Smoothing periodogram

Description

This function returns the smoothing periodogram of a stationary time serie, its plot and its Fourier frequency.

Usage

smooth.periodogram(y, plot = TRUE, spar = 0)

Arguments

Details

smooth.periodogram computes the periodogram from y vector and then smooth it with smoothing spline method, which basically approximates a curve using a cubic spline (see more details in smooth.spline). λ is the Fourier frequency obtained through periodogram.

It must have caution with the minimum length of y, because smooth.spline requires the entered vector has at least length 4 and the length of y does not equal to the length of the data of the periodogram that smooth.spline receives. If it presents problems with tol (tolerance), see smooth.spline.

Value

A list with the following components:

Author(s)

Ricardo Olea <raolea@uc.cl>

See Also

To more information please check smooth.spline and periodogram.

Examples

## Require "rdatamarket"
library(rdatamarket)

malleco = dmlist("22tn")
mammothcreek = dmlist("22r7")

## Example 1: malleco
periodogram(malleco$Value)
aux = smooth.periodogram(malleco$Value, plot = FALSE, spar = .8)
lines(aux$smooth.periodogram ~ aux$lambda, lwd = 2, col = "orange")

## Example 2: mammothcreek$Value
periodogram(mammothcreek$Value)
aux = smooth.periodogram(mammothcreek$Value, plot = FALSE, spar = .4)
lines(aux$smooth.periodogram ~ aux$lambda, lwd = 2, col = "orange")

## Example 3: AR(1) simulated
ts.sim = arima.sim(n = 1000, model = list(order = c(1,0,0), ar = 0.7))
periodogram(ts.sim)
aux = smooth.periodogram(ts.sim, plot = FALSE, spar = .7)
lines(aux$smooth.periodogram ~ aux$lambda, lwd = 2, col = "orange")
lines(fdensity(ar = 0.7, lambda = aux$lambda)~aux$lambda, col = "red")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LSTS)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LSTS/smooth.periodogram.Rd_%03d_medium.png", width=480, height=480)
> ### Name: smooth.periodogram
> ### Title: Smoothing periodogram
> ### Aliases: smooth.periodogram
> ### Keywords: Fourier periodogram smooth timeseries
> 
> ### ** Examples
> 
> ## Require "rdatamarket"
> library(rdatamarket)
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

