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Type 'q()' to quit R. > library(Bessel) > > ### Replicate some testing "ideas" from zqcai.f (TOMS 644 test program) > > if(!require("sfsmisc")) # from >>> sfsmisc/R/relErr.R <<< + ## Componentwise aka "Vectorized" relative error: + ## Must not be NA/NaN unless one of the components is ==> deal with {0, Inf, NA} + relErrV <- function(target, current, eps0 = .Machine$double.xmin) { + n <- length(target <- as.vector(target)) + ## assert( is multiple of ) : + lc <- length(current) + if(!n) { + if(!lc) return(numeric()) # everything length 0 + else stop("length(target) == 0 differing from length(current)") + } else if(!lc) + stop("length(current) == 0 differing from length(target)") + ## else n, lc > 0 + if(lc %% n) + stop("length(current) must be a multiple of length(target)") + recycle <- (lc != n) # explicitly recycle + R <- if(recycle) + target[rep(seq_len(n), length.out=lc)] + else + target # (possibly "mpfr") + R[] <- 0 + ## use *absolute* error when target is zero {and deal with NAs}: + t0 <- abs(target) < eps0 & !(na.t <- is.na(target)) + R[t0] <- current[t0] + ## absolute error also when it is infinite, as (-Inf, Inf) would give NaN: + dInf <- is.infinite(E <- current - target) + R[dInf] <- E[dInf] + useRE <- !dInf & !t0 & (na.t | is.na(current) | (current != target)) + R[useRE] <- (current/target)[useRE] - 1 + ## preserve {dim, dimnames, names} from 'current' : + if(!is.null(d <- dim(current))) + array(R, dim=d, dimnames=dimnames(current)) + else if(!is.null(nm <- names(current)) && is.null(names(R))) # not needed for mpfr + `names<-`(R, nm) + else R + } Loading required package: sfsmisc > ## Generates airy functions and their derivatives from zairy > ## and zbiry and checks them against the wronskian evaluation in the > ## region -pi/3 <= arg(z) <= pi/3: > ## > ## Ai(z)*Bi'(z)-Ai'(z)*Bi(z) = 1/pi. > ## > ## in the remainder of the cut plane, the identities > ## > ## Ai(z) = sqrt(-z)*( J(-1/3,zr) + J(1/3,zr) )/3 > ## > ## Ai'(z) = z*( J(-2/3,zr) - J(2/3,zr) )/3 > ## > ## Bi(z) = i* sqrt(-z/3) *( c1* H(1/3,1,zr) - c2* H(1/3,2,zr) )/2 > ## > ## Bi'(z) = i*(-z)/sqrt(3)*( c2* H(2/3,1,zr) - c1* H(2/3,2,zr) )/2 > ## > ## are checked where zr = (2/3)(-z)^(3/2) with > ## c1 = exp(pi*i/6), > ## c2 = conjg(c1) and i^2 = -1. > > > all.equal12 <- function(a,b) all.equal(a,b, tolerance = 1e-12) > all.equal9e9 <- function(a,b) all.equal(a,b, tolerance = 9e-9) > op <- options(digits = 4, nwarnings = 1e4) > > ### Wronskian Ai(z)*Bi'(z) - Ai'(z)*Bi(z) == 1/pi --- *only* for pi/3 <= Arg(z) <= pi/3 > N <- 100 > I.pi <- rep.int(1/pi + 0*1i, N) > c1 <- exp(pi * 1i/6) ## = sqrt(3)/2 + i/2 > c2 <- Conj(c1) > verbose <- TRUE # <-- activate by commenting the next line: > verbose <- FALSE > > set.seed(101) > for(n in 1:250) { # use longtailed different random samples + cat(".") ## limit to not more extreme than Cauchy (df = 1) + z <- complex(real = rt(N, df = max(1, 1/rexp(1))), + imaginary = rt(N, df = max(1, 1/rexp(1)))) + ai <- AiryA(z) + dai <- AiryA(z, deriv=1) + bi <- AiryB(z) + dbi <- AiryB(z, deriv=1) + + ## First identity: only for |Arg(z)| <= pi/3 <==> z[in1] : + Lz <- abs(Arg(z)) > pi/3 + in1 <- !Lz + print(table(in1)) + addb <- ai * dbi - dai * bi + rE1 <- relErrV(I.pi[in1], addb[in1]) + cat("summary(|relE.id.1|):\n"); print(summary(Mod(rE1))) # sometimes shows NAs + + ## next stopifnot() fails for large |Mod(z[in1])| where addb[] is NaN;; + ## partly Ai, Bi is already NaN, but less extreme: {Ai = 0, Bi = Inf} ==> addb = NaN (0*Inf or Inf-Inf!) + if(verbose) + print(data.frame(z=z, Ai=ai, "Ai'"=dai, Bi=bi, "Bi'"=dbi, "|z|"= Mod(z), "|addb|"=Mod(addb))[in1,]) + if(anyNA(addb[in1])) { + cat("==> NAs in addb[in1] at [", deparse1(which(is.na(addb[in1]))), "]\n") + in1 <- in1 & !is.na(addb) + } + stopifnot(all.equal(addb[in1], I.pi[in1], tolerance = 1e-13)) + + ## The remaining checks are only valid in this z-plane "sector": + z <- z[Lz] + ai <- ai[Lz] + dai <- dai[Lz] + bi <- bi[Lz] + dbi <- dbi[Lz] + + zr <- 2/3 * (-z)^(3/2) + if(any(Lrg <- abs(Im(zr)) > 700.921)) { + cat("n = ", n, "; Lrg zr[i=", deparse1(which(Lrg), control={}),"]\n", sep="") + ok <- which(!Lrg) + z <- z [ok] + zr <- zr[ok] + ai <- ai[ok] + dai <- dai[ok] + bi <- bi[ok] + dbi <- dbi[ok] + } + if(any(isInf <- !is.finite(ai) | !is.finite(bi) | !is.finite(dai) | !is.finite(dbi))) { + io <- which(!isInf) + ai <- ai [io] + bi <- bi [io] + dai <-dai[io] + dbi <-dbi[io] + z <- z[io] + zr <- zr[io] + } + stopifnot(exprs = { + ## Ai(z) = sqrt(-z)*( J(-1/3,zr) + J(1/3,zr) )/3 + ## Ai'(z) = z*( J(-2/3,zr) - J(2/3,zr) )/3 + ## needs BesselJ() for *NEGATIVE* nu : + all.equal9e9(ai, sqrt(-z)*(BesselJ(zr, -1/3) + BesselJ(zr, 1/3))/3) + all.equal9e9(dai, z*(BesselJ(zr, -2/3) - BesselJ(zr, 2/3))/3) + ## Bi(z) = i* sqrt(-z/3) *( c1* H(1/3,1,zr) - c2* H(1/3,2,zr) )/2 + ## Bi'(z) = i*(-z)/sqrt(3)*( c2* H(2/3,1,zr) - c1* H(2/3,2,zr) )/2 + all.equal9e9(bi, 1i*sqrt(-z/3)* + (c1*BesselH(1, zr, 1/3) - c2*BesselH(2, zr, 1/3))/2) + all.equal9e9(dbi, -1i*z/sqrt(3)* + (c2*BesselH(1, zr, 2/3) - c1*BesselH(2, zr, 2/3))/2) + }) + }; cat("\n") .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.50e-16 7.22e-16 1.86e-15 1.81e-15 1.27e-14 .