NPMLE via ebnm
Jason Willwerscheid
4/29/2020
Last updated: 2020-04-29
Checks: 6 0
Knit directory: FLASHvestigations/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 8420f5d | Jason Willwerscheid | 2020-04-29 | wflow_publish(“analysis/ebnm_npmle.Rmd”) |
I want to test out approximations of NPMLEs using a dense ashr grid. Let \(x_1, \ldots, x_n\) be \(n\) observations with standard errors equal to 1. Dicker and Zhao show that when the true NPMLE has compact support, then a good approximation can be obtained by optimizing over the family of distributions that’s supported on \(\sqrt{n}\) equally spaced points between \(\min (x)\) and \(\max (x)\). Instead of using point masses, I use an ashr grid with \(\sqrt{n}\) uniform components of equal width. Let’s see how it works in practice.
Here’s the true distribution which I’ll be sampling from. It’s bimodal with peaks at -5 and 5, so a unimodal prior family wouldn’t work very well.
suppressMessages(library(tidyverse))
true_g <- ashr::normalmix(pi = rep(0.1, 10),
mean = c(rep(-5, 5), rep(5, 5)),
sd = c(0:4, 0:4))
cdf_grid <- seq(-20, 20, by = 0.1)
true_cdf <- drop(ashr::mixcdf(true_g, cdf_grid))
ggplot(tibble(x = cdf_grid, y = true_cdf), aes(x = x, y = y)) + geom_line()
Now I sample 100, 1000, and 10000 observations from the true distribution, add normally distributed noise, and call ebnm_npmle.
samp_from_g <- function(g, n) {
comp <- sample(1:length(g$pi), n, replace = TRUE, prob = g$pi)
mean <- g$mean[comp]
sd <- g$sd[comp]
return(rnorm(n, mean = mean, sd = sd))
}
estimate_g <- function(true_g, n, verbose = FALSE) {
samp <- samp_from_g(true_g, n) + rnorm(n) # Add N(0, 1) noise
ebnm_res <- ebnm::ebnm_npmle(samp, control = list(verbose = verbose))
return(ebnm_res$fitted_g)
}
set.seed(666)
g100 <- estimate_g(true_g, 100)
g1000 <- estimate_g(true_g, 1000)
g10000 <- estimate_g(true_g, 10000)
cdf100 <- drop(ashr::mixcdf(g100, cdf_grid))
cdf1000 <- drop(ashr::mixcdf(g1000, cdf_grid))
cdf10000 <- drop(ashr::mixcdf(g10000, cdf_grid))
res <- tibble(x = rep(cdf_grid, 4),
y = c(true_cdf, cdf100, cdf1000, cdf10000),
cdf = c(rep("True", length(cdf_grid)),
rep("n = 100", length(cdf_grid)),
rep("n = 1000", length(cdf_grid)),
rep("n = 10000", length(cdf_grid))))
ggplot(res, aes(x = x, y = y, col = cdf)) + geom_line()
When \(n\) gets too large, mixsqp gets bogged down. Compare \(n = 10000\):
g10000 <- estimate_g(true_g, 10000, verbose = TRUE)#> Running mix-SQP algorithm 0.3-31 on 10000 x 100 matrix
#> convergence tol. (SQP): 1.0e-08
#> conv. tol. (active-set): 1.0e-10
#> zero threshold (solution): 1.0e-08
#> zero thresh. (search dir.): 1.0e-14
#> l.s. sufficient decrease: 1.0e-02
#> step size reduction factor: 7.5e-01
#> minimum step size: 1.0e-08
#> max. iter (SQP): 1000
#> max. iter (active-set): 20
#> number of EM iterations: 20
#> Computing SVD of 10000 x 100 matrix.
#> Matrix is not low-rank; falling back to full matrix.
#> iter objective max(rdual) nnz stepsize max.diff nqp nls
#> 1 +2.030462224e+00 -- EM -- 100 1.00e+00 1.98e-02 -- --
#> 2 +2.012745932e+00 -- EM -- 100 1.00e+00 6.26e-03 -- --
#> 3 +2.009553447e+00 -- EM -- 100 1.00e+00 3.17e-03 -- --
#> 4 +2.008362079e+00 -- EM -- 100 1.00e+00 1.99e-03 -- --
#> 5 +2.007711941e+00 -- EM -- 100 1.00e+00 1.45e-03 -- --
#> 6 +2.007298230e+00 -- EM -- 100 1.00e+00 1.15e-03 -- --
#> 7 +2.007016171e+00 -- EM -- 100 1.00e+00 9.60e-04 -- --
#> 8 +2.006815351e+00 -- EM -- 100 1.00e+00 8.24e-04 -- --
#> 9 +2.006667310e+00 -- EM -- 100 1.00e+00 7.20e-04 -- --
#> 10 +2.006554748e+00 -- EM -- 100 1.00e+00 6.37e-04 -- --
#> 11 +2.006466694e+00 -- EM -- 100 1.00e+00 5.69e-04 -- --
#> 12 +2.006395982e+00 -- EM -- 100 1.00e+00 5.13e-04 -- --
#> 13 +2.006337819e+00 -- EM -- 100 1.00e+00 4.65e-04 -- --
#> 14 +2.006288934e+00 -- EM -- 100 1.00e+00 4.25e-04 -- --
#> 15 +2.006247056e+00 -- EM -- 100 1.00e+00 3.90e-04 -- --
#> 16 +2.006210580e+00 -- EM -- 100 1.00e+00 3.60e-04 -- --
#> 17 +2.006178354e+00 -- EM -- 100 1.00e+00 3.34e-04 -- --
#> 18 +2.006149537e+00 -- EM -- 100 1.00e+00 3.12e-04 -- --
#> 19 +2.006123508e+00 -- EM -- 100 1.00e+00 2.92e-04 -- --
#> 20 +2.006099797e+00 -- EM -- 100 1.00e+00 2.74e-04 -- --
#> 1 +2.006078047e+00 +1.332e-02 100 ------ ------ -- --
#> 2 +2.006057850e+00 +1.326e-02 80 1.00e+00 2.61e-03 20 1
#> 3 +2.006039264e+00 +1.287e-02 60 1.00e+00 1.92e-02 20 1
#> 4 +2.006019180e+00 +1.182e-02 40 1.00e+00 1.02e-01 20 1
#> 5 +2.005511332e+00 +2.118e-03 28 1.00e+00 1.18e-01 20 1
#> 6 +2.005496997e+00 +2.665e-04 30 1.00e+00 2.56e-02 20 1
#> 7 +2.005460778e+00 +1.722e-04 30 1.00e+00 1.50e-01 20 1
#> 8 +2.005452812e+00 +1.484e-04 30 1.00e+00 3.73e-02 20 1
#> 9 +2.005437216e+00 +9.627e-05 28 1.00e+00 4.61e-02 20 1
#> 10 +2.005432708e+00 +5.942e-05 27 1.00e+00 3.49e-02 20 1
#> 11 +2.005432478e+00 +6.458e-05 29 1.00e+00 3.71e-03 20 1
#> 12 +2.005430497e+00 +4.191e-05 29 1.00e+00 5.46e-02 20 1
#> 13 +2.005429142e+00 +1.908e-05 29 1.00e+00 2.41e-02 20 1
#> 14 +2.005429142e+00 +1.908e-05 29 1.00e+00 7.53e-08 20 1
#> 15 +2.005429142e+00 +1.908e-05 29 1.00e+00 3.38e-11 20 1
#> 16 +2.005429142e+00 +1.908e-05 29 1.00e+00 2.01e-12 20 1
#> 17 +2.005429142e+00 +1.908e-05 29 1.00e+00 1.80e-12 20 1
#> 18 +2.005429142e+00 +1.908e-05 29 1.00e+00 1.77e-12 20 1
#> 19 +2.005429142e+00 +1.908e-05 29 1.00e+00 2.49e-12 20 1
#> 20 +2.005429142e+00 +1.908e-05 29 1.00e+00 9.50e-13 20 1
#> 21 +2.005429142e+00 +1.908e-05 29 1.00e+00 5.77e-13 20 1
#> 22 +2.005429142e+00 +1.908e-05 29 1.00e+00 5.39e-13 20 1
#> 23 +2.005429142e+00 +1.908e-05 29 1.00e+00 9.52e-13 20 1
#> 24 +2.005429142e+00 +1.908e-05 29 1.00e+00 1.70e-12 20 1
#> 25 +2.005429142e+00 +1.908e-05 29 1.00e+00 1.21e-12 20 1
#> 26 +2.005429142e+00 +1.908e-05 29 1.00e+00 1.32e-12 20 1
#> 27 +2.005429142e+00 +1.908e-05 29 1.00e+00 9.14e-13 20 1
#> 28 +2.005429142e+00 +1.908e-05 29 1.00e+00 1.10e-12 20 1
#> 29 +2.005429142e+00 +1.908e-05 29 1.00e+00 9.27e-13 20 1
#> 30 +2.005429137e+00 +1.918e-05 30 1.00e+00 5.73e-04 20 1
#> 31 +2.005429137e+00 +1.918e-05 30 1.00e+00 5.78e-07 20 1
#> 32 +2.005429137e+00 +1.918e-05 30 1.00e+00 6.30e-10 20 1
#> 33 +2.005429137e+00 +1.918e-05 30 1.00e+00 8.29e-13 20 1
#> 34 +2.005429137e+00 +1.918e-05 30 1.00e+00 4.11e-12 20 1
#> 35 +2.005429137e+00 +1.918e-05 30 1.00e+00 4.02e-12 20 1
#> 36 +2.005429137e+00 +1.918e-05 30 1.00e+00 2.41e-12 20 1
#> 37 +2.005429137e+00 +1.918e-05 30 1.00e+00 1.10e-12 20 1
#> 38 +2.005429137e+00 +1.918e-05 30 1.00e+00 9.77e-13 20 1
#> 39 +2.005429137e+00 +1.918e-05 30 1.00e+00 3.06e-12 20 1
#> 40 +2.005429137e+00 +1.918e-05 30 1.00e+00 2.58e-12 20 1
#> 41 +2.005429137e+00 +1.918e-05 30 1.00e+00 1.01e-12 20 1
#> 42 +2.005429002e+00 -5.999e-06 30 1.00e+00 9.49e-03 20 1
#> Optimization took 3.34 seconds.
#> Convergence criteria met---optimal solution found.and \(n = 100000\):
g100000 <- estimate_g(true_g, 100000, verbose = TRUE)#> Running mix-SQP algorithm 0.3-31 on 100000 x 317 matrix
#> convergence tol. (SQP): 1.0e-08
#> conv. tol. (active-set): 1.0e-10
#> zero threshold (solution): 1.0e-08
#> zero thresh. (search dir.): 1.0e-14
#> l.s. sufficient decrease: 1.0e-02
#> step size reduction factor: 7.5e-01
#> minimum step size: 1.0e-08
#> max. iter (SQP): 1000
#> max. iter (active-set): 20
#> number of EM iterations: 20
#> Computing SVD of 100000 x 317 matrix.
#> SVD computation took 28.23 seconds.
#> Rank of matrix is estimated to be 80.
#> iter objective max(rdual) nnz stepsize max.diff nqp nls
#> 1 +2.025005873e+00 -- EM -- 317 1.00e+00 8.17e-03 -- --
#> 2 +2.005919110e+00 -- EM -- 317 1.00e+00 2.44e-03 -- --
#> 3 +2.002278085e+00 -- EM -- 317 1.00e+00 1.24e-03 -- --
#> 4 +2.000870033e+00 -- EM -- 317 1.00e+00 7.75e-04 -- --
#> 5 +2.000107437e+00 -- EM -- 317 1.00e+00 5.55e-04 -- --
#> 6 +1.999636078e+00 -- EM -- 317 1.00e+00 4.31e-04 -- --
#> 7 +1.999326526e+00 -- EM -- 317 1.00e+00 3.50e-04 -- --
#> 8 +1.999115017e+00 -- EM -- 317 1.00e+00 2.93e-04 -- --
#> 9 +1.998965586e+00 -- EM -- 317 1.00e+00 2.49e-04 -- --
#> 10 +1.998856663e+00 -- EM -- 317 1.00e+00 2.15e-04 -- --
#> 11 +1.998774855e+00 -- EM -- 317 1.00e+00 1.88e-04 -- --
