-13, 4.23051443667433e-14, 8.15300298593863e-15, 
3.99072715883438e-22, 2.83505501562795e-14, 2.29827820215666e-10, 
5.41529050920267e-09, 2.04082809865002e-07, 2.17246335811100e-05, 
0.00589627815433526, 0.264755146645107, 0.794255221042976, 0.188611633044143, 
0.0058892450264806, 4.81497713458769e-05, 5.23480571790264e-07, 
2.90107005693282e-08, 2.28108910907203e-09, 2.41888199776289e-10, 
3.09098051610835e-11, 4.47297169082052e-12, 7.05971252516243e-13, 
1.18646681896628e-13, 2.09007567575968e-14, 8.06100365206625e-25, 
2.18287769171281e-12, 3.07070436176694e-11, 4.77976958766606e-10, 
9.29640006576001e-09, 2.85897928086818e-07, 2.45914840639008e-05, 
0.00625816114089017, 0.289727465683434, 0.954240423750235, 0.260767136275309, 
0.00937565110886506, 8.04807869366302e-05, 4.13417517052559e-07, 
2.58678609575225e-08, 1.74581722289468e-09, 1.64522993158554e-10, 
1.90706199624332e-11, 2.53949873007858e-12, 3.72937444797563e-13, 
5.88524940943896e-14, 3.65274225587674e-33, 4.9389582496641e-13, 
5.65186883970257e-12, 6.65975799830656e-11, 8.6809873616086e-10, 
1.41133330282008e-08, 3.60982749125254e-07, 2.59299077617796e-05, 
0.00620782524427522, 0.286042286522196, 1, 0.308581298903377, 
0.012787802505642, 0.000119814119096249, 3.89699972443826e-07, 
4.28239635744095e-09, 1.23578822564739e-09, 1.03967816983612e-10, 
1.09920523132901e-11, 1.35456065143129e-12, 1.86115310490081e-13, 
1.56145767292107e-41, 1.33774563914851e-13, 1.31018253984329e-12, 
1.26291081169715e-11, 1.25596067133136e-10, 1.38451927615464e-09, 
1.90623084689258e-08, 4.13346862060707e-07, 2.57000620053891e-05, 
0.00584257176393386, 0.258897858120271, 0.928289223693575, 0.316472953831898, 
0.0150604098742057, 0.000157636305579563, 4.66131468431873e-07, 
1.02471388660295e-09, 8.14501436992245e-10, 6.14139871202027e-11, 
5.95236937841971e-12, 6.82398718856752e-13, 3.59696367652483e-45, 
4.17012864602969e-14, 3.61582027534016e-13, 2.99359617683961e-12, 
2.44700291837697e-11, 2.07141151264903e-10, 1.95144184735262e-09, 
2.3063051089858e-08, 4.32380395847584e-07, 2.42199262846122e-05, 
0.00528608113143016, 0.217875130836358, 0.774532881221181, 0.284901732794224, 
0.0154537854803841, 0.000183185641023271, 7.49559849539294e-07, 
7.11024159705725e-09, 5.03182614447118e-10, 3.41104188233311e-11, 
3.04474903274232e-12, 2.91565192035724e-49, 1.45537916525653e-14, 
1.14411789285803e-13, 8.40641488198468e-13, 5.92035604270047e-12, 
4.13543450691788e-11, 3.00704186586863e-10, 2.44790109904596e-09, 
2.51842772491441e-08, 4.16658016813605e-07, 2.2030173910067e-05, 
0.00464757376571756, 0.172524827842122, 0.588668692999348, 0.227992352386208, 
0.0139517782319954, 0.000188633229943610, 8.86576659202643e-07, 
8.13397456171407e-09, 2.93295902434683e-10, 1.79158142536354e-11, 
7.45440431708058e-47, 5.57324949893741e-15, 4.04199649080243e-14, 
2.69734042179215e-13, 1.68938567781956e-12, 1.01927093362378e-11, 
6.13516958431207e-11, 3.86968272588105e-10, 2.75370252448967e-09, 
2.50248238015754e-08, 3.7340350663148e-07, 1.97272833278079e-05, 
0.00400365893374786, 0.129796777376395, 0.412414570496338, 0.164160599019082, 
0.0111950329180545, 0.000173055912545285, 8.82222548801061e-07, 
4.80789035062023e-09, 1.62361855274262e-10, 4.83378466824916e-56, 
8.87835079570885e-18, 6.32443372364351e-17, 4.07759026116548e-16, 
2.41133621758854e-15, 1.32984475458358e-14, 6.98407810862943e-14, 
3.5876395093759e-13, 1.86752746531279e-12, 1.03460205332741e-11, 
6.5602704947161e-11, 5.36647863367684e-10, 7.15363285132962e-09, 
2.90880056585854e-07, 3.40712247087175e-05, 0.000889612332838851, 
0.00257111974780624, 0.000787883478550474, 3.37033079485353e-05, 
3.19292591662659e-07, 1.25686609615895e-09, 2.20162002662816e-172, 
1.18597942112121e-48, 6.527184937565e-15, 3.76449635250464e-14, 
1.98306897773082e-13, 9.70704477624762e-13, 4.51159875267329e-12, 
2.04683300082797e-11, 9.4028641613087e-11, 4.60396075448249e-10, 
2.59711739759405e-09, 1.92985480623786e-08, 2.52186810950586e-07, 
1.66549678505953e-05, 0.00284973810807315, 0.0647861189211352, 
0.164928028751616, 0.0648087223198986, 0.00527057924509832,
0.000105880347544938,
6.77764435724914e-07, 2.28917610742849e-62, 4.77089470347806e-16, 
2.90684328179923e-15, 1.58418783461786e-14, 7.81422076667516e-14, 
3.54025380712877e-13, 1.49985566240899e-12, 6.0772181174916e-12, 
2.42262881670020e-11, 9.86595400000035e-11, 4.32695300245282e-10, 
2.21589694896341e-09, 1.52732771943930e-08, 1.95128248997183e-07, 
1.6227265119312e-05, 0.00236310192186473, 0.0433722389788253, 
0.0956364137992563, 0.0362445630341557, 0.00315366776340453, 
7.16975146683838e-05, 5.80651995967573e-63, 2.34504934024876e-16, 
1.36875718371988e-15, 7.1042764643222e-15, 3.31337397882331e-14, 
1.40655421593731e-13, 5.51935966365771e-13, 2.04006223917774e-12, 
7.26797589881895e-12, 2.56974962454299e-11, 9.37288857779561e-11, 
3.72485772585405e-10, 1.75589938246813e-09, 1.14398993072651e-08, 
1.48193436103776e-07, 1.63921456901643e-05, 0.00193532901795850, 
0.028105645771033, 0.052765310952557, 0.0189719774467987, 0.00174369601611880
), .Dim = c(21, 18), .Dimnames = list(c("1.4", "1.42",
"1.44",
"1.46", "1.48", "1.5", "1.52",
"1.54", "1.56", "1.58", "1.6",
"1.62", "1.64", "1.66", "1.68",
"1.7", "1.72", "1.74", "1.76",
"1.78", "1.8"), c("2.32", "2.345",
"2.37", "2.395", "2.42", "2.445",
"2.47", "2.495", "2.52", "2.545",
"2.57", "2.595", "2.62", "2.645",
"2.67", "2.695", "2.72", "2.745")))