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 5.30e-16 1.75e-15 3.01e-15 4.25e-15 1.65e-14 .in1 FALSE TRUE 79 21 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 5.55e-16 1.78e-15 4.10e-15 3.51e-15 2.22e-14 n = 3; Lrg zr[i=48] .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.23e-16 8.97e-16 2.29e-15 3.11e-15 1.32e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.27e-17 3.10e-16 1.13e-15 2.93e-15 5.00e-15 1.24e-14 .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 6.91e-16 2.91e-15 2.68e-15 3.15e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.69e-16 8.64e-16 1.57e-15 1.71e-15 1.04e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.41e-16 1.32e-15 2.72e-15 3.78e-15 1.65e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 4.00e-16 1.21e-15 2.96e-15 3.43e-15 1.65e-14 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.09e-18 2.26e-16 4.10e-16 1.57e-15 1.11e-15 1.72e-14 .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 6.70e-16 2.10e-15 2.47e-15 8.77e-15 n = 11; Lrg zr[i=c(40, 50)] .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 3.96e-16 2.37e-15 2.68e-15 1.74e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.30e-16 8.92e-16 2.29e-15 2.11e-15 1.68e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 8.18e-18 2.32e-16 1.64e-15 3.72e-15 4.64e-15 2.15e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.39e-16 5.66e-16 1.60e-15 1.62e-15 1.38e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 9.54e-18 2.23e-16 4.02e-16 1.84e-15 1.80e-15 1.04e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.33e-16 1.27e-15 3.75e-15 4.07e-15 3.04e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.38e-16 1.07e-15 1.84e-15 2.16e-15 8.88e-15 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 2.25e-16 9.90e-16 2.84e-15 3.62e-15 1.78e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.31e-16 1.45e-15 2.32e-15 2.92e-15 1.40e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.26e-16 8.98e-16 3.23e-15 4.42e-15 2.22e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.31e-16 3.95e-16 2.11e-15 8.66e-16 1.71e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.84e-16 1.60e-15 4.36e-15 4.76e-15 3.12e-14 .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.43e-16 7.08e-16 1.91e-15 1.98e-15 1.81e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 1.09e-15 3.45e-15 4.08e-15 3.11e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 8.18e-18 5.03e-16 1.42e-15 1.86e-15 2.86e-15 5.65e-15 n = 26; Lrg zr[i=63] .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 7.90e-16 2.11e-15 2.00e-15 1.27e-14 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.33e-16 8.27e-16 1.75e-15 1.67e-15 7.80e-15 .in1 FALSE TRUE 58 42 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.36e-18 2.23e-16 6.13e-16 2.09e-15 1.98e-15 1.70e-14 .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 4.60e-16 1.02e-15 3.61e-15 3.54e-15 2.25e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 9.19e-16 2.37e-15 3.72e-15 1.31e-14 n = 31; Lrg zr[i=54] .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 2.58e-16 8.99e-16 2.79e-15 3.65e-15 2.24e-14 2 ==> NAs in addb[in1] at [ c(6L, 12L) ] .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.53e-16 4.63e-16 1.89e-15 3.47e-15 4.71e-15 2.15e-14 .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.23e-16 4.44e-16 9.28e-16 9.58e-16 6.95e-15 n = 34; Lrg zr[i=41] .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.86e-16 5.62e-16 2.29e-15 2.71e-15 1.81e-14 .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 6.33e-16 1.66e-15 2.07e-15 8.50e-15 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 4.12e-16 1.19e-15 1.20e-15 8.38e-15 n = 37; Lrg zr[i=38] .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 2.24e-16 6.68e-16 2.67e-15 4.00e-15 1.56e-14 2 ==> NAs in addb[in1] at [ c(28L, 36L) ] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.93e-16 1.39e-15 2.86e-15 3.43e-15 1.69e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 9.07e-16 2.00e-15 3.11e-15 9.42e-15 .in1 FALSE TRUE 52 48 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.04e-18 2.26e-16 1.03e-15 1.38e-15 1.73e-15 6.49e-15 .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 3.52e-16 9.77e-16 4.56e-15 6.47e-15 2.29e-14 1 ==> NAs in addb[in1] at [ 41L ] .in1 FALSE TRUE 79 21 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.74e-16 2.26e-16 8.16e-16 1.37e-15 2.18e-15 5.84e-15 n = 43; Lrg zr[i=55] .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.13e-18 3.18e-16 1.11e-15 3.00e-15 3.67e-15 1.69e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.23e-16 3.78e-16 8.93e-16 1.10e-15 4.46e-15 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.30e-16 1.67e-15 3.86e-15 4.22e-15 3.04e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 4.92e-16 2.37e-15 3.92e-15 1.85e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.82e-16 1.09e-15 2.51e-15 2.64e-15 2.04e-14 .in1 FALSE TRUE 78 22 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 2.22e-16 3.52e-16 1.15e-15 2.04e-15 3.78e-15 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.41e-18 2.26e-16 1.34e-15 2.38e-15 2.58e-15 1.69e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 2.60e-16 1.30e-15 3.09e-15 3.66e-15 1.87e-14 n = 51; Lrg zr[i=71] .