#> 12 +1.998711637e+00 -- EM -- 317 1.00e+00 1.66e-04 -- --
#> 13 +1.998661462e+00 -- EM -- 317 1.00e+00 1.47e-04 -- --
#> 14 +1.998620653e+00 -- EM -- 317 1.00e+00 1.32e-04 -- --
#> 15 +1.998586726e+00 -- EM -- 317 1.00e+00 1.20e-04 -- --
#> 16 +1.998557972e+00 -- EM -- 317 1.00e+00 1.09e-04 -- --
#> 17 +1.998533194e+00 -- EM -- 317 1.00e+00 1.01e-04 -- --
#> 18 +1.998511540e+00 -- EM -- 316 1.00e+00 9.33e-05 -- --
#> 19 +1.998492389e+00 -- EM -- 316 1.00e+00 8.70e-05 -- --
#> 20 +1.998475286e+00 -- EM -- 316 1.00e+00 8.16e-05 -- --
#> 1 +1.998459886e+00 +1.302e-02 316 ------ ------ -- --
#> 2 +1.998445889e+00 +1.239e-02 296 1.00e+00 7.59e-05 20 1
#> 3 +1.998433145e+00 +1.178e-02 276 1.00e+00 8.88e-05 20 1
#> 4 +1.998421482e+00 +1.119e-02 256 1.00e+00 1.09e-04 20 1
#> 5 +1.998410753e+00 +1.063e-02 236 1.00e+00 4.56e-04 20 1
#> 6 +1.998400863e+00 +1.008e-02 216 1.00e+00 9.47e-04 20 1
#> 7 +1.998391701e+00 +9.538e-03 196 1.00e+00 2.94e-03 20 1
#> 8 +1.998383206e+00 +9.022e-03 176 1.00e+00 1.94e-03 20 1
#> 9 +1.998375309e+00 +8.535e-03 156 1.00e+00 2.14e-03 20 1
#> 10 +1.998367951e+00 +8.072e-03 136 1.00e+00 3.22e-03 20 1
#> 11 +1.998361093e+00 +7.643e-03 116 1.00e+00 5.87e-03 20 1
#> 12 +1.998354621e+00 +7.223e-03 96 1.00e+00 1.02e-02 20 1
#> 13 +1.998348497e+00 +7.140e-03 76 1.00e+00 1.68e-02 20 1
#> 14 +1.998342127e+00 +6.999e-03 56 1.00e+00 4.50e-02 20 1
#> 15 +1.998256234e+00 +4.139e-03 36 1.00e+00 1.13e-01 20 1
#> 16 +1.998224811e+00 +3.176e-03 35 1.00e+00 2.94e-02 20 1
#> 17 +1.998222421e+00 +2.119e-04 35 1.00e+00 1.23e-03 20 1
#> 18 +1.998222016e+00 +2.157e-04 34 1.00e+00 6.01e-04 20 1
#> 19 +1.998221910e+00 +2.154e-04 35 1.00e+00 1.90e-04 20 1
#> 20 +1.998221865e+00 +2.164e-04 35 1.00e+00 1.49e-04 20 1
#> 21 +1.998219530e+00 +1.514e-04 35 1.00e+00 1.92e-02 20 1
#> 22 +1.998216396e+00 +7.652e-05 35 1.00e+00 5.28e-02 20 1
#> 23 +1.998216133e+00 +7.796e-05 35 1.00e+00 4.36e-03 20 1
#> 24 +1.998215900e+00 +7.869e-05 35 1.00e+00 2.19e-03 20 1
#> 25 +1.998214921e+00 +6.126e-05 36 1.00e+00 2.19e-02 20 1
#> 26 +1.998214534e+00 +6.132e-05 35 1.00e+00 4.42e-03 20 1
#> 27 +1.998214534e+00 +6.132e-05 35 1.00e+00 2.90e-07 20 1
#> 28 +1.998214534e+00 +6.132e-05 35 1.00e+00 6.37e-10 20 1
#> 29 +1.998214534e+00 +6.132e-05 35 1.00e+00 2.82e-12 20 1
#> 30 +1.998214534e+00 +6.132e-05 35 1.00e+00 1.44e-12 20 1
#> 31 +1.998214534e+00 +6.132e-05 35 1.00e+00 4.28e-13 20 1
#> 32 +1.998214534e+00 +6.132e-05 35 1.00e+00 4.04e-13 20 1
#> 33 +1.998214534e+00 +6.132e-05 35 1.00e+00 1.08e-12 20 1
#> 34 +1.998214513e+00 +6.135e-05 34 1.00e+00 2.48e-04 20 1
#> 35 +1.998214513e+00 +6.135e-05 34 1.00e+00 6.00e-07 20 1
#> 36 +1.998214513e+00 +6.135e-05 34 1.00e+00 8.12e-09 20 1
#> 37 +1.998214513e+00 +6.135e-05 34 1.00e+00 3.29e-10 20 1
#> 38 +1.998214513e+00 +6.135e-05 34 1.00e+00 1.36e-11 20 1
#> 39 +1.998214513e+00 +6.135e-05 34 1.00e+00 1.41e-12 20 1
#> 40 +1.998214513e+00 +6.135e-05 34 1.00e+00 3.21e-13 20 1
#> 41 +1.998214513e+00 +6.135e-05 34 1.00e+00 5.57e-13 20 1
#> 42 +1.998214513e+00 +6.135e-05 34 1.00e+00 1.62e-12 20 1
#> 43 +1.998214513e+00 +6.135e-05 34 1.00e+00 5.30e-13 20 1
#> 44 +1.998214513e+00 +6.135e-05 34 1.00e+00 3.29e-13 20 1
#> 45 +1.998214513e+00 +6.135e-05 34 1.00e+00 1.20e-13 20 1
#> 46 +1.998214513e+00 +6.135e-05 34 1.00e+00 4.23e-13 20 1
#> 47 +1.998214513e+00 +6.135e-05 34 1.00e+00 2.82e-13 20 1
#> 48 +1.998214513e+00 +6.135e-05 34 1.00e+00 2.08e-13 20 1
#> 49 +1.998214513e+00 +6.135e-05 34 1.00e+00 3.70e-13 20 1
#> 50 +1.998214513e+00 +6.135e-05 34 1.00e+00 4.62e-13 20 1
#> 51 +1.998214513e+00 +6.135e-05 34 1.00e+00 2.39e-13 20 1
#> 52 +1.998214513e+00 +6.135e-05 34 1.00e+00 2.27e-13 20 1
#> 53 +1.998214141e+00 +6.155e-05 34 1.00e+00 6.20e-03 20 1
#> 54 +1.998214141e+00 +6.155e-05 34 1.00e+00 2.60e-07 20 1
#> 55 +1.998214141e+00 +6.155e-05 34 1.00e+00 6.55e-11 20 1
#> 56 +1.998214141e+00 +6.155e-05 34 1.00e+00 1.39e-12 20 1
#> 57 +1.998214141e+00 +6.155e-05 34 1.00e+00 4.20e-13 20 1
#> 58 +1.998214141e+00 +6.155e-05 34 1.00e+00 2.20e-13 20 1
#> 59 +1.998214141e+00 +6.155e-05 34 1.00e+00 1.14e-12 20 1
#> 60 +1.998214141e+00 +6.155e-05 34 1.00e+00 1.61e-12 20 1
#> 61 +1.998214141e+00 +6.155e-05 34 1.00e+00 5.89e-13 20 1
#> 62 +1.998214141e+00 +6.155e-05 34 1.00e+00 9.85e-14 20 1
#> 63 +1.998214141e+00 +6.155e-05 34 1.00e+00 1.36e-12 20 1
#> 64 +1.998214141e+00 +6.155e-05 34 1.00e+00 3.28e-13 20 1
#> 65 +1.998214141e+00 +6.155e-05 34 1.00e+00 6.38e-13 20 1
#> 66 +1.998214141e+00 +6.155e-05 34 1.00e+00 3.87e-13 20 1
#> 67 +1.998214141e+00 +6.155e-05 34 1.00e+00 2.81e-13 20 1
#> 68 +1.998214141e+00 +6.155e-05 34 1.00e+00 8.49e-13 20 1
#> 69 +1.998214141e+00 +6.155e-05 34 1.00e+00 9.71e-13 20 1
#> 70 +1.998214141e+00 +6.155e-05 34 1.00e+00 5.34e-13 20 1
#> 71 +1.998214141e+00 +6.155e-05 34 1.00e+00 1.78e-12 20 1
#> 72 +1.998214141e+00 +6.155e-05 34 1.00e+00 7.69e-13 20 1
#> 73 +1.998214141e+00 +6.155e-05 34 1.00e+00 5.69e-13 20 1
#> 74 +1.998214141e+00 +6.155e-05 34 1.00e+00 2.76e-13 20 1
#> 75 +1.998214141e+00 +6.155e-05 34 1.00e+00 5.74e-13 20 1
#> 76 +1.998214141e+00 +6.155e-05 34 1.00e+00 1.05e-12 20 1
#> 77 +1.998214141e+00 +6.155e-05 34 1.00e+00 3.71e-13 20 1
#> 78 +1.998213990e+00 +6.151e-05 34 1.00e+00 1.75e-03 20 1
#> 79 +1.998213990e+00 +6.151e-05 34 1.00e+00 2.93e-07 20 1
#> 80 +1.998213990e+00 +6.151e-05 34 1.00e+00 6.05e-10 20 1
#> 81 +1.998213990e+00 +6.151e-05 34 1.00e+00 1.94e-12 20 1
#> 82 +1.998213990e+00 +6.151e-05 34 1.00e+00 1.37e-12 20 1
#> 83 +1.998213990e+00 +6.151e-05 34 1.00e+00 6.46e-13 20 1
#> 84 +1.998213990e+00 +6.151e-05 34 1.00e+00 4.40e-13 20 1
#> 85 +1.998213990e+00 +6.151e-05 34 1.00e+00 4.34e-13 20 1
#> 86 +1.998213990e+00 +6.151e-05 34 1.00e+00 1.08e-13 20 1
#> 87 +1.998213990e+00 +6.151e-05 34 1.00e+00 1.36e-12 20 1
#> 88 +1.998210175e+00 +2.189e-05 33 1.00e+00 6.01e-02 20 1
#> 89 +1.998210028e+00 +5.608e-05 33 1.00e+00 7.12e-03 20 1
#> 90 +1.998210028e+00 +5.566e-05 33 1.00e+00 7.82e-07 20 1
#> 91 +1.998210028e+00 +5.566e-05 33 1.00e+00 1.94e-10 20 1
#> 92 +1.998210028e+00 +5.566e-05 33 1.00e+00 3.96e-12 20 1
#> 93 +1.998209902e+00 +9.049e-05 34 1.00e+00 5.72e-03 20 1
#> 94 +1.998209495e+00 +2.169e-05 34 1.00e+00 8.85e-03 20 1
#> 95 +1.998209181e+00 +1.170e-05 35 1.00e+00 1.17e-02 20 1
#> 96 +1.998209133e+00 +1.178e-05 35 1.00e+00 1.91e-03 20 1
#> 97 +1.998208570e+00 +2.110e-05 35 1.00e+00 5.88e-02 20 1
#> 98 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.83e-06 20 1
#> 99 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.19e-09 20 1
#> 100 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.02e-10 20 1
#> 101 +1.998208570e+00 +2.060e-05 35 1.00e+00 8.87e-12 20 1
#> 102 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.12e-12 20 1
#> 103 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.32e-12 20 1
#> 104 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.56e-12 20 1
#> 105 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.96e-13 20 1
#> 106 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.61e-12 20 1
#> 107 +1.998208570e+00 +2.060e-05 35 1.00e+00 5.98e-12 20 1
#> 108 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.60e-12 20 1
#> 109 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.89e-12 20 1
#> 110 +1.998208570e+00 +2.060e-05 35 1.00e+00 7.26e-13 20 1
#> 111 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.03e-12 20 1
#> 112 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.04e-13 20 1
#> 113 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.22e-12 20 1
#> 114 +1.998208570e+00 +2.060e-05 35 1.00e+00 6.69e-13 20 1
#> 115 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.41e-12 20 1
#> 116 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.56e-13 20 1
#> 117 +1.998208570e+00 +2.060e-05 35 1.00e+00 9.13e-13 20 1
#> 118 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.50e-12 20 1
#> 119 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.73e-13 20 1
#> 120 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.16e-12 20 1
#> 121 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.57e-12 20 1
#> 122 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.09e-12 20 1