> 
> malleco = dmlist("22tn")
> mammothcreek = dmlist("22r7")
> 
> ## Example 1: malleco
> periodogram(malleco$Value)
$periodogram
  [1] 8.413598e-03 5.732448e-02 1.594216e-02 3.217250e-02 9.713365e-03
  [6] 4.642294e-02 1.840110e-02 1.817718e-02 2.605043e-03 8.060886e-03
 [11] 4.814937e-02 2.359084e-02 7.679772e-03 5.842868e-02 3.067409e-02
 [16] 7.286829e-04 7.228155e-03 7.408862e-05 9.175538e-03 6.884151e-03
 [21] 9.057442e-03 8.640594e-03 1.401456e-02 1.223166e-02 6.255162e-03
 [26] 7.477990e-03 8.688870e-03 6.029713e-03 2.548465e-02 1.791451e-03
 [31] 1.127453e-02 9.735813e-03 1.723470e-02 2.034594e-02 1.122905e-03
 [36] 1.159822e-02 2.069839e-02 8.347229e-03 5.458117e-03 3.947342e-03
 [41] 4.896066e-02 1.366321e-02 2.761929e-02 1.313623e-02 7.149880e-03
 [46] 3.579144e-02 1.244885e-02 1.064815e-03 2.678874e-05 1.085126e-02
 [51] 8.404575e-03 2.006665e-03 3.532128e-02 1.961878e-02 8.276464e-04
 [56] 1.050364e-02 4.465145e-03 2.816199e-02 1.019760e-03 6.680050e-03
 [61] 2.954852e-02 1.955937e-02 3.095838e-04 2.481567e-04 4.184696e-03
 [66] 4.940090e-04 1.407443e-02 1.371285e-02 4.285936e-03 7.061438e-04
 [71] 2.645022e-03 8.373118e-03 6.862595e-03 1.738947e-03 2.845537e-03
 [76] 7.896003e-03 4.906457e-03 1.390812e-03 2.117417e-03 8.747900e-03
 [81] 3.581103e-03 1.633171e-03 1.354725e-02 5.337646e-03 8.460699e-03
 [86] 6.382771e-03 1.683677e-03 8.677140e-03 6.158797e-03 5.922785e-03
 [91] 7.039080e-03 1.014464e-04 4.786996e-03 6.866024e-04 5.168842e-03
 [96] 5.901669e-03 1.538452e-03 5.794985e-03 6.454151e-04 9.685541e-03
[101] 3.960061e-04 4.515357e-03 7.319359e-03 5.602311e-03 2.962123e-03
[106] 2.734886e-04 1.909488e-04 7.328655e-03 5.372593e-04 2.161080e-03
[111] 1.346645e-03 5.205242e-04 7.026090e-03 3.367930e-03 5.388497e-03
[116] 5.398913e-03 1.805536e-03 1.516381e-03 4.109529e-04 7.029038e-03
[121] 2.476520e-03 1.309555e-02 3.154078e-03 1.789253e-03 7.220336e-03
[126] 1.535081e-03 1.116387e-03 3.133941e-04 3.506327e-04 6.366938e-03
[131] 2.736304e-03 1.576032e-05 2.750834e-03 3.575805e-05 8.983408e-04
[136] 6.444698e-04 6.232874e-04 7.304710e-04 1.040903e-03 4.039585e-03
[141] 4.854392e-04 2.099878e-03 2.867121e-03 2.814981e-03 7.206911e-04
[146] 1.688777e-03 7.513687e-03 1.239874e-03 3.897913e-03 7.973206e-04
[151] 7.126382e-03 1.532166e-03 4.554296e-03 3.455219e-05 2.502186e-03
[156] 1.007421e-03 1.052110e-03 2.783686e-03 4.432346e-04 1.785738e-03
[161] 1.058336e-03 1.306520e-02 1.107366e-03 1.281636e-03 2.336705e-03
[166] 1.443878e-03 7.243589e-04 1.507143e-03 2.087099e-03 6.179670e-04
[171] 2.805573e-03 2.721912e-03 8.007849e-04 2.849465e-04 1.206821e-03
[176] 7.184769e-04 2.111896e-03 1.128421e-03 2.796669e-03 9.113730e-04
[181] 3.244898e-04 3.199485e-03 8.912886e-04 4.038252e-03 1.290134e-03
[186] 3.664921e-03 3.189729e-03 1.233415e-03 6.429465e-04 1.029707e-03
[191] 2.972858e-03 6.218369e-04 4.538461e-03 1.391716e-03 3.098285e-03
[196] 9.217108e-04 3.266865e-03 4.057234e-03 3.154268e-03 1.496232e-03
[201] 1.586943e-03 1.086059e-03 4.224466e-05 3.843853e-04 1.005577e-03
[206] 4.217696e-03 5.898688e-04 7.146056e-04 1.007397e-03 1.006937e-03
[211] 1.681423e-03 7.114579e-04 1.576145e-03 1.575887e-03 2.941137e-04
[216] 2.984150e-04 6.290921e-04 2.916766e-04 3.530476e-04 1.476823e-03
[221] 9.653093e-05 2.997184e-03 2.258737e-03 2.733044e-04 8.190529e-04
[226] 1.270467e-03 3.916629e-05 2.333237e-04 1.940631e-03 5.964693e-05
[231] 8.940354e-04 1.051847e-03 2.488059e-04 1.838505e-03 1.109792e-03
[236] 1.108031e-03 2.443387e-03 2.456082e-03 1.201263e-04 3.693075e-03
[241] 6.096183e-04 2.456739e-03 1.452309e-03 5.660990e-04 4.390858e-05
[246] 1.379379e-04 8.017373e-04 8.985033e-04 1.509473e-04 4.726054e-04
[251] 6.700091e-03 5.357473e-05 2.321892e-04 1.787253e-03 8.338695e-04
[256] 1.215906e-03 8.677027e-04 1.007025e-03 4.743717e-04 1.406944e-03
[261] 5.591323e-04 1.265524e-03 3.030436e-03 1.356520e-03 1.050742e-04
[266] 9.818479e-04 4.878372e-04 1.780409e-03 3.035566e-04 2.559445e-03
[271] 1.388153e-03 8.408980e-03 7.686041e-04 1.625600e-03 1.215598e-03
[276] 4.820968e-04 6.530076e-04 7.342437e-04 3.154774e-04 2.915222e-05
[281] 7.402380e-04 1.068047e-03 9.479237e-05 2.551589e-03 3.477627e-03
[286] 1.578289e-03 2.612542e-04 2.460466e-04 2.136521e-03 3.206857e-04
[291] 5.586850e-03 2.427521e-03 6.572634e-04 6.228267e-04 5.934981e-04
[296] 2.899021e-03 4.166449e-04 3.429114e-04 2.212894e-03 2.368428e-03
[301] 1.802399e-04 3.747764e-03 1.909671e-04 1.836992e-03 3.447516e-05
[306] 1.651988e-04 2.598949e-03 3.001466e-04 2.466164e-03 8.558006e-04
[311] 2.746299e-03 1.047580e-04 1.296118e-03 6.792595e-04 3.301821e-04
[316] 2.250258e-03 3.089557e-04 9.916999e-04 7.328119e-04 1.865319e-03
[321] 4.839919e-04 2.398887e-04 1.314410e-03 9.467021e-04 6.390902e-04
[326] 1.300444e-04 1.505770e-04 4.502860e-04 2.044221e-03 3.184008e-04
[331] 8.470188e-04 9.076418e-05 1.638995e-03 1.356454e-04 1.018855e-05
[336] 1.261029e-03 1.918176e-04 1.135659e-05 4.072278e-04 5.675270e-04
[341] 2.933340e-03 3.915748e-04 6.419085e-04 2.988052e-03 1.742921e-05
[346] 2.195327e-03 4.178423e-04 6.425283e-05 1.886395e-03 6.100374e-04
[351] 1.380847e-03 1.199149e-03 9.518346e-04 1.316443e-03 1.562199e-04
[356] 7.437670e-04 2.069620e-04 4.606816e-04 2.475252e-04 1.641136e-03
[361] 6.291115e-06 3.802519e-04 1.595049e-03 8.862561e-05 3.650017e-04
[366] 1.961946e-05 1.187374e-04