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 1.09e-17 4.62e-16 1.56e-15 3.82e-15 3.56e-15 2.11e-14 2 ==> NAs in addb[in1] at [ c(25L, 27L) ] .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 2.18e-17 2.39e-16 1.54e-15 3.49e-15 4.14e-15 2.29e-14 1 ==> NAs in addb[in1] at [ 37L ] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 1.00e-15 1.96e-15 3.70e-15 5.25e-15 1.77e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 4.45e-16 9.63e-16 1.98e-15 1.57e-15 1.66e-14 n = 55; Lrg zr[i=60] .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 4.62e-16 9.40e-16 2.84e-15 2.79e-15 1.62e-14 2 ==> NAs in addb[in1] at [ c(10L, 23L) ] .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.27e-17 2.22e-16 4.11e-16 2.85e-15 2.49e-15 1.75e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.96e-16 9.73e-16 2.90e-15 2.71e-15 2.27e-14 .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 4.39e-16 1.06e-15 2.00e-15 2.58e-15 1.10e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.35e-16 9.54e-16 3.48e-15 4.56e-15 3.11e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 3.23e-16 9.71e-16 4.32e-15 4.44e-15 3.26e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.27e-16 1.01e-15 2.13e-15 3.16e-15 1.29e-14 n = 62; Lrg zr[i=37] .in1 FALSE TRUE 56 44 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 2.85e-16 1.31e-15 3.25e-15 3.78e-15 2.29e-14 1 ==> NAs in addb[in1] at [ 37L ] .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 3.02e-16 1.81e-15 1.89e-15 1.41e-14 .in1 FALSE TRUE 78 22 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 4.66e-16 1.57e-15 3.78e-15 5.65e-15 1.69e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 1.45e-18 2.28e-16 9.54e-16 4.72e-15 5.25e-15 3.28e-14 1 ==> NAs in addb[in1] at [ 32L ] .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.96e-16 8.67e-16 1.62e-15 1.22e-15 1.83e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.24e-16 1.20e-15 3.99e-15 2.97e-15 3.12e-14 .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.58e-16 1.01e-15 2.83e-15 3.58e-15 2.18e-14 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 4.68e-16 1.67e-15 1.52e-15 1.64e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.40e-16 9.89e-16 1.29e-15 1.68e-15 4.49e-15 n = 71; Lrg zr[i=26] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 3.62e-16 1.72e-15 4.18e-15 4.50e-15 2.98e-14 1 ==> NAs in addb[in1] at [ 7L ] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 2.18e-17 4.46e-16 1.69e-15 5.85e-15 6.44e-15 3.12e-14 2 ==> NAs in addb[in1] at [ c(2L, 8L) ] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 6.14e-16 1.91e-15 2.36e-15 1.77e-14 .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.26e-16 6.54e-16 3.08e-15 1.59e-15 3.24e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 6.10e-16 1.79e-15 1.62e-15 1.08e-14 n = 76; Lrg zr[i=27] .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 5.56e-16 1.71e-15 3.29e-15 4.44e-15 3.15e-14 .in1 FALSE TRUE 85 15 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 3.33e-16 9.54e-16 1.00e-15 5.33e-15 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.39e-16 6.54e-16 2.27e-15 2.42e-15 1.77e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.23e-16 4.46e-16 1.30e-15 1.75e-15 7.75e-15 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.11e-16 1.51e-15 3.16e-15 4.78e-15 1.81e-14 n = 81; Lrg zr[i=c(41, 51)] .in1 FALSE TRUE 76 24 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 4.23e-16 7.93e-16 2.00e-15 1.67e-15 1.70e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.62e-16 5.88e-16 1.64e-15 1.71e-15 1.18e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 7.66e-19 2.42e-16 8.58e-16 2.80e-15 3.71e-15 2.30e-14 .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.01e-16 8.21e-16 2.94e-15 3.56e-15 3.04e-14 .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 2.29e-16 7.32e-16 1.29e-15 2.04e-15 4.95e-15 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.31e-16 9.80e-16 2.30e-15 3.56e-15 1.69e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 3.63e-16 1.78e-15 2.98e-15 4.98e-15 1.04e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.32e-16 8.34e-16 2.41e-15 2.82e-15 1.97e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.33e-16 1.13e-15 3.62e-15 3.46e-15 3.33e-14 .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 5.57e-16 1.09e-15 2.35e-15 2.42e-15 2.20e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 3.38e-16 1.51e-15 3.00e-15 4.14e-15 1.68e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.35e-16 1.36e-15 2.78e-15 3.89e-15 2.17e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 2.55e-16 1.11e-15 2.83e-15 4.23e-15 1.44e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.63e-17 7.18e-16 1.32e-15 2.28e-15 3.42e-15 9.33e-15 n = 95; Lrg zr[i=c(4, 34)] .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.36e-18 2.22e-16 2.31e-16 7.81e-16 5.82e-16 5.20e-15 n = 96; Lrg zr[i=12] .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.36e-18 2.26e-16 5.73e-16 1.15e-15 1.53e-15 6.68e-15 n = 97; Lrg zr[i=33] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 5.45e-18 3.47e-16 1.10e-15 3.18e-15 3.17e-15 2.16e-14 1 ==> NAs in addb[in1] at [ 24L ] n = 98; Lrg zr[i=60] .