#> 123 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.40e-13 20 1
#> 124 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.28e-12 20 1
#> 125 +1.998208570e+00 +2.060e-05 35 1.00e+00 7.11e-12 20 1
#> 126 +1.998208570e+00 +2.060e-05 35 1.00e+00 8.12e-12 20 1
#> 127 +1.998208570e+00 +2.060e-05 35 1.00e+00 8.44e-13 20 1
#> 128 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.51e-12 20 1
#> 129 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.33e-12 20 1
#> 130 +1.998208570e+00 +2.060e-05 35 1.00e+00 5.67e-13 20 1
#> 131 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.48e-12 20 1
#> 132 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.16e-12 20 1
#> 133 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.67e-13 20 1
#> 134 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.42e-12 20 1
#> 135 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.55e-12 20 1
#> 136 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.40e-12 20 1
#> 137 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.43e-12 20 1
#> 138 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.28e-12 20 1
#> 139 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.29e-12 20 1
#> 140 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.03e-12 20 1
#> 141 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.92e-12 20 1
#> 142 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.18e-12 20 1
#> 143 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.75e-13 20 1
#> 144 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.97e-12 20 1
#> 145 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.82e-12 20 1
#> 146 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.29e-12 20 1
#> 147 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.47e-12 20 1
#> 148 +1.998208570e+00 +2.060e-05 35 1.00e+00 6.87e-13 20 1
#> 149 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.00e-12 20 1
#> 150 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.56e-12 20 1
#> 151 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.72e-12 20 1
#> 152 +1.998208570e+00 +2.060e-05 35 1.00e+00 5.87e-13 20 1
#> 153 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.17e-12 20 1
#> 154 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.42e-12 20 1
#> 155 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.18e-12 20 1
#> 156 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.77e-12 20 1
#> 157 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.83e-13 20 1
#> 158 +1.998208570e+00 +2.060e-05 35 1.00e+00 7.45e-12 20 1
#> 159 +1.998208570e+00 +2.060e-05 35 1.00e+00 7.23e-12 20 1
#> 160 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.79e-12 20 1
#> 161 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.57e-12 20 1
#> 162 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.02e-12 20 1
#> 163 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.78e-12 20 1
#> 164 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.34e-12 20 1
#> 165 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.43e-12 20 1
#> 166 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.94e-13 20 1
#> 167 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.50e-12 20 1
#> 168 +1.998208570e+00 +2.060e-05 35 1.00e+00 7.26e-13 20 1
#> 169 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.56e-13 20 1
#> 170 +1.998208570e+00 +2.060e-05 35 1.00e+00 7.54e-13 20 1
#> 171 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.24e-12 20 1
#> 172 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.66e-12 20 1
#> 173 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.91e-12 20 1
#> 174 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.67e-13 20 1
#> 175 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.36e-12 20 1
#> 176 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.18e-12 20 1
#> 177 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.29e-13 20 1
#> 178 +1.998208570e+00 +2.060e-05 35 1.00e+00 4.70e-12 20 1
#> 179 +1.998208570e+00 +2.060e-05 35 1.00e+00 5.61e-13 20 1
#> 180 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.10e-12 20 1
#> 181 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.95e-12 20 1
#> 182 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.70e-12 20 1
#> 183 +1.998208570e+00 +2.060e-05 35 1.00e+00 5.81e-13 20 1
#> 184 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.64e-12 20 1
#> 185 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.03e-12 20 1
#> 186 +1.998208570e+00 +2.060e-05 35 1.00e+00 1.93e-12 20 1
#> 187 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.91e-12 20 1
#> 188 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.70e-13 20 1
#> 189 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.19e-12 20 1
#> 190 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.84e-12 20 1
#> 191 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.85e-13 20 1
#> 192 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.91e-12 20 1
#> 193 +1.998208570e+00 +2.060e-05 35 1.00e+00 2.05e-13 20 1
#> 194 +1.998208570e+00 +2.060e-05 35 1.00e+00 3.19e-12 20 1
#> 195 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.31e-05 20 1
#> 196 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.39e-07 20 1
#> 197 +1.998208569e+00 +2.064e-05 36 1.00e+00 1.24e-08 20 1
#> 198 +1.998208569e+00 +2.064e-05 36 1.00e+00 5.55e-10 20 1
#> 199 +1.998208569e+00 +2.064e-05 36 1.00e+00 3.02e-11 20 1
#> 200 +1.998208569e+00 +2.064e-05 36 1.00e+00 3.99e-12 20 1
#> 201 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.47e-13 20 1
#> 202 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.14e-12 20 1
#> 203 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.08e-12 20 1
#> 204 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.51e-12 20 1
#> 205 +1.998208569e+00 +2.064e-05 36 1.00e+00 1.17e-12 20 1
#> 206 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.48e-12 20 1
#> 207 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.21e-13 20 1
#> 208 +1.998208569e+00 +2.064e-05 36 1.00e+00 1.04e-12 20 1
#> 209 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.68e-12 20 1
#> 210 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.21e-12 20 1
#> 211 +1.998208569e+00 +2.064e-05 36 1.00e+00 3.08e-12 20 1
#> 212 +1.998208569e+00 +2.064e-05 36 1.00e+00 7.50e-14 20 1
#> 213 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.69e-12 20 1
#> 214 +1.998208569e+00 +2.064e-05 36 1.00e+00 1.44e-13 20 1
#> 215 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.70e-12 20 1
#> 216 +1.998208569e+00 +2.064e-05 36 1.00e+00 1.31e-12 20 1
#> 217 +1.998208569e+00 +2.064e-05 36 1.00e+00 3.82e-12 20 1
#> 218 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.98e-12 20 1
#> 219 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.00e-12 20 1
#> 220 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.94e-12 20 1
#> 221 +1.998208569e+00 +2.064e-05 36 1.00e+00 3.41e-12 20 1
#> 222 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.80e-13 20 1
#> 223 +1.998208569e+00 +2.064e-05 36 1.00e+00 2.21e-12 20 1
#> 224 +1.998208569e+00 +2.064e-05 36 1.00e+00 6.21e-13 20 1
#> 225 +1.998208569e+00 +2.064e-05 36 1.00e+00 4.80e-12 20 1
#> 226 +1.998208569e+00 +2.064e-05 36 1.00e+00 5.43e-12 20 1
#> 227 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.29e-05 20 1
#> 228 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.73e-07 20 1
#> 229 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.38e-09 20 1
#> 230 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.93e-10 20 1
#> 231 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.92e-11 20 1
#> 232 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.27e-13 20 1
#> 233 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.50e-13 20 1
#> 234 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.97e-12 20 1
#> 235 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.02e-12 20 1
#> 236 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.76e-12 20 1
#> 237 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.44e-12 20 1
#> 238 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.46e-12 20 1