$lambda
  [1] 0.008560198 0.017120396 0.025680594 0.034240792 0.042800990 0.051361188
  [7] 0.059921386 0.068481584 0.077041782 0.085601980 0.094162178 0.102722376
 [13] 0.111282574 0.119842772 0.128402969 0.136963167 0.145523365 0.154083563
 [19] 0.162643761 0.171203959 0.179764157 0.188324355 0.196884553 0.205444751
 [25] 0.214004949 0.222565147 0.231125345 0.239685543 0.248245741 0.256805939
 [31] 0.265366137 0.273926335 0.282486533 0.291046731 0.299606929 0.308167127
 [37] 0.316727325 0.325287523 0.333847721 0.342407919 0.350968117 0.359528315
 [43] 0.368088513 0.376648711 0.385208908 0.393769106 0.402329304 0.410889502
 [49] 0.419449700 0.428009898 0.436570096 0.445130294 0.453690492 0.462250690
 [55] 0.470810888 0.479371086 0.487931284 0.496491482 0.505051680 0.513611878
 [61] 0.522172076 0.530732274 0.539292472 0.547852670 0.556412868 0.564973066
 [67] 0.573533264 0.582093462 0.590653660 0.599213858 0.607774056 0.616334254
 [73] 0.624894452 0.633454649 0.642014847 0.650575045 0.659135243 0.667695441
 [79] 0.676255639 0.684815837 0.693376035 0.701936233 0.710496431 0.719056629
 [85] 0.727616827 0.736177025 0.744737223 0.753297421 0.761857619 0.770417817
 [91] 0.778978015 0.787538213 0.796098411 0.804658609 0.813218807 0.821779005
 [97] 0.830339203 0.838899401 0.847459599 0.856019797 0.864579995 0.873140193
[103] 0.881700391 0.890260588 0.898820786 0.907380984 0.915941182 0.924501380
[109] 0.933061578 0.941621776 0.950181974 0.958742172 0.967302370 0.975862568
[115] 0.984422766 0.992982964 1.001543162 1.010103360 1.018663558 1.027223756
[121] 1.035783954 1.044344152 1.052904350 1.061464548 1.070024746 1.078584944
[127] 1.087145142 1.095705340 1.104265538 1.112825736 1.121385934 1.129946132
[133] 1.138506330 1.147066527 1.155626725 1.164186923 1.172747121 1.181307319
[139] 1.189867517 1.198427715 1.206987913 1.215548111 1.224108309 1.232668507
[145] 1.241228705 1.249788903 1.258349101 1.266909299 1.275469497 1.284029695
[151] 1.292589893 1.301150091 1.309710289 1.318270487 1.326830685 1.335390883
[157] 1.343951081 1.352511279 1.361071477 1.369631675 1.378191873 1.386752071
[163] 1.395312268 1.403872466 1.412432664 1.420992862 1.429553060 1.438113258
[169] 1.446673456 1.455233654 1.463793852 1.472354050 1.480914248 1.489474446
[175] 1.498034644 1.506594842 1.515155040 1.523715238 1.532275436 1.540835634
[181] 1.549395832 1.557956030 1.566516228 1.575076426 1.583636624 1.592196822
[187] 1.600757020 1.609317218 1.617877416 1.626437614 1.634997812 1.643558010
[193] 1.652118207 1.660678405 1.669238603 1.677798801 1.686358999 1.694919197
[199] 1.703479395 1.712039593 1.720599791 1.729159989 1.737720187 1.746280385
[205] 1.754840583 1.763400781 1.771960979 1.780521177 1.789081375 1.797641573
[211] 1.806201771 1.814761969 1.823322167 1.831882365 1.840442563 1.849002761
[217] 1.857562959 1.866123157 1.874683355 1.883243553 1.891803751 1.900363948
[223] 1.908924146 1.917484344 1.926044542 1.934604740 1.943164938 1.951725136
[229] 1.960285334 1.968845532 1.977405730 1.985965928 1.994526126 2.003086324
[235] 2.011646522 2.020206720 2.028766918 2.037327116 2.045887314 2.054447512
[241] 2.063007710 2.071567908 2.080128106 2.088688304 2.097248502 2.105808700
[247] 2.114368898 2.122929096 2.131489294 2.140049492 2.148609690 2.157169887
[253] 2.165730085 2.174290283 2.182850481 2.191410679 2.199970877 2.208531075
[259] 2.217091273 2.225651471 2.234211669 2.242771867 2.251332065 2.259892263
[265] 2.268452461 2.277012659 2.285572857 2.294133055 2.302693253 2.311253451
[271] 2.319813649 2.328373847 2.336934045 2.345494243 2.354054441 2.362614639
[277] 2.371174837 2.379735035 2.388295233 2.396855431 2.405415628 2.413975826
[283] 2.422536024 2.431096222 2.439656420 2.448216618 2.456776816 2.465337014
[289] 2.473897212 2.482457410 2.491017608 2.499577806 2.508138004 2.516698202
[295] 2.525258400 2.533818598 2.542378796 2.550938994 2.559499192 2.568059390
[301] 2.576619588 2.585179786 2.593739984 2.602300182 2.610860380 2.619420578
[307] 2.627980776 2.636540974 2.645101172 2.653661370 2.662221567 2.670781765
[313] 2.679341963 2.687902161 2.696462359 2.705022557 2.713582755 2.722142953
[319] 2.730703151 2.739263349 2.747823547 2.756383745 2.764943943 2.773504141
[325] 2.782064339 2.790624537 2.799184735 2.807744933 2.816305131 2.824865329
[331] 2.833425527 2.841985725 2.850545923 2.859106121 2.867666319 2.876226517
[337] 2.884786715 2.893346913 2.901907111 2.910467309 2.919027506 2.927587704
[343] 2.936147902 2.944708100 2.953268298 2.961828496 2.970388694 2.978948892
[349] 2.987509090 2.996069288 3.004629486 3.013189684 3.021749882 3.030310080
[355] 3.038870278 3.047430476 3.055990674 3.064550872 3.073111070 3.081671268
[361] 3.090231466 3.098791664 3.107351862 3.115912060 3.124472258 3.133032456
[367] 3.141592654