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 4.46e-16 1.03e-15 2.60e-15 3.57e-15 2.20e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.24e-16 6.48e-16 1.12e-15 1.41e-15 6.80e-15 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.61e-16 1.25e-15 3.97e-15 3.18e-15 3.15e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.25e-16 1.55e-15 2.84e-15 4.00e-15 1.03e-14 n = 102; Lrg zr[i=62] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 3.81e-17 2.35e-16 5.43e-16 2.20e-15 1.21e-15 1.81e-14 1 ==> NAs in addb[in1] at [ 1L ] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.80e-19 2.22e-16 5.59e-16 4.51e-15 3.10e-15 3.19e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 7.43e-16 1.61e-15 1.91e-15 7.77e-15 .in1 FALSE TRUE 58 42 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.33e-16 9.21e-16 2.26e-15 2.55e-15 2.93e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 4.24e-16 7.73e-16 1.72e-15 1.39e-15 1.75e-14 .in1 FALSE TRUE 58 42 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.36e-16 1.36e-15 3.32e-15 3.95e-15 2.89e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.22e-16 8.45e-16 1.90e-15 2.42e-15 8.61e-15 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 4.86e-16 1.08e-15 2.43e-15 3.36e-15 1.42e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 8.17e-18 2.26e-16 1.11e-15 3.68e-15 2.22e-15 3.23e-14 1 ==> NAs in addb[in1] at [ 5L ] .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.58e-16 5.55e-16 2.29e-15 1.76e-15 2.25e-14 .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.81e-19 2.22e-16 3.34e-16 1.23e-15 1.44e-15 6.40e-15 .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.31e-16 5.28e-16 9.89e-16 3.02e-15 4.01e-15 3.15e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.31e-16 5.56e-16 2.71e-15 3.56e-15 2.29e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 4.63e-16 2.02e-15 2.39e-15 2.01e-14 .in1 FALSE TRUE 76 24 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.25e-16 2.90e-16 1.82e-15 1.47e-15 1.73e-14 .in1 FALSE TRUE 58 42 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 3.98e-16 2.58e-15 1.42e-15 3.14e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.72e-16 9.97e-16 3.03e-15 2.57e-15 2.25e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 4.13e-16 1.25e-15 2.86e-15 3.94e-15 1.73e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.93e-16 1.02e-15 2.82e-15 2.84e-15 1.93e-14 .in1 FALSE TRUE 78 22 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 8.72e-17 3.33e-16 2.66e-15 4.92e-15 4.67e-15 3.11e-14 1 ==> NAs in addb[in1] at [ 8L ] n = 122; Lrg zr[i=15] .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 5.60e-16 1.15e-15 1.39e-15 4.24e-15 .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.58e-16 1.01e-15 2.19e-15 2.37e-15 2.14e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 8.18e-18 2.45e-16 6.83e-16 3.31e-15 4.91e-15 2.07e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.95e-16 7.95e-16 2.93e-15 3.84e-15 2.16e-14 .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 8.72e-17 2.64e-16 8.47e-16 2.35e-15 3.40e-15 1.42e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 3.06e-16 9.68e-16 2.47e-15 2.37e-15 2.22e-14 .in1 FALSE TRUE 82 18 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 3.64e-16 1.66e-15 3.38e-15 8.22e-15 .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.99e-16 6.89e-16 1.38e-15 1.56e-15 4.66e-15 .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 6.28e-16 1.56e-15 2.23e-15 3.02e-15 1.33e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 8.72e-17 2.32e-16 5.12e-16 1.73e-15 1.82e-15 1.29e-14 n = 132; Lrg zr[i=51] .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 2.22e-16 8.58e-16 2.34e-15 3.55e-15 1.69e-14 1 ==> NAs in addb[in1] at [ 29L ] .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 2.97e-16 1.16e-15 1.02e-15 1.02e-14 n = 134; Lrg zr[i=2] .in1 FALSE TRUE 55 45 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.95e-16 1.09e-15 2.89e-15 3.33e-15 1.74e-14 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 9.09e-16 1.93e-15 2.41e-15 1.20e-14 n = 136; Lrg zr[i=56] .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.27e-16 1.82e-15 3.23e-15 3.91e-15 1.65e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 3.62e-16 9.65e-16 2.19e-15 3.06e-15 1.80e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 2.18e-17 4.44e-16 1.49e-15 2.85e-15 3.48e-15 1.24e-14 1 ==> NAs in addb[in1] at [ 5L ] .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.26e-16 4.68e-16 6.98e-16 9.30e-16 3.49e-15 n = 140; Lrg zr[i=44] .in1 FALSE TRUE 58 42 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 8.72e-17 2.39e-16 1.06e-15 2.42e-15 3.34e-15 1.27e-14 1 ==> NAs in addb[in1] at [ 17L ] .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.61e-16 9.68e-16 1.69e-15 1.84e-15 8.24e-15 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 1.09e-17 2.22e-16 1.29e-15 4.86e-15 8.44e-15 2.31e-14 1 ==> NAs in addb[in1] at [ 16L ] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 6.66e-16 1.53e-15 1.87e-15 1.10e-14 .in1 FALSE TRUE 78 22 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 4.75e-16 1.91e-15 2.48e-15 1.01e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-16 3.89e-16 1.27e-15 2.47e-15 3.57e-15 1.04e-14 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.96e-16 9.08e-16 4.14e-15 3.81e-15 2.98e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 8.18e-18 2.23e-16 6.91e-16 1.31e-15 2.09e-15 5.92e-15 .