#> 239 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.57e-12 20 1
#> 240 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.99e-12 20 1
#> 241 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.04e-12 20 1
#> 242 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.57e-12 20 1
#> 243 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.88e-12 20 1
#> 244 +1.998208569e+00 +2.064e-05 35 1.00e+00 9.19e-13 20 1
#> 245 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.43e-13 20 1
#> 246 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.25e-12 20 1
#> 247 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.49e-12 20 1
#> 248 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.53e-12 20 1
#> 249 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.04e-12 20 1
#> 250 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.90e-12 20 1
#> 251 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.24e-13 20 1
#> 252 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.36e-12 20 1
#> 253 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.73e-13 20 1
#> 254 +1.998208569e+00 +2.064e-05 35 1.00e+00 8.91e-13 20 1
#> 255 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.64e-12 20 1
#> 256 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.13e-13 20 1
#> 257 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.52e-12 20 1
#> 258 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.19e-13 20 1
#> 259 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.79e-13 20 1
#> 260 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.14e-13 20 1
#> 261 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.88e-13 20 1
#> 262 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.74e-12 20 1
#> 263 +1.998208569e+00 +2.064e-05 35 1.00e+00 8.24e-13 20 1
#> 264 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.15e-12 20 1
#> 265 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.85e-13 20 1
#> 266 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.77e-12 20 1
#> 267 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.50e-12 20 1
#> 268 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.51e-12 20 1
#> 269 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.31e-12 20 1
#> 270 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.17e-12 20 1
#> 271 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.22e-12 20 1
#> 272 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.45e-13 20 1
#> 273 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.38e-12 20 1
#> 274 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.95e-12 20 1
#> 275 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.16e-12 20 1
#> 276 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.11e-13 20 1
#> 277 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.12e-12 20 1
#> 278 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.72e-12 20 1
#> 279 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.11e-13 20 1
#> 280 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.04e-12 20 1
#> 281 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.63e-12 20 1
#> 282 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.52e-12 20 1
#> 283 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.93e-13 20 1
#> 284 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.35e-12 20 1
#> 285 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.86e-13 20 1
#> 286 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.81e-13 20 1
#> 287 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.39e-12 20 1
#> 288 +1.998208569e+00 +2.064e-05 35 1.00e+00 9.78e-13 20 1
#> 289 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.43e-13 20 1
#> 290 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.89e-13 20 1
#> 291 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.85e-12 20 1
#> 292 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.36e-12 20 1
#> 293 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.91e-12 20 1
#> 294 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.80e-12 20 1
#> 295 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.79e-12 20 1
#> 296 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.18e-12 20 1
#> 297 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.21e-12 20 1
#> 298 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.44e-14 20 1
#> 299 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.95e-12 20 1
#> 300 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.50e-12 20 1
#> 301 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.52e-12 20 1
#> 302 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.45e-12 20 1
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#> 304 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.25e-12 20 1
#> 305 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.09e-13 20 1
#> 306 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.80e-12 20 1
#> 307 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.37e-13 20 1
#> 308 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.07e-12 20 1
#> 309 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.83e-13 20 1
#> 310 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.39e-12 20 1
#> 311 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.77e-13 20 1
#> 312 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.81e-12 20 1
#> 313 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.62e-13 20 1
#> 314 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.24e-12 20 1
#> 315 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.99e-12 20 1
#> 316 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.60e-12 20 1
#> 317 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.15e-12 20 1
#> 318 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.49e-13 20 1
#> 319 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.49e-12 20 1
#> 320 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.12e-13 20 1
#> 321 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.32e-12 20 1
#> 322 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.95e-12 20 1
#> 323 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.62e-12 20 1
#> 324 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.28e-12 20 1
#> 325 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.07e-12 20 1
#> 326 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.40e-12 20 1
#> 327 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.37e-12 20 1
#> 328 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.63e-12 20 1
#> 329 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.16e-12 20 1
#> 330 +1.998208569e+00 +2.064e-05 35 1.00e+00 8.11e-13 20 1
#> 331 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.05e-13 20 1
#> 332 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.15e-13 20 1
#> 333 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.86e-12 20 1
#> 334 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.03e-12 20 1
#> 335 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.13e-12 20 1
#> 336 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.46e-12 20 1
#> 337 +1.998208569e+00 +2.064e-05 35 1.00e+00 8.73e-13 20 1
#> 338 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.19e-12 20 1
#> 339 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.40e-12 20 1
#> 340 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.91e-12 20 1
#> 341 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.87e-12 20 1
#> 342 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.19e-12 20 1
#> 343 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.10e-12 20 1
#> 344 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.97e-12 20 1
#> 345 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.24e-12 20 1
#> 346 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.62e-12 20 1
#> 347 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.18e-12 20 1
#> 348 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.40e-12 20 1
#> 349 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.00e-13 20 1
#> 350 +1.998208569e+00 +2.064e-05 35 1.00e+00 9.28e-14 20 1