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ripley@stats.ox.ac.uk

1999-Nov-16 11:03 UTC

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spikes in contour and persp (PR#327)

> From: jlindsey@alpha.luc.ac.be
> Date: Tue, 16 Nov 1999 08:57:00 +0100 (MET)
> 
> The following matrix of normed likelihoods should give a smooth
> surface but instead gives a series of spikes in both persp and contour
> (the dim labels are the axes values). I know an algorithm cannot be
> infallible but it would be nice to have some parameters to control the
> smoothing. (It takes close to an hour to produce this matrix on a
> Pentium II 300mh. It was after that that it crashed with the Inf in my
> previous bug message...)

I am sorry, but I don't understand. contour does not do any
smoothing, but interpolates assuming smoothness.  The data
appears to me to be a series of spikes just off the diagonal, and not
what contour thinks of as a smooth surface.  It is common to 
interpolate the data from such a coarse grid before contouring.

persp just plots the data with visual linear interpolation.
> round(like*100,0)     2.32 2.345 2.37 2.395 2.42 2.445 2.47 2.495 2.52 2.545 2.57 2.595 2.62
1.4     0     0    0     0    0     0    0     0    0     0    0     0    0
1.42    0     1    0     0    0     0    0     0    0     0    0     0    0
1.44    0     1    2     0    0     0    0     0    0     0    0     0    0
1.46    0     0    2     5    0     0    0     0    0     0    0     0    0
1.48    0     0    0     7    9     0    0     0    0     0    0     0    0
1.5     0     0    0     1   17    15    1     0    0     0    0     0    0
1.52    0     0    0     0    3    34   21     1    0     0    0     0    0
1.54    0     0    0     0    0     6   57    26    1     0    0     0    0
1.56    0     0    0     0    0     0   12    79   29     1    0     0    0
1.58    0     0    0     0    0     0    0    19   95    29    1     0    0
1.6     0     0    0     0    0     0    0     1   26   100   26     1    0
1.62    0     0    0     0    0     0    0     0    1    31   93    22    0
1.64    0     0    0     0    0     0    0     0    0     1   32    77   17
1.66    0     0    0     0    0     0    0     0    0     0    2    28   59
1.68    0     0    0     0    0     0    0     0    0     0    0     2   23
1.7     0     0    0     0    0     0    0     0    0     0    0     0    1
1.72    0     0    0     0    0     0    0     0    0     0    0     0    0
1.74    0     0    0     0    0     0    0     0    0     0    0     0    0
1.76    0     0    0     0    0     0    0     0    0     0    0     0    0
1.78    0     0    0     0    0     0    0     0    0     0    0     0    0
1.8     0     0    0     0    0     0    0     0    0     0    0     0    0
     2.645 2.67 2.695 2.72 2.745
1.4      0    0     0    0     0
1.42     0    0     0    0     0
1.44     0    0     0    0     0
1.46     0    0     0    0     0
1.48     0    0     0    0     0
1.5      0    0     0    0     0
1.52     0    0     0    0     0
1.54     0    0     0    0     0
1.56     0    0     0    0     0
1.58     0    0     0    0     0
1.6      0    0     0    0     0
1.62     0    0     0    0     0
1.64     0    0     0    0     0
1.66    13    0     0    0     0
1.68    41    0     0    0     0
1.7     16    0     6    0     0
1.72     1    0    16    4     0
1.74     0    0     6   10     3
1.76     0    0     1    4     5
1.78     0    0     0    0     2
1.8      0    0     0    0     0


If I do some interpolation

library(akima)
x <- as.numeric(rownames(like))
y <- as.numeric(colnames(like))
xx <- expand.grid(x=x, y=y)
like1 <- interp(xx$x, xx$y, like, seq(1.4, 1.8, len=50), seq(2.3, 2.8,
len=50))
contour(like1$x, like1$y,like1$z)

I get a slightly smoother result, but still five peaks.  (Are the
values for col=2.67 correct?)

I guess you need to evaluate this on a finer grid near the diagonal,
and probably adjust the coordinate system to get enough resolution
on the anti-diagonal.


-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


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