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 2.35e-16 6.66e-16 3.12e-15 4.11e-15 3.23e-14 1 ==> NAs in addb[in1] at [ 7L ] .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 4.46e-16 1.89e-15 3.15e-15 4.47e-15 2.95e-14 1 ==> NAs in addb[in1] at [ 28L ] .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.30e-16 5.64e-16 2.65e-15 3.33e-15 1.77e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.45e-16 8.92e-16 1.77e-15 1.75e-15 7.78e-15 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 1.11e-15 3.32e-15 4.45e-15 2.24e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 9.54e-18 2.26e-16 4.63e-16 1.70e-15 1.85e-15 9.89e-15 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 1.01e-15 2.10e-15 2.64e-15 4.13e-15 8.70e-15 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 3.04e-16 9.10e-16 2.79e-15 4.45e-15 1.74e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.23e-16 7.87e-16 2.83e-15 1.91e-15 3.21e-14 .in1 FALSE TRUE 76 24 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.26e-16 4.68e-16 1.68e-15 2.16e-15 1.03e-14 n = 158; Lrg zr[i=37] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 3.34e-16 1.44e-15 1.43e-15 8.67e-15 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.37e-16 9.29e-16 2.97e-15 4.45e-15 1.69e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.23e-16 9.62e-16 1.74e-15 2.24e-15 1.27e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.39e-16 1.08e-15 2.70e-15 3.57e-15 1.26e-14 .in1 FALSE TRUE 76 24 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 3.91e-16 1.61e-15 1.95e-15 7.66e-15 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.33e-16 1.03e-15 2.92e-15 3.21e-15 3.24e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 8.60e-16 1.39e-15 1.46e-15 8.44e-15 .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.23e-16 5.96e-16 1.78e-15 1.16e-15 1.20e-14 n = 166; Lrg zr[i=51] .in1 FALSE TRUE 76 24 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.68e-16 1.42e-15 3.34e-15 4.14e-15 2.24e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.22e-16 1.57e-15 2.88e-15 3.79e-15 1.74e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 3.51e-16 1.42e-15 2.29e-15 2.90e-15 1.38e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.53e-16 7.55e-16 1.91e-15 2.37e-15 1.15e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 2.22e-16 3.33e-16 1.10e-15 3.39e-15 3.98e-15 2.29e-14 1 ==> NAs in addb[in1] at [ 11L ] n = 171; Lrg zr[i=49] .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 2.18e-17 2.24e-16 6.91e-16 1.98e-15 1.90e-15 1.27e-14 2 ==> NAs in addb[in1] at [ c(22L, 24L) ] .in1 FALSE TRUE 63 37 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 2.82e-16 1.52e-15 3.18e-15 4.00e-15 2.24e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 3.43e-16 1.84e-15 3.30e-15 4.72e-15 2.15e-14 .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.26e-16 1.22e-15 5.27e-15 4.48e-15 3.35e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 4.45e-16 1.53e-15 3.73e-15 4.35e-15 3.27e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 4.36e-17 4.29e-16 1.17e-15 3.12e-15 3.94e-15 1.77e-14 1 ==> NAs in addb[in1] at [ 23L ] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 4.34e-16 1.75e-15 3.93e-15 3.64e-15 3.26e-14 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.41e-16 5.04e-16 1.79e-15 1.33e-15 8.67e-15 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 5.45e-18 4.94e-16 3.05e-15 3.52e-15 4.17e-15 1.73e-14 1 ==> NAs in addb[in1] at [ 17L ] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 3.84e-16 1.01e-15 1.70e-15 2.21e-15 8.08e-15 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.41e-18 2.22e-16 6.85e-16 1.40e-15 1.80e-15 8.10e-15 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 3.76e-16 1.56e-15 2.73e-15 4.00e-15 1.77e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 6.72e-16 1.55e-15 3.80e-15 4.00e-15 1.63e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 5.45e-18 7.96e-16 2.41e-15 2.58e-15 3.73e-15 9.11e-15 1 ==> NAs in addb[in1] at [ 18L ] n = 185; Lrg zr[i=c(21, 24)] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.26e-16 1.07e-15 2.67e-15 1.71e-15 2.01e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 2.31e-16 1.00e-15 2.35e-15 2.98e-15 1.83e-14 .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.33e-16 5.64e-16 1.20e-15 1.41e-15 8.22e-15 .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 5.56e-16 1.13e-15 2.40e-15 2.36e-15 1.12e-14 n = 189; Lrg zr[i=c(24, 42, 60)] .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 6.40e-16 1.88e-15 3.19e-15 4.71e-15 1.22e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.26e-16 8.06e-16 1.28e-15 1.59e-15 4.70e-15 .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 1.00e-15 3.48e-15 2.97e-15 2.26e-14 n = 192; Lrg zr[i=44] .