#> 351 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.06e-13 20 1
#> 352 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.75e-12 20 1
#> 353 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.29e-12 20 1
#> 354 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.42e-13 20 1
#> 355 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.09e-12 20 1
#> 356 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.98e-12 20 1
#> 357 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.83e-12 20 1
#> 358 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.38e-12 20 1
#> 359 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.66e-12 20 1
#> 360 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.24e-12 20 1
#> 361 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.99e-12 20 1
#> 362 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.81e-13 20 1
#> 363 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.61e-12 20 1
#> 364 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.64e-12 20 1
#> 365 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.86e-12 20 1
#> 366 +1.998208569e+00 +2.064e-05 35 1.00e+00 6.49e-12 20 1
#> 367 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.09e-12 20 1
#> 368 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.37e-13 20 1
#> 369 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.27e-12 20 1
#> 370 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.47e-12 20 1
#> 371 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.64e-12 20 1
#> 372 +1.998208569e+00 +2.064e-05 35 1.00e+00 8.46e-14 20 1
#> 373 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.69e-12 20 1
#> 374 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.45e-13 20 1
#> 375 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.16e-12 20 1
#> 376 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.68e-12 20 1
#> 377 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.56e-13 20 1
#> 378 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.96e-12 20 1
#> 379 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.16e-12 20 1
#> 380 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.56e-12 20 1
#> 381 +1.998208569e+00 +2.064e-05 35 1.00e+00 9.11e-13 20 1
#> 382 +1.998208569e+00 +2.064e-05 35 1.00e+00 9.20e-13 20 1
#> 383 +1.998208569e+00 +2.064e-05 35 1.00e+00 5.96e-13 20 1
#> 384 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.26e-12 20 1
#> 385 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.19e-12 20 1
#> 386 +1.998208569e+00 +2.064e-05 35 1.00e+00 7.61e-14 20 1
#> 387 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.62e-12 20 1
#> 388 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.40e-12 20 1
#> 389 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.78e-12 20 1
#> 390 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.25e-12 20 1
#> 391 +1.998208569e+00 +2.064e-05 35 1.00e+00 8.96e-13 20 1
#> 392 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.17e-13 20 1
#> 393 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.89e-12 20 1
#> 394 +1.998208569e+00 +2.064e-05 35 1.00e+00 9.02e-13 20 1
#> 395 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.57e-12 20 1
#> 396 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.50e-12 20 1
#> 397 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.00e-12 20 1
#> 398 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.20e-13 20 1
#> 399 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.67e-12 20 1
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#> 401 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.04e-12 20 1
#> 402 +1.998208569e+00 +2.064e-05 35 1.00e+00 2.77e-12 20 1
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#> 407 +1.998208569e+00 +2.064e-05 35 1.00e+00 1.76e-12 20 1
#> 408 +1.998208569e+00 +2.064e-05 35 1.00e+00 3.19e-12 20 1
#> 409 +1.998208569e+00 +2.064e-05 35 1.00e+00 4.52e-13 20 1
#> 410 +1.998208529e+00 +5.499e-06 36 1.00e+00 1.49e-02 20 1
#> 411 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.70e-07 20 1
#> 412 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.04e-09 20 1
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#> 415 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.35e-12 20 1
#> 416 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.48e-13 20 1
#> 417 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.64e-12 20 1
#> 418 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.18e-12 20 1
#> 419 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.79e-13 20 1
#> 420 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.83e-12 20 1
#> 421 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.76e-13 20 1
#> 422 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.61e-12 20 1
#> 423 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.12e-12 20 1
#> 424 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.02e-11 20 1
#> 425 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.58e-12 20 1
#> 426 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.59e-13 20 1
#> 427 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.23e-11 20 1
#> 428 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.88e-12 20 1
#> 429 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.47e-13 20 1
#> 430 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.05e-12 20 1
#> 431 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.43e-13 20 1
#> 432 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.06e-12 20 1
#> 433 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.04e-11 20 1
#> 434 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.76e-12 20 1
#> 435 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.03e-12 20 1
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#> 437 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.43e-12 20 1
#> 438 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.51e-12 20 1
#> 439 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.12e-12 20 1
#> 440 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.96e-12 20 1
#> 441 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.72e-12 20 1
#> 442 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.10e-12 20 1
#> 443 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.04e-12 20 1
#> 444 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.16e-12 20 1
#> 445 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.09e-12 20 1
#> 446 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.10e-12 20 1
#> 447 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.23e-13 20 1
#> 448 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.28e-12 20 1
#> 449 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.96e-13 20 1
#> 450 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.31e-12 20 1
#> 451 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.37e-13 20 1
#> 452 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.17e-12 20 1
#> 453 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.49e-12 20 1
#> 454 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.74e-12 20 1
#> 455 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.98e-12 20 1
#> 456 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.45e-12 20 1
#> 457 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.06e-12 20 1
#> 458 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.26e-12 20 1
#> 459 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.29e-13 20 1
#> 460 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.58e-12 20 1
#> 461 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.52e-12 20 1
#> 462 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.49e-12 20 1
#> 463 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.31e-12 20 1
#> 464 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.31e-13 20 1
#> 465 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.86e-12 20 1
#> 466 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.71e-12 20 1
#> 467 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.78e-12 20 1
