R Under development (unstable) (2024-08-21 r87038 ucrt) -- "Unsuffered Consequences" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 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. > #### dt() : Density of t-dist ----------- was Martin's ~/R/MM/NUMERICS/dpq-functions/dt-ex.R (since 2002) > #### ==-----================= > > ### -> ...../MM/..../pt-ex.R for the cumulative dist. density > ### -> ...../MM/..../qt-ex.R for its inverse > (doExtras <- DPQ:::doExtras()) [1] FALSE > (noLdbl <- (.Machine$sizeof.longdouble <= 8)) ## TRUE when --disable-long-double [1] FALSE > options(width = 100, nwarnings = 1e5) > > ###============================================================================ > ###========= 1. Numerics about the integration constant for nu -> Inf ========= > ###============================================================================ > > ### The simple naive gamma ratio -- breaks down numerically for nu ~= 10^17 > lg.ratio <- function(nu) lgamma((nu+1)/2)- lgamma(nu/2) > gratio <- function(nu) exp(lg.ratio(nu)) > > ## Factor(nu) in dt() density : > ## c(nu) = gamma((nu+1)/2) / (gamma(nu/2) * sqrt(nu)) ---> 1/sqrt(2) > > ### and the same with log(c(nu)) {for direct log density!} > ldt.fact.naive <- function(df) lgamma((df+1)/2)- lgamma(df/2) - log(df)/2 > dt.fact.naive <- function(df) exp(ldt.fact.naive(df)) > > dt.fact0 <- function(df) (1 - (1 - 1/(8*df))/(4*df)) / sqrt(2) > > dt.fact <- function(df, cut.val = 200) { + ## Use asymptotic expansion only for df -> oo + ifelse(df > cut.val, + dt.fact0 (df), + dt.fact.naive(df)) + } > > ## on this range, they look already the same! > curve(dt.fact.naive(x), 5, 1000) ; abline(h= sqrt(1/2), col = "gray") > curve(dt.fact0 (x), 5, 1000, col = 2, add = TRUE) > ## still : > curve(dt.fact (x), 100, 1e7, log = 'x') > curve(dt.fact0(x), 100, 1e7, col = 2, add = TRUE) > ## look at difference > p.dtdiff <- function(df, log='x', cut = 5000) + { + dd <- dt.fact(df, cut= cut) - dt.fact.naive(df) + plot(df, dd, ylab = "dt.fact(*, cut) - dt.fact.naive()", + ylim = quantile(dd, c(.001,.999)), + type = 'l', col = 2, log = log) + abline(v=cut, col = "green", lty = 2) + abline(h=0, col = "gray", lty=3) + } > p.dtdiff(df = seq(5,1000, by=1/2), log= "") # all "zero" > p.dtdiff(df = 2^seq(9,16, len=10001), cut = 800) > ## --> at cut: bias, then noise from about 5000 -- good pic! > ## maximally about 6e-11 > > p.dtdiff(df = 2^seq( 9,30, len=10001))## noise up to 2e-6 > p.dtdiff(df = 2^seq(20,45, len=10001))## noise up to 0.06 > p.dtdiff(df = 2^seq(20,50, len=10001))## break down after 1e14 > > > ldt.fact0 <- function(df) { + ## formula from Maple (instead of Abramowitz & Stegun): + t <- 1/(2*df) + -.5* log(2) + t * (-1/2 + t*t/3) + } > ldt.fact1 <- function(df) { + ## formula from Maple -- 1 term more than ldt.fact0 : + t <- 1/(2*df) + -.5* log(2) + t * (-1/2 + t*t *(1/3 - 8/5*t*t)) + } > ldt.fact <- function(df, cut.val = 200) { + ## Use asymptotic expansion only for df -> oo + ifelse(df > cut.val, + ldt.fact1 (df), + ldt.fact.naive(df)) + } > > ## at the very beginning: difference > curve(ldt.fact.naive(x), .5, 10000, log = 'x', n = 2001) > abline(h= -log(2)/2, col = "gray") > curve(ldt.fact0 (x), col = 2, add = TRUE, n = 2001) > curve(ldt.fact1 (x), col = 3, add = TRUE, n = 2001) > > ## fact1 is `better' : > curve(abs(ldt.fact0(x) - ldt.fact.naive(x)), 2, 10000, n = 2001, log='x', + main = "Absolute error") > curve(abs(ldt.fact1(x) - ldt.fact.naive(x)), col = 3, add = TRUE, n = 2001) > ## log-zooming: -- see very small l*naive() error coming in as well > curve(abs(ldt.fact0(x) - ldt.fact.naive(x)), 2, 10000, log = 'xy', n = 2001, + main = "Absolute error") > curve(abs(ldt.fact1(x) - ldt.fact.naive(x)), col = 3, add = TRUE, n = 2001) > ## rel.err: ~ the same > curve(abs(1 - ldt.fact0(x) / ldt.fact.naive(x)), 2, 10000, log = 'xy', n = 2001, + main = "Relative error") > curve(abs(1 - ldt.fact1(x) / ldt.fact.naive(x)), col = 3, add = TRUE, n = 2001) > > ## on this range, they look the same > curve(ldt.fact.naive(x), 10, 1e10, log = 'x', n = 2001) > abline(h= -log(2)/2, col = "gray") > curve(ldt.fact0 (x), col = 2, add = TRUE, n = 2001) > curve(ldt.fact1 (x), col = 3, add = TRUE, n = 2001) > > ## now watch breakdown of naive: > curve(ldt.fact.naive(x), 10, 1e18, log = 'x', n = 2001)## 1e14 ! > > curve(ldt.fact.naive(x), 10, 1e18, log = 'x', n = 2001, ylim = c(-.35,-.34)) > ## even from 1e9 > curve(ldt.fact0 (x), col = 2, add = TRUE, n = 2001) > curve(ldt.fact1 (x), col = 3, add = TRUE, n = 2001) > > ### note dt.1() checking below suggest to use ldt.fact1() down to about 100! > > > ### Use maple to get much longer expansion: > ### /u/maechler/maple/gamma-expansions.txt > ### /u/maechler/maple/gamma-exp2.txt > rr <- seq(0,1.2, by = 1/128) > > ## c(nu) := GAMMA((nu+1)/2) / GAMMA(nu/2) * sqrt(2 / nu) { = above * sqrt(2) } > ## r := 1/(4 * nu) > ## c() = 1 - r + r*r/2 + 5/2*r^3 - 21/8*r^4 - 399/8*r^5 + 869/16*r^6 > ## + 39325/16*r^7 - 334477/128*r^8 > > cs0 <- function(r) { + 1 - r + r*r/2 + 5/2*r^3 - 21/8*r^4 - 399/8*r^5 + + + 869/16*r^6 + 39325/16*r^7 - 334477/128*r^8 + } > > cs <- function(r) { + ## == cs0 but in Horner form ( + coefficients factored a bit) + 1 + r * (-1 + r/2 * + (1 + r * + (5 + r/4 * + (-21 + r * + (-399 + r/2 * + (869 + r * (39325 - 334477/8 *r))))))) + } > > all.equal(cs0(rr), cs(rr), tol = 1e-12) [1] TRUE > > > ## s := 1/(8 * nu) == r / 2 > cs2 <- function(s) { + ## == cs(), using s = r/2 = 1/(8 nu) + 1 + 2*s * (-1 + s * + (1 + s * + (10 + s * + (-21 + s * 2 * + (-399 + s * (869 + s * (2*39325 - 334477/2 *s))))))) + } > > all.equal(cs(rr), cs2(rr/2), tol = 1e-12)# TRUE [1] TRUE > > ### Now using many more terms -- (thanks to maple): > ### at the end we see it does not help at all: These terms "diverge"... > css0 <- function(s) { + 1 + 2*s*(-1+ s* ## Set of prime factors; "^" := at least ^2 + (1+ s* + (10+ s* ## # 2 5 + (-21+ s* ## # 3 7 + (-798+ s* ## # 2 3 7 19 + (1738+ s* ## # 2 11 79 + (157300+ s* ## # 2^ 5^ 11^ 13 + (-334477+ s* ## # 11 13 2339 + (-57434806+ s* ## # 2 11 13 17 11813 + (119394366+ s* ## # 2 3 7 13 17 19 677 + (33601489740+ s* ## # 2^3^5 7 13 17 19 29 73 + (-68858583810+ s* ## # 2 3 5 17 19 23 509 607 + (-28797022447980+ s*# 2^3 5 17 19 23 3607 17911 + (58526378304180+ s*# 2^3 5 17 19 23 131301607 + 340096557365034000# 2^3 5^ 17 19 23 29^ 71 127781 + )))))))))))))) + } > css <- function(s) { + 1 + 2*s*(-1+ s* ## Set of prime factors; "^" := at least ^2 + (1+ s* + (10+ s* ## # 2 5 + (-21+ s* ## # 3 7 + (-798+ s* ## # 2 3 7 19 + (1738+ s* ## # 2 11 79 + (157300+ s* ## # 2^ 5^ 11^ 13 + (-334477+ s* 2*17* ## # 11 13 2339 + (-1689259+ s* 3*19* ## # 2 11 13 17 11813 + ( 61607 + s* 5* ## # 2 3 7 13 17 19 677 + (3467646 + s* 23* ## # 2^3^5 7 13 17 19 29 73 + (-308963 + s* 2* ## # 2 3 5 17 19 23 509 607 + (-64604977+ s* ## # 2^3 5 17 19 23 3607 17911 + (131301607+ s* ## # 2^3 5 17 19 23 131301607 + 76299312910 ## # 2^3 5^ 17 19 23 29^ 71 127781 + )))))))))))))) + } > > > all.equal(cs(rr), css(rr/2))# not at all! [1] "Mean relative difference: 11126122866" > all.equal(css(rr/2), css0(rr/2))## neither 8.99 [1] "Mean relative difference: 8.996686" > > > p.cs <- function(nu, col = 1:k) + { + ## Purpose: plotting + ## ------------------------------------------------------------------------- + ## Author: Martin Maechler, Date: 5 Apr 2002, 20:42 + + r <- 1/(4*nu) + s <- r/2 + mat <- cbind(dt.fact.naive(nu)*sqrt(2) + ,dt.fact0 (nu)*sqrt(2) + ,cs0(r) + ,cs (r) + ,cs2 (s) + ,css0(s) + ,css (s) + ) + k <- ncol(mat) + ## one sees an initial departure ( nu < 3) + matplot(nu, mat, type = 'b', log = 'x', col = col, + ylim = c(0.8, 1))# rrange(mat))## + legend(quantile(nu,.3), mean(par("usr")[3:4]), + c("dt.fact.naive", "dt.fact0", "cs0", "cs", "cs2", "css0", "css"), + lty=1:k, col=col, pch = paste(1:k)) + mtext("r = 1 / (4 nu)", line = 2) + pr <- 10^pretty(log10(r)) + axis(3, at = 1/(4*pr), labels = formatC(pr,dig=1)) + invisible(list(nu=nu,mat=mat, pr=pr)) + } > > (dfs <- 2^seq(0,20, by = 1/16))[1:10] [1] 1.000000 1.044274 1.090508 1.138789 1.189207 1.241858 1.296840 1.354256 1.414214 1.476826 > ## different at the beginning ; the longer the series the *worse* !!!! > p.cs(dfs) > ## Now we see the breakdown of the naive dt.fact.0(): > p.cs(nu = 2^seq(0,64, by = 1/4)) > > ###-- Application to dt() : > > dt.naive <- function (x, df, log = FALSE) + { + n1h <- (df+1)/2 + rt <- sqrt(pi*df) + if(log) + lgamma(n1h) - lgamma(df/2) - log(rt) - n1h * log1p(x^2/df) + else ## following worse than exp(..above..) ? + gamma(n1h)/(gamma(df/2) * rt) * (1 + x^2/df)^-n1h + } > > dt.1 <- function (x, df, log = FALSE, cuts = c(log=100, 1000)) + { + ## Use asymptotic expansion for df -> oo + n1h <- (df+1)/2 + if(log) + ldt.fact(df, cut= cuts[1]) -.5 *log(pi) - n1h * log1p(x^2/df) + else + dt.fact(df, cut=cuts[2])/sqrt(pi) * (1 + x^2/df)^-n1h + } > > curve(dt(x=9, df=x), 1, 100) > curve(dt(x=9, df=x), 1, 100, log = 'x') > curve(dt (x=9, df=x, log = TRUE), 1, 400, log = 'x') > ## no visibile difference: > curve(dt.naive(x=9, df=x, log = TRUE), 1, 400, log = 'x', add = TRUE, col=2) > > curve(dt (x=9, df=x, log = TRUE),.25,1000, log = 'x') > ## no visibile difference: > curve(dt.naive(x=9, df=x, log = TRUE),.25,1000, log = 'x', add = TRUE, col=2) > > ### log density comparison : > > ### "smallish" nu : > (dfs <- seq(1,500, by = 1/4))[1:10] [1] 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 > plot(dfs, + dt (9,df=dfs, log = TRUE) - + dt.naive(9,df=dfs, log = TRUE), type = 'l', col = 2) > ## increasing upto 6e-13 (1000); 4e-12 (5000) > lines(dfs, + dt (9,df=dfs, log = TRUE) - + dt.1(9,df=dfs, log = TRUE, cuts = 50), col = 3)# 50 too small! > lines(dfs, + dt (9,df=dfs, log = TRUE) - + dt.1(9,df=dfs, log = TRUE, cuts = 80), col = 4) > > ### "medium" nu : > (dfs <- seq(200, 10000, by = 1/4))[1:10] [1] 200.00 200.25 200.50 200.75 201.00 201.25 201.50 201.75 202.00 202.25 > plot(dfs, + dt (9,df=dfs, log = TRUE) - + dt.naive(9,df=dfs, log = TRUE), type = 'l', col = 2) > ## increasing upto 1e-11 > lines(dfs, + dt (9,df=dfs, log = TRUE) - + dt.1(9,df=dfs, log = TRUE, cuts = 80), col = 4) > > ## larger -- using log nu > (dfs <- 2^seq(15, 25, len = 2001))[1:10] [1] 32768.00 32881.76 32995.92 33110.47 33225.42 33340.77 33456.53 33572.68 33689.23 33806.19 > plot(dfs, + dt (9,df=dfs, log = TRUE) - + dt.naive(9,df=dfs, log = TRUE), type = 'l', log = 'x') > ## increasing upto 1e-9 (nu = 1e6), 6e-8 (nu= 4e+7) > lines(dfs, + dt (9,df=dfs, log = TRUE) - + dt.1(9,df=dfs, log = TRUE, cuts = 80), col = 4) > > ## LARGE for break down of dt.naive(): > dfs <- 2^seq(15, 64, len = 2001) > plot(dfs, ylim = 1e-5*c(-1,1), + dt (9,df=dfs, log = TRUE) - + dt.naive(9,df=dfs, log = TRUE), type = 'l', log = 'x') > lines(dfs, + dt (9,df=dfs, log = TRUE) - + dt.1(9,df=dfs, log = TRUE, cuts = 80), col = 4) > > ## log in y as well: -- nice pic: > require(sfsmisc) # mult.fig(), p.datum(), .. Loading required package: sfsmisc > dfs <- 2^seq(5, 64, len = 2001) > op <- mult.fig(3, main = "dt(x, df -> oo) testing")$old.par > for(x in c(-9, 0, 90)) { + plot(dfs, main = paste("x = ", format(x)), ylim = c(1e-16, 1e+2), + abs(dt (x,df=dfs, log = TRUE) - + dt.naive(x,df=dfs, log = TRUE)), type = 'l', log = 'xy') + lines(dfs, ## many 0's --> missing for y-log + abs(dt (x,df=dfs, log = TRUE) - + dt.1(x,df=dfs, log = TRUE, cuts = 80)), col = 4) + } Warning messages: 1: In xy.coords(x, y, xlabel, ylabel, log) : 16 y values <= 0 omitted from logarithmic plot 2: In xy.coords(x, y, xlabel, ylabel, log) : 77 y values <= 0 omitted from logarithmic plot > p.datum(); mtext(file.path(getwd(),"dt-ex.R"), + side = 1, line = 2.5, adj = 1, cex=.8) > par(op) > > > ###============================================================================ > ###========= 2. t - Distributions, scaled to Variance == 1 : > ###============================================================================ > > ###--- t-distributions -- scaled to Var = 1 : > p.tdensity <- + function(nu, nout = 501, add = FALSE, col = 2, lty = 1, + xmax = if(add) par("usr")[2] else 6, + xmin = if(add) par("usr")[1] else -xmax, + main = substitute(t[n] * " - distribution, scaled to Var = 1", + list(n = nu)), + ylim = c(0, max(y)), ...) + { + if(nu <= 2) stop("Var(t_{nu}) = oo for nu <= 2") + v <- if(nu < 1/.Machine$double.eps) nu / (nu - 2) else 1 ## = Var(t[nu]) + s <- sqrt(v) + x <- seq(xmin,xmax, len = nout) + y <- dt(x * s, df = nu) * s + if(add) + lines(x, y, col = col, lty = lty) + else { + plot(x, y, type = "l", col = col, lty = lty, ylim = ylim, + main = main, ...) + abline(h = 0, lty = 3, col = "gray20") + } + + invisible(list(x=x, y=y)) + } > > leg.dens <- function(x = u[1] + (u[2]-u[1])/32, + y = u[4] - (u[4]-u[3])/32, lty = 1) + { + abline(h = 0, lty = 3, col = "gray20") + u <- par("usr") + legend(x, y, paste("nu =",nus), lty = lty, col = cols) + p.datum() + mtext("/u/maechler/R/MM/NUMERICS/dpq-functions/dt-ex.R", + side=4, adj=1, cex=.75) + } > > > nus <- c(2.2, 2.5, 3:5,7,10, Inf) > pal <- palette() > pal[pal == "white"] <- "gray70" > old.pal <- palette(pal) > > cols <- 1+ seq(nus)# or something better > > if(!dev.interactive(orNone=TRUE)) ## evaluate manually : + pdf("dt-ex_t-dens.pdf") > > p.tdensity(nu = nus[1], col = cols[1], + main = expression(t[nu] * " - distributions, scaled to Var = 1")) > for(j in 2:length(nus)) + p.tdensity(nu = nus[j], add = TRUE, col = cols[j]) > leg.dens() > > ## Only close to y = 0: > p.tdensity(nu = nus[1], col = cols[1], ylim = c(0, 0.02), xmax = 12, + main = expression(t[nu] * " - distributions, scaled to Var = 1")) > for(j in 2:length(nus)) + p.tdensity(nu = nus[j], add = TRUE, col = cols[j], lty=j) > leg.dens(lty = seq(nus)) > > ## y ~ 0 -- use log-log-scale and x > 0 > xl <- 0.1; xU <- 50 > p.tdensity(nu = nus[1], col = cols[1], ylim = c(1e-8, 1), + xmin=xl, xmax = xU, log="xy", + main = expression(t[nu] * + " - distributions, scaled to Var = 1; log-log scale, x > 0")) > for(j in 2:length(nus)) + p.tdensity(nu = nus[j], add = TRUE, col = cols[j], xmin=xl,xmax=xU) > leg.dens(xl, 0.01) > > ### Now the same graphic for the usual unscaled t's: > x <- seq(-6,6, len = 201) > matplot(x, outer(x, nus, dt), type = "l", lty = 1, col = cols, + main = expression(t[nu] * " - distributions (unscaled)")) > leg.dens() > > palette(old.pal)# restoring to original palette > > > ## Really small df < 1 and even df << 1 ===================== > ## ======----- ======= > ## notably as stirlerr(df) used lgamma(1+df) ... > > ## ====> for now in ~/R/Pkgs/Rmpfr/tests/special-fun-ex.R > ## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > > ###------------------- Non-central ------------------------------- > > ## source("t-nonc-fn.R") ## __ DONE: Replaced by library(DPQ) > require(DPQ) Loading required package: DPQ > ## > if(!require(sfsmisc)) + lseq <- function (from, to, length) + 2^seq(log2(from), log2(to), length.out = length) > > tst <- c(1e-12, 1e-13, 1e-14, 1e-15, 1e-16, 1e-17, 0) > dt(tst, df = 16, ncp=1) [1] 0.2382217 0.2382217 0.2382217 0.2382217 0.2382217 0.2382217 0.2382217 > ## [1] 0.2380318 0.2398082 0.2220446 0.0000000 0.0000000 0.0000000 0.2382217 > > x <- lseq(1e-3, 1e-33, length= 301) > > plot(x, dt(x, df=16, ncp=1 ), type = "o", cex=.5, log = "x") > plot(x, dt(x, df=16, ncp=0.1), type = "o", cex=.5, log = "x") > plot(x, dt(x, df= 3, ncp=0.1), type = "o", cex=.5, log = "x") > plot(x, dt(x, df= 3, ncp=0.1, log=TRUE), type = "o", cex=.5, log = "x") > plot(x, dt(x, df= 3, ncp=0.001), type = "o", cex=.5, log = "x") ## <- "noise" around 1e-8 > ## This shows that there's room for more improvement: > curve( dt(x, df= 3, ncp=0.001), 1e-20, 1.2e-3, log = "x", n=2^10)## ditto > curve( dt(x, df= 3, ncp=0.001), 1e-20, 1e-5, log = "x", n=2^10)## ditto > cc <- curve( dt(x, df= 3, ncp=0.001), 1e-8, 1e-5, log = "x", n=2^10)## ditto > ## --- but *NOT* a big problem: accuracy (rel.error) still around 10^-9 > plot(x, dt(x, df=.03, ncp=1), type = "o", cex=.5, log = "x") > > ## MM: Check the new direct formula dtR() -- notably with Rmpfr > require(Rmpfr) Loading required package: Rmpfr Loading required package: gmp Attaching package: 'gmp' The following objects are masked from 'package:sfsmisc': factorize, is.whole The following objects are masked from 'package:base': %*%, apply, crossprod, matrix, tcrossprod C code of R package 'Rmpfr': GMP using 64 bits per limb Attaching package: 'Rmpfr' The following object is masked from 'package:gmp': outer The following object is masked from 'package:DPQ': log1mexp The following objects are masked from 'package:stats': dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm The following objects are masked from 'package:base': cbind, pmax, pmin, rbind > stopifnot(all.equal(dntJKBf(mpfr(0, 64), 5,10), ## gave NaN + 3.66083172640611114864e-23, tolerance=1e-20)) > > dntM <- dntJKBf # from DPQ, should just work > > system.time(dt.5.10 <- dntM(mpfr(-4:4, 256), 5, 10))# 2.158 sec on lynne[2014]; 2023: 0.568 user system elapsed 1.25 0.00 1.25 > dt.5.10 ##--> heureka! 9 'mpfr' numbers of precision 256 bits [1] 2.60411193283363008816174203664672521049598232817191096334231768533123433930554e-29 [2] 1.402390045022762576904908969928231134641459245433370510245082462639551869912683e-28 [3] 1.423497061270720045959087598996775429320328607547260643299749804014121024358857e-27 [4] 5.449436753201393001156967930749166463526468918232281745544244816776279420757684e-26 [5] 3.660831726406111150918497564522165417454008321092157460964035675595080684479716e-23 [6] 1.035962495942093066639658406747234090777907965780567084318709388913711965340062e-16 [7] 2.85854048117620027304802327696150987469187879228812294414362851419136085231108e-10 [8] 3.65628559654324497017621253550780270928261249913747846398933155144922638545515e-6 [9] 0.0006233252495097859026032404406354378980224459220868988071467401913727754970112061 > > if(doExtras && dir.exists(M_dir <- "~/R/MM/NUMERICS/dpq-functions/t-nonc_mathematica")) + withAutoprint({ + ## compare with the Mathematica computations {documented to be "arbitrary exact"} + str(dtM.5.10 <- read.table(file.path(M_dir, "fp-noncent_x_5_10.out"), + row.names = 1, col.names=c("","dtM"), + colClasses="character")) + x.dtM <- rownames(dtM.5.10) + (dtM.5.10 <- as(dtM.5.10[,"dtM"], "mpfr")) + system.time(dt.5.10 <- dntM(mpfr(x.dtM, 256), 5, 10))# {M=1000} --> 5.1s on lynne{2021} (21.7s lynne{'14}) + all.equal(dt.5.10, dtM.5.10) # TRUE + all.equal(dt.5.10, dtM.5.10, tol = 1e-15) # TRUE + all.equal(dt.5.10, dtM.5.10, tol = 1e-20) # TRUE + all.equal(dt.5.10, dtM.5.10, tol = 1e-30) # "Mean relative difference: 3.664....e-23" + }) > > ### --- this is from 2006 .. back to 2002 > > log.dnt <- function(x, df, ncp) { + ## dt(*, ncp) { ~/R/D/r-devel/R/src/nmath/dnt.c } + ## uses pt(*, ncp) internally -- for x !=0 + stopifnot(length(df) == 1, length(ncp) == 1) + + r <- x + is.sml <- abs(x) < sqrt(df * .Machine$double.eps) + xb <- x[ib <- !is.sml] + pt1 <- pt(xb*sqrt((df+2)/df), df=df+2, ncp=ncp) + pt2 <- pt(xb, df=df, ncp=ncp) + r[ib] <- log(df) - log(abs(xb)) + log(abs(pt1 - pt2)) + r[is.sml] <- dt(0, df = df, ncp = ncp, log = TRUE) + r + } > stopifnot(all.equal(log.dnt(x, df=3, ncp=0.1), + dt (x, df=3, ncp=0.1, log = TRUE))) > > plot(x, log.dnt(x, df= 3, ncp=0.001), type = "o", cex=.5, log = "x") > > ldt <- log.dnt(x, df= 3, ncp=0.001) > (ry <- rrange(ldt, 2)) + 1.00088935 # -1.08e-9 2.37e-9 [1] 3.764902e-10 3.764902e-10 > plot(x, ldt, type = "o", cex=.5, log = "x", ylim = ry) > > x <- lseq(1e-10, 1e-4, 2001) > plot (x, log.dnt(x, df= 3, ncp= 1e-5), type = "l", cex=.5, log = "x") > ## tons of pnt() "full precision was not achieved" warnings: > lines(x, log.dnt(x, df= 3, ncp= 1e-7), col = "blue") > lines(x, dt(x, df= 3, log=TRUE), col = 2)## central t : ncp = 0; has no problem > > df <- 3 > ncp <- 0.1 > > dnt.stats <- function(x, df, ncp) { + ## Purpose: + ## ---------------------------------------------------------------------- + ## Arguments: as dt() + ## ---------------------------------------------------------------------- + ## Author: Martin Maechler, Date: 19 May 2006, 12:25 + + ## simple vectorization: + n <- max(length(x), length(df), length(ncp)) + if(n > 1) { + x <- rep(x, length = n) + df <- rep(df, length = n) + ncp <- rep(ncp, length = n) + } + ## The relevant quantity (whose abs|difference| needs to become accurate: + cbind(pt1 = pt(x*sqrt((df+2)/df), df=df+2, ncp=ncp), + pt2 = pt(x, df=df, ncp=ncp)) + } > > del.pt <- function(x, df, ncp) + pt(x*sqrt((df+2)/df), df=df+2, ncp=ncp) - pt(x, df=df, ncp=ncp) > > > cbind(x, dnt.stats(x, df = 3, ncp = 0.1)) x pt1 pt2 [1,] 1.000000e-10 0.4601722 0.4601722 [2,] 1.006932e-10 0.4601722 0.4601722 [3,] 1.013911e-10 0.4601722 0.4601722 [4,] 1.020939e-10 0.4601722 0.4601722 [5,] 1.028016e-10 0.4601722 0.4601722 [6,] 1.035142e-10 0.4601722 0.4601722 [7,] 1.042317e-10 0.4601722 0.4601722 [8,] 1.049542e-10 0.4601722 0.4601722 [9,] 1.056818e-10 0.4601722 0.4601722 [10,] 1.064143e-10 0.4601722 0.4601722 [11,] 1.071519e-10 0.4601722 0.4601722 [12,] 1.078947e-10 0.4601722 0.4601722 [13,] 1.086426e-10 0.4601722 0.4601722 [14,] 1.093956e-10 0.4601722 0.4601722 [15,] 1.101539e-10 0.4601722 0.4601722 [16,] 1.109175e-10 0.4601722 0.4601722 [17,] 1.116863e-10 0.4601722 0.4601722 [18,] 1.124605e-10 0.4601722 0.4601722 [19,] 1.132400e-10 0.4601722 0.4601722 [20,] 1.140250e-10 0.4601722 0.4601722 [21,] 1.148154e-10 0.4601722 0.4601722 [22,] 1.156112e-10 0.4601722 0.4601722 [23,] 1.164126e-10 0.4601722 0.4601722 [24,] 1.172195e-10 0.4601722 0.4601722 [25,] 1.180321e-10 0.4601722 0.4601722 [26,] 1.188502e-10 0.4601722 0.4601722 [27,] 1.196741e-10 0.4601722 0.4601722 [28,] 1.205036e-10 0.4601722 0.4601722 [29,] 1.213389e-10 0.4601722 0.4601722 [30,] 1.221800e-10 0.4601722 0.4601722 [31,] 1.230269e-10 0.4601722 0.4601722 [32,] 1.238797e-10 0.4601722 0.4601722 [33,] 1.247384e-10 0.4601722 0.4601722 [34,] 1.256030e-10 0.4601722 0.4601722 [35,] 1.264736e-10 0.4601722 0.4601722 [36,] 1.273503e-10 0.4601722 0.4601722 [37,] 1.282331e-10 0.4601722 0.4601722 [38,] 1.291219e-10 0.4601722 0.4601722 [39,] 1.300170e-10 0.4601722 0.4601722 [40,] 1.309182e-10 0.4601722 0.4601722 [41,] 1.318257e-10 0.4601722 0.4601722 [42,] 1.327394e-10 0.4601722 0.4601722 [43,] 1.336596e-10 0.4601722 0.4601722 [44,] 1.345860e-10 0.4601722 0.4601722 [45,] 1.355189e-10 0.4601722 0.4601722 [46,] 1.364583e-10 0.4601722 0.4601722 [47,] 1.374042e-10 0.4601722 0.4601722 [48,] 1.383566e-10 0.4601722 0.4601722 [49,] 1.393157e-10 0.4601722 0.4601722 [50,] 1.402814e-10 0.4601722 0.4601722 [51,] 1.412538e-10 0.4601722 0.4601722 [52,] 1.422329e-10 0.4601722 0.4601722 [53,] 1.432188e-10 0.4601722 0.4601722 [54,] 1.442115e-10 0.4601722 0.4601722 [55,] 1.452112e-10 0.4601722 0.4601722 [56,] 1.462177e-10 0.4601722 0.4601722 [57,] 1.472313e-10 0.4601722 0.4601722 [58,] 1.482518e-10 0.4601722 0.4601722 [59,] 1.492794e-10 0.4601722 0.4601722 [60,] 1.503142e-10 0.4601722 0.4601722 [61,] 1.513561e-10 0.4601722 0.4601722 [62,] 1.524053e-10 0.4601722 0.4601722 [63,] 1.534617e-10 0.4601722 0.4601722 [64,] 1.545254e-10 0.4601722 0.4601722 [65,] 1.555966e-10 0.4601722 0.4601722 [66,] 1.566751e-10 0.4601722 0.4601722 [67,] 1.577611e-10 0.4601722 0.4601722 [68,] 1.588547e-10 0.4601722 0.4601722 [69,] 1.599558e-10 0.4601722 0.4601722 [70,] 1.610646e-10 0.4601722 0.4601722 [71,] 1.621810e-10 0.4601722 0.4601722 [72,] 1.633052e-10 0.4601722 0.4601722 [73,] 1.644372e-10 0.4601722 0.4601722 [74,] 1.655770e-10 0.4601722 0.4601722 [75,] 1.667247e-10 0.4601722 0.4601722 [76,] 1.678804e-10 0.4601722 0.4601722 [77,] 1.690441e-10 0.4601722 0.4601722 [78,] 1.702159e-10 0.4601722 0.4601722 [79,] 1.713957e-10 0.4601722 0.4601722 [80,] 1.725838e-10 0.4601722 0.4601722 [81,] 1.737801e-10 0.4601722 0.4601722 [82,] 1.749847e-10 0.4601722 0.4601722 [83,] 1.761976e-10 0.4601722 0.4601722 [84,] 1.774189e-10 0.4601722 0.4601722 [85,] 1.786488e-10 0.4601722 0.4601722 [86,] 1.798871e-10 0.4601722 0.4601722 [87,] 1.811340e-10 0.4601722 0.4601722 [88,] 1.823896e-10 0.4601722 0.4601722 [89,] 1.836538e-10 0.4601722 0.4601722 [90,] 1.849269e-10 0.4601722 0.4601722 [91,] 1.862087e-10 0.4601722 0.4601722 [92,] 1.874995e-10 0.4601722 0.4601722 [93,] 1.887991e-10 0.4601722 0.4601722 [94,] 1.901078e-10 0.4601722 0.4601722 [95,] 1.914256e-10 0.4601722 0.4601722 [96,] 1.927525e-10 0.4601722 0.4601722 [97,] 1.940886e-10 0.4601722 0.4601722 [98,] 1.954339e-10 0.4601722 0.4601722 [99,] 1.967886e-10 0.4601722 0.4601722 [100,] 1.981527e-10 0.4601722 0.4601722 [101,] 1.995262e-10 0.4601722 0.4601722 [102,] 2.009093e-10 0.4601722 0.4601722 [103,] 2.023019e-10 0.4601722 0.4601722 [104,] 2.037042e-10 0.4601722 0.4601722 [105,] 2.051162e-10 0.4601722 0.4601722 [106,] 2.065380e-10 0.4601722 0.4601722 [107,] 2.079697e-10 0.4601722 0.4601722 [108,] 2.094112e-10 0.4601722 0.4601722 [109,] 2.108628e-10 0.4601722 0.4601722 [110,] 2.123244e-10 0.4601722 0.4601722 [111,] 2.137962e-10 0.4601722 0.4601722 [112,] 2.152782e-10 0.4601722 0.4601722 [113,] 2.167704e-10 0.4601722 0.4601722 [114,] 2.182730e-10 0.4601722 0.4601722 [115,] 2.197860e-10 0.4601722 0.4601722 [116,] 2.213095e-10 0.4601722 0.4601722 [117,] 2.228435e-10 0.4601722 0.4601722 [118,] 2.243882e-10 0.4601722 0.4601722 [119,] 2.259436e-10 0.4601722 0.4601722 [120,] 2.275097e-10 0.4601722 0.4601722 [121,] 2.290868e-10 0.4601722 0.4601722 [122,] 2.306747e-10 0.4601722 0.4601722 [123,] 2.322737e-10 0.4601722 0.4601722 [124,] 2.338837e-10 0.4601722 0.4601722 [125,] 2.355049e-10 0.4601722 0.4601722 [126,] 2.371374e-10 0.4601722 0.4601722 [127,] 2.387811e-10 0.4601722 0.4601722 [128,] 2.404363e-10 0.4601722 0.4601722 [129,] 2.421029e-10 0.4601722 0.4601722 [130,] 2.437811e-10 0.4601722 0.4601722 [131,] 2.454709e-10 0.4601722 0.4601722 [132,] 2.471724e-10 0.4601722 0.4601722 [133,] 2.488857e-10 0.4601722 0.4601722 [134,] 2.506109e-10 0.4601722 0.4601722 [135,] 2.523481e-10 0.4601722 0.4601722 [136,] 2.540973e-10 0.4601722 0.4601722 [137,] 2.558586e-10 0.4601722 0.4601722 [138,] 2.576321e-10 0.4601722 0.4601722 [139,] 2.594179e-10 0.4601722 0.4601722 [140,] 2.612161e-10 0.4601722 0.4601722 [141,] 2.630268e-10 0.4601722 0.4601722 [142,] 2.648500e-10 0.4601722 0.4601722 [143,] 2.666859e-10 0.4601722 0.4601722 [144,] 2.685344e-10 0.4601722 0.4601722 [145,] 2.703958e-10 0.4601722 0.4601722 [146,] 2.722701e-10 0.4601722 0.4601722 [147,] 2.741574e-10 0.4601722 0.4601722 [148,] 2.760578e-10 0.4601722 0.4601722 [149,] 2.779713e-10 0.4601722 0.4601722 [150,] 2.798981e-10 0.4601722 0.4601722 [151,] 2.818383e-10 0.4601722 0.4601722 [152,] 2.837919e-10 0.4601722 0.4601722 [153,] 2.857591e-10 0.4601722 0.4601722 [154,] 2.877398e-10 0.4601722 0.4601722 [155,] 2.897344e-10 0.4601722 0.4601722 [156,] 2.917427e-10 0.4601722 0.4601722 [157,] 2.937650e-10 0.4601722 0.4601722 [158,] 2.958012e-10 0.4601722 0.4601722 [159,] 2.978516e-10 0.4601722 0.4601722 [160,] 2.999163e-10 0.4601722 0.4601722 [161,] 3.019952e-10 0.4601722 0.4601722 [162,] 3.040885e-10 0.4601722 0.4601722 [163,] 3.061963e-10 0.4601722 0.4601722 [164,] 3.083188e-10 0.4601722 0.4601722 [165,] 3.104560e-10 0.4601722 0.4601722 [166,] 3.126079e-10 0.4601722 0.4601722 [167,] 3.147748e-10 0.4601722 0.4601722 [168,] 3.169567e-10 0.4601722 0.4601722 [169,] 3.191538e-10 0.4601722 0.4601722 [170,] 3.213661e-10 0.4601722 0.4601722 [171,] 3.235937e-10 0.4601722 0.4601722 [172,] 3.258367e-10 0.4601722 0.4601722 [173,] 3.280953e-10 0.4601722 0.4601722 [174,] 3.303695e-10 0.4601722 0.4601722 [175,] 3.326596e-10 0.4601722 0.4601722 [176,] 3.349654e-10 0.4601722 0.4601722 [177,] 3.372873e-10 0.4601722 