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 4.14e-16 1.86e-15 3.02e-15 3.83e-15 1.27e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 7.54e-16 1.81e-15 3.36e-15 3.09e-15 2.04e-14 1 ==> NAs in addb[in1] at [ 30L ] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 5.05e-16 1.78e-15 3.31e-15 4.16e-15 1.69e-14 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 4.44e-16 9.79e-16 3.08e-15 5.33e-15 2.14e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.24e-16 1.11e-15 1.50e-15 2.07e-15 6.42e-15 .in1 FALSE TRUE 82 18 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.25e-16 1.32e-15 2.15e-15 4.26e-15 6.85e-15 n = 198; Lrg zr[i=50] .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.29e-16 5.62e-16 1.91e-15 2.09e-15 1.27e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 2.23e-16 5.04e-16 1.18e-15 1.19e-15 9.59e-15 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 9.54e-18 3.34e-16 1.73e-15 3.39e-15 5.01e-15 1.66e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-16 2.26e-16 5.61e-16 1.83e-15 1.48e-15 1.81e-14 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 9.42e-16 2.38e-15 3.26e-15 1.66e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 4.89e-16 1.20e-15 9.36e-16 8.65e-15 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.27e-17 2.26e-16 5.63e-16 1.81e-15 1.92e-15 1.06e-14 .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.23e-16 1.33e-15 2.01e-15 2.71e-15 8.88e-15 n = 206; Lrg zr[i=c(3, 19, 69)] .in1 FALSE TRUE 77 23 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 7.16e-16 1.57e-15 3.37e-15 4.21e-15 1.73e-14 n = 207; Lrg zr[i=44] .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.27e-17 2.39e-16 6.48e-16 1.83e-15 2.36e-15 1.18e-14 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.98e-16 1.02e-15 2.66e-15 3.68e-15 3.19e-14 .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 2.39e-16 9.03e-16 2.22e-15 2.71e-15 1.22e-14 .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.27e-16 1.22e-15 3.10e-15 4.37e-15 1.77e-14 n = 211; Lrg zr[i=c(13, 65)] .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.28e-16 4.47e-16 3.46e-15 2.61e-15 3.19e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 4.56e-16 1.44e-15 2.36e-15 3.40e-15 1.38e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 5.56e-16 1.17e-15 1.58e-15 6.11e-15 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.33e-16 8.77e-16 1.58e-15 1.90e-15 6.03e-15 .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.47e-16 1.50e-15 4.60e-15 5.11e-15 2.24e-14 n = 216; Lrg zr[i=8] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.74e-16 2.23e-16 6.69e-16 3.06e-15 3.05e-15 1.87e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.42e-16 9.27e-16 3.26e-15 3.62e-15 3.19e-14 .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 4.27e-16 1.53e-15 3.60e-15 4.82e-15 2.04e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.69e-16 7.74e-16 1.30e-15 1.24e-15 1.25e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.35e-16 4.65e-16 3.26e-15 3.01e-15 3.19e-14 .in1 FALSE TRUE 61 39 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.24e-16 5.82e-16 2.10e-15 1.75e-15 2.09e-14 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 2.26e-16 1.36e-15 3.33e-15 4.47e-15 1.67e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 4.36e-17 4.41e-16 1.56e-15 3.48e-15 4.70e-15 1.75e-14 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 0.00e+00 2.25e-16 1.95e-15 4.95e-15 7.11e-15 3.05e-14 1 ==> NAs in addb[in1] at [ 25L ] .in1 FALSE TRUE 66 34 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.43e-16 1.16e-15 2.33e-15 3.32e-15 1.96e-14 .in1 FALSE TRUE 83 17 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.22e-16 9.02e-16 2.83e-15 2.96e-15 1.65e-14 n = 227; Lrg zr[i=3] .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.99e-17 2.22e-16 9.20e-16 2.60e-15 2.15e-15 2.90e-14 n = 228; Lrg zr[i=35] .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.23e-16 2.97e-16 9.79e-16 9.46e-16 8.85e-15 .in1 FALSE TRUE 62 38 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 4.72e-16 1.75e-15 3.24e-15 3.84e-15 1.81e-14 n = 230; Lrg zr[i=4] .in1 FALSE TRUE 67 33 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 2.18e-17 2.30e-16 9.03e-16 2.18e-15 2.70e-15 1.81e-14 1 ==> NAs in addb[in1] at [ 16L ] .in1 FALSE TRUE 80 20 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.39e-16 6.82e-16 9.66e-16 1.05e-15 3.56e-15 n = 232; Lrg zr[i=57] .in1 FALSE TRUE 73 27 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.22e-16 4.44e-16 8.32e-16 8.50e-16 7.42e-15 n = 233; Lrg zr[i=60] .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 6.54e-17 2.30e-16 5.83e-16 2.86e-15 4.00e-15 1.62e-14 n = 234; Lrg zr[i=25] .in1 FALSE TRUE 72 28 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.30e-16 5.59e-16 1.51e-15 1.59e-15 1.20e-14 .in1 FALSE TRUE 59 41 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 3.34e-16 1.22e-15 2.85e-15 4.44e-15 2.11e-14 .in1 FALSE TRUE 78 22 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 2.39e-16 6.94e-16 1.26e-15 2.28e-15 n = 237; Lrg zr[i=4] .in1 FALSE TRUE 65 35 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 3.27e-17 3.44e-16 1.35e-15 2.69e-15 3.67e-15 1.82e-14 .in1 FALSE TRUE 54 46 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. NAs 1.64e-17 2.47e-16 9.62e-16 3.04e-15 2.92e-15 3.19e-14 2 ==> NAs in addb[in1] at [ 7:8 ] .