#> 468 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.10e-12 20 1
#> 469 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.80e-12 20 1
#> 470 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.36e-12 20 1
#> 471 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.74e-12 20 1
#> 472 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.29e-12 20 1
#> 473 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.85e-12 20 1
#> 474 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.64e-12 20 1
#> 475 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.47e-12 20 1
#> 476 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.61e-12 20 1
#> 477 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.34e-12 20 1
#> 478 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.35e-12 20 1
#> 479 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.55e-12 20 1
#> 480 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.72e-12 20 1
#> 481 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.83e-12 20 1
#> 482 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.39e-12 20 1
#> 483 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.32e-12 20 1
#> 484 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.96e-13 20 1
#> 485 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.84e-12 20 1
#> 486 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.81e-12 20 1
#> 487 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.75e-12 20 1
#> 488 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.74e-12 20 1
#> 489 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.45e-12 20 1
#> 490 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.21e-13 20 1
#> 491 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.95e-12 20 1
#> 492 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.20e-12 20 1
#> 493 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.74e-13 20 1
#> 494 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.44e-12 20 1
#> 495 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.09e-13 20 1
#> 496 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.68e-13 20 1
#> 497 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.94e-12 20 1
#> 498 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.33e-12 20 1
#> 499 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.94e-12 20 1
#> 500 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.33e-12 20 1
#> 501 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.96e-12 20 1
#> 502 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.76e-12 20 1
#> 503 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.04e-12 20 1
#> 504 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.26e-12 20 1
#> 505 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.95e-12 20 1
#> 506 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.25e-12 20 1
#> 507 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.91e-13 20 1
#> 508 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.29e-12 20 1
#> 509 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.66e-12 20 1
#> 510 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.13e-12 20 1
#> 511 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.22e-13 20 1
#> 512 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.41e-12 20 1
#> 513 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.20e-12 20 1
#> 514 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.42e-11 20 1
#> 515 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.70e-12 20 1
#> 516 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.76e-12 20 1
#> 517 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.93e-12 20 1
#> 518 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.15e-12 20 1
#> 519 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.83e-12 20 1
#> 520 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.37e-12 20 1
#> 521 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.44e-12 20 1
#> 522 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.46e-12 20 1
#> 523 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.36e-12 20 1
#> 524 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.56e-12 20 1
#> 525 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.10e-12 20 1
#> 526 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.06e-12 20 1
#> 527 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.66e-13 20 1
#> 528 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.69e-13 20 1
#> 529 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.89e-13 20 1
#> 530 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.02e-12 20 1
#> 531 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.28e-12 20 1
#> 532 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.21e-12 20 1
#> 533 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.91e-12 20 1
#> 534 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.41e-12 20 1
#> 535 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.39e-13 20 1
#> 536 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.40e-12 20 1
#> 537 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.17e-12 20 1
#> 538 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.03e-12 20 1
#> 539 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.39e-12 20 1
#> 540 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.54e-12 20 1
#> 541 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.50e-12 20 1
#> 542 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.79e-12 20 1
#> 543 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.02e-13 20 1
#> 544 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.41e-12 20 1
#> 545 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.41e-12 20 1
#> 546 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.96e-12 20 1
#> 547 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.03e-12 20 1
#> 548 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.07e-12 20 1
#> 549 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.76e-12 20 1
#> 550 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.45e-13 20 1
#> 551 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.04e-12 20 1
#> 552 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.74e-12 20 1
#> 553 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.92e-12 20 1
#> 554 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.99e-12 20 1
#> 555 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.91e-12 20 1
#> 556 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.24e-12 20 1
#> 557 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.97e-12 20 1
#> 558 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.87e-12 20 1
#> 559 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.26e-12 20 1
#> 560 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.85e-12 20 1
#> 561 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.23e-12 20 1
#> 562 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.71e-13 20 1
#> 563 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.58e-12 20 1
#> 564 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.16e-12 20 1
#> 565 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.87e-13 20 1
#> 566 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.08e-12 20 1
#> 567 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.38e-12 20 1
#> 568 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.64e-12 20 1
#> 569 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.39e-12 20 1
#> 570 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.00e-11 20 1
#> 571 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.13e-12 20 1
#> 572 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.68e-12 20 1
#> 573 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.79e-12 20 1
#> 574 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.10e-12 20 1
#> 575 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.43e-12 20 1
#> 576 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.24e-12 20 1
#> 577 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.80e-12 20 1
#> 578 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.37e-12 20 1