0.4601722 [178,] 3.396253e-10 0.4601722 0.4601722 [179,] 3.419794e-10 0.4601722 0.4601722 [180,] 3.443499e-10 0.4601722 0.4601722 [181,] 3.467369e-10 0.4601722 0.4601722 [182,] 3.491403e-10 0.4601722 0.4601722 [183,] 3.515604e-10 0.4601722 0.4601722 [184,] 3.539973e-10 0.4601722 0.4601722 [185,] 3.564511e-10 0.4601722 0.4601722 [186,] 3.589219e-10 0.4601722 0.4601722 [187,] 3.614099e-10 0.4601722 0.4601722 [188,] 3.639150e-10 0.4601722 0.4601722 [189,] 3.664376e-10 0.4601722 0.4601722 [190,] 3.689776e-10 0.4601722 0.4601722 [191,] 3.715352e-10 0.4601722 0.4601722 [192,] 3.741106e-10 0.4601722 0.4601722 [193,] 3.767038e-10 0.4601722 0.4601722 [194,] 3.793150e-10 0.4601722 0.4601722 [195,] 3.819443e-10 0.4601722 0.4601722 [196,] 3.845918e-10 0.4601722 0.4601722 [197,] 3.872576e-10 0.4601722 0.4601722 [198,] 3.899420e-10 0.4601722 0.4601722 [199,] 3.926449e-10 0.4601722 0.4601722 [200,] 3.953666e-10 0.4601722 0.4601722 [201,] 3.981072e-10 0.4601722 0.4601722 [202,] 4.008667e-10 0.4601722 0.4601722 [203,] 4.036454e-10 0.4601722 0.4601722 [204,] 4.064433e-10 0.4601722 0.4601722 [205,] 4.092607e-10 0.4601722 0.4601722 [206,] 4.120975e-10 0.4601722 0.4601722 [207,] 4.149540e-10 0.4601722 0.4601722 [208,] 4.178304e-10 0.4601722 0.4601722 [209,] 4.207266e-10 0.4601722 0.4601722 [210,] 4.236430e-10 0.4601722 0.4601722 [211,] 4.265795e-10 0.4601722 0.4601722 [212,] 4.295364e-10 0.4601722 0.4601722 [213,] 4.325138e-10 0.4601722 0.4601722 [214,] 4.355119e-10 0.4601722 0.4601722 [215,] 4.385307e-10 0.4601722 0.4601722 [216,] 4.415704e-10 0.4601722 0.4601722 [217,] 4.446313e-10 0.4601722 0.4601722 [218,] 4.477133e-10 0.4601722 0.4601722 [219,] 4.508167e-10 0.4601722 0.4601722 [220,] 4.539416e-10 0.4601722 0.4601722 [221,] 4.570882e-10 0.4601722 0.4601722 [222,] 4.602566e-10 0.4601722 0.4601722 [223,] 4.634469e-10 0.4601722 0.4601722 [224,] 4.666594e-10 0.4601722 0.4601722 [225,] 4.698941e-10 0.4601722 0.4601722 [226,] 4.731513e-10 0.4601722 0.4601722 [227,] 4.764310e-10 0.4601722 0.4601722 [228,] 4.797334e-10 0.4601722 0.4601722 [229,] 4.830588e-10 0.4601722 0.4601722 [230,] 4.864072e-10 0.4601722 0.4601722 [231,] 4.897788e-10 0.4601722 0.4601722 [232,] 4.931738e-10 0.4601722 0.4601722 [233,] 4.965923e-10 0.4601722 0.4601722 [234,] 5.000345e-10 0.4601722 0.4601722 [235,] 5.035006e-10 0.4601722 0.4601722 [236,] 5.069907e-10 0.4601722 0.4601722 [237,] 5.105050e-10 0.4601722 0.4601722 [238,] 5.140437e-10 0.4601722 0.4601722 [239,] 5.176068e-10 0.4601722 0.4601722 [240,] 5.211947e-10 0.4601722 0.4601722 [241,] 5.248075e-10 0.4601722 0.4601722 [242,] 5.284453e-10 0.4601722 0.4601722 [243,] 5.321083e-10 0.4601722 0.4601722 [244,] 5.357967e-10 0.4601722 0.4601722 [245,] 5.395106e-10 0.4601722 0.4601722 [246,] 5.432503e-10 0.4601722 0.4601722 [247,] 5.470160e-10 0.4601722 0.4601722 [248,] 5.508077e-10 0.4601722 0.4601722 [249,] 5.546257e-10 0.4601722 0.4601722 [250,] 5.584702e-10 0.4601722 0.4601722 [251,] 5.623413e-10 0.4601722 0.4601722 [252,] 5.662393e-10 0.4601722 0.4601722 [253,] 5.701643e-10 0.4601722 0.4601722 [254,] 5.741165e-10 0.4601722 0.4601722 [255,] 5.780960e-10 0.4601722 0.4601722 [256,] 5.821032e-10 0.4601722 0.4601722 [257,] 5.861382e-10 0.4601722 0.4601722 [258,] 5.902011e-10 0.4601722 0.4601722 [259,] 5.942922e-10 0.4601722 0.4601722 [260,] 5.984116e-10 0.4601722 0.4601722 [261,] 6.025596e-10 0.4601722 0.4601722 [262,] 6.067363e-10 0.4601722 0.4601722 [263,] 6.109420e-10 0.4601722 0.4601722 [264,] 6.151769e-10 0.4601722 0.4601722 [265,] 6.194411e-10 0.4601722 0.4601722 [266,] 6.237348e-10 0.4601722 0.4601722 [267,] 6.280584e-10 0.4601722 0.4601722 [268,] 6.324119e-10 0.4601722 0.4601722 [269,] 6.367955e-10 0.4601722 0.4601722 [270,] 6.412096e-10 0.4601722 0.4601722 [271,] 6.456542e-10 0.4601722 0.4601722 [272,] 6.501297e-10 0.4601722 0.4601722 [273,] 6.546362e-10 0.4601722 0.4601722 [274,] 6.591739e-10 0.4601722 0.4601722 [275,] 6.637431e-10 0.4601722 0.4601722 [276,] 6.683439e-10 0.4601722 0.4601722 [277,] 6.729767e-10 0.4601722 0.4601722 [278,] 6.776415e-10 0.4601722 0.4601722 [279,] 6.823387e-10 0.4601722 0.4601722 [280,] 6.870684e-10 0.4601722 0.4601722 [281,] 6.918310e-10 0.4601722 0.4601722 [282,] 6.966265e-10 0.4601722 0.4601722 [283,] 7.014553e-10 0.4601722 0.4601722 [284,] 7.063176e-10 0.4601722 0.4601722 [285,] 7.112135e-10 0.4601722 0.4601722 [286,] 7.161434e-10 0.4601722 0.4601722 [287,] 7.211075e-10 0.4601722 0.4601722 [288,] 7.261060e-10 0.4601722 0.4601722 [289,] 7.311391e-10 0.4601722 0.4601722 [290,] 7.362071e-10 0.4601722 0.4601722 [291,] 7.413102e-10 0.4601722 0.4601722 [292,] 7.464488e-10 0.4601722 0.4601722 [293,] 7.516229e-10 0.4601722 0.4601722 [294,] 7.568329e-10 0.4601722 0.4601722 [295,] 7.620790e-10 0.4601722 0.4601722 [296,] 7.673615e-10 0.4601722 0.4601722 [297,] 7.726806e-10 0.4601722 0.4601722 [298,] 7.780366e-10 0.4601722 0.4601722 [299,] 7.834296e-10 0.4601722 0.4601722 [300,] 7.888601e-10 0.4601722 0.4601722 [301,] 7.943282e-10 0.4601722 0.4601722 [302,] 7.998343e-10 0.4601722 0.4601722 [303,] 8.053784e-10 0.4601722 0.4601722 [304,] 8.109611e-10 0.4601722 0.4601722 [305,] 8.165824e-10 0.4601722 0.4601722 [306,] 8.222426e-10 0.4601722 0.4601722 [307,] 8.279422e-10 0.4601722 0.4601722 [308,] 8.336812e-10 0.4601722 0.4601722 [309,] 8.394600e-10 0.4601722 0.4601722 [310,] 8.452788e-10 0.4601722 0.4601722 [311,] 8.511380e-10 0.4601722 0.4601722 [312,] 8.570378e-10 0.4601722 0.4601722 [313,] 8.629785e-10 0.4601722 0.4601722 [314,] 8.689604e-10 0.4601722 0.4601722 [315,] 8.749838e-10 0.4601722 0.4601722 [316,] 8.810489e-10 0.4601722 0.4601722 [317,] 8.871560e-10 0.4601722 0.4601722 [318,] 8.933055e-10 0.4601722 0.4601722 [319,] 8.994976e-10 0.4601722 0.4601722 [320,] 9.057326e-10 0.4601722 0.4601722 [321,] 9.120108e-10 0.4601722 0.4601722 [322,] 9.183326e-10 0.4601722 0.4601722 [323,] 9.246982e-10 0.4601722 0.4601722 [324,] 9.311079e-10 0.4601722 0.4601722 [325,] 9.375620e-10 0.4601722 0.4601722 [326,] 9.440609e-10 0.4601722 0.4601722 [327,] 9.506048e-10 0.4601722 0.4601722 [328,] 9.571941e-10 0.4601722 0.4601722 [329,] 9.638290e-10 0.4601722 0.4601722 [330,] 9.705100e-10 0.4601722 0.4601722 [331,] 9.772372e-10 0.4601722 0.4601722 [332,] 9.840111e-10 0.4601722 0.4601722 [333,] 9.908319e-10 0.4601722 0.4601722 [334,] 9.977001e-10 0.4601722 0.4601722 [335,] 1.004616e-09 0.4601722 0.4601722 [336,] 1.011579e-09 0.4601722 0.4601722 [337,] 1.018591e-09 0.4601722 0.4601722 [338,] 1.025652e-09 0.4601722 0.4601722 [339,] 1.032761e-09 0.4601722 0.4601722 [340,] 1.039920e-09 0.4601722 0.4601722 [341,] 1.047129e-09 0.4601722 0.4601722 [342,] 1.054387e-09 0.4601722 0.4601722 [343,] 1.061696e-09 0.4601722 0.4601722 [344,] 1.069055e-09 0.4601722 0.4601722 [345,] 1.076465e-09 0.4601722 0.4601722 [346,] 1.083927e-09 0.4601722 0.4601722 [347,] 1.091440e-09 0.4601722 0.4601722 [348,] 1.099006e-09 0.4601722 0.4601722 [349,] 1.106624e-09 0.4601722 0.4601722 [350,] 1.114295e-09 0.4601722 0.4601722 [351,] 1.122018e-09 0.4601722 0.4601722 [352,] 1.129796e-09 0.4601722 0.4601722 [353,] 1.137627e-09 0.4601722 0.4601722 [354,] 1.145513e-09 0.4601722 0.4601722 [355,] 1.153453e-09 0.4601722 0.4601722 [356,] 1.161449e-09 0.4601722 0.4601722 [357,] 1.169499e-09 0.4601722 0.4601722 [358,] 1.177606e-09 0.4601722 0.4601722 [359,] 1.185769e-09 0.4601722 0.4601722 [360,] 1.193988e-09 0.4601722 0.4601722 [361,] 1.202264e-09 0.4601722 0.4601722 [362,] 1.210598e-09 0.4601722 0.4601722 [363,] 1.218990e-09 0.4601722 0.4601722 [364,] 1.227439e-09 0.4601722 0.4601722 [365,] 1.235947e-09 0.4601722 0.4601722 [366,] 1.244515e-09 0.4601722 0.4601722 [367,] 1.253141e-09 0.4601722 0.4601722 [368,] 1.261828e-09 0.4601722 0.4601722 [369,] 1.270574e-09 0.4601722 0.4601722 [370,] 1.279381e-09 0.4601722 0.4601722 [371,] 1.288250e-09 0.4601722 0.4601722 [372,] 1.297179e-09 0.4601722 0.4601722 [373,] 1.306171e-09 0.4601722 0.4601722 [374,] 1.315225e-09 0.4601722 0.4601722 [375,] 1.324342e-09 0.4601722 0.4601722 [376,] 1.333521e-09 0.4601722 0.4601722 [377,] 1.342765e-09 0.4601722 0.4601722 [378,] 1.352073e-09 0.4601722 0.4601722 [379,] 1.361445e-09 0.4601722 0.4601722 [380,] 1.370882e-09 0.4601722 0.4601722 [381,] 1.380384e-09 0.4601722 0.4601722 [382,] 1.389953e-09 0.4601722 0.4601722 [383,] 1.399587e-09 0.4601722 0.4601722 [384,] 1.409289e-09 0.4601722 0.4601722 [385,] 1.419058e-09 0.4601722 0.4601722 [386,] 1.428894e-09 0.4601722 0.4601722 [387,] 1.438799e-09 0.4601722 0.4601722 [388,] 1.448772e-09 0.4601722 0.4601722 [389,] 1.458814e-09 0.4601722 0.4601722 [390,] 1.468926e-09 0.4601722 0.4601722 [391,] 1.479108e-09 0.4601722 0.4601722 [392,] 1.489361e-09 0.4601722 0.4601722 [393,] 1.499685e-09 0.4601722 0.4601722 [394,] 1.510080e-09 0.4601722 0.4601722 [395,] 1.520548e-09 0.4601722 0.4601722 [396,] 1.531087e-09 0.4601722 0.4601722 [397,] 1.541700e-09 0.4601722 0.4601722 [398,] 1.552387e-09 0.4601722 0.4601722 [399,] 1.563148e-09 0.4601722 0.4601722 [400,] 1.573983e-09 0.4601722 0.4601722 [401,] 1.584893e-09 0.4601722 0.4601722 [402,] 1.595879e-09 0.4601722 0.4601722 [403,] 1.606941e-09 0.4601722 0.4601722 [404,] 1.618080e-09 0.4601722 0.4601722 [405,] 1.629296e-09 0.4601722 0.4601722 [406,] 1.640590e-09 0.4601722 0.4601722 [407,] 1.651962e-09 0.4601722 0.4601722 [408,] 1.663413e-09 0.4601722 0.4601722 [409,] 1.674943e-09 0.4601722 0.4601722 [410,] 1.686553e-09 0.4601722 0.4601722 [411,] 1.698244e-09 0.4601722 0.4601722 [412,] 1.710015e-09 0.4601722 0.4601722 [413,] 1.721869e-09 0.4601722 0.4601722 [414,] 1.733804e-09 0.4601722 0.4601722 [415,] 1.745822e-09 0.4601722 0.4601722 [416,] 1.757924e-09 0.4601722 0.4601722 [417,] 1.770109e-09 0.4601722 0.4601722 [418,] 1.782379e-09 0.4601722 0.4601722 [419,] 1.794734e-09 0.4601722 0.4601722 [420,] 1.807174e-09 0.4601722 0.4601722 [421,] 1.819701e-09 0.4601722 0.4601722 [422,] 1.832314e-09 0.4601722 0.4601722 [423,] 1.845015e-09 0.4601722 0.4601722 [424,] 1.857804e-09 0.4601722 0.4601722 [425,] 1.870682e-09 0.4601722 0.4601722 [426,] 1.883649e-09 0.4601722 0.4601722 [427,] 1.896706e-09 0.4601722 0.4601722 [428,] 1.909853e-09 0.4601722 0.4601722 [429,] 1.923092e-09 0.4601722 0.4601722 [430,] 1.936422e-09 0.4601722 0.4601722 [431,] 1.949845e-09 0.4601722 0.4601722 [432,] 1.963360e-09 0.4601722 0.4601722 [433,] 1.976970e-09 0.4601722 0.4601722 [434,] 1.990673e-09 0.4601722 0.4601722 [435,] 2.004472e-09 0.4601722 0.4601722 [436,] 2.018366e-09 0.4601722 0.4601722 [437,] 2.032357e-09 0.4601722 0.4601722 [438,] 2.046445e-09 0.4601722 0.4601722 [439,] 2.060630e-09 0.4601722 0.4601722 [440,] 2.074914e-09 0.4601722 0.4601722 [441,] 2.089296e-09 0.4601722 0.4601722 [442,] 2.103778e-09 0.4601722 0.4601722 [443,] 2.118361e-09 0.4601722 0.4601722 [444,] 2.133045e-09 0.4601722 0.4601722 [445,] 2.147830e-09 0.4601722 0.4601722 [446,] 2.162719e-09 0.4601722 0.4601722 [447,] 2.177710e-09 0.4601722 0.4601722 [448,] 2.192805e-09 0.4601722 0.4601722 [449,] 2.208005e-09 0.4601722 0.4601722 [450,] 2.223310e-09 0.4601722 0.4601722 [451,] 2.238721e-09 0.4601722 0.4601722 [452,] 2.254239e-09 0.4601722 0.4601722 [453,] 2.269865e-09 0.4601722 0.4601722 [454,] 2.285599e-09 0.4601722 0.4601722 [455,] 2.301442e-09 0.4601722 0.4601722 [456,] 2.317395e-09 0.4601722 0.4601722 [457,] 2.333458e-09 0.4601722 0.4601722 [458,] 2.349633e-09 0.4601722 0.4601722 [459,] 2.365920e-09 0.4601722 0.4601722 [460,] 2.382319e-09 0.4601722 0.4601722 [461,] 2.398833e-09 0.4601722 0.4601722 [462,] 2.415461e-09 0.4601722 0.4601722 [463,] 2.432204e-09 0.4601722 0.4601722 [464,] 2.449063e-09 0.4601722 0.4601722 [465,] 2.466039e-09 0.4601722 0.4601722 [466,] 2.483133e-09 0.4601722 0.4601722 [467,] 2.500345e-09 0.4601722 0.4601722 [468,] 2.517677e-09 0.4601722 0.4601722 [469,] 2.535129e-09 0.4601722 0.4601722 [470,] 2.552701e-09 0.4601722 0.4601722 [471,] 2.570396e-09 0.4601722 0.4601722 [472,] 2.588213e-09 0.4601722 0.4601722 [473,] 2.606154e-09 0.4601722 0.4601722 [474,] 2.624219e-09 0.4601722 0.4601722 [475,] 2.642409e-09 0.4601722 0.4601722 [476,] 2.660725e-09 0.4601722 0.4601722 [477,] 2.679168e-09 0.4601722 0.4601722 [478,] 2.697739e-09 0.4601722 0.4601722 [479,] 2.716439e-09 0.4601722 0.4601722 [480,] 2.735269e-09 0.4601722 0.4601722 [481,] 2.754229e-09 0.4601722 0.4601722 [482,] 2.773320e-09 0.4601722 0.4601722 [483,] 2.792544e-09 0.4601722 0.4601722 [484,] 2.811901e-09 0.4601722 0.4601722 [485,] 2.831392e-09 0.4601722 0.4601722 [486,] 2.851018e-09 0.4601722 0.4601722 [487,] 2.870781e-09 0.4601722 0.4601722 [488,] 2.890680e-09 0.4601722 0.4601722 [489,] 2.910717e-09 0.4601722 0.4601722 [490,] 2.930893e-09 0.4601722 0.4601722 [491,] 2.951209e-09 0.4601722 0.4601722 [492,] 2.971666e-09 0.4601722 0.4601722 [493,] 2.992265e-09 0.4601722 0.4601722 [494,] 3.013006e-09 0.4601722 0.4601722 [495,] 3.033891e-09 0.4601722 0.4601722 [496,] 3.054921e-09 0.4601722 0.4601722 [497,] 3.076097e-09 0.4601722 0.4601722 [498,] 3.097419e-09 0.4601722 0.4601722 [499,] 3.118890e-09 0.4601722 0.4601722 [500,] 3.140509e-09 0.4601722 0.4601722 [501,] 3.162278e-09 0.4601722 0.4601722 [502,] 3.184198e-09 0.4601722 0.4601722 [503,] 3.206269e-09 0.4601722 0.4601722 [504,] 3.228494e-09 0.4601722 0.4601722 [505,] 3.250873e-09 0.4601722 0.4601722 [506,] 3.273407e-09 0.4601722 0.4601722 [507,] 3.296097e-09 0.4601722 0.4601722 [508,] 3.318945e-09 0.4601722 0.4601722 [509,] 3.341950e-09 0.4601722 0.4601722 [510,] 3.365116e-09 0.4601722 0.4601722 [511,] 3.388442e-09 0.4601722 0.4601722 [512,] 3.411929e-09 0.4601722 0.4601722 [513,] 3.435579e-09 0.4601722 0.4601722 [514,] 3.459394e-09 0.4601722 0.4601722 [515,] 3.483373e-09 0.4601722 0.4601722 [516,] 3.507519e-09 0.4601722 0.4601722 [517,] 3.531832e-09 0.4601722 0.4601722 [518,] 3.556313e-09 0.4601722 0.4601722 [519,] 3.580964e-09 0.4601722 0.4601722 [520,] 3.605786e-09 0.4601722 0.4601722 [521,] 3.630781e-09 