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.58e-16 9.07e-16 2.50e-15 2.45e-15 1.61e-14 .in1 FALSE TRUE 70 30 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.73e-18 3.32e-16 9.85e-16 1.85e-15 2.19e-15 1.07e-14 .in1 FALSE TRUE 79 21 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.22e-16 2.23e-16 1.29e-15 1.32e-15 9.62e-15 n = 242; Lrg zr[i=c(2, 62)] .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.26e-16 5.78e-16 2.24e-15 2.82e-15 1.29e-14 .in1 FALSE TRUE 74 26 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.27e-16 5.42e-16 1.62e-15 1.93e-15 9.25e-15 .in1 FALSE TRUE 71 29 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00e+00 2.47e-16 6.66e-16 3.25e-15 5.17e-15 1.77e-14 .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 5.45e-18 2.24e-16 1.13e-15 2.55e-15 4.44e-15 1.31e-14 .in1 FALSE TRUE 68 32 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 1.09e-17 2.26e-16 8.86e-16 2.58e-15 3.04e-15 3.30e-14 .in1 FALSE TRUE 69 31 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 4.72e-16 1.13e-15 2.39e-15 2.37e-15 1.47e-14 .in1 FALSE TRUE 64 36 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.18e-17 2.26e-16 1.15e-15 2.51e-15 3.82e-15 1.24e-14 .in1 FALSE TRUE 75 25 summary(|relE.id.1|): Min. 1st Qu. Median Mean 3rd Qu. Max. 2.22e-16 2.23e-16 4.44e-16 1.92e-15 2.00e-15 1.27e-14 n = 250; Lrg zr[i=31] There were 80 warnings (use warnings() to see them) > warnings() # .... large arguments --> precision loss (of at least half machine accuracy) Warning messages: 1: In AiryA(z) : 'zairy(-10868.7 + 0.355243i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 2: In AiryA(z, deriv = 1) : 'zairy(-10868.7 + 0.355243i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 3: In AiryB(z) : 'zairy(-10868.7 + 0.355243i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 4: In AiryB(z, deriv = 1) : 'zairy(-10868.7 + 0.355243i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 5: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(755393 - 37.0351i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 6: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(755393 - 37.0351i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 7: In BesselJ(zr, 1/3) : 'zbesj(755393 - 37.0351i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 8: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(755393 - 37.0351i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 9: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(755393 - 37.0351i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 10: In BesselJ(zr, 2/3) : 'zbesj(755393 - 37.0351i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 11: In BesselH(1, zr, 1/3) : 'zbesh(755393 - 37.0351i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 12: In BesselH(2, zr, 1/3) : 'zbesh(755393 - 37.0351i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 13: In BesselH(1, zr, 2/3) : 'zbesh(755393 - 37.0351i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 14: In BesselH(2, zr, 2/3) : 'zbesh(755393 - 37.0351i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 15: In AiryA(z) : 'zairy(2129.11 - 4.49939i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 16: In AiryA(z, deriv = 1) : 'zairy(2129.11 - 4.49939i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 17: In AiryA(z) : 'zairy(-1572.37 + 0.244951i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 18: In AiryA(z, deriv = 1) : 'zairy(-1572.37 + 0.244951i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 19: In AiryB(z) : 'zairy(-1572.37 + 0.244951i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 20: In AiryB(z, deriv = 1) : 'zairy(-1572.37 + 0.244951i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 21: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(41566.4 - 9.71309i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 22: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(41566.4 - 9.71309i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 23: In BesselJ(zr, 1/3) : 'zbesj(41566.4 - 9.71309i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 24: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(41566.4 - 9.71309i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 25: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(41566.4 - 9.71309i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 26: In BesselJ(zr, 2/3) : 'zbesj(41566.4 - 9.71309i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 27: In BesselH(1, zr, 1/3) : 'zbesh(41566.4 - 9.71309i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 28: In BesselH(2, zr, 1/3) : 'zbesh(41566.4 - 9.71309i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 29: In BesselH(1, zr, 2/3) : 'zbesh(41566.4 - 9.71309i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 30: In BesselH(2, zr, 2/3) : 'zbesh(41566.4 - 9.71309i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 31: In AiryA(z) : 'zairy(6246.98 - 0.934053i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 32: In AiryA(z, deriv = 1) : 'zairy(6246.98 - 0.934053i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 33: In AiryA(z) : 'zairy(1843.92 + 1.2239i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 34: In AiryA(z, deriv = 1) : 'zairy(1843.92 + 1.2239i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 35: In AiryA(z) : 'zairy(-5476.09 + 0.163299i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 