#> 579 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.68e-12 20 1
#> 580 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.93e-12 20 1
#> 581 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.60e-12 20 1
#> 582 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.28e-12 20 1
#> 583 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.55e-12 20 1
#> 584 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.52e-11 20 1
#> 585 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.98e-12 20 1
#> 586 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.56e-12 20 1
#> 587 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.47e-13 20 1
#> 588 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.09e-12 20 1
#> 589 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.46e-12 20 1
#> 590 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.75e-12 20 1
#> 591 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.01e-12 20 1
#> 592 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.79e-12 20 1
#> 593 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.78e-12 20 1
#> 594 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.60e-12 20 1
#> 595 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.28e-12 20 1
#> 596 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.43e-12 20 1
#> 597 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.45e-12 20 1
#> 598 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.78e-13 20 1
#> 599 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.37e-12 20 1
#> 600 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.02e-11 20 1
#> 601 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.75e-12 20 1
#> 602 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.25e-12 20 1
#> 603 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.63e-12 20 1
#> 604 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.62e-12 20 1
#> 605 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.08e-12 20 1
#> 606 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.63e-12 20 1
#> 607 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.51e-12 20 1
#> 608 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.26e-12 20 1
#> 609 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.22e-12 20 1
#> 610 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.73e-12 20 1
#> 611 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.29e-12 20 1
#> 612 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.31e-12 20 1
#> 613 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.58e-12 20 1
#> 614 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.26e-11 20 1
#> 615 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.08e-13 20 1
#> 616 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.86e-13 20 1
#> 617 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.82e-12 20 1
#> 618 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.76e-12 20 1
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#> 623 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.62e-12 20 1
#> 624 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.05e-11 20 1
#> 625 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.62e-12 20 1
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#> 629 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.80e-12 20 1
#> 630 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.83e-12 20 1
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#> 632 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.29e-12 20 1
#> 633 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.40e-12 20 1
#> 634 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.40e-12 20 1
#> 635 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.07e-11 20 1
#> 636 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.50e-13 20 1
#> 637 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.51e-12 20 1
#> 638 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.36e-12 20 1
#> 639 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.65e-12 20 1
#> 640 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.63e-13 20 1
#> 641 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.88e-12 20 1
#> 642 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.84e-13 20 1
#> 643 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.99e-12 20 1
#> 644 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.16e-12 20 1
#> 645 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.57e-12 20 1
#> 646 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.95e-12 20 1
#> 647 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.28e-12 20 1
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#> 649 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.06e-12 20 1
#> 650 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.11e-12 20 1
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#> 652 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.62e-12 20 1
#> 653 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.62e-12 20 1
#> 654 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.18e-12 20 1
#> 655 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.77e-12 20 1
#> 656 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.41e-12 20 1
#> 657 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.27e-12 20 1
#> 658 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.94e-13 20 1
#> 659 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.06e-12 20 1
#> 660 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.44e-13 20 1
#> 661 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.43e-12 20 1
#> 662 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.68e-12 20 1
#> 663 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.03e-12 20 1
#> 664 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.26e-13 20 1
#> 665 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.38e-12 20 1
#> 666 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.48e-12 20 1
#> 667 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.14e-12 20 1
#> 668 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.80e-12 20 1
#> 669 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.88e-12 20 1
#> 670 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.84e-13 20 1
#> 671 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.76e-12 20 1
#> 672 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.99e-12 20 1
#> 673 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.60e-12 20 1
#> 674 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.23e-12 20 1
#> 675 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.90e-13 20 1
#> 676 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.31e-12 20 1
#> 677 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.54e-12 20 1
#> 678 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.29e-12 20 1
#> 679 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.13e-12 20 1
#> 680 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.44e-12 20 1
#> 681 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.58e-12 20 1
#> 682 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.11e-11 20 1
#> 683 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.37e-12 20 1
#> 684 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.63e-13 20 1
#> 685 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.23e-13 20 1
#> 686 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.22e-12 20 1
#> 687 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.20e-12 20 1
#> 688 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.54e-13 20 1
#> 689 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.02e-12 20 1
#> 690 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.49e-12 20 1
#> 691 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.36e-13 20 1
#> 692 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.38e-12 20 1
#> 693 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.30e-12 20 1
#> 694 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.39e-13 20 1
#> 695 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.29e-12 20 1