> aux = smooth.periodogram(malleco$Value, plot = FALSE, spar = .8)
> lines(aux$smooth.periodogram ~ aux$lambda, lwd = 2, col = "orange")
> 
> ## Example 2: mammothcreek$Value
> periodogram(mammothcreek$Value)
$periodogram
  [1] 1.168096e-01 1.215474e-01 1.377516e-01 2.101610e-01 3.024144e-01
  [6] 2.999331e-01 6.186504e-02 3.847972e-02 7.257348e-02 3.156782e-01
 [11] 8.777256e-02 2.836700e-02 2.545154e-01 3.315281e-02 4.291403e-02
 [16] 3.067188e-01 2.431863e-02 9.329140e-02 4.672578e-02 5.713256e-02
 [21] 3.815515e-02 2.501238e-02 4.307107e-02 6.707426e-02 2.113907e-02
 [26] 3.149712e-02 5.478316e-03 3.444574e-01 1.922008e-02 9.676943e-03
 [31] 2.769811e-02 3.907353e-02 5.012769e-02 1.349474e-01 5.645804e-02
 [36] 6.236984e-03 3.806640e-02 1.212721e-02 1.448167e-03 1.354200e-01
 [41] 1.491800e-02 4.803499e-02 1.260681e-01 5.874784e-02 1.298817e-04
 [46] 1.617560e-02 7.909304e-02 1.070367e-02 3.666571e-02 4.192146e-02
 [51] 1.959588e-02 9.847510e-02 9.475858e-03 4.320295e-02 5.778589e-02
 [56] 1.484496e-01 1.345871e-02 3.695418e-03 6.082476e-03 9.791291e-02
 [61] 9.073580e-03 1.494409e-02 6.696429e-02 7.445811e-02 3.565079e-02
 [66] 9.331530e-03 2.462345e-02 8.897646e-03 3.768081e-02 8.167186e-03
 [71] 1.890801e-02 3.814168e-02 5.242256e-02 6.072683e-02 1.155965e-02
 [76] 5.966286e-04 8.235138e-02 3.257130e-03 2.548761e-02 9.334663e-03
 [81] 8.510746e-03 5.119129e-02 3.245521e-02 4.066040e-03 1.446559e-02
 [86] 2.276955e-02 2.657874e-02 9.213400e-02 3.126085e-03 2.834313e-03
 [91] 2.208890e-02 6.156293e-02 1.198596e-01 5.116359e-02 7.570273e-03
 [96] 4.333367e-02 5.413620e-02 5.127455e-03 4.652614e-03 2.899954e-02
[101] 5.278367e-02 1.157010e-02 2.199937e-02 2.907279e-02 2.902725e-02
[106] 2.373604e-02 6.032119e-02 9.038746e-02 3.157716e-03 6.609970e-02
[111] 1.866682e-02 1.244388e-02 1.339865e-02 5.248238e-03 4.501487e-02
[116] 1.633899e-02 1.082750e-02 1.645754e-02 6.182979e-03 2.333657e-03
[121] 1.278306e-03 8.306383e-03 3.224522e-02 2.495788e-02 7.642562e-03
[126] 8.342837e-03 6.628936e-02 1.194751e-02 3.127022e-04 3.494121e-03
[131] 9.186215e-03 5.161352e-02 4.479317e-02 5.047816e-03 5.282203e-02
[136] 8.624969e-03 2.622015e-02 8.395003e-02 8.771485e-03 3.498068e-03
[141] 7.200564e-02 2.147539e-03 8.908944e-02 6.028930e-02 8.549016e-04
[146] 9.011034e-03 3.406319e-03 1.425051e-03 2.426805e-03 1.980728e-02
[151] 3.779104e-02 1.201190e-02 1.450048e-02 3.765770e-02 2.586711e-02
[156] 4.751641e-03 2.506726e-02 3.243100e-02 2.684474e-03 1.906117e-02
[161] 4.566409e-03 3.294380e-02 2.409319e-02 4.450980e-03 1.067276e-02
[166] 1.679958e-02 3.834488e-03 1.231249e-02 2.683776e-02 8.890711e-03
[171] 4.010065e-03 5.964444e-03 3.868031e-02 5.931136e-02 8.436090e-03
[176] 3.030221e-03 7.111683e-02 8.008326e-03 8.981451e-04 1.815487e-03
[181] 3.905385e-03 2.412650e-02 1.607438e-02 8.195550e-03 6.370894e-04
[186] 1.005858e-02 3.516891e-02 1.092279e-02 1.962604e-02 2.639389e-02
[191] 4.002199e-04 1.235470e-02 2.785709e-02 9.395825e-03 1.008890e-02
[196] 5.070886e-02 1.732762e-04 6.634470e-03 5.387157e-02 4.845212e-02
[201] 9.139455e-03 8.721733e-03 1.191872e-02 2.243856e-02 9.337970e-03
[206] 8.767206e-03 2.413629e-02 2.246463e-02 7.691138e-02 2.187837e-04
[211] 6.776751e-02 5.031625e-02 1.057600e-02 2.265654e-03 3.721930e-03
[216] 9.300557e-04 5.847219e-03 1.261227e-02 3.070046e-02 4.562422e-02
[221] 3.207144e-02 3.454868e-02 1.940816e-02 4.112226e-02 3.213964e-03
[226] 3.264098e-03 2.868207e-03 2.283956e-02 2.013394e-02 1.909117e-02
[231] 9.128907e-03 3.399724e-02 4.310008e-02 1.585981e-02 3.192149e-02