0.4601722 0.4601722 [522,] 3.655948e-09 0.4601722 0.4601722 [523,] 3.681290e-09 0.4601722 0.4601722 [524,] 3.706807e-09 0.4601722 0.4601722 [525,] 3.732502e-09 0.4601722 0.4601722 [526,] 3.758374e-09 0.4601722 0.4601722 [527,] 3.784426e-09 0.4601722 0.4601722 [528,] 3.810658e-09 0.4601722 0.4601722 [529,] 3.837072e-09 0.4601722 0.4601722 [530,] 3.863670e-09 0.4601722 0.4601722 [531,] 3.890451e-09 0.4601722 0.4601722 [532,] 3.917419e-09 0.4601722 0.4601722 [533,] 3.944573e-09 0.4601722 0.4601722 [534,] 3.971915e-09 0.4601722 0.4601722 [535,] 3.999447e-09 0.4601722 0.4601722 [536,] 4.027170e-09 0.4601722 0.4601722 [537,] 4.055085e-09 0.4601722 0.4601722 [538,] 4.083194e-09 0.4601722 0.4601722 [539,] 4.111497e-09 0.4601722 0.4601722 [540,] 4.139997e-09 0.4601722 0.4601722 [541,] 4.168694e-09 0.4601722 0.4601722 [542,] 4.197590e-09 0.4601722 0.4601722 [543,] 4.226686e-09 0.4601722 0.4601722 [544,] 4.255984e-09 0.4601722 0.4601722 [545,] 4.285485e-09 0.4601722 0.4601722 [546,] 4.315191e-09 0.4601722 0.4601722 [547,] 4.345102e-09 0.4601722 0.4601722 [548,] 4.375221e-09 0.4601722 0.4601722 [549,] 4.405549e-09 0.4601722 0.4601722 [550,] 4.436086e-09 0.4601722 0.4601722 [551,] 4.466836e-09 0.4601722 0.4601722 [552,] 4.497799e-09 0.4601722 0.4601722 [553,] 4.528976e-09 0.4601722 0.4601722 [554,] 4.560369e-09 0.4601722 0.4601722 [555,] 4.591980e-09 0.4601722 0.4601722 [556,] 4.623810e-09 0.4601722 0.4601722 [557,] 4.655861e-09 0.4601722 0.4601722 [558,] 4.688134e-09 0.4601722 0.4601722 [559,] 4.720630e-09 0.4601722 0.4601722 [560,] 4.753352e-09 0.4601722 0.4601722 [561,] 4.786301e-09 0.4601722 0.4601722 [562,] 4.819478e-09 0.4601722 0.4601722 [563,] 4.852885e-09 0.4601722 0.4601722 [564,] 4.886524e-09 0.4601722 0.4601722 [565,] 4.920395e-09 0.4601722 0.4601722 [566,] 4.954502e-09 0.4601722 0.4601722 [567,] 4.988845e-09 0.4601722 0.4601722 [568,] 5.023426e-09 0.4601722 0.4601722 [569,] 5.058247e-09 0.4601722 0.4601722 [570,] 5.093309e-09 0.4601722 0.4601722 [571,] 5.128614e-09 0.4601722 0.4601722 [572,] 5.164164e-09 0.4601722 0.4601722 [573,] 5.199960e-09 0.4601722 0.4601722 [574,] 5.236004e-09 0.4601722 0.4601722 [575,] 5.272299e-09 0.4601722 0.4601722 [576,] 5.308844e-09 0.4601722 0.4601722 [577,] 5.345644e-09 0.4601722 0.4601722 [578,] 5.382698e-09 0.4601722 0.4601722 [579,] 5.420009e-09 0.4601722 0.4601722 [580,] 5.457579e-09 0.4601722 0.4601722 [581,] 5.495409e-09 0.4601722 0.4601722 [582,] 5.533501e-09 0.4601722 0.4601722 [583,] 5.571857e-09 0.4601722 0.4601722 [584,] 5.610480e-09 0.4601722 0.4601722 [585,] 5.649370e-09 0.4601722 0.4601722 [586,] 5.688529e-09 0.4601722 0.4601722 [587,] 5.727960e-09 0.4601722 0.4601722 [588,] 5.767665e-09 0.4601722 0.4601722 [589,] 5.807644e-09 0.4601722 0.4601722 [590,] 5.847901e-09 0.4601722 0.4601722 [591,] 5.888437e-09 0.4601722 0.4601722 [592,] 5.929253e-09 0.4601722 0.4601722 [593,] 5.970353e-09 0.4601722 0.4601722 [594,] 6.011737e-09 0.4601722 0.4601722 [595,] 6.053409e-09 0.4601722 0.4601722 [596,] 6.095369e-09 0.4601722 0.4601722 [597,] 6.137620e-09 0.4601722 0.4601722 [598,] 6.180164e-09 0.4601722 0.4601722 [599,] 6.223003e-09 0.4601722 0.4601722 [600,] 6.266139e-09 0.4601722 0.4601722 [601,] 6.309573e-09 0.4601722 0.4601722 [602,] 6.353309e-09 0.4601722 0.4601722 [603,] 6.397348e-09 0.4601722 0.4601722 [604,] 6.441693e-09 0.4601722 0.4601722 [605,] 6.486344e-09 0.4601722 0.4601722 [606,] 6.531306e-09 0.4601722 0.4601722 [607,] 6.576578e-09 0.4601722 0.4601722 [608,] 6.622165e-09 0.4601722 0.4601722 [609,] 6.668068e-09 0.4601722 0.4601722 [610,] 6.714289e-09 0.4601722 0.4601722 [611,] 6.760830e-09 0.4601722 0.4601722 [612,] 6.807694e-09 0.4601722 0.4601722 [613,] 6.854882e-09 0.4601722 0.4601722 [614,] 6.902398e-09 0.4601722 0.4601722 [615,] 6.950243e-09 0.4601722 0.4601722 [616,] 6.998420e-09 0.4601722 0.4601722 [617,] 7.046931e-09 0.4601722 0.4601722 [618,] 7.095778e-09 0.4601722 0.4601722 [619,] 7.144963e-09 0.4601722 0.4601722 [620,] 7.194490e-09 0.4601722 0.4601722 [621,] 7.244360e-09 0.4601722 0.4601722 [622,] 7.294575e-09 0.4601722 0.4601722 [623,] 7.345139e-09 0.4601722 0.4601722 [624,] 7.396053e-09 0.4601722 0.4601722 [625,] 7.447320e-09 0.4601722 0.4601722 [626,] 7.498942e-09 0.4601722 0.4601722 [627,] 7.550922e-09 0.4601722 0.4601722 [628,] 7.603263e-09 0.4601722 0.4601722 [629,] 7.655966e-09 0.4601722 0.4601722 [630,] 7.709035e-09 0.4601722 0.4601722 [631,] 7.762471e-09 0.4601722 0.4601722 [632,] 7.816278e-09 0.4601722 0.4601722 [633,] 7.870458e-09 0.4601722 0.4601722 [634,] 7.925013e-09 0.4601722 0.4601722 [635,] 7.979947e-09 0.4601722 0.4601722 [636,] 8.035261e-09 0.4601722 0.4601722 [637,] 8.090959e-09 0.4601722 0.4601722 [638,] 8.147043e-09 0.4601722 0.4601722 [639,] 8.203515e-09 0.4601722 0.4601722 [640,] 8.260379e-09 0.4601722 0.4601722 [641,] 8.317638e-09 0.4601722 0.4601722 [642,] 8.375293e-09 0.4601722 0.4601722 [643,] 8.433348e-09 0.4601722 0.4601722 [644,] 8.491805e-09 0.4601722 0.4601722 [645,] 8.550667e-09 0.4601722 0.4601722 [646,] 8.609938e-09 0.4601722 0.4601722 [647,] 8.669619e-09 0.4601722 0.4601722 [648,] 8.729714e-09 0.4601722 0.4601722 [649,] 8.790225e-09 0.4601722 0.4601722 [650,] 8.851156e-09 0.4601722 0.4601722 [651,] 8.912509e-09 0.4601722 0.4601722 [652,] 8.974288e-09 0.4601722 0.4601722 [653,] 9.036495e-09 0.4601722 0.4601722 [654,] 9.099133e-09 0.4601722 0.4601722 [655,] 9.162205e-09 0.4601722 0.4601722 [656,] 9.225714e-09 0.4601722 0.4601722 [657,] 9.289664e-09 0.4601722 0.4601722 [658,] 9.354057e-09 0.4601722 0.4601722 [659,] 9.418896e-09 0.4601722 0.4601722 [660,] 9.484185e-09 0.4601722 0.4601722 [661,] 9.549926e-09 0.4601722 0.4601722 [662,] 9.616123e-09 0.4601722 0.4601722 [663,] 9.682779e-09 0.4601722 0.4601722 [664,] 9.749896e-09 0.4601722 0.4601722 [665,] 9.817479e-09 0.4601722 0.4601722 [666,] 9.885531e-09 0.4601722 0.4601722 [667,] 9.954054e-09 0.4601722 0.4601722 [668,] 1.002305e-08 0.4601722 0.4601722 [669,] 1.009253e-08 0.4601722 0.4601722 [670,] 1.016249e-08 0.4601722 0.4601722 [671,] 1.023293e-08 0.4601722 0.4601722 [672,] 1.030386e-08 0.4601722 0.4601722 [673,] 1.037528e-08 0.4601722 0.4601722 [674,] 1.044720e-08 0.4601722 0.4601722 [675,] 1.051962e-08 0.4601722 0.4601722 [676,] 1.059254e-08 0.4601722 0.4601722 [677,] 1.066596e-08 0.4601722 0.4601722 [678,] 1.073989e-08 0.4601722 0.4601722 [679,] 1.081434e-08 0.4601722 0.4601722 [680,] 1.088930e-08 0.4601722 0.4601722 [681,] 1.096478e-08 0.4601722 0.4601722 [682,] 1.104079e-08 0.4601722 0.4601722 [683,] 1.111732e-08 0.4601722 0.4601722 [684,] 1.119438e-08 0.4601722 0.4601722 [685,] 1.127197e-08 0.4601722 0.4601722 [686,] 1.135011e-08 0.4601722 0.4601722 [687,] 1.142878e-08 0.4601722 0.4601722 [688,] 1.150800e-08 0.4601722 0.4601722 [689,] 1.158777e-08 0.4601722 0.4601722 [690,] 1.166810e-08 0.4601722 0.4601722 [691,] 1.174898e-08 0.4601722 0.4601722 [692,] 1.183042e-08 0.4601722 0.4601722 [693,] 1.191242e-08 0.4601722 0.4601722 [694,] 1.199499e-08 0.4601722 0.4601722 [695,] 1.207814e-08 0.4601722 0.4601722 [696,] 1.216186e-08 0.4601722 0.4601722 [697,] 1.224616e-08 0.4601722 0.4601722 [698,] 1.233105e-08 0.4601722 0.4601722 [699,] 1.241652e-08 0.4601722 0.4601722 [700,] 1.250259e-08 0.4601722 0.4601722 [701,] 1.258925e-08 0.4601722 0.4601722 [702,] 1.267652e-08 0.4601722 0.4601722 [703,] 1.276439e-08 0.4601722 0.4601722 [704,] 1.285287e-08 0.4601722 0.4601722 [705,] 1.294196e-08 0.4601722 0.4601722 [706,] 1.303167e-08 0.4601722 0.4601722 [707,] 1.312200e-08 0.4601722 0.4601722 [708,] 1.321296e-08 0.4601722 0.4601722 [709,] 1.330454e-08 0.4601722 0.4601722 [710,] 1.339677e-08 0.4601722 0.4601722 [711,] 1.348963e-08 0.4601722 0.4601722 [712,] 1.358313e-08 0.4601722 0.4601722 [713,] 1.367729e-08 0.4601722 0.4601722 [714,] 1.377209e-08 0.4601722 0.4601722 [715,] 1.386756e-08 0.4601722 0.4601722 [716,] 1.396368e-08 0.4601722 0.4601722 [717,] 1.406048e-08 0.4601722 0.4601722 [718,] 1.415794e-08 0.4601722 0.4601722 [719,] 1.425608e-08 0.4601722 0.4601722 [720,] 1.435489e-08 0.4601722 0.4601722 [721,] 1.445440e-08 0.4601722 0.4601722 [722,] 1.455459e-08 0.4601722 0.4601722 [723,] 1.465548e-08 0.4601722 0.4601722 [724,] 1.475707e-08 0.4601722 0.4601722 [725,] 1.485936e-08 0.4601722 0.4601722 [726,] 1.496236e-08 0.4601722 0.4601722 [727,] 1.506607e-08 0.4601722 0.4601722 [728,] 1.517050e-08 0.4601722 0.4601722 [729,] 1.527566e-08 0.4601722 0.4601722 [730,] 1.538155e-08 0.4601722 0.4601722 [731,] 1.548817e-08 0.4601722 0.4601722 [732,] 1.559553e-08 0.4601722 0.4601722 [733,] 1.570363e-08 0.4601722 0.4601722 [734,] 1.581248e-08 0.4601722 0.4601722 [735,] 1.592209e-08 0.4601722 0.4601722 [736,] 1.603245e-08 0.4601722 0.4601722 [737,] 1.614359e-08 0.4601722 0.4601722 [738,] 1.625549e-08 0.4601722 0.4601722 [739,] 1.636817e-08 0.4601722 0.4601722 [740,] 1.648162e-08 0.4601722 0.4601722 [741,] 1.659587e-08 0.4601722 0.4601722 [742,] 1.671091e-08 0.4601722 0.4601722 [743,] 1.682674e-08 0.4601722 0.4601722 [744,] 1.694338e-08 0.4601722 0.4601722 [745,] 1.706082e-08 0.4601722 0.4601722 [746,] 1.717908e-08 0.4601722 0.4601722 [747,] 1.729816e-08 0.4601722 0.4601722 [748,] 1.741807e-08 0.4601722 0.4601722 [749,] 1.753881e-08 0.4601722 0.4601722 [750,] 1.766038e-08 0.4601722 0.4601722 [751,] 1.778279e-08 0.4601722 0.4601722 [752,] 1.790606e-08 0.4601722 0.4601722 [753,] 1.803018e-08 0.4601722 0.4601722 [754,] 1.815516e-08 0.4601722 0.4601722 [755,] 1.828100e-08 0.4601722 0.4601722 [756,] 1.840772e-08 0.4601722 0.4601722 [757,] 1.853532e-08 0.4601722 0.4601722 [758,] 1.866380e-08 0.4601722 0.4601722 [759,] 1.879317e-08 0.4601722 0.4601722 [760,] 1.892344e-08 0.4601722 0.4601722 [761,] 1.905461e-08 0.4601722 0.4601722 [762,] 1.918669e-08 0.4601722 0.4601722 [763,] 1.931968e-08 0.4601722 0.4601722 [764,] 1.945360e-08 0.4601722 0.4601722 [765,] 1.958845e-08 0.4601722 0.4601722 [766,] 1.972423e-08 0.4601722 0.4601722 [767,] 1.986095e-08 0.4601722 0.4601722 [768,] 1.999862e-08 0.4601722 0.4601722 [769,] 2.013724e-08 0.4601722 0.4601722 [770,] 2.027683e-08 0.4601722 0.4601722 [771,] 2.041738e-08 0.4601722 0.4601722 [772,] 2.055891e-08 0.4601722 0.4601722 [773,] 2.070141e-08 0.4601722 0.4601722 [774,] 2.084491e-08 0.4601722 0.4601722 [775,] 2.098940e-08 0.4601722 0.4601722 [776,] 2.113489e-08 0.4601722 0.4601722 [777,] 2.128139e-08 0.4601722 0.4601722 [778,] 2.142891e-08 0.4601722 0.4601722 [779,] 2.157744e-08 0.4601722 0.4601722 [780,] 2.172701e-08 0.4601722 0.4601722 [781,] 2.187762e-08 0.4601722 0.4601722 [782,] 2.202926e-08 0.4601722 0.4601722 [783,] 2.218196e-08 0.4601722 0.4601722 [784,] 2.233572e-08 0.4601722 0.4601722 [785,] 2.249055e-08 0.4601722 0.4601722 [786,] 2.264644e-08 0.4601722 0.4601722 [787,] 2.280342e-08 0.4601722 0.4601722 [788,] 2.296149e-08 0.4601722 0.4601722 [789,] 2.312065e-08 0.4601722 0.4601722 [790,] 2.328091e-08 0.4601722 0.4601722 [791,] 2.344229e-08 0.4601722 0.4601722 [792,] 2.360478e-08 0.4601722 0.4601722 [793,] 2.376840e-08 0.4601722 0.4601722 [794,] 2.393316e-08 0.4601722 0.4601722 [795,] 2.409905e-08 0.4601722 0.4601722 [796,] 2.426610e-08 0.4601722 0.4601722 [797,] 2.443431e-08 0.4601722 0.4601722 [798,] 2.460368e-08 0.4601722 0.4601722 [799,] 2.477422e-08 0.4601722 0.4601722 [800,] 2.494595e-08 0.4601722 0.4601722 [801,] 2.511886e-08 0.4601722 0.4601722 [802,] 2.529298e-08 0.4601722 0.4601722 [803,] 2.546830e-08 0.4601722 0.4601722 [804,] 2.564484e-08 0.4601722 0.4601722 [805,] 2.582260e-08 0.4601722 0.4601722 [806,] 2.600160e-08 0.4601722 0.4601722 [807,] 2.618183e-08 0.4601722 0.4601722 [808,] 2.636331e-08 0.4601722 0.4601722 [809,] 2.654606e-08 0.4601722 0.4601722 [810,] 2.673006e-08 0.4601722 0.4601722 [811,] 2.691535e-08 0.4601722 0.4601722 [812,] 2.710192e-08 0.4601722 0.4601722 [813,] 2.728978e-08 0.4601722 0.4601722 [814,] 2.747894e-08 0.4601722 0.4601722 [815,] 2.766942e-08 0.4601722 0.4601722 [816,] 2.786121e-08 0.4601722 0.4601722 [817,] 2.805434e-08 0.4601722 0.4601722 [818,] 2.824880e-08 0.4601722 0.4601722 [819,] 2.844461e-08 0.4601722 0.4601722 [820,] 2.864178e-08 0.4601722 0.4601722 [821,] 2.884032e-08 0.4601722 0.4601722 [822,] 2.904023e-08 0.4601722 0.4601722 [823,] 2.924152e-08 0.4601722 0.4601722 [824,] 2.944422e-08 0.4601722 0.4601722 [825,] 2.964831e-08 0.4601722 0.4601722 [826,] 2.985383e-08 0.4601722 0.4601722 [827,] 3.006076e-08 0.4601722 0.4601722 [828,] 3.026913e-08 0.4601722 0.4601722 [829,] 3.047895e-08 0.4601722 0.4601722 [830,] 3.069022e-08 0.4601722 0.4601722 [831,] 3.090295e-08 0.4601722 0.4601722 [832,] 3.111716e-08 0.4601722 0.4601722 [833,] 3.133286e-08 0.4601722 0.4601722 [834,] 3.155005e-08 0.4601722 0.4601722 [835,] 3.176874e-08 0.4601722 0.4601722 [836,] 3.198895e-08 0.4601722 0.4601722 [837,] 3.221069e-08 0.4601722 0.4601722 [838,] 3.243396e-08 0.4601722 0.4601722 [839,] 3.265878e-08 0.4601722 0.4601722 [840,] 3.288516e-08 0.4601722 0.4601722 [841,] 3.311311e-08 0.4601722 0.4601722 [842,] 3.334264e-08 0.4601722 0.4601722 [843,] 3.357376e-08 0.4601722 0.4601722 [844,] 3.380648e-08 0.4601722 0.4601722 [845,] 3.404082e-08 0.4601722 0.4601722 [846,] 3.427678e-08 0.4601722 0.4601722 [847,] 3.451437e-08 0.4601722 0.4601722 [848,] 3.475362e-08 0.4601722 0.4601722 [849,] 3.499452e-08 0.4601722 0.4601722 [850,] 3.523709e-08 0.4601722 0.4601722 [851,] 3.548134e-08 0.4601722 0.4601722 [852,] 3.572728e-08 0.4601722 0.4601722 [853,] 3.597493e-08 0.4601722 0.4601722 [854,] 3.622430e-08 0.4601722 0.4601722 [855,] 3.647539e-08 0.4601722 0.4601722 [856,] 3.672823e-08 0.4601722 0.4601722 [857,] 3.698282e-08 0.4601722 0.4601722 [858,] 3.723917e-08 0.4601722 0.4601722 [859,] 3.749730e-08 0.4601722 0.4601722 [860,] 3.775722e-08 0.4601722 0.4601722 [861,] 3.801894e-08 0.4601722 0.4601722 [862,] 3.828247e-08 0.4601722 0.4601722 [863,] 3.854784e-08 0.4601722 0.4601722 [864,] 3.881504e-08 0.4601722 0.4601722 [865,] 