#> 696 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.65e-12 20 1
#> 697 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.97e-13 20 1
#> 698 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.32e-13 20 1
#> 699 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.94e-12 20 1
#> 700 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.85e-12 20 1
#> 701 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.71e-12 20 1
#> 702 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.30e-12 20 1
#> 703 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.32e-12 20 1
#> 704 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.89e-12 20 1
#> 705 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.08e-12 20 1
#> 706 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.09e-12 20 1
#> 707 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.95e-12 20 1
#> 708 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.00e-12 20 1
#> 709 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.22e-12 20 1
#> 710 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.13e-11 20 1
#> 711 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.58e-11 20 1
#> 712 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.33e-12 20 1
#> 713 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.73e-12 20 1
#> 714 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.36e-12 20 1
#> 715 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.95e-12 20 1
#> 716 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.24e-12 20 1
#> 717 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.01e-12 20 1
#> 718 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.78e-12 20 1
#> 719 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.01e-14 20 1
#> 720 +1.998208529e+00 +5.516e-06 36 1.00e+00 2.30e-12 20 1
#> 721 +1.998208529e+00 +5.516e-06 36 1.00e+00 8.54e-13 20 1
#> 722 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.86e-12 20 1
#> 723 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.35e-12 20 1
#> 724 +1.998208529e+00 +5.516e-06 36 1.00e+00 4.73e-12 20 1
#> 725 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.01e-12 20 1
#> 726 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.66e-13 20 1
#> 727 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.55e-12 20 1
#> 728 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.72e-13 20 1
#> 729 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.95e-12 20 1
#> 730 +1.998208529e+00 +5.516e-06 36 1.00e+00 5.00e-12 20 1
#> 731 +1.998208529e+00 +5.516e-06 36 1.00e+00 9.47e-13 20 1
#> 732 +1.998208529e+00 +5.516e-06 36 1.00e+00 6.06e-12 20 1
#> 733 +1.998208529e+00 +5.516e-06 36 1.00e+00 7.21e-12 20 1
#> 734 +1.998208529e+00 +5.516e-06 36 1.00e+00 3.50e-12 20 1
#> 735 +1.998208529e+00 +5.516e-06 36 1.00e+00 1.18e-11 20 1
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#> 954 +1.998208359e+00 +5.396e-06 36 1.00e+00 4.12e-12 20 1
#> 955 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.12e-12 20 1
#> 956 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.04e-11 20 1
#> 957 +1.998208359e+00 +5.396e-06 36 1.00e+00 8.38e-12 20 1
#> 958 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.15e-12 20 1
#> 959 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.86e-12 20 1
#> 960 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.18e-11 20 1
#> 961 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.32e-11 20 1
#> 962 +1.998208359e+00 +5.396e-06 36 1.00e+00 8.12e-12 20 1
#> 963 +1.998208359e+00 +5.396e-06 36 1.00e+00 7.02e-12 20 1
#> 964 +1.998208359e+00 +5.396e-06 36 1.00e+00 6.09e-12 20 1
#> 965 +1.998208359e+00 +5.396e-06 36 1.00e+00 5.21e-12 20 1
#> 966 +1.998208359e+00 +5.396e-06 36 1.00e+00 2.55e-12 20 1
#> 967 +1.998208359e+00 +5.396e-06 36 1.00e+00 7.31e-12 20 1
#> 968 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.26e-11 20 1
#> 969 +1.998208359e+00 +5.396e-06 36 1.00e+00 7.81e-12 20 1
#> 970 +1.998208359e+00 +5.396e-06 36 1.00e+00 4.99e-12 20 1
#> 971 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.02e-11 20 1
#> 972 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.50e-12 20 1
#> 973 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.74e-12 20 1
#> 974 +1.998208359e+00 +5.396e-06 36 1.00e+00 2.16e-12 20 1
#> 975 +1.998208359e+00 +5.396e-06 36 1.00e+00 6.40e-13 20 1
#> 976 +1.998208359e+00 +5.396e-06 36 1.00e+00 5.87e-13 20 1
#> 977 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.54e-12 20 1
#> 978 +1.998208359e+00 +5.396e-06 36 1.00e+00 8.25e-13 20 1
#> 979 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.42e-12 20 1
#> 980 +1.998208359e+00 +5.396e-06 36 1.00e+00 4.50e-12 20 1
#> 981 +1.998208359e+00 +5.396e-06 36 1.00e+00 5.58e-12 20 1
#> 982 +1.998208359e+00 +5.396e-06 36 1.00e+00 6.35e-12 20 1
#> 983 +1.998208359e+00 +5.396e-06 36 1.00e+00 5.40e-12 20 1
#> 984 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.98e-12 20 1
#> 985 +1.998208359e+00 +5.396e-06 36 1.00e+00 8.82e-12 20 1
#> 986 +1.998208359e+00 +5.396e-06 36 1.00e+00 9.41e-12 20 1
#> 987 +1.998208359e+00 +5.396e-06 36 1.00e+00 4.87e-12 20 1
#> 988 +1.998208359e+00 +5.396e-06 36 1.00e+00 9.22e-12 20 1
#> 989 +1.998208359e+00 +5.396e-06 36 1.00e+00 5.63e-13 20 1
#> 990 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.96e-12 20 1
#> 991 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.13e-12 20 1
#> 992 +1.998208359e+00 +5.396e-06 36 1.00e+00 2.08e-12 20 1
#> 993 +1.998208359e+00 +5.396e-06 36 1.00e+00 3.35e-12 20 1
#> 994 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.19e-12 20 1
#> 995 +1.998208359e+00 +5.396e-06 36 1.00e+00 2.56e-13 20 1
#> 996 +1.998208359e+00 +5.396e-06 36 1.00e+00 2.41e-13 20 1
#> 997 +1.998208359e+00 +5.396e-06 36 1.00e+00 2.86e-12 20 1
#> 998 +1.998208359e+00 +5.396e-06 36 1.00e+00 5.48e-13 20 1
#> 999 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.75e-12 20 1
#> 1000 +1.998208359e+00 +5.396e-06 36 1.00e+00 1.85e-12 20 1
#> Optimization took 668.76 seconds.#> Warning in mixsqp::mixsqp(A, w, pi_init, control = control): Failed to converge within iterations limit. If "maxiter.sqp" is
#> small, consider increasing it. Otherwise, convergence failure is
#> typically a numerical issue remedied by increasing "eps" slightly,
#> at the cost of slightly less accurate solution; see help(mixsqp).
#> An issue report may also be submitted to
#> https://github.com/stephenslab/mixsqp/issues, accompanied by an
#> .rds or .RData file containing the mixsqp inputs. If these inputs
#> are not accessible, an .RData file containing the inputs can be
#> generated by setting options(mixsqp.debug.mode = TRUE) before
#> running mixsqp.#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
sessionInfo()#> R version 3.5.3 (2019-03-11)
#> Platform: x86_64-apple-darwin15.6.0 (64-bit)
#> Running under: macOS Mojave 10.14.6
#>
#> Matrix products: default
#> BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
#>
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] forcats_0.4.0 stringr_1.4.0 dplyr_0.8.0.1 purrr_0.3.2
#> [5] readr_1.3.1 tidyr_0.8.3 tibble_2.1.1 ggplot2_3.2.0
#> [9] tidyverse_1.2.1
#>
#> loaded via a namespace (and not attached):
#> [1] tidyselect_0.2.5 xfun_0.6 ashr_2.2-50
#> [4] haven_2.1.1 lattice_0.20-38 colorspace_1.4-1
#> [7] generics_0.0.2 htmltools_0.3.6 yaml_2.2.0
#> [10] rlang_0.4.2 mixsqp_0.3-31 pillar_1.3.1
#> [13] glue_1.3.1 withr_2.1.2 modelr_0.1.5
#> [16] readxl_1.3.1 munsell_0.5.0 gtable_0.3.0
#> [19] workflowr_1.2.0 cellranger_1.1.0 rvest_0.3.4
#> [22] evaluate_0.13 labeling_0.3 knitr_1.22
#> [25] invgamma_1.1 irlba_2.3.3 broom_0.5.1
#> [28] Rcpp_1.0.1 scales_1.0.0 backports_1.1.3
#> [31] jsonlite_1.6 truncnorm_1.0-8 fs_1.2.7
#> [34] hms_0.4.2 digest_0.6.18 stringi_1.4.3
#> [37] ebnm_0.1-21 grid_3.5.3 rprojroot_1.3-2
#> [40] cli_1.1.0 tools_3.5.3 magrittr_1.5
#> [43] lazyeval_0.2.2 crayon_1.3.4 whisker_0.3-2
#> [46] pkgconfig_2.0.2 Matrix_1.2-15 SQUAREM_2017.10-1
#> [49] xml2_1.2.0 lubridate_1.7.4 assertthat_0.2.1
#> [52] rmarkdown_1.12 httr_1.4.0 rstudioapi_0.10
#> [55] R6_2.4.0 nlme_3.1-137 git2r_0.25.2
#> [58] compiler_3.5.3