[236] 5.381048e-03 3.794690e-03 5.218893e-02 2.434799e-02 7.866286e-03
[241] 4.062445e-03 2.860039e-02 2.171952e-02 2.552874e-03 3.207242e-02
[246] 1.452255e-02 1.280922e-05 4.657362e-03 3.301639e-03 8.243311e-03
[251] 3.759327e-02 3.382105e-03 3.840457e-03 5.494172e-02 3.641472e-02
[256] 1.104753e-02 2.505529e-03 6.801909e-03 9.752969e-03 3.513628e-03
[261] 1.410869e-02 2.560913e-03 6.442181e-04 1.228587e-01 2.283266e-02
[266] 4.727474e-05 5.945585e-03 8.695046e-03 6.365521e-03 1.080313e-02
[271] 8.653663e-03 1.881928e-02 7.303358e-03 8.997134e-03 7.731282e-03
[276] 3.095130e-02 2.398819e-02 8.040641e-03 5.124785e-03 6.516323e-02
[281] 5.654834e-02 2.255329e-02 7.928472e-03 1.380095e-02 6.962257e-03
[286] 4.377241e-02 1.466068e-02 9.290561e-02 9.340723e-03 6.840236e-03
[291] 3.374632e-02 6.699383e-03 1.095838e-03 2.987176e-02 4.653311e-02
[296] 9.881574e-04 1.183715e-02 9.640440e-03 9.449390e-04 1.284918e-03
[301] 4.124005e-02 2.780929e-02 4.444445e-02 2.797720e-02 3.075404e-02
[306] 9.688093e-03 9.360515e-03 1.489008e-02 1.540268e-03 2.344205e-02
[311] 8.928381e-03 3.354794e-03 8.393180e-04 1.586840e-02 3.260953e-02
[316] 8.791523e-03 3.052951e-02 3.831624e-03 1.609452e-02 3.356702e-03
[321] 1.871071e-02 8.071142e-03 5.545924e-03 7.625410e-05 2.023771e-02
[326] 1.410706e-02 6.146318e-03 2.629840e-03 9.323352e-03 1.401214e-02
[331] 2.342335e-02 5.114071e-03 4.723883e-02 1.642390e-02 4.151712e-02
[336] 2.250554e-03 1.516482e-02 8.720176e-03 6.303277e-03 1.598791e-02
[341] 1.915641e-02 1.691288e-02 1.702560e-03 2.151734e-03 3.784605e-02
[346] 1.198591e-02 1.491378e-02 6.613405e-02 3.478406e-03 1.100736e-02
[351] 1.244305e-02 5.586541e-03 4.013049e-04 3.659490e-04 6.435735e-03
[356] 6.594484e-03 1.344041e-02 8.121145e-03 2.468451e-02 1.028924e-02
[361] 3.401383e-02 1.244274e-02 1.584339e-02 8.576797e-03 1.102084e-02
[366] 9.090053e-03 4.131070e-02 2.299237e-03 1.512078e-02 9.686725e-04
[371] 5.400661e-03 8.368539e-03 4.406363e-03 3.100711e-02 2.777330e-03
[376] 1.711359e-03 1.526880e-02 1.233780e-02 3.380941e-03 5.665811e-02
[381] 3.619098e-02 2.673318e-02 9.479100e-03 2.239966e-02 4.347841e-03
[386] 1.521993e-03 3.960379e-02 5.230341e-03 7.772726e-03 8.473913e-03
[391] 1.707294e-02 4.973327e-03 1.099403e-02 2.309808e-03 9.014141e-03
[396] 1.355791e-02 4.503023e-03 3.285750e-02 2.471219e-03 4.551197e-03
[401] 2.968682e-02 1.272568e-02 6.659112e-03 7.797449e-03 1.601307e-03
[406] 8.528493e-03 8.228873e-03 1.088386e-03 5.855547e-03 1.842469e-03
[411] 1.262605e-02 4.352417e-04 9.353733e-03 8.590350e-03 6.054044e-04
[416] 1.328668e-02 2.438028e-03 9.825994e-03 1.556701e-03 1.740926e-02
[421] 1.596987e-02 1.526071e-02 2.995624e-04 1.177945e-03 6.846646e-03
[426] 1.487984e-02 3.355411e-02 2.601996e-02 3.389971e-02 6.853450e-03
[431] 1.537402e-02 5.359855e-02 7.370406e-05 4.027039e-02 2.980490e-02
[436] 1.106125e-02 7.649094e-03 6.132825e-03 3.922123e-04 1.864773e-02
[441] 4.914453e-03 4.024555e-03 7.548127e-03 3.025355e-03 2.574067e-03
[446] 2.892879e-03 6.984991e-03 2.765391e-03 6.339744e-03 2.975480e-03
[451] 1.022959e-02 7.434622e-02 1.078280e-02 9.239072e-02 3.429287e-02
[456] 5.506712e-03 9.520386e-04 3.299334e-02 9.020567e-03 6.823686e-03
[461] 1.594673e-02 2.574013e-03 4.516025e-03 1.203482e-02 1.025205e-02
[466] 2.631644e-02 1.668708e-03 1.551983e-03 6.019940e-03 1.684011e-03
[471] 3.588173e-03 6.416885e-05 2.666300e-03 1.967141e-02 1.428290e-02
[476] 9.782213e-03 3.742762e-02 2.064667e-02 8.327375e-03 3.076630e-03
[481] 5.971145e-04 4.333323e-02 3.610706e-03 2.317061e-03 6.929013e-02
[486] 6.462506e-03 6.687718e-03 2.524933e-02 8.221779e-03 4.583866e-03