3.908409e-08 0.4601722 0.4601722 [866,] 3.935501e-08 0.4601722 0.4601722 [867,] 3.962780e-08 0.4601722 0.4601722 [868,] 3.990249e-08 0.4601722 0.4601722 [869,] 4.017908e-08 0.4601722 0.4601722 [870,] 4.045759e-08 0.4601722 0.4601722 [871,] 4.073803e-08 0.4601722 0.4601722 [872,] 4.102041e-08 0.4601722 0.4601722 [873,] 4.130475e-08 0.4601722 0.4601722 [874,] 4.159106e-08 0.4601722 0.4601722 [875,] 4.187936e-08 0.4601722 0.4601722 [876,] 4.216965e-08 0.4601722 0.4601722 [877,] 4.246196e-08 0.4601722 0.4601722 [878,] 4.275629e-08 0.4601722 0.4601722 [879,] 4.305266e-08 0.4601722 0.4601722 [880,] 4.335109e-08 0.4601722 0.4601722 [881,] 4.365158e-08 0.4601722 0.4601722 [882,] 4.395416e-08 0.4601722 0.4601722 [883,] 4.425884e-08 0.4601722 0.4601722 [884,] 4.456562e-08 0.4601722 0.4601722 [885,] 4.487454e-08 0.4601722 0.4601722 [886,] 4.518559e-08 0.4601722 0.4601722 [887,] 4.549881e-08 0.4601722 0.4601722 [888,] 4.581419e-08 0.4601722 0.4601722 [889,] 4.613176e-08 0.4601722 0.4601722 [890,] 4.645153e-08 0.4601722 0.4601722 [891,] 4.677351e-08 0.4601722 0.4601722 [892,] 4.709773e-08 0.4601722 0.4601722 [893,] 4.742420e-08 0.4601722 0.4601722 [894,] 4.775293e-08 0.4601722 0.4601722 [895,] 4.808393e-08 0.4601722 0.4601722 [896,] 4.841724e-08 0.4601722 0.4601722 [897,] 4.875285e-08 0.4601722 0.4601722 [898,] 4.909079e-08 0.4601722 0.4601722 [899,] 4.943107e-08 0.4601722 0.4601722 [900,] 4.977371e-08 0.4601722 0.4601722 [901,] 5.011872e-08 0.4601722 0.4601722 [902,] 5.046613e-08 0.4601722 0.4601722 [903,] 5.081594e-08 0.4601722 0.4601722 [904,] 5.116818e-08 0.4601722 0.4601722 [905,] 5.152286e-08 0.4601722 0.4601722 [906,] 5.188000e-08 0.4601722 0.4601722 [907,] 5.223962e-08 0.4601722 0.4601722 [908,] 5.260173e-08 0.4601722 0.4601722 [909,] 5.296634e-08 0.4601722 0.4601722 [910,] 5.333349e-08 0.4601722 0.4601722 [911,] 5.370318e-08 0.4601722 0.4601722 [912,] 5.407543e-08 0.4601722 0.4601722 [913,] 5.445027e-08 0.4601722 0.4601722 [914,] 5.482770e-08 0.4601722 0.4601722 [915,] 5.520774e-08 0.4601722 0.4601722 [916,] 5.559043e-08 0.4601722 0.4601722 [917,] 5.597576e-08 0.4601722 0.4601722 [918,] 5.636377e-08 0.4601722 0.4601722 [919,] 5.675446e-08 0.4601722 0.4601722 [920,] 5.714786e-08 0.4601722 0.4601722 [921,] 5.754399e-08 0.4601722 0.4601722 [922,] 5.794287e-08 0.4601722 0.4601722 [923,] 5.834451e-08 0.4601722 0.4601722 [924,] 5.874894e-08 0.4601722 0.4601722 [925,] 5.915616e-08 0.4601722 0.4601722 [926,] 5.956621e-08 0.4601722 0.4601722 [927,] 5.997911e-08 0.4601722 0.4601722 [928,] 6.039486e-08 0.4601722 0.4601722 [929,] 6.081350e-08 0.4601722 0.4601722 [930,] 6.123504e-08 0.4601722 0.4601722 [931,] 6.165950e-08 0.4601722 0.4601722 [932,] 6.208690e-08 0.4601722 0.4601722 [933,] 6.251727e-08 0.4601722 0.4601722 [934,] 6.295062e-08 0.4601722 0.4601722 [935,] 6.338697e-08 0.4601722 0.4601722 [936,] 6.382635e-08 0.4601722 0.4601722 [937,] 6.426877e-08 0.4601722 0.4601722 [938,] 6.471426e-08 0.4601722 0.4601722 [939,] 6.516284e-08 0.4601722 0.4601722 [940,] 6.561453e-08 0.4601722 0.4601722 [941,] 6.606934e-08 0.4601722 0.4601722 [942,] 6.652732e-08 0.4601722 0.4601722 [943,] 6.698846e-08 0.4601722 0.4601722 [944,] 6.745280e-08 0.4601722 0.4601722 [945,] 6.792036e-08 0.4601722 0.4601722 [946,] 6.839116e-08 0.4601722 0.4601722 [947,] 6.886523e-08 0.4601722 0.4601722 [948,] 6.934258e-08 0.4601722 0.4601722 [949,] 6.982324e-08 0.4601722 0.4601722 [950,] 7.030723e-08 0.4601722 0.4601722 [951,] 7.079458e-08 0.4601722 0.4601722 [952,] 7.128530e-08 0.4601722 0.4601722 [953,] 7.177943e-08 0.4601722 0.4601722 [954,] 7.227698e-08 0.4601722 0.4601722 [955,] 7.277798e-08 0.4601722 0.4601722 [956,] 7.328245e-08 0.4601722 0.4601722 [957,] 7.379042e-08 0.4601722 0.4601722 [958,] 7.430191e-08 0.4601722 0.4601722 [959,] 7.481695e-08 0.4601722 0.4601722 [960,] 7.533556e-08 0.4601722 0.4601722 [961,] 7.585776e-08 0.4601722 0.4601722 [962,] 7.638358e-08 0.4601722 0.4601722 [963,] 7.691304e-08 0.4601722 0.4601722 [964,] 7.744618e-08 0.4601722 0.4601722 [965,] 7.798301e-08 0.4601722 0.4601722 [966,] 7.852356e-08 0.4601722 0.4601722 [967,] 7.906786e-08 0.4601722 0.4601722 [968,] 7.961594e-08 0.4601722 0.4601722 [969,] 8.016781e-08 0.4601722 0.4601722 [970,] 8.072350e-08 0.4601722 0.4601722 [971,] 8.128305e-08 0.4601722 0.4601722 [972,] 8.184648e-08 0.4601722 0.4601722 [973,] 8.241381e-08 0.4601722 0.4601722 [974,] 8.298508e-08 0.4601722 0.4601722 [975,] 8.356030e-08 0.4601722 0.4601722 [976,] 8.413951e-08 0.4601722 0.4601722 [977,] 8.472274e-08 0.4601722 0.4601722 [978,] 8.531001e-08 0.4601722 0.4601722 [979,] 8.590135e-08 0.4601722 0.4601722 [980,] 8.649679e-08 0.4601722 0.4601722 [981,] 8.709636e-08 0.4601722 0.4601722 [982,] 8.770008e-08 0.4601722 0.4601722 [983,] 8.830799e-08 0.4601722 0.4601722 [984,] 8.892011e-08 0.4601722 0.4601722 [985,] 8.953648e-08 0.4601722 0.4601722 [986,] 9.015711e-08 0.4601722 0.4601722 [987,] 9.078205e-08 0.4601722 0.4601722 [988,] 9.141132e-08 0.4601722 0.4601722 [989,] 9.204496e-08 0.4601722 0.4601722 [990,] 9.268298e-08 0.4601722 0.4601722 [991,] 9.332543e-08 0.4601722 0.4601722 [992,] 9.397233e-08 0.4601722 0.4601722 [993,] 9.462372e-08 0.4601722 0.4601722 [994,] 9.527962e-08 0.4601722 0.4601722 [995,] 9.594006e-08 0.4601722 0.4601722 [996,] 9.660509e-08 0.4601722 0.4601722 [997,] 9.727472e-08 0.4601722 0.4601722 [998,] 9.794900e-08 0.4601722 0.4601722 [999,] 9.862795e-08 0.4601722 0.4601722 [1000,] 9.931160e-08 0.4601722 0.4601722 [1001,] 1.000000e-07 0.4601722 0.4601722 [1002,] 1.006932e-07 0.4601722 0.4601722 [1003,] 1.013911e-07 0.4601722 0.4601722 [1004,] 1.020939e-07 0.4601722 0.4601722 [1005,] 1.028016e-07 0.4601722 0.4601722 [1006,] 1.035142e-07 0.4601722 0.4601722 [1007,] 1.042317e-07 0.4601722 0.4601722 [1008,] 1.049542e-07 0.4601722 0.4601722 [1009,] 1.056818e-07 0.4601722 0.4601722 [1010,] 1.064143e-07 0.4601722 0.4601722 [1011,] 1.071519e-07 0.4601722 0.4601722 [1012,] 1.078947e-07 0.4601722 0.4601722 [1013,] 1.086426e-07 0.4601722 0.4601722 [1014,] 1.093956e-07 0.4601722 0.4601722 [1015,] 1.101539e-07 0.4601722 0.4601722 [1016,] 1.109175e-07 0.4601722 0.4601722 [1017,] 1.116863e-07 0.4601722 0.4601722 [1018,] 1.124605e-07 0.4601722 0.4601722 [1019,] 1.132400e-07 0.4601722 0.4601722 [1020,] 1.140250e-07 0.4601722 0.4601722 [1021,] 1.148154e-07 0.4601722 0.4601722 [1022,] 1.156112e-07 0.4601722 0.4601722 [1023,] 1.164126e-07 0.4601722 0.4601722 [1024,] 1.172195e-07 0.4601722 0.4601722 [1025,] 1.180321e-07 0.4601722 0.4601722 [1026,] 1.188502e-07 0.4601722 0.4601722 [1027,] 1.196741e-07 0.4601722 0.4601722 [1028,] 1.205036e-07 0.4601722 0.4601722 [1029,] 1.213389e-07 0.4601722 0.4601722 [1030,] 1.221800e-07 0.4601722 0.4601722 [1031,] 1.230269e-07 0.4601722 0.4601722 [1032,] 1.238797e-07 0.4601722 0.4601722 [1033,] 1.247384e-07 0.4601722 0.4601722 [1034,] 1.256030e-07 0.4601722 0.4601722 [1035,] 1.264736e-07 0.4601722 0.4601722 [1036,] 1.273503e-07 0.4601722 0.4601722 [1037,] 1.282331e-07 0.4601722 0.4601722 [1038,] 1.291219e-07 0.4601722 0.4601722 [1039,] 1.300170e-07 0.4601722 0.4601722 [1040,] 1.309182e-07 0.4601722 0.4601722 [1041,] 1.318257e-07 0.4601722 0.4601722 [1042,] 1.327394e-07 0.4601722 0.4601722 [1043,] 1.336596e-07 0.4601722 0.4601722 [1044,] 1.345860e-07 0.4601722 0.4601722 [1045,] 1.355189e-07 0.4601722 0.4601722 [1046,] 1.364583e-07 0.4601722 0.4601722 [1047,] 1.374042e-07 0.4601722 0.4601722 [1048,] 1.383566e-07 0.4601722 0.4601722 [1049,] 1.393157e-07 0.4601722 0.4601722 [1050,] 1.402814e-07 0.4601722 0.4601722 [1051,] 1.412538e-07 0.4601722 0.4601722 [1052,] 1.422329e-07 0.4601722 0.4601722 [1053,] 1.432188e-07 0.4601722 0.4601722 [1054,] 1.442115e-07 0.4601722 0.4601722 [1055,] 1.452112e-07 0.4601722 0.4601722 [1056,] 1.462177e-07 0.4601722 0.4601722 [1057,] 1.472313e-07 0.4601722 0.4601722 [1058,] 1.482518e-07 0.4601722 0.4601722 [1059,] 1.492794e-07 0.4601722 0.4601722 [1060,] 1.503142e-07 0.4601722 0.4601722 [1061,] 1.513561e-07 0.4601722 0.4601722 [1062,] 1.524053e-07 0.4601722 0.4601722 [1063,] 1.534617e-07 0.4601722 0.4601722 [1064,] 1.545254e-07 0.4601722 0.4601722 [1065,] 1.555966e-07 0.4601722 0.4601722 [1066,] 1.566751e-07 0.4601722 0.4601722 [1067,] 1.577611e-07 0.4601722 0.4601722 [1068,] 1.588547e-07 0.4601722 0.4601722 [1069,] 1.599558e-07 0.4601722 0.4601722 [1070,] 1.610646e-07 0.4601722 0.4601722 [1071,] 1.621810e-07 0.4601722 0.4601722 [1072,] 1.633052e-07 0.4601722 0.4601722 [1073,] 1.644372e-07 0.4601722 0.4601722 [1074,] 1.655770e-07 0.4601722 0.4601722 [1075,] 1.667247e-07 0.4601722 0.4601722 [1076,] 1.678804e-07 0.4601722 0.4601722 [1077,] 1.690441e-07 0.4601722 0.4601722 [1078,] 1.702159e-07 0.4601722 0.4601722 [1079,] 1.713957e-07 0.4601722 0.4601722 [1080,] 1.725838e-07 0.4601722 0.4601722 [1081,] 1.737801e-07 0.4601722 0.4601722 [1082,] 1.749847e-07 0.4601722 0.4601722 [1083,] 1.761976e-07 0.4601722 0.4601722 [1084,] 1.774189e-07 0.4601722 0.4601722 [1085,] 1.786488e-07 0.4601722 0.4601722 [1086,] 1.798871e-07 0.4601723 0.4601722 [1087,] 1.811340e-07 0.4601723 0.4601722 [1088,] 1.823896e-07 0.4601723 0.4601722 [1089,] 1.836538e-07 0.4601723 0.4601722 [1090,] 1.849269e-07 0.4601723 0.4601722 [1091,] 1.862087e-07 0.4601723 0.4601722 [1092,] 1.874995e-07 0.4601723 0.4601722 [1093,] 1.887991e-07 0.4601723 0.4601722 [1094,] 1.901078e-07 0.4601723 0.4601722 [1095,] 1.914256e-07 0.4601723 0.4601722 [1096,] 1.927525e-07 0.4601723 0.4601722 [1097,] 1.940886e-07 0.4601723 0.4601722 [1098,] 1.954339e-07 0.4601723 0.4601722 [1099,] 1.967886e-07 0.4601723 0.4601722 [1100,] 1.981527e-07 0.4601723 0.4601722 [1101,] 1.995262e-07 0.4601723 0.4601722 [1102,] 2.009093e-07 0.4601723 0.4601722 [1103,] 2.023019e-07 0.4601723 0.4601722 [1104,] 2.037042e-07 0.4601723 0.4601722 [1105,] 2.051162e-07 0.4601723 0.4601722 [1106,] 2.065380e-07 0.4601723 0.4601722 [1107,] 2.079697e-07 0.4601723 0.4601722 [1108,] 2.094112e-07 0.4601723 0.4601722 [1109,] 2.108628e-07 0.4601723 0.4601722 [1110,] 2.123244e-07 0.4601723 0.4601722 [1111,] 2.137962e-07 0.4601723 0.4601722 [1112,] 2.152782e-07 0.4601723 0.4601722 [1113,] 2.167704e-07 0.4601723 0.4601722 [1114,] 2.182730e-07 0.4601723 0.4601722 [1115,] 2.197860e-07 0.4601723 0.4601722 [1116,] 2.213095e-07 0.4601723 0.4601722 [1117,] 2.228435e-07 0.4601723 0.4601722 [1118,] 2.243882e-07 0.4601723 0.4601722 [1119,] 2.259436e-07 0.4601723 0.4601722 [1120,] 2.275097e-07 0.4601723 0.4601722 [1121,] 2.290868e-07 0.4601723 0.4601722 [1122,] 2.306747e-07 0.4601723 0.4601722 [1123,] 2.322737e-07 0.4601723 0.4601722 [1124,] 2.338837e-07 0.4601723 0.4601722 [1125,] 2.355049e-07 0.4601723 0.4601722 [1126,] 2.371374e-07 0.4601723 0.4601722 [1127,] 2.387811e-07 0.4601723 0.4601723 [1128,] 2.404363e-07 0.4601723 0.4601723 [1129,] 2.421029e-07 0.4601723 0.4601723 [1130,] 2.437811e-07 0.4601723 0.4601723 [1131,] 2.454709e-07 0.4601723 0.4601723 [1132,] 2.471724e-07 0.4601723 0.4601723 [1133,] 2.488857e-07 0.4601723 0.4601723 [1134,] 2.506109e-07 0.4601723 0.4601723 [1135,] 2.523481e-07 0.4601723 0.4601723 [1136,] 2.540973e-07 0.4601723 0.4601723 [1137,] 2.558586e-07 0.4601723 0.4601723 [1138,] 2.576321e-07 0.4601723 0.4601723 [1139,] 2.594179e-07 0.4601723 0.4601723 [1140,] 2.612161e-07 0.4601723 0.4601723 [1141,] 2.630268e-07 0.4601723 0.4601723 [1142,] 2.648500e-07 0.4601723 0.4601723 [1143,] 2.666859e-07 0.4601723 0.4601723 [1144,] 2.685344e-07 0.4601723 0.4601723 [1145,] 2.703958e-07 0.4601723 0.4601723 [1146,] 2.722701e-07 0.4601723 0.4601723 [1147,] 2.741574e-07 0.4601723 0.4601723 [1148,] 2.760578e-07 0.4601723 0.4601723 [1149,] 2.779713e-07 0.4601723 0.4601723 [1150,] 2.798981e-07 0.4601723 0.4601723 [1151,] 2.818383e-07 0.4601723 0.4601723 [1152,] 2.837919e-07 0.4601723 0.4601723 [1153,] 2.857591e-07 0.4601723 0.4601723 [1154,] 2.877398e-07 0.4601723 0.4601723 [1155,] 2.897344e-07 0.4601723 0.4601723 [1156,] 2.917427e-07 0.4601723 0.4601723 [1157,] 2.937650e-07 0.4601723 0.4601723 [1158,] 2.958012e-07 0.4601723 0.4601723 [1159,] 2.978516e-07 0.4601723 0.4601723 [1160,] 2.999163e-07 0.4601723 0.4601723 [1161,] 3.019952e-07 0.4601723 0.4601723 [1162,] 3.040885e-07 0.4601723 0.4601723 [1163,] 3.061963e-07 0.4601723 0.4601723 [1164,] 3.083188e-07 0.4601723 0.4601723 [1165,] 3.104560e-07 0.4601723 0.4601723 [1166,] 3.126079e-07 0.4601723 0.4601723 [1167,] 3.147748e-07 0.4601723 0.4601723 [1168,] 3.169567e-07 0.4601723 0.4601723 [1169,] 3.191538e-07 0.4601723 0.4601723 [1170,] 3.213661e-07 0.4601723 0.4601723 [1171,] 3.235937e-07 0.4601723 0.4601723 [1172,] 3.258367e-07 0.4601723 0.4601723 [1173,] 3.280953e-07 0.4601723 0.4601723 [1174,] 3.303695e-07 0.4601723 0.4601723 [1175,] 3.326596e-07 0.4601723 0.4601723 [1176,] 3.349654e-07 0.4601723 0.4601723 [1177,] 3.372873e-07 0.4601723 0.4601723 [1178,] 3.396253e-07 0.4601723 0.4601723 [1179,] 3.419794e-07 0.4601723 0.4601723 [1180,] 3.443499e-07 0.4601723 0.4601723 [1181,] 3.467369e-07 0.4601723 0.4601723 [1182,] 3.491403e-07 0.4601723 0.4601723 [1183,] 3.515604e-07 0.4601723 0.4601723 [1184,] 3.539973e-07 0.4601723 0.4601723 [1185,] 3.564511e-07 0.4601723 0.4601723 [1186,] 3.589219e-07 0.4601723 0.4601723 [1187,] 3.614099e-07 0.4601723 0.4601723 [1188,] 3.639150e-07 0.4601723 0.4601723 [1189,] 3.664376e-07 0.4601723 0.4601723 [1190,] 3.689776e-07 0.4601723 0.4601723 [1191,] 3.715352e-07 0.4601723 0.4601723 [1192,] 3.741106e-07 0.4601723 0.4601723 [1193,] 3.767038e-07 0.4601723 0.4601723 [1194,] 3.793150e-07 0.4601723 0.4601723 [1195,] 3.819443e-07 0.4601723 0.4601723 [1196,] 3.845918e-07 0.4601724 0.4601723 [1197,] 3.872576e-07 0.4601724 0.4601723 [1198,] 3.899420e-07 0.4601724 0.4601723 [1199,] 3.926449e-07 0.4601724 0.4601723 [1200,] 3.953666e-07 0.4601724 0.4601723 [1201,] 3.981072e-07 0.4601724 0.4601723 [1202,] 4.008667e-07 0.4601724 0.4601723 [1203,] 4.036454e-07 0.4601724 0.4601723 [1204,] 4.064433e-07 0.4601724 0.4601723 [1205,] 4.092607e-07 0.4601724 0.4601723 [1206,] 4.120975e-07 0.4601724 0.4601723 [1207,] 4.149540e-07 0.4601724 0.4601723 [1208,] 4.178304e-07 0.4601724 0.4601723 [1209,] 4.207266e-07 0.4601724 0.4601723 [1210,] 4.236430e-07 0.4601724 0.4601723 [1211,] 4.265795e-07 0.4601724 0.4601723 [1212,] 4.295364e-07 0.4601724 0.4601723 [1213,] 4.325138e-07 0.4601724 0.4601723 [1214,] 4.355119e-07 0.4601724 0.4601723 [1215,] 4.385307e-07 0.4601724 0.4601723 [1216,] 4.415704e-07 0.4601724 0.4601723 [1217,] 4.446313e-07 0.4601724 0.4601723 [1218,] 4.477133e-07 0.4601724 0.4601723 [1219,] 4.508167e-07 0.4601724 0.4601723 [1220,] 4.539416e-07 0.4601724 0.4601723 [1221,] 4.570882e-07 0.4601724 0.4601723 [1222,] 4.602566e-07 0.4601724 0.4601723 [1223,] 4.634469e-07 0.4601724 0.4601723 [1224,] 4.666594e-07 0.4601724 0.4601723 [1225,] 4.698941e-07 0.4601724 0.4601723 [1226,] 4.731513e-07 0.4601724 0.4601723 [1227,] 4.764310e-07 0.4601724 0.4601723 [1228,] 4.797334e-07 0.4601724 0.4601723 [1229,] 4.830588e-07 0.4601724 0.4601723 [1230,] 4.864072e-07 0.4601724 0.4601723 [1231,] 4.897788e-07 0.4601724 0.4601723 [1232,] 4.931738e-07 0.4601724 0.4601723 [1233,] 4.965923e-07 0.4601724 0.4601723 [1234,] 5.000345e-07 0.4601724 0.4601723 [1235,] 5.035006e-07 0.4601724 0.4601723 [1236,] 5.069907e-07 0.4601724 0.4601723 [1237,] 5.105050e-07 0.4601724 0.4601723 [1238,] 5.140437e-07 0.4601724 0.4601724 [1239,] 5.176068e-07 0.4601724 0.4601724 [1240,] 5.211947e-07 0.4601724 0.4601724 [1241,] 5.248075e-07 0.4601724 0.4601724 [1242,] 5.284453e-07 0.4601724 0.4601724 [1243,] 5.321083e-07 0.4601724 0.4601724 [1244,] 5.357967e-07 0.4601724 0.4601724 [1245,] 5.395106e-07 0.4601724 0.4601724 [1246,] 5.432503e-07 0.4601724 0.4601724 [1247,] 5.470160e-07 0.4601724 0.4601724 [1248,] 5.508077e-07 0.4601724 0.4601724 [1249,] 5.546257e-07 0.4601724 0.4601724 [1250,] 5.584702e-07 0.4601724 0.4601724 [1251,] 5.623413e-07 0.4601724 0.4601724 [1252,] 5.662393e-07 0.4601724 0.4601724 [1253,] 5.701643e-07 0.4601724 0.4601724 [1254,] 5.741165e-07 0.4601724 0.4601724 [1255,] 5.780960e-07 0.4601724 0.4601724 [1256,] 5.821032e-07 0.4601724 0.4601724 [1257,] 5.861382e-07 0.4601724 0.4601724 [1258,] 5.902011e-07 0.4601725 0.4601724 [1259,] 5.942922e-07 0.4601725 0.4601724 [1260,] 5.984116e-07 0.4601725 0.4601724 [1261,] 6.025596e-07 0.4601725 0.4601724 [1262,] 6.067363e-07 0.4601725 0.4601724 [1263,] 6.109420e-07 0.4601725 0.4601724 [1264,] 6.151769e-07 0.4601725 0.4601724 [1265,] 6.194411e-07 0.4601725 0.4601724 [1266,] 6.237348e-07 0.4601725 0.4601724 [1267,] 6.280584e-07 0.4601725 0.4601724 [1268,] 6.324119e-07 0.4601725 0.4601724 [1269,] 6.367955e-07 0.4601725 0.4601724 [1270,] 6.412096e-07 0.4601725 0.4601724 [1271,] 6.456542e-07 0.4601725 0.4601724 [1272,] 6.501297e-07 0.4601725 0.4601724 [1273,] 6.546362e-07 0.4601725 0.4601724 [1274,] 6.591739e-07 0.4601725 0.4601724 [1275,] 6.637431e-07 0.4601725 0.4601724 [1276,] 6.683439e-07 0.4601725 0.4601724 [1277,] 6.729767e-07 0.4601725 0.4601724 [1278,] 6.776415e-07 0.4601725 0.4601724 [1279,] 6.823387e-07 0.4601725 0.4601724 [1280,] 6.870684e-07 0.4601725 0.4601724 [1281,] 6.918310e-07 0.4601725 0.4601724 [1282,] 6.966265e-07 0.4601725 0.4601724 [1283,] 7.014553e-07 0.4601725 0.4601724 [1284,] 7.063176e-07 0.4601725 0.4601724 [1285,] 7.112135e-07 0.4601725 0.4601724 [1286,] 7.161434e-07 0.4601725 0.4601724 [1287,] 7.211075e-07 0.4601725 0.4601724 [1288,] 7.261060e-07 0.4601725 0.4601724 [1289,] 7.311391e-07 0.4601725 0.4601724 [1290,] 7.362071e-07 0.4601725 0.4601724 [1291,] 7.413102e-07 0.4601725 0.4601724 [1292,] 7.464488e-07 0.4601725 0.4601724 [1293,] 7.516229e-07 0.4601725 0.4601724 [1294,] 7.568329e-07 0.4601725 0.4601724 [1295,] 7.620790e-07 0.4601725 0.4601724 [1296,] 7.673615e-07 0.4601725 0.4601724 [1297,] 7.726806e-07 0.4601725 0.4601724 [1298,] 7.780366e-07 0.4601725 0.4601724 [1299,] 7.834296e-07 0.4601725 0.4601724 [1300,] 7.888601e-07 0.4601725 0.4601725 [1301,] 7.943282e-07 0.4601726 0.4601725 [1302,] 7.998343e-07 0.4601726 0.4601725 [1303,] 8.053784e-07 0.4601726 0.4601725 [1304,] 8.109611e-07 0.4601726 0.4601725 [1305,] 8.165824e-07 0.4601726 0.4601725 [1306,] 8.222426e-07 0.4601726 0.4601725 [1307,] 8.279422e-07 0.4601726 0.4601725 [1308,] 8.336812e-07 0.4601726 0.4601725 [1309,] 8.394600e-07 0.4601726 0.4601725 [1310,] 8.452788e-07 0.4601726 0.4601725 [1311,] 8.511380e-07 0.4601726 0.4601725 [1312,] 8.570378e-07 0.4601726 0.4601725 [1313,] 8.629785e-07 0.4601726 0.4601725 [1314,] 8.689604e-07 0.4601726 0.4601725 [1315,] 8.749838e-07 0.4601726 0.4601725 [1316,] 8.810489e-07 0.4601726 0.4601725 [1317,] 8.871560e-07 0.4601726 0.4601725 [1318,] 8.933055e-07 0.4601726 0.4601725 [1319,] 8.994976e-07 0.4601726 0.4601725 [1320,] 9.057326e-07 0.4601726 0.4601725 [1321,] 9.120108e-07 0.4601726 0.4601725 [1322,] 9.183326e-07 0.4601726 0.4601725 [1323,] 9.246982e-07 0.4601726 0.4601725 [1324,] 9.311079e-07 0.4601726 0.4601725 [1325,] 9.375620e-07 0.4601726 0.4601725 [1326,] 9.440609e-07 0.4601726 0.4601725 [1327,] 9.506048e-07 0.4601726 0.4601725 [1328,] 9.571941e-07 0.4601726 0.4601725 [1329,] 9.638290e-07 0.4601726 0.4601725 [1330,] 9.705100e-07 0.4601726 0.4601725 [1331,] 9.772372e-07 0.4601726 0.4601725 [1332,] 9.840111e-07 0.4601726 0.4601725 [1333,] 9.908319e-07 0.4601726 0.4601725 [1334,] 9.977001e-07 0.4601726 0.4601725 [1335,] 1.004616e-06 0.4601727 0.4601725 [1336,] 1.011579e-06 0.4601727 0.4601725 [1337,] 1.018591e-06 0.4601727 0.4601725 [1338,] 1.025652e-06 0.4601727 0.4601725 [1339,] 1.032761e-06 0.4601727 0.4601725 [1340,] 1.039920e-06 0.4601727 0.4601725 [1341,] 1.047129e-06 0.4601727 0.4601725 [1342,] 1.054387e-06 0.4601727 0.4601725 [1343,] 1.061696e-06 0.4601727 0.4601726 [1344,] 1.069055e-06 0.4601727 0.4601726 [1345,] 1.076465e-06 0.4601727 0.4601726 [1346,] 1.083927e-06 0.4601727 0.4601726 [1347,] 1.091440e-06 0.4601727 0.4601726 [1348,] 1.099006e-06 0.4601727 0.4601726 [1349,] 1.106624e-06 0.4601727 0.4601726 [1350,] 1.114295e-06 0.4601727 0.4601726 [1351,] 1.122018e-06 0.4601727 0.4601726 [1352,] 1.129796e-06 0.4601727 0.4601726 [1353,] 1.137627e-06 0.4601727 0.4601726 [1354,] 1.145513e-06 0.4601727 0.4601726 [1355,] 1.153453e-06 0.4601727 0.4601726 [1356,] 1.161449e-06 0.4601727 0.4601726 [1357,] 1.169499e-06 0.4601727 0.4601726 [1358,] 1.177606e-06 0.4601727 0.4601726 [1359,] 1.185769e-06 0.4601727 0.4601726 [1360,] 1.193988e-06 0.4601727 0.4601726 [1361,] 1.202264e-06 0.4601727 0.4601726 [1362,] 1.210598e-06 0.4601728 0.4601726 [1363,] 1.218990e-06 0.4601728 0.4601726 [1364,] 1.227439e-06 0.4601728 0.4601726 [1365,] 1.235947e-06 0.4601728 0.4601726 [1366,] 1.244515e-06 0.4601728 0.4601726 [1367,] 1.253141e-06 0.4601728 0.4601726 [1368,] 1.261828e-06 0.4601728 0.4601726 [1369,] 1.270574e-06 0.4601728 0.4601726 [1370,] 1.279381e-06 0.4601728 0.4601726 [1371,] 1.288250e-06 0.4601728 0.4601726 [1372,] 1.297179e-06 0.4601728 0.4601726 [1373,] 1.306171e-06 0.4601728 0.4601726 [1374,] 1.315225e-06 0.4601728 0.4601726 [1375,] 1.324342e-06 0.4601728 0.4601726 [1376,] 1.333521e-06 0.4601728 0.4601727 [1377,] 1.342765e-06 0.4601728 0.4601727 [1378,] 1.352073e-06 0.4601728 0.4601727 [1379,] 1.361445e-06 0.4601728 0.4601727 [1380,] 1.370882e-06 0.4601728 0.4601727 [1381,] 1.380384e-06 0.4601728 0.4601727 [1382,] 1.389953e-06 0.4601728 0.4601727 [1383,] 1.399587e-06 0.4601728 0.4601727 [1384,] 1.409289e-06 0.4601728 0.4601727 [1385,] 1.419058e-06 0.4601729 0.4601727 [1386,] 1.428894e-06 0.4601729 0.4601727 [1387,] 1.438799e-06 0.4601729 0.4601727 [1388,] 1.448772e-06 0.4601729 0.4601727 [1389,] 1.458814e-06 0.4601729 0.4601727 [1390,] 1.468926e-06 0.4601729 0.4601727 [1391,] 1.479108e-06 0.4601729 0.4601727 [1392,] 1.489361e-06 0.4601729 0.4601727 [1393,] 1.499685e-06 0.4601729 0.4601727 [1394,] 1.510080e-06 0.4601729 0.4601727 [1395,] 1.520548e-06 0.4601729 0.4601727 [1396,] 1.531087e-06 0.4601729 0.4601727 [1397,] 1.541700e-06 0.4601729 0.4601727 [1398,] 1.552387e-06 0.4601729 0.4601727 [1399,] 1.563148e-06 0.4601729 0.4601727 [1400,] 1.573983e-06 0.4601729 0.4601727 [1401,] 1.584893e-06 0.4601729 0.4601727 [1402,] 1.595879e-06 0.4601729 0.4601727 [1403,] 1.606941e-06 0.4601729 0.4601728 [1404,] 1.618080e-06 0.4601730 0.4601728 [1405,] 1.629296e-06 0.4601730 0.4601728 [1406,] 1.640590e-06 0.4601730 0.4601728 [1407,] 1.651962e-06 0.4601730 0.4601728 [1408,] 1.663413e-06 0.4601730 0.4601728 [1409,] 1.674943e-06 0.4601730 0.4601728 [1410,] 1.686553e-06 0.4601730 0.4601728 [1411,] 1.698244e-06 0.4601730 0.4601728 [1412,] 1.710015e-06 0.4601730 0.4601728 [1413,] 1.721869e-06 0.4601730 0.4601728 [1414,] 1.733804e-06 0.4601730 0.4601728 [1415,] 1.745822e-06 0.4601730 0.4601728 [1416,] 1.757924e-06 0.4601730 0.4601728 [1417,] 1.770109e-06 0.4601730 0.4601728 [1418,] 1.782379e-06 0.4601730 0.4601728 [1419,] 1.794734e-06 0.4601730 0.4601728 [1420,] 1.807174e-06 0.4601730 0.4601728 [1421,] 1.819701e-06 0.4601731 0.4601728 [1422,] 1.832314e-06 0.4601731 0.4601728 [1423,] 1.845015e-06 0.4601731 0.4601728 [1424,] 1.857804e-06 0.4601731 0.4601728 [1425,] 1.870682e-06 0.4601731 0.4601728 [1426,] 1.883649e-06 0.4601731 0.4601729 [1427,] 1.896706e-06 0.4601731 0.4601729 [1428,] 1.909853e-06 0.4601731 0.4601729 [1429,] 1.923092e-06 0.4601731 0.4601729 [1430,] 1.936422e-06 0.4601731 0.4601729 [1431,] 1.949845e-06 0.4601731 0.4601729 [1432,] 1.963360e-06 0.4601731 0.4601729 [1433,] 1.976970e-06 0.4601731 0.4601729 [1434,] 1.990673e-06 0.4601731 0.4601729 [1435,] 2.004472e-06 0.4601731 0.4601729 [1436,] 2.018366e-06 0.4601731 0.4601729 [1437,] 2.032357e-06 0.4601732 0.4601729 [1438,] 2.046445e-06 0.4601732 0.4601729 [1439,] 2.060630e-06 0.4601732 0.4601729 [1440,] 2.074914e-06 0.4601732 0.4601729 [1441,] 2.089296e-06 0.4601732 0.4601729 [1442,] 2.103778e-06 0.4601732 0.4601729 [1443,] 2.118361e-06 0.4601732 0.4601729 [1444,] 2.133045e-06 0.4601732 0.4601729 [1445,] 2.147830e-06 0.4601732 0.4601729 [1446,] 2.162719e-06 0.4601732 0.4601730 [1447,] 2.177710e-06 0.4601732 0.4601730 [1448,] 2.192805e-06 0.4601732 0.4601730 [1449,] 2.208005e-06 0.4601732 0.4601730 [1450,] 2.223310e-06 0.4601732 0.4601730 [1451,] 2.238721e-06 0.4601733 0.4601730 [1452,] 2.254239e-06 0.4601733 0.4601730 [1453,] 2.269865e-06 0.4601733 0.4601730 [1454,] 2.285599e-06 0.4601733 0.4601730 [1455,] 2.301442e-06 0.4601733 0.4601730 [1456,] 2.317395e-06 0.4601733 0.4601730 [1457,] 2.333458e-06 0.4601733 0.4601730 [1458,] 2.349633e-06 0.4601733 0.4601730 [1459,] 2.365920e-06 0.4601733 0.4601730 [1460,] 2.382319e-06 0.4601733 0.4601730 [1461,] 2.398833e-06 0.4601733 0.4601730 [1462,] 2.415461e-06 0.4601733 0.4601730 [1463,] 2.432204e-06 0.4601733 0.4601731 [1464,] 2.449063e-06 0.4601734 0.4601731 [1465,] 2.466039e-06 0.4601734 0.4601731 [1466,] 2.483133e-06 0.4601734 0.4601731 [1467,] 2.500345e-06 0.4601734 0.4601731 [1468,] 2.517677e-06 0.4601734 0.4601731 [1469,] 2.535129e-06 0.4601734 0.4601731 [1470,] 2.552701e-06 0.4601734 0.4601731 [1471,] 2.570396e-06 0.4601734 0.4601731 [1472,] 2.588213e-06 0.4601734 0.4601731 [1473,] 2.606154e-06 0.4601734 0.4601731 [1474,] 2.624219e-06 0.4601734 0.4601731 [1475,] 2.642409e-06 0.4601735 0.4601731 [1476,] 2.660725e-06 0.4601735 0.4601731 [1477,] 2.679168e-06 0.4601735 0.4601731 [1478,] 2.697739e-06 0.4601735 0.4601731 [1479,] 2.716439e-06 0.4601735 0.4601732 [1480,] 2.735269e-06 0.4601735 0.4601732 [1481,] 2.754229e-06 0.4601735 0.4601732 [1482,] 2.773320e-06 0.4601735 0.4601732 [1483,] 2.792544e-06 0.4601735 0.4601732 [1484,] 2.811901e-06 0.4601735 0.4601732 [1485,] 2.831392e-06 0.4601735 0.4601732 [1486,] 2.851018e-06 0.4601736 0.4601732 [1487,] 2.870781e-06 0.4601736 0.4601732 [1488,] 2.890680e-06 0.4601736 0.4601732 [1489,] 2.910717e-06 0.4601736 0.4601732 [1490,] 2.930893e-06 0.4601736 0.4601732 [1491,] 2.951209e-06 0.4601736 0.4601732 [1492,] 2.971666e-06 0.4601736 0.4601732 [1493,] 2.992265e-06 0.4601736 0.4601733 [1494,] 3.013006e-06 0.4601736 0.4601733 [1495,] 3.033891e-06 0.4601736 0.4601733 [1496,] 3.054921e-06 0.4601737 0.4601733 [1497,] 3.076097e-06 0.4601737 0.4601733 [1498,] 3.097419e-06 0.4601737 0.4601733 [1499,] 3.118890e-06 0.4601737 0.4601733 [1500,] 3.140509e-06 0.4601737 0.4601733 [1501,] 3.162278e-06 0.4601737 0.4601733 [1502,] 3.184198e-06 0.4601737 0.4601733 [1503,] 3.206269e-06 0.4601737 0.4601733 [1504,] 3.228494e-06 0.4601737 0.4601733 [1505,] 3.250873e-06 0.4601737 0.4601734 [1506,] 3.273407e-06 0.4601738 0.4601734 [1507,] 3.296097e-06 0.4601738 0.4601734 [1508,] 3.318945e-06 0.4601738 0.4601734 [1509,] 3.341950e-06 0.4601738 0.4601734 [1510,] 3.365116e-06 0.4601738 0.4601734 [1511,] 3.388442e-06 0.4601738 0.4601734 [1512,] 3.411929e-06 0.4601738 0.4601734 [1513,] 3.435579e-06 0.4601738 0.4601734 [1514,] 3.459394e-06 0.4601738 0.4601734 [1515,] 3.483373e-06 0.4601739 0.4601734 [1516,] 3.507519e-06 0.4601739 0.4601734 [1517,] 3.531832e-06 0.4601739 0.4601735 [1518,] 3.556313e-06 0.4601739 0.4601735 [1519,] 3.580964e-06 0.4601739 0.4601735 [1520,] 3.605786e-06 0.4601739 0.4601735 [1521,] 3.630781e-06 0.4601739 0.4601735 [1522,] 3.655948e-06 0.4601739 0.4601735 [1523,] 3.681290e-06 0.4601740 0.4601735 [1524,] 3.706807e-06 0.4601740 0.4601735 [1525,] 3.732502e-06 0.4601740 0.4601735 [1526,] 3.758374e-06 0.4601740 0.4601735 [1527,] 3.784426e-06 0.4601740 0.4601735 [1528,] 3.810658e-06 0.4601740 0.4601736 [1529,] 3.837072e-06 0.4601740 0.4601736 [1530,] 3.863670e-06 0.4601740 0.4601736 [1531,] 3.890451e-06 0.4601741 0.4601736 [1532,] 3.917419e-06 0.4601741 0.4601736 [1533,] 3.944573e-06 0.4601741 0.4601736 [1534,] 3.971915e-06 0.4601741 0.4601736 [1535,] 3.999447e-06 0.4601741 0.4601736 [1536,] 4.027170e-06 0.4601741 0.4601736 [1537,] 4.055085e-06 0.4601741 0.4601736 [1538,] 4.083194e-06 0.4601742 0.4601737 [1539,] 4.111497e-06 