36: In AiryA(z, deriv = 1) : 'zairy(-5476.09 + 0.163299i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 37: In AiryB(z) : 'zairy(-5476.09 + 0.163299i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 38: In AiryB(z, deriv = 1) : 'zairy(-5476.09 + 0.163299i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 39: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(270156 - 12.0842i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 40: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(270156 - 12.0842i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 41: In BesselJ(zr, 1/3) : 'zbesj(270156 - 12.0842i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 42: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(270156 - 12.0842i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 43: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(270156 - 12.0842i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 44: In BesselJ(zr, 2/3) : 'zbesj(270156 - 12.0842i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 45: In BesselH(1, zr, 1/3) : 'zbesh(270156 - 12.0842i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 46: In BesselH(2, zr, 1/3) : 'zbesh(270156 - 12.0842i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 47: In BesselH(1, zr, 2/3) : 'zbesh(270156 - 12.0842i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 48: In BesselH(2, zr, 2/3) : 'zbesh(270156 - 12.0842i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 49: In AiryA(z) : 'zairy(-6678.46 - 0.1502i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 50: In AiryA(z, deriv = 1) : 'zairy(-6678.46 - 0.1502i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 51: In AiryB(z) : 'zairy(-6678.46 - 0.1502i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 52: In AiryB(z, deriv = 1) : 'zairy(-6678.46 - 0.1502i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 53: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(363850 + 12.2746i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 54: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(363850 + 12.2746i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 55: In BesselJ(zr, 1/3) : 'zbesj(363850 + 12.2746i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 56: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(363850 + 12.2746i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 57: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(363850 + 12.2746i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 58: In BesselJ(zr, 2/3) : 'zbesj(363850 + 12.2746i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 59: In BesselH(1, zr, 1/3) : 'zbesh(363850 + 12.2746i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 60: In BesselH(2, zr, 1/3) : 'zbesh(363850 + 12.2746i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 61: In BesselH(1, zr, 2/3) : 'zbesh(363850 + 12.2746i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 62: In BesselH(2, zr, 2/3) : 'zbesh(363850 + 12.2746i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 63: In AiryA(z) : 'zairy(1760.64 + 1.10373i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 64: In AiryA(z, deriv = 1) : 'zairy(1760.64 + 1.10373i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 65: In AiryA(z) : 'zairy(-2108.4 - 1.03094i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 66: In AiryA(z, deriv = 1) : 'zairy(-2108.4 - 1.03094i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 67: In AiryB(z) : 'zairy(-2108.4 - 1.03094i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 68: In AiryB(z, deriv = 1) : 'zairy(-2108.4 - 1.03094i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) 69: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(64541.4 + 47.3379i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 70: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(64541.4 + 47.3379i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 71: In BesselJ(zr, 1/3) : 'zbesj(64541.4 + 47.3379i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 72: In BesselJ(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesj(64541.4 + 47.3379i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 73: In BesselY(z, -nu, nSeq = nSeq, verbose = verbose) : 'zbesy(64541.4 + 47.3379i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 74: In BesselJ(zr, 2/3) : 'zbesj(64541.4 + 47.3379i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 75: In BesselH(1, zr, 1/3) : 'zbesh(64541.4 + 47.3379i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 76: In BesselH(2, zr, 1/3) : 'zbesh(64541.4 + 47.3379i, nu=0.333333)' large arguments -> precision loss (of at least half machine accuracy) 77: In BesselH(1, zr, 2/3) : 'zbesh(64541.4 + 47.3379i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 78: In BesselH(2, zr, 2/3) : 'zbesh(64541.4 + 47.3379i, nu=0.666667)' large arguments -> precision loss (of at least half machine accuracy) 79: In AiryA(z) : 'zairy(4529.16 + 5.11984i, deriv=0)' large arguments -> precision loss (of at least half machine accuracy) 80: In AiryA(z, deriv = 1) : 'zairy(4529.16 + 5.11984i, deriv=1)' large arguments -> precision loss (of at least half machine accuracy) > > proc.time() user system elapsed 3.09 0.17 3.26