[491] 6.521785e-03 3.936254e-02 4.227452e-02 4.559569e-03 4.898056e-02
[496] 1.066420e-03 2.145185e-02 4.398631e-03 1.503431e-02 2.939197e-03
[501] 2.681503e-03 1.589540e-02 3.520376e-02 4.199882e-02 2.539065e-03
[506] 5.040564e-03 1.662835e-02 8.768562e-03 1.623175e-03 7.749104e-03
[511] 1.465555e-02 1.510360e-02 5.732564e-03 1.047584e-02 2.703814e-03
[516] 2.380851e-02 2.399448e-02 3.304309e-03 5.030776e-04 2.084126e-02
[521] 1.849366e-03 7.577136e-03 5.055269e-03 2.162295e-02 1.583305e-03
[526] 1.783055e-02 9.722291e-02 2.787021e-02 2.423557e-02 3.409770e-02
[531] 1.968754e-04 1.244158e-02 3.009430e-02 6.193876e-03 1.957316e-03
[536] 8.483297e-03 8.400131e-05 2.891431e-04 1.916314e-03 3.075560e-02
[541] 4.193322e-03 2.542848e-02 7.414276e-03 4.702897e-03 7.827430e-03
[546] 1.319669e-02 1.114552e-02 7.095099e-04 1.408005e-02 1.242955e-02
[551] 7.598557e-03 1.180842e-02 3.086392e-03 6.976102e-03 6.204215e-04
[556] 2.276851e-02 5.239595e-03 3.795335e-02 5.766834e-03 8.808419e-03
[561] 2.822702e-02 4.884026e-04 1.216510e-03 3.130867e-03 1.011923e-02
[566] 2.316556e-04 1.396901e-02 4.954456e-03 1.772680e-02 1.419018e-02
[571] 4.026488e-02 1.957157e-02 5.714606e-03 2.443783e-03 4.113959e-02
[576] 1.186405e-02 3.508990e-04 1.230082e-03 1.401775e-02 6.394701e-03
[581] 1.576665e-02 9.180751e-03 1.494006e-02 1.443841e-02 2.149009e-02
[586] 1.732791e-02 9.215334e-03 1.205589e-03 9.000413e-03 5.027471e-02
[591] 1.681765e-02 2.833301e-03 5.139998e-03 2.381955e-02 1.147808e-02
[596] 2.912759e-02 1.390103e-02 1.826330e-03 3.832978e-03 1.186534e-02
[601] 9.034059e-03 1.930202e-02 2.333364e-02 7.615913e-03 2.027082e-02
[606] 3.273027e-02 5.870028e-03 1.261960e-02 7.138787e-04 7.189843e-02
[611] 1.902579e-03 7.382422e-03 2.185071e-03 3.892418e-02 2.753315e-02
[616] 2.183279e-02 3.101140e-02 1.482195e-02 1.116427e-02 3.660809e-02
[621] 7.395357e-03 2.093352e-02 5.560402e-04 2.264648e-02 4.520930e-03
[626] 2.788458e-02 1.556572e-02 2.062277e-02 3.252938e-03 1.840906e-03
[631] 1.526190e-03 4.334636e-04 5.330920e-02 4.511353e-02 2.366367e-02
[636] 2.563325e-02 2.037928e-02 2.402398e-02 2.314965e-02 1.660150e-02
[641] 2.261737e-02 7.140930e-03 5.118058e-04 5.087984e-02 3.070351e-02
[646] 3.533415e-02 6.348652e-03 1.542291e-02 1.272690e-04 3.430211e-02
[651] 2.393561e-02 1.783570e-02 1.063509e-02 1.140026e-02 3.079534e-02
[656] 1.308920e-02 2.841576e-03 5.970422e-03 5.574027e-03 2.950678e-02
[661] 5.268110e-03 6.381418e-03 8.819365e-03 5.615661e-03 1.030290e-03
[666] 1.210524e-02 7.766608e-03 8.466205e-03 4.822818e-02 2.877321e-03
[671] 1.729120e-02 1.842906e-02 2.474912e-03 2.484474e-03 3.046461e-02
[676] 2.299849e-02 7.896202e-04 3.655098e-03 2.360180e-03 8.684141e-03
[681] 4.812131e-03 9.495747e-03 5.693829e-03 8.598872e-03 1.083933e-02
[686] 2.672401e-02 8.908311e-03 4.874454e-02 5.230533e-03 6.470780e-03
[691] 7.858308e-04 6.353189e-03 8.708234e-03 8.365058e-03 6.800333e-03
[696] 1.843894e-02 1.902376e-03 1.100110e-02 1.709489e-03 3.700727e-02
[701] 5.523786e-04 1.361066e-03 1.735555e-02 6.569162e-03 1.723191e-03
[706] 6.164475e-03 8.694195e-03 9.702381e-03 1.464037e-02 2.158363e-03
[711] 5.373951e-03 4.580480e-03 1.297647e-05 4.419801e-04 2.160524e-03
[716] 1.014857e-02 3.000056e-03 2.806287e-03 1.878324e-02 1.926942e-02
[721] 5.805672e-03 1.685277e-02 1.496875e-02 2.662901e-02 2.274423e-03
[726] 1.428921e-02 1.105152e-03 2.457468e-03 2.773145e-02 1.017722e-02
[731] 2.673087e-03 2.196806e-02 6.231356e-03 1.356610e-02 1.657693e-02
[736] 5.142536e-02 4.895094e-03 1.314919e-02 5.062712e-02 2.481646e-02