0.4601742 0.4601737 [1540,] 4.139997e-06 0.4601742 0.4601737 [1541,] 4.168694e-06 0.4601742 0.4601737 [1542,] 4.197590e-06 0.4601742 0.4601737 [1543,] 4.226686e-06 0.4601742 0.4601737 [1544,] 4.255984e-06 0.4601742 0.4601737 [1545,] 4.285485e-06 0.4601743 0.4601737 [1546,] 4.315191e-06 0.4601743 0.4601737 [1547,] 4.345102e-06 0.4601743 0.4601738 [1548,] 4.375221e-06 0.4601743 0.4601738 [1549,] 4.405549e-06 0.4601743 0.4601738 [1550,] 4.436086e-06 0.4601743 0.4601738 [1551,] 4.466836e-06 0.4601743 0.4601738 [1552,] 4.497799e-06 0.4601744 0.4601738 [1553,] 4.528976e-06 0.4601744 0.4601738 [1554,] 4.560369e-06 0.4601744 0.4601738 [1555,] 4.591980e-06 0.4601744 0.4601738 [1556,] 4.623810e-06 0.4601744 0.4601739 [1557,] 4.655861e-06 0.4601744 0.4601739 [1558,] 4.688134e-06 0.4601744 0.4601739 [1559,] 4.720630e-06 0.4601745 0.4601739 [1560,] 4.753352e-06 0.4601745 0.4601739 [1561,] 4.786301e-06 0.4601745 0.4601739 [1562,] 4.819478e-06 0.4601745 0.4601739 [1563,] 4.852885e-06 0.4601745 0.4601739 [1564,] 4.886524e-06 0.4601745 0.4601739 [1565,] 4.920395e-06 0.4601746 0.4601740 [1566,] 4.954502e-06 0.4601746 0.4601740 [1567,] 4.988845e-06 0.4601746 0.4601740 [1568,] 5.023426e-06 0.4601746 0.4601740 [1569,] 5.058247e-06 0.4601746 0.4601740 [1570,] 5.093309e-06 0.4601746 0.4601740 [1571,] 5.128614e-06 0.4601747 0.4601740 [1572,] 5.164164e-06 0.4601747 0.4601741 [1573,] 5.199960e-06 0.4601747 0.4601741 [1574,] 5.236004e-06 0.4601747 0.4601741 [1575,] 5.272299e-06 0.4601747 0.4601741 [1576,] 5.308844e-06 0.4601748 0.4601741 [1577,] 5.345644e-06 0.4601748 0.4601741 [1578,] 5.382698e-06 0.4601748 0.4601741 [1579,] 5.420009e-06 0.4601748 0.4601741 [1580,] 5.457579e-06 0.4601748 0.4601742 [1581,] 5.495409e-06 0.4601748 0.4601742 [1582,] 5.533501e-06 0.4601749 0.4601742 [1583,] 5.571857e-06 0.4601749 0.4601742 [1584,] 5.610480e-06 0.4601749 0.4601742 [1585,] 5.649370e-06 0.4601749 0.4601742 [1586,] 5.688529e-06 0.4601749 0.4601742 [1587,] 5.727960e-06 0.4601750 0.4601743 [1588,] 5.767665e-06 0.4601750 0.4601743 [1589,] 5.807644e-06 0.4601750 0.4601743 [1590,] 5.847901e-06 0.4601750 0.4601743 [1591,] 5.888437e-06 0.4601750 0.4601743 [1592,] 5.929253e-06 0.4601751 0.4601743 [1593,] 5.970353e-06 0.4601751 0.4601743 [1594,] 6.011737e-06 0.4601751 0.4601744 [1595,] 6.053409e-06 0.4601751 0.4601744 [1596,] 6.095369e-06 0.4601751 0.4601744 [1597,] 6.137620e-06 0.4601752 0.4601744 [1598,] 6.180164e-06 0.4601752 0.4601744 [1599,] 6.223003e-06 0.4601752 0.4601744 [1600,] 6.266139e-06 0.4601752 0.4601745 [1601,] 6.309573e-06 0.4601752 0.4601745 [1602,] 6.353309e-06 0.4601753 0.4601745 [1603,] 6.397348e-06 0.4601753 0.4601745 [1604,] 6.441693e-06 0.4601753 0.4601745 [1605,] 6.486344e-06 0.4601753 0.4601745 [1606,] 6.531306e-06 0.4601753 0.4601746 [1607,] 6.576578e-06 0.4601754 0.4601746 [1608,] 6.622165e-06 0.4601754 0.4601746 [1609,] 6.668068e-06 0.4601754 0.4601746 [1610,] 6.714289e-06 0.4601754 0.4601746 [1611,] 6.760830e-06 0.4601755 0.4601746 [1612,] 6.807694e-06 0.4601755 0.4601747 [1613,] 6.854882e-06 0.4601755 0.4601747 [1614,] 6.902398e-06 0.4601755 0.4601747 [1615,] 6.950243e-06 0.4601756 0.4601747 [1616,] 6.998420e-06 0.4601756 0.4601747 [1617,] 7.046931e-06 0.4601756 0.4601747 [1618,] 7.095778e-06 0.4601756 0.4601748 [1619,] 7.144963e-06 0.4601756 0.4601748 [1620,] 7.194490e-06 0.4601757 0.4601748 [1621,] 7.244360e-06 0.4601757 0.4601748 [1622,] 7.294575e-06 0.4601757 0.4601748 [1623,] 7.345139e-06 0.4601757 0.4601748 [1624,] 7.396053e-06 0.4601758 0.4601749 [1625,] 7.447320e-06 0.4601758 0.4601749 [1626,] 7.498942e-06 0.4601758 0.4601749 [1627,] 7.550922e-06 0.4601758 0.4601749 [1628,] 7.603263e-06 0.4601759 0.4601749 [1629,] 7.655966e-06 0.4601759 0.4601750 [1630,] 7.709035e-06 0.4601759 0.4601750 [1631,] 7.762471e-06 0.4601759 0.4601750 [1632,] 7.816278e-06 0.4601760 0.4601750 [1633,] 7.870458e-06 0.4601760 0.4601750 [1634,] 7.925013e-06 0.4601760 0.4601751 [1635,] 7.979947e-06 0.4601761 0.4601751 [1636,] 8.035261e-06 0.4601761 0.4601751 [1637,] 8.090959e-06 0.4601761 0.4601751 [1638,] 8.147043e-06 0.4601761 0.4601751 [1639,] 8.203515e-06 0.4601762 0.4601752 [1640,] 8.260379e-06 0.4601762 0.4601752 [1641,] 8.317638e-06 0.4601762 0.4601752 [1642,] 8.375293e-06 0.4601762 0.4601752 [1643,] 8.433348e-06 0.4601763 0.4601752 [1644,] 8.491805e-06 0.4601763 0.4601753 [1645,] 8.550667e-06 0.4601763 0.4601753 [1646,] 8.609938e-06 0.4601764 0.4601753 [1647,] 8.669619e-06 0.4601764 0.4601753 [1648,] 8.729714e-06 0.4601764 0.4601754 [1649,] 8.790225e-06 0.4601764 0.4601754 [1650,] 8.851156e-06 0.4601765 0.4601754 [1651,] 8.912509e-06 0.4601765 0.4601754 [1652,] 8.974288e-06 0.4601765 0.4601754 [1653,] 9.036495e-06 0.4601766 0.4601755 [1654,] 9.099133e-06 0.4601766 0.4601755 [1655,] 9.162205e-06 0.4601766 0.4601755 [1656,] 9.225714e-06 0.4601767 0.4601755 [1657,] 9.289664e-06 0.4601767 0.4601756 [1658,] 9.354057e-06 0.4601767 0.4601756 [1659,] 9.418896e-06 0.4601768 0.4601756 [1660,] 9.484185e-06 0.4601768 0.4601756 [1661,] 9.549926e-06 0.4601768 0.4601757 [1662,] 9.616123e-06 0.4601769 0.4601757 [1663,] 9.682779e-06 0.4601769 0.4601757 [1664,] 9.749896e-06 0.4601769 0.4601757 [1665,] 9.817479e-06 0.4601769 0.4601758 [1666,] 9.885531e-06 0.4601770 0.4601758 [1667,] 9.954054e-06 0.4601770 0.4601758 [1668,] 1.002305e-05 0.4601771 0.4601758 [1669,] 1.009253e-05 0.4601771 0.4601759 [1670,] 1.016249e-05 0.4601771 0.4601759 [1671,] 1.023293e-05 0.4601772 0.4601759 [1672,] 1.030386e-05 0.4601772 0.4601759 [1673,] 1.037528e-05 0.4601772 0.4601760 [1674,] 1.044720e-05 0.4601773 0.4601760 [1675,] 1.051962e-05 0.4601773 0.4601760 [1676,] 1.059254e-05 0.4601773 0.4601760 [1677,] 1.066596e-05 0.4601774 0.4601761 [1678,] 1.073989e-05 0.4601774 0.4601761 [1679,] 1.081434e-05 0.4601774 0.4601761 [1680,] 1.088930e-05 0.4601775 0.4601761 [1681,] 1.096478e-05 0.4601775 0.4601762 [1682,] 1.104079e-05 0.4601775 0.4601762 [1683,] 1.111732e-05 0.4601776 0.4601762 [1684,] 1.119438e-05 0.4601776 0.4601763 [1685,] 1.127197e-05 0.4601777 0.4601763 [1686,] 1.135011e-05 0.4601777 0.4601763 [1687,] 1.142878e-05 0.4601777 0.4601763 [1688,] 1.150800e-05 0.4601778 0.4601764 [1689,] 1.158777e-05 0.4601778 0.4601764 [1690,] 1.166810e-05 0.4601779 0.4601764 [1691,] 1.174898e-05 0.4601779 0.4601765 [1692,] 1.183042e-05 0.4601779 0.4601765 [1693,] 1.191242e-05 0.4601780 0.4601765 [1694,] 1.199499e-05 0.4601780 0.4601765 [1695,] 1.207814e-05 0.4601781 0.4601766 [1696,] 1.216186e-05 0.4601781 0.4601766 [1697,] 1.224616e-05 0.4601781 0.4601766 [1698,] 1.233105e-05 0.4601782 0.4601767 [1699,] 1.241652e-05 0.4601782 0.4601767 [1700,] 1.250259e-05 0.4601783 0.4601767 [1701,] 1.258925e-05 0.4601783 0.4601768 [1702,] 1.267652e-05 0.4601783 0.4601768 [1703,] 1.276439e-05 0.4601784 0.4601768 [1704,] 1.285287e-05 0.4601784 0.4601769 [1705,] 1.294196e-05 0.4601785 0.4601769 [1706,] 1.303167e-05 0.4601785 0.4601769 [1707,] 1.312200e-05 0.4601786 0.4601770 [1708,] 1.321296e-05 0.4601786 0.4601770 [1709,] 1.330454e-05 0.4601787 0.4601770 [1710,] 1.339677e-05 0.4601787 0.4601771 [1711,] 1.348963e-05 0.4601787 0.4601771 [1712,] 1.358313e-05 0.4601788 0.4601771 [1713,] 1.367729e-05 0.4601788 0.4601772 [1714,] 1.377209e-05 0.4601789 0.4601772 [1715,] 1.386756e-05 0.4601789 0.4601772 [1716,] 1.396368e-05 0.4601790 0.4601773 [1717,] 1.406048e-05 0.4601790 0.4601773 [1718,] 1.415794e-05 0.4601791 0.4601773 [1719,] 1.425608e-05 0.4601791 0.4601774 [1720,] 1.435489e-05 0.4601792 0.4601774 [1721,] 1.445440e-05 0.4601792 0.4601774 [1722,] 1.455459e-05 0.4601793 0.4601775 [1723,] 1.465548e-05 0.4601793 0.4601775 [1724,] 1.475707e-05 0.4601794 0.4601776 [1725,] 1.485936e-05 0.4601794 0.4601776 [1726,] 1.496236e-05 0.4601795 0.4601776 [1727,] 1.506607e-05 0.4601795 0.4601777 [1728,] 1.517050e-05 0.4601796 0.4601777 [1729,] 1.527566e-05 0.4601796 0.4601777 [1730,] 1.538155e-05 0.4601797 0.4601778 [1731,] 1.548817e-05 0.4601797 0.4601778 [1732,] 1.559553e-05 0.4601798 0.4601779 [1733,] 1.570363e-05 0.4601798 0.4601779 [1734,] 1.581248e-05 0.4601799 0.4601779 [1735,] 1.592209e-05 0.4601799 0.4601780 [1736,] 1.603245e-05 0.4601800 0.4601780 [1737,] 1.614359e-05 0.4601800 0.4601781 [1738,] 1.625549e-05 0.4601801 0.4601781 [1739,] 1.636817e-05 0.4601801 0.4601781 [1740,] 1.648162e-05 0.4601802 0.4601782 [1741,] 1.659587e-05 0.4601803 0.4601782 [1742,] 1.671091e-05 0.4601803 0.4601783 [1743,] 1.682674e-05 0.4601804 0.4601783 [1744,] 1.694338e-05 0.4601804 0.4601784 [1745,] 1.706082e-05 0.4601805 0.4601784 [1746,] 1.717908e-05 0.4601805 0.4601784 [1747,] 1.729816e-05 0.4601806 0.4601785 [1748,] 1.741807e-05 0.4601807 0.4601785 [1749,] 1.753881e-05 0.4601807 0.4601786 [1750,] 1.766038e-05 0.4601808 0.4601786 [1751,] 1.778279e-05 0.4601808 0.4601787 [1752,] 1.790606e-05 0.4601809 0.4601787 [1753,] 1.803018e-05 0.4601810 0.4601788 [1754,] 1.815516e-05 0.4601810 0.4601788 [1755,] 1.828100e-05 0.4601811 0.4601788 [1756,] 1.840772e-05 0.4601811 0.4601789 [1757,] 1.853532e-05 0.4601812 0.4601789 [1758,] 1.866380e-05 0.4601813 0.4601790 [1759,] 1.879317e-05 0.4601813 0.4601790 [1760,] 1.892344e-05 0.4601814 0.4601791 [1761,] 1.905461e-05 0.4601815 0.4601791 [1762,] 1.918669e-05 0.4601815 0.4601792 [1763,] 1.931968e-05 0.4601816 0.4601792 [1764,] 1.945360e-05 0.4601816 0.4601793 [1765,] 1.958845e-05 0.4601817 0.4601793 [1766,] 1.972423e-05 0.4601818 0.4601794 [1767,] 1.986095e-05 0.4601818 0.4601794 [1768,] 1.999862e-05 0.4601819 0.4601795 [1769,] 2.013724e-05 0.4601820 0.4601795 [1770,] 2.027683e-05 0.4601821 0.4601796 [1771,] 2.041738e-05 0.4601821 0.4601796 [1772,] 2.055891e-05 0.4601822 0.4601797 [1773,] 2.070141e-05 0.4601823 0.4601797 [1774,] 2.084491e-05 0.4601823 0.4601798 [1775,] 2.098940e-05 0.4601824 0.4601798 [1776,] 2.113489e-05 0.4601825 0.4601799 [1777,] 2.128139e-05 0.4601825 0.4601799 [1778,] 2.142891e-05 0.4601826 0.4601800 [1779,] 2.157744e-05 0.4601827 0.4601801 [1780,] 2.172701e-05 0.4601828 0.4601801 [1781,] 2.187762e-05 0.4601828 0.4601802 [1782,] 2.202926e-05 0.4601829 0.4601802 [1783,] 2.218196e-05 0.4601830 0.4601803 [1784,] 2.233572e-05 0.4601831 0.4601803 [1785,] 2.249055e-05 0.4601831 0.4601804 [1786,] 2.264644e-05 0.4601832 0.4601804 [1787,] 2.280342e-05 0.4601833 0.4601805 [1788,] 2.296149e-05 0.4601834 0.4601806 [1789,] 2.312065e-05 0.4601834 0.4601806 [1790,] 2.328091e-05 0.4601835 0.4601807 [1791,] 2.344229e-05 0.4601836 0.4601807 [1792,] 2.360478e-05 0.4601837 0.4601808 [1793,] 2.376840e-05 0.4601838 0.4601809 [1794,] 2.393316e-05 0.4601838 0.4601809 [1795,] 2.409905e-05 0.4601839 0.4601810 [1796,] 2.426610e-05 0.4601840 0.4601810 [1797,] 2.443431e-05 0.4601841 0.4601811 [1798,] 2.460368e-05 0.4601842 0.4601812 [1799,] 2.477422e-05 0.4601842 0.4601812 [1800,] 2.494595e-05 0.4601843 0.4601813 [1801,] 2.511886e-05 0.4601844 0.4601813 [1802,] 2.529298e-05 0.4601845 0.4601814 [1803,] 2.546830e-05 0.4601846 0.4601815 [1804,] 2.564484e-05 0.4601847 0.4601815 [1805,] 2.582260e-05 0.4601848 0.4601816 [1806,] 2.600160e-05 0.4601848 0.4601817 [1807,] 2.618183e-05 0.4601849 0.4601817 [1808,] 2.636331e-05 0.4601850 0.4601818 [1809,] 2.654606e-05 0.4601851 0.4601819 [1810,] 2.673006e-05 0.4601852 0.4601819 [1811,] 2.691535e-05 0.4601853 0.4601820 [1812,] 2.710192e-05 0.4601854 0.4601821 [1813,] 2.728978e-05 0.4601855 0.4601821 [1814,] 2.747894e-05 0.4601856 0.4601822 [1815,] 2.766942e-05 0.4601857 0.4601823 [1816,] 2.786121e-05 0.4601857 0.4601824 [1817,] 2.805434e-05 0.4601858 0.4601824 [1818,] 2.824880e-05 0.4601859 0.4601825 [1819,] 2.844461e-05 0.4601860 0.4601826 [1820,] 2.864178e-05 0.4601861 0.4601826 [1821,] 2.884032e-05 0.4601862 0.4601827 [1822,] 2.904023e-05 0.4601863 0.4601828 [1823,] 2.924152e-05 0.4601864 0.4601829 [1824,] 2.944422e-05 0.4601865 0.4601829 [1825,] 2.964831e-05 0.4601866 0.4601830 [1826,] 2.985383e-05 0.4601867 0.4601831 [1827,] 3.006076e-05 0.4601868 0.4601832 [1828,] 3.026913e-05 0.4601869 0.4601832 [1829,] 3.047895e-05 0.4601870 0.4601833 [1830,] 3.069022e-05 0.4601871 0.4601834 [1831,] 3.090295e-05 0.4601872 0.4601835 [1832,] 3.111716e-05 0.4601873 0.4601835 [1833,] 3.133286e-05 0.4601874 0.4601836 [1834,] 3.155005e-05 0.4601875 0.4601837 [1835,] 3.176874e-05 0.4601877 0.4601838 [1836,] 3.198895e-05 0.4601878 0.4601839 [1837,] 3.221069e-05 0.4601879 0.4601839 [1838,] 3.243396e-05 0.4601880 0.4601840 [1839,] 3.265878e-05 0.4601881 0.4601841 [1840,] 3.288516e-05 0.4601882 0.4601842 [1841,] 3.311311e-05 0.4601883 0.4601843 [1842,] 3.334264e-05 0.4601884 0.4601844 [1843,] 3.357376e-05 0.4601885 0.4601844 [1844,] 3.380648e-05 0.4601886 0.4601845 [1845,] 3.404082e-05 0.4601888 0.4601846 [1846,] 3.427678e-05 0.4601889 0.4601847 [1847,] 3.451437e-05 0.4601890 0.4601848 [1848,] 3.475362e-05 0.4601891 0.4601849 [1849,] 3.499452e-05 0.4601892 0.4601850 [1850,] 3.523709e-05 0.4601893 0.4601850 [1851,] 3.548134e-05 0.4601895 0.4601851 [1852,] 3.572728e-05 0.4601896 0.4601852 [1853,] 3.597493e-05 0.4601897 0.4601853 [1854,] 3.622430e-05 0.4601898 0.4601854 [1855,] 3.647539e-05 0.4601899 0.4601855 [1856,] 3.672823e-05 0.4601901 0.4601856 [1857,] 3.698282e-05 0.4601902 0.4601857 [1858,] 3.723917e-05 0.4601903 0.4601858 [1859,] 3.749730e-05 0.4601904 0.4601859 [1860,] 3.775722e-05 0.4601906 0.4601860 [1861,] 3.801894e-05 0.4601907 0.4601861 [1862,] 3.828247e-05 0.4601908 0.4601862 [1863,] 3.854784e-05 0.4601910 0.4601863 [1864,] 3.881504e-05 0.4601911 0.4601864 [1865,] 3.908409e-05 0.4601912 0.4601865 [1866,] 3.935501e-05 0.4601914 0.4601866 [1867,] 3.962780e-05 0.4601915 0.4601867 [1868,] 3.990249e-05 0.4601916 0.4601868 [1869,] 4.017908e-05 0.4601918 0.4601869 [1870,] 4.045759e-05 0.4601919 0.4601870 [1871,] 4.073803e-05 0.4601920 0.4601871 [1872,] 4.102041e-05 0.4601922 0.4601872 [1873,] 4.130475e-05 0.4601923 0.4601873 [1874,] 4.159106e-05 0.4601924 