[741] 7.016540e-03 2.862949e-02 6.529286e-03 4.072598e-03 4.917749e-04
[746] 2.139521e-02 9.255107e-04 9.831251e-05 8.545932e-03 1.218507e-02
[751] 4.504122e-03 2.835144e-02 2.393669e-02 1.008488e-02 1.025236e-02
[756] 1.185529e-02 5.443013e-02 2.846711e-02 2.102459e-03 6.165567e-03
[761] 3.164947e-03 2.989490e-03 6.794576e-04 7.896245e-03 2.397485e-03
[766] 1.287046e-02 3.783963e-02 3.146571e-02 2.064759e-03 9.332673e-03
[771] 1.940159e-02 1.638969e-02 5.864769e-02 1.853269e-02 2.586149e-05
[776] 9.438649e-03 6.800899e-03 1.033177e-02 1.624048e-02 3.948619e-03
[781] 2.364386e-02 2.098020e-03 5.730503e-03 1.505541e-02 2.784961e-03
[786] 2.840956e-03 2.386911e-03 3.501377e-04 1.398451e-02 8.845397e-03
[791] 6.003022e-02 1.763634e-02 4.405811e-02 3.318850e-03 2.890022e-03
[796] 6.751867e-03 1.058075e-02 1.831025e-02 4.099878e-04 6.392970e-03
[801] 6.157104e-03 2.621915e-03 2.532424e-02 1.657864e-02 3.074999e-04
[806] 3.288129e-03 1.367260e-02 6.935133e-05 1.358022e-02 1.331815e-02
[811] 1.383506e-02 1.771333e-03 5.965417e-03 3.757976e-03 8.054092e-03
[816] 7.773386e-03 6.775922e-03 3.151217e-03 2.545825e-03 2.417400e-02
[821] 4.917410e-03 8.909121e-03 6.493028e-02 6.297176e-03 6.493523e-03
[826] 1.029606e-02 1.060637e-02 3.012645e-03 1.014932e-01 8.286551e-03
[831] 8.286824e-03 5.737294e-03 4.123121e-02 4.750020e-03 3.011607e-03
[836] 3.544902e-03 9.655224e-04 4.601625e-02 1.692448e-02 1.125508e-02
[841] 3.729607e-03 6.979432e-03 8.879827e-03 7.934524e-03 1.528163e-03
[846] 2.171533e-02 1.434064e-03 4.713692e-03 2.854299e-02 6.406923e-03
[851] 4.222586e-03 1.077779e-02 1.595673e-02 5.728297e-03 1.146085e-03
[856] 9.630877e-03 4.466626e-03 3.988826e-03 2.154741e-02 8.452997e-03
[861] 2.320483e-03 5.722553e-04 6.397074e-03 1.486058e-03 1.788661e-02
[866] 2.183736e-02 4.718617e-03 7.835185e-03 4.053046e-02 1.057772e-02
[871] 4.188462e-03 2.958778e-02 6.867204e-04 5.239801e-02 5.921888e-02
[876] 3.282137e-03 3.242781e-02 1.418105e-02 3.620769e-02 6.705130e-03
[881] 4.282836e-03 1.191288e-02 9.767569e-03 8.052501e-03 2.664590e-02
[886] 1.855409e-02 8.799719e-03 2.165458e-02 7.252988e-03 2.776546e-02
[891] 7.003658e-03 4.564386e-02 1.815390e-03 2.661890e-02 2.769757e-03
[896] 3.759193e-02 8.200782e-03 1.181409e-03 2.725366e-03 5.481016e-03
[901] 1.942010e-03 5.209689e-03 2.895797e-04 1.375813e-02 2.310055e-02
[906] 1.025960e-04 4.076942e-03 1.683883e-02 5.587871e-03 1.352235e-02
[911] 1.973082e-03 1.440076e-02 1.387150e-02 1.017530e-02 4.202157e-04
[916] 7.972062e-04 3.886573e-02 1.001034e-02 2.020856e-02 1.392195e-02
[921] 1.549269e-03 2.721110e-02 8.899475e-04 8.182224e-04 1.797526e-02
[926] 2.667307e-02 3.653068e-02 6.330881e-03 2.925685e-04 9.174189e-02
[931] 6.042661e-04 8.982725e-04 1.770031e-02 3.044103e-02 9.095096e-03
[936] 2.163582e-03 6.031081e-03 3.698348e-03 2.338280e-02 3.523367e-02
[941] 1.078632e-02 2.736258e-03 2.143204e-02 1.055998e-02 2.452472e-02
[946] 3.285244e-03 3.267303e-03 6.451638e-03 3.481572e-02 3.296083e-03
[951] 2.008984e-02 1.217415e-02 1.232303e-02 3.237251e-02 1.946943e-03
[956] 8.133636e-03 1.565931e-02 1.064178e-03 1.174345e-02 5.865443e-04
[961] 4.184440e-02 1.754480e-02 1.095896e-02 1.634226e-02 3.169510e-03
[966] 1.883069e-02 1.470376e-02 6.723841e-03 8.614042e-04 4.395409e-03
[971] 9.597354e-03 4.631750e-04 3.532201e-02 1.144066e-02 1.091473e-02
[976] 5.995358e-03 2.253499e-03 6.715566e-03 2.716735e-02 1.826309e-02
[981] 1.243875e-02 2.139861e-02 2.998369e-02 1.043490e-02 9.128783e-03
[986] 8.704744e-03 2.177414e-02 1.187771e-03 2.568475e-03 1.831643e-02
[991] 2.107453e-02 3.194602e-02 1.685694e-02 2.647795e-03 5.399998e-03