0.4601874 [1875,] 4.187936e-05 0.4601926 0.4601875 [1876,] 4.216965e-05 0.4601927 0.4601876 [1877,] 4.246196e-05 0.4601929 0.4601877 [1878,] 4.275629e-05 0.4601930 0.4601878 [1879,] 4.305266e-05 0.4601932 0.4601879 [1880,] 4.335109e-05 0.4601933 0.4601880 [1881,] 4.365158e-05 0.4601934 0.4601881 [1882,] 4.395416e-05 0.4601936 0.4601882 [1883,] 4.425884e-05 0.4601937 0.4601883 [1884,] 4.456562e-05 0.4601939 0.4601885 [1885,] 4.487454e-05 0.4601940 0.4601886 [1886,] 4.518559e-05 0.4601942 0.4601887 [1887,] 4.549881e-05 0.4601943 0.4601888 [1888,] 4.581419e-05 0.4601945 0.4601889 [1889,] 4.613176e-05 0.4601947 0.4601890 [1890,] 4.645153e-05 0.4601948 0.4601892 [1891,] 4.677351e-05 0.4601950 0.4601893 [1892,] 4.709773e-05 0.4601951 0.4601894 [1893,] 4.742420e-05 0.4601953 0.4601895 [1894,] 4.775293e-05 0.4601954 0.4601896 [1895,] 4.808393e-05 0.4601956 0.4601897 [1896,] 4.841724e-05 0.4601958 0.4601899 [1897,] 4.875285e-05 0.4601959 0.4601900 [1898,] 4.909079e-05 0.4601961 0.4601901 [1899,] 4.943107e-05 0.4601963 0.4601902 [1900,] 4.977371e-05 0.4601964 0.4601904 [1901,] 5.011872e-05 0.4601966 0.4601905 [1902,] 5.046613e-05 0.4601968 0.4601906 [1903,] 5.081594e-05 0.4601969 0.4601907 [1904,] 5.116818e-05 0.4601971 0.4601909 [1905,] 5.152286e-05 0.4601973 0.4601910 [1906,] 5.188000e-05 0.4601975 0.4601911 [1907,] 5.223962e-05 0.4601976 0.4601913 [1908,] 5.260173e-05 0.4601978 0.4601914 [1909,] 5.296634e-05 0.4601980 0.4601915 [1910,] 5.333349e-05 0.4601982 0.4601917 [1911,] 5.370318e-05 0.4601983 0.4601918 [1912,] 5.407543e-05 0.4601985 0.4601919 [1913,] 5.445027e-05 0.4601987 0.4601921 [1914,] 5.482770e-05 0.4601989 0.4601922 [1915,] 5.520774e-05 0.4601991 0.4601924 [1916,] 5.559043e-05 0.4601993 0.4601925 [1917,] 5.597576e-05 0.4601995 0.4601926 [1918,] 5.636377e-05 0.4601996 0.4601928 [1919,] 5.675446e-05 0.4601998 0.4601929 [1920,] 5.714786e-05 0.4602000 0.4601931 [1921,] 5.754399e-05 0.4602002 0.4601932 [1922,] 5.794287e-05 0.4602004 0.4601934 [1923,] 5.834451e-05 0.4602006 0.4601935 [1924,] 5.874894e-05 0.4602008 0.4601936 [1925,] 5.915616e-05 0.4602010 0.4601938 [1926,] 5.956621e-05 0.4602012 0.4601939 [1927,] 5.997911e-05 0.4602014 0.4601941 [1928,] 6.039486e-05 0.4602016 0.4601943 [1929,] 6.081350e-05 0.4602018 0.4601944 [1930,] 6.123504e-05 0.4602020 0.4601946 [1931,] 6.165950e-05 0.4602022 0.4601947 [1932,] 6.208690e-05 0.4602024 0.4601949 [1933,] 6.251727e-05 0.4602026 0.4601950 [1934,] 6.295062e-05 0.4602029 0.4601952 [1935,] 6.338697e-05 0.4602031 0.4601953 [1936,] 6.382635e-05 0.4602033 0.4601955 [1937,] 6.426877e-05 0.4602035 0.4601957 [1938,] 6.471426e-05 0.4602037 0.4601958 [1939,] 6.516284e-05 0.4602039 0.4601960 [1940,] 6.561453e-05 0.4602042 0.4601962 [1941,] 6.606934e-05 0.4602044 0.4601963 [1942,] 6.652732e-05 0.4602046 0.4601965 [1943,] 6.698846e-05 0.4602048 0.4601967 [1944,] 6.745280e-05 0.4602051 0.4601968 [1945,] 6.792036e-05 0.4602053 0.4601970 [1946,] 6.839116e-05 0.4602055 0.4601972 [1947,] 6.886523e-05 0.4602057 0.4601973 [1948,] 6.934258e-05 0.4602060 0.4601975 [1949,] 6.982324e-05 0.4602062 0.4601977 [1950,] 7.030723e-05 0.4602064 0.4601979 [1951,] 7.079458e-05 0.4602067 0.4601981 [1952,] 7.128530e-05 0.4602069 0.4601982 [1953,] 7.177943e-05 0.4602072 0.4601984 [1954,] 7.227698e-05 0.4602074 0.4601986 [1955,] 7.277798e-05 0.4602077 0.4601988 [1956,] 7.328245e-05 0.4602079 0.4601990 [1957,] 7.379042e-05 0.4602081 0.4601991 [1958,] 7.430191e-05 0.4602084 0.4601993 [1959,] 7.481695e-05 0.4602086 0.4601995 [1960,] 7.533556e-05 0.4602089 0.4601997 [1961,] 7.585776e-05 0.4602092 0.4601999 [1962,] 7.638358e-05 0.4602094 0.4602001 [1963,] 7.691304e-05 0.4602097 0.4602003 [1964,] 7.744618e-05 0.4602099 0.4602005 [1965,] 7.798301e-05 0.4602102 0.4602007 [1966,] 7.852356e-05 0.4602105 0.4602009 [1967,] 7.906786e-05 0.4602107 0.4602011 [1968,] 7.961594e-05 0.4602110 0.4602013 [1969,] 8.016781e-05 0.4602113 0.4602015 [1970,] 8.072350e-05 0.4602115 0.4602017 [1971,] 8.128305e-05 0.4602118 0.4602019 [1972,] 8.184648e-05 0.4602121 0.4602021 [1973,] 8.241381e-05 0.4602124 0.4602023 [1974,] 8.298508e-05 0.4602126 0.4602025 [1975,] 8.356030e-05 0.4602129 0.4602027 [1976,] 8.413951e-05 0.4602132 0.4602029 [1977,] 8.472274e-05 0.4602135 0.4602031 [1978,] 8.531001e-05 0.4602138 0.4602034 [1979,] 8.590135e-05 0.4602141 0.4602036 [1980,] 8.649679e-05 0.4602143 0.4602038 [1981,] 8.709636e-05 0.4602146 0.4602040 [1982,] 8.770008e-05 0.4602149 0.4602042 [1983,] 8.830799e-05 0.4602152 0.4602045 [1984,] 8.892011e-05 0.4602155 0.4602047 [1985,] 8.953648e-05 0.4602158 0.4602049 [1986,] 9.015711e-05 0.4602161 0.4602051 [1987,] 9.078205e-05 0.4602164 0.4602054 [1988,] 9.141132e-05 0.4602167 0.4602056 [1989,] 9.204496e-05 0.4602170 0.4602058 [1990,] 9.268298e-05 0.4602174 0.4602061 [1991,] 9.332543e-05 0.4602177 0.4602063 [1992,] 9.397233e-05 0.4602180 0.4602065 [1993,] 9.462372e-05 0.4602183 0.4602068 [1994,] 9.527962e-05 0.4602186 0.4602070 [1995,] 9.594006e-05 0.4602189 0.4602073 [1996,] 9.660509e-05 0.4602193 0.4602075 [1997,] 9.727472e-05 0.4602196 0.4602077 [1998,] 9.794900e-05 0.4602199 0.4602080 [1999,] 9.862795e-05 0.4602203 0.4602082 [2000,] 9.931160e-05 0.4602206 0.4602085 [2001,] 1.000000e-04 0.4602209 0.4602087 > ##--> Aha: pt1 & pt2 are very close, and there's `` full cancellation'' > dt.s <- dnt.stats(x, df=3, ncp=0.1) > plot(x, abs(dt.s[,2] - dt.s[,1])) > > > > ## now have almost the original "bad dt(*, ncp) picture" from the beginning: > plot(x, abs(dt.s[,2] - dt.s[,1])/abs(x), log = "x") > > plot (x, del.pt(x, df=3, ncp=1) / x, type = "l", col=2, log = "x") > ## almost the same for x < 0 : > lines (x, del.pt(-x, df=3, ncp=1) / (-x), col = 5, lty=2) > lines(x, del.pt(x, df=2, ncp=1) / x, col=3) > lines(x, del.pt(x, df=2, ncp=2) / x, col=4) > lines(x, del.pt(x, df=2, ncp=10) / x, col=4) > lines(x, del.pt(x, df=.2, ncp=10) / x, col=4) > > x <- lseq(1e-14, 1e-3, length=1001) > plot (x, del.pt(x, df= 3, ncp=1) / x, type = "l", col=2, log = "x", ylim = c(0,0.2)) > lines(x, del.pt(x, df= 2, ncp=1) / x, col=3) > lines(x, del.pt(x, df= 2, ncp=2) / x, col=4) > lines(x, del.pt(x, df= 2, ncp=10) / x, col=4) > lines(x, del.pt(x, df=20, ncp=10) / x, col=5) > > plot (x, dt(x, df= 3, ncp=1) , type = "l", col=2, log = "x", ylim = c(0, 0.8)) > lines(x, dt(x, df= 2, ncp=1) , col=3) > lines(x, dt(x, df= 2, ncp=2) , col=4) > lines(x, dt(x, df= 2, ncp=10), col=4) > lines(x, dt(x, df=20, ncp=10), col=5) > lines(x, dt(x, df=1e-2, ncp=10), col=6) > > mult.fig(20, marP=-c(0,0,2,1)) > for(n in 1:20) { + plot (x, dt(x, df= 3, ncp=rlnorm(1)), + type = "l", col=2, log = "x", ylim = c(0, 0.45)) + for(i in 1:100) { + df <- 10/runif(1, 0.1,100); ncp <- rlnorm(1) + lines(x, dt(x, df=df, ncp=ncp)) + if(!isTRUE(ae <- all.equal(dt(1e-8, df=df, ncp=ncp), + dt(0, df=df, ncp=ncp), tol = 1e-7))) + cat(sprintf("df=%g, ncp=%g : not equal: %s\n", df, ncp, ae)) + } + } df=0.173502, ncp=3.95345 : not equal: Mean relative difference: 2.225532e-07 df=0.27461, ncp=5.28164 : not equal: Mean relative difference: 4.731012e-07 df=0.335635, ncp=4.94102 : not equal: Mean relative difference: 3.26876e-07 df=0.126247, ncp=5.25967 : not equal: Mean relative difference: 3.877609e-07 df=0.130531, ncp=2.92929 : not equal: Mean relative difference: 1.347627e-07 df=0.103361, ncp=3.41419 : not equal: Mean relative difference: 1.850365e-07 df=0.13189, ncp=2.63548 : not equal: Mean relative difference: 1.156745e-07 df=0.179956, ncp=3.53456 : not equal: Mean relative difference: 1.933366e-07 df=0.282501, ncp=3.53662 : not equal: Mean relative difference: 2.029116e-07 df=0.27088, ncp=2.65267 : not equal: Mean relative difference: 1.086141e-07 df=0.176864, ncp=3.21073 : not equal: Mean relative difference: 1.545699e-07 df=0.132892, ncp=2.60576 : not equal: Mean relative difference: 1.160624e-07 df=0.103626, ncp=3.23888 : not equal: Mean relative difference: 1.690656e-07 df=0.262561, ncp=2.73074 : not equal: Mean relative difference: 1.055938e-07 df=0.266476, ncp=2.62614 : not equal: Mean relative difference: 1.030355e-07 df=0.259024, ncp=4.21318 : not equal: Mean relative difference: 2.42772e-07 df=0.126116, ncp=2.86291 : not equal: Mean relative difference: 1.217552e-07 df=0.169589, ncp=4.14847 : not equal: Mean relative difference: 2.300552e-07 df=0.126693, ncp=3.50141 : not equal: Mean relative difference: 1.732733e-07 df=0.358901, ncp=4.78562 : not equal: Mean relative difference: 1.8058e-07 df=0.252826, ncp=3.24428 : not equal: Mean relative difference: 1.344174e-07 df=0.101349, ncp=4.41503 : not equal: Mean relative difference: 2.84307e-07 df=0.125774, ncp=2.70438 : not equal: Mean relative difference: 1.0986e-07 df=0.127156, ncp=3.4336 : not equal: Mean relative difference: 1.688516e-07 df=0.18118, ncp=3.18478 : not equal: Mean relative difference: 1.595477e-07 df=0.103364, ncp=2.50702 : not equal: Mean relative difference: 1.103197e-07 df=0.133, ncp=3.38501 : not equal: Mean relative difference: 1.834786e-07 df=0.128802, ncp=2.91563 : not equal: Mean relative difference: 1.313908e-07 df=0.265132, ncp=2.7247 : not equal: Mean relative difference: 1.074551e-07 df=0.261763, ncp=3.58622 : not equal: Mean relative difference: 1.781795e-07 df=0.130517, ncp=3.14977 : not equal: Mean relative difference: 1.536092e-07 df=0.120479, ncp=4.05916 : not equal: Mean relative difference: 1.073836e-07 df=0.269003, ncp=4.97319 : not equal: Mean relative difference: 3.889439e-07 df=0.25756, ncp=2.70187 : not equal: Mean relative difference: 1.016288e-07 df=0.360878, ncp=4.55203 : not equal: Mean relative difference: 1.48283e-07 df=0.102577, ncp=3.03959 : not equal: Mean relative difference: 1.467231e-07 df=0.128287, ncp=4.58839 : not equal: Mean relative difference: 3.050109e-07 df=0.127323, ncp=3.0347 : not equal: Mean relative difference: 1.373323e-07 df=0.259377, ncp=2.85205 : not equal: Mean relative difference: 1.141338e-07 df=0.125113, ncp=4.35068 : not equal: Mean relative difference: 2.522676e-07 df=0.102789, ncp=2.44196 : not equal: Mean relative difference: 1.048034e-07 df=0.253737, ncp=2.92718 : not equal: Mean relative difference: 1.118973e-07 df=0.177353, ncp=3.47321 : not equal: Mean relative difference: 1.809423e-07 df=0.164844, ncp=4.18083 : not equal: Mean relative difference: 1.004592e-07 df=0.430719, ncp=5.1463 : not equal: Mean relative difference: 1.232745e-07 df=0.171976, ncp=4.80124 : not equal: Mean relative difference: 3.26878e-07 df=0.170692, ncp=3.48556 : not equal: Mean relative difference: 1.659573e-07 df=0.367687, ncp=5.01461 : not equal: Mean relative difference: 1.987391e-07 df=0.169384, ncp=3.06619 : not equal: Mean relative difference: 1.281849e-07 df=0.258489, ncp=3.56341 : not equal: Mean relative difference: 1.701174e-07 df=0.102199, ncp=4.22586 : not equal: Mean relative difference: 2.666743e-07 df=0.12918, ncp=4.04775 : not equal: Mean relative difference: 2.40515e-07 df=0.128095, ncp=3.65495 : not equal: Mean relative difference: 1.92705e-07 df=0.163756, ncp=4.50788 : not equal: Mean relative difference: 1.050493e-07 df=0.105176, ncp=2.39853 : not equal: Mean relative difference: 1.048735e-07 df=0.266321, ncp=3.70023 : not equal: Mean relative difference: 1.972587e-07 df=0.259791, ncp=4.00418 : not equal: Mean relative difference: 2.187114e-07 df=0.128088, ncp=4.27213 : not equal: Mean relative difference: 2.608215e-07 df=0.171034, ncp=5.13297 : not equal: Mean relative difference: 3.73943e-07 > > df <- lseq(1e-4, 100, length=1001) > plot (df, dt(1e-5, df=df, ncp= 3), type = "l", log="xy", ylim = c(1e-9, 1.5)) > lines(df, dt(1e-5, df=df, ncp= 1e-5),col=2) > lines(df, dt(1e-5, df=df, ncp= 0.1), col="pink")# "same" as ncp= 10 ^ -5 > lines(df, dt(1e-5, df=df, ncp= 1), col="pink") > lines(df, dt(1e-5, df=df, ncp= 1.5), col=3) > lines(df, dt(1e-5, df=df, ncp= 5), col=4) > lines(df, dt(1e-5, df=df, ncp= 20), col=5) > > > > ncp <- seq(0, 5, length=1001) > plot (ncp, dt(1e-5, df= 100, ncp= ncp), type = "l", log="y") > ##-> precision warning from 'pnt' ! > ## or > plot (ncp, dt(1e-5, df= 100, ncp= ncp), type = "l") > lines(ncp, dt(1e-5, df= 10, ncp= ncp), col=2) > lines(ncp, dt(1e-5, df= 3, ncp= ncp), col=3) > lines(ncp, dt(1e-5, df= 1, ncp= ncp), col=3) > lines(ncp, dt(1e-5, df= 0.1, ncp= ncp), col=4) > > plot (ncp, dt(-1e-5, df= 100, ncp= ncp), type = "l") > lines(ncp, dt(-1e-5, df= 10, ncp= ncp), col=2) > lines(ncp, dt(-1e-5, df= 3, ncp= ncp), col=3) > lines(ncp, dt(-1e-5, df= 1, ncp= ncp), col=3) > lines(ncp, dt( 1e-5, df= 0.1, ncp= ncp), col=4) > > > > > 1 [1] 1 > > ##==> Explore pt(x, ) for small x a bit -- is there a simple "asymptotic" ( x --> 0 ) ? > ## --------------- > ## --> Rather see ./t-nonc-tst.R (algo. in R!) and ./pnt-prec.R > ## ~~~~~~~~~~~~~~ ~~~~~~~~~~~~ > > ### NOTE: pt() is fine --- > ncp <- lseq(1e-10,10, length=201)## for log-log plot below > ## or > ncp <- seq(0,50, length=201) > > plot(ncp, -pt(1e-14, df=3, ncp = ncp, log = TRUE), log = "y", type="b", cex=0.5) > ## or log-log: > plot(ncp, -pt(1e-14, df=3, ncp = ncp, log = TRUE), log = "xy", type="b", cex=0.5) Warning message: In xy.coords(x, y, xlabel, ylabel, log) : 1 x value <= 0 omitted from logarithmic plot > ## Warning message: > ## full precision was not achieved in 'pnt' <<<<< almost always here!! > ## ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > lines(ncp, -pt(1e-16, df= 3, ncp = ncp, log = TRUE), col=2) > lines(ncp, -pt(1e-12, df= 3, ncp = ncp, log = TRUE), col=4) > lines(ncp, -pt(1e-12, df= 4, ncp = ncp, log = TRUE), col= "brown") > lines(ncp, -pt(1e-10, df=40, ncp = ncp, log = TRUE), col= "purple") > > ## 'x' *and* 'df' do not seem to matter really (for largish ncp' > all.equal(pt(1e-12, df= 4, ncp = ncp, log = TRUE), + pt(1e-16, df= 10, ncp = ncp, log = TRUE))# TRUE !! [1] TRUE > > proc.time() user system elapsed 10.06 0.54 10.71