$lambda
  [1] 0.003157380 0.006314759 0.009472139 0.012629518 0.015786898 0.018944277
  [7] 0.022101657 0.025259036 0.028416416 0.031573796 0.034731175 0.037888555
 [13] 0.041045934 0.044203314 0.047360693 0.050518073 0.053675452 0.056832832
 [19] 0.059990211 0.063147591 0.066304971 0.069462350 0.072619730 0.075777109
 [25] 0.078934489 0.082091868 0.085249248 0.088406627 0.091564007 0.094721387
 [31] 0.097878766 0.101036146 0.104193525 0.107350905 0.110508284 0.113665664
 [37] 0.116823043 0.119980423 0.123137803 0.126295182 0.129452562 0.132609941
 [43] 0.135767321 0.138924700 0.142082080 0.145239459 0.148396839 0.151554218
 [49] 0.154711598 0.157868978 0.161026357 0.164183737 0.167341116 0.170498496
 [55] 0.173655875 0.176813255 0.179970634 0.183128014 0.186285394 0.189442773
 [61] 0.192600153 0.195757532 0.198914912 0.202072291 0.205229671 0.208387050
 [67] 0.211544430 0.214701809 0.217859189 0.221016569 0.224173948 0.227331328
 [73] 0.230488707 0.233646087 0.236803466 0.239960846 0.243118225 0.246275605
 [79] 0.249432985 0.252590364 0.255747744 0.258905123 0.262062503 0.265219882
 [85] 0.268377262 0.271534641 0.274692021 0.277849401 0.281006780 0.284164160
 [91] 0.287321539 0.290478919 0.293636298 0.296793678 0.299951057 0.303108437
 [97] 0.306265816 0.309423196 0.312580576 0.315737955 0.318895335 0.322052714
[103] 0.325210094 0.328367473 0.331524853 0.334682232 0.337839612 0.340996992
[109] 0.344154371 0.347311751 0.350469130 0.353626510 0.356783889 0.359941269
[115] 0.363098648 0.366256028 0.369413408 0.372570787 0.375728167 0.378885546
[121] 0.382042926 0.385200305 0.388357685 0.391515064 0.394672444 0.397829823
[127] 0.400987203 0.404144583 0.407301962 0.410459342 0.413616721 0.416774101
[133] 0.419931480 0.423088860 0.426246239 0.429403619 0.432560999 0.435718378
[139] 0.438875758 0.442033137 0.445190517 0.448347896 0.451505276 0.454662655
[145] 0.457820035 0.460977414 0.464134794 0.467292174 0.470449553 0.473606933
[151] 0.476764312 0.479921692 0.483079071 0.486236451 0.489393830 0.492551210
[157] 0.495708590 0.498865969 0.502023349 0.505180728 0.508338108 0.511495487
[163] 0.514652867 0.517810246 0.520967626 0.524125006 0.527282385 0.530439765
[169] 0.533597144 0.536754524 0.539911903 0.543069283 0.546226662 0.549384042
[175] 0.552541421 0.555698801 0.558856181 0.562013560 0.565170940 0.568328319
[181] 0.571485699 0.574643078 0.577800458 0.580957837 0.584115217 0.587272597
[187] 0.590429976 0.593587356 0.596744735 0.599902115 0.603059494 0.606216874
[193] 0.609374253 0.612531633 0.615689013 0.618846392 0.622003772 0.625161151
[199] 0.628318531 0.631475910 0.634633290 0.637790669 0.640948049 0.644105428
[205] 0.647262808 0.650420188 0.653577567 0.656734947 0.659892326 0.663049706
[211] 0.666207085 0.669364465 0.672521844 0.675679224 0.678836604 0.681993983
[217] 0.685151363 0.688308742 0.691466122 0.694623501 0.697780881 0.700938260
[223] 0.704095640 0.707253020 0.710410399 0.713567779 0.716725158 0.719882538
[229] 0.723039917 0.726197297 0.729354676 0.732512056 0.735669435 0.738826815
[235] 0.741984195 0.745141574 0.748298954 0.751456333 0.754613713 0.757771092
[241] 0.760928472 0.764085851 0.767243231 0.770400611 0.773557990 0.776715370
[247] 0.779872749 0.783030129 0.786187508 0.789344888 0.792502267 0.795659647
[253] 0.798817026 0.801974406 0.805131786 0.808289165 0.811446545 0.814603924
[259] 0.817761304 0.820918683 0.824076063 0.827233442 0.830390822 0.833548202
[265] 0.836705581 0.839862961 0.843020340 0.846177720 0.849335099 0.852492479
[271] 0.855649858 0.858807238 0.861964618 0.865121997 0.868279377 0.871436756
[277] 0.874594136 0.877751515 0.880908895 0.884066274 0.887223654 0.890381033
[283] 0.893538413 0.896695793 0.899853172 0.903010552 0.906167931 0.909325311
[289] 0.912482690 0.915640070 0.918797449 0.921954829 0.925112209 0.928269588
[295] 0.931426968 0.934584347 0.937741727 0.940899106 0.944056486 0.947213865
[301] 0.950371245 0.953528625 0.956686004 0.959843384 0.963000763 0.966158143
[307] 0.969315522 0.972472902 0.975630281 0.978787661 0.981945040 0.985102420
[313] 0.988259800 0.991417179 0.994574559 0.997731938 1.000889318 1.004046697
[319] 1.007204077 1.010361456 1.013518836 1.016676216 1.019833595 1.022990975
[325] 1.026148354 1.029305734 1.032463113 1.035620493 1.038777872 1.041935252
[331] 1.045092631 1.048250011 1.051407391 1.054564770 1.057722150 1.060879529
[3